Complex self-consistent field

J.F. McNutt, C.W. McCurdy, Complex self-consistent-field and configuration-interaction studies of the lowest 2P resonance state of lie, Phys. Rev. A 27 (1983) 132. 

We close these introductory remarks with a few comments on the methods which are actually used to study these models. They will for the most part be mentioned only very briefly. In the rest of this chapter, we shall focus mainly on computer simulations. Even those will not be explained in detail, for the simple reason that the models are too different and the simulation methods too many. Rather, we refer the reader to the available textbooks on simulation methods, e.g.. Ref. 32-35, and discuss only a few technical aspects here. In the case of atomistically realistic models, simulations are indeed the only possible way to approach these systems. Idealized microscopic models have usually been explored extensively by mean field methods. Even those can become quite involved for complex models, especially for chain models. One particularly popular and successful method to deal with chain molecules has been the self-consistent field theory. In a nutshell, it treats chains as random walks in a position-dependent chemical potential, which depends in turn on the conformational distributions of the chains in... 

Unlike reactive diatomic chalcogen-nitrogen species NE (E = S, Se) (Section 5.2.1), the prototypical chalcogenonitrosyls HNE (E = S, Se) have not been characterized spectroscopically, although HNS has been trapped as a bridging ligand in the complex (HNS)Fc2(CO)6 (Section 7.4). Ab initio molecular orbital calculations at the self-consistent field level, with inclusion of electron correlation, reveal that HNS is ca. 23 kcal mof more stable than the isomer NSH. There is no low-lying barrier that would allow thermal isomerization of HNS to occur in preference to dissociation into H -1- NS. The most common form of HNS is the cyclic tetramer (HNS)4 (Section 6.2.1). 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

Self-consistent field molecular orbital calculations by Fenske and coworkers have confirmed that nucleophilic additions to Fischer and related complexes [e.g., (CO)sCr=CXY, (T)5-C5H5)(CO)2Mn=CXY], are frontier orbital-controlled rather than charge-controlled reactions (7-9). Interaction of the HOMO of the nucleophile with the carbene complex LUMO (localized on Ca) destroys the metal-carbon w-interaction and converts the bond to a single one. 

It is evident that the approach described so far to derive the electronic structure of lanthanide ions, based on perturbation theory, requires a large number of parameters to be determined. While state-of-the-art ab initio calculation procedures, based on complete active space self consistent field (CASSCF) approach, are reaching an extremely high degree of accuracy [34-37], the CF approach remains widely used, especially in spectroscopic studies. However, for low point symmetry, such as those commonly observed in molecular complexes, the number of CF... 

Meijer, L. A., Leermakers, F. A. M. and Lyklema, J. (1999). Self-consistent-field modeling of complex molecules with united atom detail in inhomogeneous systems. Cyclic and branched foreign molecules in dimyristoylphosphatidylcho-line membranes, J. Chem. Phys., 110, 6560-6579. 

The selection of configuration state functions to be included in MCSCF calculations is not a trivial task. Two approaches which can reduce the complexity of the problem are the complete active space self-consistent-field (CASSCF) [68] and the restricted active space self-consistent-field (RASSCF) [69] approach. Both are implemented in the Dalton program package [57] and are used in this study. Throughout the paper a CASSCF calculation is denoted by i active gactive RASSCF calculation by For the active spaces of HF, H2O, and CH4... 

A successful theoretical description of polymer brushes has now been established, explaining the morphology and most of the brush behavior, based on scaling laws as developed by Alexander [180] and de Gennes [181]. More sophisticated theoretical models (self-consistent field methods [182], statistical mechanical models [183], numerical simulations [184] and recently developed approaches [185]) refined the view of brush-type systems and broadened the application of the theoretical models to more complex systems, although basically confirming the original predictions [186]. A comprehensive overview of theoretical models and experimental evidence of polymer bmshes was recently compiled by Zhao and Brittain [187] and a more detailed survey by Netz and Adehnann [188]. 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

In earlier theoretical studies Shen and coworkers used Hartree-Fock self-consistent-field (HF) calculations with different basis sets to study water complexes of anionic ONO—0 Two stable ONO—O isomers, cis and trans, formed hydrogen bonds with... 

In earlier theoretical studies Shen and coworkers used Hartree-Fock self-consistent-field (HF) calculations with different basis sets to study water complexes of anionic ONO—O-30. Two stable ONO—O isomers, cis and trans, formed hydrogen bonds with H2O molecules at different positions. Second-order Mpller-Plesset perturbation theory (MP2) with a 6-311+G(d,p) basis set has also been applied to the study of ONO—O-, (H2O), (n = 1 or 2) complexes31. Koppenol and Klasinc studied the cis and trans conformers as well as the transition state for torsional motion of ONO—O- at the HF/6-31(d) level32. In their calculations, the trans conformer is slightly more stable than the cis form, and the rotational barrier was thought to be quite high. However, correlated methods (MP2) were also used to study this molecule, and they predict that the cis conformer is more stable than the trans conformer33,34. 

This expression excludes self-interaction. There have been a number of attempts to include into the Hartree-Fock equations the main terms of relativistic and correlation effects, however without great success, because the appropriate equations become much more complex. For a large variety of atoms and ions both these effects are fairly small. Therefore, they can be easily accounted for as corrections in the framework of first-order perturbation theory. Having in mind the constantly growing possibilities of computers, the Hartree-Fock self-consistent field method in various... 

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