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TCL_EE2.h
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#ifndef TCLEE2h
#define TCLEE2h
// <Loggins> DANGERZONEEE...<\Loggins>
#ifndef ARMA_NO_DEBUG
#define ARMA_NO_DEBUG 1
#endif
#ifndef ARMA_CHECK
#define ARMA_CHECK 0
#endif
// Must have user defined reductions which were a feature of OMP 4.0 in 2013.
#ifdef _OPENMP
#if _OPENMP > 201300
#define HASUDR 1
#else
#define HASUDR 0
#endif
#else
#define HASUDR 0
#endif
#include <iostream>
#include <fstream>
#include <sstream>
#include <string>
#include <map>
#include <algorithm>
#ifdef _OPENMP
#include <omp.h>
#endif
#include <armadillo>
#include "math.h"
#include "rks.h"
#include "TCL.h"
#include "TCL_polematrices.h"
// To grab our 2e integrals.
#include "../cdman/rimp2grad.h"
#include "../cdman/ricispd.h"
//#include "noci_mp2.h"
//#include "KeyVtoM.hh"
#include <liblas/liblas.h>
#include "fileman_util.h"
using namespace arma;
class EE2{
public:
int n_ao, n_mo, n_occ, n_aux;
std::map<std::string,double> params;
int ActiveFirst, ActiveLast; // Mostly to avoid rapidly oscillating terms. NYI.
bool B_Built;
double nuclear_energy,Ehf,Epseudo,lambda,Emp2; // Lambda is an adiabatic parameter to warm the system.
cube BpqR; // Lowdin basis, calculated once on construction and fixed throughout.
mat RSinv;
mat H,X;
cx_mat V,C;
vec eigs;
// This is handy to reduce B rebuilds, if V=Curr then CurrInt is not rebuilt
cx_mat IntCur, VCur;
typedef complex<double> cx;
cx j; // The imaginary unit.
EE2(int n_mo_, int n_occ_, rks* the_scf, cx_mat& Rho_, cx_mat& V_,const std::map<std::string,double>& params_ = std::map<std::string,double>(), int ActiveFirst_=0, int ActiveLast_=0): n_mo(n_mo_), j(0.0,1.0), n_occ(n_occ_), H(the_scf->H), X(the_scf->X), V(V_), B_Built(false), params(params_), lambda(1.0)
{
int LenV = megtot();
int IBASIS = rem_read(REM_IBASIS);
int stat = STAT_NBASIS;
int Job;
int IBasisAux = rem_read(REM_AUX_BASIS);
nuclear_energy = the_scf->nuclear_energy();
ftnshlsstats(&n_aux,&stat, &IBasisAux);
cout << "------------------------------" << endl;
cout << "-------- EE2 JAP 2015 --------" << endl;
cout << "-------- Corr On --------" << endl;
cout << "------------------------------" << endl;
cout << "RIFock:" << params["RIFock"] << endl;
#ifdef _OPENMP
cout << "OMP spec" << _OPENMP << " n_threads " << omp_get_num_threads() << endl;
#if HASUDR
cout << "Your compiler supports parallism in EE2. You'll be toasty warm soon." << endl;
#else
cout << "Your compiler does not support OMP parallism in EE2, please recompile with GCC 5.0 or Intel 16.0 or later" << endl;
#endif
#endif
cout << "NMO: " << n_mo << " NAux: " << n_aux << " Size BpqR " << n_mo*n_mo*n_aux*8/(1024*1024) << "MB" << endl;
BpqR.resize(n_mo,n_mo,n_aux);
RSinv.resize(n_aux,n_aux);
{
// get (P|Q)**(-1/2) and save it to disk
//
// First, fool trnjob into thinking we want RIMP2
int tmp1 = rem_read(REM_LEVCOR);
rem_write(103, REM_LEVCOR);
trnjob(&Job);
// Then, write it back
rem_write(tmp1, REM_LEVCOR);
// form (P|Q)^-1/2 matrix and saves it to FILE_2C2E_INV_INTS
//
threading_policy::enable_blas_only();
invsqrtpq(&n_aux, &Job);
threading_policy::pop();
// read (P|Q)^-1/2
FileMan(FM_OPEN_RW, FILE_2C2E_INVSQ_INTS, 0, 0, 0, 0, 0);
LongFileMan(FM_READ, FILE_2C2E_INVSQ_INTS, FM_DP, n_aux*n_aux, 0, FM_BEG, RSinv.memptr(), 0);
FileMan(FM_CLOSE, FILE_2C2E_INVSQ_INTS, 0, 0, 0, 0, 0);
}
//RSinv.print("RSinv");
BuildB();
UpdateB(V_);
Rho_.eye(); Rho_.submat(n_occ,n_occ,n_mo-1,n_mo-1) *= 0.0;
// To run external to Q-Chem and avoid the two minute link.
if (params["DumpEE2"])
{
V_.save("V",arma_binary);
X.save("X",arma_binary);
BpqR.save("BpqR",arma_binary);
}
// Fock build, integral build and initialize the density.
CorrelateInitial(Rho_,V_);
}
// Try to adiabatically turn on the correlation.
void GML(arma::cx_mat& Rho_, arma::cx_mat& V_)
{
cout << "Adiabatically Correlating the system." << endl;
double dt=0.02; int NGML=300;
cx_mat RhoM12_(Rho_);
for(int i=0; i<NGML; ++i)
{
lambda=(1.0+i)/((double)NGML);
cx_mat newrho(Rho_);
cx_mat Rot = FockBuild(Rho_, V_); // updates eigs, C, V, F, etc. etc. etc.
// Rot.print("Rot");
Rho_ = Rot.t()*Rho_*Rot;
RhoM12_ = Rot.t()*RhoM12_*Rot;
// Make the exponential propagator.
arma::cx_mat F(Rho_); F.zeros(); F.set_real(diagmat(eigs));
vec Gd; cx_mat Cu;
eig_sym(Gd,Cu,F);
// Full step RhoM12 to make new RhoM12.
cx_mat NewRhoM12(Rho_);
cx_mat NewRho(Rho_);
Split_RK4_Step_MMUT(Gd, Cu, RhoM12_, NewRhoM12, 0.0, dt);
// NewRhoM12.print("NewRhoM12");
// Half step that to make the new Rho.
Split_RK4_Step_MMUT(Gd, Cu, NewRhoM12, NewRho, 0.0, dt/2.0);
Rho_ = 0.5*(NewRho+NewRho.t());//0.5*(NewRho+NewRho.t());
RhoM12_ = 0.5*(NewRhoM12+NewRhoM12.t());//0.5*(NewRhoM12+NewRhoM12.t());
if (i%10==0)
cout << "Gell-Man Low Iteration:" << i << " Lambda " << lambda << " ehf:" << Ehf << endl;
}
}
// Generate rate matrix for populations
void Stability(cx_mat& Rho)
{
cout << "calculating stability matrix... " << endl;
cx_mat tore(Rho); tore.eye();
cx_mat ref(Rho); ref.zeros();
double dn=0.001;
RhoDot(Rho,ref,0.0);
int n=n_mo;
for (int j=0; j<n; ++j)
{
cx_mat tmp(Rho);
tmp(j,j)+=dn;
cx_mat tmp2(Rho); tmp2.zeros();
RhoDot(tmp,tmp2,0.0);
for (int i=0; i<n; ++i)
{
tore(i,j) += (tmp2(i,i)-ref(i,i))/dn;
}
}
tore.print("Rate Matrix:");
cout << "Rate Trace? " << trace(tore) << endl;
for (int j=0; j<n; ++j)
cout << "Normed Probability:" << j << " " << accu(tore.col(j)) << endl;
cx_mat sstates; cx_vec rates;
eig_gen(rates, sstates, tore);
rates.print("Rates:");
cout << "State sum: "<< accu(sstates.row(n-1)) << endl;
sstates.row(n-1).print("steady state");
}
// Obtain the initial state for the dynamics.
void CorrelateInitial(cx_mat& Rho,cx_mat& V_)
{
cout << "Solving the RI-HF problem to ensure self-consistency." << endl;
double err=100.0;
int maxit = 400; int it=1;
while (abs(err) > pow(10.0,-10) && it<maxit)
{
cx_mat Rot = FockBuild(Rho,V_);
Rho = Rot.t()*Rho*Rot;
Rho.diag() *= 0.0;
err=accu(abs(Rho));
Rho.eye(); Rho.submat(n_occ,n_occ,n_mo-1,n_mo-1)*=0.0;
if (it%10==0)
cout << " Fock-Roothan: " << it << std::setprecision(9) << " Ehf" << Ehf << endl;
it++;
}
cx wks0 = eigs(n_occ)-eigs(n_occ-1);
// Various options for non-idempotent initial state:
// gell-man-low, fermi-dirac, and mp2NO.
cx_mat Pmp2=MP2(Rho); // Won't actually solve for Pmp2 unless we want it. Otherwise just gets the CE.
if ((bool)params["GML"] && !params["Mp2NOGuess"])
GML(Rho,V_);
lambda = 1.0;
if (params["Mp2NOGuess"])
{
cout << "Generating MP2 1 particle density matrix..." << endl;
if (params["Mp2NOGuess"]==2.0)
Rho = diagmat(Pmp2);
else
Rho = Pmp2;
}
if (params["FD"])
{
vec pops(eigs.n_elem);
double EvPerAu=27.2113;
double Kb = 8.61734315e-5/EvPerAu;
double Beta = 1.0/(params["Temp"]*Kb);
cout << "Finding " << n_occ*2 << " Fermions at Beta " << Beta << endl;
double mu = eigs(n_occ);
mu -= 0.010;
pops = 1.0/(1.0+exp(Beta*(eigs-mu)));
double sm = sum(pops);
mu += 0.020;
pops = 1.0/(1.0+exp(Beta*(eigs-mu)));
double sp = sum(pops);
// Linear fit for mu
mu = eigs(n_occ)-0.01 + ((0.02)/(sp-sm))*(n_occ - sm);
pops = 1.0/(1.0+exp(Beta*(eigs-mu)));
cout << "Populated with " << sum(pops) << " Fermions at mu = " << mu << endl;
//Repeat
double dmu=0.001;
while(abs(accu(pops)-n_occ)>pow(10.0,-10.0))
{
mu -= dmu;
pops = 1.0/(1.0+exp(Beta*(eigs-mu)));
sm = sum(pops);
mu += 2*dmu;
pops = 1.0/(1.0+exp(Beta*(eigs-mu)));
sp = sum(pops);
// Linear fit for mu
mu = mu-2.0*dmu + ((2.0*dmu)/(sp-sm))*(n_occ - sm);
pops = 1.0/(1.0+exp(Beta*(eigs-mu)));
cout << "Populated with " << accu(pops) << " Fermions at mu = " << mu << endl;
if ( abs(sum(pops)-n_occ) < pow(10.0,-10.0))
break;
dmu /= max(min(10.0,abs(((2.0*dmu)/(sp-sm))*(n_occ - sm))),1.1);
}
Rho.diag().zeros();
for (int i=0; i<n_mo; ++i)
if( abs(pops(i)) > pow(10.0,-16.0))
Rho(i,i) = pops(i);
cout << "Populated with " << sum(pops) << " Fermions at mu = " << mu << endl;
Rho.diag().st().print("Rho(fd)");
}
if (params["InitialCondition"]==1)
{
cx tmp = Rho(n_occ-1,n_occ-1);
Rho(n_occ,n_occ)+=tmp;
Rho(n_occ-1,n_occ-1)*=0.0;
}
cout << "Initial Trace: " << trace(Rho) << endl;
eigs.st().print("Eigs Before Rebuild");
FockBuild(Rho,V_);
UpdateB(V_);
eigs.st().print("Eigs After Rebuild");
cx wks1 = eigs(n_occ)-eigs(n_occ-1);
// Print the initial Step, Density, Noccs, and DNoccs.
{
Rho.diag().st().print("Inital Rho: ");
vec noccs; cx_mat u;
if(!eig_sym(noccs, u, Rho, "std"))
{
cout << "Warning... initial density did not diagonalize..." << endl;
return;
}
noccs.st().print("initial natural occupations");
// Check to see what effect the nonlinearity has...
cx_mat tmp(Rho),tmp2(Rho),tmp3(Rho); tmp.zeros(); tmp3.zeros();
tmp2.diag(1)+=0.0001;
tmp2.diag(-1)+=0.0001;
RhoDot(tmp2,tmp,1.0);
tmp2.diag(1)+=0.002;
tmp2.diag(-1)+=0.002;
RhoDot(tmp2,tmp3,3.0);
// Obtain the correction to a particle hole excitation energy.
cout << "-------------------------" << endl;
cout << "Omega_hf 0: " << wks0 << " " << 27.2113*wks0 << "eV"<< endl;
cout << "Omega_c 0: " << wks1 << " " << 27.2113*wks1 << "eV"<< endl;
cx ehbe(2.0*IntCur((n_occ)*n_mo+(n_occ),(n_occ-1)*n_mo+n_occ-1)-IntCur((n_occ)*n_mo+(n_occ-1),(n_occ)*n_mo+n_occ-1));
double cr=(imag(tmp(n_occ,n_occ-1)/0.0001));
cout << "E-H binding energy. " << ehbe << " " << 27.2113*ehbe << "eV"<< endl;
cout << "GS MP2 Correlation energy. " << Emp2 << " " << 27.2113*Emp2 << "eV"<< endl;
cout << "CIS Transition energy. " << ehbe << " " << 27.2113*(wks0+ehbe) << "eV"<< endl;
cout << "EE2 Correction: " << cr << " " << 27.2113*cr<< "eV"<< endl;
cout << "EE2 Correction (2): " << " " << 27.2113*(imag(tmp3(n_occ,n_occ-1)/0.002))<< "eV"<< endl;
cout << "-------------------------" << endl;
cout << " Total Estimated Homo Lumo xsition Energy: " << 27.2113*(cr+wks1+ehbe) << "eV"<< endl;
cout << " Total Estimated Homo Lumo xsition Energy+MP2: " << 27.2113*(cr+wks1+ehbe+Emp2) << "eV"<< endl;
cout << "-------------------------" << endl;
vec dnoccs;
if(!eig_sym(dnoccs, u, Rho+0.02*tmp, "std"))
{
cout << "Warning... change in density did not diagonalize..." << endl;
return;
}
dnoccs -= noccs;
dnoccs.st().print("initial NO change");
tmp.print("Initial RhoDot");
}
lambda = 1.0;
UpdateB(V_);
return;
}
// Finds the Chemical Potential, and then the best effective temperature to obtain pops.
// Based on the current eigs to obtain as close to pops as possible.
double EffectiveTemperature(const vec& pops)
{
if (n_occ+2 >= n_mo or n_occ-2<=0)
return 0.0;
cout << "Finding effective Temperature..." << endl;
double EvPerAu=27.2113;
double Kb = 8.61734315e-5/EvPerAu;
vec reigs = real(eigs);
vec spops = sort(pops, "descend");
double dmu = pow(10.0,-3.0); double mui = reigs(n_occ-2); double muf = reigs(n_occ+2); // Assume the chemical potential is bw h-2,l+2
double hldiff =reigs(n_occ) - reigs(n_occ-1);
double dB = 10.0*hldiff;
double Bi=dB; double Bf=100.0/hldiff;
double BestMu = 0.0;
double BestTemp = 0.0;
double BestError = n_occ;
for(double mu=mui; mu<muf; mu+=dmu)
{
for(double Beta=Bi; Beta<Bf; Beta+=dB)
{
vec p = pow(exp(Beta*(reigs-mu))+1.0,-1.0);
double Error = accu((spops-p)%(spops-p));
if (Error != Error)
Error = 8.0;
else if (Error < BestError)
{
BestTemp=1.0/(Beta*Kb);
BestMu=mu;
BestError = Error;
}
}
}
double Beta = 1.0/(BestTemp*Kb);
cout << "Effective Temperature: " << BestTemp << " at mu= " << BestMu << " beta= " << Beta << " Fermi-Deviance " << sqrt(BestError) << endl;
vec p = pow(exp(Beta*(reigs-BestMu))+1.0,-1.0);
(p-spops).st().print("Deviation From Thermality.");
return BestTemp;
}
// Calculate the MP2 energy and opdm blockwise in the fock eigenbasis to avoid singles.
// Use this as a density guess for the dynamics.
// Since HF is probably very far from the desired initial state
cx_mat MP2(cx_mat& RhoHF)
{
int n = n_mo;
int no=n_occ;
int nv=n_mo-n_occ;
typedef std::complex<double> cx;
int n1=nv;
int n2=nv*n1;
int n3=n2*no;
int n4=no*n3;
std::vector<cx> Vs(n4),T(n4);
std::fill(Vs.begin(), Vs.end(), std::complex<double>(0.0,0.0));
std::fill(T.begin(), T.end(), std::complex<double>(0.0,0.0));
cx_mat d2 = Delta2();
for(int R=0; R<n_aux; ++R)
{
cx_mat B = V.t()*BpqR.slice(R)*V;
for (int i=0; i<no; ++i)
{
for (int j=0; j<no; ++j)
{
for (int a=0; a<nv; ++a)
{
for (int b=0; b<nv; ++b)
{
Vs[i*n3+j*n2+a*n1+b] += B(i,a+no)*B(j,b+no);
}
}
}
}
}
Emp2=0.0;
for (int i=0; i<no; ++i)
{
for (int j=0; j<no; ++j)
{
for (int a=0; a<nv; ++a)
{
for (int b=0; b<nv; ++b)
{
T[i*n3+j*n2+a*n1+b] = (2*Vs[i*n3+j*n2+a*n1+b] - Vs[i*n3+j*n2+b*n1+a])/(d2(a+no,i)+d2(b+no,j));
Emp2 += real(T[i*n3+j*n2+a*n1+b]*Vs[i*n3+j*n2+a*n1+b]);
}
}
}
}
cout << std::setprecision(9) << "Mp2 Correlation energy: " << Emp2 << endl;
cx_mat Poo(no,no); Poo.zeros();
cx_mat Pvv(nv,nv); Pvv.zeros();
cx_mat Pov(no,no); Pov.zeros();
cx_mat Pmp2(RhoHF);
if (params["Mp2NOGuess"])
{
// Now make the PDMs.
// I'm taking these from JCC Ishimura, Pulay, and Nagase
// and CPL 166,3 Frisch, HG, Pople.
for (int i=0; i<no; ++i)
{
for (int j=0; j<no; ++j)
{
for (int k=0; k<no; ++k)
{
for (int a=0; a<nv; ++a)
{
for (int b=0; b<nv; ++b)
{
Poo(i,j) -= 2.0*T[i*n3+k*n2+a*n1+b]*Vs[j*n3+k*n2+a*n1+b]/(d2(a+no,k)+d2(b+no,j));
}
}
}
}
}
for (int i=0; i<no; ++i)
{
for (int j=0; j<no; ++j)
{
for (int c=0; c<nv; ++c)
{
for (int a=0; a<nv; ++a)
{
for (int b=0; b<nv; ++b)
{
Pvv(a,b) += 2.0*T[i*n3+j*n2+a*n1+c]*Vs[i*n3+j*n2+b*n1+c]/(d2(b+no,i)+d2(c+no,j));
}
}
}
}
}
cout << "Tr(oo) " << trace(Poo) << " Tr(vv)" << trace(Pvv) << endl;
// finally do the lag. pieces.
// Which require new integrals. (-_-)
cx_mat Lai(nv,no); Lai.zeros();
for(int R=0; R<n_aux; ++R)
{
cx_mat B = V.t()*BpqR.slice(R)*V;
for (int i=0; i<no; ++i)
{
for (int j=0; j<no; ++j)
{
for (int a=0; a<nv; ++a)
{
for (int b=0; b<nv; ++b)
{
for (int k=0; k<no; ++k)
{
Lai(a,i) += Poo(j,k)*(4.0*B(i,a+no)*B(j,k)-2.0*B(i,k)*B(a+no,j));
Lai(a,i) -= 4.0*T[j*n3+k*n2+a*n1+b]*B(i,j)*B(k,b+no);
}
for (int c=0; c<nv; ++c)
{
Lai(a,i) += Pvv(b,c)*(4.0*B(i,a+no)*B(b+no,c+no)-2.0*B(i,b+no)*B(a+no,c+no));
Lai(a,i) += 4.0*T[i*n3+j*n2+b*n1+c]*B(a+no,b+no)*B(j,c+no);
}
}
}
}
}
}
Lai.print("Lai");
// Solve the z-vector equation by iteration.
// The equation has the form:
// DP + L + VP = 0
// Initalize P = L/D
// Then calculate residual R = -L - VP
// Then P = -R/D. Iterate.
double dP=1.0; int iter=100;
cx_mat dvo=d2.submat(no,0,n-1,no-1);
cx_mat Pbj=-1.0*Lai/dvo;
// dvo.print("dvo");
// Pbj.print("Pbj0");
cx_mat R(Pbj); R.zeros();
while(dP>pow(10.0,-8.0) && iter>0)
{
// Calculate R.
R = -1.0*Lai;
for(int S=0; S<n_aux; ++S)
{
cx_mat B = V.t()*BpqR.slice(S)*V;
for (int i=0; i<no; ++i)
{
for (int j=0; j<no; ++j)
{
for (int a=0; a<nv; ++a)
{
for (int b=0; b<nv; ++b)
{
R(a,i) -= ( 4.0*B(a+no,i)*B(b+no,j)-B(a+no,j)*B(b+no,i)-B(a+no,b+no)*B(i,j) )*Pbj(b,j);
}
}
}
}
}
dP = accu(abs(Pbj-R/dvo));
Pbj = R/dvo;
cout << "Z-Iter:" << 100-iter << " dP: " << dP << endl;
// Pbj.print("Pbj");
iter--;
}
Poo.print("Poo");
Pvv.print("Pvv");
Pmp2.submat(0,0,no-1,no-1) += Poo;
Pmp2.submat(no,no,n-1,n-1) += Pvv;
Pmp2.submat(0,no,no-1,n-1) += Pbj.t();
Pmp2.submat(no,0,n-1,no-1) += Pbj;
Pmp2.print("Pmp2");
}
return Pmp2;
}
// Just to see if this is faster than Job 32...
// Rho is passed in the fock eigenbasis.
// F is built in the lowdin basis,
// then transformed into the fock eigenbasis and diagonalized.
cx_mat FockBuild(cx_mat& Rho, cx_mat& V_, bool debug=false)
{
if (!B_Built)
{
cout << "cannot build fock without B" << endl;
return Rho;
}
mat Xt = X.t();
cx_mat Vt = V.t();
cx_mat F(Rho); F.zeros();
mat J(Rho.n_rows,Rho.n_cols); J.zeros();
cx_mat K(Rho); K.zeros();
cx_mat Rhol = V*Rho*Vt; // Get Rho into the lowdin basis for the fock build.
mat h = 2.0*(Xt)*(H)*X; // h is stored in the ao basis.
F.set_real(h);
#if HASUDR
#pragma omp declare reduction( + : cx_mat : \
std::transform(omp_in.begin( ), omp_in.end( ), omp_out.begin( ), omp_out.begin( ), std::plus< std::complex<double> >( )) ) initializer (omp_priv(omp_orig))
#pragma omp declare reduction( + : mat : \
std::transform(omp_in.begin( ), omp_in.end( ), omp_out.begin( ), omp_out.begin( ), std::plus< double >( )) ) initializer (omp_priv(omp_orig))
#endif
cx_mat Rhot=Rhol.t();
#if HASUDR
#pragma omp parallel for reduction(+:J,K) schedule(static)
#endif
for (int R=0; R<n_aux; ++R)
{
mat B=BpqR.slice(R);
mat I1=real(Rhol%B); // Because Rho is hermitian and B is hermitian only the real part of this matrix should actually contribute to J
J += 2.0*B*accu(I1); // J should be a Hermitian matrix.
K -= B*(Rhot)*B;
}
F = 0.5*h + J + K;
F = Vt*F*V; // Move it back into the Prev eigenbasis.
cx_mat Jx = Vt*J*V; // Move it back into the Prev eigenbasis.
cx_mat hx = Vt*h*V; // Move it back into the Prev eigenbasis.
K = Vt*K*V; // Move it back into the Prev eigenbasis.
F = 0.5*(F+F.t());
double Eone= real(trace(Rho*hx));
double EJ= real(trace(Rho*Jx));
double EK= real(trace(Rho*K));
Ehf = Eone + EJ + EK + nuclear_energy;
cx_mat Vprime; eigs.zeros();
if (!eig_sym(eigs, Vprime, F))
{
cout << "eig_sym failed to diagonalize fock matrix ... " << endl;
throw 1;
}
if (params["Print"]>0.0)
{
cout << std::setprecision(9) << endl;
cout << "HF Energy" << Ehf << endl;
cout << "J Energy" << EJ << endl;
cout << "K Energy" << EK << endl;
cout << "nuclear_energy " << nuclear_energy << endl << endl;
eigs.st().print("Eigs");
}
V_ = V = V*Vprime;
C = X*V;
return Vprime;
}
cx_mat Delta2(bool Sign=true)
{
cx_mat tore(eigs.n_elem,eigs.n_elem);
for(int i=0; i<eigs.n_elem; ++i)
for(int j=0; j<eigs.n_elem; ++j)
tore(i,j) = (Sign)? (eigs(i) - eigs(j)) : eigs(i) + eigs(j);
tore.diag().zeros();
return tore;
}
// Updates BpqR
void BuildB()
{
FileMan(FM_WRITE, FILE_MO_COEFS, FM_DP, n_mo*n_mo, 0, FM_BEG, X.memptr(), 0); // B is now built in the Lowdin basis and kept that way.
BpqR*=0.0;
mat Btmp(n_mo,n_aux);
INTEGER ip[2], iq[2], iFile;
iq[0] = 1; iq[1] = n_mo;
ip[0] = 1; ip[1] = n_mo;
int p_len = ip[1]-ip[0]+1;
int q_len = iq[1]-iq[0]+1;
iFile = FILE_3C2Ea_INTS;
threading_policy::enable_omp_only();
double* qas=qalloc_start();
int LenV = megtot();
formpqr(&iFile, iq, ip, qas, &LenV);
threading_policy::pop();
// Effn' qchem and its BS disk communication...
// ($*%(*$%*@(@(*
int fileNum = FILE_BIJQa_INTS;
for (int q=0; q<q_len; q++)
{
int Off8 = q * p_len * n_aux; Btmp *= 0.0;
LongFileMan(FM_READ, FILE_3C2Ea_INTS, FM_DP, p_len*n_aux, Off8, FM_BEG, Btmp.memptr(), 0);
// Q.subcube( first_row, first_col, first_slice, last_row, last_col, last_slice )
BpqR.subcube(q,0,0,q,n_mo-1,n_aux-1) += Btmp*RSinv;
}
// Ensure B is perfectly Hermitian.
for (int R=0; R<n_aux; ++R)
BpqR.slice(R) = 0.5*(BpqR.slice(R)+BpqR.slice(R).t());
if (false)
{
// This works! Keeping it in as a check for now.
double* f_diag = new double[n_mo];
FileMan(FM_READ, FILE_MO_COEFS, FM_DP, n_mo, n_mo*n_mo*2 , FM_BEG, f_diag, 0);
std::complex<double> ECorr = 0.0;
cx_mat Vt = V.t();
for (int R=0; R<n_aux; ++R)
{
cx_mat bR = Vt*BpqR.slice(R)*V;
for (int S=0; S<n_aux; ++S)
{
cx_mat bS = Vt*BpqR.slice(S)*V;
for (int i=0; i<n_occ; ++i)
for (int j=0; j<n_occ; ++j)
for (int a=n_occ; a<n_mo; ++a)
for (int b=n_occ; b<n_mo; ++b)
{
double d = (f_diag[a]+f_diag[b]-f_diag[i]-f_diag[j]);
{
ECorr += bR(i,a)*bR(j,b)*(2.0*bS(i,a)*bS(j,b) - bS(i,b)*bS(j,a))/d;
}
}
}
}
cout << "Mp2 Correlation Energy: " << std::setprecision(9) << ECorr << endl;
}
B_Built = true;
}
bool cx_mat_equals(const arma::cx_mat& X,const arma::cx_mat& Y, double tol=pow(10.0,-12.0)) const
{
if (X.n_rows != Y.n_rows)
return false;
if (X.n_cols != Y.n_cols)
return false;
bool close(false);
if(arma::max(arma::max(arma::abs(X-Y))) < tol)
close = true;
return close;
}
void UpdateB(const cx_mat& V_)
{
if (cx_mat_equals(V_,VCur))
return;
int n2=n_mo*n_mo;
cx_mat Vi(n2,n2); Vi.zeros();
#if HASUDR
#pragma omp declare reduction( + : cx_mat : \
std::transform(omp_in.begin( ), omp_in.end( ), omp_out.begin( ), omp_out.begin( ), std::plus< std::complex<double> >( )) ) initializer (omp_priv(omp_orig))
#pragma omp parallel for reduction(+: Vi) schedule(static)
#endif
for(int R=0; R<n_aux; ++R)
{
cx_mat B = V_.t()*BpqR.slice(R)*V_; // No need to xform 5 times/iteration. I could do this once for a 5x speedup.
Vi += kron(B,B).st();
}
IntCur = Vi;
VCur = V_;
}
void Split_RK4_Step_MMUT(const arma::vec& eigval, const arma::cx_mat& Cu , const arma::cx_mat& oldrho, arma::cx_mat& newrho, const double tnow, const double dt)
{
cx_mat Ud = exp(eigval*0.5*j*dt);
cx_mat U = Cu*diagmat(Ud)*Cu.t();
cx_mat RhoHalfStepped = U*oldrho*U.t();
arma::cx_mat k1(newrho),k2(newrho),k3(newrho),k4(newrho),v2(newrho),v3(newrho),v4(newrho);
k1.zeros(); k2.zeros(); k3.zeros(); k4.zeros();
v2.zeros(); v3.zeros(); v4.zeros();
RhoDot( RhoHalfStepped, k1,tnow);
v2 = (dt/2.0) * k1;
v2 += RhoHalfStepped;
RhoDot( RhoHalfStepped, k2,tnow+(dt/2.0));
v3 = (dt/2.0) * k2;
v3 += RhoHalfStepped;
RhoDot( RhoHalfStepped, k3,tnow+(dt/2.0));
v4 = (dt) * k3;
v4 += RhoHalfStepped;
RhoDot( RhoHalfStepped, k4,tnow+dt);
newrho = RhoHalfStepped;
newrho += dt*(1.0/6.0)*k1;
newrho += dt*(2.0/6.0)*k2;
newrho += dt*(2.0/6.0)*k3;
newrho += dt*(1.0/6.0)*k4;
newrho = U*newrho*U.t();
}
// Two mmut steps of length dt/2 and one ee2 step (calc'd with RK4)
double step(rhf* the_scf, FieldMatrices* Mus, arma::vec& eigs_, arma::cx_mat& V_, arma::cx_mat& Rho_, arma::cx_mat& RhoM12_, const double tnow , const double dt,bool& IsOn)
{
cx_mat newrho(Rho_);
cx_mat Rot = FockBuild(Rho_, V_); // updates eigs, C, V, F, etc. etc. etc.
UpdateB(V_); // Updates CurrInts to avoid rebuilds in the steps that follow.
vec noc0; cx_mat nos0;
if (params["Print"]>0.0)
eig_sym(noc0,nos0,Rho_);
eigs_ = eigs;
Mus->update(X*V_);
Rho_ = Rot.t()*Rho_*Rot;
RhoM12_ = Rot.t()*RhoM12_*Rot;
// Make the exponential propagator.
arma::cx_mat F(Rho_); F.zeros(); F.set_real(diagmat(eigs));
Mus->ApplyField(F,tnow,IsOn);
vec Gd; cx_mat Cu;
eig_sym(Gd,Cu,F);
// Full step RhoM12 to make new RhoM12.
cx_mat NewRhoM12(Rho_);
cx_mat NewRho(Rho_);
Split_RK4_Step_MMUT(Gd, Cu, RhoM12_, NewRhoM12, tnow, dt);
// Half step that to make the new Rho.
Split_RK4_Step_MMUT(Gd, Cu, NewRhoM12, NewRho, tnow, dt/2.0);
Rho_ = 0.5*(NewRho+NewRho.t());//0.5*(NewRho+NewRho.t());
RhoM12_ = 0.5*(NewRhoM12+NewRhoM12.t());//0.5*(NewRhoM12+NewRhoM12.t());
//Epseudo=real(RhoDot(Rho_, NewRho, tnow));
// Get the change in noccs.
if (params["Print"]>1.0)
{
vec noc1; cx_mat nos1;
eig_sym(noc1,nos1,Rho_);
noc1-=noc0;
noc1.st().print("Delta N-Occ Nums: ");
}
return Ehf;
}
cx RhoDot(const cx_mat& Rho_, cx_mat& RhoDot_, const double& time)
{
int n=n_mo;
int n2=n_mo*n_mo;
int n3=n2*n_mo;
int n4=n3*n_mo;
cx_mat Rho(Rho_);
for (int i=0; i<n; ++i)
{
if (real(Rho(i,i))<0)
Rho(i,i)=0.0;
if( abs(Rho(i,i))>1.0)
Rho(i,i)=1.0;
}
#if HASUDR
#pragma omp declare reduction( + : cx_mat : \
std::transform(omp_in.begin( ), omp_in.end( ), omp_out.begin( ), omp_out.begin( ), std::plus< std::complex<double> >( )) ) initializer (omp_priv(omp_orig))
#endif
if (params["RIFock"]!=0.0)
return 0.0;
threading_policy::enable_omp_only();
cx_mat Eta(Rho); Eta.eye();
Eta -= Rho;
cx_vec rho(Rho.diag());
cx_vec eta(Eta.diag());
cx_mat Out(RhoDot_); Out.zeros();
cx_mat d2 = Delta2();
cx_mat Vsm(n2,n2); Vsm.zeros();
cx_mat Vtm(n2,n2); Vtm.zeros();
cx* Vs = Vsm.memptr();
cx* Vt = Vtm.memptr();
cx* Vi = IntCur.memptr();
#pragma omp parallel for schedule(static)
for(int p=0; p<n_mo; ++p)
{
for(int q=0; q<n_mo; ++q)
{
for(int r=0; r<n_mo; ++r)
{
for(int s=0; s<n_mo; ++s)
{
// This appears to work great.
cx d = (d2(p,r)+d2(q,s));
Vt[p*n3+q*n2+r*n+s] = (Vi[p*n3+q*n2+r*n+s]);
if( (abs(d)>pow(10.0,-10.0)) )
Vs[p*n3+q*n2+r*n+s] = (1.0/(j*d))*(2.0*Vi[p*n3+q*n2+r*n+s] - Vi[p*n3+q*n2+s*n+r]);
}
}
}
}
cx_mat I1(n,n), I2(n,n); I1.zeros(); I2.zeros();
cx_mat I3(n,n), I4(n,n); I3.zeros(); I4.zeros();
{
//#pragma omp parallel for reduction(+:I1,I2,I3,I4,Out) schedule(static)
for(int x=0; x<n_mo; ++x)
{
int y=x;
//for(int y=0; y<n_mo; ++y)
{
for(int s=0; s<n_mo; ++s)
{
for(int u=0; u<n_mo; ++u)
{
for(int w=0; w<n_mo; ++w)
{
// Precise changes I would like to make to this:
// I would like the ia ia MP2 like terms.
// More precise spin integration.
// These are ESC like.
I1(y,x) += (0.5)*Vs[n3*s+n2*y+n*u+w]*Vt[n3*u+n2*w+n*s+x]*rho(u)*rho(w)*eta(s); // Dsign. v (y) o o
I1(y,x) += (-0.5)*Vs[n3*s+n2*u+n*w+x]*Vt[n3*w+n2*y+n*s+u]*rho(w)*eta(s)*eta(u); // Dsign. v v o (x)
I2(x,y) += (0.5)*Vs[n3*u+n2*w+n*s+y]*Vt[n3*s+n2*x+n*u+w]*rho(u)*rho(w)*eta(s); // Dsign. o o v (y)
I2(x,y) += (-0.5)*Vs[n3*w+n2*x+n*s+u]*Vt[n3*s+n2*u+n*w+y]*rho(w)*eta(s)*eta(u); // Dsign. o (x) v v
}
}
}
}
}
for(int x=0; x<n_mo; ++x)
{
int y=x;
// for(int y=0; y<n_mo; ++y)
{
for(int s=0; s<n_mo; ++s)
{
for(int u=0; u<n_mo; ++u)
{
for(int w=0; w<n_mo; ++w)
{
// These are Mp2 like terms, I'm not sure a diagonal appx. is good here....
// would make the method O(N^5)
// The correct secular approximation fixes the outer indices of Rho Rho and eta eta to be the same.
I3(y,x) += (-0.5)*Vs[n3*s+n2*u+n*w+x]*Vt[n3*w+n2*y+n*s+u]*rho(w)*eta(s)*eta(u); // Dsign v v o (x)
I3(y,x) += (-0.5)*Vs[n3*w+n2*y+n*s+u]*Vt[n3*s+n2*u+n*w+x]*rho(w)*eta(s)*eta(u); // Dsign o (y) v v
I4(y,x) += (0.5)*Vs[n3*s+n2*y+n*u+w]*Vt[n3*u+n2*w+n*s+x]*rho(u)*rho(w)*eta(s); // Dsign v (y) o o
I4(y,x) += (0.5)*Vs[n3*u+n2*w+n*s+x]*Vt[n3*s+n2*y+n*u+w]*rho(u)*rho(w)*eta(s); // Dsign o o v (x)
}
}
}
}
}
I3.print("I3");
I4.print("I4");
cx_mat t1 = Rho*I1*Eta;
cx_mat t2 = Eta*I2*Rho;
t1.print("t1");
t2.print("t2");
cx_mat t3 = Rho*I3*Rho;
t3.print("t3");
cx_mat t4 = Eta*I4*Eta;
t3.print("t4");
Out += Rho*I1*Eta;
Out += Eta*I2*Rho; // Mp2 Like Terms.
Out += Rho*I3*Rho; //vo|ov
Out += Eta*I4*Eta; // Ex.State Correlation Terms.
}
RhoDot_.zeros();
RhoDot_ += lambda*0.5*(Out+Out.t());
if (params["Print"]>=1.0)
{
RhoDot_.print("RhoDot(fast)");
// Rho.print("Rho");
// cout << "d(trace)" << trace(RhoDot_) << endl;
// Check positivity.
if (params["Print"]>1.0)
{
bool Positive=true;
for (int i=0; i<n_mo; ++i)
{
if(real(Rho(i,i)+0.02*RhoDot_(i,i))<0 or real(Rho(i,i)+0.02*RhoDot_(i,i))>1)
{
cout << " Nonpositive " << i << Rho(i,i) << RhoDot_(i,i) << Rho(i,i)+0.02*RhoDot_(i,i) << endl;
Positive = false;
}
}
}
}
threading_policy::pop();
return (trace(RhoDot_%Rho));
}
cx RhoDotGood(const cx_mat& Rho_, cx_mat& RhoDot_, const double& time)
{
int n=n_mo;
int n2=n_mo*n_mo;
int n3=n2*n_mo;
int n4=n3*n_mo;
cx_mat Rho(Rho_);
for (int i=0; i<n; ++i)
{
if (real(Rho(i,i))<0)
Rho(i,i)=0.0;
if( abs(Rho(i,i))>1.0)
Rho(i,i)=1.0;