Molecular orbitals semiempirical methods

Quantum-chemical calculations were carried out using the LabVision Software Package on a Silicon Graphics Iris Indigo workstation. The molecular orbital semiempirical method was performed using the AMI Hamiltonian. 

The semiempirical molecular orbital (MO) methods of quantum chemistry [1-12] are widely used in computational studies of large molecules. A number of such methods are available for calculating thermochemical properties of ground state molecules in the gas phase, including MNDO [13], MNDOC [14], MNDO/d [15-18], AMI [19], PM3 [20], SAMI [21,22], OM1 [23], OM2 [24,25] MINDO/3 [26], SINDOl [27,28], and MSINDO [29-31]. MNDO, AMI, and PM3 are widely distributed in a number of software packages, and they are probably the most popular semiempirical methods for thermochemical calculations. We shall therefore concentrate on these methods, but shall also address other NDDO-based approaches with orthogonalization corrections [23-25],... 

In principle there are three methods of calculation the ab initio molecular orbital (MO) method, the semiempirical MO method, and molecular mechanics. The choice depends on a number of factors such as the size of the molecule, the type of information required, and the budget. Whereas the ab initio method is the most basic and reliable quantum mechanical method,t the time requirement is so... 

The quantum mechanical methods described in this book are all molecular orbital (MO) methods, or oriented toward the molecular orbital approach ab initio and semiempirical methods use the MO method, and density functional methods are oriented toward the MO approach. There is another approach to applying the Schrodinger equation to chemistry, namely the valence bond method. Basically the MO method allows atomic orbitals to interact to create the molecular orbitals of a molecule, and does not focus on individual bonds as shown in conventional structural formulas. The VB method, on the other hand, takes the molecule, mathematically, as a sum (linear combination) of structures each of which corresponds to a structural formula with a certain pairing of electrons [16]. The MO method explains in a relatively simple way phenomena that can be understood only with difficulty using the VB method, like the triplet nature of dioxygen or the fact that benzene is aromatic but cyclobutadiene is not [17]. With the application of computers to quantum chemistry the MO method almost eclipsed the VB approach, but the latter has in recent years made a limited comeback [18],... 

In particularly thorough examples of the traditional physical organic approach, Parker (1969) and Abraham (1974) interpreted solvent effects on Walden inversion reactions by using thermodynamic transfer functions. However, in order to explain the reaction rate decrease upon solvation from a microscopic point of view, quantum mechanical electronic structure calculations must be carried out. Micro-solvated Sn-2 reactions were initially studied in this way, with the CNDO/2 semiempirical molecular orbital (MO) method, by using the supermolecule... 

Semiempirical molecular orbital (SEMO) methods have been used widely in computational studies [1,2]. Various reviews [3-6] describe the underlying theory, the different variations of SEMO methods, and their numerical results. Semiempirical approaches normally originate within the same conceptual framework as ab initio methods, but they overlook minor integrals to increase the speed of the calculations. The mistakes arising from them are compensated by empirical parameters that are introduced into the outstanding integrals and standardized against reliable experimental or theoretical reference data. This approach is successful if the semiempirical model keeps the essential physics and chemistry that describe the behavior of the process. 

In no case is an exo-endo isomerization at C-5 observed. This finding rules out a migration of C-5 with retention ( suprafacial retention, sr) in the bicyclopen-tene systems, a process calculated by semiempirical molecular orbital (MO) methods to be the favored one (28). The observed stereochemistry corresponds to an inversion at C-5 ( suprafacial inversion, si) and is in accord with the stereochemical requirements for an orbital symmetry controlled process. 

Over the past decades the semiempirical molecular orbital (MO) methods of quantum chemistry have been used widely in computational studies. Self-consistent-field (SCF) tr-electron calculations have been carried out since the 1950s and valence-electron calculations since the 1960s. Several books [1-8] and reviews [9-15] describe the underlying theory, the variants of semiempirical methods, and the numerical results in much... 

Most semiempirical molecular orbital methods are known to be inadequate to describe intermolecular interactions, especially on hydrogen bonding interactions because molecular polarizabilities are systematically underestimated in comparison with experiments. Recently, we introduced a polarized molecular orbital (PMO) method which is based on the formalism with... 

A question of philosophy arises concerning the molecular properties to be predicted by semiempirical treatments. On the one hand, the molecular orbital NDO methods were designed to mimic minimum basis set ab initio self-consistent field (SCF) property calculations parameters were chosen accordingly. Although internally consistent, this procedure is limited in accuracy by the minimum basis ab initio SCF results themselves. An alternative approach is to fit, and predia, measured physical properties. This is not internally consistent because experimental values cannot, in principle, be obtained from self-consistent field molecular orbital theory, regardless of basis set, because of the lack of elearon correlation. Furthermore, experimental values of properties obtained at room temperature cannot be equated to those calculated for 0° K. Nonetheless, the relatively high level of accuracy that can be achieved makes such an approach useful, and that is why it has been pursued by Dewar and co-workers in their series of M(odified)NDO methods. 

Stewart J J P 1991 Semiempirical molecular orbital methods Reviews in Computationai Chemistry vo 1, ed K B Lipkowitz and D B Boyd (New York VCH) pp 45-81... 

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 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. 

The cornerstone of semiempirical and ab initio molecular orbital methods is the Harhee equation and its extensions and variants, the Harhee-Fock and Roothaan-Hall equations. We have seen that the Hamiltonian for the hydrogen atom. 

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... 

A basis set is a set of functions used to describe the shape of the orbitals in an atom. Molecular orbitals and entire wave functions are created by taking linear combinations of basis functions and angular functions. Most semiempirical methods use a predehned basis set. When ah initio or density functional theory calculations are done, a basis set must be specihed. Although it is possible to create a basis set from scratch, most calculations are done using existing basis sets. The type of calculation performed and basis set chosen are the two biggest factors in determining the accuracy of results. This chapter discusses these standard basis sets and how to choose an appropriate one. 

One way that molecular mechanics methods have been adapted to transition metal applications is by including one orbital-based term in the force field to describe the metal center. These terms are typically based on semiempirical methods or even some variation of ligand field theory. 

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