Configuration-interaction methods electronic structure calculations

Atextbook describing the theory associated with calculations of the electronic structure of molecular systems. While the book focuses on ab initio calculations, much of the information is also relevant to semi-empirical methods. The sections on the Hartree-Fock and Configuration Interactions methods, in particular, apply to HyperChem. The self-paced exercises are useful for the beginning computational chemist. 

In the RISM-SCF theory, the statistical solvent distribution around the solute is determined by the electronic structure of the solute, whereas the electronic strucmre of the solute is influenced by the surrounding solvent distribution. Therefore, the ab initio MO calculation and the RISM equation must be solved in a self-consistent manner. It is noted that SCF (self-consistent field) applies not only to the electronic structure calculation but to the whole system, e.g., a self-consistent treatment of electronic structure and solvent distribution. The MO part of the method can be readily extended to the more sophisticated levels beyond Hartree-Fock (HF), such as configuration interaction (Cl) and coupled cluster (CC). 

The Section on More Quantitive Aspects of Electronic Structure Calculations introduces many of the computational chemistry methods that are used to quantitatively evaluate molecular orbital and configuration mixing amplitudes. The Hartree-Fock self-consistent field (SCF), configuration interaction (Cl), multiconfigurational SCF (MCSCF), many-body and Mpller-Plesset perturbation theories,... 

Other theoretical studies of ozone and its excited states have been previously reported and also indicate a relatively low lying state corresponding to a six jr-electron cyclic structure. In particular, recent ab initio calculations using the generalized valence bond and configuration interaction methods with a double zeta basis set, predict that trioxirane lies about 35 kcal/mol higher in energy than ozone but that it is a potential minimum. 

Degeneracies of the SCF states are an obvious cause for breakdown of the approximation in the form discussed in the previous sections. We discuss now an extension of the method that applies to such cases, that is, to resonances and near-resonances between SCF modes. Just as the vibrational SCF method is an adaptation of the Hartree approximation from electronic structure calculations, so is the generalization discussed here an application of the configuration interaction (Cl) method, which uses for the wavefunctions a linear combination of the strongly interacting SCF states. Quantum Cl for polyatomic vibrations was introduced by Bowman and co-workers,7-21 the semi-classical version is due to Ratner et al.33... 

Presently, the widely used post-Hartree-Fock approaches to the correlation problem in molecular electronic structure calculations are basically of two kinds, namely, those of variational and those of perturbative nature. The former are typified by various configuration interaction (Cl) or shell-model methods, and employ the linear Ansatz for the wave function in the spirit of Ritz variation principle (c/, e.g. Ref. [21]). However, since the dimension of the Cl problem rapidly increases with increasing size of the system and size of the atomic orbital (AO) basis set employed (see, e.g. the so-called Paldus-Weyl dimension formula [22,23]), one has to rely in actual applications on truncated Cl expansions (referred to as a limited Cl), despite the fact that these expansions are slowly convergent, even when based on the optimal natural orbitals (NOs). Unfortunately, such limited Cl expansions (usually truncated at the doubly excited level relative to the IPM reference, resulting in the CISD method) are unable to properly describe the so-called dynamic correlation, which requires that higher than doubly excited configurations be taken into account. Moreover, the energies obtained with the limited Cl method are not size-extensive. 

Several sets of theoretical calculations have been performed on the parent ring system. HMO calculations of total rr-electron densities and frontier electron densities successfully predicted that the nucleus would undergo electrophilic substitution at the 6- and 8-positions. Two groups, " have compared the electronic structure of indolizine and various aza derivatives using the SCF or semiempirical antisymmetric configuration interaction method. The results allowed interpretations of the electronic spectrum to be made which were in good agreement with experiment. 

The conceptually simplest approach to solve for the -matrix elements is to require the wavefunction to have the form of equation (B3 4.4). supplemented by a bound function which vanishes in the as5miptote [32, 33, 34 and 35] This approach is analogous to the full configuration-interaction (Cl) expansion in electronic structure calculations, except that now one is expanding the nuclear wavefunction. While successful for intermediate size problems, the resulting matrices are not very sparse because of the use of multiple coordinate systems, so that this t5q)e of method is prohibitively expensive for diatom-diatom reactions at high energies. 

For most atomic and molecular states for which AREP calculations at the HF or post-HF levels are manageable, one can also perform two-component REP calculations. When spin-orbit interactions represented by the ESO of Eq.(6) are added in electronic structure calculations, the resulting electronic state may be called a fine-structure state. By definition, states calculated by the two-component REP methods are fine structure states unless special provision is made to produce spin-averaged configurations. At the HF level of theory starting from a single determinant, AREP and REP calculations may be performed for the identical configuration for a closed shell state, but that may not... 

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal enviromnent to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment. 

There is clearly no extension of (1) aiming at the description of correlation effects among all possible pairs of electrons—or better (spin) orbitals—within a product ansatz for the total wavefunction. As a consequence, pair theories have developed in various directions and were not a really uniform undertaking. Their development was, of course, intimately tied to other techniques of electronic structure calculations, such as the configuration-interaction (Cl) or perturbation theory methods. 

Mochizuki and Okamoto applied the Dirac program for the estimation of stabilities of trivalent actinide elements and water or ammine complexes (Mochizuki and Okamoto 2002). Mochizuki and Tatewaki (2002) also carried out the electronic structure calculation on the hexa-hydrated ions of curium and gadolinium. They used the Dirac program and also predicted the fluorescence transition energy using the Complete Open-Shell Configuration Interaction (COSCI) method. Even the hexa-hydrate curium ion needs 2,108 basis functions for the fully relativistic four-component calculation. 

Most popular in the ab initio calculation of intermolecular potentials is the so-called supermolecule method, because it allows the use of standard computer programs for electronic structure calculations. This method automatically includes all the electrostatic, penetration and exchange effects. If the calculations are performed at the SCF (self-consistent field) level the induction effects are included, too, but the dispersion energy is not. The latter, which is an intermolecular electron correlation effect, can be obtained by configuration interaction (Cl), coupled cluster (CC) calculations or many-body perturbation theory (MBPT). These calculations are all plagued... 

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