NMR Indirect Nuclear Spin-Spin Coupling Tensor

Documentation on the relativistic calculation of Nuclear Magnetic Resonance (NMR) indirect nuclear spin-spin coupling constants/tensors (SSCC).

Feature List


  • relativistic 4c matrix/modified Dirac-Hartree-Fock (mDHF) and Dirac-Kohn-Sham (mDKS)
  • scalable speed of light
  • switchable spin-orbit interaction

DFT non-collinear functionals

  • local (SVWN5)
  • GGA (PBE,BLYP,KT2,BP86,PP86)
  • hybrid (PBE0,B3LYP)

DFT non-collinear analytical kernels

  • full expressions including the GGA part
  • adiabatic local density approximation (ALDA/XALDA)

Reference (perturbation-free) wave function models

  • Kramers restricted determinant for closed-shell singlets

Nuclear charge distribution models

  • point
  • finite Gaussian-type

Nuclear magnetic moment distribution models

  • point

Integral evaluation techniques

  • analytic with an in-built restricted kinetic balanced (RKB) condition for the small-component
  • analytic with an in-built restricted magnetic balanced (RMB) condition for the small-component
  • one-center approximation for the SSSS-type electron repulsion integrals

Additional features

  • DIIS convergence acceleration
  • molecular orbital analysis of the paramagnetic contribution
  • parallel execution on shared-memory parallel architectures (SMPs)


  • restart from a previous run is not implemented
  • four-center two-electron integrals containing RMB basis are neglected
  • contributions to the GGA-type DFT kernels from response density containing RMB basis are neglected

Related Publications

M. Repisky, S. Komorovsky, O. L. Malkina, and V. G. Malkin
Restricted magnetically balanced basis applied for relativistic calculations of indirect nuclear spin-spin coupling tensors in the matrix Dirac-Kohn-Sham framework
Chem. Phys. 356, 236–242 (2009)

Book Chapters

M. Repisky, S. Komorovsky, R. Bast, and K. Ruud
Relativistic calculations of nuclear magnetic resonance parameters
Gas Phase NMR , edited by K. Jackowski, M. Jaszunski (The Royal Society of Chemistry) 267–303 (2016)

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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Useful Links

Our Contacts

Hylleraas Centre
Department of Chemistry
UiT The Arctic University of Norway
Tromsø, NO-9037 Norway
Email: info@respectprogram.eu