Molecular electronic structure transferability

An important general motivation for the search for transferability of certain elements of molecular electronic structure is a well-known possibility to express the numerous experimental characteristics of molecules as additive functions of the increments of the respective characteristics attributable to the parts of these molecules. The most striking is the precision of this approach called the additive scheme . The sets of parameters describing heats of formation, dipole moments, polarizabilities etc. in terms of atomic and/or bond increments had been developed a long time ago, yet in the 40s and 50s of the last century. Clearly the classical MM theory [1,2] as we know it and as briefly described in Section 2.5 is a result of refining these concepts in the direction of including more and more subtle effects of geometry dependence. 

Previous attempts to sequentially construct additive systematics for molecular energies (which a fortiori include MM) reviewed in [20] had the following common points the transferability hypothesis, one-determinant approximation for the underlying QM wave function, and a posteriori localization of the orbitals. These features collectively prevented authors reviewed in [20] from constructing a sequential route from the QM description of the molecular electronic structure to any additive systematics. The reason is that the real derivation of any additive systematics must include both a proof of transferability and a procedure of defining the relevant local states (whether transferable or not). The derivation of MM from QM consists of several steps ... 

The fundamental reasons for the difficulties faced by the MM methods when metal (both transition and nontransition) complexes are involved can be understood if one does not consider the MM as a purely empirical scheme (as it is frequently done), but think about them as of some reflection of specific features of molecular electronic structure, formalized by the form of the trial wave function of that class of compounds where such a parameterization might be possible. As shown in Chapter 3, organic compounds for which the MM methods are known to demonstrate significant successes can be described by the QC method, which directly leads to local and transferable two-center bonds. It is shown in Chapter 3 that the derivation of the MM method from the QC description is possible due to a common background of the MM and SLG description, which consists in the physical presence of two-center, two-electron bonds in organic molecules (in strict terms of Section 1.7 - numbers of electrons in each of the geminals weakly fluctuate). 

While it is possible to develop MM parameters specifically for reactions, but this is highly laborious, and the resulting parameters may not be transferable. Also, the form of the potential function can impose serious limitations, such as the neglect of electronic polarization. Methods that take the fundamental quantum mechanics of electronic structure into account are more generally applicable. Quantum mechanical methods (i.e. methods to calculate molecular electronic structure) are often preferable and can be easier to apply than involved molecular mechanics type approaches. The major problem with electronic structure calculations on enzymes is the large computational resources required, which significantly limits the size of the system that can be treated. Quantum chemical approaches to modelling enzyme reactions are described in the next couple of sections. 

The adoption of different localization criteria does not lead to equivalent orbitals, as the given procedure usually applies iterative method. The iteration is repeated until the criterion chosen is fulfilled. In spite of this, LMOs obtained by different algorithms are quite similar. This similarity increases the hope, that a) the LMOs imply a serious, general (even interpretative) significance in the study of molecular electronic structure and b) the use of LMOs (especially their transferability property) might be helpful in studying extended/weakly interacting systems. 

It is certainly transferable to students, and the aim of this book is to encourage that process. By learning this method for the theoretical analysis of molecular electronic structure, a method which has so profoundly changed our approach to chemistry, the reader may be... 

Ab initio molecular dynamics simulations usually describe fluctuations of molecular electronic structures and can broaden knowledge of electric dipole moments, polarization processes, or possible charge-transfer effects, and complement classic MD methods. However, AIMD simulations are computationally demanding, and only relatively small systems of tens of ion pairs can be propagated over short time periods of tenths of picoseconds. These simulations typically begin from liquid state conflgurations that are equilibrated with classic MD using empirical interaction potentials. 

The molecular electronic structure methods described in Chapter 10 may be used to predict the spin density distribution in a radical. Recent EPR studies have shown that the amino acid tyrosine participates in a number of biological electron transfer reactions, including the processes of water oxidation to O2 in plant photosystem II and of O2 reduction to water in cytochrome c oxidase. During the course of these electron transfer reactions a tyrosine radical forms, with spin density delocalized over the side chain of the amino acid. 

Computer simulations of electron transfer proteins often entail a variety of calculation techniques electronic structure calculations, molecular mechanics, and electrostatic calculations. In this section, general considerations for calculations of metalloproteins are outlined in subsequent sections, details for studying specific redox properties are given. Quantum chemistry electronic structure calculations of the redox site are important in the calculation of the energetics of the redox site and in obtaining parameters and are discussed in Sections III.A and III.B. Both molecular mechanics and electrostatic calculations of the protein are important in understanding the outer shell energetics and are discussed in Section III.C, with a focus on molecular mechanics. 

The author would like to thank all the group members in the past and present who carried out all the researches discussed in this chapter Drs. C. Zhu, G. V. Mil nikov, Y. Teranishi, K. Nagaya, A. Kondorskiy, H. Fujisaki, S. Zou, H. Tamura, and P. Oloyede. He is indebted to Professors S. Nanbu and T. Ishida for their contributions, especially on molecular functions and electronic structure calculations. He also thanks Professor Y. Zhao for his work on the nonadiabatic transition state theory and electron transfer. The work was supported by a Grant-in-Aid for Specially Promoted Research on Studies of Nonadiabatic Chemical Dynamics based on the Zhu-Nakamura Theory from MEXT of Japan. 

From the early advances in the quantum-chemical description of molecular electron densities [1-9] to modem approaches to the fundamental connections between experimental electron density analysis, such as crystallography [10-13] and density functional theories of electron densities [14-43], patterns of electron densities based on the theory of catastrophes and related methods [44-52], and to advances in combining theoretical and experimental conditions on electron densities [53-68], local approximations have played an important role. Considering either the formal charges in atomic regions or the representation of local electron densities in the structure refinement process, some degree of approximate transferability of at least some of the local structural features has been assumed. 

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