Coupled self-consistent field calculations

Tab. 3.1 Selected vibrational energies (cm ) of H5OJ calculated by a variety of methods and experiment for the OH-monomer stretches. 2d+2d are the adiabatic 4d calculations of Ref [56], 4d are the fully coupled 4d calculations of Ref [27], CC-VSCF are the correlation-consistent vibrational self-consistent field calculations of Ref [58] and VCI are the virtual configuration interaction calculations of Ref [27]. The potential used in these calculations is indicated after the back-slash.

More recently gas-phase nitration was treated theoretically with MNDO (modified neglect of diatomic differential overlap) and INDO (intermediate neglect of differential overlap) self-consistent field calculations (34). Electron transfer and radical-pair recombination were favored for the nitration of toluene and the xylenes but not for nitrobenzene, for which a classical nitration route via a tt complex was favored. The calculations could not make a distinction between the two routes in the nitration of benzene. More information is needed about these coupling reactions and how they differ in the gas and heterogeneous-solution phases. 

The isodensity surface is varied in each iteration of the self-consistent field calculation. In each iteration the solute density is updated, and consequently, the isodensity surface used for the cavity is relaxed to the isodensity surface of the solvated molecule. However, it is important to realize that this process is not fully self-consistent with respect to the isodensity surface, since there are no direct terms in the Hamiltonian that couple the isodensity surface to the solute. 

MCSCF, multi-configuration self-consistent field calculations all calculations are without spin-oibit coupling Cerium-ring distance 2.08 A. 

Finally, we note that consideration of the interactions between the quantum motif atoms and classical region atoms must be given. This is true not only for the electrostatic interactions but also the shorter range repulsive and dispersive forces. In the case of the electrostatic effects a very good, and widely used, approximation is to assume that the classical charge centers within the classical region provide an external electric field to the quantum motif and this is simply coupled into the quantum self-consistant field calculation at every step using standard methods [45]. 

Guilleme, J. and San Fabian, J. (1998). Basis sets and active space in multiconfig-urational self-consistent field calculations of nuclear magnetic resonance spin-spin coupling constants. J. Chem. Phys., 109, 8168-8181. 

Multiconfiguration self-consistent-field calculations of hyperfine coupling constants. Journal of Chemical Physics, 97, 3412. 

As I have argued, errors are seldom computed by independent ab inito criteria in any of the calculations in theoretical chemistry which I discuss. Only the Self-Consistent Field calculations provide an upper bound whereas Many-Body Perturbation Theory and Coupled Cluster methods do not. More importantly perhaps, none of these methods computes a lower bound. As was remarked earlier the calculation of the ground state energies of atoms has been achieved to a remarkable degree of accuracy and similarly calculations on small or even medium sized molecules have given encouraging results. However, whether one can draw the conclusion that chemistry has been reduced rather depends on one s criteria of reduction. If we are to define approximate reduction as has been suggested in this paper then it must be concluded that chemistry is not even approximately reduced to quantum mechanics. The point I wish to emphasize is that we should not be misled by the apparent quantitative successes achieved and should appreciate the full nature of the approximation procedures employed. 

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). 

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. 

Besides the elementary properties of index permutational symmetry considered in eq. (7), and intrinsic point group symmetry of a given tensor accounted for in eqs. (8)-(14), much more powerful group-theoretical tools [6] can be developed to speed up coupled Hartree-Fock (CHF) calculations [7-11] of hyperpolarizabilities, which are nowadays almost routinely periformed in a number of studies dealing with non linear response of molecular systems [12-35], in particular at the self-consistent-field (SCF) level of accuracy. 

The combination of modem valence bond theory, in its spin-coupled (SC) form, and intrinsic reaction coordinate calculations utilizing a complete-active-space self-consistent field (CASSCF) wavefunction, is demonstrated to provide quantitative and yet very easy-to-visualize models for the electronic mechanisms of three gas-phase six-electron pericyclic reactions, namely the Diels-Alder reaction between butadiene and ethene, the 1,3-dipolar cycloaddition of fulminic acid to ethyne, and the disrotatory electrocyclic ringopening of cyclohexadiene. 

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Another more successful MO approach, referred to as INDO (intermediate neglect of differential overlap), avoids the average electronic energy approximation [115]. Its concept is a self-consistent field perturbation calculation. The INDO approach permits computation of one-bond carbon-13 coupling constants. The results obtained for JCH agree well with the experimental data for hydrocarbons and molecules with — F, —OR,... 

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