NMR Shielding Tensor

Documentation on the relativistic calculation of Nuclear Magnetic Resonance (NMR) chemical shielding (CS) tensors.

Feature List


  • non-relativistic one-component (1c) Hartree-Fock (HF) and Kohn-Sham (KS)
  • 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
  • Kramers unrestricted determinant for open-shell doublets

Methods for solving the gauge origin problem

  • common gauge origin (CGO)
  • gauge including atomic orbitals (GIAO), also known as London atomic orbitals (LAO)

Nuclear charge distribution models

  • point
  • finite Gaussian-type

Nuclear magnetic moment distribution models

  • point

Integral evaluation techniques

  • analytic with an in-built LAO phase factor
  • 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

Perturbation theory-based spin-orbit contribution to the NMR shielding tensor (recommended for analysis)

  • << FC;SO,L >>
  • << SD;SO,L >>

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
  • non-relativistic 1c Hamiltonians are only available for CGO method
  • hybrid DFT functionals are only available for closed-shell singlets
  • the calculation for open-shell doublets is only available with ALDA/XALDA DFT kernels
  • full expression for analytical DFT kernels including the GGA part is only available for closed-shell singlets
  • four-center two-electron integrals in the RMB basis are neglected in the framework of CGO

Related Publications

S. Komorovsky, M. Repisky, O. L. Malkina, V. G. Malkin, I. Malkin-Ondik, and M. Kaupp
A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac-Kohn-Sham equation
J. Chem. Phys. 128, 104101 (2008)

S. Komorovsky, M. Repisky, O. L. Malkina, and V. G. Malkin
Fully relativistic calculations of NMR shielding tensors using restricted magnetically balanced basis and gauge including atomic orbitals
J. Chem. Phys. 132, 154101 (2010)

S. Komorovsky, M. Repisky, K. Ruud, O. L. Malkina, and V. G. Malkin
Four-component relativistic density functional theory calculations of NMR shielding tensors for paramagnetic systems
J. Phys. Chem. A 117, 14209–14219 (2013)

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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Our Contacts

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