TY - JOUR

T1 - Some coherent-states aspects of the electron nuclear dynamics theory

T2 - Past and present

AU - Morales, Jorge A.

N1 - Funding Information:
The author would like to thank Professor Rod Bartlett, Professor Sam Trickey, and the other organizers of the historical 50th Sanibel Symposium for their invitation to present a research talk at that event and to submit this article to the 50th Sanibel Symposium Special Edition of Molecular Physics. The author would like to thank his former PhD advisors: Professor N. Yngve Öhrn and Dr. Erik Deumens, for their past mentorship and support. The author is indebted to S. Ajith Perera, Thomas V. Grimes and Patrick M. McLaurin for their assistance to prepare the results of Fig. 1. Some of the present calculations were conducted in the Texas Tech University High Performance Computer Center. This material is based upon work partially supported by the National Science Foundation under grant CHE-0645374 (CAREER) and by the Robert A. Welch Foundation under grant D-1539. Also, acknowledgement is made to the donors of The American Chemical Society Petroleum Research Fund for partial support of this research.

PY - 2010/11/10

Y1 - 2010/11/10

N2 - Past and present coherent-states (CS) efforts with the electron nuclear dynamics (END) theory at its simplest level (SL-END) are reviewed. END is a time-dependent, variational, non-adiabatic, direct-dynamics method that describes simultaneously the nuclei and electrons of a molecular system. Within that characterization, SL-END adopts a classical-mechanics description for the nuclei and a quantum single-determinantal representation for the electrons. From its very inception, SL-END has been associated with the CS theory. CS sets are continuous and over-complete sets that satisfy the resolution of identity with a positive measure. Different CS sets can play an astonishing number of roles within SL-END that have several practical consequences. Originally, SL-END utilized the canonical and Thouless CS sets to correctly represent the nuclear and electronic parts of the SL-END wavefunction, respectively, thus defining a proper phase space for the SL-END dynamical equations. Later, canonical and rotational CS sets were used for reconstructing quantum vibrational and quantum rotational descriptions from the SL-END classical nuclear dynamics. That development proved essential to calculate state-resolved properties in ion-molecule and atom-molecule collisions with SL-END. Present CS efforts include a time-dependent Kohn-Sham density-functional-theory direct-dynamic method in the END framework and a CS approach to the charge-equilibration model inter alia.

AB - Past and present coherent-states (CS) efforts with the electron nuclear dynamics (END) theory at its simplest level (SL-END) are reviewed. END is a time-dependent, variational, non-adiabatic, direct-dynamics method that describes simultaneously the nuclei and electrons of a molecular system. Within that characterization, SL-END adopts a classical-mechanics description for the nuclei and a quantum single-determinantal representation for the electrons. From its very inception, SL-END has been associated with the CS theory. CS sets are continuous and over-complete sets that satisfy the resolution of identity with a positive measure. Different CS sets can play an astonishing number of roles within SL-END that have several practical consequences. Originally, SL-END utilized the canonical and Thouless CS sets to correctly represent the nuclear and electronic parts of the SL-END wavefunction, respectively, thus defining a proper phase space for the SL-END dynamical equations. Later, canonical and rotational CS sets were used for reconstructing quantum vibrational and quantum rotational descriptions from the SL-END classical nuclear dynamics. That development proved essential to calculate state-resolved properties in ion-molecule and atom-molecule collisions with SL-END. Present CS efforts include a time-dependent Kohn-Sham density-functional-theory direct-dynamic method in the END framework and a CS approach to the charge-equilibration model inter alia.

KW - coherent-states theory

KW - direct-dynamics method

KW - electron nuclear dynamics theory

UR - http://www.scopus.com/inward/record.url?scp=78649552238&partnerID=8YFLogxK

U2 - 10.1080/00268976.2010.512568

DO - 10.1080/00268976.2010.512568

M3 - Article

AN - SCOPUS:78649552238

SN - 0026-8976

VL - 108

SP - 3199

EP - 3211

JO - Molecular Physics

JF - Molecular Physics

IS - 21-23

ER -