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MultiHydrogen Class Reference

Deprecated test class for Hydrogen molecule system. More...

#include <multihydrogen.h>

Inheritance diagram for MultiHydrogen:
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Collaboration diagram for MultiHydrogen:
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Public Member Functions

 MultiHydrogen (mat nucleiPositions)
 
virtual ~MultiHydrogen ()
 
virtual double coupledIntegral (int p, int r, int q, int s)
 
virtual double kineticIntegral (int p, int q)
 HartreeSolver::kineticIntegral is the solution of the the integral $$ | -{1}{2} ^2 | $$. More...
 
virtual double nuclearAttractionIntegral (int p, int q)
 HartreeSolver::kineticIntegral is the solution of the the integral $$ | -{1}{2} ^2 | $$. More...
 
virtual double overlapIntegral (int p, int q)
 
virtual uint nBasisFunctions ()
 
virtual uint nParticles ()
 
double errorFunction (double arg)
 
double additionalEnergyTerms ()
 
double uncoupledIntegral (int p, int q)
 
- Public Member Functions inherited from ElectronSystem
 ElectronSystem ()
 
virtual uint nParticlesUp ()
 
virtual uint nParticlesDown ()
 
void setNParticlesDown (uint nParticlesDown)
 

Public Attributes

mat R
 
vec alpha
 
const double powPi5over2 = pow(M_PI, 5./2.)
 

Detailed Description

Deprecated test class for Hydrogen molecule system.

Deprecated:

Definition at line 11 of file multihydrogen.h.

Constructor & Destructor Documentation

MultiHydrogen::MultiHydrogen ( mat  nucleiPositions)

Definition at line 11 of file multihydrogen.cpp.

11  :
12  R(nucleiPositions),
13  m_nNuclei(nucleiPositions.n_rows),
14  m_nOrbitalsPerNuclei(4)
15 {
16  alpha = zeros(m_nOrbitalsPerNuclei);
17  alpha(0) = 13.00773;
18  alpha(1) = 1.962079;
19  alpha(2) = 0.444529;
20  alpha(3) = 0.1219492;
21 }
MultiHydrogen::~MultiHydrogen ( )
virtual

Definition at line 23 of file multihydrogen.cpp.

24 {
25 }

Member Function Documentation

double MultiHydrogen::additionalEnergyTerms ( )
virtual

Implements ElectronSystem.

Definition at line 51 of file multihydrogen.cpp.

51  {
52  double repulsionEnergy = 0;
53  for(uint i = 0; i < m_nNuclei; i++) {
54  for(uint j = i + 1; j < m_nNuclei; j++) {
55  rowvec Rij = R.row(i) - R.row(j);
56  repulsionEnergy += 1/sqrt(dot(Rij, Rij));
57  }
58  }
59  return repulsionEnergy;
60 }
double MultiHydrogen::coupledIntegral ( int  p,
int  r,
int  q,
int  s 
)
virtual

Implements ElectronSystem.

Definition at line 27 of file multihydrogen.cpp.

27  {
28  int pIndex = p % m_nOrbitalsPerNuclei;
29  int qIndex = q % m_nOrbitalsPerNuclei;
30  int rIndex = r % m_nOrbitalsPerNuclei;
31  int sIndex = s % m_nOrbitalsPerNuclei;
32 
33  int Rp = p / m_nOrbitalsPerNuclei;
34  int Rq = q / m_nOrbitalsPerNuclei;
35  int Rr = r / m_nOrbitalsPerNuclei;
36  int Rs = s / m_nOrbitalsPerNuclei;
37 
38  double A = alpha[pIndex] + alpha[qIndex];
39  double B = alpha[rIndex] + alpha[sIndex];
40 
41  rowvec Ra = (alpha[pIndex]*R.row(Rp) + alpha[qIndex]*R.row(Rq))/A;
42  rowvec Rb = (alpha[rIndex]*R.row(Rr) + alpha[sIndex]*R.row(Rs))/B;
43 
44 
45  double t = (A*B/(A + B))*dot(Ra-Rb,Ra-Rb);
46 
47  double arg = 2*sqrt(A*B/(acos(-1)*(A+B)))*errorFunction(t)*overlapIntegral(p,q)*overlapIntegral(s,r);
48  return arg;
49 }
double MultiHydrogen::errorFunction ( double  arg)

Definition at line 62 of file multihydrogen.cpp.

62  {
63 
64  if (arg < 1.0E-6){
65  return 1.0;
66  }
67 
68  else{
69  arg = sqrt(arg);
70  double f = 1.0/arg * erf(arg) *sqrt(acos(-1))/2.0;
71  return f;
72  }
73 
74 }
double MultiHydrogen::kineticIntegral ( int  p,
int  q 
)
virtual

HartreeSolver::kineticIntegral is the solution of the the integral $$ | -{1}{2} ^2 | $$.

Parameters
p
q
Returns

Definition at line 83 of file multihydrogen.cpp.

83  {
84  int pIndex = p % m_nOrbitalsPerNuclei;
85  int qIndex = q % m_nOrbitalsPerNuclei;
86 
87  double ap = alpha(pIndex);
88  double aq = alpha(qIndex);
89 
90  double factor = ap*aq/(ap+aq);
91 
92  int RpIndex = p / m_nOrbitalsPerNuclei;
93  int RqIndex = q / m_nOrbitalsPerNuclei;
94 
95  rowvec Rp = R.row(RpIndex);
96  rowvec Rq = R.row(RqIndex);
97 
98  double Rpq = dot(Rp-Rq,Rp-Rq);
99  double expTerm = exp(-factor*Rpq);
100  double kin = 0.5*factor*(6-4*factor*Rpq)*pow(acos(-1)/(ap+aq),3.0/2.0)*expTerm;
101 
102  return kin;
103 }
uint MultiHydrogen::nBasisFunctions ( )
inlinevirtual

Implements ElectronSystem.

Definition at line 47 of file multihydrogen.h.

48 {
49  return m_nNuclei * m_nOrbitalsPerNuclei;
50 }
uint MultiHydrogen::nParticles ( )
inlinevirtual

Implements ElectronSystem.

Definition at line 43 of file multihydrogen.h.

43  {
44  return m_nNuclei;
45 }
double MultiHydrogen::nuclearAttractionIntegral ( int  p,
int  q 
)
virtual

HartreeSolver::kineticIntegral is the solution of the the integral $$ | -{1}{2} ^2 | $$.

Parameters
p
q
Returns

Definition at line 112 of file multihydrogen.cpp.

112  {
113  int pIndex = p % m_nOrbitalsPerNuclei;
114  int qIndex = q % m_nOrbitalsPerNuclei;
115 
116  double ap = alpha(pIndex);
117  double aq = alpha(qIndex);
118 
119  double apPlusAq = ap + aq;
120  double oneOverApPlusAq = 1.0/(apPlusAq);
121 
122  int RpIndex = p / m_nOrbitalsPerNuclei;
123  int RqIndex = q / m_nOrbitalsPerNuclei;
124 
125  rowvec Rp = R.row(RpIndex);
126  rowvec Rq = R.row(RqIndex);
127 
128  int Z = 1;
129 
130  double Rpq =dot(Rp-Rq,Rp-Rq);
131  double expTerm = exp(-ap*aq*oneOverApPlusAq*Rpq);
132 
133  rowvec RP = (ap*Rp + aq*Rq)*oneOverApPlusAq;
134 
135  double errorFunctionSum = 0;
136 
137  for(uint i = 0; i < m_nNuclei; i++) {
138  errorFunctionSum += errorFunction(apPlusAq*dot(RP-R.row(i),RP-R.row(i)));
139  }
140 
141  double nucAtt = -2*Z*oneOverApPlusAq*acos(-1)*expTerm*errorFunctionSum;
142 
143  return nucAtt;
144 }
double MultiHydrogen::overlapIntegral ( int  p,
int  q 
)
virtual

Implements ElectronSystem.

Definition at line 146 of file multihydrogen.cpp.

146  {
147  int pIndex = p % m_nOrbitalsPerNuclei;
148  int qIndex = q % m_nOrbitalsPerNuclei;
149 
150  double ap = alpha(pIndex);
151  double aq = alpha(qIndex);
152 
153  double factor = 1.0/(ap+aq);
154 
155  int RpIndex = p / m_nOrbitalsPerNuclei;
156  int RqIndex = q / m_nOrbitalsPerNuclei;
157 
158  rowvec Rp = R.row(RpIndex);
159  rowvec Rq = R.row(RqIndex);
160 
161  double Rpq = dot(Rp-Rq,Rp-Rq);
162  double expTerm = exp(-ap*aq*factor*Rpq);
163  double overlap = pow(acos(-1)*factor,3.0/2.0)*expTerm;
164 
165  return overlap;
166 }
double MultiHydrogen::uncoupledIntegral ( int  p,
int  q 
)
virtual

Implements ElectronSystem.

Definition at line 169 of file multihydrogen.cpp.

170 {
171  return kineticIntegral(p,q) + nuclearAttractionIntegral(p,q);
172 }

Member Data Documentation

vec MultiHydrogen::alpha

Definition at line 27 of file multihydrogen.h.

const double MultiHydrogen::powPi5over2 = pow(M_PI, 5./2.)

Definition at line 30 of file multihydrogen.h.

mat MultiHydrogen::R

Definition at line 25 of file multihydrogen.h.

The documentation for this class was generated from the following files:
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