Direct self-consistent field theory

Most of these developments may be applied most directly within the framework of the isolated molecule method, in which the reactivity indices are the charges and self-polarizabilities of the unperturbed ground state of a given molecule calculations based on the localization model (e.g. Nesbet, 1962) have made less progress, and will not be considered. It is therefore natural to enquire whether indices similar to and tt,, in Hiickel theory can still be defined, and calculated more precisely, in self-consistent field theory. The obvious questions are... 

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

Ufimtsev, I.S., Martinez, T.J. Quantum chemistry on graphical processing units. 2. Direct self-consistent-field implementation. J. Chem. Theory Comput. 2009, 5(4), 1004-15. 

II. Second-order Direct Multiconfiguration Self-consistent Field Theory... 

II. SECOND-ORDER DIRECT MULTICONFIGURATION SELF-CONSISTENT FIELD THEORY... 

The self-consistent field theory phase diagram is also likely to be inaccurate at low relative molecular mass, because, like any mean-field theory, it neglects fluctuations. The effect of fluctuations is to stabilise the disordered phase somewhat (Fredrickson and Helfand 1987) in addition the seeond-order transition predicted for the symmetrical diblock is replaced by a first-order transition and, for asymmetrical diblocks, there are first-order transitions directly from the disordered into the hexagonal and lamellar phases. In addition it seems likely that fluctuations tend to stabilise high symmetry states such as the gyroid (Bates et al. 1994). 

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]. 

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

This book explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory, and generalized Sturmian basis functions and introduces methods which may be used to solve many-electron problems directly, without the use of the self-consistent-field approximation. ... 

Hartree s original idea of the self-consistent field involved only the direct Coulomb interaction between electrons. This is not inconsistent with variational theory [163], but requires an essential modification in order to correspond to the true physics of electrons. In neglecting electronic exchange, the pure Coulombic Hartree mean field inherently allowed an electron to interact with itself, one of the most unsatisfactory aspects of pre-quantum theories. Hartree simply removed the self-interaction by fiat, at the cost of making the mean field different for each electron. Orbital orthogonality, necessary to the concept of independent electrons, could only be imposed by an artificial variational constraint. The need for an ad hoc self-interaction correction (SIC) persists in recent theories based on approximate local exchange potentials. 

Direct ab initio methods, in which data are recomputed when required, rather than being stored and retrieved, provide an alternative that seems more useful for parallel development. The simplest level of ad initio treatment (self-consistent field methods) can be readily parallelized when direct approaches are being exploited. Experience demonstrates, however, that data replication methods will not lead to truly scalable implementations, and several distributed-data schemes (described later) have been tried. These general approaches have also been used to develop scalable parallel implementations of density functional theory (DFT) methods and the simplest conventional treatment of electron correlation (second-order perturbation theory, MP2) by several groups. 3-118... 

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