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\usepackage{longtable} |
| 10 |
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\pagestyle{plain} |
| 11 |
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\pagenumbering{arabic} |
| 12 |
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\usepackage{floatrow} |
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\oddsidemargin 0.0cm |
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\evensidemargin 0.0cm |
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\topmargin -21pt |
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\textwidth 6.5in |
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\brokenpenalty=10000 |
| 20 |
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\renewcommand{\baselinestretch}{1.2} |
| 21 |
+ |
\usepackage[square, comma, sort&compress]{natbib} |
| 22 |
+ |
\bibpunct{[}{]}{,}{n}{}{;} |
| 23 |
|
|
| 24 |
+ |
\DeclareFloatFont{tiny}{\scriptsize}% "scriptsize" is defined by floatrow, "tiny" not |
| 25 |
+ |
\floatsetup[table]{font=tiny} |
| 26 |
+ |
|
| 27 |
+ |
|
| 28 |
|
%\renewcommand\citemid{\ } % no comma in optional reference note |
| 29 |
< |
\lstset{language=C,frame=TB,basicstyle=\tiny,basicstyle=\ttfamily, % |
| 29 |
> |
\lstset{language=C,frame=TB,basicstyle=\footnotesize\ttfamily, % |
| 30 |
|
xleftmargin=0.25in, xrightmargin=0.25in,captionpos=b, % |
| 31 |
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abovecaptionskip=0.5cm, belowcaptionskip=0.5cm, escapeinside={~}{~}} |
| 32 |
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\renewcommand{\lstlistingname}{Scheme} |
| 45 |
|
\newcolumntype{H}{p{0.75in}} |
| 46 |
|
\newcolumntype{I}{p{5in}} |
| 47 |
|
|
| 48 |
+ |
\newcolumntype{J}{p{1.5in}} |
| 49 |
+ |
\newcolumntype{K}{p{1.2in}} |
| 50 |
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\newcolumntype{L}{p{1.5in}} |
| 51 |
+ |
\newcolumntype{M}{p{1.55in}} |
| 52 |
|
|
| 42 |
– |
\title{{\sc OpenMD}: Molecular Dynamics in the Open} |
| 53 |
|
|
| 54 |
< |
\author{Kelsey M. Stocker, Shenyu Kuang, Charles F. Vardeman II, \\ |
| 55 |
< |
Teng Lin, Christopher J. Fennell, Xiuquan Sun, \\ |
| 54 |
> |
\title{{\sc OpenMD-2.2}: Molecular Dynamics in the Open} |
| 55 |
> |
|
| 56 |
> |
\author{Joseph Michalka, James Marr, Kelsey Stocker, Madan Lamichhane, |
| 57 |
> |
Patrick Louden, \\ |
| 58 |
> |
Teng Lin, Charles F. Vardeman II, Christopher J. Fennell, Shenyu |
| 59 |
> |
Kuang, Xiuquan Sun, \\ |
| 60 |
|
Chunlei Li, Kyle Daily, Yang Zheng, Matthew A. Meineke, and \\ |
| 61 |
|
J. Daniel Gezelter \\ |
| 62 |
|
Department of Chemistry and Biochemistry\\ |
| 147 |
|
leave an interaction region. |
| 148 |
|
|
| 149 |
|
{\tt Atoms} may also be grouped in more traditional ways into {\tt |
| 150 |
< |
bonds}, {\tt bends}, and {\tt torsions}. These groupings allow the |
| 151 |
< |
correct choice of interaction parameters for short-range interactions |
| 152 |
< |
to be chosen from the definitions in the {\tt forceField}. |
| 150 |
> |
bonds}, {\tt bends}, {\tt torsions}, and {\tt inversions}. These |
| 151 |
> |
groupings allow the correct choice of interaction parameters for |
| 152 |
> |
short-range interactions to be chosen from the definitions in the {\tt |
| 153 |
> |
forceField}. |
| 154 |
|
|
| 155 |
|
All of these groups of {\tt atoms} are brought together in the {\tt |
| 156 |
|
molecule}, which is the fundamental structure for setting up and {\sc |
| 506 |
|
\endhead |
| 507 |
|
\hline |
| 508 |
|
\endfoot |
| 509 |
< |
{\tt forceField} & string & Sets the force field. & Possible force |
| 510 |
< |
fields are DUFF, WATER, LJ, EAM, SC, and CLAY. \\ |
| 509 |
> |
{\tt forceField} & string & Sets the base name for the force field file & |
| 510 |
> |
OpenMD appends a {\tt .frc} to the end of this to look for a force |
| 511 |
> |
field file.\\ |
| 512 |
|
{\tt component} & & Defines the molecular components of the system & |
| 513 |
|
Every {\tt $<$MetaData$>$} block must have a component statement. \\ |
| 514 |
|
{\tt minimizer} & string & Chooses a minimizer & Possible minimizers |
| 578 |
|
default is the first eight of these columns in order.) \\ |
| 579 |
|
& & \multicolumn{2}{p{3.5in}}{Allowed |
| 580 |
|
column names are: {\sc time, total\_energy, potential\_energy, kinetic\_energy, |
| 581 |
< |
temperature, pressure, volume, conserved\_quantity, |
| 581 |
> |
temperature, pressure, volume, conserved\_quantity, hullvolume, gyrvolume, |
| 582 |
|
translational\_kinetic, rotational\_kinetic, long\_range\_potential, |
| 583 |
|
short\_range\_potential, vanderwaals\_potential, |
| 584 |
< |
electrostatic\_potential, bond\_potential, bend\_potential, |
| 585 |
< |
dihedral\_potential, improper\_potential, vraw, vharm, |
| 586 |
< |
pressure\_tensor\_x, pressure\_tensor\_y, pressure\_tensor\_z}} \\ |
| 584 |
> |
electrostatic\_potential, metallic\_potential, |
| 585 |
> |
hydrogen\_bonding\_potential, bond\_potential, bend\_potential, |
| 586 |
> |
dihedral\_potential, inversion\_potential, raw\_potential, restraint\_potential, |
| 587 |
> |
pressure\_tensor, system\_dipole, heatflux, electronic\_temperature}} \\ |
| 588 |
|
{\tt printPressureTensor} & logical & sets whether {\sc OpenMD} will print |
| 589 |
|
out the pressure tensor & can be useful for calculations of the bulk |
| 590 |
|
modulus \\ |
| 779 |
|
allowing the user to gauge the stability of the integrator. The |
| 780 |
|
statistics file is denoted with the \texttt{.stat} file extension. |
| 781 |
|
|
| 782 |
< |
\chapter{\label{section:empiricalEnergy}The Empirical Energy |
| 766 |
< |
Functions} |
| 782 |
> |
\chapter{\label{section:forceFields}Force Fields} |
| 783 |
|
|
| 784 |
< |
Like many simulation packages, {\sc OpenMD} splits the potential energy |
| 785 |
< |
into the short-ranged (bonded) portion and a long-range (non-bonded) |
| 786 |
< |
potential, |
| 784 |
> |
Like many molecular simulation packages, {\sc OpenMD} splits the |
| 785 |
> |
potential energy into the short-ranged (bonded) portion and a |
| 786 |
> |
long-range (non-bonded) potential, |
| 787 |
|
\begin{equation} |
| 788 |
|
V = V_{\mathrm{short-range}} + V_{\mathrm{long-range}}. |
| 789 |
|
\end{equation} |
| 790 |
< |
The short-ranged portion includes the explicit bonds, bends, and |
| 791 |
< |
torsions which have been defined in the meta-data file for the |
| 792 |
< |
molecules which are present in the simulation. The functional forms and |
| 793 |
< |
parameters for these interactions are defined by the force field which |
| 794 |
< |
is chosen. |
| 790 |
> |
The short-ranged portion includes the bonds, bends, torsions, and |
| 791 |
> |
inversions which have been defined in the meta-data file for the |
| 792 |
> |
molecules. The functional forms and parameters for these interactions |
| 793 |
> |
are defined by the force field which is selected in the MetaData |
| 794 |
> |
section. |
| 795 |
|
|
| 796 |
< |
Calculating the long-range (non-bonded) potential involves a sum over |
| 781 |
< |
all pairs of atoms (except for those atoms which are involved in a |
| 782 |
< |
bond, bend, or torsion with each other). If done poorly, calculating |
| 783 |
< |
the the long-range interactions for $N$ atoms would involve $N(N-1)/2$ |
| 784 |
< |
evaluations of atomic distances. To reduce the number of distance |
| 785 |
< |
evaluations between pairs of atoms, {\sc OpenMD} uses a switched cutoff |
| 786 |
< |
with Verlet neighbor lists.\cite{Allen87} It is well known that |
| 787 |
< |
neutral groups which contain charges will exhibit pathological forces |
| 788 |
< |
unless the cutoff is applied to the neutral groups evenly instead of |
| 789 |
< |
to the individual atoms.\cite{leach01:mm} {\sc OpenMD} allows users to |
| 790 |
< |
specify cutoff groups which may contain an arbitrary number of atoms |
| 791 |
< |
in the molecule. Atoms in a cutoff group are treated as a single unit |
| 792 |
< |
for the evaluation of the switching function: |
| 793 |
< |
\begin{equation} |
| 794 |
< |
V_{\mathrm{long-range}} = \sum_{a} \sum_{b>a} s(r_{ab}) \sum_{i \in a} \sum_{j \in b} V_{ij}(r_{ij}), |
| 795 |
< |
\end{equation} |
| 796 |
< |
where $r_{ab}$ is the distance between the centers of mass of the two |
| 797 |
< |
cutoff groups ($a$ and $b$). |
| 796 |
> |
\section{\label{section:shortRange}The basic interactions} |
| 797 |
|
|
| 798 |
< |
The sums over $a$ and $b$ are over the cutoff groups that are present |
| 799 |
< |
in the simulation. Atoms which are not explicitly defined as members |
| 801 |
< |
of a {\tt cutoffGroup} are treated as a group consisting of only one |
| 802 |
< |
atom. The switching function, $s(r)$ is the standard cubic switching |
| 803 |
< |
function, |
| 798 |
> |
The energy function for a system composed of $N$ molecules is |
| 799 |
> |
traditionally written |
| 800 |
|
\begin{equation} |
| 801 |
< |
S(r) = |
| 802 |
< |
\begin{cases} |
| 803 |
< |
1 & \text{if $r \le r_{\text{sw}}$},\\ |
| 808 |
< |
\frac{(r_{\text{cut}} + 2r - 3r_{\text{sw}})(r_{\text{cut}} - r)^2} |
| 809 |
< |
{(r_{\text{cut}} - r_{\text{sw}})^3} |
| 810 |
< |
& \text{if $r_{\text{sw}} < r \le r_{\text{cut}}$}, \\ |
| 811 |
< |
0 & \text{if $r > r_{\text{cut}}$.} |
| 812 |
< |
\end{cases} |
| 813 |
< |
\label{eq:dipoleSwitching} |
| 801 |
> |
V = \sum^{N}_{I=1} V^{I}_{\text{Internal}} |
| 802 |
> |
+ \sum^{N-1}_{I=1} \sum_{J>I} V^{IJ}_{\text{Cross}}, |
| 803 |
> |
\label{eq:totalPotential} |
| 804 |
|
\end{equation} |
| 805 |
< |
Here, $r_{\text{sw}}$ is the {\tt switchingRadius}, or the distance |
| 806 |
< |
beyond which interactions are reduced, and $r_{\text{cut}}$ is the |
| 807 |
< |
{\tt cutoffRadius}, or the distance at which interactions are |
| 808 |
< |
truncated. |
| 805 |
> |
where $V^{IJ}_{\text{Cross}}$ contains all intermolecular interactions |
| 806 |
> |
between molecules $I$ and $J$, and $V^{I}_{\text{Internal}}$ is the |
| 807 |
> |
internal potential of molecule $I$: |
| 808 |
> |
\begin{align*} |
| 809 |
> |
V^{I}_{\text{Internal}} = & |
| 810 |
> |
\sum_{r_{ij} \in I} V_{\text{bond}}(r_{ij}) |
| 811 |
> |
+ \sum_{\theta_{ijk} \in I} V_{\text{bend}}(\theta_{ijk}) |
| 812 |
> |
+ \sum_{\phi_{ijkl} \in I} V_{\text{torsion}}(\phi_{ijkl}) |
| 813 |
> |
+ \sum_{\omega_{ijkl} \in I} V_{\text{inversion}}(\omega_{ijkl}) \\ |
| 814 |
> |
& + \sum_{i \in I} \sum_{(j>i+4) \in I} |
| 815 |
> |
\biggl[ V_{\text{dispersion}}(r_{ij}) + V_{\text{electrostatic}} |
| 816 |
> |
(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) |
| 817 |
> |
\biggr]. |
| 818 |
> |
\label{eq:internalPotential} |
| 819 |
> |
\end{align*} |
| 820 |
> |
Here $V_{\text{bond}}, V_{\text{bend}}, |
| 821 |
> |
V_{\text{torsion}},\mathrm{~and~} V_{\text{inversion}}$ represent the |
| 822 |
> |
bond, bend, torsion, and inversion potentials for all |
| 823 |
> |
topologically-connected sets of atoms within the molecule. Bonds are |
| 824 |
> |
the primary way of specifying how the atoms are connected together to |
| 825 |
> |
form the molecule (i.e. they define the molecular topology). The |
| 826 |
> |
other short-range interactions may be specified explicitly in the |
| 827 |
> |
molecule definition, or they may be deduced from bonding information. |
| 828 |
> |
For example, bends can be implicitly deduced from two bonds which |
| 829 |
> |
share an atom. Torsions can be deduced from two bends that share a |
| 830 |
> |
bond. Inversion potentials are utilized primarily to enforce |
| 831 |
> |
planarity around $sp^2$-hybridized sites, and these are specified with |
| 832 |
> |
central atoms and satellites (or an atom with bonds to exactly three |
| 833 |
> |
satellites). The pairwise portions of the non-bonded interactions are |
| 834 |
> |
usually excluded for atom pairs that are involved in the same bond, |
| 835 |
> |
bend, or torsion. All other atom pairs within a molecule are subject |
| 836 |
> |
to non-bonded pair potentials. |
| 837 |
|
|
| 838 |
< |
Users of {\sc OpenMD} do not need to specify the {\tt cutoffRadius} or |
| 839 |
< |
{\tt switchingRadius}. In simulations containing only Lennard-Jones |
| 840 |
< |
atoms, the cutoff radius has a default value of $2.5\sigma_{ii}$, |
| 841 |
< |
where $\sigma_{ii}$ is the largest Lennard-Jones length parameter |
| 842 |
< |
present in the simulation. In simulations containing charged or |
| 825 |
< |
dipolar atoms, the default cutoff radius is $15 \mbox{\AA}$. |
| 838 |
> |
The types of atoms being simulated, as well as the specific functional |
| 839 |
> |
forms and parameters of the intra-molecular functions and the |
| 840 |
> |
long-range potentials are defined by the force field. In the following |
| 841 |
> |
sections we discuss the stucture of an OpenMD force field file and the |
| 842 |
> |
specification of blocks that may be present within these files. |
| 843 |
|
|
| 844 |
< |
The {\tt switchingRadius} is set to a default value of 95\% of the |
| 828 |
< |
{\tt cutoffRadius}. In the special case of a simulation containing |
| 829 |
< |
{\it only} Lennard-Jones atoms, the default switching radius takes the |
| 830 |
< |
same value as the cutoff radius, and {\sc OpenMD} will use a shifted |
| 831 |
< |
potential to remove discontinuities in the potential at the cutoff. |
| 832 |
< |
Both radii may be specified in the meta-data file. |
| 844 |
> |
\section{\label{section:frcFile}Force Field Files} |
| 845 |
|
|
| 846 |
< |
Force fields can be added to {\sc OpenMD}, although it comes with a few |
| 847 |
< |
simple examples (Lennard-Jones, {\sc duff}, {\sc water}, and {\sc |
| 848 |
< |
eam}) which are explained in the following sections. |
| 846 |
> |
Force field files have a number of ``Blocks'' to delineate different |
| 847 |
> |
types of information. The blocks contain AtomType data, which provide |
| 848 |
> |
properties belonging to a single AtomType, as well as interaction |
| 849 |
> |
information which provides information about bonded or non-bonded |
| 850 |
> |
interactions that cannot be deduced from AtomType information alone. |
| 851 |
> |
A simple example of a forceField file is shown in scheme |
| 852 |
> |
\ref{sch:frcExample}. |
| 853 |
|
|
| 854 |
< |
\section{\label{sec:LJPot}The Lennard Jones Force Field} |
| 854 |
> |
\begin{lstlisting}[float,caption={[An example of a complete OpenMD |
| 855 |
> |
force field file for straight-chain united-atom alkanes.] An example |
| 856 |
> |
showing a complete OpenMD force field for straight-chain united-atom |
| 857 |
> |
alkanes.}, label={sch:frcExample}] |
| 858 |
> |
begin Options |
| 859 |
> |
Name = "alkane" |
| 860 |
> |
end Options |
| 861 |
|
|
| 862 |
< |
The most basic force field implemented in {\sc OpenMD} is the |
| 863 |
< |
Lennard-Jones force field, which mimics the van der Waals interaction |
| 864 |
< |
at long distances and uses an empirical repulsion at short |
| 865 |
< |
distances. The Lennard-Jones potential is given by: |
| 862 |
> |
begin BaseAtomTypes |
| 863 |
> |
//name mass |
| 864 |
> |
C 12.0107 |
| 865 |
> |
end BaseAtomTypes |
| 866 |
> |
|
| 867 |
> |
begin AtomTypes |
| 868 |
> |
//name base mass |
| 869 |
> |
CH4 C 16.05 |
| 870 |
> |
CH3 C 15.04 |
| 871 |
> |
CH2 C 14.03 |
| 872 |
> |
end AtomTypes |
| 873 |
> |
|
| 874 |
> |
begin LennardJonesAtomTypes |
| 875 |
> |
//name epsilon sigma |
| 876 |
> |
CH4 0.2941 3.73 |
| 877 |
> |
CH3 0.1947 3.75 |
| 878 |
> |
CH2 0.09140 3.95 |
| 879 |
> |
end LennardJonesAtomTypes |
| 880 |
> |
|
| 881 |
> |
begin BondTypes |
| 882 |
> |
//AT1 AT2 Type r0 k |
| 883 |
> |
CH3 CH3 Harmonic 1.526 260 |
| 884 |
> |
CH3 CH2 Harmonic 1.526 260 |
| 885 |
> |
CH2 CH2 Harmonic 1.526 260 |
| 886 |
> |
end BondTypes |
| 887 |
> |
|
| 888 |
> |
begin BendTypes |
| 889 |
> |
//AT1 AT2 AT3 Type theta0 k |
| 890 |
> |
CH3 CH2 CH3 Harmonic 114.0 124.19 |
| 891 |
> |
CH3 CH2 CH2 Harmonic 114.0 124.19 |
| 892 |
> |
CH2 CH2 CH2 Harmonic 114.0 124.19 |
| 893 |
> |
end BendTypes |
| 894 |
> |
|
| 895 |
> |
begin TorsionTypes |
| 896 |
> |
//AT1 AT2 AT3 AT4 Type |
| 897 |
> |
CH3 CH2 CH2 CH3 Trappe 0.0 0.70544 -0.13549 1.5723 |
| 898 |
> |
CH3 CH2 CH2 CH2 Trappe 0.0 0.70544 -0.13549 1.5723 |
| 899 |
> |
CH2 CH2 CH2 CH2 Trappe 0.0 0.70544 -0.13549 1.5723 |
| 900 |
> |
end TorsionTypes |
| 901 |
> |
\end{lstlisting} |
| 902 |
> |
|
| 903 |
> |
\subsection{\label{section:ffOptions}The Options block} |
| 904 |
> |
|
| 905 |
> |
The Options block defines properties governing how the force field |
| 906 |
> |
interactions are carried out. This block is delineated with the text |
| 907 |
> |
tags {\tt begin Options} and {\tt end Options}. Most options don't |
| 908 |
> |
need to be set as they come with fairly sensible default values, but |
| 909 |
> |
the various keywords and their possible values are given in Scheme |
| 910 |
> |
\ref{sch:optionsBlock}. |
| 911 |
> |
|
| 912 |
> |
\begin{lstlisting}[caption={[A force field Options block showing default values |
| 913 |
> |
for many force field options.] A force field Options block showing default values |
| 914 |
> |
for many force field options. Most of these options do not need to be |
| 915 |
> |
specified if the default values are working.}, |
| 916 |
> |
label={sch:optionsBlock}] |
| 917 |
> |
begin Options |
| 918 |
> |
Name = "alkane" // any string |
| 919 |
> |
vdWtype = "Lennard-Jones" |
| 920 |
> |
DistanceMixingRule = "arithmetic" // can also be "geometric" or "cubic" |
| 921 |
> |
DistanceType = "sigma" // can also be Rmin |
| 922 |
> |
EnergyMixingRule = "geometric" // can also be "arithmetic" or "hhg" |
| 923 |
> |
EnergyUnitScaling = 1.0 |
| 924 |
> |
MetallicEnergyUnitScaling = 1.0 |
| 925 |
> |
DistanceUnitScaling = 1.0 |
| 926 |
> |
AngleUnitScaling = 1.0 |
| 927 |
> |
TorsionAngleConvention = "180_is_trans" // can also be "0_is_trans" |
| 928 |
> |
vdW-12-scale = 0.0 |
| 929 |
> |
vdW-13-scale = 0.0 |
| 930 |
> |
vdW-14-scale = 0.0 |
| 931 |
> |
electrostatic-12-scale = 0.0 |
| 932 |
> |
electrostatic-13-scale = 0.0 |
| 933 |
> |
electrostatic-14-scale = 0.0 |
| 934 |
> |
GayBerneMu = 2.0 |
| 935 |
> |
GayBerneNu = 1.0 |
| 936 |
> |
EAMMixingMethod = "Johnson" // can also be "Daw" |
| 937 |
> |
end Options |
| 938 |
> |
\end{lstlisting} |
| 939 |
> |
|
| 940 |
> |
\subsection{\label{section:ffBase}The BaseAtomTypes block} |
| 941 |
> |
|
| 942 |
> |
An AtomType the primary data structure that OpenMD uses to store |
| 943 |
> |
static data about an atom. Things that belong to AtomType are |
| 944 |
> |
universal properties (i.e. does this atom have a fixed charge? What |
| 945 |
> |
is its mass?) Dynamic properties of an atom are not intended to be |
| 946 |
> |
properties of an atom type. A BaseAtomType can be used to build |
| 947 |
> |
extended sets of related atom types that all fall back to one |
| 948 |
> |
particular type. For example, one might want a series of atomTypes |
| 949 |
> |
that inherit from more basic types: |
| 950 |
> |
\begin{displaymath} |
| 951 |
> |
\mathtt{ALA-CA} \rightarrow \mathtt{CT} \rightarrow \mathtt{CSP3} \rightarrow \mathtt{C} |
| 952 |
> |
\end{displaymath} |
| 953 |
> |
where for each step to the right, the atomType falls back to more |
| 954 |
> |
primitive data. That is, the mass could be a property of the {\tt C} |
| 955 |
> |
type, while Lennard-Jones parameters could be properties of the {\tt |
| 956 |
> |
CSP3} type. {\tt CT} could have charge information and its own set |
| 957 |
> |
of Lennard-Jones parameter that override the CSP3 parameters. And the |
| 958 |
> |
{\tt ALA-CA} type might have specific torsion or charge information |
| 959 |
> |
that override the lower level types. A BaseAtomType contains only |
| 960 |
> |
information a primitive name and the mass of this atom type. |
| 961 |
> |
BaseAtomTypes can also be useful in creating files that can be easily |
| 962 |
> |
viewed in visualization programs. The {\tt Dump2XYZ} utility has the |
| 963 |
> |
ability to print out the names of the base atom types for displaying |
| 964 |
> |
simulations in Jmol or VMD. |
| 965 |
> |
|
| 966 |
> |
\begin{lstlisting}[caption={[A simple example of a BaseAtomTypes |
| 967 |
> |
block.] A simple example of a BaseAtomTypes block.}, |
| 968 |
> |
label={sch:baseAtomTypesBlock}] |
| 969 |
> |
begin BaseAtomTypes |
| 970 |
> |
//Name mass (amu) |
| 971 |
> |
H 1.0079 |
| 972 |
> |
O 15.9994 |
| 973 |
> |
Si 28.0855 |
| 974 |
> |
Al 26.981538 |
| 975 |
> |
Mg 24.3050 |
| 976 |
> |
Ca 40.078 |
| 977 |
> |
Fe 55.845 |
| 978 |
> |
Li 6.941 |
| 979 |
> |
Na 22.98977 |
| 980 |
> |
K 39.0983 |
| 981 |
> |
Cs 132.90545 |
| 982 |
> |
Ca 40.078 |
| 983 |
> |
Ba 137.327 |
| 984 |
> |
Cl 35.453 |
| 985 |
> |
end BaseAtomTypes |
| 986 |
> |
\end{lstlisting} |
| 987 |
> |
|
| 988 |
> |
\subsection{\label{section:ffAtom}The AtomTypes block} |
| 989 |
> |
|
| 990 |
> |
AtomTypes inherit most properties from BaseAtomTypes, but can override |
| 991 |
> |
their lower-level properties as well. Scheme \ref{sch:atomTypesBlock} |
| 992 |
> |
shows an example where multiple types of oxygen atoms can inherit mass |
| 993 |
> |
from the oxygen base type. |
| 994 |
> |
|
| 995 |
> |
\begin{lstlisting}[caption={[An example of a AtomTypes block.] A |
| 996 |
> |
simple example of an AtomTypes block which |
| 997 |
> |
shows how multiple types can inherit from the same base type.}, |
| 998 |
> |
label={sch:atomTypesBlock}] |
| 999 |
> |
begin AtomTypes |
| 1000 |
> |
//Name baseatomtype |
| 1001 |
> |
h* H |
| 1002 |
> |
ho H |
| 1003 |
> |
o* O |
| 1004 |
> |
oh O |
| 1005 |
> |
ob O |
| 1006 |
> |
obos O |
| 1007 |
> |
obts O |
| 1008 |
> |
obss O |
| 1009 |
> |
ohs O |
| 1010 |
> |
st Si |
| 1011 |
> |
ao Al |
| 1012 |
> |
at Al |
| 1013 |
> |
mgo Mg |
| 1014 |
> |
mgh Mg |
| 1015 |
> |
cao Ca |
| 1016 |
> |
cah Ca |
| 1017 |
> |
feo Fe |
| 1018 |
> |
lio Li |
| 1019 |
> |
end AtomTypes |
| 1020 |
> |
\end{lstlisting} |
| 1021 |
> |
|
| 1022 |
> |
\subsection{\label{section:ffDirectionalAtom}The DirectionalAtomTypes |
| 1023 |
> |
block} |
| 1024 |
> |
DirectionalAtoms have orientational degrees of freedom as well as |
| 1025 |
> |
translation, so moving these atoms requires information about the |
| 1026 |
> |
moments of inertias in the same way that translational motion requires |
| 1027 |
> |
mass. For DirectionalAtoms, OpenMD treats the mass distribution with |
| 1028 |
> |
higher priority than electrostatic distributions; the moment of |
| 1029 |
> |
inertia tensor, $\overleftrightarrow{\mathsf I}$, should be |
| 1030 |
> |
diagonalized to obtain body-fixed axes, and the three diagonal moments |
| 1031 |
> |
should correspond to rotational motion \textit{around} each of these |
| 1032 |
> |
body-fixed axes. Charge distributions may then result in dipole |
| 1033 |
> |
vectors that are oriented along a linear combination of the body-axes, |
| 1034 |
> |
and in quadrupole tensors that are not necessarily diagonal in the |
| 1035 |
> |
body frame. |
| 1036 |
> |
|
| 1037 |
> |
\begin{lstlisting}[caption={[An example of a DirectionalAtomTypes block.] A |
| 1038 |
> |
simple example of a DirectionalAtomTypes block.}, |
| 1039 |
> |
label={sch:datomTypesBlock}] |
| 1040 |
> |
begin DirectionalAtomTypes |
| 1041 |
> |
//Name I_xx I_yy I_zz (All moments in (amu*Ang^2) |
| 1042 |
> |
SSD 1.7696 0.6145 1.1550 |
| 1043 |
> |
GBC6H6 88.781 88.781 177.561 |
| 1044 |
> |
GBCH3OH 4.056 20.258 20.999 |
| 1045 |
> |
GBH2O 1.777 0.581 1.196 |
| 1046 |
> |
CO2 43.06 43.06 0.0 // single-site model for CO2 |
| 1047 |
> |
end DirectionalAtomTypes |
| 1048 |
> |
|
| 1049 |
> |
\end{lstlisting} |
| 1050 |
> |
|
| 1051 |
> |
For a DirectionalAtom that represents a linear object, it is |
| 1052 |
> |
appropriate for one of the moments of inertia to be zero. In this |
| 1053 |
> |
case, OpenMD identifies that DirectionalAtom as having only 5 degrees |
| 1054 |
> |
of freedom (three translations and two rotations), and will alter |
| 1055 |
> |
calculation of temperatures to reflect this. |
| 1056 |
> |
|
| 1057 |
> |
\subsection{\label{section::ffAtomProperties}AtomType properties} |
| 1058 |
> |
\subsubsection{\label{section:ffLJ}The LennardJonesAtomTypes block} |
| 1059 |
> |
One of the most basic interatomic interactions implemented in {\sc |
| 1060 |
> |
OpenMD} is the Lennard-Jones potential, which mimics the van der |
| 1061 |
> |
Waals interaction at long distances and uses an empirical repulsion at |
| 1062 |
> |
short distances. The Lennard-Jones potential is given by: |
| 1063 |
|
\begin{equation} |
| 1064 |
|
V_{\text{LJ}}(r_{ij}) = |
| 1065 |
|
4\epsilon_{ij} \biggl[ |
| 1070 |
|
\end{equation} |
| 1071 |
|
where $r_{ij}$ is the distance between particles $i$ and $j$, |
| 1072 |
|
$\sigma_{ij}$ scales the length of the interaction, and |
| 1073 |
< |
$\epsilon_{ij}$ scales the well depth of the potential. Scheme |
| 855 |
< |
\ref{sch:LJFF} gives an example meta-data file that |
| 856 |
< |
sets up a system of 108 Ar particles to be simulated using the |
| 857 |
< |
Lennard-Jones force field. |
| 1073 |
> |
$\epsilon_{ij}$ scales the well depth of the potential. |
| 1074 |
|
|
| 859 |
– |
\begin{lstlisting}[float,caption={[Invocation of the Lennard-Jones |
| 860 |
– |
force field] A sample startup file for a small Lennard-Jones |
| 861 |
– |
simulation.},label={sch:LJFF}] |
| 862 |
– |
<OpenMD> |
| 863 |
– |
<MetaData> |
| 864 |
– |
#include "argon.md" |
| 865 |
– |
|
| 866 |
– |
component{ |
| 867 |
– |
type = "Ar"; |
| 868 |
– |
nMol = 108; |
| 869 |
– |
} |
| 870 |
– |
|
| 871 |
– |
forceField = "LJ"; |
| 872 |
– |
</MetaData> |
| 873 |
– |
<Snapshot> // not shown in this scheme |
| 874 |
– |
</Snapshot> |
| 875 |
– |
</OpenMD> |
| 876 |
– |
\end{lstlisting} |
| 877 |
– |
|
| 1075 |
|
Interactions between dissimilar particles requires the generation of |
| 1076 |
|
cross term parameters for $\sigma$ and $\epsilon$. These parameters |
| 1077 |
< |
are determined using the Lorentz-Berthelot mixing |
| 1077 |
> |
are usually determined using the Lorentz-Berthelot mixing |
| 1078 |
|
rules:\cite{Allen87} |
| 1079 |
|
\begin{equation} |
| 1080 |
|
\sigma_{ij} = \frac{1}{2}[\sigma_{ii} + \sigma_{jj}], |
| 1086 |
|
\label{eq:epsilonMix} |
| 1087 |
|
\end{equation} |
| 1088 |
|
|
| 1089 |
< |
\section{\label{section:DUFF}Dipolar Unified-Atom Force Field} |
| 1089 |
> |
The values of $\sigma_{ii}$ and $\epsilon_{ii}$ are properties of atom |
| 1090 |
> |
type $i$, and must be specified in a section of the force field file |
| 1091 |
> |
called the {\tt LennardJonesAtomTypes} block (see listing |
| 1092 |
> |
\ref{sch:LJatomTypesBlock}). Separate Lennard-Jones interactions |
| 1093 |
> |
which are not determined by the mixing rules can also be specified in |
| 1094 |
> |
the {\tt NonbondedInteractionTypes} block (see section |
| 1095 |
> |
\ref{section:ffNBinteraction}). |
| 1096 |
|
|
| 1097 |
< |
The dipolar unified-atom force field ({\sc duff}) was developed to |
| 1098 |
< |
simulate lipid bilayers. These types of simulations require a model |
| 1099 |
< |
capable of forming bilayers, while still being sufficiently |
| 1100 |
< |
computationally efficient to allow large systems ($\sim$100's of |
| 1101 |
< |
phospholipids, $\sim$1000's of waters) to be simulated for long times |
| 1102 |
< |
($\sim$10's of nanoseconds). With this goal in mind, {\sc duff} has no |
| 1103 |
< |
point charges. Charge-neutral distributions are replaced with dipoles, |
| 1104 |
< |
while most atoms and groups of atoms are reduced to Lennard-Jones |
| 1105 |
< |
interaction sites. This simplification reduces the length scale of |
| 1106 |
< |
long range interactions from $\frac{1}{r}$ to $\frac{1}{r^3}$, |
| 1107 |
< |
removing the need for the computationally expensive Ewald |
| 1108 |
< |
sum. Instead, Verlet neighbor-lists and cutoff radii are used for the |
| 1109 |
< |
dipolar interactions, and, if desired, a reaction field may be added |
| 1110 |
< |
to mimic longer range interactions. |
| 1111 |
< |
|
| 1112 |
< |
As an example, lipid head-groups in {\sc duff} are represented as |
| 1113 |
< |
point dipole interaction sites. Placing a dipole at the head group's |
| 911 |
< |
center of mass mimics the charge separation found in common |
| 912 |
< |
phospholipid head groups such as phosphatidylcholine.\cite{Cevc87} |
| 913 |
< |
Additionally, a large Lennard-Jones site is located at the |
| 914 |
< |
pseudoatom's center of mass. The model is illustrated by the red atom |
| 915 |
< |
in Fig.~\ref{fig:lipidModel}. The water model we use to |
| 916 |
< |
complement the dipoles of the lipids is a |
| 917 |
< |
reparameterization\cite{fennell04} of the soft sticky dipole (SSD) |
| 918 |
< |
model of Ichiye |
| 919 |
< |
\emph{et al.}\cite{liu96:new_model} |
| 920 |
< |
|
| 921 |
< |
\begin{figure} |
| 922 |
< |
\centering |
| 923 |
< |
\includegraphics[width=\linewidth]{lipidModel.pdf} |
| 924 |
< |
\caption[A representation of a lipid model in {\sc duff}]{A |
| 925 |
< |
representation of the lipid model. $\phi$ is the torsion angle, |
| 926 |
< |
$\theta$ is the bend angle, and $\mu$ is the dipole moment of the head |
| 927 |
< |
group.} |
| 928 |
< |
\label{fig:lipidModel} |
| 929 |
< |
\end{figure} |
| 930 |
< |
|
| 931 |
< |
A set of scalable parameters has been used to model the alkyl groups |
| 932 |
< |
with Lennard-Jones sites. For this, parameters from the TraPPE force |
| 933 |
< |
field of Siepmann \emph{et al.}\cite{Siepmann1998} have been |
| 934 |
< |
utilized. TraPPE is a unified-atom representation of n-alkanes which |
| 935 |
< |
is parametrized against phase equilibria using Gibbs ensemble Monte |
| 936 |
< |
Carlo simulation techniques.\cite{Siepmann1998} One of the advantages |
| 937 |
< |
of TraPPE is that it generalizes the types of atoms in an alkyl chain |
| 938 |
< |
to keep the number of pseudoatoms to a minimum; thus, the parameters |
| 939 |
< |
for a unified atom such as $\text{CH}_2$ do not change depending on |
| 940 |
< |
what species are bonded to it. |
| 941 |
< |
|
| 942 |
< |
As is required by TraPPE, {\sc duff} also constrains all bonds to be |
| 943 |
< |
of fixed length. Typically, bond vibrations are the fastest motions in |
| 944 |
< |
a molecular dynamic simulation. With these vibrations present, small |
| 945 |
< |
time steps between force evaluations must be used to ensure adequate |
| 946 |
< |
energy conservation in the bond degrees of freedom. By constraining |
| 947 |
< |
the bond lengths, larger time steps may be used when integrating the |
| 948 |
< |
equations of motion. A simulation using {\sc duff} is illustrated in |
| 949 |
< |
Scheme \ref{sch:DUFF}. |
| 950 |
< |
|
| 951 |
< |
\begin{lstlisting}[float,caption={[Invocation of {\sc duff}]A portion |
| 952 |
< |
of a startup file showing a simulation utilizing {\sc |
| 953 |
< |
duff}},label={sch:DUFF}] |
| 954 |
< |
<OpenMD> |
| 955 |
< |
<MetaData> |
| 956 |
< |
#include "water.md" |
| 957 |
< |
#include "lipid.md" |
| 958 |
< |
|
| 959 |
< |
component{ |
| 960 |
< |
type = "simpleLipid_16"; |
| 961 |
< |
nMol = 60; |
| 962 |
< |
} |
| 963 |
< |
|
| 964 |
< |
component{ |
| 965 |
< |
type = "SSD_water"; |
| 966 |
< |
nMol = 1936; |
| 967 |
< |
} |
| 968 |
< |
|
| 969 |
< |
forceField = "DUFF"; |
| 970 |
< |
</MetaData> |
| 971 |
< |
<Snapshot> // not shown in this scheme |
| 972 |
< |
</Snapshot> |
| 973 |
< |
</OpenMD> |
| 1097 |
> |
\begin{lstlisting}[caption={[An example of a LennardJonesAtomTypes block.] A |
| 1098 |
> |
simple example of a LennardJonesAtomTypee block. Units for |
| 1099 |
> |
$\epsilon$ are kcal / mol and for $\sigma$ are \AA\ .}, |
| 1100 |
> |
label={sch:LJatomTypesBlock}] |
| 1101 |
> |
begin LennardJonesAtomTypes |
| 1102 |
> |
//Name epsilon sigma |
| 1103 |
> |
O_TIP4P 0.1550 3.15365 |
| 1104 |
> |
O_TIP4P-Ew 0.16275 3.16435 |
| 1105 |
> |
O_TIP5P 0.16 3.12 |
| 1106 |
> |
O_TIP5P-E 0.178 3.097 |
| 1107 |
> |
O_SPCE 0.15532 3.16549 |
| 1108 |
> |
O_SPC 0.15532 3.16549 |
| 1109 |
> |
CH4 0.279 3.73 |
| 1110 |
> |
CH3 0.185 3.75 |
| 1111 |
> |
CH2 0.0866 3.95 |
| 1112 |
> |
CH 0.0189 4.68 |
| 1113 |
> |
end LennardJonesAtomTypes |
| 1114 |
|
\end{lstlisting} |
| 1115 |
|
|
| 1116 |
< |
\subsection{\label{section:energyFunctions}{\sc duff} Energy Functions} |
| 1116 |
> |
\subsubsection{\label{section:ffCharge}The ChargeAtomTypes block} |
| 1117 |
|
|
| 1118 |
< |
The total potential energy function in {\sc duff} is |
| 1118 |
> |
In molecular simulations, proper accumulation of the electrostatic |
| 1119 |
> |
interactions is essential and is one of the most |
| 1120 |
> |
computationally-demanding tasks. Most common molecular mechanics |
| 1121 |
> |
force fields represent atomic sites with full or partial charges |
| 1122 |
> |
protected by Lennard-Jones (short range) interactions. Partial charge |
| 1123 |
> |
values, $q_i$ are empirical representations of the distribution of |
| 1124 |
> |
electronic charge in a molecule. This means that nearly every pair |
| 1125 |
> |
interaction involves a calculation of charge-charge forces. Coupled |
| 1126 |
> |
with relatively long-ranged $r^{-1}$ decay, the monopole interactions |
| 1127 |
> |
quickly become the most expensive part of molecular simulations. The |
| 1128 |
> |
interactions between point charges can be handled via a number of |
| 1129 |
> |
different algorithms, but Coulomb's law is the fundamental physical |
| 1130 |
> |
principle governing these interactions, |
| 1131 |
|
\begin{equation} |
| 1132 |
< |
V = \sum^{N}_{I=1} V^{I}_{\text{Internal}} |
| 1133 |
< |
+ \sum^{N-1}_{I=1} \sum_{J>I} V^{IJ}_{\text{Cross}}, |
| 982 |
< |
\label{eq:totalPotential} |
| 1132 |
> |
V_{\text{charge}}(r_{ij}) = \sum_{ij}\frac{q_iq_je^2}{4 \pi \epsilon_0 |
| 1133 |
> |
r_{ij}}, |
| 1134 |
|
\end{equation} |
| 1135 |
< |
where $V^{I}_{\text{Internal}}$ is the internal potential of molecule $I$: |
| 1136 |
< |
\begin{equation} |
| 1137 |
< |
V^{I}_{\text{Internal}} = |
| 987 |
< |
\sum_{\theta_{ijk} \in I} V_{\text{bend}}(\theta_{ijk}) |
| 988 |
< |
+ \sum_{\phi_{ijkl} \in I} V_{\text{torsion}}(\phi_{ijkl}) |
| 989 |
< |
+ \sum_{i \in I} \sum_{(j>i+4) \in I} |
| 990 |
< |
\biggl[ V_{\text{LJ}}(r_{ij}) + V_{\text{dipole}} |
| 991 |
< |
(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) |
| 992 |
< |
\biggr]. |
| 993 |
< |
\label{eq:internalPotential} |
| 994 |
< |
\end{equation} |
| 995 |
< |
Here $V_{\text{bend}}$ is the bend potential for all 1, 3 bonded pairs |
| 996 |
< |
within the molecule $I$, and $V_{\text{torsion}}$ is the torsion |
| 997 |
< |
potential for all 1, 4 bonded pairs. The pairwise portions of the |
| 998 |
< |
non-bonded interactions are excluded for atom pairs that are involved |
| 999 |
< |
in the smae bond, bend, or torsion. All other atom pairs within a |
| 1000 |
< |
molecule are subject to the LJ pair potential. |
| 1135 |
> |
where $q$ represents the charge on particle $i$ or $j$, and $e$ is the |
| 1136 |
> |
charge of an electron in Coulombs. $\epsilon_0$ is the permittivity |
| 1137 |
> |
of free space. |
| 1138 |
|
|
| 1139 |
< |
The bend potential of a molecule is represented by the following function: |
| 1140 |
< |
\begin{equation} |
| 1141 |
< |
V_{\text{bend}}(\theta_{ijk}) = k_{\theta}( \theta_{ijk} - \theta_0 |
| 1142 |
< |
)^2, \label{eq:bendPot} |
| 1143 |
< |
\end{equation} |
| 1144 |
< |
where $\theta_{ijk}$ is the angle defined by atoms $i$, $j$, and $k$ |
| 1145 |
< |
(see Fig.~\ref{fig:lipidModel}), $\theta_0$ is the equilibrium |
| 1146 |
< |
bond angle, and $k_{\theta}$ is the force constant which determines the |
| 1147 |
< |
strength of the harmonic bend. The parameters for $k_{\theta}$ and |
| 1148 |
< |
$\theta_0$ are borrowed from those in TraPPE.\cite{Siepmann1998} |
| 1139 |
> |
\begin{lstlisting}[caption={[An example of a ChargeAtomTypes block.] A |
| 1140 |
> |
simple example of a ChargeAtomTypes block. Units for |
| 1141 |
> |
charge are in multiples of electron charge.}, |
| 1142 |
> |
label={sch:ChargeAtomTypesBlock}] |
| 1143 |
> |
begin ChargeAtomTypes |
| 1144 |
> |
// Name charge |
| 1145 |
> |
O_TIP3P -0.834 |
| 1146 |
> |
O_SPCE -0.8476 |
| 1147 |
> |
H_TIP3P 0.417 |
| 1148 |
> |
H_TIP4P 0.520 |
| 1149 |
> |
H_SPCE 0.4238 |
| 1150 |
> |
EP_TIP4P -1.040 |
| 1151 |
> |
Na+ 1.0 |
| 1152 |
> |
Cl- -1.0 |
| 1153 |
> |
end ChargeAtomTypes |
| 1154 |
> |
\end{lstlisting} |
| 1155 |
|
|
| 1156 |
< |
The torsion potential and parameters are also borrowed from TraPPE. It is |
| 1157 |
< |
of the form: |
| 1156 |
> |
\subsubsection{\label{section:ffMultipole}The MultipoleAtomTypes |
| 1157 |
> |
block} |
| 1158 |
> |
For complex charge distributions that are centered on single sites, it |
| 1159 |
> |
is convenient to write the total electrostatic potential in terms of |
| 1160 |
> |
multipole moments, |
| 1161 |
|
\begin{equation} |
| 1162 |
< |
V_{\text{torsion}}(\phi) = c_1[1 + \cos \phi] |
| 1017 |
< |
+ c_2[1 + \cos(2\phi)] |
| 1018 |
< |
+ c_3[1 + \cos(3\phi)], |
| 1019 |
< |
\label{eq:origTorsionPot} |
| 1162 |
> |
U_{\bf{ab}}(r)=\hat{M}_{\bf a} \hat{M}_{\bf b} \frac{1}{r} \label{kernel}. |
| 1163 |
|
\end{equation} |
| 1164 |
< |
where: |
| 1164 |
> |
where the multipole operator on site $\bf a$, |
| 1165 |
|
\begin{equation} |
| 1166 |
< |
\cos\phi = (\hat{\mathbf{r}}_{ij} \times \hat{\mathbf{r}}_{jk}) \cdot |
| 1167 |
< |
(\hat{\mathbf{r}}_{jk} \times \hat{\mathbf{r}}_{kl}). |
| 1168 |
< |
\label{eq:torsPhi} |
| 1166 |
> |
\hat{M}_{\bf a} = C_{\bf a} - D_{{\bf a}\alpha} \frac{\partial}{\partial r_{\alpha}} |
| 1167 |
> |
+ Q_{{\bf a}\alpha\beta} |
| 1168 |
> |
\frac{\partial^2}{\partial r_{\alpha} \partial r_{\beta}} + \dots |
| 1169 |
|
\end{equation} |
| 1170 |
< |
Here, $\hat{\mathbf{r}}_{\alpha\beta}$ are the set of unit bond |
| 1171 |
< |
vectors between atoms $i$, $j$, $k$, and $l$. For computational |
| 1172 |
< |
efficiency, the torsion potential has been recast after the method of |
| 1173 |
< |
{\sc charmm},\cite{Brooks83} in which the angle series is converted to |
| 1174 |
< |
a power series of the form: |
| 1175 |
< |
\begin{equation} |
| 1176 |
< |
V_{\text{torsion}}(\phi) = |
| 1177 |
< |
k_3 \cos^3 \phi + k_2 \cos^2 \phi + k_1 \cos \phi + k_0, |
| 1178 |
< |
\label{eq:torsionPot} |
| 1179 |
< |
\end{equation} |
| 1180 |
< |
where: |
| 1181 |
< |
\begin{align*} |
| 1182 |
< |
k_0 &= c_1 + c_3, \\ |
| 1183 |
< |
k_1 &= c_1 - 3c_3, \\ |
| 1041 |
< |
k_2 &= 2 c_2, \\ |
| 1042 |
< |
k_3 &= 4c_3. |
| 1043 |
< |
\end{align*} |
| 1044 |
< |
By recasting the potential as a power series, repeated trigonometric |
| 1045 |
< |
evaluations are avoided during the calculation of the potential |
| 1046 |
< |
energy. |
| 1170 |
> |
Here, the point charge, dipole, and quadrupole for site $\bf a$ are |
| 1171 |
> |
given by $C_{\bf a}$, $D_{{\bf a}\alpha}$, and $Q_{{\bf |
| 1172 |
> |
a}\alpha\beta}$, respectively. These are the primitive |
| 1173 |
> |
multipoles. If the site is representing a distribution of charges, |
| 1174 |
> |
these can be expressed as, |
| 1175 |
> |
\begin{align} |
| 1176 |
> |
C_{\bf a} =&\sum_{k \, \text{in \bf a}} q_k , \label{eq:charge} \\ |
| 1177 |
> |
D_{{\bf a}\alpha} =&\sum_{k \, \text{in \bf a}} q_k r_{k\alpha}, \label{eq:dipole}\\ |
| 1178 |
> |
Q_{{\bf a}\alpha\beta} =& \frac{1}{2} \sum_{k \, \text{in \bf a}} q_k |
| 1179 |
> |
r_{k\alpha} r_{k\beta} . \label{eq:quadrupole} |
| 1180 |
> |
\end{align} |
| 1181 |
> |
Note that the definition of the primitive quadrupole here differs from |
| 1182 |
> |
the standard traceless form, and contains an additional Taylor-series |
| 1183 |
> |
based factor of $1/2$. |
| 1184 |
|
|
| 1185 |
< |
|
| 1186 |
< |
The cross potential between molecules $I$ and $J$, |
| 1050 |
< |
$V^{IJ}_{\text{Cross}}$, is as follows: |
| 1185 |
> |
The details of the multipolar interactions will be given later, but |
| 1186 |
> |
many readers are familiar with the dipole-dipole potential: |
| 1187 |
|
\begin{equation} |
| 1052 |
– |
V^{IJ}_{\text{Cross}} = |
| 1053 |
– |
\sum_{i \in I} \sum_{j \in J} |
| 1054 |
– |
\biggl[ V_{\text{LJ}}(r_{ij}) + V_{\text{dipole}} |
| 1055 |
– |
(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) |
| 1056 |
– |
+ V_{\text{sticky}} |
| 1057 |
– |
(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) |
| 1058 |
– |
\biggr], |
| 1059 |
– |
\label{eq:crossPotentail} |
| 1060 |
– |
\end{equation} |
| 1061 |
– |
where $V_{\text{LJ}}$ is the Lennard Jones potential, |
| 1062 |
– |
$V_{\text{dipole}}$ is the dipole dipole potential, and |
| 1063 |
– |
$V_{\text{sticky}}$ is the sticky potential defined by the SSD model |
| 1064 |
– |
(Sec.~\ref{section:SSD}). Note that not all atom types include all |
| 1065 |
– |
interactions. |
| 1066 |
– |
|
| 1067 |
– |
The dipole-dipole potential has the following form: |
| 1068 |
– |
\begin{equation} |
| 1188 |
|
V_{\text{dipole}}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i}, |
| 1189 |
< |
\boldsymbol{\Omega}_{j}) = \frac{|\mu_i||\mu_j|}{4\pi\epsilon_{0}r_{ij}^{3}} \biggl[ |
| 1189 |
> |
\boldsymbol{\Omega}_{j}) = \frac{|{\bf D}_i||{\bf D}_j|}{4\pi\epsilon_{0}r_{ij}^{3}} \biggl[ |
| 1190 |
|
\boldsymbol{\hat{u}}_{i} \cdot \boldsymbol{\hat{u}}_{j} |
| 1191 |
|
- |
| 1192 |
|
3(\boldsymbol{\hat{u}}_i \cdot \hat{\mathbf{r}}_{ij}) % |
| 1196 |
|
Here $\mathbf{r}_{ij}$ is the vector starting at atom $i$ pointing |
| 1197 |
|
towards $j$, and $\boldsymbol{\Omega}_i$ and $\boldsymbol{\Omega}_j$ |
| 1198 |
|
are the orientational degrees of freedom for atoms $i$ and $j$ |
| 1199 |
< |
respectively. The magnitude of the dipole moment of atom $i$ is |
| 1200 |
< |
$|\mu_i|$, $\boldsymbol{\hat{u}}_i$ is the standard unit orientation |
| 1199 |
> |
respectively. The magnitude of the dipole moment of atom $i$ is $|{\bf |
| 1200 |
> |
D}_i|$, $\boldsymbol{\hat{u}}_i$ is the standard unit orientation |
| 1201 |
|
vector of $\boldsymbol{\Omega}_i$, and $\boldsymbol{\hat{r}}_{ij}$ is |
| 1202 |
|
the unit vector pointing along $\mathbf{r}_{ij}$ |
| 1203 |
|
($\boldsymbol{\hat{r}}_{ij}=\mathbf{r}_{ij}/|\mathbf{r}_{ij}|$). |
| 1204 |
|
|
| 1086 |
– |
\subsection{\label{section:SSD}The {\sc duff} Water Models: SSD/E |
| 1087 |
– |
and SSD/RF} |
| 1205 |
|
|
| 1206 |
< |
In the interest of computational efficiency, the default solvent used |
| 1207 |
< |
by {\sc OpenMD} is the extended Soft Sticky Dipole (SSD/E) water |
| 1208 |
< |
model.\cite{fennell04} The original SSD was developed by Ichiye |
| 1209 |
< |
\emph{et al.}\cite{liu96:new_model} as a modified form of the hard-sphere |
| 1206 |
> |
\begin{lstlisting}[caption={[An example of a MultipoleAtomTypes block.] A |
| 1207 |
> |
simple example of a MultipoleAtomTypes block. Dipoles are given in |
| 1208 |
> |
units of Debyes, and Quadrupole moments are given in units of Debye |
| 1209 |
> |
\AA~(or $10^{-26} \mathrm{~esu~cm}^2$)}, |
| 1210 |
> |
label={sch:MultipoleAtomTypesBlock}] |
| 1211 |
> |
begin MultipoleAtomTypes |
| 1212 |
> |
// Euler angles are given in zxz convention in units of degrees. |
| 1213 |
> |
// |
| 1214 |
> |
// point dipoles: |
| 1215 |
> |
// name d phi theta psi dipole_moment |
| 1216 |
> |
DIP d 0.0 0.0 0.0 1.91 // dipole points along z-body axis |
| 1217 |
> |
// |
| 1218 |
> |
// point quadrupoles: |
| 1219 |
> |
// name q phi theta psi Qxx Qyy Qzz |
| 1220 |
> |
CO2 q 0.0 0.0 0.0 0.0 0.0 -0.430592 //quadrupole tensor has zz element |
| 1221 |
> |
// |
| 1222 |
> |
// Atoms with both dipole and quadrupole moments: |
| 1223 |
> |
// name dq phi theta psi dipole_moment Qxx Qyy Qzz |
| 1224 |
> |
SSD dq 0.0 0.0 0.0 2.35 -1.682 1.762 -0.08 |
| 1225 |
> |
end MultipoleAtomTypes |
| 1226 |
> |
\end{lstlisting} |
| 1227 |
> |
|
| 1228 |
> |
Specifying a MultipoleAtomType requires declaring how the |
| 1229 |
> |
electrostatic frame for the site is rotated relative to the body-fixed |
| 1230 |
> |
axes for that atom. The Euler angles $(\phi, \theta, \psi)$ for this |
| 1231 |
> |
rotation must be given, and then the dipole, quadrupole, or all of |
| 1232 |
> |
these moments are specified in the electrostatic frame. In OpenMD, |
| 1233 |
> |
the Euler angles are specified in the $zxz$ convention and are entered |
| 1234 |
> |
in units of degrees. Dipole moments are entered in units of Debye, |
| 1235 |
> |
and Quadrupole moments in units of Debye \AA. |
| 1236 |
> |
|
| 1237 |
> |
\subsubsection{\label{section:ffGB}The FluctuatingChargeAtomTypes block} |
| 1238 |
> |
\subsubsection{\label{section:ffPol}The PolarizableAtomTypes block} |
| 1239 |
> |
\subsubsection{\label{section:ffGB}The GayBerneAtomTypes block} |
| 1240 |
> |
|
| 1241 |
> |
The Gay-Berne potential has been widely used in the liquid crystal |
| 1242 |
> |
community to describe this anisotropic phase |
| 1243 |
> |
behavior.~\cite{Gay:1981yu,Berne:1972pb,Kushick:1976xy,Luckhurst:1990fy,Cleaver:1996rt} |
| 1244 |
> |
The form of the Gay-Berne potential implemented in OpenMD was |
| 1245 |
> |
generalized by Cleaver {\it et al.} and is appropriate for dissimilar |
| 1246 |
> |
uniaxial ellipsoids.\cite{Cleaver:1996rt} The potential is constructed in the |
| 1247 |
> |
familiar form of the Lennard-Jones function using |
| 1248 |
> |
orientation-dependent $\sigma$ and $\epsilon$ parameters, |
| 1249 |
> |
\begin{equation*} |
| 1250 |
> |
V_{ij}({{\bf \hat u}_i}, {{\bf \hat u}_j}, {{\bf \hat |
| 1251 |
> |
r}_{ij}}) = 4\epsilon ({{\bf \hat u}_i}, {{\bf \hat u}_j}, |
| 1252 |
> |
{{\bf \hat r}_{ij}})\left[\left(\frac{\sigma_0}{r_{ij}-\sigma({{\bf \hat u |
| 1253 |
> |
}_i}, |
| 1254 |
> |
{{\bf \hat u}_j}, {{\bf \hat r}_{ij}})+\sigma_0}\right)^{12} |
| 1255 |
> |
-\left(\frac{\sigma_0}{r_{ij}-\sigma({{\bf \hat u}_i}, {{\bf \hat u}_j}, |
| 1256 |
> |
{{\bf \hat r}_{ij}})+\sigma_0}\right)^6\right] |
| 1257 |
> |
\label{eq:gb} |
| 1258 |
> |
\end{equation*} |
| 1259 |
> |
|
| 1260 |
> |
The range $(\sigma({\bf \hat{u}}_{i},{\bf \hat{u}}_{j},{\bf |
| 1261 |
> |
\hat{r}}_{ij}))$, and strength $(\epsilon({\bf \hat{u}}_{i},{\bf |
| 1262 |
> |
\hat{u}}_{j},{\bf \hat{r}}_{ij}))$ parameters |
| 1263 |
> |
are dependent on the relative orientations of the two ellipsoids (${\bf |
| 1264 |
> |
\hat{u}}_{i},{\bf \hat{u}}_{j}$) as well as the direction of the |
| 1265 |
> |
inter-ellipsoid separation (${\bf \hat{r}}_{ij}$). The shape and |
| 1266 |
> |
attractiveness of each ellipsoid is governed by a relatively small set |
| 1267 |
> |
of parameters: |
| 1268 |
> |
\begin{itemize} |
| 1269 |
> |
\item $d$: range parameter for the side-by-side (S) and cross (X) configurations |
| 1270 |
> |
\item $l$: range parameter for the end-to-end (E) configuration |
| 1271 |
> |
\item $\epsilon_X$: well-depth parameter for the cross (X) configuration |
| 1272 |
> |
\item $\epsilon_S$: well-depth parameter for the side-by-side (S) configuration |
| 1273 |
> |
\item $\epsilon_E$: well depth parameter for the end-to-end (E) configuration |
| 1274 |
> |
\item $dw$: The ``softness'' of the potential |
| 1275 |
> |
\end{itemize} |
| 1276 |
> |
Additionally, there are two universal paramters to govern the overall |
| 1277 |
> |
importance of the purely orientational ($\nu$) and the mixed |
| 1278 |
> |
orientational / translational ($\mu$) parts of strength of the |
| 1279 |
> |
interactions. These parameters have default or ``canonical'' values, |
| 1280 |
> |
but may be changed as a force field option: |
| 1281 |
> |
\begin{itemize} |
| 1282 |
> |
\item $\nu$: purely orientational part : defaults to 1 |
| 1283 |
> |
\item $\mu$: mixed orientational / translational part : defaults to |
| 1284 |
> |
2 |
| 1285 |
> |
\end{itemize} |
| 1286 |
> |
Further details of the potential are given |
| 1287 |
> |
elsewhere,\cite{Luckhurst:1990fy,Golubkov06,SunX._jp0762020} and an |
| 1288 |
> |
excellent overview of the computational methods that can be used to |
| 1289 |
> |
efficiently compute forces and torques for this potential can be found |
| 1290 |
> |
in Ref. \citealp{Golubkov06} |
| 1291 |
> |
|
| 1292 |
> |
\begin{lstlisting}[caption={[An example of a GayBerneAtomTypes block.] A |
| 1293 |
> |
simple example of a GayBerneAtomTypes block. Distances ($d$ and $l$) |
| 1294 |
> |
are given in \AA\ and energies ($\epsilon_X, \epsilon_S, \epsilon_E$) |
| 1295 |
> |
are in units of kcal/mol. $dw$ is unitless.}, |
| 1296 |
> |
label={sch:GayBerneAtomTypes}] |
| 1297 |
> |
begin GayBerneAtomTypes |
| 1298 |
> |
//Name d l eps_X eps_S eps_E dw |
| 1299 |
> |
GBlinear 2.8104 9.993 0.774729 0.774729 0.116839 1.0 |
| 1300 |
> |
GBC6H6 4.65 2.03 0.540 0.540 1.9818 0.6 |
| 1301 |
> |
GBCH3OH 2.55 3.18 0.542 0.542 0.55826 1.0 |
| 1302 |
> |
end GayBerneAtomTypes |
| 1303 |
> |
\end{lstlisting} |
| 1304 |
> |
|
| 1305 |
> |
\subsubsection{\label{section:ffSticky}The StickyAtomTypes block} |
| 1306 |
> |
|
| 1307 |
> |
One of the solvents that can be simulated by {\sc OpenMD} is the |
| 1308 |
> |
extended Soft Sticky Dipole (SSD/E) water model.\cite{fennell04} The |
| 1309 |
> |
original SSD was developed by Ichiye \emph{et |
| 1310 |
> |
al.}\cite{liu96:new_model} as a modified form of the hard-sphere |
| 1311 |
|
water model proposed by Bratko, Blum, and |
| 1312 |
|
Luzar.\cite{Bratko85,Bratko95} It consists of a single point dipole |
| 1313 |
|
with a Lennard-Jones core and a sticky potential that directs the |
| 1373 |
|
\label{fig:ssd} |
| 1374 |
|
\end{figure} |
| 1375 |
|
|
| 1158 |
– |
|
| 1376 |
|
Since SSD/E is a single-point {\it dipolar} model, the force |
| 1377 |
|
calculations are simplified significantly relative to the standard |
| 1378 |
|
{\it charged} multi-point models. In the original Monte Carlo |
| 1391 |
|
|
| 1392 |
|
Recent constant pressure simulations revealed issues in the original |
| 1393 |
|
SSD model that led to lower than expected densities at all target |
| 1394 |
< |
pressures.\cite{Ichiye03,fennell04} The default model in {\sc OpenMD} |
| 1395 |
< |
is therefore SSD/E, a density corrected derivative of SSD that |
| 1396 |
< |
exhibits improved liquid structure and transport behavior. If the use |
| 1397 |
< |
of a reaction field long-range interaction correction is desired, it |
| 1398 |
< |
is recommended that the parameters be modified to those of the SSD/RF |
| 1399 |
< |
model (an SSD variant parameterized for reaction field). These solvent |
| 1183 |
< |
parameters are listed and can be easily modified in the {\sc duff} |
| 1184 |
< |
force field file ({\tt DUFF.frc}). A table of the parameter values |
| 1185 |
< |
and the drawbacks and benefits of the different density corrected SSD |
| 1186 |
< |
models can be found in reference~\cite{fennell04}. |
| 1394 |
> |
pressures,\cite{Ichiye03,fennell04} so variants on the sticky |
| 1395 |
> |
potential can be specified by using one of a number of substitute atom |
| 1396 |
> |
types (see listing \ref{sch:StickyAtomTypes}). A table of the |
| 1397 |
> |
parameter values and the drawbacks and benefits of the different |
| 1398 |
> |
density corrected SSD models can be found in |
| 1399 |
> |
reference~\citealp{fennell04}. |
| 1400 |
|
|
| 1401 |
< |
\section{\label{section:WATER}The {\sc water} Force Field} |
| 1401 |
> |
\begin{lstlisting}[caption={[An example of a StickyAtomTypes block.] A |
| 1402 |
> |
simple example of a StickyAtomTypes block. Distances ($r_l$, $r_u$, |
| 1403 |
> |
$r_{l}'$ and $r_{u}'$) are given in \AA\ and energies ($v_0, v_{0}'$) |
| 1404 |
> |
are in units of kcal/mol. $w_0$ is unitless.}, |
| 1405 |
> |
label={sch:StickyAtomTypes}] |
| 1406 |
> |
begin StickyAtomTypes |
| 1407 |
> |
//name w0 v0 (kcal/mol) v0p rl (Ang) ru rlp rup |
| 1408 |
> |
SSD_E 0.07715 3.90 3.90 2.40 3.80 2.75 3.35 |
| 1409 |
> |
SSD_RF 0.07715 3.90 3.90 2.40 3.80 2.75 3.35 |
| 1410 |
> |
SSD 0.07715 3.7284 3.7284 2.75 3.35 2.75 4.0 |
| 1411 |
> |
SSD1 0.07715 3.6613 3.6613 2.75 3.35 2.75 4.0 |
| 1412 |
> |
end StickyAtomTypes |
| 1413 |
> |
\end{lstlisting} |
| 1414 |
|
|
| 1415 |
< |
In addition to the {\sc duff} force field's solvent description, a |
| 1191 |
< |
separate {\sc water} force field has been included for simulating most |
| 1192 |
< |
of the common rigid-body water models. This force field includes the |
| 1193 |
< |
simple and point-dipolar models (SSD, SSD1, SSD/E, SSD/RF, and DPD |
| 1194 |
< |
water), as well as the common charge-based models (SPC, SPC/E, TIP3P, |
| 1195 |
< |
TIP4P, and |
| 1196 |
< |
TIP5P).\cite{liu96:new_model,Ichiye03,fennell04,Marrink01,Berendsen81,Berendsen87,Jorgensen83,Mahoney00} |
| 1197 |
< |
In order to handle these models, charge-charge interactions were |
| 1198 |
< |
included in the force-loop: |
| 1199 |
< |
\begin{equation} |
| 1200 |
< |
V_{\text{charge}}(r_{ij}) = \sum_{ij}\frac{q_iq_je^2}{r_{ij}}, |
| 1201 |
< |
\end{equation} |
| 1202 |
< |
where $q$ represents the charge on particle $i$ or $j$, and $e$ is the |
| 1203 |
< |
charge of an electron in Coulombs. The charge-charge interaction |
| 1204 |
< |
support is rudimentary in the current version of {\sc OpenMD}. As with |
| 1205 |
< |
the other pair interactions, charges can be simulated with a pure |
| 1206 |
< |
cutoff or a reaction field. The various methods for performing the |
| 1207 |
< |
Ewald summation have not yet been included. The {\sc water} force |
| 1208 |
< |
field can be easily expanded through modification of the {\sc water} |
| 1209 |
< |
force field file ({\tt WATER.frc}). By adding atom types and inserting |
| 1210 |
< |
the appropriate parameters, it is possible to extend the force field |
| 1211 |
< |
to handle rigid molecules other than water. |
| 1415 |
> |
\subsection{\label{section::ffMetals}Metallic Atom Types} |
| 1416 |
|
|
| 1417 |
< |
\section{\label{section:eam}Embedded Atom Method} |
| 1418 |
< |
|
| 1419 |
< |
{\sc OpenMD} implements a potential that describes bonding in |
| 1420 |
< |
transition metal |
| 1421 |
< |
systems.~\cite{Finnis84,Ercolessi88,Chen90,Qi99,Ercolessi02} This |
| 1422 |
< |
potential has an attractive interaction which models ``Embedding'' a |
| 1423 |
< |
positively charged pseudo-atom core in the electron density due to the |
| 1424 |
< |
free valance ``sea'' of electrons created by the surrounding atoms in |
| 1221 |
< |
the system. A pairwise part of the potential (which is primarily |
| 1222 |
< |
repulsive) describes the interaction of the positively charged metal |
| 1223 |
< |
core ions with one another. The Embedded Atom Method ({\sc |
| 1224 |
< |
eam})~\cite{Daw84,FBD86,johnson89,Lu97} has been widely adopted in the |
| 1225 |
< |
materials science community and has been included in {\sc OpenMD}. A |
| 1226 |
< |
good review of {\sc eam} and other formulations of metallic potentials |
| 1227 |
< |
was given by Voter.\cite{Voter:95} |
| 1228 |
< |
|
| 1229 |
< |
The {\sc eam} potential has the form: |
| 1417 |
> |
{\sc OpenMD} implements a number of related potentials that describe |
| 1418 |
> |
bonding in transition metals. These potentials have an attractive |
| 1419 |
> |
interaction which models ``Embedding'' a positively charged |
| 1420 |
> |
pseudo-atom core in the electron density due to the free valance |
| 1421 |
> |
``sea'' of electrons created by the surrounding atoms in the system. |
| 1422 |
> |
A pairwise part of the potential (which is primarily repulsive) |
| 1423 |
> |
describes the interaction of the positively charged metal core ions |
| 1424 |
> |
with one another. These potentials have the form: |
| 1425 |
|
\begin{equation} |
| 1426 |
|
V = \sum_{i} F_{i}\left[\rho_{i}\right] + \sum_{i} \sum_{j \neq i} |
| 1427 |
|
\phi_{ij}({\bf r}_{ij}) |
| 1438 |
|
transition metal potentials require two loops through the atom pairs |
| 1439 |
|
to compute the inter-atomic forces. |
| 1440 |
|
|
| 1441 |
< |
The pairwise portion of the potential, $\phi_{ij}$, is a primarily |
| 1442 |
< |
repulsive interaction between atoms $i$ and $j$. In the original |
| 1248 |
< |
formulation of {\sc eam}\cite{Daw84}, $\phi_{ij}$ was an entirely |
| 1249 |
< |
repulsive term; however later refinements to {\sc eam} allowed for |
| 1250 |
< |
more general forms for $\phi$.\cite{Daw89} The effective cutoff |
| 1251 |
< |
distance, $r_{{\text cut}}$ is the distance at which the values of |
| 1252 |
< |
$f(r)$ and $\phi(r)$ drop to zero for all atoms present in the |
| 1253 |
< |
simulation. In practice, this distance is fairly small, limiting the |
| 1254 |
< |
summations in the {\sc eam} equation to the few dozen atoms |
| 1255 |
< |
surrounding atom $i$ for both the density $\rho$ and pairwise $\phi$ |
| 1256 |
< |
interactions. |
| 1441 |
> |
The pairwise portion of the potential, $\phi_{ij}$, is usually a |
| 1442 |
> |
repulsive interaction between atoms $i$ and $j$. |
| 1443 |
|
|
| 1444 |
< |
In computing forces for alloys, mixing rules as outlined by |
| 1445 |
< |
Johnson~\cite{johnson89} are used to compute the heterogenous pair |
| 1446 |
< |
potential, |
| 1444 |
> |
\subsubsection{\label{section:ffEAM}The EAMAtomTypes block} |
| 1445 |
> |
The Embedded Atom Method ({\sc eam}) is one of the most widely-used |
| 1446 |
> |
potentials for transition |
| 1447 |
> |
metals.~\cite{Finnis84,Ercolessi88,Chen90,Qi99,Ercolessi02,Daw84,FBD86,johnson89,Lu97} |
| 1448 |
> |
It has been widely adopted in the materials science community and a |
| 1449 |
> |
good review of {\sc eam} and other formulations of metallic potentials |
| 1450 |
> |
was given by Voter.\cite{Voter:95} |
| 1451 |
> |
|
| 1452 |
> |
In the original formulation of {\sc eam}\cite{Daw84}, the pair |
| 1453 |
> |
potential, $\phi_{ij}$ was an entirely repulsive term; however later |
| 1454 |
> |
refinements to {\sc eam} allowed for more general forms for |
| 1455 |
> |
$\phi$.\cite{Daw89} The effective cutoff distance, $r_{{\text cut}}$ |
| 1456 |
> |
is the distance at which the values of $f(r)$ and $\phi(r)$ drop to |
| 1457 |
> |
zero for all atoms present in the simulation. In practice, this |
| 1458 |
> |
distance is fairly small, limiting the summations in the {\sc eam} |
| 1459 |
> |
equation to the few dozen atoms surrounding atom $i$ for both the |
| 1460 |
> |
density $\rho$ and pairwise $\phi$ interactions. |
| 1461 |
> |
|
| 1462 |
> |
In computing forces for alloys, OpenMD uses mixing rules outlined by |
| 1463 |
> |
Johnson~\cite{johnson89} to compute the heterogenous pair potential, |
| 1464 |
|
\begin{equation} |
| 1465 |
|
\label{eq:johnson} |
| 1466 |
|
\phi_{ab}(r)=\frac{1}{2}\left( |
| 1492 |
|
$\mbox{kcal mol}^{-1}$ as in the rest of the {\sc OpenMD} force field |
| 1493 |
|
files. |
| 1494 |
|
|
| 1495 |
< |
\section{\label{section:sc}The Sutton-Chen Force Field} |
| 1495 |
> |
\begin{lstlisting}[caption={[An example of a EAMAtomTypes block.] A |
| 1496 |
> |
simple example of a EAMAtomTypes block. Here the only data provided is |
| 1497 |
> |
the name of a {\tt funcfl} file which contains the raw data for spline |
| 1498 |
> |
interpolations for the density, functional, and pair potential.}, |
| 1499 |
> |
label={sch:EAMAtomTypes}] |
| 1500 |
> |
begin EAMAtomTypes |
| 1501 |
> |
Au Au.u3.funcfl |
| 1502 |
> |
Ag Ag.u3.funcfl |
| 1503 |
> |
Cu Cu.u3.funcfl |
| 1504 |
> |
Ni Ni.u3.funcfl |
| 1505 |
> |
Pd Pd.u3.funcfl |
| 1506 |
> |
Pt Pt.u3.funcfl |
| 1507 |
> |
end EAMAtomTypes |
| 1508 |
> |
\end{lstlisting} |
| 1509 |
|
|
| 1510 |
+ |
|
| 1511 |
+ |
\subsubsection{\label{section:ffSC}The SuttonChenAtomTypes block} |
| 1512 |
+ |
|
| 1513 |
|
The Sutton-Chen ({\sc sc})~\cite{Chen90} potential has been used to |
| 1514 |
< |
study a wide range of phenomena in metals. Although it is similar in |
| 1515 |
< |
form to the {\sc eam} potential, the Sutton-Chen model takes on a |
| 1516 |
< |
simpler form, |
| 1514 |
> |
study a wide range of phenomena in metals. Although it has the same |
| 1515 |
> |
basic form as the {\sc eam} potential, the Sutton-Chen model takes on |
| 1516 |
> |
a simpler form, |
| 1517 |
|
\begin{equation} |
| 1518 |
|
\label{eq:SCP1} |
| 1519 |
|
U_{tot}=\sum _{i}\left[ \frac{1}{2}\sum _{j\neq |
| 1520 |
< |
i}D_{ij}V^{pair}_{ij}(r_{ij})-c_{i}D_{ii}\sqrt{\rho_{i}}\right] , |
| 1520 |
> |
i}\epsilon_{ij}V^{pair}_{ij}(r_{ij})-c_{i}\epsilon_{ii}\sqrt{\rho_{i}}\right] , |
| 1521 |
|
\end{equation} |
| 1522 |
|
where $V^{pair}_{ij}$ and $\rho_{i}$ are given by |
| 1523 |
|
\begin{equation} |
| 1524 |
|
\label{eq:SCP2} |
| 1525 |
|
V^{pair}_{ij}(r)=\left( |
| 1526 |
< |
\frac{\alpha_{ij}}{r_{ij}}\right)^{n_{ij}}, \rho_{i}=\sum_{j\neq i}\left( |
| 1526 |
> |
\frac{\alpha_{ij}}{r_{ij}}\right)^{n_{ij}} \hspace{1in} \rho_{i}=\sum_{j\neq i}\left( |
| 1527 |
|
\frac{\alpha_{ij}}{r_{ij}}\right) ^{m_{ij}} |
| 1528 |
|
\end{equation} |
| 1529 |
|
|
| 1531 |
|
interactions of the pseudo-atom cores. The $\sqrt{\rho_i}$ term in |
| 1532 |
|
Eq. (\ref{eq:SCP1}) is an attractive many-body potential that models |
| 1533 |
|
the interactions between the valence electrons and the cores of the |
| 1534 |
< |
pseudo-atoms. $D_{ij}$, $D_{ii}$, $c_i$ and $\alpha_{ij}$ are |
| 1535 |
< |
parameters used to tune the potential for different transition |
| 1536 |
< |
metals. |
| 1534 |
> |
pseudo-atoms. $\epsilon_{ij}$, $\epsilon_{ii}$, $c_i$ and |
| 1535 |
> |
$\alpha_{ij}$ are parameters used to tune the potential for different |
| 1536 |
> |
transition metals. |
| 1537 |
|
|
| 1538 |
|
The {\sc sc} potential form has also been parameterized by Qi {\it et |
| 1539 |
|
al.}\cite{Qi99} These parameters were obtained via empirical and {\it |
| 1540 |
|
ab initio} calculations to match structural features of the FCC |
| 1541 |
< |
crystal. To specify the original Sutton-Chen variant of the {\sc sc} |
| 1542 |
< |
force field, the user would add the {\tt forceFieldVariant = "SC";} |
| 1543 |
< |
line to the meta-data file, while specification of the Qi {\it et al.} |
| 1544 |
< |
quantum-adapted variant of the {\sc sc} potential, the user would add |
| 1545 |
< |
the {\tt forceFieldVariant = "QSC";} line to the meta-data file. |
| 1541 |
> |
crystal. Interested readers are encouraged to consult reference |
| 1542 |
> |
\citealp{Qi99} for further details. |
| 1543 |
> |
|
| 1544 |
> |
\begin{lstlisting}[caption={[An example of a SCAtomTypes block.] A |
| 1545 |
> |
simple example of a SCAtomTypes block. Distances ($\alpha$) |
| 1546 |
> |
are given in \AA\ and energies ($\epsilon$) are (by convention) given in |
| 1547 |
> |
units of eV. These units must be specified in the {\tt Options} block |
| 1548 |
> |
using the keyword {\tt MetallicEnergyUnitScaling}. Without this {\tt |
| 1549 |
> |
Options} keyword, the default units for $\epsilon$ are kcal/mol. The |
| 1550 |
> |
other parameters, $m$, $n$, and $c$ are unitless.}, |
| 1551 |
> |
label={sch:SCAtomTypes}] |
| 1552 |
> |
begin SCAtomTypes |
| 1553 |
> |
// Name epsilon(eV) c m n alpha(angstroms) |
| 1554 |
> |
Ni 0.0073767 84.745 5.0 10.0 3.5157 |
| 1555 |
> |
Cu 0.0057921 84.843 5.0 10.0 3.6030 |
| 1556 |
> |
Rh 0.0024612 305.499 5.0 13.0 3.7984 |
| 1557 |
> |
Pd 0.0032864 148.205 6.0 12.0 3.8813 |
| 1558 |
> |
Ag 0.0039450 96.524 6.0 11.0 4.0691 |
| 1559 |
> |
Ir 0.0037674 224.815 6.0 13.0 3.8344 |
| 1560 |
> |
Pt 0.0097894 71.336 7.0 11.0 3.9163 |
| 1561 |
> |
Au 0.0078052 53.581 8.0 11.0 4.0651 |
| 1562 |
> |
Au2 0.0078052 53.581 8.0 11.0 4.0651 |
| 1563 |
> |
end SCAtomTypes |
| 1564 |
> |
\end{lstlisting} |
| 1565 |
> |
|
| 1566 |
> |
\subsection{\label{section::ffShortRange}Short Range Interactions} |
| 1567 |
> |
\subsubsection{\label{section:ffBond}The BondTypes block} |
| 1568 |
> |
\subsubsection{\label{section:ffBend}The BendTypes block} |
| 1569 |
> |
A harmonic bend potential is represented by the following function: |
| 1570 |
> |
\begin{equation} |
| 1571 |
> |
V_{\text{bend}}(\theta_{ijk}) = k_{\theta}( \theta_{ijk} - \theta_0 |
| 1572 |
> |
)^2, \label{eq:bendPot} |
| 1573 |
> |
\end{equation} |
| 1574 |
> |
where $\theta_{ijk}$ is the angle defined by atoms $i$, $j$, and $k$, |
| 1575 |
> |
$\theta_0$ is the equilibrium bond angle, and $k_{\theta}$ is the |
| 1576 |
> |
force constant which determines the strength of the harmonic bend. |
| 1577 |
> |
|
| 1578 |
> |
\subsubsection{\label{section:ffTorsion}The TorsionTypes block} |
| 1579 |
> |
The torsion potential is often represented as a cosine series of the |
| 1580 |
> |
form: |
| 1581 |
> |
\begin{equation} |
| 1582 |
> |
V_{\text{torsion}}(\phi) = c_1[1 + \cos \phi] |
| 1583 |
> |
+ c_2[1 + \cos(2\phi)] |
| 1584 |
> |
+ c_3[1 + \cos(3\phi)], |
| 1585 |
> |
\label{eq:origTorsionPot} |
| 1586 |
> |
\end{equation} |
| 1587 |
> |
where: |
| 1588 |
> |
\begin{equation} |
| 1589 |
> |
\cos\phi = (\hat{\mathbf{r}}_{ij} \times \hat{\mathbf{r}}_{jk}) \cdot |
| 1590 |
> |
(\hat{\mathbf{r}}_{jk} \times \hat{\mathbf{r}}_{kl}). |
| 1591 |
> |
\label{eq:torsPhi} |
| 1592 |
> |
\end{equation} |
| 1593 |
> |
Here, $\hat{\mathbf{r}}_{\alpha\beta}$ are the set of unit bond |
| 1594 |
> |
vectors between atoms $i$, $j$, $k$, and $l$. For computational |
| 1595 |
> |
efficiency, the torsion potential has been recast after the method of |
| 1596 |
> |
{\sc charmm},\cite{Brooks83} in which the angle series is converted to |
| 1597 |
> |
a power series of the form: |
| 1598 |
> |
\begin{equation} |
| 1599 |
> |
V_{\text{torsion}}(\phi) = |
| 1600 |
> |
k_3 \cos^3 \phi + k_2 \cos^2 \phi + k_1 \cos \phi + k_0, |
| 1601 |
> |
\label{eq:torsionPot} |
| 1602 |
> |
\end{equation} |
| 1603 |
> |
where: |
| 1604 |
> |
\begin{align*} |
| 1605 |
> |
k_0 &= c_1 + c_3, \\ |
| 1606 |
> |
k_1 &= c_1 - 3c_3, \\ |
| 1607 |
> |
k_2 &= 2 c_2, \\ |
| 1608 |
> |
k_3 &= 4c_3. |
| 1609 |
> |
\end{align*} |
| 1610 |
> |
By recasting the potential as a power series, repeated trigonometric |
| 1611 |
> |
evaluations are avoided during the calculation of the potential |
| 1612 |
> |
energy. |
| 1613 |
|
|
| 1614 |
+ |
\subsubsection{\label{section:ffInversion}The InversionTypes block} |
| 1615 |
+ |
\subsection{\label{section::ffLongRange}Long Range Interactions} |
| 1616 |
+ |
\subsubsection{\label{section:ffNBinteraction}The NonBondedInteraction block} |
| 1617 |
+ |
|
| 1618 |
+ |
|
| 1619 |
+ |
|
| 1620 |
+ |
(see Fig.~\ref{fig:lipidModel}), The parameters for $k_{\theta}$ and |
| 1621 |
+ |
$\theta_0$ are borrowed from those in TraPPE.\cite{Siepmann1998} |
| 1622 |
+ |
|
| 1623 |
+ |
Calculating the long-range (non-bonded) potential involves a sum over |
| 1624 |
+ |
all pairs of atoms (except for those atoms which are involved in a |
| 1625 |
+ |
bond, bend, or torsion with each other). If done poorly, calculating |
| 1626 |
+ |
the the long-range interactions for $N$ atoms would involve $N(N-1)/2$ |
| 1627 |
+ |
evaluations of atomic distances. To reduce the number of distance |
| 1628 |
+ |
evaluations between pairs of atoms, {\sc OpenMD} allows the use of |
| 1629 |
+ |
switched cutoffs with Verlet neighbor lists.\cite{Allen87} Neutral |
| 1630 |
+ |
groups which contain charges will exhibit pathological forces unless |
| 1631 |
+ |
the cutoff is applied to the neutral groups evenly instead of to the |
| 1632 |
+ |
individual atoms.\cite{leach01:mm} {\sc OpenMD} allows users to |
| 1633 |
+ |
specify cutoff groups which may contain an arbitrary number of atoms |
| 1634 |
+ |
in the molecule. Atoms in a cutoff group are treated as a single unit |
| 1635 |
+ |
for the evaluation of the switching function: |
| 1636 |
+ |
\begin{equation} |
| 1637 |
+ |
V_{\mathrm{long-range}} = \sum_{a} \sum_{b>a} s(r_{ab}) \sum_{i \in a} \sum_{j \in b} V_{ij}(r_{ij}), |
| 1638 |
+ |
\end{equation} |
| 1639 |
+ |
where $r_{ab}$ is the distance between the centers of mass of the two |
| 1640 |
+ |
cutoff groups ($a$ and $b$). |
| 1641 |
+ |
|
| 1642 |
+ |
The sums over $a$ and $b$ are over the cutoff groups that are present |
| 1643 |
+ |
in the simulation. Atoms which are not explicitly defined as members |
| 1644 |
+ |
of a {\tt cutoffGroup} are treated as a group consisting of only one |
| 1645 |
+ |
atom. The switching function, $s(r)$ is the standard cubic switching |
| 1646 |
+ |
function, |
| 1647 |
+ |
\begin{equation} |
| 1648 |
+ |
S(r) = |
| 1649 |
+ |
\begin{cases} |
| 1650 |
+ |
1 & \text{if $r \le r_{\text{sw}}$},\\ |
| 1651 |
+ |
\frac{(r_{\text{cut}} + 2r - 3r_{\text{sw}})(r_{\text{cut}} - r)^2} |
| 1652 |
+ |
{(r_{\text{cut}} - r_{\text{sw}})^3} |
| 1653 |
+ |
& \text{if $r_{\text{sw}} < r \le r_{\text{cut}}$}, \\ |
| 1654 |
+ |
0 & \text{if $r > r_{\text{cut}}$.} |
| 1655 |
+ |
\end{cases} |
| 1656 |
+ |
\label{eq:dipoleSwitching} |
| 1657 |
+ |
\end{equation} |
| 1658 |
+ |
Here, $r_{\text{sw}}$ is the {\tt switchingRadius}, or the distance |
| 1659 |
+ |
beyond which interactions are reduced, and $r_{\text{cut}}$ is the |
| 1660 |
+ |
{\tt cutoffRadius}, or the distance at which interactions are |
| 1661 |
+ |
truncated. |
| 1662 |
+ |
|
| 1663 |
+ |
Users of {\sc OpenMD} do not need to specify the {\tt cutoffRadius} or |
| 1664 |
+ |
{\tt switchingRadius}. In simulations containing only Lennard-Jones |
| 1665 |
+ |
atoms, the cutoff radius has a default value of $2.5\sigma_{ii}$, |
| 1666 |
+ |
where $\sigma_{ii}$ is the largest Lennard-Jones length parameter |
| 1667 |
+ |
present in the simulation. In simulations containing charged or |
| 1668 |
+ |
dipolar atoms, the default cutoff radius is $15 \mbox{\AA}$. |
| 1669 |
+ |
|
| 1670 |
+ |
The {\tt switchingRadius} is set to a default value of 95\% of the |
| 1671 |
+ |
{\tt cutoffRadius}. In the special case of a simulation containing |
| 1672 |
+ |
{\it only} Lennard-Jones atoms, the default switching radius takes the |
| 1673 |
+ |
same value as the cutoff radius, and {\sc OpenMD} will use a shifted |
| 1674 |
+ |
potential to remove discontinuities in the potential at the cutoff. |
| 1675 |
+ |
Both radii may be specified in the meta-data file. |
| 1676 |
+ |
|
| 1677 |
+ |
Force fields can be added to {\sc OpenMD}, although it comes with a few |
| 1678 |
+ |
simple examples (Lennard-Jones, {\sc duff}, {\sc water}, and {\sc |
| 1679 |
+ |
eam}) which are explained in the following sections. |
| 1680 |
+ |
|
| 1681 |
+ |
\section{\label{sec:LJPot}The Lennard Jones Force Field} |
| 1682 |
+ |
|
| 1683 |
+ |
Scheme |
| 1684 |
+ |
\ref{sch:LJFF} gives an example meta-data file that |
| 1685 |
+ |
sets up a system of 108 Ar particles to be simulated using the |
| 1686 |
+ |
Lennard-Jones force field. |
| 1687 |
+ |
|
| 1688 |
+ |
\begin{lstlisting}[float,caption={[Invocation of the Lennard-Jones |
| 1689 |
+ |
force field] A sample startup file for a small Lennard-Jones |
| 1690 |
+ |
simulation.},label={sch:LJFF}] |
| 1691 |
+ |
<OpenMD> |
| 1692 |
+ |
<MetaData> |
| 1693 |
+ |
#include "argon.md" |
| 1694 |
+ |
|
| 1695 |
+ |
component{ |
| 1696 |
+ |
type = "Ar"; |
| 1697 |
+ |
nMol = 108; |
| 1698 |
+ |
} |
| 1699 |
+ |
|
| 1700 |
+ |
forceField = "LJ"; |
| 1701 |
+ |
</MetaData> |
| 1702 |
+ |
<Snapshot> // not shown in this scheme |
| 1703 |
+ |
</Snapshot> |
| 1704 |
+ |
</OpenMD> |
| 1705 |
+ |
\end{lstlisting} |
| 1706 |
+ |
|
| 1707 |
+ |
|
| 1708 |
+ |
\section{\label{section:DUFF}Dipolar Unified-Atom Force Field} |
| 1709 |
+ |
|
| 1710 |
+ |
The dipolar unified-atom force field ({\sc duff}) was developed to |
| 1711 |
+ |
simulate lipid bilayers. These types of simulations require a model |
| 1712 |
+ |
capable of forming bilayers, while still being sufficiently |
| 1713 |
+ |
computationally efficient to allow large systems ($\sim$100's of |
| 1714 |
+ |
phospholipids, $\sim$1000's of waters) to be simulated for long times |
| 1715 |
+ |
($\sim$10's of nanoseconds). With this goal in mind, {\sc duff} has no |
| 1716 |
+ |
point charges. Charge-neutral distributions are replaced with dipoles, |
| 1717 |
+ |
while most atoms and groups of atoms are reduced to Lennard-Jones |
| 1718 |
+ |
interaction sites. This simplification reduces the length scale of |
| 1719 |
+ |
long range interactions from $\frac{1}{r}$ to $\frac{1}{r^3}$, |
| 1720 |
+ |
removing the need for the computationally expensive Ewald |
| 1721 |
+ |
sum. Instead, Verlet neighbor-lists and cutoff radii are used for the |
| 1722 |
+ |
dipolar interactions, and, if desired, a reaction field may be added |
| 1723 |
+ |
to mimic longer range interactions. |
| 1724 |
+ |
|
| 1725 |
+ |
As an example, lipid head-groups in {\sc duff} are represented as |
| 1726 |
+ |
point dipole interaction sites. Placing a dipole at the head group's |
| 1727 |
+ |
center of mass mimics the charge separation found in common |
| 1728 |
+ |
phospholipid head groups such as phosphatidylcholine.\cite{Cevc87} |
| 1729 |
+ |
Additionally, a large Lennard-Jones site is located at the |
| 1730 |
+ |
pseudoatom's center of mass. The model is illustrated by the red atom |
| 1731 |
+ |
in Fig.~\ref{fig:lipidModel}. The water model we use to |
| 1732 |
+ |
complement the dipoles of the lipids is a |
| 1733 |
+ |
reparameterization\cite{fennell04} of the soft sticky dipole (SSD) |
| 1734 |
+ |
model of Ichiye |
| 1735 |
+ |
\emph{et al.}\cite{liu96:new_model} |
| 1736 |
+ |
|
| 1737 |
+ |
\begin{figure} |
| 1738 |
+ |
\centering |
| 1739 |
+ |
\includegraphics[width=\linewidth]{lipidModel.pdf} |
| 1740 |
+ |
\caption[A representation of a lipid model in {\sc duff}]{A |
| 1741 |
+ |
representation of the lipid model. $\phi$ is the torsion angle, |
| 1742 |
+ |
$\theta$ is the bend angle, and $\mu$ is the dipole moment of the head |
| 1743 |
+ |
group.} |
| 1744 |
+ |
\label{fig:lipidModel} |
| 1745 |
+ |
\end{figure} |
| 1746 |
+ |
|
| 1747 |
+ |
A set of scalable parameters has been used to model the alkyl groups |
| 1748 |
+ |
with Lennard-Jones sites. For this, parameters from the TraPPE force |
| 1749 |
+ |
field of Siepmann \emph{et al.}\cite{Siepmann1998} have been |
| 1750 |
+ |
utilized. TraPPE is a unified-atom representation of n-alkanes which |
| 1751 |
+ |
is parametrized against phase equilibria using Gibbs ensemble Monte |
| 1752 |
+ |
Carlo simulation techniques.\cite{Siepmann1998} One of the advantages |
| 1753 |
+ |
of TraPPE is that it generalizes the types of atoms in an alkyl chain |
| 1754 |
+ |
to keep the number of pseudoatoms to a minimum; thus, the parameters |
| 1755 |
+ |
for a unified atom such as $\text{CH}_2$ do not change depending on |
| 1756 |
+ |
what species are bonded to it. |
| 1757 |
+ |
|
| 1758 |
+ |
As is required by TraPPE, {\sc duff} also constrains all bonds to be |
| 1759 |
+ |
of fixed length. Typically, bond vibrations are the fastest motions in |
| 1760 |
+ |
a molecular dynamic simulation. With these vibrations present, small |
| 1761 |
+ |
time steps between force evaluations must be used to ensure adequate |
| 1762 |
+ |
energy conservation in the bond degrees of freedom. By constraining |
| 1763 |
+ |
the bond lengths, larger time steps may be used when integrating the |
| 1764 |
+ |
equations of motion. A simulation using {\sc duff} is illustrated in |
| 1765 |
+ |
Scheme \ref{sch:DUFF}. |
| 1766 |
+ |
|
| 1767 |
+ |
\begin{lstlisting}[float,caption={[Invocation of {\sc duff}]A portion |
| 1768 |
+ |
of a startup file showing a simulation utilizing {\sc |
| 1769 |
+ |
duff}},label={sch:DUFF}] |
| 1770 |
+ |
<OpenMD> |
| 1771 |
+ |
<MetaData> |
| 1772 |
+ |
#include "water.md" |
| 1773 |
+ |
#include "lipid.md" |
| 1774 |
+ |
|
| 1775 |
+ |
component{ |
| 1776 |
+ |
type = "simpleLipid_16"; |
| 1777 |
+ |
nMol = 60; |
| 1778 |
+ |
} |
| 1779 |
+ |
|
| 1780 |
+ |
component{ |
| 1781 |
+ |
type = "SSD_water"; |
| 1782 |
+ |
nMol = 1936; |
| 1783 |
+ |
} |
| 1784 |
+ |
|
| 1785 |
+ |
forceField = "DUFF"; |
| 1786 |
+ |
</MetaData> |
| 1787 |
+ |
<Snapshot> // not shown in this scheme |
| 1788 |
+ |
</Snapshot> |
| 1789 |
+ |
</OpenMD> |
| 1790 |
+ |
\end{lstlisting} |
| 1791 |
+ |
|
| 1792 |
+ |
|
| 1793 |
+ |
|
| 1794 |
+ |
The cross potential between molecules $I$ and $J$, |
| 1795 |
+ |
$V^{IJ}_{\text{Cross}}$, is as follows: |
| 1796 |
+ |
\begin{equation} |
| 1797 |
+ |
V^{IJ}_{\text{Cross}} = |
| 1798 |
+ |
\sum_{i \in I} \sum_{j \in J} |
| 1799 |
+ |
\biggl[ V_{\text{LJ}}(r_{ij}) + V_{\text{dipole}} |
| 1800 |
+ |
(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) |
| 1801 |
+ |
+ V_{\text{sticky}} |
| 1802 |
+ |
(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i},\boldsymbol{\Omega}_{j}) |
| 1803 |
+ |
\biggr], |
| 1804 |
+ |
\label{eq:crossPotentail} |
| 1805 |
+ |
\end{equation} |
| 1806 |
+ |
where $V_{\text{LJ}}$ is the Lennard Jones potential, |
| 1807 |
+ |
$V_{\text{dipole}}$ is the dipole dipole potential, and |
| 1808 |
+ |
$V_{\text{sticky}}$ is the sticky potential defined by the SSD model |
| 1809 |
+ |
(Sec.~\ref{section:SSD}). Note that not all atom types include all |
| 1810 |
+ |
interactions. |
| 1811 |
+ |
|
| 1812 |
+ |
|
| 1813 |
+ |
\section{\label{section:WATER}The {\sc water} Force Field} |
| 1814 |
+ |
|
| 1815 |
+ |
In addition to the {\sc duff} force field's solvent description, a |
| 1816 |
+ |
separate {\sc water} force field has been included for simulating most |
| 1817 |
+ |
of the common rigid-body water models. This force field includes the |
| 1818 |
+ |
simple and point-dipolar models (SSD, SSD1, SSD/E, SSD/RF, and DPD |
| 1819 |
+ |
water), as well as the common charge-based models (SPC, SPC/E, TIP3P, |
| 1820 |
+ |
TIP4P, and |
| 1821 |
+ |
TIP5P).\cite{liu96:new_model,Ichiye03,fennell04,Marrink01,Berendsen81,Berendsen87,Jorgensen83,Mahoney00} |
| 1822 |
+ |
In order to handle these models, charge-charge interactions were |
| 1823 |
+ |
included in the force-loop: |
| 1824 |
+ |
\begin{equation} |
| 1825 |
+ |
V_{\text{charge}}(r_{ij}) = \sum_{ij}\frac{q_iq_je^2}{r_{ij}}, |
| 1826 |
+ |
\end{equation} |
| 1827 |
+ |
where $q$ represents the charge on particle $i$ or $j$, and $e$ is the |
| 1828 |
+ |
charge of an electron in Coulombs. The charge-charge interaction |
| 1829 |
+ |
support is rudimentary in the current version of {\sc OpenMD}. As with |
| 1830 |
+ |
the other pair interactions, charges can be simulated with a pure |
| 1831 |
+ |
cutoff or a reaction field. The various methods for performing the |
| 1832 |
+ |
Ewald summation have not yet been included. The {\sc water} force |
| 1833 |
+ |
field can be easily expanded through modification of the {\sc water} |
| 1834 |
+ |
force field file ({\tt WATER.frc}). By adding atom types and inserting |
| 1835 |
+ |
the appropriate parameters, it is possible to extend the force field |
| 1836 |
+ |
to handle rigid molecules other than water. |
| 1837 |
+ |
|
| 1838 |
+ |
|
| 1839 |
+ |
\section{\label{section:sc}The Sutton-Chen Force Field} |
| 1840 |
+ |
|
| 1841 |
+ |
|
| 1842 |
|
\section{\label{section:clay}The CLAY force field} |
| 1843 |
|
|
| 1844 |
|
The {\sc clay} force field is based on an ionic (nonbonded) |
| 3135 |
|
|
| 3136 |
|
\section{Constant Pressure without periodic boundary conditions (The LangevinHull)} |
| 3137 |
|
|
| 3138 |
< |
The Langevin Hull uses an external bath at a fixed constant pressure |
| 3138 |
> |
The Langevin Hull\cite{Vardeman2011} uses an external bath at a fixed constant pressure |
| 3139 |
|
($P$) and temperature ($T$) with an effective solvent viscosity |
| 3140 |
|
($\eta$). This bath interacts only with the objects on the exterior |
| 3141 |
|
hull of the system. Defining the hull of the atoms in a simulation is |
| 3447 |
|
\label{table:zconParams} |
| 3448 |
|
\end{longtable} |
| 3449 |
|
|
| 3450 |
< |
\chapter{\label{section:restraints}Restraints} |
| 3451 |
< |
Restraints are external potentials that are added to a system to keep |
| 3452 |
< |
particular molecules or collections of particles close to some |
| 3453 |
< |
reference structure. A restraint can be a collective |
| 3450 |
> |
% \chapter{\label{section:restraints}Restraints} |
| 3451 |
> |
% Restraints are external potentials that are added to a system to |
| 3452 |
> |
% keep particular molecules or collections of particles close to some |
| 3453 |
> |
% reference structure. A restraint can be a collective |
| 3454 |
|
|
| 3455 |
|
\chapter{\label{section:thermInt}Thermodynamic Integration} |
| 3456 |
|
|
| 3589 |
|
Einstein crystal |
| 3590 |
|
\label{table:thermIntParams} |
| 3591 |
|
\end{longtable} |
| 3592 |
+ |
|
| 3593 |
+ |
\chapter{\label{section:rnemd}Reverse Non-Equilibrium Molecular Dynamics (RNEMD)} |
| 3594 |
+ |
|
| 3595 |
+ |
There are many ways to compute transport properties from molecular |
| 3596 |
+ |
dynamics simulations. Equilibrium Molecular Dynamics (EMD) |
| 3597 |
+ |
simulations can be used by computing relevant time correlation |
| 3598 |
+ |
functions and assuming linear response theory holds. For some transport properties (notably thermal conductivity), EMD approaches |
| 3599 |
+ |
are subject to noise and poor convergence of the relevant |
| 3600 |
+ |
correlation functions. Traditional Non-equilibrium Molecular Dynamics |
| 3601 |
+ |
(NEMD) methods impose a gradient (e.g. thermal or momentum) on a |
| 3602 |
+ |
simulation. However, the resulting flux is often difficult to |
| 3603 |
+ |
measure. Furthermore, problems arise for NEMD simulations of |
| 3604 |
+ |
heterogeneous systems, such as phase-phase boundaries or interfaces, |
| 3605 |
+ |
where the type of gradient to enforce at the boundary between |
| 3606 |
+ |
materials is unclear. |
| 3607 |
+ |
|
| 3608 |
+ |
{\it Reverse} Non-Equilibrium Molecular Dynamics (RNEMD) methods adopt |
| 3609 |
+ |
a different approach in that an unphysical {\it flux} is imposed |
| 3610 |
+ |
between different regions or ``slabs'' of the simulation box. The |
| 3611 |
+ |
response of the system is to develop a temperature or momentum {\it |
| 3612 |
+ |
gradient} between the two regions. Since the amount of the applied |
| 3613 |
+ |
flux is known exactly, and the measurement of gradient is generally |
| 3614 |
+ |
less complicated, imposed-flux methods typically take shorter |
| 3615 |
+ |
simulation times to obtain converged results for transport properties. |
| 3616 |
+ |
|
| 3617 |
+ |
\begin{figure} |
| 3618 |
+ |
\includegraphics[width=\linewidth]{rnemdDemo} |
| 3619 |
+ |
\caption{The (VSS) RNEMD approach imposes unphysical transfer of both |
| 3620 |
+ |
linear momentum and kinetic energy between a ``hot'' slab and a |
| 3621 |
+ |
``cold'' slab in the simulation box. The system responds to this |
| 3622 |
+ |
imposed flux by generating both momentum and temperature gradients. |
| 3623 |
+ |
The slope of the gradients can then be used to compute transport |
| 3624 |
+ |
properties (e.g. shear viscosity and thermal conductivity).} |
| 3625 |
+ |
\label{rnemdDemo} |
| 3626 |
+ |
\end{figure} |
| 3627 |
+ |
|
| 3628 |
+ |
\section{\label{section:algo}Three algorithms for carrying out RNEMD simulations} |
| 3629 |
+ |
\subsection{\label{subsection:swapping}The swapping algorithm} |
| 3630 |
+ |
The original ``swapping'' approaches by M\"{u}ller-Plathe {\it et |
| 3631 |
+ |
al.}\cite{ISI:000080382700030,MullerPlathe:1997xw} can be understood |
| 3632 |
+ |
as a sequence of imaginary elastic collisions between particles in |
| 3633 |
+ |
opposite slabs. In each collision, the entire momentum vectors of |
| 3634 |
+ |
both particles may be exchanged to generate a thermal |
| 3635 |
+ |
flux. Alternatively, a single component of the momentum vectors may be |
| 3636 |
+ |
exchanged to generate a shear flux. This algorithm turns out to be |
| 3637 |
+ |
quite useful in many simulations. However, the M\"{u}ller-Plathe |
| 3638 |
+ |
swapping approach perturbs the system away from ideal |
| 3639 |
+ |
Maxwell-Boltzmann distributions, and this may leads to undesirable |
| 3640 |
+ |
side-effects when the applied flux becomes large.\cite{Maginn:2010} |
| 3641 |
+ |
This limits the applicability of the swapping algorithm, so in OpenMD, |
| 3642 |
+ |
we have implemented two additional algorithms for RNEMD in addition to the |
| 3643 |
+ |
original swapping approach. |
| 3644 |
+ |
|
| 3645 |
+ |
\subsection{\label{subsection:nivs}Non-Isotropic Velocity Scaling (NIVS)} |
| 3646 |
+ |
Instead of having momentum exchange between {\it individual particles} |
| 3647 |
+ |
in each slab, the NIVS algorithm applies velocity scaling to all of |
| 3648 |
+ |
the selected particles in both slabs.\cite{kuang:164101} A combination of linear |
| 3649 |
+ |
momentum, kinetic energy, and flux constraint equations governs the |
| 3650 |
+ |
amount of velocity scaling performed at each step. Interested readers |
| 3651 |
+ |
should consult ref. \citealp{kuang:164101} for further details on the |
| 3652 |
+ |
methodology. |
| 3653 |
+ |
|
| 3654 |
+ |
NIVS has been shown to be very effective at producing thermal |
| 3655 |
+ |
gradients and for computing thermal conductivities, particularly for |
| 3656 |
+ |
heterogeneous interfaces. Although the NIVS algorithm can also be |
| 3657 |
+ |
applied to impose a directional momentum flux, thermal anisotropy was |
| 3658 |
+ |
observed in relatively high flux simulations, and the method is not |
| 3659 |
+ |
suitable for imposing a shear flux or for computing shear viscosities. |
| 3660 |
+ |
|
| 3661 |
+ |
\subsection{\label{subsection:vss}Velocity Shearing and Scaling (VSS)} |
| 3662 |
+ |
The third RNEMD algorithm implemented in OpenMD utilizes a series of |
| 3663 |
+ |
simultaneous velocity shearing and scaling exchanges between the two |
| 3664 |
+ |
slabs.\cite{2012MolPh.110..691K} This method results in a set of simpler equations to satisfy |
| 3665 |
+ |
the conservation constraints while creating a desired flux between the |
| 3666 |
+ |
two slabs. |
| 3667 |
+ |
|
| 3668 |
+ |
The VSS approach is versatile in that it may be used to implement both |
| 3669 |
+ |
thermal and shear transport either separately or simultaneously. |
| 3670 |
+ |
Perturbations of velocities away from the ideal Maxwell-Boltzmann |
| 3671 |
+ |
distributions are minimal, and thermal anisotropy is kept to a |
| 3672 |
+ |
minimum. This ability to generate simultaneous thermal and shear |
| 3673 |
+ |
fluxes has been utilized to map out the shear viscosity of SPC/E water |
| 3674 |
+ |
over a wide range of temperatures (90~K) just with a single simulation. |
| 3675 |
+ |
VSS-RNEMD also allows the directional momentum flux to have |
| 3676 |
+ |
arbitary directions, which could aid in the study of anisotropic solid |
| 3677 |
+ |
surfaces in contact with liquid environments. |
| 3678 |
+ |
|
| 3679 |
+ |
\section{\label{section:usingRNEMD}Using OpenMD to perform a RNEMD simulation} |
| 3680 |
+ |
\subsection{\label{section:rnemdParams} What the user needs to specify} |
| 3681 |
+ |
To carry out a RNEMD simulation, |
| 3682 |
+ |
a user must specify a number of parameters in the MetaData (.md) file. |
| 3683 |
+ |
Because the RNEMD methods have a large number of parameters, these |
| 3684 |
+ |
must be enclosed in a {\it separate} {\tt RNEMD\{...\}} block. The most important |
| 3685 |
+ |
parameters to specify are the {\tt useRNEMD}, {\tt fluxType} and flux |
| 3686 |
+ |
parameters. Most other parameters (summarized in table |
| 3687 |
+ |
\ref{table:rnemd}) have reasonable default values. {\tt fluxType} |
| 3688 |
+ |
sets up the kind of exchange that will be carried out between the two |
| 3689 |
+ |
slabs (either Kinetic Energy ({\tt KE}) or momentum ({\tt Px, Py, Pz, |
| 3690 |
+ |
Pvector}), or some combination of these). The flux is specified |
| 3691 |
+ |
with the use of three possible parameters: {\tt kineticFlux} for |
| 3692 |
+ |
kinetic energy exchange, as well as {\tt momentumFlux} or {\tt |
| 3693 |
+ |
momentumFluxVector} for simulations with directional exchange. |
| 3694 |
+ |
|
| 3695 |
+ |
\subsection{\label{section:rnemdResults} Processing the results} |
| 3696 |
+ |
OpenMD will generate a {\tt .rnemd} |
| 3697 |
+ |
file with the same prefix as the original {\tt .md} file. This file |
| 3698 |
+ |
contains a running average of properties of interest computed within a |
| 3699 |
+ |
set of bins that divide the simulation cell along the $z$-axis. The |
| 3700 |
+ |
first column of the {\tt .rnemd} file is the $z$ coordinate of the |
| 3701 |
+ |
center of each bin, while following columns may contain the average |
| 3702 |
+ |
temperature, velocity, or density within each bin. The output format |
| 3703 |
+ |
in the {\tt .rnemd} file can be altered with the {\tt outputFields}, |
| 3704 |
+ |
{\tt outputBins}, and {\tt outputFileName} parameters. A report at |
| 3705 |
+ |
the top of the {\tt .rnemd} file contains the current exchange totals |
| 3706 |
+ |
as well as the average flux applied during the simulation. Using the |
| 3707 |
+ |
slope of the temperature or velocity gradient obtaine from the {\tt |
| 3708 |
+ |
.rnemd} file along with the applied flux, the user can very simply |
| 3709 |
+ |
arrive at estimates of thermal conductivities ($\lambda$), |
| 3710 |
+ |
\begin{equation} |
| 3711 |
+ |
J_z = -\lambda \frac{\partial T}{\partial z}, |
| 3712 |
+ |
\end{equation} |
| 3713 |
+ |
and shear viscosities ($\eta$), |
| 3714 |
+ |
\begin{equation} |
| 3715 |
+ |
j_z(p_x) = -\eta \frac{\partial \langle v_x \rangle}{\partial z}. |
| 3716 |
+ |
\end{equation} |
| 3717 |
+ |
Here, the quantities on the left hand side are the actual flux values |
| 3718 |
+ |
(in the header of the {\tt .rnemd} file), while the slopes are |
| 3719 |
+ |
obtained from linear fits to the gradients observed in the {\tt |
| 3720 |
+ |
.rnemd} file. |
| 3721 |
|
|
| 3722 |
+ |
More complicated simulations (including interfaces) require a bit more |
| 3723 |
+ |
care. Here the second derivative may be required to compute the |
| 3724 |
+ |
interfacial thermal conductance, |
| 3725 |
+ |
\begin{align} |
| 3726 |
+ |
G^\prime &= \left(\nabla\lambda \cdot \mathbf{\hat{n}}\right)_{z_0} \\ |
| 3727 |
+ |
&= \frac{\partial}{\partial z}\left(-\frac{J_z}{ |
| 3728 |
+ |
\left(\frac{\partial T}{\partial z}\right)}\right)_{z_0} \\ |
| 3729 |
+ |
&= J_z\left(\frac{\partial^2 T}{\partial z^2}\right)_{z_0} \Big/ |
| 3730 |
+ |
\left(\frac{\partial T}{\partial z}\right)_{z_0}^2. |
| 3731 |
+ |
\label{derivativeG} |
| 3732 |
+ |
\end{align} |
| 3733 |
+ |
where $z_0$ is the location of the interface between two materials and |
| 3734 |
+ |
$\mathbf{\hat{n}}$ is a unit vector normal to the interface. We |
| 3735 |
+ |
suggest that users interested in interfacial conductance consult |
| 3736 |
+ |
reference \citealp{kuang:AuThl} for other approaches to computing $G$. |
| 3737 |
+ |
Users interested in {\it friction coefficients} at heterogeneous |
| 3738 |
+ |
interfaces may also find reference \citealp{2012MolPh.110..691K} |
| 3739 |
+ |
useful. |
| 3740 |
|
|
| 3741 |
+ |
\newpage |
| 3742 |
+ |
|
| 3743 |
+ |
\begin{longtable}[c]{JKLM} |
| 3744 |
+ |
\caption{Meta-data Keywords: Parameters for RNEMD simulations}\\ |
| 3745 |
+ |
\multicolumn{4}{c}{The following keywords must be enclosed inside a {\tt RNEMD\{...\}} block.} |
| 3746 |
+ |
\\ \hline |
| 3747 |
+ |
{\bf keyword} & {\bf units} & {\bf use} & {\bf remarks} \\ \hline |
| 3748 |
+ |
\endhead |
| 3749 |
+ |
\hline |
| 3750 |
+ |
\endfoot |
| 3751 |
+ |
{\tt useRNEMD} & logical & perform RNEMD? & default is ``false'' \\ |
| 3752 |
+ |
{\tt objectSelection} & string & see section \ref{section:syntax} |
| 3753 |
+ |
for selection syntax & default is ``select all'' \\ |
| 3754 |
+ |
{\tt method} & string & exchange method & one of the following: |
| 3755 |
+ |
{\tt Swap, NIVS,} or {\tt VSS} (default is {\tt VSS}) \\ |
| 3756 |
+ |
{\tt fluxType} & string & what is being exchanged between slabs? & one |
| 3757 |
+ |
of the following: {\tt KE, Px, Py, Pz, Pvector, KE+Px, KE+Py, KE+Pvector} \\ |
| 3758 |
+ |
{\tt kineticFlux} & kcal mol$^{-1}$ \AA$^{-2}$ fs$^{-1}$ & specify the kinetic energy flux & \\ |
| 3759 |
+ |
{\tt momentumFlux} & amu \AA$^{-1}$ fs$^{-2}$ & specify the momentum flux & \\ |
| 3760 |
+ |
{\tt momentumFluxVector} & amu \AA$^{-1}$ fs$^{-2}$ & specify the momentum flux when |
| 3761 |
+ |
{\tt Pvector} is part of the exchange & Vector3d input\\ |
| 3762 |
+ |
{\tt exchangeTime} & fs & how often to perform the exchange & default is 100 fs\\ |
| 3763 |
+ |
|
| 3764 |
+ |
{\tt slabWidth} & $\mbox{\AA}$ & width of the two exchange slabs & default is $\mathsf{H}_{zz} / 10.0$ \\ |
| 3765 |
+ |
{\tt slabAcenter} & $\mbox{\AA}$ & center of the end slab & default is 0 \\ |
| 3766 |
+ |
{\tt slabBcenter} & $\mbox{\AA}$ & center of the middle slab & default is $\mathsf{H}_{zz} / 2$ \\ |
| 3767 |
+ |
{\tt outputFileName} & string & file name for output histograms & default is the same prefix as the |
| 3768 |
+ |
.md file, but with the {\tt .rnemd} extension \\ |
| 3769 |
+ |
{\tt outputBins} & int & number of $z$-bins in the output histogram & |
| 3770 |
+ |
default is 20 \\ |
| 3771 |
+ |
{\tt outputFields} & string & columns to print in the {\tt .rnemd} |
| 3772 |
+ |
file where each column is separated by a pipe ($\mid$) symbol. & Allowed column names are: {\sc z, temperature, velocity, density} \\ |
| 3773 |
+ |
\label{table:rnemd} |
| 3774 |
+ |
\end{longtable} |
| 3775 |
+ |
|
| 3776 |
|
\chapter{\label{section:minimizer}Energy Minimization} |
| 3777 |
|
|
| 3778 |
< |
As one of the basic procedures of molecular modeling, energy |
| 3083 |
< |
minimization is used to identify local configurations that are stable |
| 3778 |
> |
Energy minimization is used to identify local configurations that are stable |
| 3779 |
|
points on the potential energy surface. There is a vast literature on |
| 3780 |
|
energy minimization algorithms have been developed to search for the |
| 3781 |
|
global energy minimum as well as to find local structures which are |
| 3902 |
|
\begin{figure} |
| 3903 |
|
\centering |
| 3904 |
|
\includegraphics[width=3in]{heirarchy.pdf} |
| 3905 |
< |
\caption[Class heirarchy for StuntDoubles in {\sc OpenMD}-4]{ \\ The |
| 3906 |
< |
class heirarchy of StuntDoubles in {\sc OpenMD}-4. The selection |
| 3905 |
> |
\caption[Class heirarchy for StuntDoubles in {\sc OpenMD}]{ \\ The |
| 3906 |
> |
class heirarchy of StuntDoubles in {\sc OpenMD}. The selection |
| 3907 |
|
syntax allows the user to select any of the objects that are descended |
| 3908 |
|
from a StuntDouble.} |
| 3909 |
|
\label{fig:heirarchy} |
| 4083 |
|
-z & {\tt -{}-zconstraint} & replace the atom types of zconstraint molecules (default=off) \\ |
| 4084 |
|
-r & {\tt -{}-rigidbody} & add a pseudo COM atom to rigidbody (default=off) \\ |
| 4085 |
|
-t & {\tt -{}-watertype} & replace the atom type of water model (default=on) \\ |
| 4086 |
< |
-b & {\tt -{}-basetype} & using base atom type (default=off) \\ |
| 4086 |
> |
-b & {\tt -{}-basetype} & using base atom type |
| 4087 |
> |
(default=off) \\ |
| 4088 |
> |
-v& {\tt -{}-velocities} & Print velocities in xyz file (default=off)\\ |
| 4089 |
> |
-f& {\tt -{}-forces} & Print forces xyz file (default=off)\\ |
| 4090 |
> |
-u& {\tt -{}-vectors} & Print vectors (dipoles, etc) in xyz file |
| 4091 |
> |
(default=off)\\ |
| 4092 |
> |
-c& {\tt -{}-charges} & Print charges in xyz file (default=off)\\ |
| 4093 |
> |
-e& {\tt -{}-efield} & Print electric field vector in xyz file |
| 4094 |
> |
(default=off)\\ |
| 4095 |
|
& {\tt -{}-repeatX=INT} & The number of images to repeat in the x direction (default=`0') \\ |
| 4096 |
|
& {\tt -{}-repeatY=INT} & The number of images to repeat in the y direction (default=`0') \\ |
| 4097 |
|
& {\tt -{}-repeatZ=INT} & The number of images to repeat in the z direction (default=`0') \\ |
| 4183 |
|
& {\tt -{}-sele1=selection script} & select the first StuntDouble set \\ |
| 4184 |
|
& {\tt -{}-sele2=selection script} & select the second StuntDouble set \\ |
| 4185 |
|
& {\tt -{}-sele3=selection script} & select the third StuntDouble set \\ |
| 4186 |
< |
& {\tt -{}-refsele=selection script} & select reference (can only be used with {\tt -{}-gxyz}) \\ |
| 4186 |
> |
& {\tt -{}-refsele=selection script} & select reference (can only |
| 4187 |
> |
be used with {\tt -{}-gxyz}) \\ |
| 4188 |
> |
& {\tt -{}-comsele=selection script} |
| 4189 |
> |
& select stunt doubles for center-of-mass |
| 4190 |
> |
reference point\\ |
| 4191 |
> |
& {\tt -{}-seleoffset=INT} & global index offset for a second object (used |
| 4192 |
> |
to define a vector between sites in molecule)\\ |
| 4193 |
> |
|
| 4194 |
|
& {\tt -{}-molname=STRING} & molecule name \\ |
| 4195 |
|
& {\tt -{}-begin=INT} & begin internal index \\ |
| 4196 |
|
& {\tt -{}-end=INT} & end internal index \\ |
| 4197 |
+ |
& {\tt -{}-radius=DOUBLE} & nanoparticle radius\\ |
| 4198 |
|
\hline |
| 4199 |
|
\multicolumn{3}{|l|}{One option from the following group of options is required:} \\ |
| 4200 |
|
\hline |
| 4201 |
< |
& {\tt -{}-gofr} & $g(r)$ \\ |
| 4202 |
< |
& {\tt -{}-r\_theta} & $g(r, \cos(\theta))$ \\ |
| 4203 |
< |
& {\tt -{}-r\_omega} & $g(r, \cos(\omega))$ \\ |
| 4204 |
< |
& {\tt -{}-theta\_omega} & $g(\cos(\theta), \cos(\omega))$ \\ |
| 4205 |
< |
& {\tt -{}-gxyz} & $g(x, y, z)$ \\ |
| 4206 |
< |
& {\tt -{}-p2} & $P_2$ order parameter ({\tt -{}-sele1} and {\tt -{}-sele2} must be specified) \\ |
| 4201 |
> |
& {\tt -{}-bo} & bond order parameter ({\tt -{}-rcut} must be specified) \\ |
| 4202 |
> |
& {\tt -{}-bor} & bond order parameter as a function of |
| 4203 |
> |
radius ({\tt -{}-rcut} must be specified) \\ |
| 4204 |
> |
& {\tt -{}-bad} & $N(\theta)$ bond angle density within ({\tt -{}-rcut} must be specified) \\ |
| 4205 |
> |
& {\tt -{}-count} & count of molecules matching selection |
| 4206 |
> |
criteria (and associated statistics) \\ |
| 4207 |
> |
-g& {\tt -{}-gofr} & $g(r)$ \\ |
| 4208 |
> |
& {\tt -{}-gofz} & $g(z)$ \\ |
| 4209 |
> |
& {\tt -{}-r\_theta} & $g(r, \cos(\theta))$ \\ |
| 4210 |
> |
& {\tt -{}-r\_omega} & $g(r, \cos(\omega))$ \\ |
| 4211 |
> |
& {\tt -{}-r\_z} & $g(r, z)$ \\ |
| 4212 |
> |
& {\tt -{}-theta\_omega} & $g(\cos(\theta), \cos(\omega))$ \\ |
| 4213 |
> |
& {\tt -{}-gxyz} & $g(x, y, z)$ \\ |
| 4214 |
> |
& {\tt -{}-twodgofr} & 2D $g(r)$ (Slab width {\tt -{}-dz} must be specified)\\ |
| 4215 |
> |
-p& {\tt -{}-p2} & $P_2$ order parameter ({\tt -{}-sele1} must be specified, {\tt -{}-sele2} is optional) \\ |
| 4216 |
> |
& {\tt -{}-rp2} & Ripple order parameter ({\tt -{}-sele1} and {\tt -{}-sele2} must be specified) \\ |
| 4217 |
|
& {\tt -{}-scd} & $S_{CD}$ order parameter(either {\tt -{}-sele1}, {\tt -{}-sele2}, {\tt -{}-sele3} are specified or {\tt -{}-molname}, {\tt -{}-begin}, {\tt -{}-end} are specified) \\ |
| 4218 |
< |
& {\tt -{}-density} & density plot ({\tt -{}-sele1} must be specified) \\ |
| 4219 |
< |
& {\tt -{}-slab\_density} & slab density ({\tt -{}-sele1} must be specified) |
| 4218 |
> |
-d& {\tt -{}-density} & density plot \\ |
| 4219 |
> |
& {\tt -{}-slab\_density} & slab density \\ |
| 4220 |
> |
& {\tt -{}-p\_angle} & $p(\cos(\theta))$ ($\theta$ |
| 4221 |
> |
is the angle between molecular axis and radial vector from origin\\ |
| 4222 |
> |
& {\tt -{}-hxy} & Calculates the undulation spectrum, $h(x,y)$, of an interface \\ |
| 4223 |
> |
& {\tt -{}-rho\_r} & $\rho(r)$\\ |
| 4224 |
> |
& {\tt -{}-angle\_r} & $\theta(r)$ (spatially resolves the |
| 4225 |
> |
angle between the molecular axis and the radial vector from the |
| 4226 |
> |
origin)\\ |
| 4227 |
> |
& {\tt -{}-hullvol} & hull volume of nanoparticle\\ |
| 4228 |
> |
& {\tt -{}-rodlength} & length of nanorod\\ |
| 4229 |
> |
-Q& {\tt -{}-tet\_param} & tetrahedrality order parameter ($Q$)\\ |
| 4230 |
> |
& {\tt -{}-tet\_param\_z} & spatially-resolved tetrahedrality order |
| 4231 |
> |
parameter $Q(z)$\\ |
| 4232 |
> |
& {\tt -{}-rnemdz} & slab-resolved RNEMD statistics (temperature, |
| 4233 |
> |
density, velocity)\\ |
| 4234 |
> |
& {\tt -{}-rnemdr} & shell-resolved RNEMD statistics (temperature, |
| 4235 |
> |
density, angular velocity) |
| 4236 |
|
\end{longtable} |
| 4237 |
|
|
| 4238 |
|
\subsection{\label{section:DynamicProps}DynamicProps} |
| 4273 |
|
-o& {\tt -{}-output=filename} & output file name \\ |
| 4274 |
|
& {\tt -{}-sele1=selection script} & select first StuntDouble set \\ |
| 4275 |
|
& {\tt -{}-sele2=selection script} & select second StuntDouble set (if sele2 is not set, use script from sele1) \\ |
| 4276 |
+ |
& {\tt -{}-order=INT} & Lengendre Polynomial Order\\ |
| 4277 |
+ |
-z& {\tt -{}-nzbins=INT} & Number of $z$ bins (default=`100`)\\ |
| 4278 |
+ |
-m& {\tt -{}-memory=memory specification} |
| 4279 |
+ |
&Available memory |
| 4280 |
+ |
(default=`2G`)\\ |
| 4281 |
|
\hline |
| 4282 |
|
\multicolumn{3}{|l|}{One option from the following group of options is required:} \\ |
| 4283 |
|
\hline |
| 4284 |
< |
-r& {\tt -{}-rcorr} & compute mean square displacement \\ |
| 4285 |
< |
-v& {\tt -{}-vcorr} & compute velocity correlation function \\ |
| 4286 |
< |
-d& {\tt -{}-dcorr} & compute dipole correlation function |
| 4284 |
> |
-s& {\tt -{}-selecorr} & selection correlation function \\ |
| 4285 |
> |
-r& {\tt -{}-rcorr} & compute mean squared displacement \\ |
| 4286 |
> |
-v& {\tt -{}-vcorr} & velocity autocorrelation function \\ |
| 4287 |
> |
-d& {\tt -{}-dcorr} & dipole correlation function \\ |
| 4288 |
> |
-l& {\tt -{}-lcorr} & Lengendre correlation function \\ |
| 4289 |
> |
& {\tt -{}-lcorrZ} & Lengendre correlation function binned by $z$ \\ |
| 4290 |
> |
& {\tt -{}-cohZ} & Lengendre correlation function for OH bond vectors binned by $z$\\ |
| 4291 |
> |
-M& {\tt -{}-sdcorr} & System dipole correlation function\\ |
| 4292 |
> |
& {\tt -{}-r\_rcorr} & Radial mean squared displacement\\ |
| 4293 |
> |
& {\tt -{}-thetacorr} & Angular mean squared displacement\\ |
| 4294 |
> |
& {\tt -{}-drcorr} & Directional mean squared displacement for particles with unit vectors\\ |
| 4295 |
> |
& {\tt -{}-helfandEcorr} & Helfand moment for thermal conductvity\\ |
| 4296 |
> |
-p& {\tt -{}-momentum} & Helfand momentum for viscosity\\ |
| 4297 |
> |
& {\tt -{}-stresscorr} & Stress tensor correlation function |
| 4298 |
|
\end{longtable} |
| 4299 |
|
|
| 4300 |
|
\chapter{\label{section:PreparingInput} Preparing Input Configurations} |
| 4361 |
|
to {\tt atom2md}, but they use a specific input format and do not |
| 4362 |
|
expect the the input specifier on the command line. |
| 4363 |
|
|
| 4364 |
+ |
|
| 4365 |
|
\section{\label{section:SimpleBuilder}SimpleBuilder} |
| 4366 |
|
|
| 4367 |
|
{\tt SimpleBuilder} creates simple lattice structures. It requires an |
| 4388 |
|
& {\tt -{}-nz=INT} & number of unit cells in z |
| 4389 |
|
\end{longtable} |
| 4390 |
|
|
| 4391 |
+ |
\section{\label{section:icosahedralBuilder}icosahedralBuilder} |
| 4392 |
+ |
|
| 4393 |
+ |
{\tt icosahedralBuilder} creates single-component geometric solids |
| 4394 |
+ |
that can be useful in simulating nanostructures. Like the other |
| 4395 |
+ |
builders, it requires an initial, but skeletal {\sc OpenMD} file to |
| 4396 |
+ |
specify the component that is to be placed on the lattice. The total |
| 4397 |
+ |
number of placed molecules will be shown at the top of the |
| 4398 |
+ |
configuration file that is generated, and that number may not match |
| 4399 |
+ |
the original meta-data file, so a new meta-data file is also generated |
| 4400 |
+ |
which matches the lattice structure. |
| 4401 |
+ |
|
| 4402 |
+ |
The options available for icosahedralBuilder are as follows: |
| 4403 |
+ |
\begin{longtable}[c]{|EFG|} |
| 4404 |
+ |
\caption{icosahedralBuilder Command-line Options} |
| 4405 |
+ |
\\ \hline |
| 4406 |
+ |
{\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline |
| 4407 |
+ |
\endhead |
| 4408 |
+ |
\hline |
| 4409 |
+ |
\endfoot |
| 4410 |
+ |
-h& {\tt -{}-help} & Print help and exit\\ |
| 4411 |
+ |
-V& {\tt -{}-version} & Print version and exit\\ |
| 4412 |
+ |
-o& {\tt -{}-output=STRING} & Output file name\\ |
| 4413 |
+ |
-n& {\tt -{}-shells=INT} & Nanoparticle shells\\ |
| 4414 |
+ |
-d& {\tt -{}-latticeConstant=DOUBLE} & Lattice spacing in Angstroms for cubic lattice.\\ |
| 4415 |
+ |
-c& {\tt -{}-columnAtoms=INT} & Number of atoms along central |
| 4416 |
+ |
column (Decahedron only)\\ |
| 4417 |
+ |
-t& {\tt -{}-twinAtoms=INT} & Number of atoms along twin |
| 4418 |
+ |
boundary (Decahedron only) \\ |
| 4419 |
+ |
-p& {\tt -{}-truncatedPlanes=INT} & Number of truncated planes (Curling-stone Decahedron only)\\ |
| 4420 |
+ |
\hline |
| 4421 |
+ |
\multicolumn{3}{|l|}{One option from the following group of options is required:} \\ |
| 4422 |
+ |
\hline |
| 4423 |
+ |
& {\tt -{}-ico} & Create an Icosahedral cluster \\ |
| 4424 |
+ |
& {\tt -{}-deca} & Create a regualar Decahedral cluster\\ |
| 4425 |
+ |
& {\tt -{}-ino} & Create an Ino Decahedral cluster\\ |
| 4426 |
+ |
& {\tt -{}-marks} & Create a Marks Decahedral cluster\\ |
| 4427 |
+ |
& {\tt -{}-stone} & Create a Curling-stone Decahedral cluster |
| 4428 |
+ |
\end{longtable} |
| 4429 |
+ |
|
| 4430 |
+ |
|
| 4431 |
|
\section{\label{section:Hydro}Hydro} |
| 4432 |
|
{\tt Hydro} generates resistance tensor ({\tt .diff}) files which are |
| 4433 |
|
required when using the Langevin integrator using complex rigid |
| 4461 |
|
\end{longtable} |
| 4462 |
|
|
| 4463 |
|
|
| 4464 |
+ |
|
| 4465 |
+ |
|
| 4466 |
+ |
|
| 4467 |
|
\chapter{\label{section:parallelization} Parallel Simulation Implementation} |
| 4468 |
|
|
| 4469 |
|
Although processor power is continually improving, it is still |
| 4547 |
|
DMR-0079647. |
| 4548 |
|
|
| 4549 |
|
|
| 4550 |
< |
\bibliographystyle{jcc} |
| 4550 |
> |
\bibliographystyle{aip} |
| 4551 |
|
\bibliography{openmdDoc} |
| 4552 |
|
|
| 4553 |
|
\end{document} |
