Hartree-Fock approximation coupled values

Coupled Hartree-Fock values within the Random Phase approximation... 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

The 5s manifold shows great complexity. For the lowest state S23.4(5s) = 0.37. This value is considerably lower than many structure calculations predict, but the perturbation calculation of Kheifets and Amusia (1992) obtains 0.384. The orbital energy ess (11.18) is 27.6+0.3eV, which is to be compared to the Dirac—Fock value 27.49 eV. The Hartree—Fock value is 25.70 eV. The criterion for the strength of the perturbation, given by the ratio of the standard deviation to the mean of the 5s manifold is 0.18. The ratios S29.i(5s) S23.4(5s) and S23.4(5s) Z/S/(5s) are compared at different momenta in fig. 11.10. The condition for the validity of the weak-coupling binary-encounter approximation is completely satisfied within experimental error. 

Allen et al. [11] obtained for of 3-(l,l-dicyanonethenyl)-l-phenyl-4,5-dihydro-l//-pyrazole very good agreement between the measured quantity and the theoretical value calculated by combining this mean-field approximation with semiempirical P results. Typical p or determinations also include the ab initio CPHF (coupled-perturbed Hartree Fock) study of Hamada on 3-aminoxanthone (AX) and 2-methyl-4-nitroaniline (MNA) [12 13] in which... 

In Table 6.3, the values of De for RfCU are compared with those obtained within various approximations using relativistic effective core potentials (RECP) Kramers-restricted Hartree-Fock (KRHF) (Han et al 1999), averaged RECP including second-order M0ller-Plesset perturbation theory (AREP-MP2) for the correlation part (Han et al. 1999), RECP coupled-cluster single double (triple) [CCSD(T)] excitations (Han et al. 1999), and a Dirac-Fock-Breit (DFB) method (Malli and Styszynski 1998). The AREP-MP2 calculation of De gives 20.4 eV, while the RECP-CCSD(T) method with correlation leads to 18.8 eV. Our value of De of 19.5 eV is just between these calculated values. 

The major advantage of the scheme lies in the facile incorporation of approximate methods, though. If spin-orbit coupling effects are so small that they can be treated perturbatively, one uses the spinfree Hartree-Fock procedure to achieve the exact connection Ms = Mk. With this identification it is then e.g. possible to restrict the Cl space by a cut-off value of AMs or even to run the... 

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