Molecular structure semi-empirical approach

In this section we aim to introduce some of the main theoretical ideas which underlie the strategies for modelling liquid crystal molecules. It is clear that there are a very wide range of methods available and we will not attempt to be comprehensive. Instead, we will begin with a brief overview of traditional semi-empirical approaches and then progress to concentrate on treating fully predictive parameter-free calculations of molecular electronic structure and properties in some depth. 

Semi-empirical approaches are available to predict selected solid-state properties of thermoplastics from molecular structure. Example predictions for about 30 types of thermoplastics, including SAN copolymers, may be found elsewhere [34]. 

Properties such as photoconduc.tivityl l t l and photoluminescence of silicon polymers have been reported because of their wider optical band gap compared with crystalline silicon. Theoretical investigations of silicon polymers have been also reported ll2l-[21] Xakeda, Matsumoto and Fukuchi calculated the electronic structure of polysilane chains using the semi-empirical approach called the Complete Neglect of Differential Overlaps (CNDO) Molecular-Orbital (MO) method They discussed the dependence of the size and... 

Energy calculation and minimization One of the fundamental properties of molecules is their energy content and energy level. Three major theoretical computational methods in their calculation include empirical (molecular mechanics), semi-empirical and ab initio (quantum mechanics) approaches. Energy minimization results in geometry optimization of the molecular structure. 

In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semi-empirical models of electronic structure. Ab Initio approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semi-empirical methods, most of which also require access to a computer, are treated in this section and in Appendix F. 

Molecular orbital theory is a semi-empirical method devoted to interpreting the energy-level structure of optical centers where the valence electron cannot be considered as belonging to a specific ion. In our ABe reference center, this would mean that the valence electrons are shared by A and B ions. The approach is based on the calculation of molecular orbitals (MO) of the ABe pseudo-molecule, V mo, from various trial combinations of the individual atomic orbitals, V a and of the A and B ions, respectively. The molecular orbitals V mo of the center ABe are conveniently written in the form... 

As presented, semi-empirical methods are based on a single-configuration picture of electronic structure. Extensions of such approaches to permit consideration of more than a single important configuration have been made (for excellent overviews, see Approximate Molecular Orbital Theory by J. A. Pople and D. L. Beveridge, McGraw-Hill, New York... 

Although both the ab-initio derivative method and the semi-empirical sum-over-states approach have been used with some success to predict qualitative trends, they are not sufficiently developed to have predictive capabilities for structure-property relationship. Clearly, there is a need to develop semi-empirical theoretical methods which can reliably be used to predict, with cost-effectiveness and with reasonable computational time, molecular and polymeric structures with enhanced optical nonlinearity. 

Specific solute-solvent interactions, such as hydrogen bonding or protonation, may be included in the calculation of the shielding of solute nuclei by a supermolecule approach. The appropriate structure of the solute-solvent supermolecule may be obtained by the use of molecular mechanics simulations. At the semi-empirical MO level this approach has been successfully used to describe the effects of hydrogen bonding on the nuclear shielding of small molecules. 

The basis of molecular modeling is that all important molecular properties, i. e., stabilities, reactivities and electronic properties, are related to the molecular structure (Fig. 1.1). Therefore, if it is possible to develop algorithms that are able to calculate a structure with a given stoichiometry and connectivity, it must be possible to compute the molecular properties based on the calculated structure, and vice versa. There are many different approaches and related computer programs, including ab-initio calculations, various semi-empirical molecular orbital (MO) methods, ligand field calculations, molecular mechanics, purely geometrical approaches, and neural networks, that can calculate structures and one or more additional molecular properties. 

In the MO theory, the most reliable approach for the study of reaction pathways perhaps is CASSCF [12, 13], but multi-VBSCF is essentially at the same level with CASSCF [14]. Since a VB wave function can be expanded into the combination of numerous Slater determinants that are used to define configurations in the MO theory, the VB theory provides a very compact, accurate description for chemical reactions. While both MO and VB theories have their own advantages as well as disadvantages, in our opinions, there are some areas where the VB theory is particularly superior to the MO theory 1) the refinement of molecular mechanics force field 2) the development of empirical or semi-empirical VB approaches 3) the impact of intermolecular charge transfer or intramolecular electron delocalization on the structure and properties 4) the validation of classical chemical theories and concepts at the quantitative level 5) the elucidation of chemical reactions and excited states intuitively. 

---