Molecular-orbital theory of a solute in a continuum with an arbitrarily shaped boundary represented by finite surface elements

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Abstract
A complete formalism is presented for the molecular-orbital study of a solute in a continuum. The Schrodinger equation of the solute in the solvent is derived from that for the entire solute-solvent system. An arbitrarily shaped cavity boundary is constructed using finite element techniques based on hexagonal and pentagonal surface elements and the induced charge on its surface calculated using analytical formulas for the electrostatic field strength. The Fock operator, which differs from one in widespread use, is modified by two terms resulting from variations in both the electrostatic field of the solute and the induced charges. An Austin Model 1 (AM1) version of the theory is developed with the addition of no new semiempirical parameters and illustrated with calculations on dimethyl ether and propane.