Coupled electronic and nuclear fluxes in molecules:
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| Anatole Kenfack | |
| Freie Universität Berlin | |
| We propose a new approach for evaluating combined nuclear and electronic fluxes in molecules[1]. This is based on the Born-Oppenheimer approximation (BO) [2] which is excellent for densities and time dependent molecular properties [3,4]- but which fails to reproduce electronic flux densities. Specifically, the electronic flux density is always zero in BO as the electronic wavefunction is real-valued. Here we circumvent this failure by means of both the Gauss's theorem and the continuity equation, that make possible the evaluation of fluxes in terms of integrals of electronic and nuclear densities. The accurate method (non-BO), that treats this problem in full dimensionality is until now still restricted to 3 or 4-body problems[4,5]. For the purposes of tracking fluxes in larger molecules, approximate and efficient approaches are thus essential[1]. We have applied the proposed approach to small molecules and discover novel effects of concerted electronic and nuclear fluxes which are in excellent agreement with the accurate method. In particular, for coherent vibrations of H2+ and D2+, we found that (i) the electronic flux is not zero, (ii) the electronic and the nuclear motions are not always synchronized as one would expect, (iii) the ratio of the magnitudes of the nuclear versus the electronic fluxes systematically increases with the amplitude of the nuclear motion. Movies of the coupled electronic and nuclear densities and densities support the present analysis of the concerted effects of the electronic and nuclear fluxes. Moreover we found that the initial state preparation[6] matters, depending on wether the process starts in the inner or the outer turning points. The nuclear flux exhibits high frequency oscillations in the inner starting regions that do not exist in the outer one. Likewise, the initial state affects the synchronicity as well as the directionality of both nuclear and electronic fluxes[7]. Our findings suggest further applications to large molecules and can help for instance to compute the electronic flux during a chemical reaction and to understand the influence of electron correlation on the fluxes. [1] I. Barth et al. Chem. Phys. Lett. (2009), doi:10.1016/j.cplett.2009.09.011 (in press) [2] M. Born, R. Oppenheimer, Ann. der Physik 84, 457 (1927). [3] M. F. Kling et al. Science 312, 246 (2006), A. D. Bandrauk et al. Phys. Rev. Lett. 101, 153901 (2008), H. Kono et al. Bull. Chem. Soc. Jpn. 79, 196 (2006). [4] F. Martin et al. Science 315, 629 (2007) [5] Chelkowsky et al. Phys. Rev. A 52, 2977 (1995), G. K. Paramonov, Chem. Phys. Lett. 411, 350 (2005) [6] W. Li et al. Science 322, 1207 (2008) [7] A. Kenfack et al. Phys. Rev. A., (in preparation) (2009) |