Configuration interaction coefficients

The configuration interaction coefficients can be obtained as a normalized eigenvector of the Hamiltonian matrix with elements given by... 

Clearly equation (64) is the familiar Cl expansion of a general A-fermion state and the parameters zj the configurational interaction coefficients. The normalization of these CSs is given by... 

The next step might be to perform a configuration interaction calculation, in order to get a more accurate representation of the excited states. We touched on this for dihydrogen in an earlier chapter. To do this, we take linear combinations of the 10 states given above, and solve a 10 x 10 matrix eigenvalue problem to find the expansion coefficients. The diagonal elements of the Hamiltonian matrix are given above (equation 8.7), and it turns out that there is a simplification. 

This is perhaps the easiest method to understand. It is based on the variational principle (Appendix B), analogous to the HF method. The trial wave function is written as a linear combination of determinants with the expansion coefficients determined by requiring that the energy should be a minimum (or at least stationary), a procedure known as Configuration Interaction (Cl). The MOs used for building the excited Slater determinants are taken from a Hartree-Fock calculation and held fixed. Subscripts S, D, T etc. indicate determinants which are singly, doubly, triply etc. excited relative to the... 

This reaction was investigated by Klippenstein and Harding [57] using multireference configuration interaction quantum chemistry (CAS + 1 + 2) to define the PES, variable reaction coordinate TST to determine microcanonical rate coefficients, and a one-dimensional (ID) master equation to evaluate the temperature and pressure dependence of the reaction kinetics. There are no experimental investigations of pathway branching in this reaction. 

A description as a MMCT transition is not very obvious for this case. However, there is no essential difference between the physical origin of the colors of Pb(N02)2 and, for example, CU2WO4. Unfortunately the literature shows sometimes discussions on the nature of their excited states in terms of either MMCT or metal-ion-induced CT transitions. To us, such a discussion does not seem to be very fruitful. In the classification it is a matter of taste which nomenclature is used, in the (more difficult) characterization it is essential to determine the coefficients which indicate the amount of configuration interaction. The latter describe the nature of the excited state. 

C4 hydrocarbons, presence of water in NaX, self-diffusion coefficients, 39 391-393 Chymotrypsin, 20 344, 356, 386, 387 Cl, see Configuration interaction Cirmarttaldehyde, hydrogenation of, 42 490... 

Table 2. Configuration interaction expansion coefficients for the wavefunctions...

The matrix elements of co can be calculated from the expansion coefficient of the ab initio configuration interaction method. The Cl wavefunction with single and double excitations can be written... 

Configuration Interaction Calculations. For the ground state of a molecule, the optimal coefficients for the MC wave function in Eq. 5 are those that cause F to satisfy the Schrodinger equation with the lowest energy. Other sets of coefficients that cause F to satisfy Eq. 1 give the wave functions for excited states of the molecule. 

Although shear rate effects are more pronounced in good solvents, the intrinsic viscosity decreases with shear rate even in 0-solvents, where excluded volume is zero (317,318). The Zimm model employs the hydrodynamic interaction coefficients in the mean equilibrium configuration for all shear rates, despite the fact that the mean segment spacings change with coil deformation. Fixman has allowed the interaction matrix to vary in an appropriate way with coil deformation (334). The initial departure from [ ]0 was calculated by a perturbation scheme, and a decrease with increasing shear rate in 0-systems was predicted to take place in the vicinity of / = 1. 

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