Interaction and Localization of One-electron Orbitals in an Organic   Molecule: Fictitious Parameter Analysis for Multi-physics Simulations
  We present a new methodology to analyze complicated multi-physics simulations by introducing a fictitious parameter. Using the method, we study quantum mechanical aspects of an organic molecule in water. The simulation is variationally constructed from the ab initio molecular orbital method and the classical statistical mechanics with the fictitious parameter representing the coupling strength between solute and solvent. We obtain a number of one-electron orbital energies of the solute molecule derived from the Hartree-Fock approximation, and eigenvalue-statistical analysis developed in the study of nonintegrable systems is applied to them. Based on the results, we analyze localization properties of the electronic wavefunctions under the influence of the solvent. 
Toshiya Takami, Jun Maki, Jun-ichi Ooba, Taizo Kobayashi, Rie Nogita,   and Mutsumi Aoyagi