Molecular SCF

Documentation on the self-consistent field (SCF) calculation of ground-state electronic structure of molecules using relativistic Hartree-Fock or Kohn-Sham density functional theory. The methodology can be combined in the current version of ReSpect with the 1C, (e)amfX2C or 4C Hamiltonian and applied to closed-shell and open-shell molecular systems.

Feature List

Wave function models

  • Kramers restricted Hartree-Fock or Kohn-Sham determinant for closed-shell singlets
  • Kramers unrestricted Hartree-Fock or Kohn-Sham determinant for high-spin open-shells


  • non-relativistic one-component (1c)
  • relativistic four-component (4c) Dirac-Coulomb
  • relativistic two-component (2c) involving 1eX2C, amfX2C, eamfX2C or mmfX2C Hamiltonian models
  • scalable speed of light
  • scalable one-electron spin-orbit interaction

DFT non-collinear functionals

  • local (SVWN5)
  • GGA (PBE,BLYP,KT2,BP86,PP86)
  • hybrid (PBE0,B3LYP)
  • range-separated (LC-SVWN5,LC-BLYP,CAM-B3LYP)

Nuclear charge distribution models

  • point
  • finite Gaussian-type

Integral evaluation techniques

  • analytic with an in-built restricted kinetic balanced (RKB) condition for the small-component
  • resolution-of-the-identity for the Coulomb two-electron term (RI-J)
  • one-center approximation for the SSSS-type electron repulsion integrals

Additional features

  • DIIS convergence acceleration
  • molecular orbital analysis for 1c Hamiltonians
  • diagonalization-free SCF for closed-shell singlets
  • fractional-occupation approach for atomic calculations
  • parallel execution on shared-memory parallel architectures (SMPs)

Related Publications

S. Knecht, M. Repisky, H. J. Aa. Jensen, and T. Saue
Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple
J. Chem. Phys. 157, 114106 (2022)

Program Reference

M. Repisky, S. Komorovsky, M. Kadek, L. Konecny, U. Ekstrom, E. Malkin,
M. Kaupp, K. Ruud, O. L. Malkina, and V. G. Malkin
ReSpect: Relativistic spectroscopy DFT program package
J. Chem. Phys. 152, 184101 (2020)

Additional contributions from
R. Bast (AutoCMake), R. Di Remigio (PCMSolver), I. Malkin-Ondik (DKH2), and S. Knecht (MPI parallelization)

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Our Contacts

Hylleraas Centre
Department of Chemistry
UiT The Arctic University of Norway
Tromsø, NO-9037 Norway