Line data Source code
1 : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 : Copyright (c) 2014-2018 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 first coordination shell around any atom, \f$i\f$ is
38 : tetrahedrally ordered 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 fo 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 tetrahedrality parameter for a set of 64 atoms all of the same type
55 : and outputs this quantity to a file called colvar.
56 :
57 : \verbatim
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 : \endverbatim
61 :
62 : The following command calculates the number of tetrahedrality 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 : \verbatim
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 : \endverbatim
71 :
72 : */
73 : //+ENDPLUMEDOC
74 :
75 :
76 2 : 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 ;
81 : };
82 :
83 2524 : PLUMED_REGISTER_ACTION(Tetrahedral,"TETRAHEDRAL")
84 :
85 2 : void Tetrahedral::registerKeywords( Keywords& keys ) {
86 2 : CubicHarmonicBase::registerKeywords( keys );
87 2 : }
88 :
89 1 : Tetrahedral::Tetrahedral(const ActionOptions&ao):
90 : Action(ao),
91 1 : CubicHarmonicBase(ao)
92 : {
93 1 : checkRead();
94 1 : }
95 :
96 4032 : double Tetrahedral::calculateCubicHarmonic( const Vector& distance, const double& d2, Vector& myder ) const {
97 4032 : double sp1 = +distance[0]+distance[1]+distance[2];
98 4031 : double sp2 = +distance[0]-distance[1]-distance[2];
99 4031 : double sp3 = -distance[0]+distance[1]-distance[2];
100 4032 : double sp4 = -distance[0]-distance[1]+distance[2];
101 :
102 4032 : double sp1c = pow( sp1, 3 );
103 4031 : double sp2c = pow( sp2, 3 );
104 4032 : double sp3c = pow( sp3, 3 );
105 4031 : double sp4c = pow( sp4, 3 );
106 :
107 4031 : double d1 = distance.modulo();
108 4032 : double r3 = pow( d1, 3 );
109 4032 : double r5 = pow( d1, 5 );
110 :
111 4031 : double tmp = sp1c/r3 + sp2c/r3 + sp3c/r3 + sp4c/r3;
112 :
113 4031 : double t1=(3*sp1c)/r5; double tt1=((3*sp1*sp1)/r3);
114 4031 : double t2=(3*sp2c)/r5; double tt2=((3*sp2*sp2)/r3);
115 4031 : double t3=(3*sp3c)/r5; double tt3=((3*sp3*sp3)/r3);
116 4031 : double t4=(3*sp4c)/r5; double tt4=((3*sp4*sp4)/r3);
117 :
118 4031 : myder[0] = (tt1-(distance[0]*t1)) + (tt2-(distance[0]*t2)) + (-tt3-(distance[0]*t3)) + (-tt4-(distance[0]*t4));
119 4032 : myder[1] = (tt1-(distance[1]*t1)) + (-tt2-(distance[1]*t2)) + (tt3-(distance[1]*t3)) + (-tt4-(distance[1]*t4));
120 4032 : myder[2] = (tt1-(distance[2]*t1)) + (-tt2-(distance[2]*t2)) + (-tt3-(distance[2]*t3)) + (tt4-(distance[2]*t4));
121 :
122 4032 : return tmp;
123 : }
124 :
125 : }
126 2523 : }
127 :
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