Self-consistent field method overview

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]. 

In this paper we present an overview of the various strategies developed to insert a quantum computation on the chemically active part of a large system into a molecular mechanical description, leading to the so-called QM/MM approaches, with a particular emphasis on the Local Self Consistent Field method developed in our group. 

We start out with a section on the energy functionals and Hamiltonians that are relevant for molecular systems interacting with a structured environment. We continue with a section that briefly describes the correlated electron structure method, the multiconfigurational self-consistent field (MCSCF) electronic structure method. In the following section we cover the procedure for obtaining the correlated MCSCF response equations for the two different models describing molecules in structured environments. The final sections provide a brief overview of the results obtained using the two methods and a conclusion. 

The present contribution concerns an outline of the response tlieory for the multiconfigurational self-consistent field electronic structure method coupled to molecular mechanics force fields and it gives an overview of the theoretical developments presented in the work by Poulsen et al. [7, 8, 9], The multiconfigurational self-consistent field molecular mechanics (MCSCF/MM) response method has been developed to include third order molecular properties [7, 8, 9], This contribution contains a section that describes the establisment of the energy functional for the situation where a multiconfigurational self-consistent field electronic structure method is coupled to a classical molecular mechanics field. The second section provides the necessary background for forming the fundamental equations within response theory. The third and fourth sections present the linear and quadratic, respectively, response equations for the MCSCF/MM response method. The fifth 283... 

Our approach uses essentially the same free energy functional as in many self-consistent field (SCF) calculations [18-21] (see also [22] for an excellent overview). In the past decade the SCF methods have been widely used for static calculations in various polymeric systems. The dynamic DFT approach complements the static SCF calculations by providing a detailed dynamical picture of system evolution, which is crucial, for example, for the investigation of metastable intermediate mesophases and for the study of the influence of shear and other processing conditions. 

Here we give an overview of the current status and perspectives of theoretical treatments of solvent effects based on continuum solvation models where the solute is treated quantum mechanically. It is worth noting that our aim is not to give a detailed description of the physical and mathematical formalisms that underlie the different quantum mechanical self-consistent reaction field (QM-SCRF) models, since these issues have been covered in other contributions to the book. Rather, our goal is to illustrate the features that have contributed to make QM-SCRF continuum methods successful and to discuss their reliability for the study of chemical reactivity in solution. 

The overview by Pleskov covers the literature on electrochemical behavior of synthetic diamond films, as well as the use of electrochemical methods in their characterization. The rapid advancement of the field of diamond electrochemistry was triggered by progress in the technology of deposition of polycrystalline diamond thin films on diamond and other substrates. Advances around the world have by now led to formation of a self-consistent, but as yet incomplete, view of electrochemical behavior of diamond. While discrepancies and scatter between data from different research groups still exist, the rapid advance in film quality and in reliable methods of evaluation point to a promising future. 

A short overview of the quantum chemical and statistical physical methods of modelling the solvent effects in condensed disordered media is presented. In particular, the methods for the calculation of the electrostatic, dispersion and cavity formation contributions to the solvation energy of electroneutral solutes are considered. The calculated solvation free energies, proceeding from different geometrical shapes for the solute cavity are compared with the experimental data. The self-consistent reaction field theory has been used for a correct prediction of the tautomeric equilibrium constant of acetylacetone in different dielectric media,. Finally, solvent effects on the molecular geometry and charge distribution in condensed media are discussed. 

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