1 /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 Copyright (c) 2014-2021 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 "CubicHarmonicBase.h"
23 #include "core/ActionRegister.h"
24
25 #include <string>
26 #include <cmath>
27
28 using namespace std;
29
30 namespace PLMD {
31 namespace crystallization {
32
33 //+PLUMEDOC MCOLVAR TETRAHEDRAL
34 /*
35 Calculate the degree to which the environment about ions has a tetrahedral order.
36
37 We can measure the degree to which the atoms in the first coordination shell around any atom, \f$i\f$ is
38 is arranged like a tetrahedron using the following function.
39
40 \f[
41 s(i) = \frac{1}{\sum_j \sigma( r_{ij} )} \sum_j \sigma( r_{ij} )\left[ \frac{(x_{ij} + y_{ij} + z_{ij})^3}{r_{ij}^3} +
42 \frac{(x_{ij} - y_{ij} - z_{ij})^3}{r_{ij}^3} +
43 \frac{(-x_{ij} + y_{ij} - z_{ij})^3}{r_{ij}^3} +
44 \frac{(-x_{ij} - y_{ij} + z_{ij})^3}{r_{ij}^3} \right]
45 \f]
46
47 Here \f$r_{ij}\f$ is the magnitude of the vector connecting atom \f$i\f$ to atom \f$j\f$ and \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$
48 are its three components. The function \f$\sigma( r_{ij} )\f$ is a \ref switchingfunction that acts on the distance between
49 atoms \f$i\f$ and \f$j\f$. The parameters of this function should be set so that the function is equal to one
50 when atom \f$j\f$ is in the first coordination sphere of atom \f$i\f$ and is zero otherwise.
51
52 \par Examples
53
54 The following command calculates the average value of the TETRAHEDRAL parameter for a set of 64 atoms all of the same type
55 and outputs this quantity to a file called colvar.
56
57 \plumedfile
58 tt: TETRAHEDRAL SPECIES=1-64 SWITCH={RATIONAL D_0=1.3 R_0=0.2} MEAN
59 PRINT ARG=tt.mean FILE=colvar
60 \endplumedfile
61
62 The following command calculates the number of TETRAHEDRAL parameters that are greater than 0.8 in a set of 10 atoms.
63 In this calculation it is assumed that there are two atom types A and B and that the first coordination sphere of the
64 10 atoms of type A contains atoms of type B. The formula above is thus calculated for ten different A atoms and within
65 it the sum over \f$j\f$ runs over 40 atoms of type B that could be in the first coordination sphere.
66
67 \plumedfile
68 tt: TETRAHEDRAL SPECIESA=1-10 SPECIESB=11-40 SWITCH={RATIONAL D_0=1.3 R_0=0.2} MORE_THAN={RATIONAL R_0=0.8}
69 PRINT ARG=tt.* FILE=colvar
70 \endplumedfile
71
72 */
73 //+ENDPLUMEDOC
74
75
76 class Tetrahedral : public CubicHarmonicBase {
77 public:
78 static void registerKeywords( Keywords& keys );
79 explicit Tetrahedral(const ActionOptions&);
80 double calculateCubicHarmonic( const Vector& distance, const double& d2, Vector& myder ) const override;
81 };
82
83 PLUMED_REGISTER_ACTION(Tetrahedral,"TETRAHEDRAL")
84
registerKeywords(Keywords & keys)85 void Tetrahedral::registerKeywords( Keywords& keys ) {
86 CubicHarmonicBase::registerKeywords( keys );
87 }
88
Tetrahedral(const ActionOptions & ao)89 Tetrahedral::Tetrahedral(const ActionOptions&ao):
90 Action(ao),
91 CubicHarmonicBase(ao)
92 {
93 checkRead();
94 }
95
calculateCubicHarmonic(const Vector & distance,const double & d2,Vector & myder) const96 double Tetrahedral::calculateCubicHarmonic( const Vector& distance, const double& d2, Vector& myder ) const {
97 double sp1 = +distance[0]+distance[1]+distance[2];
98 double sp2 = +distance[0]-distance[1]-distance[2];
99 double sp3 = -distance[0]+distance[1]-distance[2];
100 double sp4 = -distance[0]-distance[1]+distance[2];
101
102 double sp1c = pow( sp1, 3 );
103 double sp2c = pow( sp2, 3 );
104 double sp3c = pow( sp3, 3 );
105 double sp4c = pow( sp4, 3 );
106
107 double d1 = distance.modulo();
108 double r3 = pow( d1, 3 );
109 double r5 = pow( d1, 5 );
110
111 double tmp = sp1c/r3 + sp2c/r3 + sp3c/r3 + sp4c/r3;
112
113 double t1=(3*sp1c)/r5; double tt1=((3*sp1*sp1)/r3);
114 double t2=(3*sp2c)/r5; double tt2=((3*sp2*sp2)/r3);
115 double t3=(3*sp3c)/r5; double tt3=((3*sp3*sp3)/r3);
116 double t4=(3*sp4c)/r5; double tt4=((3*sp4*sp4)/r3);
117
118 myder[0] = (tt1-(distance[0]*t1)) + (tt2-(distance[0]*t2)) + (-tt3-(distance[0]*t3)) + (-tt4-(distance[0]*t4));
119 myder[1] = (tt1-(distance[1]*t1)) + (-tt2-(distance[1]*t2)) + (tt3-(distance[1]*t3)) + (-tt4-(distance[1]*t4));
120 myder[2] = (tt1-(distance[2]*t1)) + (-tt2-(distance[2]*t2)) + (-tt3-(distance[2]*t3)) + (tt4-(distance[2]*t4));
121
122 return tmp;
123 }
124
125 }
126 }
127
128