Related Experiment Video
Updated: Dec 11, 2025
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
8.8K
Hyperfine-Coupling Tensors from Projected Hartree-Fock Theory
Shadan Ghassemi Tabrizi1, Alexei V Arbuznikov1, Carlos A Jiménez-Hoyos2
1Institut für Chemie, Theoretische Chemie, Technische Universität Berlin, Sekr. C7, Strasse des 17. Juni 135, 10623 Berlin, Germany.
Journal of Chemical Theory and Computation
|August 26, 2020
Summary
Projected Hartree-Fock (PHF) theory accurately calculates hyperfine coupling (HFC) tensors in small radicals. Advanced symmetry restoration in PHF significantly improves results compared to older methods.
Area of Science:
- Quantum Chemistry
- Computational Chemistry
- Theoretical Chemistry
Background:
- Hyperfine coupling (HFC) tensor calculations are crucial for understanding molecular properties.
- Traditional methods using Projected Hartree-Fock (PHF) theory with only spin-symmetry restoration yield unsatisfactory HFC results.
- Modern computational chemistry requires more accurate and efficient methods for HFC calculations.
Purpose of the Study:
- To evaluate the performance of different Projected Hartree-Fock (PHF) variants for calculating hyperfine coupling (HFC) tensors.
- To investigate the impact of restoring spin-symmetry, complex-conjugation, and point-group symmetry on HFC tensor accuracy.
- To present the detailed equations for combined symmetry restoration in the density-matrix/diagonalization formulation of PHF theory.
Main Methods:
- Application of modern Projected Hartree-Fock (PHF) theory to small main-group S=1/2 radicals (BO, CO+, CN, AlO, vinyl, methyl, ethynyl).
- Breaking and variational restoration of spin-symmetry, complex-conjugation, and point-group symmetry.
- Utilizing generalized determinants that completely break spin symmetry to lower variational energy.
- Developing and reporting detailed equations for combined symmetry projection in the density-matrix/diagonalization formulation.
Main Results:
- Projected Hartree-Fock (PHF) theory with restored spin-symmetry, complex-conjugation, and point-group symmetry yields significantly improved hyperfine coupling (HFC) tensor calculations.
- Restoring complex-conjugation symmetry recovers a substantial fraction of dynamical correlation energy.
- The compact representation of the PHF wave function simplifies the evaluation of spin-density matrices and HFC tensors.
Conclusions:
- Advanced symmetry restoration in Projected Hartree-Fock (PHF) theory provides accurate hyperfine coupling (HFC) tensor calculations for small radicals.
- The developed PHF formulation offers a more efficient and accurate approach compared to historical methods.
- The promising results suggest potential applications of post-PHF methods for HFC tensor computations.
More Related Videos
05:51Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
Published on: July 19, 2019
6.5K
08:44Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
Published on: August 22, 2017
8.0K
Related Concept Videos
01:22Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)
1.3K
Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
1.3K
01:27¹H NMR: Long-Range Coupling
2.4K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
2.4K
01:17Spin–Spin Coupling: One-Bond Coupling
1.3K
Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
1.3K
01:20Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)
1.4K
Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
1.4K
01:08Spin–Spin Coupling Constant: Overview
1.3K
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
1.3K
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
1.3K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.3K