Orbital Theory Calculations

Molecular Orbital Theory—Electronic Structure Methods 

Electronic structure methods use the laws of quantum mechanics as their basis for computations. Quantum mechanics state that the energy and other related properties of a molecule may be obtained by solving the SchrOdinger equation  

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Rauk, A. Cannings, R., SUMO, A Simple Huckel Molecular Orbital Theory Calculator, http //www.chem.ucalgary.ca/SHMO/. 

Kubicki, J.D., Interpretation of vibrational spectra using molecular orbital theory calculations, in Molecular Modeling Theory Applications in the Geosciences, Cygan, R.T. and Kubicki, J.D., Eds., Geochemical Society of America, Washington, D.C., 2001, p. 459. 

W. G. Richards and D. L. Cooper, Ab Initio Molecular Orbital Theory Calculations for Chemists , Clarendon Press, Oxford, 1983. 

C. J. Cramer and D. G. Truhlar,/. Am. Chem. Soc., 113, 8552 (1991). Molecular Orbital Theory Calculations of Aqueous Solvation Effects on Chemical Equilibria. 

In any case, it must be kept in mind that bond multiplicities, or bond orders in current terms, do not usually coincide with bond orders of molecular orbital theory calculated from the a.o. coefficients in the expressions of the occupied m.o.s. This point will be resumed in Chapter 9 in the context of 7T bonding. 

Fukui et al.20), using the simple molecular orbital theory, calculated the stabilization energy arising from -conjugation in the transition state of radical and ionic polymerization of vinyl monomers. Further correlation of monomer structures with reactivities revealed that the rate constant of crosspropagation with one chosen active center increases with the basicity of the comonomer. 

Alkali and alkaline earth oxides are the best catalysts for the gasification reactions of carbon by CO2 and H2O, which are the bases of coal gasification processes. Because of its importance, a voluminous literature has been devoted to this area, and much progress has been made during the past over three decades toward an understanding of the mechanism of these catalyzed reactions, possible active intermediates, and phenomena involved in catalyst behaviors [80,81], Molecular orbital theory calculations were again found to be an effective tool in the investigation of catalyzed gas-carbon reactions. 

The Gaussian representation, of the numerical radial wave functions in atoms, is at the heart of modem molecular orbital theory. The different formulations are known as basis sets and the most common and proven basis sets are included in the various packages for molecular orbital theory calculations. In this book, the symbol sto-ng) identifies a linear combination of n Gaussian orbitals used, in the present context, to model the corresponding Slater function. 

Chapter 1 ended with a short survey of modem methodology in the application of Gaussian basis set theory to molecular orbital theory calculations. In real calculations it is standard to use a variety of larger basis sets tailored to particular applications (49) with the minimum basis sto-3g) sets widely used for general use and then these more complicated basis sets being applied to obtain better agreement with particular experimental results. 

Molecular orbital theory calculation on the hydrogen molecule ion... 

Static band-structure calculations have recently flourished due to developments in the accuracy and computational efficiency of density functional theory calculations [31]. These calculations were originally developed to evaluate the properties of solids, in a similar way to how molecular orbital theory calculations are used to evaluate the properties of molecules. From a reaction point of view, the electronic and atomistic properties of reactant, product, intermediate, and transition states can also be evaluated using these methods, allowing... 

Interpretation of Vibrational Spectra Using Molecular Orbital Theory Calculations... 

Figure 9.10. Potential energy as a function of internuclear distance from semi-empirical (INDO) molecular orbital theory calculation (see Chapter 8) (Chen and Yang, 1993, with permission). The absolute values from INDO are too high, but the relative values for different systems are correct. The edge plane is the zigzag edge.

For ab initio molecular orbital theory calculations on [NeBFf + at the HF/6-31G level, see [21]. 

Describe the electronic structure of each of the following, using molecular orbital theory. Calculate the bond or-... 

Cramer, C. Truhlar, D. G. (1991). Molecular orbital theory calculations of aqueous solvation effects on chemical equilibria. Journal of the American Chemical Society, 113, 8552. 

Calculations.—Molecular orbital theory calculations of complexes of borane (BH3) with such molecules as dimethyl ether, nitriles and isonitriles, and ammonia have been made. Ab initio calculations on systems of the types XNH3+, XCH3, and XBHs have been used to develop a theoretical approach to substituent effects.A genealogical electronic coupling procedure has been applied in calculations of the excited states of borane. ... 

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