Ab Initio Calculation of Potential Energy Surfaces

To obtain information concerning a system of n electrons and N nuclei in the absence of external fields, one must solve the time-independent Schrodinger equation 

One can distinguish three levels of approximation in obtaining solutions to equation (l) a (i) the Bom-Oppenheimer approximation, often referred to as the 

Mathematically, this separation of the kinetic motions of the electrons and nuclei amounts to approximating the total wavefunction P (x, R) by a simple product of electronic and nuclear wavefunctions 

The electronic function y i(x, R) is obtained by solving the electronic Schrodinger equation for a fixed nuclear configuration, 

The use of the semi-colon in the notation y (x R) is to denote the explicit dependence of y i on the electronic space-spin co-ordinates x and its implicit dependence, along with Ei on the nuclear co-ordinates R. Clearly, the solution of equation (5) for all spatial arrangements of the nuclei will generate an energy (hyper)-surface, the 

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Ab initio Calculation of Potential Energy Surfaces where, for a closed-shell system... 

Because of the difficulties involved in ab initio calculations of potential-energy surfaces for reactions, it would be highly desirable to have a semiempirical method that gives reliable reaction PES results. The MNDO, AMI, and PM3 methods have been widely applied to calculate relevant portions of PESs for chemical reactions (often with inclusion of solvent effects) so as to elucidate reaction mechanisms and transition-state structures. 

Li, Q.-S., E. Zhang, W.-H. Eang, and J.-G Yu (2006), Probing mechanistic photochemistry of glyoxal in the gas phase by ab initio calculations of potential-energy surfaces and adiabatic and nonadiabatic rates, J. Chem. Phys., 124, 054324-1-054324-10. 

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