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#include "config.h" |
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#include <cmath> |
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#include <cstdlib> |
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#include <iostream> |
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#include "math/Factorials.hpp" |
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#include "utils/NumericConstant.hpp" |
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#ifndef NONBONDED_SLATERINTEGRALS_HPP |
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#define NONBONDED_SLATERINTEGRALS_HPP |
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* \frac{\alpha^\nu}{\nu!} |
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* \f] |
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* @param n - principal quantum number |
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* @param alpha - Slater exponent |
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* @param a - Slater exponent |
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* @return the value of Rosen's A integral |
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* @note N. Rosen, Phys. Rev., 38 (1931), 255 |
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*/ |
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{ |
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RealType Term = 1.; |
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RosenA_ = Term; |
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for (unsigned nu=1; nu<=n; nu++) |
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for (int nu=1; nu<=n; nu++) |
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{ |
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Term *= a / nu; |
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RosenA_ += Term; |
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{ |
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RealType TheSum, Term; |
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RealType RosenB_, PSinhRosenA, PCoshRosenA, PHyperRosenA; |
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int nu; |
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bool IsPositive; |
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|
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if (alpha != 0.) |
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{ |
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Term = 1.; |
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TheSum = 1.; |
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IsPositive = true; |
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bool IsPositive = true; |
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|
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// These two expressions are (up to constant factors) equivalent |
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// to computing the hyperbolic sine and cosine of a respectively |
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* @note N. Rosen, Phys. Rev., 38 (1931), 255 |
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*/ |
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inline RealType RosenD(int m, int n, int p) |
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// [?ERROR?] can't return int |
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{ |
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printf("RosenD\n"); |
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exit(0); |
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if (m+n+p > maxFact) |
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{ |
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printf("Error, arguments exceed maximum factorial computed %d > %d\n", m+n+p, maxFact); |
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*/ |
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inline RealType sSTOCoulInt(RealType a, RealType b, int m, int n, RealType R) |
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{ |
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int nu, p; |
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RealType x, K2; |
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RealType Factor1, Factor2, Term, OneElectronTerm; |
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RealType eps, epsi; |
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// First compute the two-electron component |
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RealType sSTOCoulInt_ = 0.; |
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if (x == 0.) // Pathological case |
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if (std::fabs(x) < OpenMD::NumericConstant::epsilon) // Pathological case |
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{ |
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if ((a==b) && (m==n)) |
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{ |
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for (int nu=0; nu<=2*n-1; nu++) |
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{ |
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K2 = 0.; |
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for (unsigned p=0; p<=2*n+m; p++) K2 += 1. / fact[p]; |
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sSTOCoulInt_ += K2 * fact[2*n+m] / fact[m]; |
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} |
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sSTOCoulInt_ = 2 * a / (n * fact[2*n]) * sSTOCoulInt_; |
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} |
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else |
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{ |
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// Not implemented |
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printf("ERROR, sSTOCoulInt cannot compute from arguments\n"); |
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printf("a = %lf b = %lf m = %d n = %d R = %lf\n",a, b, m, n, R); |
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exit(0); |
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} |
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|
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// This solution for the one-center coulomb integrals comes from |
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// Yoshiyuki Hase, Computers & Chemistry 9(4), pp. 285-287 (1985). |
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|
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RealType Term1 = fact[2*m - 1] / pow(2*a, 2*m); |
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RealType Term2 = 0.; |
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for (int nu = 1; nu <= 2*n; nu++) { |
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Term2 += nu * pow(2*b, 2*n - nu) * fact[2*(m+n)-nu-1] / (fact[2*n-nu]*2*n * pow(2*(a+b), 2*(m+n)-nu)); |
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} |
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sSTOCoulInt_ = pow(2*a, 2*m+1) * (Term1 - Term2) / fact[2*m]; |
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|
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// Original QTPIE code for the one-center case is below. Doesn't |
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// appear to generate the correct one-center results. |
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// |
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// if ((a==b) && (m==n)) |
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// { |
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// for (int nu=0; nu<=2*n-1; nu++) |
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// { |
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// K2 = 0.; |
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// for (unsigned p=0; p<=2*n+m; p++) K2 += 1. / fact[p]; |
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// sSTOCoulInt_ += K2 * fact[2*n+m] / fact[m]; |
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// } |
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// sSTOCoulInt_ = 2 * a / (n * fact[2*n]) * sSTOCoulInt_; |
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// } |
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// else |
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// { |
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// // Not implemented |
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// printf("ERROR, sSTOCoulInt cannot compute from arguments\n"); |
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// printf("a = %lf b = %lf m = %d n = %d R = %lf\n",a, b, m, n, R); |
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// exit(0); |
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// } |
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|
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} |
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else |
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{ |
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/** |
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* @brief Calculates a Slater-type orbital exponent based on the hardness parameters |
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* @param Hardness: chemical hardness in atomic units |
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* @param hardness: chemical hardness in atomic units |
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* @param n: principal quantum number |
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* @note Modified for use with OpenMD by Gezelter and Michalka. |
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*/ |
