gw_uks.cc

Go to the documentation of this file.

/*
 *            Copyright 2009-2026 The VOTCA Development Team
 *                       (http://www.votca.org)
 *
 *      Licensed under the Apache License, Version 2.0 (the "License")
 */
 
#include <fstream>
#include <iostream>
#include <limits>
 
#include "votca/xtp/IndexParser.h"
#include "votca/xtp/anderson_mixing.h"
#include "votca/xtp/gw_uks.h"
#include "votca/xtp/newton_rapson.h"
#include "votca/xtp/openmp_cuda.h"
#include "votca/xtp/rpa_uks.h"
#include "votca/xtp/sigmafactory_uks.h"
 
#include "self_energy_evaluators/sigma_ppm_uks.h"
 
namespace votca {
namespace xtp {
 
GW_UKS::GW_UKS(Logger& log, TCMatrix_gwbse_spin& Mmn,
               const Eigen::MatrixXd& vxc_alpha,
               const Eigen::MatrixXd& vxc_beta,
               const Eigen::VectorXd& dft_energies_alpha,
               const Eigen::VectorXd& dft_energies_beta)
    : log_(log),
      Mmn_(Mmn),
      vxc_alpha_(vxc_alpha),
      vxc_beta_(vxc_beta),
      dft_energies_alpha_(dft_energies_alpha),
      dft_energies_beta_(dft_energies_beta),
      rpa_(log, Mmn) {}
 
void GW_UKS::configure(const options& opt) {
  opt_ = opt;
  qptotal_ = opt_.qpmax - opt_.qpmin + 1;
  rpa_.configure(opt_.homo_alpha, opt_.homo_beta, opt_.rpamin, opt_.rpamax);
 
  sigma_alpha_ = SigmaFactory_UKS().Create(opt_.sigma_integration, Mmn_, rpa_,
                                           TCMatrix::SpinChannel::Alpha);
  sigma_beta_ = SigmaFactory_UKS().Create(opt_.sigma_integration, Mmn_, rpa_,
                                          TCMatrix::SpinChannel::Beta);
 
  if (!sigma_alpha_ || !sigma_beta_) {
    throw std::runtime_error(
        "GW_UKS currently supports only implemented unrestricted sigma "
        "evaluators. At present this is 'ppm', 'cda', and 'exact'.");
  }
 
  Sigma_base_UKS::options sigma_opt;
  sigma_opt.homo = opt_.homo_alpha;
  sigma_opt.qpmax = opt_.qpmax;
  sigma_opt.qpmin = opt_.qpmin;
  sigma_opt.rpamin = opt_.rpamin;
  sigma_opt.rpamax = opt_.rpamax;
  sigma_opt.eta = opt_.eta;
  sigma_opt.alpha = opt_.alpha;
  sigma_opt.quadrature_scheme = opt_.quadrature_scheme;
  sigma_opt.order = opt_.order;
  sigma_alpha_->configure(sigma_opt);
  sigma_opt.homo = opt_.homo_beta;
  sigma_beta_->configure(sigma_opt);
 
  Sigma_x_alpha_ = Eigen::MatrixXd::Zero(qptotal_, qptotal_);
  Sigma_x_beta_ = Eigen::MatrixXd::Zero(qptotal_, qptotal_);
  Sigma_c_alpha_ = Eigen::MatrixXd::Zero(qptotal_, qptotal_);
  Sigma_c_beta_ = Eigen::MatrixXd::Zero(qptotal_, qptotal_);
 
  auto print_spin_ranges = [&](Spin spin, Index homo) {
    const Index lumo = homo + 1;
 
    const Index n_occ_rpa =
        (opt_.rpamin <= homo) ? (homo - opt_.rpamin + 1) : 0;
    const Index n_virt_rpa =
        (lumo <= opt_.rpamax) ? (opt_.rpamax - lumo + 1) : 0;
 
    const Index qp_occ_min = opt_.qpmin;
    const Index qp_occ_max = std::min(opt_.qpmax, homo);
    const Index n_occ_qp =
        (qp_occ_min <= qp_occ_max) ? (qp_occ_max - qp_occ_min + 1) : 0;
 
    const Index qp_virt_min = std::max(opt_.qpmin, lumo);
    const Index qp_virt_max = opt_.qpmax;
    const Index n_virt_qp =
        (qp_virt_min <= qp_virt_max) ? (qp_virt_max - qp_virt_min + 1) : 0;
 
    XTP_LOG(Log::error, log_)
        << TimeStamp() << " UKS " << SpinName(spin)
        << " effective ranges: HOMO=" << homo << " LUMO=" << lumo
        << " | RPA occ[" << opt_.rpamin << ":" << homo << "]"
        << " virt[" << lumo << ":" << opt_.rpamax << "]"
        << " (#occ=" << n_occ_rpa << ", #virt=" << n_virt_rpa << ")"
        << " | GW occ[" << qp_occ_min << ":" << qp_occ_max << "]"
        << " virt[" << qp_virt_min << ":" << qp_virt_max << "]"
        << " (#occ=" << n_occ_qp << ", #virt=" << n_virt_qp << ")"
        << std::flush;
  };
 
  print_spin_ranges(Spin::Alpha, opt_.homo_alpha);
  print_spin_ranges(Spin::Beta, opt_.homo_beta);
 
  if (opt_.sigma_integration == "ppm") {
    auto* ppm_a = dynamic_cast<Sigma_PPM_UKS*>(sigma_alpha_.get());
    auto* ppm_b = dynamic_cast<Sigma_PPM_UKS*>(sigma_beta_.get());
 
    if (ppm_a == nullptr || ppm_b == nullptr) {
      throw std::runtime_error(
          "GW_UKS: expected Sigma_PPM_UKS evaluators for "
          "sigma_integration=ppm");
    }
 
    ppm_a->SetSharedPPM(ppm_);
    ppm_b->SetSharedPPM(ppm_);
  }
}
 
const Eigen::VectorXd& GW_UKS::DftEnergies(Spin spin) const {
  return (spin == Spin::Alpha) ? dft_energies_alpha_ : dft_energies_beta_;
}
const Eigen::MatrixXd& GW_UKS::Vxc(Spin spin) const {
  return (spin == Spin::Alpha) ? vxc_alpha_ : vxc_beta_;
}
Eigen::MatrixXd& GW_UKS::SigmaX(Spin spin) {
  return (spin == Spin::Alpha) ? Sigma_x_alpha_ : Sigma_x_beta_;
}
Eigen::MatrixXd& GW_UKS::SigmaC(Spin spin) {
  return (spin == Spin::Alpha) ? Sigma_c_alpha_ : Sigma_c_beta_;
}
const Eigen::MatrixXd& GW_UKS::SigmaX(Spin spin) const {
  return (spin == Spin::Alpha) ? Sigma_x_alpha_ : Sigma_x_beta_;
}
const Eigen::MatrixXd& GW_UKS::SigmaC(Spin spin) const {
  return (spin == Spin::Alpha) ? Sigma_c_alpha_ : Sigma_c_beta_;
}
Sigma_base_UKS& GW_UKS::SigmaEvaluator(Spin spin) {
  return (spin == Spin::Alpha) ? *sigma_alpha_ : *sigma_beta_;
}
const Sigma_base_UKS& GW_UKS::SigmaEvaluator(Spin spin) const {
  return (spin == Spin::Alpha) ? *sigma_alpha_ : *sigma_beta_;
}
Index GW_UKS::Homo(Spin spin) const {
  return (spin == Spin::Alpha) ? opt_.homo_alpha : opt_.homo_beta;
}
const char* GW_UKS::SpinName(Spin spin) const {
  return (spin == Spin::Alpha) ? "alpha" : "beta";
}
 
std::string GW_UKS::LevelLabel(Spin spin, Index level) const {
  if (level == Homo(spin)) {
    return "  HOMO ";
  } else if (level == Homo(spin) + 1) {
    return "  LUMO ";
  } else {
    return "  Level";
  }
}
 
const char* GW_UKS::OccupationTag(Spin spin, Index level) const {
  return (level <= Homo(spin)) ? "occ" : "virt";
}
 
Eigen::VectorXd GW_UKS::ScissorShift_DFTlevel(
    const Eigen::VectorXd& dft_energies, Index homo) const {
  Eigen::VectorXd shifted_energies = dft_energies;
  shifted_energies.segment(homo + 1, dft_energies.size() - homo - 1).array() +=
      opt_.shift;
  return shifted_energies;
}
 
double GW_UKS::CalcSpinHomoLumoShift(const Eigen::VectorXd& frequencies,
                                     Spin spin) const {
  const Index homo = Homo(spin);
  const Eigen::VectorXd& dft = DftEnergies(spin);
  const double DFTgap = dft(homo + 1) - dft(homo);
  const double QPgap =
      frequencies(homo + 1 - opt_.qpmin) - frequencies(homo - opt_.qpmin);
  return QPgap - DFTgap;
}
 
void GW_UKS::CalculateGWPerturbation() {
  Sigma_x_alpha_ = (1 - opt_.ScaHFX) * sigma_alpha_->CalcExchangeMatrix();
  Sigma_x_beta_ = (1 - opt_.ScaHFX) * sigma_beta_->CalcExchangeMatrix();
  XTP_LOG(Log::error, log_)
      << TimeStamp()
      << " Calculated spin-resolved Hartree exchange contribution"
      << std::flush;
 
  Eigen::VectorXd dft_shifted_alpha =
      ScissorShift_DFTlevel(dft_energies_alpha_, opt_.homo_alpha);
  Eigen::VectorXd dft_shifted_beta =
      ScissorShift_DFTlevel(dft_energies_beta_, opt_.homo_beta);
 
  XTP_LOG(Log::error, log_)
      << TimeStamp()
      << " Scissor shifting alpha/beta DFT energies by: " << opt_.shift
      << " Hrt" << std::flush;
 
  rpa_.setRPAInputEnergies(
      dft_shifted_alpha.segment(opt_.rpamin, opt_.rpamax - opt_.rpamin + 1),
      dft_shifted_beta.segment(opt_.rpamin, opt_.rpamax - opt_.rpamin + 1));
 
  Eigen::VectorXd frequencies_alpha =
      dft_shifted_alpha.segment(opt_.qpmin, qptotal_);
  Eigen::VectorXd frequencies_beta =
      dft_shifted_beta.segment(opt_.qpmin, qptotal_);
 
  Anderson mixing_alpha;
  Anderson mixing_beta;
  mixing_alpha.Configure(opt_.gw_mixing_order, opt_.gw_mixing_alpha);
  mixing_beta.Configure(opt_.gw_mixing_order, opt_.gw_mixing_alpha);
 
  for (Index i_gw = 0; i_gw < opt_.gw_sc_max_iterations; ++i_gw) {
    if (i_gw % opt_.reset_3c == 0 && i_gw != 0) {
      Mmn_.alpha.Rebuild();
      Mmn_.beta.Rebuild();
      XTP_LOG(Log::info, log_)
          << TimeStamp() << " Rebuilding alpha/beta 3c integrals" << std::flush;
    }
 
    if (opt_.sigma_integration == "ppm") {
      ppm_.PPM_construct_parameters(rpa_);
      sigma_alpha_->PrepareScreening();
      sigma_beta_->PrepareScreening();
    } else {
      sigma_alpha_->PrepareScreening();
      sigma_beta_->PrepareScreening();
    }
 
    XTP_LOG(Log::info, log_)
        << TimeStamp() << " Calculated unrestricted screening via RPA"
        << std::flush;
 
    if (opt_.gw_mixing_order > 0 && i_gw > 0) {
      mixing_alpha.UpdateInput(frequencies_alpha);
      mixing_beta.UpdateInput(frequencies_beta);
    }
 
    frequencies_alpha = SolveQP(Spin::Alpha, frequencies_alpha);
    frequencies_beta = SolveQP(Spin::Beta, frequencies_beta);
 
    if (opt_.gw_sc_max_iterations > 1) {
      Eigen::VectorXd rpa_alpha_old = rpa_.getRPAInputEnergiesAlpha();
      Eigen::VectorXd rpa_beta_old = rpa_.getRPAInputEnergiesBeta();
 
      if (opt_.gw_mixing_order > 0 && i_gw > 0) {
        mixing_alpha.UpdateOutput(frequencies_alpha);
        mixing_beta.UpdateOutput(frequencies_beta);
        frequencies_alpha = mixing_alpha.MixHistory();
        frequencies_beta = mixing_beta.MixHistory();
      }
 
      rpa_.UpdateRPAInputEnergies(dft_energies_alpha_, dft_energies_beta_,
                                  frequencies_alpha, frequencies_beta,
                                  opt_.qpmin);
 
      XTP_LOG(Log::info, log_)
          << TimeStamp() << " GW_Iteration:" << i_gw << " Shift_alpha[Hrt]:"
          << CalcSpinHomoLumoShift(frequencies_alpha, Spin::Alpha)
          << " Shift_beta[Hrt]:"
          << CalcSpinHomoLumoShift(frequencies_beta, Spin::Beta) << std::flush;
 
      const bool converged_alpha = Converged(rpa_.getRPAInputEnergiesAlpha(),
                                             rpa_alpha_old, opt_.gw_sc_limit);
      const bool converged_beta = Converged(rpa_.getRPAInputEnergiesBeta(),
                                            rpa_beta_old, opt_.gw_sc_limit);
      if (converged_alpha && converged_beta) {
        XTP_LOG(Log::info, log_)
            << TimeStamp() << " Converged after " << i_gw + 1
            << " unrestricted GW iterations." << std::flush;
        break;
      } else if (i_gw == opt_.gw_sc_max_iterations - 1) {
        XTP_LOG(Log::error, log_)
            << TimeStamp()
            << " WARNING! UKS GW-self-consistency cycle not converged after "
            << opt_.gw_sc_max_iterations << " iterations." << std::flush;
        break;
      }
    }
  }
 
  Sigma_c_alpha_.diagonal() =
      sigma_alpha_->CalcCorrelationDiag(frequencies_alpha);
  Sigma_c_beta_.diagonal() = sigma_beta_->CalcCorrelationDiag(frequencies_beta);
  PrintGWA_Energies(Spin::Alpha);
  PrintGWA_Energies(Spin::Beta);
}
 
Eigen::VectorXd GW_UKS::getGWAResultsAlpha() const {
  return Sigma_x_alpha_.diagonal() + Sigma_c_alpha_.diagonal() -
         vxc_alpha_.diagonal() +
         dft_energies_alpha_.segment(opt_.qpmin, qptotal_);
}
Eigen::VectorXd GW_UKS::getGWAResultsBeta() const {
  return Sigma_x_beta_.diagonal() + Sigma_c_beta_.diagonal() -
         vxc_beta_.diagonal() +
         dft_energies_beta_.segment(opt_.qpmin, qptotal_);
}
const Eigen::VectorXd& GW_UKS::RPAInputEnergiesAlpha() const {
  return rpa_.getRPAInputEnergiesAlpha();
}
const Eigen::VectorXd& GW_UKS::RPAInputEnergiesBeta() const {
  return rpa_.getRPAInputEnergiesBeta();
}
 
Eigen::VectorXd GW_UKS::SolveQP(Spin spin,
                                const Eigen::VectorXd& frequencies) const {
  const Eigen::VectorXd intercepts =
      DftEnergies(spin).segment(opt_.qpmin, qptotal_) +
      SigmaX(spin).diagonal() - Vxc(spin).diagonal();
  Eigen::VectorXd frequencies_new = frequencies;
  Eigen::Array<bool, Eigen::Dynamic, 1> converged =
      Eigen::Array<bool, Eigen::Dynamic, 1>::Zero(qptotal_);
  Index use_threads = qptotal_;
#ifdef _OPENMP
  use_threads =
      OPENMP::getMaxThreads() > qptotal_ ? qptotal_ : OPENMP::getMaxThreads();
#endif
#pragma omp parallel for schedule(dynamic) num_threads(use_threads)
  for (Index gw_level = 0; gw_level < qptotal_; ++gw_level) {
    const double initial_f = frequencies[gw_level];
    const double intercept = intercepts[gw_level];
    boost::optional<double> newf;
    if (opt_.qp_solver == "fixedpoint") {
      newf = SolveQP_FixedPoint(spin, intercept, initial_f, gw_level);
    }
    if (newf) {
      frequencies_new[gw_level] = newf.value();
      converged[gw_level] = true;
    } else {
      newf = SolveQP_Grid(spin, intercept, initial_f, gw_level);
      if (newf) {
        frequencies_new[gw_level] = newf.value();
        converged[gw_level] = true;
      } else {
        newf = SolveQP_Linearisation(spin, intercept, initial_f, gw_level);
        if (newf) {
          frequencies_new[gw_level] = newf.value();
        }
      }
    }
  }
  return frequencies_new;
}
 
boost::optional<double> GW_UKS::SolveQP_Linearisation(Spin spin,
                                                      double intercept0,
                                                      double frequency0,
                                                      Index gw_level) const {
  boost::optional<double> newf = boost::none;
  const auto& sigma = SigmaEvaluator(spin);
  const double sig = sigma.CalcCorrelationDiagElement(gw_level, frequency0);
  const double dsigma_domega =
      sigma.CalcCorrelationDiagElementDerivative(gw_level, frequency0);
  const double Z = 1.0 - dsigma_domega;
  if (std::abs(Z) > 1e-9) {
    newf = frequency0 + (intercept0 - frequency0 + sig) / Z;
  }
  return newf;
}
 
boost::optional<double> GW_UKS::SolveQP_Grid(Spin spin, double intercept0,
                                             double frequency0,
                                             Index gw_level) const {
  const double range =
      opt_.qp_grid_spacing * double(opt_.qp_grid_steps - 1) / 2.0;
  boost::optional<double> newf = boost::none;
  double freq_prev = frequency0 - range;
  QPFunc fqp(gw_level, SigmaEvaluator(spin), intercept0);
  double targ_prev = fqp.value(freq_prev);
  double qp_energy = 0.0;
  double gradient_max = std::numeric_limits<double>::max();
  bool pole_found = false;
  for (Index i_node = 1; i_node < opt_.qp_grid_steps; ++i_node) {
    double freq = freq_prev + opt_.qp_grid_spacing;
    double targ = fqp.value(freq);
    if (targ_prev * targ < 0.0) {
      double f = SolveQP_Bisection(freq_prev, targ_prev, freq, targ, fqp);
      double gradient = fqp.deriv(f);
      if (std::abs(gradient) < gradient_max) {
        gradient_max = std::abs(gradient);
        qp_energy = f;
        pole_found = true;
      }
    }
    freq_prev = freq;
    targ_prev = targ;
  }
  if (pole_found) {
    newf = qp_energy;
  }
  return newf;
}
 
boost::optional<double> GW_UKS::SolveQP_FixedPoint(Spin spin, double intercept0,
                                                   double frequency0,
                                                   Index gw_level) const {
  boost::optional<double> newf = boost::none;
  QPFunc f(gw_level, SigmaEvaluator(spin), intercept0);
  NewtonRapson<QPFunc> newton = NewtonRapson<QPFunc>(
      opt_.g_sc_max_iterations, opt_.g_sc_limit, opt_.qp_solver_alpha);
  double freq_new = newton.FindRoot(f, frequency0);
  if (newton.getInfo() == NewtonRapson<QPFunc>::success) {
    newf = freq_new;
  }
  return newf;
}
 
double GW_UKS::SolveQP_Bisection(double lowerbound, double f_lowerbound,
                                 double upperbound, double f_upperbound,
                                 const QPFunc& f) const {
  if (f_lowerbound * f_upperbound > 0) {
    throw std::runtime_error(
        "Bisection needs a positive and negative function value");
  }
  while (true) {
    const double c = 0.5 * (lowerbound + upperbound);
    if (std::abs(upperbound - lowerbound) < opt_.g_sc_limit) {
      return c;
    }
    const double y_c = f.value(c);
    if (std::abs(y_c) < opt_.g_sc_limit) {
      return c;
    }
    if (y_c * f_lowerbound > 0) {
      lowerbound = c;
      f_lowerbound = y_c;
    } else {
      upperbound = c;
      f_upperbound = y_c;
    }
  }
}
 
bool GW_UKS::Converged(const Eigen::VectorXd& e1, const Eigen::VectorXd& e2,
                       double epsilon) const {
  Index state = 0;
  const double diff_max = (e1 - e2).cwiseAbs().maxCoeff(&state);
  XTP_LOG(Log::info, log_) << TimeStamp() << " E_diff max=" << diff_max
                           << " StateNo:" << state << std::flush;
  return diff_max <= epsilon;
}
 
void GW_UKS::CalculateHQP() {
  Eigen::VectorXd diag_backup_alpha = Sigma_c_alpha_.diagonal();
  Eigen::VectorXd diag_backup_beta = Sigma_c_beta_.diagonal();
  Sigma_c_alpha_ = sigma_alpha_->CalcCorrelationOffDiag(getGWAResultsAlpha());
  Sigma_c_beta_ = sigma_beta_->CalcCorrelationOffDiag(getGWAResultsBeta());
  Sigma_c_alpha_.diagonal() = diag_backup_alpha;
  Sigma_c_beta_.diagonal() = diag_backup_beta;
}
 
Eigen::MatrixXd GW_UKS::getHQPAlpha() const {
  return Sigma_x_alpha_ + Sigma_c_alpha_ - vxc_alpha_ +
         Eigen::MatrixXd(
             dft_energies_alpha_.segment(opt_.qpmin, qptotal_).asDiagonal());
}
Eigen::MatrixXd GW_UKS::getHQPBeta() const {
  return Sigma_x_beta_ + Sigma_c_beta_ - vxc_beta_ +
         Eigen::MatrixXd(
             dft_energies_beta_.segment(opt_.qpmin, qptotal_).asDiagonal());
}
 
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd>
    GW_UKS::DiagonalizeQPHamiltonianAlpha() const {
  Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> qpdiag(getHQPAlpha());
  PrintQP_Energies(Spin::Alpha, qpdiag.eigenvalues());
  return qpdiag;
}
 
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd>
    GW_UKS::DiagonalizeQPHamiltonianBeta() const {
  Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> qpdiag(getHQPBeta());
  PrintQP_Energies(Spin::Beta, qpdiag.eigenvalues());
  return qpdiag;
}
 
void GW_UKS::PrintGWA_Energies(Spin spin) const {
  const Eigen::VectorXd gwa =
      (spin == Spin::Alpha) ? getGWAResultsAlpha() : getGWAResultsBeta();
 
  const Index homo = Homo(spin);
  const Eigen::VectorXd& dft = DftEnergies(spin);
 
  XTP_LOG(Log::error, log_)
      << (boost::format("  ====== Perturbative %1% quasiparticle energies "
                        "(Hartree) ======") %
          SpinName(spin))
             .str()
      << std::flush;
 
  if (opt_.qpmin <= homo && homo + 1 <= opt_.qpmax) {
    const double dft_gap = dft(homo + 1) - dft(homo);
    const double qp_gap = gwa(homo + 1 - opt_.qpmin) - gwa(homo - opt_.qpmin);
 
    XTP_LOG(Log::error, log_)
        << (boost::format("   %1% DFT gap = %2$+1.6f Hartree   %1% GWA gap = "
                          "%3$+1.6f Hartree   Delta = %4$+1.6f Hartree") %
            SpinName(spin) % dft_gap % qp_gap % (qp_gap - dft_gap))
               .str()
        << std::flush;
  }
 
  for (Index i = 0; i < qptotal_; i++) {
    const Index level = i + opt_.qpmin;
    XTP_LOG(Log::error, log_)
        << LevelLabel(spin, level)
        << (boost::format(" = %1$4d (%2%) %3% DFT = %4$+1.4f VXC = %5$+1.4f "
                          "S-X = %6$+1.4f S-C = %7$+1.4f GWA = %8$+1.4f") %
            level % OccupationTag(spin, level) % SpinName(spin) %
            DftEnergies(spin)(level) % Vxc(spin)(i, i) % SigmaX(spin)(i, i) %
            SigmaC(spin)(i, i) % gwa(i))
               .str()
        << std::flush;
  }
}
 
void GW_UKS::PrintQP_Energies(Spin spin,
                              const Eigen::VectorXd& qp_diag_energies) const {
  const Eigen::VectorXd gwa =
      (spin == Spin::Alpha) ? getGWAResultsAlpha() : getGWAResultsBeta();
 
  const Index homo = Homo(spin);
  const Eigen::VectorXd& dft = DftEnergies(spin);
 
  XTP_LOG(Log::error, log_) << TimeStamp() << " Full " << SpinName(spin)
                            << " quasiparticle Hamiltonian" << std::flush;
 
  if (opt_.qpmin <= homo && homo + 1 <= opt_.qpmax) {
    const double dft_gap = dft(homo + 1) - dft(homo);
    const double pqp_gap = gwa(homo + 1 - opt_.qpmin) - gwa(homo - opt_.qpmin);
    const double dqp_gap = qp_diag_energies(homo + 1 - opt_.qpmin) -
                           qp_diag_energies(homo - opt_.qpmin);
 
    XTP_LOG(Log::error, log_)
        << (boost::format("   %1% DFT gap = %2$+1.6f Hartree   %1% PQP gap = "
                          "%3$+1.6f Hartree   %1% DQP gap = %4$+1.6f Hartree") %
            SpinName(spin) % dft_gap % pqp_gap % dqp_gap)
               .str()
        << std::flush;
  }
 
  for (Index i = 0; i < qptotal_; i++) {
    const Index level = i + opt_.qpmin;
    XTP_LOG(Log::error, log_)
        << LevelLabel(spin, level)
        << (boost::format(" = %1$4d (%2%) %3% PQP = %4$+1.6f DQP = %5$+1.6f") %
            level % OccupationTag(spin, level) % SpinName(spin) % gwa(i) %
            qp_diag_energies(i))
               .str()
        << std::flush;
  }
}
 
}  // namespace xtp
}  // namespace votca