First-order polarization propagator approximation

In the self-consistent field linear response method [25,46,48] also known as random phase approximation (RPA) [49] or first order polarization propagator approximation [25,46], which is equivalent to the coupled Hartree-Fock theory [50], the reference state is approximated by the Hartree-Fock self-consistent field wavefunction < scf) and the set of operators /i j consists of single excitation and de-excitation operators with respect to orbital rotation operators [51],... 

In the first-order polarization propagator approximation (FOPPA) the reference state is then the Hartree-Fock wavefunction and one needs to include... 

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)... 

Electric moments, polarizabilities, and hyperpolarizabilities for BH were calculated for the first time [23], as were field and field gradient polarizabilities [24]. Spectroscopic properties were calculated for BH using the coupled electron pair approximation. The potential curve for BH was calculated at 22 points and Rq was found to be 1.23115 A and p to be 1.244 D [21]. The radiative lifetime of the A state of BH was calculated from second-order polarization propagator calculations [25], and the singlet-triplet separation in BH was calculated using ab initio MO methods. The latter, described as the singlet-triplet separation, was found to be 31.9 kcal/mol [26]. Finally, the possible dynamical pathways in the system BH + H+ were probed [27]. 

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... 

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... 

In order to calculate the GOS, one requires the excitation energies and the generalized transition moments. Oddershede and Sabin had already started in 1992 the investigation of the GOS and the stopping cross section in the first Bom approximation by means of the polarization propagator method [78]. 

The polarization corrections, and SPy, to the scalar propagation constant P for the Xq- and yo-polarized modes on the perturbed, noncircular fiber are in general unequal, and their difference describes the anisotropic, or birefringent, nature of propagation. This is of basic interest for the two fundamental modes on single-mode fibers. The calculation of the corrections from the formula in Table 13-1, page 288, requires first-order corrections to the approximation We derive these corrections for the slightly elliptical fiber in Section 18-10. 

V/e are concerned with the polarization properties of the transmitted light in the quasi-adiabatic limit. As a consequence, it is possible to assume that, in a first approximation, the backward-propagating waves are negligible since they give rise only to second or higher order effects. By explicitly considering the waves propagating in the forward direction, the transformed Berreman s matrix may be reduced to a 2x2 Jones matrix... 

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