SOPPA method

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-... 

Del Bene et calculated the SSCCs for FCCF (difluoroethyne) using the EOM-CCSD and SOPPA methods. Previous theoretical studies of SSCCs for FCCF have reported significantly different values of V(F, F). These range from 85.4 Hz to 21.5 Hz, but the experimental spectrum of FCCF... 

SOPPA as originally introduced deals with the linear response function and hence with polarizabilities. Recently Packer et al. have reimplemented the SOPPA method. They have a more efficient algorithm, and their method now scales as the fifth power of the number of basis functions rather than the sixth. Their work still only deals with linear response functions, but they state that it may be applied to frequency dependent quadratic properties, i.e., hyperpolarizabilities as well. 

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. 

In the SOPPA(CCSD) method [36] the Mqller-Plesset correlation coefficients and are replaced in all SOPPA matrix elements by the corresponding coupled cluster singles and doubles amplitudes and r , whereas in the earlier CCSDPPA method [52,53] only some of the Mqller-Plesset correlation coefficients were replaced. Although SOPPA(CCSD) is based on a CCSD wavefunction, it is still only correct through second order and not the linear... 

He also investigated the dependence of the properties on the internuclear distance in the vicinity of the equilibrium internuclear separation R. However, our goal was not to look for the most accurate values or to compare with them, but to study the performance of various linear response methods. In particular we wanted to find out which level of correlation is necessary in order to reproduce the correct dependence on the internuclear distance for a wider range of R. In Fig. 6, it can be seen that the CCSD dipole polarizability curve is sufficiently close to the results of the calculations. The SOPPA... 

SOPPA(CCSD) calculations with the CCSD or MCSCF PEC are also larger. In general the differences in the ZPVC are larger between the different PEC than between the different linear response methods. The SOPPA(CCSD) results for the equilibrium geometry as well as the vibrationally averaged polarizabilities are in both molecules in better agreement with the MCSCF results than the pure SOPPA values. 

However, until today no systematic comparison of methods based on MpUer-Plesset perturbation (MP) and Coupled Cluster theory, the SOPPA or multiconfigurational linear response theory has been presented. The present study is a first attempt to remedy this situation. Calculations of the rotational g factor of HF, H2O, NH3 and CH4 were carried out at the level of Hartree-Fock (SCF) and multiconfigurational Hartree-Fock (MCSCF) linear response theory, the SOPPA and SOPPA(CCSD) [40], MpUer-Plesset perturbation theory to second (MP2), third (MP3) and fourth order without the triples contributions (MP4SDQ) and finally coupled cluster singles and doubles theory. The same basis sets and geometries were employed in all calculations for a given molecule. The results obtained with the different methods are therefore for the first time direct comparable and consistent conclusions about the performance of the different methods can be made. 

In general, the results of the perturbation theory based methods, SOPPA, SOPPA(CCSD), MPn and CCSD become smaller with increasing level of theory, whereas the results of the CASSCF/RASSCF calculations go through a maximum for the or °°°CAS wavefunctions depending on the molecule. 

Comparing the SOPPA and SOPPA(CCSD) results one can see that both methods predict correlation corrections which are comparable to the results obtained at the CCSD or RAS iSD level. However, it is clear that SOPPA(CCSD) is in better agreement with these more expensive methods. The SOPPA(CCSD) results for HF, for gip and goop in H2O are close to the respective MP3 results. In case of NH3 and the parallel component of the g tensor of H2O, where the correlation corrections are somewhat smaller, 1.5%, SOPPA(CCSD) predicts values close to the CCSD numbers. 

SOPPA(CCSD) and RAS332 SD is interchanged. One can therefore conclude that for the molecules studied here the results of SOPPA(CCSD) calculations are comparable to results of other state-of-the-art methods. 

Comparing the results of the different methods one sees that SOPPA gives a good indication of the size and sign of the correlation correction, but that SOPPA(CCSD) is always in better agreement with MPn/CCSD and the large RASSCF calculations than SOPPA. SOPPA(CCSD) gives results which are close to the results of MP3 calculations with the exception of CH4. When the correlation effects are small, 1.5%, the SOPPA(CCSD) results are even close to the CCSD results. 

Various theoretical treatments, including DFT and two high-level ab initio methods, MCSCF and SOPPA, have been tested recently by San Fabian and Westra Hoekzema.143 These authors represented contributions to the angular dependence of 3/fccf in 1,2-difluoroethane by a truncated Fourier series ... 

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