Configuration Interaction CI

The configuration interaction (CI) method in whieh the LCAO-MO eoeffieients are determined first (and independently) via either a single-eonfiguration SCF ealeulation or an MCSCF ealeulation using a small number of CSFs. The CI eoeffieients are subsequently determined by making the expeetation value < F H F >/< F I F >... 

A single-excitation configuration interaction (CIS) calculation is probably the most common way to obtain excited-state energies. This is because it is one of the easiest calculations to perform. 

The spectroscopic properties of [Pt(2,2, 6, 2-terpyridine)(C=CR)]+ (R=H, CH2OH, and C6H5) (5.6) were theoretically studied by Zhang et al. [101], The second-order Mpller-Plesset perturbation (MP2) was used to optimize the ground state and the single-excitation configuration interaction (CIS) method was employed to obtain the excited-state structure. The spectroscopic properties of the... 

Fig. 14 Schematic illustration of SOC and configuration interaction (CI) routes being relevant for substate i of the lowest triplet state T of 3LC character in a five (sub)state model, i stands for one of the substates I, II, or III, while j and k represent substates of higher lying 3MLCT states that can couple according to the selection rules as given in the text. Note that the 1>3MLCT1 and UMLCT2 states involve different d-orbitals, but the same n orbital...

Note that only the free-electron and Htickel models predict an absorption band in the visible in agreement with observation. While the orbital calculations in Ref. 4 are poor for polymethine dyes, they are in principle a superior approach and have given excellent results for saturated hydrocarbons. Indeed unsaturated molecules like the poly-methines can be very well modeled by the semiempirical configuration interaction (CIS) method. 

Tgj is represented exactly and the exact electronic energy, which also includes dispersion effects correctly, is obtained. However, this comes with infinite computational costs. Hence, methods needed to be devised, which allow us to approximate the infinite expansion in Eq. (12.9) by a finite series to be as short as possible. A straightforward approach is the employment of truncated configuration interaction (CI) expansions. Note that (electronic) configuration refers to the set of molecular orbitals used to construct the corresponding Slater determinant. It is a helpful notation for the construction of the truncated series in a systematic manner and yields a classification scheme of Slater determinants with respect to their degree of excitation . Excitation does not mean physical excitation of the molecule but merely substitution of orbitals occupied in the Hartree-Eock determinant o by virtual, unoccupied orbitals. Within the LCAO representation of molecular orbitals the virtual orbitals are obtained automatically with the solution of the Roothaan equations for the occupied orbitals that enter the Hartree-Eock determinant. 

Although HF theory is useful in its own right for many kinds of investigations, there are some applications for which the neglect of electron correlation or the assumption that the error is constant (and so will cancel) is not warranted. Post-Hartree-Fock methods seek to improve the description of the electron-electron interactions using HF theory as a reference point. Improvements to HF theory can be made in a variety of ways, including the method of configuration interaction (CI) and by use of many-body perturbation theory (MBPT). It is beyond the scope of this text to treat CI and MBPT methods in any but the most cursory manner. However, both methods can be introduced from aspects of the theory already discussed. 

This is the oldest and perhaps the easiest method to understand, and is based on the variational principle (Appendix B), analogous to the FIF 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 (CI). The MOs used for budding the excited Slater determinants are taken from a Hartree-Fock calculation and held fixed. Subscripts S, D,T, etc., indicate determinants that are Singly, Doubly,Triply, etc., excited relative to the HF configuration. 

Configuration Interaction (ci) expansions Approximations based on ci expansions include ci D, ci SD, etc., and their multireference variants mr-ci d, mr-ci SD, etc. 

---