1 // ******************************************************************************
2 //
3 // Title: Force Field X.
4 // Description: Force Field X - Software for Molecular Biophysics.
5 // Copyright: Copyright (c) Michael J. Schnieders 2001-2024.
6 //
7 // This file is part of Force Field X.
8 //
9 // Force Field X is free software; you can redistribute it and/or modify it
10 // under the terms of the GNU General Public License version 3 as published by
11 // the Free Software Foundation.
12 //
13 // Force Field X is distributed in the hope that it will be useful, but WITHOUT
14 // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
15 // FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
16 // details.
17 //
18 // You should have received a copy of the GNU General Public License along with
19 // Force Field X; if not, write to the Free Software Foundation, Inc., 59 Temple
20 // Place, Suite 330, Boston, MA 02111-1307 USA
21 //
22 // Linking this library statically or dynamically with other modules is making a
23 // combined work based on this library. Thus, the terms and conditions of the
24 // GNU General Public License cover the whole combination.
25 //
26 // As a special exception, the copyright holders of this library give you
27 // permission to link this library with independent modules to produce an
28 // executable, regardless of the license terms of these independent modules, and
29 // to copy and distribute the resulting executable under terms of your choice,
30 // provided that you also meet, for each linked independent module, the terms
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32 // module which is not derived from or based on this library. If you modify this
33 // library, you may extend this exception to your version of the library, but
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35 // exception statement from your version.
36 //
37 // ******************************************************************************
38 package ffx.numerics.multipole;
39
40 import static ffx.numerics.special.Erf.erfc;
41 import static java.lang.Math.PI;
42 import static org.apache.commons.math3.util.FastMath.exp;
43 import static org.apache.commons.math3.util.FastMath.pow;
44 import static org.apache.commons.math3.util.FastMath.sqrt;
45
46 /**
47 * The EwaldTensorQI class computes derivatives of erfc(<b>r</b>)/|<b>r</b>| via recursion to
48 * arbitrary order for Cartesian multipoles in a quasi-internal frame.
49 *
50 * @author Michael J. Schnieders
51 * @see <a href="http://doi.org/10.1142/9789812830364_0002" target="_blank"> Matt Challacombe, Eric
52 * Schwegler and Jan Almlof, Modern developments in Hartree-Fock theory: Fast methods for
53 * computing the Coulomb matrix. Computational Chemistry: Review of Current Trends. pp. 53-107,
54 * Ed. J. Leczszynski, World Scientifc, 1996. </a>
55 * @since 1.0
56 */
57 public class EwaldTensorQI extends CoulombTensorQI {
58
59 /** Constant <code>sqrtPI = sqrt(PI)</code> */
60 private static final double sqrtPI = sqrt(PI);
61
62 /**
63 * These are the "source" terms for the recursion for the screened Coulomb operator erfc(R)/R.
64 */
65 private final double[] ewaldSource;
66
67 /**
68 * The Ewald convergence parameter.
69 */
70 private final double beta;
71
72 /**
73 * Constructor for EwaldTensorQI.
74 *
75 * @param order Tensor order.
76 * @param beta The Ewald convergence parameter.
77 */
78 public EwaldTensorQI(int order, double beta) {
79 super(order);
80 this.beta = beta;
81 operator = OPERATOR.SCREENED_COULOMB;
82
83 // Auxiliary terms for screened Coulomb (Sagui et al. Eq. 2.28)
84 ewaldSource = new double[o1];
85 double prefactor = 2.0 * beta / sqrtPI;
86 double twoBeta2 = -2.0 * beta * beta;
87 for (int n = 0; n <= order; n++) {
88 ewaldSource[n] = prefactor * pow(twoBeta2, n);
89 }
90
91 }
92
93 /**
94 * Generate source terms for the Ewald Challacombe et al. recursion.
95 *
96 * @param T000 Location to store the source terms.
97 */
98 protected void source(double[] T000) {
99 // Generate source terms for real space Ewald summation.
100 if (beta > 0.0) {
101 // Sagui et al. Eq. 2.22
102 double betaR = beta * R;
103 double betaR2 = betaR * betaR;
104 double iBetaR2 = 1.0 / (2.0 * betaR2);
105 double expBR2 = exp(-betaR2);
106 // Fnc(x^2) = Sqrt(PI) * erfc(x) / (2*x)
107 // where x = Beta*R
108 double Fnc = sqrtPI * erfc(betaR) / (2.0 * betaR);
109 for (int n = 0; n < o1; n++) {
110 T000[n] = ewaldSource[n] * Fnc;
111 // Generate F(n+1)c from Fnc (Eq. 2.24 in Sagui et al.)
112 // F(n+1)c = [(2*n+1) Fnc(x) + exp(-x)] / 2x
113 // where x = (Beta*R)^2
114 Fnc = ((2.0 * n + 1.0) * Fnc + expBR2) * iBetaR2;
115 }
116 } else {
117 // For beta = 0, generate tensors for the Coulomb operator.
118 super.source(T000);
119 }
120 }
121
122 }