Nuclear Magnetic Resonance σ-tensor

Documentation on the molecular calculation of nuclear magnetic resonance (NMR) chemical shielding (CS) constants (σ-tensors) using relativistic Kramers-restricted density functional theory. In the current version of ReSpect, the methodology can be combined with the 1C or 4C Hamiltonian and applied to closed-shell molecular systems (open-shell systems are covered in pNMR).

Tutorial

SCF Keywords

CS Keywords

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 open-shell doublets

Hamiltonians

  • non-relativistic one-component (1c)
  • relativistic four-component (4c) Dirac-Coulomb
  • scalable speed of light
  • switchable 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)

DFT non-collinear analytical kernels

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

Nuclear charge distribution models

  • point
  • finite Gaussian-type

Nuclear magnetic moment distribution models

  • point

Methods for solving the gauge origin problem

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

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)

Approximations/Limitations

  • 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
In: Jackowski and Jaszunski (eds.) Gas Phase NMR, The Royal Society of Chemistry , 267–303 (2016)

S. Komorovsky
Relativistic Theory of EPR and (p)NMR
In: Yanez, Manuel and Boyd, Russell J. (eds.) Comprehensive Computational Chemistry, Vol. 3, Elsevier , 280–314 (2024)

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)

Latest Posts

Latest Publications

Useful Links

Our Contacts

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