Spin coupling constants approximate theory

A systematic development of relativistic molecular Hamiltonians and various non-relativistic approximations are presented. Our starting point is the Dirac one-fermion Hamiltonian in the presence of an external electromagnetic field. The problems associated with generalizing Dirac s one-fermion theory smoothly to more than one fermion are discussed. The description of many-fermion systems within the framework of quantum electrodynamics (QED) will lead to Hamiltonians which do not suffer from the problems associated with the direct extension of Dirac s one-fermion theory to many-fermion system. An exhaustive discussion of the recent QED developments in the relevant area is not presented, except for cursory remarks for completeness. The non-relativistic form (NRF) of the many-electron relativistic Hamiltonian is developed as the working Hamiltonian. It is used to extract operators for the observables, which represent the response of a molecule to an external electromagnetic radiation field. In this study, our focus is mainly on the operators which eventually were used to calculate the nuclear magnetic resonance (NMR) chemical shifts and indirect nuclear spin-spin coupling constants. 

One of the most successful methods of calculating nuclear spin coupling constants involves application of SCF perturbation theory and use of the INDO molecular orbital (MO) approximations. (8-17) In most theoretical studies aAB and bAB are taken as empirical parameters, adjusted to give best agreement between theory and experiment. Values of the individual integrals calculated from Slater exponents (14) are given in Table I. 

Helgaker et alP presented a fully analytical implementation of spin-spin coupling constants at the DFT level. They used the standard procedure for linear response theory to evaluate second-order properties of PSO, FC and SD mechanisms. Their calculation involves all four contributions of the nonrelativistic Ramsey theory. They tested three different XC functionals -LDA (local density approximation), BLYP (Becke-Lee-Yang-Parr), " and B3LYP (hybrid BLYP). All three levels of theory represent a... 

Considerations similar to those made about electric dipole moments apply to other one-electron properties, for instance the nuclear spin-spin coupling constants between non-bonded hydrogen atoms in molecules like methane. These quantities are approximately equal to zero in the simple molecular orbital theory, as it is easily proved by using equivalent orbitals corresponding to the CH bonds instead of the usual delocalized MO s (34). Actually, the nuclear spins of protons cannot interact wta the electrons, since a localized MO cannot be large on two hydrogens at the same time, and correlation should be primarily responsible for all coupling constants, except perhaps for those observed for directly bonded atoms (see Sec. 4). 

T. Helgaker, M. Watson, N. Handy, Analytical calculation of nuclear magnetic resonance indirect spin-spin coupling constants at the generalized gradient approximation and hybrid levels of density-functional theory, J. Chem. Phys. 113 (2002) 9402-9409. 

Finally, it is used in the analysis of contributions to a molecular property like a polarizability or NMR spin-spin coupling constant from excitations between individual, typically localized, molecular orbitals (see, e g. Hansen and Bouman (1985), Packer and Pickup (1995), Sauer and Provasi (2008) or Provasi and Sauer (2009)). This is normally done at the level of the random phase approximation or time-dependent density functional theory. 

Krivdin and co-workers ° applied a double perturbation theory (DPT) at the second order level of approximation formalism to examine the dihedral angle dependence of the Fermi-contact (FC) contribution to nuclear spin-spin coupling constants. The authors have derived an analytical expression relating the FC term of /(H,H) across the aliphatic single carbon-carbon bond to the dihedral angle describing inner rotation around the C-C bond in the ten-electron ten-orbital moiety H-C-C-H. In particular, the authors have shown that extrema of H,H) are observed at q> = nn [n = 0, 1, 2,...), which provides a theore-... 

Coupling constants are usually analysed at present in terms of a MO theory developed by Pople and Santry. They showed that coupling constants involving directly bonded atoms arise almost entirely from the Fermi contact interaction between nuclear moments and electron spins in 5 orbitals. Using the LCAO approximation and retaining only one-centre integrals, they derived the following expression for Ja-b—... 

Christiansen et al. s tested the coupled-cluster response theory on spin-orbit coupling constants of substituted silylenes (HSiX, X = F, Cl, Br) in the atomic mean-field approximation. Comparison with the full Breit-Pauli showed that the approximation is quite accurate. The calcu-... 

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