Calculations of Electronic Potential Energy Surfaces

Roach, Alan C (1967) Calculations of Electronic Potential Energy Surfaces. PhD thesis, University of Glasgow.

Full text available as:
Download (10MB) | Preview


It is ordinarily possible to simplify the treatment of the dynamics of a general polyatomic system by first considering only the electronic motions, for all possible configurations of artificially fixed nuclei. Any particular electronic eigenvalue, as a function of nuclear geometry, then constitutes an effective potential energy surface, which governs the nuclear motion. The calculation of potential energy surfaces for practical systems represents a major quantum mechanical undertaking which in general becomes tractable only within a framework of approximation and semi empiricism. The major part of this thesis describes calculations developed to estimate the lower lying potential surfaces for the reactive system K + NaCl = KCl + Na. A model treatment is developed and discussed in detail. Essentially the problem is reduced to the consideration of the motion of a single electron in the fields of the closed shell ions Na+, K+ and Cl-. There is good evidence that these ions can be treated as classical polarisable charged spheres in their longer range electrostatic Interactions and also that their structures are not seriously modified by the presence of the single valence electron. The electronic eigenfunction is expanded in terms of a basis set of alkali atom valence s and p-orbitals The most difficult problem is the evaluation of certain close range interactions between the electron and the ions and this matter is discussed in detail. The electronic problem is first solved in neglect of the polarisation of the ion cores and this latter effect is afterwards Introduced, resulting in a first order perturbation correction to the energy surfaces. Empirical evidence used consists of values for ionic polarisabilities and radii, together with experimental ionisation potentials. A suitably reduced version of this model is applied to the calculation of potential curves for the diatomic ions Na2+ , K2+ and NaK+ and yields encouragingly close agreement with experimentally observed properties. The results for the complete system are presented and discussed. The reaction exothermicity is slightly overestimated. There is no calculated activation barrier, the reaction appearing to conform to the "early downhill" classification. A potential well indicates that, If the excess energy were removed, a triangular complex molecule could be formed, some 13 Kcal more stable than the product. Finally there appears to be some qualitative evidence that highly energetic collisions of the reactants may lead to electronically excited product atoms, a phenomenon observed experimentally for the reaction Na+ KBr = NaBr + K. The shorter second part of the thesis presents an estimate of the Jahn-Teller effect in rhenium hexafluoride. This effect arises from the coupling between electronic and nuclear motions when two or more potential surfaces have the same energy in a non linear symmetrical configuration. In such cases the degeneracy is relieved by certain vibrational displacements, leading to a distortion in the equilibrium geometry and a complication of the vibrational spectrum. In rhenium hexafluoride it is assumed that this effect arises from a purely electrostatic Interaction between the fluorine atoms and the non-bonding 5d rhenium electron in a degenerate. r8 state arising from strong spin orbit coupling of the t2g configuration. The electrostatic potential of a fluorine atom is taken as that of a fluoride ion less some variable fraction of an electron, depending on bond ionicity, taken from a hybrid orbital directed towards the central rhenium atom. The rhenium 5d orbital is taken of Slater form with variable exponent. The results, which depend essentially on the potential surface gradients in the octahedral configuration are relatively insensitive to physically reasonable choices of these parameters. A large splitting in the V2 band of the Raman spectrum is predicted, in good order of magnitude agreement with experiment. There is a corresponding very small distortion of the molecular geometry calculated, probably in a tetragonal sense.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: Physical chemistry, Computational chemistry
Date of Award: 1967
Depositing User: Enlighten Team
Unique ID: glathesis:1967-78446
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 30 Jan 2020 15:22
Last Modified: 30 Jan 2020 15:22

Actions (login required)

View Item View Item


Downloads per month over past year