Second-order polarization propagator correlation

The static and dynamic polarizability of the polyyne (C2 H2) series is treated in the TDHF and correlated second order polarization propagator methods by Dalskov et al.2i2 The calculated polarizabilities are extrapolated to the infinitely... 

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-... 

In this substection we will shortly discuss the computational methods used for calculation of the spin-spin coupling constants. Two main approaches available are ab initio theory from Hartree-Fock (or self-consistent field SCF) technique to its correlated extensions, and density function theory (DFT), where the electron density, instead of the wave function, is the fundamental quantity. The discussion here is limited to the methods actually used for calculation of the intermolecular spin-spin coupling constants, i. e. multiconfigurational self consistent field (MCSCF) theory, coupled cluster (CC) theory and density functional theory (DFT). For example, the second order polarization propagator method (SOPPA) approach is not... 

The paramagnetic contribution is more demanding to calculate and is a bit more sensitive to electron correlation, although not a great deal. For instance, for ammonia, the RPA (effectively uncorrelated) value is 38.45 ppm a.u., while the Second Order Polarization Propagator Approximation (correlated) yields 38.15 ppm a.u. 

Relativistic calculations of NMR properties of RgH ion (where Rg = Ne, Ar, Kr, Xe), Pt shielding in platinum complexes, and Pb shielding in solid ionic lead(II) halides have been reported in this review period. For the Rg nucleus in the RgH ions, the following methods were used and results compared with each other non-relativistic uncorrelated method (HF), relativistic uncorrelated methods, four component Dirac Hartree-Fock method (DHF) and two-component zeroth order regular approach (ZORA), non-relativistic correlated methods using second order polarization propagator approach SOPPA(CCSD), SOPPA(MP2), respectively coupled cluster singles and doubles or second order Moller-Plesset, and... 

However, other attempts have been made to improve on the treatment of electron correlation in SOPPA. Three SOPPA-like methods have thus been presented. All are based on the fact that a coupled cluster wavefunction gives a better description than the Mpller-Plesset first- and second-order wavefunctions, Eqs. (9.66) and (9.70). In the second-order polarization propagator with coupled cluster singles and doubles amplitudes-SOPPA(CCSD)-method (Sauer, 1997), the reference state in Eqs. (3.160) to (3.163) is approximated by a linearized CCSD wavefunction... 

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. 

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... 

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... 

In SOPPA the equations for the polarization propagator are solved by retaining all terms second order in the fluctuation potential. The reference state is a correlated Moller Plesset wavefunction with the corresponding correlation coefficients. The zeroth-order wavefunction is a single reference SCF ground state. Correlation is introduced via the fluctuation potential. SOPPA includes dynamical correlation, but not nondynamical effects. The same technique can be applied to other methods, e.g., coupled cluster, giving CCSDPPA where the cluster amplitudes replace the correlation coefficients used in SOPPA. 

Analysis of the presented data shows that energy approach (combined with ab initio relativistic many-body PT) provides a physically reasonable agreement of theoretical and experimental data. We have checked that the results for oscillator strengths obtained within our approach in different photon propagator gauges are practically equal (difference 0.1-0.3%). The calculation has confirmed a great role of the interelectron correlation effects of the second and higher PT orders, namely, effects of the interelectron polarization interaction and quasiparticle mutual... 

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