SOPPA propagator approximation

We have employed the second-order polarization propagator approximation (SOPPA) in this study, a method which was mainly developed by Jens Oddershede and his co-workers [3,4,20,51-56]. Barone et al. [32] have recently shown that SOPPA reproduces the vicinal F-F couplings reasonably well in 1,2-difluoroethene. 

SOPPA Secondary order polarization propagator approximation... 

The resulting second-order polarization propagator approximation (SOPPA) was first described in its present form by Nielsen et al. (1980). Splitting h4 up into 2p-2h and 2h-2p excitation operators as was done for h2 in Eqs (95)-(97)... 

For a polyyne chain142 the static al and dynamic a(— co)L polarizabilities have been computed using non-linear sequence transformations for the extrapolation and besides RPA the SOPPA (correlated second order polarization propagator approximation) method. In this way the authors have obtained for a C2 iH2 (polyyne) chain quite stable extrapolated values for both quantities. 

There do exist recent quantum chemical techniques which are size consistent. Among them, the Random Phase Approximation (RPA), its variants such as the Second-Order Polarization Propagator Approximation (SOPPA) [10], and the Coupled Cluster Approximation (CCA) [11] axe the most prominent and being widely used. In the SOPPA method, electron correlation effects are included in the two-particle polarization propagator to second order. The coupled cluster method uses an exponential ansatz through which higher-order exci-... 

Empirical equilibrium coupling constants can be compared as a benchmark with calculated equilibrium coupling constants obtained with various methods. A comparison of these empirical equilibrium constants with calculated equilibrium constants suggested that the restricted-active-space self-consistent field (RASSCF) method is the best approach for calculating the indirect nuclear spin-spin coupling constants of small molecules, and that the second-order polarization propagator approximation (SOPPA) and DFT are similar in performance. 

J.E. Del Bene, I. Alkorta, I.J. Elguero, A systematic comparison of second-order polarization propagator approximation (SOPPA) and equation-of-motion coupled cluster singes and doubles (EOM — CCSD) spin — spin couphng constants for selected singly bonded molecules, and the hydrides NH3, H2O, and HF and their protonated and deprotonated ions and hydrogen-bonded complexes, J. Chem. Theor. Comput. 4 (2008) 967-973. 

This keeps essentially the structure of the SOPPA equations but replaces in all matrix elements the first-order MP doubles correlation coefficients, Eq. (9.67), and the second-order MP singles correlation coefficient, Eq. (9.71), by coupled cluster singles and doubles amplitudes. In the earlier coupled cluster singles and doubles polarization propagator approximation (CCSDPPA) (Geertsen et al., 1991a), a precursor to SOPPA(CCSD), this was done only partially and in particular not in the second-order correction to the density matrix Very recently, a third method (Kjaer... 

The formulation of approximate response theory based on an exponential parame-trization of the time-dependent wave function, Eq. (11.36), and the Ehrenfest theorem, Eq. (11.40), can also be used to derive SOPPA and higher-order Mpller-Plesset perturbation theory polarization propagator approximations (Olsen et al., 2005). Contrary to the approach employed in Chapter 10, which is based on the superoperator formalism from Section 3.12 and that could not yet be extended to higher than linear response functions, the Ehrenfest-theorem-based approach can be used to derive expressions also for quadratic and higher-order response functions. In the following, it will briefly be shown how the SOPPA linear response equations, Eq. (10.29), can be derived with this approach. 

Sauer, S. P. A. (1997). Second order polarization propagator approximation with coupled cluster singles and doubles amplitudes - SOPPA(CCSD) The polarizability and hyperpolarizabihty of Li. J. Phys. B At. Mol. Opt. Phys., 30, 3773-3780. 

Enevoldsen, T., Oddershede, J., Sauer, S. P. A. (1998). Correlated calculations of indirect nuclear spin-spin coupling constants using second-order polarization propagator approximations SOPPA and SOPPA(CCSD). Theoretical Chemistry Accounts, 100, 275. 

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