Semiempirical molecular orbital methods theory

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

The aim of this chapter is to provide an overview of the theories and methodologies governing MM of crystal structure and surfaces, growth morphology, and the effects of impurities and additives on crystallization. Different computational methods are used in these modelings, including ab initio or molecular orbital calculations, semiempirical methods, molecular mechanics, molecular dynamics, and Monte Carlo (MC) simulation. The reader is recommended to some excellent reference textbooks on the principles of MM and simulation (Hinchliffe 2003 Leach 2001 Myerson 1999). 

J. N. Murrell and A. J. Harget, Semi-empirical Self-consistent Molecular Orbital Theory of Molecules, Wiley-Interscience, London, 1972 G. H. Wagniere, Introduction to Elementary Molecular Orbital Theory and to Semiempirical Methods, Springer-Verlag, Berlin, 1976 J. Sadleij, Semi-empirical Methods of Quantum Chemistry, Wiley, New York, 1985. 

G.H. Wagniere, Introduction to Elementary Molecular Orbital Theory and to Semiempirical Methods, 1976, Springer, Berlin. 

The AMI (8) approximation to molecular orbital theory has been used for these studies. This method overcomes the problems that previous semiempirical methods (notably, MNDO) (9) have in describing hydrogen-bonds. It has been used with success in several hydrogen-bonding studies. (10-12) Ab initio studies of H-bonding systems are very sensitive to basis set and correction for electron-... 

The methods available for computing enthalpies of formation fall into two general groups those based on purely empirical schemes and those founded on quantum chemistry. The quantum chemical methods can be further divided into three types ab initio molecular orbital theory, density functional theory, and semiempirical molecular orbital theory. A summary of the types of method used to calculate enthalpies of formation is given in Table 2, along with some specific examples. This is not meant to be a comprehensive tabulation, but rather a list of some of the more popular approaches in use today. Table 3 names some of the commercially available computer programs having capabilities to calculate thermochemical data. 

Semiempirical molecular orbital methods23-25 incorporate parameters derived from experimental data into molecular orbital theory to reduce the time-consuming calculation of two-electron integrals and correlation effects. Examples of semiempirical molecular orbital methods include Dewar s AMI, MNDO, and MINDO/3. Of the three quantum chemical types, the semiempirical molecular orbital methods are the least sophisticated and thus require the least amount of computational resources. However, these methods can be reasonably accurate for molecules with standard bond types. 

There are other shortcomings in semiempirical TDDFT that are not related to the self interaction. Semiempirical TDDFT has the same overall formalism and algorithmic structure as TDHF and the energy distribution of excited-state roots from these methods is much less dense than the exact distribution from FCI. In other words, while TDDFT is formally an exact theory for excited states (cf. Runge-Gross theorem [2]), semiempirical TDDFT has only one-electron excitations just as TDHF or CIS, which are the crudest approximations in excited-state molecular orbital theory. 

The most widely used semiempirical quantum chemistry technique for theoretical chemisorption studies is the Extended Hiickel Theory (EHT). The method was first proposed by Hoffmann/95/ in its nonrelativistic form, and by Lohr and Pyykko/96/ and also Messmer/97/ in its relativistic form, based on the molecular orbital theory for calculating molecular electronic and geometric properties. For a cluster the molecular orbitals are expanded as linear combinations of atomic orbitals... 

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. 

Huckel (properly, Huckel) molecular orbital theory is the simplest of the semiempirical methods and it entails the most severe approximations. In Huckel theory, we take the core to be frozen so that in the Huckel treatment of ethene, only the two unbound electrons in the pz orbitals of the carbon atoms are considered. These are the electrons that will collaborate to form a n bond. The three remaining valence electrons on each carbon are already engaged in bonding to the other carbon and to two hydrogens. Most of the molecule, which consists of nuclei, nonvalence electrons on the carbons and electrons participating in the cr... 

By ab initio we refer to quantum chemical methods in which all the integrals of the theory, be it variational or perturbative, are exactly evaluated. The level of theory then refers to the type of theory employed. Common levels of theory would include Hartree-Fock, or molecular orbital theory, configuration interaction (Cl) theory, perturbation theory (PT), coupled-cluster theory (CC, or coupled-perturbed many-electron theory, CPMET), etc. - We will use the word model to designate approximations to the Hamiltonian. For example, the zero differential overlap models can be applied at any level of theory. The distinction between semiempirical and ab initio quantum chemistry is often not clean. Basis sets, for example, are empirical in nature, as are effective core potentials. The search for basis set parameters is not usually considered to render a model empirical, whereas the search for parameters in effective core potentials is so considered. 

The underlying theoretical approach is characterized by the type of the wavefunction and the choice of the basis set. Most current general-purpose semiempirical methods are based on molecular orbital theory and employ a minimal basis set for the valence electrons. Electron correlation is treated explicitly only if this is necessary for an appropriate zero-order description (e.g., in the case of electronically excited states or transition states in chemical reactions). Correlation effects are often included in an average sense by a suitable representation of the two-electron integrals and by the overall parametrization. 

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