Self-consistent-field method advantages

Abstract Hybrid methods, combining the accuracy of Quantum Mechanics and the potency of Molecular Mechanics, the so-called QM/MM methods, arise from the desire of theoretician chemists to study electronic phenomena in large molecular systems. In this contribution, a focus, on the Physics and Chemistry on which theses methods are based on, is given. The advantages, flaws, and limitations of each type of methods are exposed. A special emphasis is put on the Local Self-Consistent Field method, developed in our group. The latest developments are detailed and illustrated by chosen examples. 

In addition to these experimental methods, there is also a role for computer simulation and theoretical modelling in providing understanding of structural and mechanical properties of mixed interfacial layers. The techniques of Brownian dynamics simulation and self-consistent-field calculations have, for example, been used to some advantage in this field (Wijmans and Dickinson, 1999 Pugnaloni et al., 2003a,b, 2004, 2005 Parkinson et al., 2005 Ettelaie et al., 2008). 

The flexibility of the valence bond self-consistent field (VBSCF) method can be exploited to calculate VB wave functions based on orbitals that are purely localized on a single atom or fragment. In such a case, the VBSCF wave function takes a classical VB form, which has the advantage of giving a very detailed description of an electronic system, as, for example, the interplay between the various covalent and ionic structures in a reaction. On the other hand, since covalent and ionic structures have to be explicitly considered for... 

Self-Consistent-Field The Open Shell SCF Case. The major point here is that the advantage of the Supermatrix methods is approximately halved over the closed shell case simply because one requires J and K matrices to be computed individually, necessitating the construction and use of 2 Supermatrices. Our present code based on the integral driven algorithm performs at 10.3 Mflops when processing cases described by Roothaan (22). 

Alternatively, reaction field calculations with the IPCM (isodensity surface polarized continuum model) [73,74] can be performed to model solvent effects. In this approach, an isodensity surface defined by a value of 0.0004 a.u. of the total electron density distribution is calculated at the level of theory employed. Such an isodensity surface has been found to define rather accurately the volume of a molecule [75] and, therefore, it should also define a reasonable cavity for the soluted molecule within the polarizable continuum where the cavity can iteratively be adjusted when improving wavefunction and electron density distribution during a self consistent field (SCF) calculation at the HF or DFT level. The IPCM method has also the advantage that geometry optimization of the solute molecule is easier than for the PISA model and, apart from this, electron correlation effects can be included into the IPCM calculation. For the investigation of Si compounds (either neutral or ionic) in solution both the PISA and IPCM methods have been used. [41-47]... 

In order to make a correct analysis of such an experimental spectrum, an appropriate theoretical calculation is indispensable. For this purpose, some of calculational methods based on the molecular orbital theory and band structure theory have been applied. Usually, the calculation is performed for the ground electronic state. However, such calculation sometimes leads to an incorrect result, because the spectrum corresponds to a transition process among the electronic states, and inevitably involves the effects due to the electronic excitation and creation of electronic hole at the core or/and valence levels. Discrete variational(DV) Xa molecular orbital (MO) method which utilizes flexible numerical atomic orbitals for the basis functions has several advantages to simulate the electronic transition processes. In the present paper, some details of the computational procedure of the self-consistent-field (SCF) DV-Xa method is firstly described. Applications of the DV-Xa method to the theoretical analysises of XPS, XES, XANES and ELNES spectra are... 

Many approximate self-consistent field molecular orbital schemes have been proposed, and the complete or partial neglect of differential overlap simplification has become widely accepted as a useful, but not too severe approximation to full ab initio methods. The advantages and justifications of the basic approximations in the CNDO and INDO method have been detailed by Pople ). Of course other considerations of time necessitate the use of empirical type calculations rather than full ab initio treatments when large numbers of calculations are required for series of molecules. 

In the 1980s and 1990s, multiconfigurational self-consistent field (MCSCF) reference perturbation theories [1-6,23-30] were proposed to overcome the defects of the singlereference PT and the QDPT, and now they are established as reliable methods that can be applied to wide variety of problems potential energies surfaces of chemical reactions, excited spectra of molecules, etc. In fact, they have many advantages ... 

A variety of pair approaches have been proposed and tested in applications which take advantage of the special properties of pair functions. All these methods are based on a reference or zeroth-order wavefunction i/zq and implicitly or explicitly assume the correlation effects to be relatively small. Until very recently 0 usually assumed to be a self-consistent field (SCF)... 

To summarize, the example of homopolymer/copolymer mixtmes demonstrates nicely how field-theoretic simulations can be used to study non-trivial fluctuation effects in polymer blends within the Gaussian chain model The main advantage of these simulations is that they can be combined in a natural way with standard self-consistent field calculations. As mentioned earlier, the self-consistent field theory is one of the most powerful methods for the theoretical description of polymer blends, and it is often accurate on a quantitative level hi many regions of the parameter space, fluctuations are irrelevant for large chain lengths (large Jf) and simulations are not necessary. Field-theoretic simulations are well suited to complement self-consistent field theories in those parameter regions where fluctuation effects become important. 

Finally, the third class of approaches encompasses all methods dealing with frozen electronic density (see Fig. 1.1c). Generally, the electronic density is obtained from orbitals (hybrid orbitals or localized molecular orbitals) determined on small molecules which contain the bond of interest [9,19,20], It is then possible to cut bonds of any polarity (P-0 in DNA for example), or multiphcity. It is even possible to cnt peptide bond, which represent a serious advantage for the study of proteins. The universality of these methods is however accompanied by an inherent coding complexity. Among these methods, the Local Self-Consistent Field approach (LSCF) developed in our group since more than fifteen years is detailed in the next section. 

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