Configuration state,

Given a set of A -electron space- and spin-synnnetty-adapted configuration state fiinctions in tenns of which is to be expanded as T = S. Cj two primary questions arise (1) how to detemiine the 9 coefficients and the energy E and (2) how to find the best spin orbitals ( ). ] Let us first consider the 1 where a single configuration is used so only the question of detemiining the spin orbitals exists. 

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

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

Simulations need a substantial number of timesteps to sample configurational states such that desired properties are represented well enough to either con —100 ps. For systems of >100 atoms, mn for 500—2,000 ps if computing resources permit. 

Note that this is also a functional of liaAr), Cas(r), and 4 ). Imposing constraints concerning the orthonormality of the configuration state function (C) and one-particle orbitals (pi) on the equation, one can derive the Eock operator from. A based on the variational principle ... 

Figure 4.3 Forming configurational state functions from Slater determinants...

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],... 

T is expanded in a basis of time-reversal adapted configuration state functions [8] (TRA-CSFs, x F)... 

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... 

Figure 1.16 Positions of anionic ligands for various configurational states A = square-planar coordination B = octahedral coordination C = tetrahedral coordination. Cation nuclei are located in center of Cartesian coordinates.

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