The integral Hellmann-Feynman theorem applied to hydrogen peroxide

Abstract

The integral Hellmann-Feynman (IHF) theorem developed by Y ~ [ t -7] has raised hopes that the origin of barriers to internal rotation could be isolated by ab-initio calculations. The me~hod is practicable for any moIecule for which a wavefunetion of reasonable quality is available. In such instances, the rotational barriers eaieulated by the I H F theorem ought to be comparable to or better than those obtained by the standard method of subtracting total SCF energies of the different conformations. To date, the successful application based on PITZER and LIPsco~a~'s [8] ethane wavefunetions has provided an eneouraging confirmation of the usefulness of the I H F approach [5, 6]. Very recently three sets of molecular orbitM wavefnnctions for the H202 molecule have become available: the LCAO-~O-SCF-STO wave functions of KaJ~DOR and S~VlTT [9], the LC(Double-Zeta)AO-~O-SCF functions with scaled hydrogens of FINK and ALL]~Zg [10, t l ] and the LCAO-M0-SCF functions of t )~KE and PITZEg [t2] using exponents optimized for H~O. Working independently, various workers have applied the I H F theorem to these wave functions: the first set has been treated by M]~L~osE and P~a~a~ [13], the second by FI~K and ALLEN [14], and the third by the present authors. In each case the resutSs for t~he cis-trans b~rrier are somewhat discouraging. Within the framework of self-consistent-field theory and the Born-Oppenheimer approximation, the IHF theorem gives the eis-trans barrier to internal rotation (A WIEF) as the sum of a nuclear-nuelear (A Vnn) and an electronic (AEe~) barrier. In particular (r v o v' .... r A W I H F = A V n . + 2 ~ I . , . , l