RASSCF

The Wd estimated from the RASCI is compared with other theoretical calculations [46, 54] in Table V. The present DF estimate of Wd deviates by 21%(29%) from the SCF (RASSCF) estimate of Kozlov et al. [46] and by 17% from the semiempirical result of Kozlov and Labzovsky [54], while our RASCI result departs by 6% (3%) from the SCF-EO (RASSCF-EO) treatment of Kozlov et al. [46] and is in good agreement with the semi-empirical result of Kozlov and Labzovsky. At this juncture, we emphasize that our computed ground state dipole moment of BaF (p(. = 3.203 debyes) is also reasonably close to experiment p(. = 3.2 debyes (see Table 5 of Ref. 38). 

Restricted active space self-consistent field (RASSCF) scheme, ab initio calculations, P,T-odd interactions, 253-259... 

The article is organized as follows. The main features of the linear response theory methods at different levels of correlation are presented in Section 2. Section 3 describes the calculation of the dipole and quadmpole polarizabilities of two small diatomic molecules LiH and HF. Different computational aspects are discussed for each of them. The LiH molecule permits very accurate MCSCF studies employing large basis sets and CASs. This gives us the opportunity to benchmark the results from the other linear response methods with respect to both the shape of the polarizability radial functions and their values in the vibrational ground states. The second molecule, HF, is undoubtedly one of the most studied molecules. We use it here in order to examine the dependence of the dipole and quadmpole polarizabilities on the size of the active space in the CAS and RASSCF approaches. The conclusions of this study will be important for our future studies of dipole and quadmpole polarizabilities of heavier diatomic molecules. 

The selection of configuration state functions to be included in MCSCF calculations is not a trivial task. Two approaches which can reduce the complexity of the problem are the complete active space self-consistent-field (CASSCF) [68] and the restricted active space self-consistent-field (RASSCF) [69] approach. Both are implemented in the Dalton program package [57] and are used in this study. Throughout the paper a CASSCF calculation is denoted by i active gactive RASSCF calculation by For the active spaces of HF, H2O, and CH4... 

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 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. 

Finally, the results for CH4 show quite a different pattern. The correlation corrections are positive and the results of MPn/CCSD calculations differ more from the results of SOPPA/SOPPA(CCSD) and the RASSCF calculations than for the other molecules. Further investigations of the correlation effects in this molecule are necessary. 

T. Helgaker, H. J. Aa. Jensen, P. J0rgensen, J. Olsen, and P. R. Taylor. ABACUS, a CASSCF and RASSCF energy derivatives program. 

There are two types of parameters that determine the RAS wave function the Cl coefficients and the molecular orbitals. When both of them are optimized the result will be a RASSCF (CASSCF) wave function, which is a extension of the SCF method to the multiconfigurational case. Below we shall briefly show how the optimization is done in practice in most modern programs (more details can, for example, be found in Ref. [25]). 

The CASSCF energy (but not RASSCF) is invariant to rotations among the inactive orbitals (compare SCF) and also to rotations among the active orbitals. This can be used, for example, to transform to localized orbitals, or to pseudo-natural orbitals,... 

With this recipe we can construct a number of different types of MCSCF wave functions. With an empty RAS2 space we obtain SDT...-CI wave functions depending how many holes we allow in RAS 1 and how many electrons we allow in RAS 3. If we add a RAS2 space and allow up to two holes in RAS 1 and max two electron sin RAS3 we obtain what has traditionally been called the second order Cl wave function. Many other choices are possible. Since we have reduced the Cl space, we can use more active orbitals distributed over the three subspaces. Recent application have used more than 30 active orbitals. The RASSCF method has so far not be extensively used because there is no obvious way to treat dynamic correlation effects unless one can use the MRCI method. However, ongoing work attempts to extend the CASPT2 method (see below) to RASPT2, which may make the RASSCF method more useful in future applications (P.-A. Malmqvist, unpublished work). 

The RASSI method can be used to compute first and second order transition densities and can thus also be used to set up an Hamiltonian in a basis of RASSCF wave function with separately optimized MOs. Such calculations have, for example, been found to be useful in studies of electron-transfer reactions where solutions in a localized basis are preferred [43], The approach has recently been extended to also include matrix elements of a spin-orbit Hamiltonian. A number of RASSCF wave functions are used as a basis set to construct the spin-orbit Hamiltonian, which is then diagonalized [19, 44],... 

As for any full Cl expansion, the CASSCF becomes unmanageably large even for quite small active spaces. A variation of the CASSCF procedure is the Restricted Active Space Self-consistent Field (RASSCF) method. Here the active MOs are further divided into three sections, RASl, RAS2 and RAS3, each having restrictions on the... 

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