Sum-over-states density functional perturbation

Malkin, V. G., Malkina, 0. L., Casida, M. E., Salahub, D. R., 1994, Nuclear Magnetic Resonance Shielding Tensors Calculated With a Sum-Over-States Density Functional Perturbation Theory , J. Am. Chem. Soc., 116, 5898. 

S = 103 ppm, which is in excellent agreement with the chemical shifts found earlier in other dioxiranes such as lb, Ic, and Id. The experimental H, and NMR spectra are in good agreement with calculated (sum-over-states density-functional perturbation theory, SOS-DFPT) chemical shifts. The oxygen nuclei in 4 are somewhat more shielded in the NMR spectrum (5 = 321 ppm) than those in DMDO lb. 

Sum-Over-States Density Functioned Perturbation Theory... 

The PSO contribution is associated with the interactions between the operators H010 for nuclei TV and M (see Eqn. (7)), respectively. To calculate the PSO contribution, we used Sum-Over-States Density Functional Perturbation Theory (SOS-DFPT). The SOS-DFPT approach leads to the well-known equations... 

Malkin VG, Malkina OL, Casida ME, Salahub DR (1994) Nuclar magnetic resonance shielding tensors calculated with a sum-over-states density functional perturbation theory. J Am Chem Soc 116 5898-5908... 

Density functional theory (DFT) calculations employing sum-over-states DF perturbation theory were applied to calculate both the H and chemical shifts of 1,3-dioxane, 1,3-oxathiane, 1,3-dithiane, and the parent cyclohexane <1997JMT(418)231>. Both normal and anomalous trends in the H chemical shifts could be reproduced well and. 

Hyperpolarizabilities can be calculated in a number of different ways. The quantum chemical calculations may be based on a perturbation approach that directly evaluates sum-over-states (SOS) expressions such as Eq. (14), or on differentiation of the energy or induced moments for which (electric field) perturbed wavefunctions and/or electron densities are explicitly calculated. These techniques may be implemented at different levels of approximation ranging from semi-empirical to density functional methods that account for electron correlation through approximations to the exact exchange-correlation functionals to high-level ab initio calculations which systematically include electron correlation effects. 

We saw earlier that a very simple form of the dispersion energy is obtained from frequency-dependent polarizabilities at the so-called uncoupled Hartree-Fock level. The sum over states appearing in second order RS perturbation theory is simply a sum over (occupied and virtual) orbitals. A first improvement of this simple model is obtained by including apparent correlation [140], i.e. by using frequency-dependent polarizabilities obtained from the TDCHF method [36,141]. This method was initially proposed in the context of the multipole expansion, but could be generalized [142-146] to charge density susceptibility functions (or polarization propagators), which avoids the use... 

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