Some changes

src/basis.cpp

@@ -2318,7 +2318,23 @@ arma::mat BasisSet::kinetic() const {
 }
 
 arma::mat BasisSet::nuclear() const {
-  // Form nuclear attraction matrix
+  std::vector<std::tuple<int,double,double,double>> nuclear_data;
+  for(size_t inuc=0;inuc<nuclei.size();inuc++) {
+    if(nuclei[inuc].bsse)
+      continue;
+    // Nuclear charge
+    int Z=nuclei[inuc].Z;
+
+    // Coordinates of nucleus
+    double cx=nuclei[inuc].r.x;
+    double cy=nuclei[inuc].r.y;
+    double cz=nuclei[inuc].r.z;
+    nuclear_data.push_back(std::make_tuple(Z,cx,cy,cz));
+  }
+  return nuclear(nuclear_data);
+}
+
+ arma::mat BasisSet::nuclear(const std::vector<std::tuple<int,double,double,double>> & nuclear_data) const {
 
   // Size of basis set
   size_t N=get_Nbf();
@@ -2332,18 +2348,9 @@ arma::mat BasisSet::nuclear() const {
 #pragma omp parallel for schedule(dynamic)
 #endif
   for(size_t ip=0;ip<shellpairs.size();ip++)
-    for(size_t inuc=0;inuc<nuclei.size();inuc++) {
-      // If BSSE nucleus, do nothing
-      if(nuclei[inuc].bsse)
-	continue;
-
-      // Nuclear charge
-      int Z=nuclei[inuc].Z;
+    for(size_t inuc=0;inuc<nuclear_data.size();inuc++) {
 
-      // Coordinates of nucleus
-      double cx=nuclei[inuc].r.x;
-      double cy=nuclei[inuc].r.y;
-      double cz=nuclei[inuc].r.z;
+      auto [Z, cx, cy, cz] = nuclear_data[inuc];
 
       // Shells in pair
       size_t i=shellpairs[ip].is;

src/basis.h

@@ -447,6 +447,8 @@ class BasisSet {
   arma::mat kinetic() const;
   /// Calculate nuclear repulsion matrix
   arma::mat nuclear() const;
+  /// Calculate nuclear repulsion matrix with given nuclei
+  arma::mat nuclear(const std::vector<std::tuple<int,double,double,double>> & nuclei) const;
   /// Calculate electric potential matrix
   arma::mat potential(coords_t r) const;
   /// Calculate superposition of atomic potentials

src/density_fitting.cpp

@@ -52,7 +52,7 @@ bool DensityFit::Bmat_enabled() const {
   return Bmat;
 }
 
-size_t DensityFit::fill(const BasisSet & orbbas, const BasisSet & auxbas, bool dir, double erithr, double linthr, bool bmat) {
+size_t DensityFit::fill(const BasisSet & orbbas, const BasisSet & auxbas, bool dir, double erithr, double linthr, double cholthr, bool bmat) {
   // Construct density fitting basis
 
   // Store amount of functions
@@ -125,28 +125,8 @@ size_t DensityFit::fill(const BasisSet & orbbas, const BasisSet & auxbas, bool d
   }
 
   if(Bmat) {
-    // Form ab^-1 and ab^-1/2
-    arma::mat abvec;
-    arma::vec abval;
-    eig_sym_ordered(abval,abvec,ab);
-
-    // Count linearly independent vectors
-    size_t Nind=0;
-    for(size_t i=0;i<abval.n_elem;i++)
-      if(abval(i)>=linthr)
-	Nind++;
-
-    // and drop the linearly dependent ones
-    abval=abval.subvec(abval.n_elem-Nind,abval.n_elem-1);
-    abvec=abvec.cols(abvec.n_cols-Nind,abvec.n_cols-1);
-
-    // Form matrices
-    ab_inv.zeros(abvec.n_rows,abvec.n_rows);
-    ab_invh.zeros(abvec.n_rows,abvec.n_rows);
-    for(size_t i=0;i<abval.n_elem;i++) {
-      ab_inv+=abvec.col(i)*arma::trans(abvec.col(i))/abval(i);
-      ab_invh+=abvec.col(i)*arma::trans(abvec.col(i))/sqrt(abval(i));
-    }
+    ab_invh = PartialCholeskyOrth(ab, cholthr, linthr);
+    ab_inv = ab_invh * ab_invh.t();
   } else {
     // Just RI-J(K), so use faster method from Eichkorn et al to form ab_inv only
     ab_inv=arma::inv(ab + DELTA*arma::eye(ab.n_rows,ab.n_cols));
@@ -803,6 +783,15 @@ arma::mat DensityFit::calcJ(const arma::mat & P) const {
 
   // Get the expansion coefficients
   arma::vec c=compute_expansion(P);
+  return digestJ(c);
+}
+
+arma::mat DensityFit::calcJ(const arma::vec & c) const {
+  if(c.n_elem != Naux) {
+    std::ostringstream oss;
+    oss << "Error in DensityFit: Naux = " << Naux << ", c.n_elem = " << c.n_elem << "!\n";
+    throw std::logic_error(oss.str());
+  }
 
   arma::mat J(Nbf,Nbf);
   J.zeros();

src/density_fitting.h

@@ -135,7 +135,7 @@ class DensityFit {
    * HF routine should be more tolerant of linear dependencies in the basis.
    * Returns amount of significant orbital shell pairs.
    */
-  size_t fill(const BasisSet & orbbas, const BasisSet & auxbas, bool direct, double erithr, double linthr, bool bmat=false);
+  size_t fill(const BasisSet & orbbas, const BasisSet & auxbas, bool direct, double erithr, double linthr, double cholthr, bool bmat=false);
 
   /// Compute estimate of necessary memory
   size_t memory_estimate(const BasisSet & orbbas, const BasisSet & auxbas, double erithr, bool direct) const;
@@ -149,6 +149,8 @@ class DensityFit {
   arma::mat calcJ(const arma::mat & P) const;
   /// Get Coulomb matrix from P
   std::vector<arma::mat> calcJ(const std::vector<arma::mat> & P) const;
+  /// Digest J matrix from computed expansion
+  arma::mat digest(const arma::vec & gamma) const;
 
   /// Calculate force from P
   arma::vec forceJ(const arma::mat & P);

src/linalg.h

@@ -104,6 +104,9 @@ arma::mat CanonicalOrth(const arma::mat & S, double cutoff);
 /// Same, but use computed decomposition
 arma::mat CanonicalOrth(const arma::mat & Svec, const arma::vec & Sval, double cutoff);
 
+/// Pivoted Cholesky orthogonalization
+arma::mat PartialCholeskyOrth(const arma::mat & S, double cholcut, double scut);
+
 /// Automatic orthonormalization.
 arma::mat BasOrth(const arma::mat & S, bool verbose);
 /// Orthogonalize basis

src/localization.cpp

@@ -1203,11 +1203,11 @@ void Pipek::cost_func_der(const arma::cx_mat & Wv, double & Dinv, arma::cx_mat &
 Edmiston::Edmiston(const BasisSet & basis, const BasisSet & fitbas, const arma::mat & Cv, bool delocalize) : UnitaryFunction(4,!delocalize) {
   // Store orbitals
   C=Cv;
-  // Initialize fitting integrals. Direct computation, linear dependence threshold 1e-8, use Hartree-Fock routine since it has better tolerance for linear dependencies
+  // Initialize fitting integrals. Direct computation, linear dependence threshold 1e-8, Cholesky threshold 1e-9, use Hartree-Fock routine since it has better tolerance for linear dependencies
   if(!fitbas.get_Nbf())
-    dfit.fill(basis,basis.density_fitting(),true,1e-8,false);
+    dfit.fill(basis,basis.density_fitting(),true,1e-8,1e-9,false);
   else
-    dfit.fill(basis,fitbas,true,1e-8,false);
+    dfit.fill(basis,fitbas,true,1e-8,1e-9,false);
 
   use_chol=false;
 }

src/scf-base.cpp

@@ -144,6 +144,8 @@ SCF::SCF(const BasisSet & basis, Checkpoint & chkpt) {
   fitmem=1000000*settings.get_int("FittingMemory");
   // Linear dependence threshold
   fitthr=settings.get_double("FittingThreshold");
+  // Linear dependence threshold
+  fitcholthr=settings.get_double("FittingCholeskyThreshold");
 
   // Use Cholesky?
   cholesky=settings.get_bool("Cholesky");
@@ -347,7 +349,7 @@ SCF::SCF(const BasisSet & basis, Checkpoint & chkpt) {
     }
 
     // Calculate the fitting integrals, don't run in B-matrix mode
-    size_t Npairs=dfit.fill(*basisp,dfitbas,direct,intthr,fitthr,false);
+    size_t Npairs=dfit.fill(*basisp,dfitbas,direct,intthr,fitthr,fitcholthr,false);
 
     if(verbose) {
       printf("done (%s)\n",t.elapsed().c_str());
@@ -505,7 +507,7 @@ void SCF::fill_rs(double omega) {
       }
 
       t.set();
-      size_t Npairs=dfit_rs.fill(*basisp,dfitbas,direct,intthr,fitthr,dfit.Bmat_enabled());
+      size_t Npairs=dfit_rs.fill(*basisp,dfitbas,direct,intthr,fitthr,fitcholthr,dfit.Bmat_enabled());
       if(verbose) {
 	printf("done (%s)\n",t.elapsed().c_str());
 	printf("%i shell pairs out of %i are significant.\n",(int) Npairs, (int) basisp->get_unique_shellpairs().size());

src/scf.h

@@ -287,6 +287,8 @@ class SCF {
   size_t fitmem;
   /// Threshold for density fitting
   double fitthr;
+  /// Pivoted Cholesky threshold for density fitting
+  double fitcholthr;
 
   /// Cholesky calculation?
   bool cholesky;

src/settings.cpp

@@ -142,6 +142,7 @@ void Settings::add_scf_settings() {
   add_int("FittingMemory", "Amount of memory in MB to use for exchange fitting",1000);
   // Threshold for screening eigenvectors
   add_double("FittingThreshold", "Linear dependence threshold for Coulomb integrals in density fitting",1e-8);
+  add_double("FittingCholeskyThreshold", "Linear dependence threshold for pivoted Cholesky of Coulomb integrals in density fitting",1e-9);
 
   // SAP basis
   add_string("SAPBasis", "Tabulated atomic effective potential \"basis set\"","helfem_large.gbs");