| 34 |
|
* work. Good starting points are: |
| 35 |
|
* |
| 36 |
|
* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). |
| 37 |
< |
* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). |
| 37 |
> |
* [2] Fennell & Gezelter, J. Chem. Phys. 124 234104 (2006). |
| 38 |
|
* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008). |
| 39 |
|
* [4] Vardeman & Gezelter, in progress (2009). |
| 40 |
|
*/ |
| 52 |
|
namespace OpenMD { |
| 53 |
|
|
| 54 |
|
Electrostatic::Electrostatic(): name_("Electrostatic"), initialized_(false), |
| 55 |
< |
forceField_(NULL), info_(NULL) {} |
| 55 |
> |
forceField_(NULL), info_(NULL), |
| 56 |
> |
haveCutoffRadius_(false), |
| 57 |
> |
haveDampingAlpha_(false), |
| 58 |
> |
haveDielectric_(false), |
| 59 |
> |
haveElectroSpline_(false) |
| 60 |
> |
{} |
| 61 |
|
|
| 62 |
|
void Electrostatic::initialize() { |
| 63 |
< |
|
| 63 |
> |
|
| 64 |
|
Globals* simParams_ = info_->getSimParams(); |
| 65 |
|
|
| 66 |
|
summationMap_["HARD"] = esm_HARD; |
| 102 |
|
screeningMethod_ = UNDAMPED; |
| 103 |
|
dielectric_ = 1.0; |
| 104 |
|
one_third_ = 1.0 / 3.0; |
| 100 |
– |
haveCutoffRadius_ = false; |
| 101 |
– |
haveDampingAlpha_ = false; |
| 102 |
– |
haveDielectric_ = false; |
| 103 |
– |
haveElectroSpline_ = false; |
| 105 |
|
|
| 106 |
|
// check the summation method: |
| 107 |
|
if (simParams_->haveElectrostaticSummationMethod()) { |
| 446 |
|
RealType ct_i, ct_j, ct_ij, a1; |
| 447 |
|
RealType riji, ri, ri2, ri3, ri4; |
| 448 |
|
RealType pref, vterm, epot, dudr; |
| 449 |
+ |
RealType vpair(0.0); |
| 450 |
|
RealType scale, sc2; |
| 451 |
|
RealType pot_term, preVal, rfVal; |
| 452 |
|
RealType c2ri, c3ri, c4rij, cti3, ctj3, ctidotj; |
| 453 |
|
RealType preSw, preSwSc; |
| 454 |
|
RealType c1, c2, c3, c4; |
| 455 |
< |
RealType erfcVal, derfcVal; |
| 455 |
> |
RealType erfcVal(1.0), derfcVal(0.0); |
| 456 |
|
RealType BigR; |
| 457 |
|
|
| 458 |
|
Vector3d Q_i, Q_j; |
| 462 |
|
Vector3d dudux_j, duduy_j, duduz_j; |
| 463 |
|
Vector3d rhatdot2, rhatc4; |
| 464 |
|
Vector3d dVdr; |
| 465 |
+ |
|
| 466 |
+ |
// variables for indirect (reaction field) interactions for excluded pairs: |
| 467 |
+ |
RealType indirect_Pot(0.0); |
| 468 |
+ |
RealType indirect_vpair(0.0); |
| 469 |
+ |
Vector3d indirect_dVdr(V3Zero); |
| 470 |
+ |
Vector3d indirect_duduz_i(V3Zero), indirect_duduz_j(V3Zero); |
| 471 |
|
|
| 472 |
|
pair<RealType, RealType> res; |
| 473 |
|
|
| 493 |
|
bool j_is_SplitDipole = data2.is_SplitDipole; |
| 494 |
|
bool j_is_Quadrupole = data2.is_Quadrupole; |
| 495 |
|
|
| 496 |
< |
if (i_is_Charge) |
| 496 |
> |
if (i_is_Charge) { |
| 497 |
|
q_i = data1.charge; |
| 498 |
+ |
if (idat.excluded) { |
| 499 |
+ |
*(idat.skippedCharge2) += q_i; |
| 500 |
+ |
} |
| 501 |
+ |
} |
| 502 |
|
|
| 503 |
|
if (i_is_Dipole) { |
| 504 |
|
mu_i = data1.dipole_moment; |
| 531 |
|
duduz_i = V3Zero; |
| 532 |
|
} |
| 533 |
|
|
| 534 |
< |
if (j_is_Charge) |
| 534 |
> |
if (j_is_Charge) { |
| 535 |
|
q_j = data2.charge; |
| 536 |
+ |
if (idat.excluded) { |
| 537 |
+ |
*(idat.skippedCharge1) += q_j; |
| 538 |
+ |
} |
| 539 |
+ |
} |
| 540 |
|
|
| 541 |
+ |
|
| 542 |
|
if (j_is_Dipole) { |
| 543 |
|
mu_j = data2.dipole_moment; |
| 544 |
|
uz_j = idat.eFrame2->getColumn(2); |
| 599 |
|
dudr = *(idat.sw) * preVal * (c2c_ - c2); |
| 600 |
|
|
| 601 |
|
} else if (summationMethod_ == esm_REACTION_FIELD) { |
| 602 |
< |
rfVal = *(idat.electroMult) * preRF_ * *(idat.rij) * *(idat.rij) ; |
| 602 |
> |
rfVal = preRF_ * *(idat.rij) * *(idat.rij); |
| 603 |
> |
|
| 604 |
|
vterm = preVal * ( riji + rfVal ); |
| 605 |
|
dudr = *(idat.sw) * preVal * ( 2.0 * rfVal - riji ) * riji; |
| 606 |
+ |
|
| 607 |
+ |
// if this is an excluded pair, there are still indirect |
| 608 |
+ |
// interactions via the reaction field we must worry about: |
| 609 |
|
|
| 610 |
+ |
if (idat.excluded) { |
| 611 |
+ |
indirect_vpair += preVal * rfVal; |
| 612 |
+ |
indirect_Pot += *(idat.sw) * preVal * rfVal; |
| 613 |
+ |
indirect_dVdr += *(idat.sw) * preVal * 2.0 * rfVal * riji * rhat; |
| 614 |
+ |
} |
| 615 |
+ |
|
| 616 |
|
} else { |
| 590 |
– |
vterm = preVal * riji * erfcVal; |
| 617 |
|
|
| 618 |
+ |
vterm = preVal * riji * erfcVal; |
| 619 |
|
dudr = - *(idat.sw) * preVal * c2; |
| 620 |
|
|
| 621 |
|
} |
| 595 |
– |
|
| 596 |
– |
*(idat.vpair) += vterm; |
| 597 |
– |
epot += *(idat.sw) * vterm; |
| 622 |
|
|
| 623 |
< |
dVdr += dudr * rhat; |
| 623 |
> |
vpair += vterm; |
| 624 |
> |
epot += *(idat.sw) * vterm; |
| 625 |
> |
dVdr += dudr * rhat; |
| 626 |
|
} |
| 627 |
|
|
| 628 |
|
if (j_is_Dipole) { |
| 635 |
|
ri3 = ri2 * riji; |
| 636 |
|
|
| 637 |
|
vterm = - pref * ct_j * ( ri2 - preRF2_ * *(idat.rij) ); |
| 638 |
< |
*(idat.vpair) += vterm; |
| 638 |
> |
vpair += vterm; |
| 639 |
|
epot += *(idat.sw) * vterm; |
| 640 |
|
|
| 641 |
|
dVdr += -preSw * (ri3 * (uz_j - 3.0 * ct_j * rhat) - preRF2_*uz_j); |
| 642 |
|
duduz_j += -preSw * rhat * (ri2 - preRF2_ * *(idat.rij) ); |
| 643 |
|
|
| 644 |
+ |
// Even if we excluded this pair from direct interactions, |
| 645 |
+ |
// we still have the reaction-field-mediated charge-dipole |
| 646 |
+ |
// interaction: |
| 647 |
+ |
|
| 648 |
+ |
if (idat.excluded) { |
| 649 |
+ |
indirect_vpair += pref * ct_j * preRF2_ * *(idat.rij); |
| 650 |
+ |
indirect_Pot += preSw * ct_j * preRF2_ * *(idat.rij); |
| 651 |
+ |
indirect_dVdr += preSw * preRF2_ * uz_j; |
| 652 |
+ |
indirect_duduz_j += preSw * rhat * preRF2_ * *(idat.rij); |
| 653 |
+ |
} |
| 654 |
+ |
|
| 655 |
|
} else { |
| 656 |
|
// determine the inverse r used if we have split dipoles |
| 657 |
|
if (j_is_SplitDipole) { |
| 684 |
|
// calculate the potential |
| 685 |
|
pot_term = scale * c2; |
| 686 |
|
vterm = -pref * ct_j * pot_term; |
| 687 |
< |
*(idat.vpair) += vterm; |
| 687 |
> |
vpair += vterm; |
| 688 |
|
epot += *(idat.sw) * vterm; |
| 689 |
|
|
| 690 |
|
// calculate derivatives for forces and torques |
| 731 |
|
qyy_j * (cy2*c3 - c2ri) + |
| 732 |
|
qzz_j * (cz2*c3 - c2ri) ); |
| 733 |
|
vterm = pref * pot_term; |
| 734 |
< |
*(idat.vpair) += vterm; |
| 734 |
> |
vpair += vterm; |
| 735 |
|
epot += *(idat.sw) * vterm; |
| 736 |
|
|
| 737 |
|
// calculate derivatives for the forces and torques |
| 759 |
|
ri3 = ri2 * riji; |
| 760 |
|
|
| 761 |
|
vterm = pref * ct_i * ( ri2 - preRF2_ * *(idat.rij) ); |
| 762 |
< |
*(idat.vpair) += vterm; |
| 762 |
> |
vpair += vterm; |
| 763 |
|
epot += *(idat.sw) * vterm; |
| 764 |
|
|
| 765 |
|
dVdr += preSw * (ri3 * (uz_i - 3.0 * ct_i * rhat) - preRF2_ * uz_i); |
| 766 |
|
|
| 767 |
|
duduz_i += preSw * rhat * (ri2 - preRF2_ * *(idat.rij) ); |
| 768 |
+ |
|
| 769 |
+ |
// Even if we excluded this pair from direct interactions, |
| 770 |
+ |
// we still have the reaction-field-mediated charge-dipole |
| 771 |
+ |
// interaction: |
| 772 |
+ |
|
| 773 |
+ |
if (idat.excluded) { |
| 774 |
+ |
indirect_vpair += -pref * ct_i * preRF2_ * *(idat.rij); |
| 775 |
+ |
indirect_Pot += -preSw * ct_i * preRF2_ * *(idat.rij); |
| 776 |
+ |
indirect_dVdr += -preSw * preRF2_ * uz_i; |
| 777 |
+ |
indirect_duduz_i += -preSw * rhat * preRF2_ * *(idat.rij); |
| 778 |
+ |
} |
| 779 |
|
|
| 780 |
|
} else { |
| 781 |
|
|
| 810 |
|
// calculate the potential |
| 811 |
|
pot_term = c2 * scale; |
| 812 |
|
vterm = pref * ct_i * pot_term; |
| 813 |
< |
*(idat.vpair) += vterm; |
| 813 |
> |
vpair += vterm; |
| 814 |
|
epot += *(idat.sw) * vterm; |
| 815 |
|
|
| 816 |
|
// calculate derivatives for the forces and torques |
| 833 |
|
|
| 834 |
|
vterm = pref * ( ri3 * (ct_ij - 3.0 * ct_i * ct_j) - |
| 835 |
|
preRF2_ * ct_ij ); |
| 836 |
< |
*(idat.vpair) += vterm; |
| 836 |
> |
vpair += vterm; |
| 837 |
|
epot += *(idat.sw) * vterm; |
| 838 |
|
|
| 839 |
|
a1 = 5.0 * ct_i * ct_j - ct_ij; |
| 842 |
|
|
| 843 |
|
duduz_i += preSw * (ri3 * (uz_j - 3.0 * ct_j * rhat) - preRF2_*uz_j); |
| 844 |
|
duduz_j += preSw * (ri3 * (uz_i - 3.0 * ct_i * rhat) - preRF2_*uz_i); |
| 845 |
+ |
|
| 846 |
+ |
if (idat.excluded) { |
| 847 |
+ |
indirect_vpair += - pref * preRF2_ * ct_ij; |
| 848 |
+ |
indirect_Pot += - preSw * preRF2_ * ct_ij; |
| 849 |
+ |
indirect_duduz_i += -preSw * preRF2_ * uz_j; |
| 850 |
+ |
indirect_duduz_j += -preSw * preRF2_ * uz_i; |
| 851 |
+ |
} |
| 852 |
|
|
| 853 |
|
} else { |
| 854 |
|
|
| 899 |
|
// calculate the potential |
| 900 |
|
pot_term = (ct_ij * c2ri - ctidotj * c3); |
| 901 |
|
vterm = pref * pot_term; |
| 902 |
< |
*(idat.vpair) += vterm; |
| 902 |
> |
vpair += vterm; |
| 903 |
|
epot += *(idat.sw) * vterm; |
| 904 |
|
|
| 905 |
|
// calculate derivatives for the forces and torques |
| 951 |
|
qzz_i * (cz2 * c3 - c2ri) ); |
| 952 |
|
|
| 953 |
|
vterm = pref * pot_term; |
| 954 |
< |
*(idat.vpair) += vterm; |
| 954 |
> |
vpair += vterm; |
| 955 |
|
epot += *(idat.sw) * vterm; |
| 956 |
|
|
| 957 |
|
// calculate the derivatives for the forces and torques |
| 966 |
|
} |
| 967 |
|
} |
| 968 |
|
|
| 914 |
– |
(*(idat.pot))[ELECTROSTATIC_FAMILY] += epot; |
| 915 |
– |
*(idat.f1) += dVdr; |
| 969 |
|
|
| 970 |
< |
if (i_is_Dipole || i_is_Quadrupole) |
| 971 |
< |
*(idat.t1) -= cross(uz_i, duduz_i); |
| 972 |
< |
if (i_is_Quadrupole) { |
| 973 |
< |
*(idat.t1) -= cross(ux_i, dudux_i); |
| 974 |
< |
*(idat.t1) -= cross(uy_i, duduy_i); |
| 975 |
< |
} |
| 976 |
< |
|
| 977 |
< |
if (j_is_Dipole || j_is_Quadrupole) |
| 978 |
< |
*(idat.t2) -= cross(uz_j, duduz_j); |
| 979 |
< |
if (j_is_Quadrupole) { |
| 980 |
< |
*(idat.t2) -= cross(uz_j, dudux_j); |
| 981 |
< |
*(idat.t2) -= cross(uz_j, duduy_j); |
| 982 |
< |
} |
| 970 |
> |
if (!idat.excluded) { |
| 971 |
> |
*(idat.vpair) += vpair; |
| 972 |
> |
(*(idat.pot))[ELECTROSTATIC_FAMILY] += epot; |
| 973 |
> |
*(idat.f1) += dVdr; |
| 974 |
> |
|
| 975 |
> |
if (i_is_Dipole || i_is_Quadrupole) |
| 976 |
> |
*(idat.t1) -= cross(uz_i, duduz_i); |
| 977 |
> |
if (i_is_Quadrupole) { |
| 978 |
> |
*(idat.t1) -= cross(ux_i, dudux_i); |
| 979 |
> |
*(idat.t1) -= cross(uy_i, duduy_i); |
| 980 |
> |
} |
| 981 |
> |
|
| 982 |
> |
if (j_is_Dipole || j_is_Quadrupole) |
| 983 |
> |
*(idat.t2) -= cross(uz_j, duduz_j); |
| 984 |
> |
if (j_is_Quadrupole) { |
| 985 |
> |
*(idat.t2) -= cross(uz_j, dudux_j); |
| 986 |
> |
*(idat.t2) -= cross(uz_j, duduy_j); |
| 987 |
> |
} |
| 988 |
|
|
| 989 |
< |
return; |
| 932 |
< |
} |
| 989 |
> |
} else { |
| 990 |
|
|
| 991 |
< |
void Electrostatic::calcSkipCorrection(InteractionData &idat) { |
| 992 |
< |
|
| 993 |
< |
if (!initialized_) initialize(); |
| 994 |
< |
|
| 995 |
< |
ElectrostaticAtomData data1 = ElectrostaticMap[idat.atypes.first]; |
| 939 |
< |
ElectrostaticAtomData data2 = ElectrostaticMap[idat.atypes.second]; |
| 940 |
< |
|
| 941 |
< |
// logicals |
| 942 |
< |
|
| 943 |
< |
bool i_is_Charge = data1.is_Charge; |
| 944 |
< |
bool i_is_Dipole = data1.is_Dipole; |
| 945 |
< |
|
| 946 |
< |
bool j_is_Charge = data2.is_Charge; |
| 947 |
< |
bool j_is_Dipole = data2.is_Dipole; |
| 948 |
< |
|
| 949 |
< |
RealType q_i, q_j; |
| 950 |
< |
|
| 951 |
< |
// The skippedCharge computation is needed by the real-space cutoff methods |
| 952 |
< |
// (i.e. shifted force and shifted potential) |
| 953 |
< |
|
| 954 |
< |
if (i_is_Charge) { |
| 955 |
< |
q_i = data1.charge; |
| 956 |
< |
*(idat.skippedCharge2) += q_i; |
| 957 |
< |
} |
| 958 |
< |
|
| 959 |
< |
if (j_is_Charge) { |
| 960 |
< |
q_j = data2.charge; |
| 961 |
< |
*(idat.skippedCharge1) += q_j; |
| 962 |
< |
} |
| 963 |
< |
|
| 964 |
< |
// the rest of this function should only be necessary for reaction field. |
| 965 |
< |
|
| 966 |
< |
if (summationMethod_ == esm_REACTION_FIELD) { |
| 967 |
< |
RealType riji, ri2, ri3; |
| 968 |
< |
RealType mu_i, ct_i; |
| 969 |
< |
RealType mu_j, ct_j; |
| 970 |
< |
RealType preVal, rfVal, vterm, dudr, pref, myPot(0.0); |
| 971 |
< |
Vector3d dVdr, uz_i, uz_j, duduz_i, duduz_j, rhat; |
| 972 |
< |
|
| 973 |
< |
// some variables we'll need independent of electrostatic type: |
| 991 |
> |
// only accumulate the forces and torques resulting from the |
| 992 |
> |
// indirect reaction field terms. |
| 993 |
> |
*(idat.vpair) += indirect_vpair; |
| 994 |
> |
(*(idat.pot))[ELECTROSTATIC_FAMILY] += indirect_Pot; |
| 995 |
> |
*(idat.f1) += indirect_dVdr; |
| 996 |
|
|
| 975 |
– |
riji = 1.0 / *(idat.rij) ; |
| 976 |
– |
rhat = *(idat.d) * riji; |
| 977 |
– |
|
| 978 |
– |
if (i_is_Dipole) { |
| 979 |
– |
mu_i = data1.dipole_moment; |
| 980 |
– |
uz_i = idat.eFrame1->getColumn(2); |
| 981 |
– |
ct_i = dot(uz_i, rhat); |
| 982 |
– |
duduz_i = V3Zero; |
| 983 |
– |
} |
| 984 |
– |
|
| 985 |
– |
if (j_is_Dipole) { |
| 986 |
– |
mu_j = data2.dipole_moment; |
| 987 |
– |
uz_j = idat.eFrame2->getColumn(2); |
| 988 |
– |
ct_j = dot(uz_j, rhat); |
| 989 |
– |
duduz_j = V3Zero; |
| 990 |
– |
} |
| 991 |
– |
|
| 992 |
– |
if (i_is_Charge) { |
| 993 |
– |
if (j_is_Charge) { |
| 994 |
– |
preVal = *(idat.electroMult) * pre11_ * q_i * q_j; |
| 995 |
– |
rfVal = preRF_ * *(idat.rij) * *(idat.rij) ; |
| 996 |
– |
vterm = preVal * rfVal; |
| 997 |
– |
myPot += *(idat.sw) * vterm; |
| 998 |
– |
dudr = *(idat.sw) * preVal * 2.0 * rfVal * riji; |
| 999 |
– |
dVdr += dudr * rhat; |
| 1000 |
– |
} |
| 1001 |
– |
|
| 1002 |
– |
if (j_is_Dipole) { |
| 1003 |
– |
ri2 = riji * riji; |
| 1004 |
– |
ri3 = ri2 * riji; |
| 1005 |
– |
pref = *(idat.electroMult) * pre12_ * q_i * mu_j; |
| 1006 |
– |
vterm = - pref * ct_j * ( ri2 - preRF2_ * *(idat.rij) ); |
| 1007 |
– |
myPot += *(idat.sw) * vterm; |
| 1008 |
– |
dVdr += - *(idat.sw) * pref * ( ri3 * ( uz_j - 3.0 * ct_j * rhat) - preRF2_ * uz_j); |
| 1009 |
– |
duduz_j += - *(idat.sw) * pref * rhat * (ri2 - preRF2_ * *(idat.rij) ); |
| 1010 |
– |
} |
| 1011 |
– |
} |
| 1012 |
– |
if (i_is_Dipole) { |
| 1013 |
– |
if (j_is_Charge) { |
| 1014 |
– |
ri2 = riji * riji; |
| 1015 |
– |
ri3 = ri2 * riji; |
| 1016 |
– |
pref = *(idat.electroMult) * pre12_ * q_j * mu_i; |
| 1017 |
– |
vterm = - pref * ct_i * ( ri2 - preRF2_ * *(idat.rij) ); |
| 1018 |
– |
myPot += *(idat.sw) * vterm; |
| 1019 |
– |
dVdr += *(idat.sw) * pref * ( ri3 * ( uz_i - 3.0 * ct_i * rhat) - preRF2_ * uz_i); |
| 1020 |
– |
duduz_i += *(idat.sw) * pref * rhat * (ri2 - preRF2_ * *(idat.rij)); |
| 1021 |
– |
} |
| 1022 |
– |
} |
| 1023 |
– |
|
| 1024 |
– |
// accumulate the forces and torques resulting from the self term |
| 1025 |
– |
(*(idat.pot))[ELECTROSTATIC_FAMILY] += myPot; |
| 1026 |
– |
*(idat.f1) += dVdr; |
| 1027 |
– |
|
| 997 |
|
if (i_is_Dipole) |
| 998 |
< |
*(idat.t1) -= cross(uz_i, duduz_i); |
| 998 |
> |
*(idat.t1) -= cross(uz_i, indirect_duduz_i); |
| 999 |
|
if (j_is_Dipole) |
| 1000 |
< |
*(idat.t2) -= cross(uz_j, duduz_j); |
| 1000 |
> |
*(idat.t2) -= cross(uz_j, indirect_duduz_j); |
| 1001 |
|
} |
| 1002 |
< |
} |
| 1002 |
> |
|
| 1003 |
> |
|
| 1004 |
> |
return; |
| 1005 |
> |
} |
| 1006 |
|
|
| 1007 |
|
void Electrostatic::calcSelfCorrection(SelfData &sdat) { |
| 1008 |
|
RealType mu1, preVal, chg1, self; |
| 1009 |
|
|
| 1010 |
|
if (!initialized_) initialize(); |
| 1011 |
< |
|
| 1011 |
> |
|
| 1012 |
|
ElectrostaticAtomData data = ElectrostaticMap[sdat.atype]; |
| 1013 |
|
|
| 1014 |
|
// logicals |
| 1043 |
– |
|
| 1015 |
|
bool i_is_Charge = data.is_Charge; |
| 1016 |
|
bool i_is_Dipole = data.is_Dipole; |
| 1017 |
|
|
| 1019 |
|
if (i_is_Dipole) { |
| 1020 |
|
mu1 = data.dipole_moment; |
| 1021 |
|
preVal = pre22_ * preRF2_ * mu1 * mu1; |
| 1022 |
< |
sdat.pot[2] -= 0.5 * preVal; |
| 1022 |
> |
(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal; |
| 1023 |
|
|
| 1024 |
|
// The self-correction term adds into the reaction field vector |
| 1025 |
|
Vector3d uz_i = sdat.eFrame->getColumn(2); |
| 1036 |
|
} else { |
| 1037 |
|
self = - 0.5 * rcuti_ * chg1 * (chg1 + *(sdat.skippedCharge)) * pre11_; |
| 1038 |
|
} |
| 1039 |
< |
sdat.pot[ELECTROSTATIC_FAMILY] += self; |
| 1039 |
> |
(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self; |
| 1040 |
|
} |
| 1041 |
|
} |
| 1042 |
|
} |