Electronic structure theory, electron nuclear dynamics

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

The introduction of the Bom-Oppenheimer approximation (BOA) set the stage for the development of electronic structure theory and molecular dynamics as separate disciplines. Certainly this separation has been fruitful and has in large measure fostered the rapid development of the fields. However, it is also clear that a comprehensive approach to chemistry must remain cognizant of the interplay between electronic structure and nuclear dynamics. Inferring dynamical behavior... 

Full quantum wavepacket studies on large molecules are impossible. This is not only due to the scaling of the method (exponential with the number of degrees of freedom), but also due to the difficulties of obtaining accurate functions of the coupled PES, which are required as analytic functions. Direct dynamics studies of photochemical systems bypass this latter problem by calculating the PES on-the-fly as it is required, and only where it is required. This is an exciting new field, which requires a synthesis of two existing branches of theoretical chemistry—electronic structure theory (quantum chemistiy) and mixed nuclear dynamics methods (quantum-semiclassical). 

In this minimal END approximation, the electronic basis functions are centered on the average nuclear positions, which are dynamical variables. In the limit of classical nuclei, these are conventional basis functions used in molecular electronic structure theory, and they follow the dynamically changing nuclear positions. As can be seen from the equations of motion discussed above the evolution of the nuclear positions and momenta is governed by Newton-like equations with Hellman-Feynman forces, while the electronic dynamical variables are complex molecular orbital coefficients that follow equations that look like those of the time-dependent Hartree-Fock (TDHF) approximation [24]. The coupling terms in the dynamical metric are the well-known nonadiabatic terms due to the fact that the basis moves with the dynamically changing nuclear positions. 

Each of the semi-classical trajectory surface hopping and quantum wave packet dynamics simulations has its pros and cons. For the semi-classical trajectory surface hopping, the lack of coherence and phase of the nuclei, and total time per trajectory are cons whereas inclusion of all nuclear degrees of freedom, the use of potentials direct from electronic structure theory, the ease of increasing accuracy by running more trajectories, and the ease of visualization of results are pros. For the quantum wave packet dynamics, the complexity of setting up an appropriate model Hamiltonian, use of approximate fitted potentials, and the... 

The simplest way to combine electronic stnicture calculations with nuclear dynamics is to use harmonic analysis to estimate both vibrational averaging effects on physico-chemical observables and reaction rates in terms of conventional transition state theory, possibly extended to incorporate tunneling corrections. This requires, at least, the knowledge of the structures, energetics, and harmonic force fields of the relevant stationary points (i.e. energy minima and first order saddle points connecting pairs of minima). Small anq)litude vibrations around stationary points are expressed in terms of normal modes Q, which are linearly related to cartesian coordinates x... 

A critical issue crossing all boundaries is the interaction of matter and radiation. Spectroscope experiments are used as both structural and dynamic probes and to initiate chemical processes (as in photochemistry and laser-induced chemistry), and such experiments must be understood theoretically. There are also many subfields of theoretical chemistry—for example, biomedical structure-activity relationships, the molecular theory of nuclear magnetic resonance spectra, and electron-molecule scattering—that fit into two or more of the areas listed. 

It is actually very difficult to solve the entire scheme down to Eq. (6.5) for systems of chemical interest, even if a very good set of >/) is available. (Note that electronic structure theory (quantum chemistry) can handle far larger molecular systems within the Born-Oppenheimer approximation) than the nuclear dynamics based on Eq. (6.5) can do.) This is because the short wavelength natme of nuclear matter wave blocks accurate computation and brings classical nature into the nuclear dynamics, in which path (trajectory) representation is quite often convenient and useful than sticking to the wave representation. Then what do the paths of nuclear dynamics look like on the occasion of nonadiabatic transitions, for which it is known that the nuclear wavepackets bifurcate, reflecting purely quantum nature. 

A combined electronic structure DFT/QND (density functional theory/quan-tum nuclear dynamics) study has been carried out by Gelabert et al. on the compressed dihydride complex [Cp lr(dmpm)H2], where dmpm denotes bis(dimethylphosphino)methane, with a goal to determine from the first-principles the unusual temperature dependence of the spin-spin coupling, Vhd, observed in its isotopomer [Cp Ir(dmpm)HD]. ... 

Transient vibrational dynamics. Perturbation theory yields an intuitive picture of adsorbate relaxation the loss of a vibrational quantum and associated nodal structure in the nuclear wave function is coupled to an irreversible transfer of momentum to the metallic electrons (see Fig. 2). To obtain time-resolved information about the dynamical processes at work, it is nonetheless necessary to go beyond this simple model. In the past decades, classical molecular dynamics has been hugely successful at shedding light on the transient vibrational evolution in a variety of adsorbate-surface systems (see, e.g., ref. 54-56). The methods of choice for including non-adiabatic effects on the dynamics can be divided in two main families friction-lype... 

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