Quantum mechanics, semiempirical molecular orbital theory

Another approach which has become available in the past decade is the use of all-valence electron, semiempirical molecular orbital theory. This approximation of quantum mechanics makes it possible to calculate for fairly large molecules, a total energy behaving in an approximately parallel fashion to the true molecular energy. The consideration of all valence electrons makes this calculated total energy sensitive to the conformation of the molecule. Thus, energy minimization as a function of bond angle variation is possible, and the prediction of a preferred conformation is a consequence. 

With any type of molecular modeling, there is generally a tradeoff between cost and reliability, and one typically shuns models that cost more without increasing reliability. In practice, this cost is usually expressed as computational effort, or computer time. In gas phase modeling, one typically finds molecular mechanics and semiempirical molecular orbital theory at the low-cost end and multireference configuration interaction or coupled-cluster theory at the other, with the choice dictated by the size of the system. System size also influences the choice of solvation model. We consider first the least expensive models, those that take no account of the quantum mechanical nature of the solute. 

Thiel W 1996 Perspectives on semiempirical molecular orbital theory New Methods in Computationai Quantum Mechanics (Adv. Chem. Phys. XCIII) ed I Prigogine I and S A Rice (New York Wiley) pp 703-57 Earlier texts dealing with semi-empirical methods include ... 

Of the three primary computational chemistry tools, two (molecular mechanics and semiempirical molecular orbital theory) rely on embedded empirical parameters, while the third [ab initio quantum chemistry) is potentially capable of reproducing experiment without such parameters. Since the first two methods depend on the availability of reliable experimental data, they are best applied in situations requiring an interpolation between known experimental quantities. The quality of the fundamental parameters on which these models are based depends on the quality and quantity of experimental data. 

MOPAC is a general-purpose semiempirical molecular orbital program for the study of chemical structures and reactions. It is available in desktop PC running Windows, Macintosh OS, and Unix-based workstation versions. It uses semiempirical quantum mechanical methods that are based on Hartree-Fock (HF) theory with some parameterized functions and empirically determined parameters replacing some sections of the complete HF treatment. The approximations in... 

The topic of interactions between Lewis acids and bases could benefit from systematic ab initio quantum chemical calculations of gas phase (two molecule) studies, for which there is a substantial body of experimental data available for comparison. Similar computations could be carried out in the presence of a dielectric medium. In addition, assemblages of molecules, for example a test acid in the presence of many solvent molecules, could be carried out with semiempirical quantum mechanics using, for example, a commercial package. This type of neutral molecule interaction study could then be enlarged in scope to determine the effects of ion-molecule interactions by way of quantum mechanical computations in a dielectric medium in solutions of low ionic strength. This approach could bring considerable order and a more convincing picture of Lewis acid base theory than the mixed spectroscopic (molecular) parameters in interactive media and the purely macroscopic (thermodynamic and kinetic) parameters in different and varied media or perturbation theory applied to the semiempirical molecular orbital or valence bond approach [11 and references therein]. 

A number of studies have compared the use of the multiple regression technique using semiempirical parameters such as tt and o-, and parameters calculated for the particular molecules from molecular orbital theory. Hermann, Culp, McMahon, and Marsh (23) studied the relationship between the maximum velocity of acetophenone substrates for a rabbit kidney reductase. These workers were interested in the reaction mechanism, and two types of quantum chemical calculations were made (1) extended Huckel treatment, and (2) complete neglect of differential overlap (CNDO/2). Hydride interaction energy and approaching transition-state energies were calculated from the CNDO/2 treatment. All these parameters plus ir and a values were then subjected to regression analysis. The best results are presented in Table II. 

The agreement between theory and experiment for commonly computed properties can be judged from the data in Tables 6-8. These data were drawn from the literature. Ab initio calculations give results that are close to experiment on average. Since the semiempirical and ab initio tests were not done on identical sets of molecules, it is hard to evaluate exactly how much better ab initio is. Although an ab initio molecular orbital calculation is based on first principles, predictions from such a calculation are not necessarily better than those from some of the recent semiempirical molecular orbital or empirical force field methods. A carefully parameterized, general force field can, in fact, predict molecular geometries as well as or better than an ab initio MO calculation. Overall, however, molecular models built quantum mechanically will be quite realistic. 

The combined QM/MM model described so far is a general procedure that can be used in various quantum mechanical schemes, although some of the energy expressions have been given in the formalism of molecular orbital theory. Because a majority of the computational results reviewed in this chapter are obtained with the use of MO theory, especially semiempirical methods, some key features of these calculations are summarized here. The combined QM/MM approach has recently been applied with the use of density functional theory in molecular dynamics simulations °2,io3. a summary of the latter method is also given in this section. 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

A key question about the use of any molecular theory or computer simulation is whether the intermolecular potential model is sufficiently accurate for the particular application of interest. For such simple fluids as argon or methane, we have accurate pair potentials with which we can calculate a wide variety of physical properties with good accuracy. For more complex polyatomic molecules, two approaches exist. The first is a full ab initio molecular orbital calculation based on a solution to the Schrddinger equation, and the second is the semiempirical method, in which a combination of approximate quantum mechanical results and experimental data (second virial coefficients, scattering, transport coefficients, solid properties, etc.) is used to arrive at an approximate and simple expression. 

This is a semiempirical all-valence electron quantum mechanical method, apart from the Tr-approximation and the neglect of overlap integrals, as those of Hiickel molecular orbital (HMO) theory. The method reproduces, relatively well, the shapes and the order of the energy levels of molecular orbitals. To consider the overlapping, it is possible to describe the net destabilization caused by the interaction of the two doubly occupied orbitals, the effect of which is not reproduced by HMO theory. 

Semiempirical approaches to quantum chemistry are thus characterized by the use of empirical parameters in a quantum mechanical framework. In this sense, many current methods contain semiempirical features. For example, some high-level at initio treatments of thermochemistry employ empirical corrections for high-order correlation effects, and several advanced density functionals include a substantial number of empirical parameters that are fitted against experimental data. We shall not cover such approaches here, but follow the conventional classification by considering only semiempirical methods that are based on molecular orbital (MO) theory and make use of integral approximations and parameters already at the MO level. 

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