Configuration interaction CI method

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 >... 

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... 

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. 

The configuration interaction (ci) method dates back to the earliest days of quantum mechanics, and is the most straightforward and versatile approach for dealing with electron correlation. 

Of the methods which have been developed in recent years to calculate the potential energy surfaces of molecular systems, we have found the generalized valence bond (GVB) and derived configuration-interaction (CI) methods to be most useful. The GVB wavefunction provides a consistent theoretical description of molecules and their fragments and, as such, is well suited for studying the reactions of atoms and molecules. In addition, the GVB wavefunction is an orbital wavefunction this allows the features of the potential energy surfaces to be correlated with changes in the orbital structure of the system. 

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. 

Besides the traditional scheme, AIMD using semiempirical, Hartree-Fock, generalized valence bond (GVB), complete active space (CASSCF), and configuration interaction (CI) electronic structure methods have been realized. Several different variations concerning the basis set... 

In the classical method of configuration interaction (CI), the are evaluated variationally, that is, by minimizing the expectation value of the energy of the correlated wavefunction To as a function of the C. As noted before, if all excitations that are possible within the space of available occupied and virtual MOs are included, this procedure is called full Cl. One feature of this method is that the result is strictly independent of the form of the one-electron wavefunctions i that is, for open-shell systems it makes no difference if UHF or ROHF MOs are used or even if the AO coefficients c, in Eq. [1] have been optimized at all. For an infinitely large (i.e., a complete) basis set, a full Cl corresponds to an exact solution of the time-independent Schrodinger equa-... 

Two other types of basis set that have been used successfully in hfs calculations are Chipman s contracted [3s,2p] bases, and basis sets based on Slater type orbitals (STOs). The former of these is mainly used in single excitation configuration interaction (CIS) calculations, and are based on a very fortuitous cancellation of errors between method and basis set. The performance of the CIS/[3s,2p] approach lies within 20-25% of experiment. One should recall, though, that once we go to larger molecular systems, the CIS method becomes computationally very demanding, STOs have mainly been used in semiempirical INDO hfcc calculations (STO-SG) and in the density functional theory (DFT) studies of Ishii and Shimitzu (STO-6G). The number of hfcc studies using these basis sets at the ab initio or DFT levels is however to date very limited. 

In an ab initio approach, the first step is to solve the Hartree-Fock problem using a suitable basis set. In the Hartree-Fock model, each electron experiences only the average potential created by the other electrons. In reality, the instantaneous position of each electron, however, depends on the instantaneous position of the other electrons but the Hartree-Fock model cannot account for this electron correlation. In order to obtain quantitative results, electron correlation (also referred to as dynamical correlation) should be included in the model and there are many methods available for accomplishing this task based on either variational or perturbation principles. The easiest method to understand conceptually is variational configuration interaction (CI). In this method, the electronic wavefunction is expanded in terms of configurations that are formed from excitations of electrons from the occupied orbitals in the Hartree-Fock wavefunction to the virtual orbitals. The expansion can be written as... 

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