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** Combination of functionalities **

In the multiconfiguration SCF (MCSCF) method, one writes the molecular wave function as a linear combination of CSFs <5, and varies not only the expansion coefficients = 2, but also the forms of the molecular orbitals in the CSFs. [Pg.447]

In general, then, an MCSCF calculation involves a specification of what MOs may be occupied in the CSFs appearing in the expansion of Eq. (7.1). Given that specification, the formalism finds a variational optimum for the shape of each MO (as a linear combination of basis functions) and for the weight of each CSF in the MCSCF wave function. [Pg.206]

The Hy-CI function used for molecular systems is based on the MO theory, in which molecular orbitals are many-center linear combinations of one-center Cartesian Gaussians. These combinations are the solutions of Hartree-Fock equations. An alternative way is to employ directly in Cl and Hylleraas-CI expansions simple one-center basis functions instead of producing first the molecular orbitals. This is a subject of the valence bond theory (VB). This type of approach, called Hy-CIVB, has been proposed by Cencek et al. (Cencek et.al. 1991). In the full-CI or full-Hy-CI limit (all possible CSF-s generated from the given one-center basis set), MO and VB wave functions become identical each term in a MO-expansion is simply a linear combination of all terms from a VB-expansion. Due to the non-orthogonality of one-center functions the mathematical formalism of the VB theory for many-electron systems is rather cumbersome. However, for two-electron systems this drawback is not important and, moreover, the VB function seems in this case more natural. [Pg.189]

Exercise 4.5 There are six determinants with two doubly occupied orbitals, six Ms = 0 determinants can be constructed with all orbitals singly occupied and the distribution with one doubly occupied orbital, two singly occupied and one empty orbital can be realized in 24 different ways. The total CAS wave function is a linear combination of 36 different determinants. Note that the use of spin symmetry reduces the expansion to 20 CSFs for 5 = 0, 15 CSFs for 5 = 1 and 1 CSF for S = 2. [Pg.234]

** Combination of functionalities **

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