Configuration state function, CSF

MCSCF methods describe a wave function by the linear combination of M configuration state functions (CSFs), with Cl coefficients, Ck,... 

With this choice for H°, equations (7) and (8) are automatically valid for the perturbation. The only restriction is that we have to use orthogonal orbitals and Slater determinants rather than Configuration State Functions (CSFs) as a basis for the perturbation. None of these restrictions is constraining, however. 

Figure 2. The P,T-odd interaction constant versus the number of configuration state functions (CSFs) for the YbF molecule.

The basis of the expansion, ifra, are configuration state functions (CSF), which are linear combinations of Slater determinants that are eigenfunctions of the spin operator and have the correct spatial symmetry and total spin of the electronic state under investigation [42],... 

The CASSCF procedure (a special case of MC methods) is a full Cl calculation among all possible configuration state functions (CSFs), which arise from the distribution of a certain number of electrons (active electrons) in a certain... 

It has been demonstrated that a given electronic configuration can yield several space- and spin- adapted determinental wavefunctions such functions are referred to as configuration state functions (CSFs). These CSF wavefunctions are not the exact eigenfunctions of the many-electron Hamiltonian, H they are simply functions which possess the space, spin, and permutational symmetry of the exact eigenstates. As such, they comprise an acceptable set of functions to use in, for example, a linear variational treatment of the true states. 

The resultant family of six electronic states can be described in terms of the six configuration state functions (CSFs) that arise when one occupies the pair of bonding o and antibonding o molecular orbitals with two electrons. The CSFs are combinations of Slater determinants formed to generate proper spin- and spatial symmetry- functions. 

We shall not perform the somewhat elaborous calculation of the MC wave function in detail. A somewhat simpler example is the dissociation of a double bond and it is given as an exercise (exercise 2). Here we only note that the number of configuration state functions (CSF s) will increase very quickly with the number of active orbitals. In most cases we do not have to worry about the exact construction of the MC wave function that leads to correct dissociation. We simply use all CSFs that can be constructed by distributing the electrons among die active orbitals. This is the idea behind the Complete Active Space SCF (CASSCF) method. The total number of such CSFs is for N2 175 for a singlet wave function. A further reduction is obtained by imposing spatial symmetry. All these CSFs are not included in a wave... 

Most of the formalism to be developed in the coming sections of these lecture notes will be independent of the specific definition of the configurational basis, in which we expand the wave function. We therefore do not have to be very explicit about the exact nature of the basis states hn>. They can be either Slater determinants or spin-adapted Configuration State Functions (CSF s). For a long time it was assumed that CSF s were to be preferred for MCSCF calculations, since it gives a much shorter Cl expansion. Efficient methods like GUGA had also been developed for the solution of the Cl problem. Recent... 

Hess et al.119 utilized a Hamiltonian matrix approach to determine the spin-orbit coupling between a spin-free correlated wave function and the configuration state functions (CSFs) of the perturbing symmetries. Havriliak and Yarkony120 proposed to solve the matrix equation... 

The idea of CASVB is based on the fact that the densities of variational wave functions are invariant under the transformations which hold the variational space unchanged. In the CASSCF case, a complete active space (CAS) is invariant under the linear transformation of active orbitals and also that of configuration state functions (CSFs). 

We consider either singlet perturbations or triplet perturbations, which in Eq. (14) correspond to the + and - signs, respectively. In Eq. (15) the same distinction corresponds to interpreting A ) as a singlet or a triplet configuration state function (CSF). 

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