Configuration interaction theory approach

In the following it will be outlined, how the parity violating potentials are computed within a sum-over-states approach, namely on the uncoupled Hartree-Fock (UCHF) level, and within the configuration interaction singles approach (CIS) which is equivalent to the Tamm-Dancoff approximation (TDA), that avoids, however, the sum over intermediate states. Then a further extension is discussed, namely the random phase approximation (RPA) and an implementation along similar lines within a density functional theory (DFT) ansatz, and finally a multi-configuration linear response approach is described, which represents a systematic procedure that... 

Real energy hermitian approaches. Extension of Fano s K-matrix, configuration interaction theory... 

Our group has already studied all the fluoro-, chloro-and bromo-carbenes [11-16]. We used the complete active space self-consistent field (CASSCF) method as well as complete active space second-order perturbation theory (CASPT2) and multi-reference configuration interaction (MRCI) approaches to compute the geometries, force constants, and vibrational frequencies of the (singlet) X and A states as well as the (triplet) a states. Our theoretical studies of most of these carbenes were carried out specifically to complement LIF studies that were pursued in our laboratories by Kable et al. [6]. In addition to the determination of spectroscopic constants, the spectroscopic and theoretical studies considered dynamics on the A surfaces, i.e. whether photodissociation or internal conversion to the ground state would occur. 

Transition metal elements are a real test of the efficacy of quantum chemical theories. Primarily, this is because many (if not most) of these systems have unpaired electrons, i.e., are open shell. Open shell systems therefore require additional approximations beyond standard Hartree-Fock theory to make the calculations tractable computationally. These include the UHF (unrestricted Hartree-Fock) and configuration interaction (Cl) approaches. Both approaches are computationally costly and have complicating considerations that make their general application more difficult and less straightforward. Also, it is often difficult to determine which spin state is the correct or natural one, and properties can vary substantially with differences in spin state. 

Wlien first proposed, density llinctional theory was not widely accepted in the chemistry conununity. The theory is not rigorous in the sense that it is not clear how to improve the estimates for the ground-state energies. For wavefiinction-based methods, one can include more Slater detenuinants as in a configuration interaction approach. As the wavellmctions improve via the variational theorem, the energy is lowered. In density fiinctional theory, there is no... 

Configuration interaction (Cl) is a systematic procedure for going beyond the Hartree-Fock approximation. A different systematic approach for finding the correlation energy is perturbation theory... 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

The difference between the Hartree-Fock energy and the exact solution of the Schrodinger equation (Figure 60), the so-called correlation energy, can be calculated approximately within the Hartree-Fock theory by the configuration interaction method (Cl) or by a perturbation theoretical approach (Mpller-Plesset perturbation calculation wth order, MPn). Within a Cl calculation the wave function is composed of a linear combination of different Slater determinants. Excited-state Slater determinants are then generated by exciting electrons from the filled SCF orbitals to the virtual ones ... 

Starting from the normal mode approximation, one can introduce anharmonicity in different ways. Anharmonic perturbation theory [206] and local mode models [204] may be useful in some cases, where anharmonic effects are small or mostly diagonal. Vibrational self-consistent-field and configuration-interaction treatments [207, 208] can also be powerful and offer a hierarchy of approximation levels. Even more rigorous multidimensional treatments include variational calculations [209], diffusion quantum Monte Carlo, and time-dependent Hartree approaches [210]. 

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