Semiempirical molecular orbital approximations

Ionization potentials of perfiuorinated diamines were calculated as energies of the highest occupied molecular orbitals using the MNDO-PM3 semiempirical molecular orbital approximation (26). Calculations were performed with MOPAC Ver.6 (27) program with a Sony News-830 work station. Bond lengths, bond angles, and edral angles were fully optimized within the MNDO-PM3 framework. 

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... 

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. 

More recently, an all valence electron, semiempirical molecular orbital theory known as the Complete Neglect of Differential Overlap (CNDO) has been proposed by Pople based on self-consistent field (SCF) formalism (5). Although this method uses a more sophisticated approximation of the wavefunction, it neglects differential overlap. 

Dynamics calculations of reaction rates by semiempirical molecular orbital theory. POLYRATE for chemical reaction rates of polyatomics. POLYMOL for wavefunctions of polymers. HONDO for ab initio calculations. RIAS for configuration interaction wavefunctions of atoms. FCI for full configuration interaction wavefunctions. MOLSIMIL-88 for molecular similarity based on CNDO-like approximation. JETNET for artificial neural network calculations. More than 1350 other programs most written in FORTRAN for physics and physical chemistry. 

In 1962, Sugano showed that the Seitz model (115) could be interpreted as a molecular orbital model (123), an interpretation that clarifies analysis of these systems. In this interpretation, the absorption bands observed in the TI(I) doped alkali halide system come from the electronic transition aigf a g) hu), but the excited states are still calculated assuming an ionic interaction between the metal and the hgand. Since the thallium-chlorine bond is actually largely covalent, Bramanti et al. (118) modified the approach and used a semiempirical molecular orbital (MO) calculation to describe the energy levels of T1(I) doped KCl. Molecular orbitals were constructed by the linear combination of atomic orbitals (LCAO) method from the 6s and 6p metal orbitals and the 3p chlorine orbitals. Initial calculations were conducted with the one-electron approximation the method was then expanded to include Coulomb and spin-orbit interactions. The results of Bramanti et al. were consistent with experimental... 

This brings us to the present volume, number 10. Here we point out an interesting evolution of pertinent journals in the field of computational chemistry that has been underway for two decades. Back in the old days, the two journals specializing in the field of what we now call computational chemistry were Theoretica Chemica Acta, founded in 1962, and the International Journal of Quantum Chemistry, founded in 1967. Both, as implied by their titles, focused on theoretical (pencil and paper) and computational quantum chemistry. Theoretica Chemica Acta tended to have papers reporting the results erf approximate semiempirical molecular orbital calculations. Routine molecular orbital studies can now be found in many journals, with perhaps one of the highest concentrations in the old issues of THEOCHEM, a journal started in 1981. In the meantime, Theoretica Chemica Acta tried to widen and strengthen its editorial stance by adding the subtitle A Journal for Structure, Dyrtamics, and Radiation in 1985. 

The Linear Combination of Atomic Orbitals (LCAO) approximation is fundamental to many of our current models of chemistry. Both the vast majority of the calculational programs that we use, be they ab initioy density functional, semiempirical molecular orbital, or even some sophisticated force-fields, and our qualitative understanding of chemistry are based on the concept that the orbitals of a given molecule can be built from the orbitals of the constituent atoms. We feel comfortable with the Ji-HOMO (Highest Occupied Molecular Orbital) of ethylene depicted as a combination of two carbon p-orbitals, as shown in Fig. 2.1, although this is not a very accurate description of the electron density of this Molecular Orbital (MO). The use of the Jt-Atomic Orbitals (AOs), however, makes it easier to understand both the characteristics of the MO itself and the transformations that it can undergo during reactions. 

In Chapter 1 Professors Zdenek Slanina, Shyi-Long Lee, and Chin-hui Yu discuss the timely topic of fullerenes and carbon aggregates. They show how ubiquitous semiempirical molecular orbital techniques need to be adjusted to correctly determine the three-dimensional geometries, energies, and properties of these species. Modern approximate methods prove useful for species too large for exploratory or routine ab initio work. Ab initio and mathematical studies of carbon clusters are also covered in the chapter. 

One way to keep the cost of the calculations low but improve the accuracy is to use semiempirical molecular orbital calculations in which some of the parameters are fit to data for the specific reaction of interest or for a limited range of reactions. We call this approach SRP for specific reaction parameters or specific range parameters. In several applications we have combined the SRP approach with semiempirical molecular orbital theory employing the neglect of diatomic differential overlap (NDDO) approximation. This is called the NDDO-SRP approach [49]. 

There have been a number of instances where EAs have been used to obtain approximate solutions to the Schrodinger equation. Zeiri et al. use a real-value encoding to aid in the calculation of bound states in a double well potential and in the non-linear density functional calculation. Rossi and Truhlar have devised a GA to fit a set of energy differences obtained by NDDO semiempirical molecular orbital theory to reference ab initio data in order to yield specific reaction parameters. The technique was applied to the reaction Cl -I- (THa. In a third example, Rodriguez et al. apply a GA to diagonalization of the... 

The KT approximation within the ab initio and semiempirical molecular orbital formalisms is unsatisfactory even for simple and well-studied organic molecules such as benzene and pyridine, as can be seen from the results presented in Table 1. 

Semiempirical molecular orbital calculations. These methods are based on the same or related quantum mechanical principles, but make approximations or assumptions to simplify the calculations. They include some empirical parameters based on experimental data. 

The logical order in which to present molecular orbital calculations is ab initio, with no approximations, through semiempirical calculations with a restricted number of approximations, to Huckel molecular orbital calculations in which the approximations are numerous and severe. Mathematically, however, the best order of presentation is just the reverse, with the progression from simple to difficult methods being from Huckel methods to ab initio calculations. We shall take this order in the following pages so that the mathematical steps can be presented in a graded way. 

Having the Slater atomic orbitals, the linear combination approximation to molecular orbitals, and the SCF method as applied to the Fock matrix, we are in a position to calculate properties of atoms and molecules ab initio, at the Hartree-Fock level of accuracy. Before doing that, however, we shall continue in the spirit of semiempirical calculations by postponing the ab initio method to Chapter 10 and invoking a rather sophisticated set of approximations and empirical substitutions... 

---