Simulation of geometric and electronic degrees of freedom using a kink-based path integral.pdf

a r X i v : p h y s i c s / 0 5 0 2 1 1 2 v 1 [ p h y s i c s .c h e m - p h ] 2 1 F e b 2 0 0 5 Simulation of electronic and geometric degrees of freedom using a kink-based path integral formulation: application to molecular systems Randall W. Hall Department of Chemistry Louisiana State University Baton Rouge, La 70803-1804 (Dated: February 2, 2008) Abstract A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH4, NH3, and H2O demonstrate this method to be accurate for both geometries and energies. Comparison with DFT and MP2 level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results. 1 I. INTRODUCTION The development of simulation methods that are capable of treating electronic degrees of freedom at finite temperatures is necessary for the study of a variety of important systems including those with multiple isomers with similar energies (such as metal clus- ters) and with dynamic bond breaking/forming processes. A fundamental difficulty in using ab initio quantum approaches to study systems at finite temperatures is the need for most algorithms to solve a quantum problem (to find, for example, the ab initio forces) at each geometric configuration. Thus the CPU requirement per time or Monte Carlo step often prevents a simulation. Feynman’s path integral formulation of quantum mechanics[1] offers the possibility of simultaneously treating geometric and electronic de- grees of freedom without the restriction of solving a quantum problem for fixed atomic positions. In addition, temperature and electron-electron correlation can be included and make this approach very tempting as a starting point for ab initio simulations. An un- fortunate aspect of the path integral approach is t