SOPPA

These results are compared with those obtained by Oddershede and Svendsen (18) using SOPPA or Sunil and Jordan (19) using MP4 or a coupled cluster approach, but without vibronic correction. 

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. 

From Table 3 we can see that the negative OP contribution is the most important term in the vicinal F-F coupling in difluoroethyne (1). The SD and FC terms are Table 3. coupling constants and their four contributions (in Hz) calculated with the best set (see Table 2) at the SOPPA level at MP2/cc-pVTZ geometry ... 

Fig. 3. Dependence of the vicinal trans F-F coupling constant in trans-1,2-difluoropropene calculated at the SOPPA level on the basis set used for the carbon atoms and hydrogen atoms Deviation (in Hz) of the locally dense basis set result from the calculation with the apTJ/apTJ/[apTJ/pD]/m basis set. Only the basis sets on the non-coupled atoms are used as labels on the basis set axis. The apTJ basis set was used for fluorine in all calculations.

Table 4. Errors in the vicinal F-F coupling constants and reduction in the number of basis functions for various locally dense basis sets in comparison with the apTJ/apTJ/apTJ basis set for difluoroethyne (1) and the 1,2-difluoroaIkanes, (2) and (4), and the apTJ/apTJ/pT basis set for the 1,2-difluoroalkanes, (6) and (8). All calculations were carried out using SOPPA...

In this work, results of high level ab initio SOPPA calculations of vicinal fluorine-fluorine indirect nuclear spin couplings are presented for 1,2-difluoroethene, -propene, -ethane and -propane. The four contributions (OD, OP, SD, FC) and the total value of the coupling constant are analyzed. 

In MCSCF linear response theory [32] and the SOPPA and SOPPA(CCSD) [5,33,36] this leads to the following expression for the static dipole polarizability, e.g.,... 

In SOPPA [5] a Mpller-Plesset perturbation theory expansion of the wave function [28,48] is employed ... 

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... 

SOPPA(CCSD) and CCSD polarizabilities. This shows that the CCSD and oooocas2010,io,4 ygj.y sjj q r in the vicinity of the equilibrium... 

Zpvc cscF between and obtained at the SOPPA level. 

The SOPPA(CCSD) results, obtained with the CCSD or the 0000(. 320,i0,i0,4... 

PEC, are in general in better agreement with the CAS results than the pure SOPPA results. This applies to the equilibrium geometry results as well as to the vibrational averaged results. This shows that SOPPA(CCSD) performs better in the calculation of polarizabilities for LiH than SOPPA as might have been expected [36,41]. 

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... 

We have compared our MCSCE results for the vibrational ground state with CCSD, SOPPA, and SOPPA(CCSD) calculations. In particular we have investigated the importance of the PEC on the ZPVCs and find that there are significant differences between LiH and HF. In LiH the CCSD results for the ZPVC are very close to the MCSCF results independent on whether the CCSD or MCSCF PEC was employed. Similarly, the differences between SOPPA(CCSD) calculations with either the CCSD or the MCSCF energy surface are very small. In HF, on the other hand somewhat larger differences are found if the CCSD polarizabilities are averaged over the CCSD PEC and the difference between... 

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. 

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