The KPACK program is intended for relativistic electronic structure computation of molecules containing heavy elements via the two-component ab initio calculations in Kramers restricted and unrestricted formalisms in the framework of the spin-orbit relativistic effective core potential (SOREP).

The spin-orbit coupling as relativistic effect enters into the calculation at the Hartree-Fock level and hence, is treated in a variational manner to generate two-component molecular spinors as one-electron wavefunctions for use in the correlated methods. As correlated methods, KPACK currently provides the two-component second-order Møller-Plesset perturbation theory, configuration interaction, and complete active space self-consistent field methods.


Atomic orbital integrals
  • Supports both spherical and Cartesian gaussian basis sets (up to h-functions)
  • One-electron integrals
    • Overlap, kinetic, nuclear attraction integrals using Obara-Saika recurrence relations and Gauss-Hermite quadrature
    • SOREP integrals (core potential, spin-orbit x, y, and z integrals)
  • Two-electron integrals
    • Electron repulsion integrals by the recursive algorithm through Rys polynomials
Self-consistent field
  • Kramers restricted and unrestricted Hartree-Fock (KRHF and KUHF)
  • Diagonalization based on quaternion algebra
  • Parallelized using OpenMP
  • Two-component modified direct inversion in iterative subspace (DIIS) acceleration
Molecular spinor integrals
  • Complex two- and four-index transformation
  • Kramers restricted and unrestricted molecular spinor integrals
    • Eight distinct integral sets for KR spinors
    • Two distinct integral sets for KU spinors
Perturbation theory
  • Kramers restricted and unrestricted second-order Møller-Plesset perturbation theory (KRMP2 and KUMP2)
Configuration interaction
  • Kramers restricted and unrestricted configuration interaction (KRCI and KUCI)
  • Direct CI using extended Davidson diagonalization for Hermitian matrix
  • Determinant construction via graph theory
  • Spin-orbit CI is also possible
Multi-configurational self-consistent field
  • Kramers restricted complete active space self-consistent field (KRCASSCF)
  • Full consideration of time-reversal symmetry
  • Two-step near second-order approach for convergence
  • Applicable for both closed- and open-shell systems


July 30, 2014 website is created.