MCSCF calculations of NMR spin–spin coupling constant of the HF molecule

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Study on potential energy curves and ro-vibrational energies of DT, HT and T2 molecules

Accurately monitoring and effectively controlling the tritium compounds based on their ro-vibrational energy structure are important issues in various nuclear systems. Because of their radioactivity, it is difficult to obtain the corresponding energies directly through experiments. In this paper, the potential energy curves and the corresponding ro-vibrational full spectrum of DT, HT and T₂ systems are derived by ab initio methods. However, it is difficult to verify the reliability of the calculated results due to the lack of direct experimental support. Therefore, a data-driven reliability analysis method is proposed, which can confirm the reliability by extracting information from the relevant calculations and multiple experimental data (the vibrational level, rotational level, and molar heat capacity) of similar systems (HD, H₂, D₂). The results show that: 1) The potential energy curves obtained by the ab initio method can provide the full ro-vibrational energy spectrum with an accuracy of approximately 10 cm^-1; 2) Macroscopic heat capacity information can be used to distinguish and calibrate the overall reliability of microscopic ro-vibrational energies; 3) For the isotopic energy level structure of hydrogen, the influence of isotopes is mainly mass effect.

Natural bond orbital/natural J-coupling study of vicinal couplings

NBO-NJC decomposition of vicinal (3)J HH spin-spin coupling constants into Lewis, delocalization, and repolarization contributions are presented. A deep study allows to assign the main contributions to specific orbitals or electron delocalizations between two orbitals. (3)J HH torsional dependence and the substituent effect are analyzed according to the main orbital contributions for ethane and fluoroethane molecules using different basis sets. The torsional dependence for the energies corresponding to electron delocalization is also studied.

Vicinal fluorine-fluorine coupling constants: Fourier analysis

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn> or =3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation.

Quadratic Response Functions in a Second-Order Polarization Propagator Framework

The linear and quadratic response functions have been derived for an exact state, based on an exponential parametrization of the time evolution consisting of products of exponentials for orbital rotations and for higher-order excitations. Truncating the linear response function such that the response function itself and its pole structure is correct to second order in Møller-Plesset perturbation theory, we arrive at the second-order polarization propagator approximation (SOPPA). Previous derivations of SOPPA have used the superoperator formalism, making the extension of SOPPA to quadratic and higher order response functions difficult. The derivation of the quadratic response function is described in detail, allowing molecular properties such as hyperpolarizabilities, two-photon cross sections, and excited-state properties to be calculated using the SOPPA model.