Line data Source code
1 : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 : Copyright (c) 2013-2023 The plumed team
3 : (see the PEOPLE file at the root of the distribution for a list of names)
4 :
5 : See http://www.plumed.org for more information.
6 :
7 : This file is part of plumed, version 2.
8 :
9 : plumed is free software: you can redistribute it and/or modify
10 : it under the terms of the GNU Lesser General Public License as published by
11 : the Free Software Foundation, either version 3 of the License, or
12 : (at your option) any later version.
13 :
14 : plumed is distributed in the hope that it will be useful,
15 : but WITHOUT ANY WARRANTY; without even the implied warranty of
16 : MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 : GNU Lesser General Public License for more details.
18 :
19 : You should have received a copy of the GNU Lesser General Public License
20 : along with plumed. If not, see <http://www.gnu.org/licenses/>.
21 : +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
22 : #include "Steinhardt.h"
23 : #include "core/PlumedMain.h"
24 : #include <complex>
25 :
26 : namespace PLMD {
27 : namespace crystallization {
28 :
29 21 : void Steinhardt::registerKeywords( Keywords& keys ) {
30 21 : VectorMultiColvar::registerKeywords( keys );
31 42 : keys.add("compulsory","NN","12","The n parameter of the switching function ");
32 42 : keys.add("compulsory","MM","0","The m parameter of the switching function; 0 implies 2*NN");
33 42 : keys.add("compulsory","D_0","0.0","The d_0 parameter of the switching function");
34 42 : keys.add("compulsory","R_0","The r_0 parameter of the switching function");
35 42 : keys.add("optional","SWITCH","This keyword is used if you want to employ an alternative to the continuous switching function defined above. "
36 : "The following provides information on the \\ref switchingfunction that are available. "
37 : "When this keyword is present you no longer need the NN, MM, D_0 and R_0 keywords.");
38 63 : keys.use("SPECIES"); keys.use("SPECIESA"); keys.use("SPECIESB");
39 84 : keys.use("MEAN"); keys.use("LESS_THAN"); keys.use("MORE_THAN"); keys.use("VMEAN");
40 105 : keys.use("BETWEEN"); keys.use("HISTOGRAM"); keys.use("MOMENTS"); keys.use("MIN"); keys.use("ALT_MIN");
41 42 : keys.use("LOWEST"); keys.use("HIGHEST");
42 21 : }
43 :
44 18 : Steinhardt::Steinhardt( const ActionOptions& ao ):
45 : Action(ao),
46 : VectorMultiColvar(ao),
47 18 : tmom(0)
48 : {
49 : // Read in the switching function
50 36 : std::string sw, errors; parse("SWITCH",sw);
51 18 : if(sw.length()>0) {
52 6 : switchingFunction.set(sw,errors);
53 : } else {
54 12 : double r_0=-1.0, d_0; int nn, mm;
55 24 : parse("NN",nn); parse("MM",mm);
56 24 : parse("R_0",r_0); parse("D_0",d_0);
57 12 : if( r_0<0.0 ) error("you must set a value for R_0");
58 12 : switchingFunction.set(nn,mm,r_0,d_0);
59 : }
60 18 : log.printf(" Steinhardt parameter of central atom and those within %s\n",( switchingFunction.description() ).c_str() );
61 36 : log<<" Bibliography "<<plumed.cite("Tribello, Giberti, Sosso, Salvalaglio and Parrinello, J. Chem. Theory Comput. 13, 1317 (2017)")<<"\n";
62 : // Set the link cell cutoff
63 18 : setLinkCellCutoff( switchingFunction.get_dmax() );
64 18 : rcut = switchingFunction.get_dmax(); rcut2 = rcut*rcut;
65 18 : std::vector<AtomNumber> all_atoms; setupMultiColvarBase( all_atoms );
66 18 : }
67 :
68 18 : void Steinhardt::setAngularMomentum( const unsigned& ang ) {
69 18 : tmom=ang; setVectorDimensionality( 2*(2*ang + 1) );
70 18 : }
71 :
72 74931 : void Steinhardt::calculateVector( multicolvar::AtomValuePack& myatoms ) const {
73 : double dfunc, dpoly_ass, md, tq6, itq6, real_z, imag_z;
74 74931 : Vector dz, myrealvec, myimagvec, real_dz, imag_dz;
75 : // The square root of -1
76 : std::complex<double> ii( 0.0, 1.0 ), dp_x, dp_y, dp_z;
77 :
78 74931 : unsigned ncomp=2*tmom+1;
79 : double sw, poly_ass, dlen; std::complex<double> powered;
80 7465705 : for(unsigned i=1; i<myatoms.getNumberOfAtoms(); ++i) {
81 : Vector& distance=myatoms.getPosition(i); // getSeparation( myatoms.getPosition(0), myatoms.getPosition(i) );
82 : double d2;
83 12224372 : if ( (d2=distance[0]*distance[0])<rcut2 &&
84 4833598 : (d2+=distance[1]*distance[1])<rcut2 &&
85 10872046 : (d2+=distance[2]*distance[2])<rcut2 &&
86 : d2>epsilon ) {
87 :
88 2408222 : dlen = sqrt(d2);
89 2408222 : sw = switchingFunction.calculate( dlen, dfunc );
90 2408222 : accumulateSymmetryFunction( -1, i, sw, (+dfunc)*distance, (-dfunc)*Tensor( distance,distance ), myatoms );
91 2408222 : double dlen3 = d2*dlen;
92 : // Do stuff for m=0
93 2408222 : poly_ass=deriv_poly( 0, distance[2]/dlen, dpoly_ass );
94 : // Derivatives of z/r wrt x, y, z
95 2408222 : dz = -( distance[2] / dlen3 )*distance; dz[2] += (1.0 / dlen);
96 : // Derivative wrt to the vector connecting the two atoms
97 2408222 : myrealvec = (+sw)*dpoly_ass*dz + poly_ass*(+dfunc)*distance;
98 : // Accumulate the derivatives
99 2408222 : accumulateSymmetryFunction( 2 + tmom, i, sw*poly_ass, myrealvec, Tensor( -myrealvec,distance ), myatoms );
100 :
101 : // The complex number of which we have to take powers
102 2408222 : std::complex<double> com1( distance[0]/dlen,distance[1]/dlen );
103 : powered = std::complex<double>(1.0,0.0);
104 :
105 : // Do stuff for all other m values
106 15435674 : for(unsigned m=1; m<=tmom; ++m) {
107 : // Calculate Legendre Polynomial
108 13027452 : poly_ass=deriv_poly( m, distance[2]/dlen, dpoly_ass );
109 : // Calculate power of complex number
110 : // if(std::abs(com1)>epsilon) powered=pow(com1,m-1);
111 : // else if(m==1) powered=std::complex<double>(1.,0);
112 : // else powered = std::complex<double>(0.,0.);
113 : // Real and imaginary parts of z
114 : real_z = real(com1*powered); imag_z = imag(com1*powered );
115 :
116 : // Calculate steinhardt parameter
117 13027452 : tq6=poly_ass*real_z; // Real part of steinhardt parameter
118 13027452 : itq6=poly_ass*imag_z; // Imaginary part of steinhardt parameter
119 :
120 : // Derivatives wrt ( x/r + iy )^m
121 13027452 : md=static_cast<double>(m);
122 13027452 : dp_x = md*powered*( (1.0/dlen)-(distance[0]*distance[0])/dlen3-ii*(distance[0]*distance[1])/dlen3 );
123 13027452 : dp_y = md*powered*( ii*(1.0/dlen)-(distance[0]*distance[1])/dlen3-ii*(distance[1]*distance[1])/dlen3 );
124 13027452 : dp_z = md*powered*( -(distance[0]*distance[2])/dlen3-ii*(distance[1]*distance[2])/dlen3 );
125 :
126 : // Derivatives of real and imaginary parts of above
127 13027452 : real_dz[0] = real( dp_x ); real_dz[1] = real( dp_y ); real_dz[2] = real( dp_z );
128 13027452 : imag_dz[0] = imag( dp_x ); imag_dz[1] = imag( dp_y ); imag_dz[2] = imag( dp_z );
129 :
130 : // Complete derivative of steinhardt parameter
131 13027452 : myrealvec = (+sw)*dpoly_ass*real_z*dz + (+dfunc)*distance*tq6 + (+sw)*poly_ass*real_dz;
132 13027452 : myimagvec = (+sw)*dpoly_ass*imag_z*dz + (+dfunc)*distance*itq6 + (+sw)*poly_ass*imag_dz;
133 :
134 : // Real part
135 13027452 : accumulateSymmetryFunction( 2 + tmom + m, i, sw*tq6, myrealvec, Tensor( -myrealvec,distance ), myatoms );
136 : // Imaginary part
137 13027452 : accumulateSymmetryFunction( 2+ncomp+tmom+m, i, sw*itq6, myimagvec, Tensor( -myimagvec,distance ), myatoms );
138 : // Store -m part of vector
139 13027452 : double pref=pow(-1.0,m);
140 : // -m part of vector is just +m part multiplied by (-1.0)**m and multiplied by complex
141 : // conjugate of Legendre polynomial
142 : // Real part
143 13027452 : accumulateSymmetryFunction( 2+tmom-m, i, pref*sw*tq6, pref*myrealvec, pref*Tensor( -myrealvec,distance ), myatoms );
144 : // Imaginary part
145 13027452 : accumulateSymmetryFunction( 2+ncomp+tmom-m, i, -pref*sw*itq6, -pref*myimagvec, pref*Tensor( myimagvec,distance ), myatoms );
146 : // Calculate next power of complex number
147 : powered *= com1;
148 : }
149 : }
150 : }
151 :
152 : // Normalize
153 74931 : updateActiveAtoms( myatoms );
154 1892577 : for(unsigned i=0; i<getNumberOfComponentsInVector(); ++i) myatoms.getUnderlyingMultiValue().quotientRule( 2+i, 2+i );
155 74931 : }
156 :
157 15435674 : double Steinhardt::deriv_poly( const unsigned& m, const double& val, double& df ) const {
158 : double fact=1.0;
159 58187996 : for(unsigned j=1; j<=m; ++j) fact=fact*j;
160 15435674 : double res=coeff_poly[m]*fact;
161 :
162 15435674 : double pow=1.0, xi=val, dxi=1.0; df=0.0;
163 58187996 : for(int i=m+1; i<=tmom; ++i) {
164 : double fact=1.0;
165 109266592 : for(unsigned j=i-m+1; j<=i; ++j) fact=fact*j;
166 42752322 : res=res+coeff_poly[i]*fact*xi;
167 42752322 : df = df + pow*coeff_poly[i]*fact*dxi;
168 42752322 : xi=xi*val; dxi=dxi*val; pow+=1.0;
169 : }
170 15435674 : df = df*normaliz[m];
171 15435674 : return normaliz[m]*res;
172 : }
173 :
174 : }
175 : }
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