Polarization propagator first-order

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... 

Ekstrom U, Norman P. X-ray absorption spectra from the resonant-convergent first-order polarization propagator approach. Phys Rev A. 2006 74 042722. 

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... 

Exeitation energies are readily obtained as poles of a polarization propagator [37-40], whereas the transition moments are known as first-order non-adiabatie... 

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]. 

An increase in the cA-stilbene concentration favors the chain propagation and decreases the probability of termination when the DCNA anion-radicals react with the stilbene cation-radicals. A decrease in the irradiation intensity has a similar effect The chain propagation is the first-order process, whereas termination of the chains is the second-order process. A temperature rise accelerates the accumulation of the stilbene cation-radicals. In this system, the free energy of electron transfer is -53- —44 kJ moD (the cation-radical generation is in fact an endothermal process). If a polar solvent is substituted for a nonpolar one, the conversion of the cii-stilbene cation-radical into the trani-stilbene cation-radical deepens. Polar solvents break ion pairs, releasing free ion-radicals. The cA-stilbene cation-radicals isomerize more easily on being released. The stilbene cation-radical not shielded with a counterion has a more positive charge, and therefore, becomes stabilized in the... 

The need for solvation in anionic polymerization manifests itself in some instances by other deviations from the normal reaction rate expressions. Thus the butyllithium polymerization of methyl methacrylate in toluene at — 60°C shows a second-order dependence of Rp on monomer concentration [L Abbe and Smets, 1967]. In the nonpolar toulene, monomer is involved in solvating the propagating species [Busson and Van Beylen, 1978]. When polymerization is carried out in the mixed solvent dioxane-toluene (a more polar solvent than toluene), the normal first-order dependence of Rp on [M] is observed. The lithium diethylamide, LiN(C2H5)2, polymerization of styrene at 25°C in THF-benzene similarly shows an increased order of dependence of Rp on [M] as the amount of tetrahydrofuran is decreased [Hurley and Tait, 1976]. 

---