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The present project involves the development of an ab initio molecular dynamics method that combines coherent states (CS) and density functional theory (DFT) capabilities. In this approach, the CS theory supplies suitable over-complete sets to represent wave functions and express quantum dynamical equations in a classical-like format; reciprocally, DFT supplies a single determinant wavefunction with adequate description of electron correlation effects at low computational cost. In the resulting method, nuclei are described by a product of narrow, frozen Gaussian wave packets, while electrons are described by a single-determinantal Thouless CS in a Kohn-Sham fashion. The nuclear wavefunction can be separated into translational, rotational, and vibrational parts associated to quasi-classical CS; through that association, it is possible to reconstruct some degree of quantum description for the nuclei, especially in regard to rotational and vibrational transitions. This method improves some features of the celebrated Car-Parrinello method by providing: (a) An ab initio quantum Lagrangian, (b) a quasi-classical CS description of dynamical properties at initial and final times, and (c) a non-redundant representation of an electronic single-determinantal state that provides a generalized phase space for the electronic dynamics.

During the third and final year of this project, our research efforts concentrated on three areas of this approach:

(1) We successfully completed the implementation of the CS/DFT method into the code CSDYN 1.0, which supersedes our previous code CSTechG. CSDYN 1.0 has been developed from the ENDyne 2.7-2.8 program (E. Deumens) of the germane electron nuclear dynamics (END) theory, but it largely differs from that originating code. Significant features of CSDYN 1.0 include: (a) The implementation of single-determinantal Thouless CS capabilities within a DFT/Kohn-Sham framework; (b) the implementation of various interfaces with the ACES II program (J.F. Stanton, S.A. Perera, R Bartlett et al.) to utilize ACESS II’s DFT capabilities in a dynamical context; this interface will permit using coupled-cluster methods for dynamics in the future; (c) the implementation of auxiliary codes to calculate dynamical properties (transition probabilities, integral and differential cross sections, etc.) via CS theory, and (d) the implementation of visualization capabilities to prepare animations (movies) of the simulated reactions. CSDYN 1.0 successfully passed several tests during simulations of both intramolecular (rotations and vibrations of molecules: H₂, LiH, HF, H₂O, etc.) and intermolecular (reactive collisions: H⁺ + H₂, H⁺ + HF, etc.) processes; properties thus tested include: conservation of total momentum, angular momentum, energy, and number of electrons, and analyses of reactions’ final products. CSDYN 1.0 is ready for production and is being systematically applied to simulate more complex processes. A communication is in preparation to document the first implementation and preliminary results of CS/DFT. This will be followed by a comprehensive paper presenting that theory and its implementation in full detail along with applications to several important chemical processes.

(2) We continued developing a valence-bond(VB)/coherent-states(CS) approach to the charge equilibration (CE) model. Here, the classical-electrostatics CE model was obtained from a quantum VB model in conjunction with the CS theory. This project has proceeded in two successive stages corresponding to the VB and the CS theories, respectively. In the VB part (published, see publication report), a generalized CE (VB/GCE) model, which contains the CE model as a subcase, was derived from a two-electron, tree-state VB model via the sequential application of seven approximations. Unlike its CE subcase, this VB/GCE model provided a satisfactory charge-transfer description at dissociation as tested with the HF molecule. Through the previous derivation, CE charges and CE Coulomb interactions were elucidated in terms of VB Mulliken charges and VB atomic interactions, respectively. Modifications in the above derivation generated a family of related VB/GCE models that includes the aforesaid VB/GCE model. Despite their classical appearance, all the VB/GCE and CE models involved VB wavefunctions corresponding to ground and first-excited states. In the CS part, the quantum/classical-electrostatics connection implicit in the VB/GCE model was further elaborated by means of novel quasi-classical VB CS sets, whose time-dependent behavior obeys classical electrodynamics.

(3) We continued applying the above-mentioned CS capability to evaluate chemical reaction properties (differential and integral cross sections) from the final states of simulated dynamics. This CS capability utilizes the above-mentioned CS factorization to resolve the calculated properties into rotational, vibrational and electronic states. Applications of this CS procedure were conducted on the final states of END simulations of the following reactions: H⁺ + CF₄ at E_Lab = 20 and 30 eV (published, see publication report), and H⁺ + CO_, N_2, and NO at E_Lab = 30 eV (to be published).

The PI communicated several results of this project during his oral presentation: "Coherent-States Approach to Chemical Dynamics: From Proton-Molecule Reactions to Quantum/Classical Charge-Equilibration Models", at the American Chemical Society National Meeting, Washington DC, August 17, 2009.

In the third year, the present project involved the training and education of one chemistry graduate student and one undergraduate student (The latter being a female Hispanic student). In addition, the developed codes were employed as educational tools during the Summer Research Academy in Theoretical and Computational Chemistry (SRATCC) 2009, which is the second annual occurrence of this program. SRATCC 2009 was conducted in the Department of Chemistry and Biochemistry at Texas Tech University from June 15 to July 10, 2009. The PI of this grant was the main organizer of this program in collaboration with other professors in the department. SRATCC encourages broadening participation in theoretical and computational chemistry research for local high school students and teachers, especially from the Hispanic community. This year, five students and one teacher were again chosen from Estacado High School, Lubbock, Texas, to work alongside the participating professors on research projects supported by the American Chemical Society Petroleum Research Fund, the National Science Foundation, and the Welch Foundation. The high school participants presented the results of their research in a public session in the Department of Chemistry and Biochemistry on July 9, 2009, followed by a closing dinner.

At the closing of this grant, the Morales Research Group would like to thank the American Chemical Society Petroleum Research Fund for its generous financial support.