Electronic structure quantum-mechanical approach

In a recent upsurge of studies on electron transfer kinetics, importance was placed on the outer shell solvent continuum, and the solvent was replaced by an effective model potential or a continuum medium with an effective dielectric constant. Studies in which the electronic and molecular structure of the solvent molecules are explicitly considered are still very rare. No further modem quantum mechanical studies were made to advance the original molecular and quantum mechanical approach of Gurney on electron and proton (ion) transfer reactions at an electrode. 

Jolibois F, Cadet J, Grand A, Subra R, Rega N, Barone V (1998) Structures and spectroscopic characteristics of 5,6-dihydro-6-thymyl and 5,6-dihydro-5-thymyl radicals by an integrated quantum mechanical approach including electronic, vibrational, and solvent effects. J Am Chem Soc 120 1864-1871... 

Unlike molecular mechanics, the quantum mechanical approach to molecular modelling does not require the use of parameters similar to those used in molecular mechanics. It is based on the realization that electrons and all material particles exhibit wavelike properties. This allows the well defined, parameter free, mathematics of wave motions to be applied to electrons, atomic and molecular structure. The basis of these calculations is the Schrodinger wave equation, which in its simplest form may be stated as ... 

Owing to recent developments in theoretical and computational methods, the quantum mechanical approach to the polymer electronic structure problem has begun to associate very fruitfully with experimental research in this field. Combination of the methods of molecular quantum theory with the ideas of theoretical solid-state physics has provided a really efficient tool, not only for the interpretation of experimental results, but also for investigation of fine details in the electronic structure which would be only barely accessible in experiments. 

This chapter describes computational strategies for investigating the species in the catalytic cycle of the enzyme cjdochrome P450, and the mechanisms of its main processes alkane hydroxylation, alkene epoxidation, arene hydroxylation, and sulfoxidation. The methods reviewed are molecular mechanical (MM)-based approaches (used e.g., to study substrate docking), quantum mechanical (QM) and QM/MM calculations (used to study electronic structure and mechanism). 

As indicated before, the ab initio electronic-structure theory of solid-state materials has largely profited from density-functional theory (DFT), and the performance of DFT has turned out well even when the one of its molecular quantum-chemical competitors - Hartree-Fock theory - has been weakest, namely for metallic materials. For these, and also for covalent materials, DFT is a very reasonable choice. On the other hand, ionic compounds (with both metals and nonmetals present) are often discussed using only the ionic model, on which most of Section 1.2 was based, and the quantum-mechanical approach is not considered at all, at least in introductory textbooks. Nonetheless, let us see, as a first instructive example, how a t5q)ical ionic material can be described and understood by the ionic and the quantum-chemical (DFT and HF) approaches, and let us also analyze the strengths and weaknesses. 

The second advantage of the quantum-mechanical approach to biochemistry and biophysics resides in the possibility that it offers to precede experimentation in a number of fields in which this experimentation seems to be particularly difficult to carry out. Thus, the calculations frequently permit determining the values (more or less exact values, according to the degree of refinement of the calculations) of a series of physicochemical characteristics of molecular systems which seem to be at present beyond the possibilities of experimental determination, or which are at least very difficult to measure presently. Among these characteristics are e.g., dipole moments, ionization potentials, electron affinities, resonance energies, etc., all of which are fundamental quantities for the understanding of the physicochemical properties of molecules. The calculation of these quantities frequently permits discovery and prediction of new correlations between structure and behaviour, and sometimes completely new aspects of biochemical problems. 

Other quantum mechanical approaches based on Gaussian wavepackets or coherent-state basis sets are those by Methiu and co-workers [46] and Martinazzo and co-workers [47] as well as the multiple spawning method developed by Martinez et al. [48] by which the moving wavepacket is expanded on a variable number of frozen Gaussians. Elsewhere [49] such an approach, especially conceived to be run on the fly, has been utilized for computing the ethylene spectrum by directly coupling it with electronic structure calculations. 

In essence, there are only two types of atomistic computational methodologies which are used for the prediction of materials properties, namely (1) empirical potential (or force field) approaches which describe the interactions between atoms in a quasi-classical form avoiding any details of the electronic structure and (2) quantum mechanical methods which take into account the motions and interactions of the electrons in a material. If the approaches are based solely on fundamental physical constants such as the mass and charge of an electron and no atom-specific parameters are introduced, then the methods are called ab initio or first principles . (In the chemical literature, the term ab initio is sometimes reserved for Hartree-Fock-based methods whereas in solid state physics it typically refers to density functional methods.) Since quantum mechanical methods are not biased towards any particular atom or bonding type, they provide powerful predictive capabilities. On the other hand, the computational effort involved in ab initio methods is several orders of magnitude larger then in the case of empirical potentials. Therefore, both approaches, empirical potential methods and quantum mechanical approaches, have their place. 

Quantum mechanical formulation. By incorporating the essential elements of reaction field theory in conventional quantum mechanical approaches of molecular electronic structure theories, such as the Hartree-Fock self-consistent field (SCF) or density functional methods, the effects of solvation on the properties of molecules can be conveniently studied. The resulting techniques, generally referred to as self-consistent reaction field (SCRF) methods, consider the classical reaction field as a perturbation to the molecular Hamiltonian and write the latter simply as... 

Density-functional theory (DFT) is one of the most widely used quantum mechanical approaches for calculating the structure and properties of matter on an atomic scale. It is nowadays routinely applied for calculating physical and chemical properties of molecules that are too large to be treatable by wave-function-based methods. The problem of determining the many-body wave function of a real system rapidly becomes prohibitively complex. Methods such as configuration interaction (Cl) expansions, coupled cluster (CC) techniques or Moller Plesset (MP) perturbation theory thus become harder and harder to apply. Computational complexity here is related to questions such as how many atoms there are in the molecule, how many electrons each atom contributes, how many basis functions are... 

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