Self-consistent field theory outline

Here, we present a general outline of the self-consistent field theory for polyelectrolyte solutions containing externally added salt ions. The theory is a generalization of the field theoretical formalism developed by Edwards [48-50] for neutral polymers to polyelectrolytes. We start from the path integral representation of a polymer chain and readers interested in the derivation of the path integral representation are referred to Ref [56]. 

A selection of the predictions of the equilibrium structure of DPPC bilayers as found by numerical self-consistent-field calculations is given in the following figures. In a series of articles, the SCF predictions for such membranes were published, starting in the late 1980s. As discussed above, we will update these early predictions for the theory outlined above with updated parameter sets. The calculations are very inexpensive with respect to the CPU time, and thus variations of the parameter-set will also provide deeper insight into the various subtle balances that eventually determine the bilayer structure - the mechanical properties as well as the thermodynamic properties. 

The description of electron motion and electronic states that is at the heart of all of chemistry is included in wave function theory, which is also referred to as self-consistent-field (SCF) or, by honouring its originators, Hartree-Fock (HF) theory [7]. In principle, this theory also includes density functional theory (DFT) approaches if one uses densities derived from SCF densities, which is common but not a precondition [2] therefore, we treat density functional theory in a separate section. Many approaches based on wave function theory date back to when desktop supercomputers were not available and scientists had to reduce the computational effort by approximating the underlying equations with data from experiment. This approach and its application to the elucidation of reaction mechanisms are outlined in Section 7.2.3. 

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... 

Calculation of spectroscopic and magnetic properties of complexes with open d shells from first principles is still a rather rapidly developing field. In this review, we have outlined the basic principles for the calculations of these properties within the framework of the complete active space self-consistent field (CASSCF) and the NEVPT2 serving as a basis for their implementation in ORCA. Furthermore, we provided a link between AI results and LFT using various parameterization schemes. More specifically, we used effective Hamiltonian theory describing a recipe allowing one to relate AI multiplet theory with LFT on a 1 1 matrix elements basis. 

Aspects of the relativistic theory of quantum electrodynamics are first reviewed in the context of the electronic structure theory of atoms and molecules. The finite basis set parametrization of this theory is then discussed, and the formulation of the Dirac-Hartree-Fock-Breit procedure presented with additional detail provided which is specific to the treatment of atoms or molecules. Issues concerned with the implementation of relativistic mean-field methods are outlined, including the computational strategies adopted in the BERTHA code. Extensions of the formalism are presented to include open-shell cases, and the accommodation of some electron correlation effects within the multi-configurational Dirac-Hartree-Fock approximation. We conclude with a survey of representative applications of the relativistic self-consistent field method to be found in the literature. 

The recent developments and ideas in the field of prebiotic chemistry can be combined with the concepts noted here to produce what we regard as a research outline, rather than a detailed hypothesis, directed toward a coherent theory of the origin of complex self-contained, self-replicating chiral assemblies. In what follows we present one possible scenario that is consistent with our current knowledge of chiral induction and amplification and with the nature of early Earth as well as early life. It is exciting that this fundamental question can be formulated in a way that allows systematic experimental testing as we enter the next century. 

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