Direct molecular dynamics, nuclear motion

Bound-state photoabsorption, direct molecular dynamics, nuclear motion Schrodinger equation, 365-373... 

Discrete Fourier transform (DFT), non-adiabatic coupling, Longuet-Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation, 153-155 Discrete variable representation (DVR) direct molecular dynamics, nuclear motion Schrodinger equation, 364-373 non-adiabatic coupling, quantum dressed classical mechanics, 177-183 formulation, 181-183... 

Nuclear motion Schrodinger equation direct molecular dynamics, 363-373 vibronic coupling, adiabatic effects, 382-384 electronic states ... 

At room temperature, these molecules occupy well-defined locations in their respective crystal lattices. However, they tumble freely and isotropically (equally in all directions) in place at their lattice positions. As a result, their solid phase NMR spectra show features highly reminiscent of liquids. We will see an illustration of this point shortly. Other molecules may reorient anisotropically (as in solid benzene). Polymer segmental motions in the melt may cause rapid reorientation about the chain axis but only relatively slow reorientation of the chain axes themselves. Large molecular aggregates in solution (such as surfactant micelles or protein complexes or nucleic acids) may appear to have solidlike spectra if their tumbling rates are sufficiently slow. There are numerous other instances in which our macroscopic motions of solid and liquid may be at odds with the molecular dynamics. Nuclear magnetic resonance is one of the foremost ways of investigating these situations. 

For larger systems, various approximate schemes have been developed, called mixed methods as they treat parts of the system using different levels of theory. Of interest to us here are quantuin-seiniclassical methods, which use full quantum mechanics to treat the electrons, but use approximations based on trajectories in a classical phase space to describe the nuclear motion. The prefix quantum may be dropped, and we will talk of seiniclassical methods. There are a number of different approaches, but here we shall concentrate on the few that are suitable for direct dynamics molecular simulations. An overview of other methods is given in the introduction of [21]. 

INS spectroscopy avoids this problematic feedback effect, in the sense that it measures nuclear motion directly. This provides a simple relation between the amplitude of the motion, the cross section of the nuclei and the vibrational frequency to determine the intensity and shape of the spectral lines. The electron density is, of course, used to determine the potential energy surface that controls the nuclear motion but it is not involved in the calculation of the spectra. The combined use of INS spectroscopy, ab initio calculations and ACLIMAX can provide a good test of the molecular model, assessing the quality of structure and dynamics. 

For a complete treatment of a laser-driven molecule, one must solve the many-body, multidimensional time-dependent Schrodinger equation (TDSE). This represents a tremendous task and direct wavepacket simulations of nuclear and electronic motions under an intense laser pulse is presently restricted to a few bodies (at most three or four) and/or to a model of low dimensionality [27]. For a more general treatment, an approximate separation of variables between electrons (fast subsystem) and nuclei (slow subsystem) is customarily made, in the spirit of the BO approximation. To lay out the ideas underlying this approximation as adapted to field-driven molecular dynamics, we will consider from now on a molecule consisting of Nn nuclei (labeled a, p,...) and Ne electrons (labeled /, j,...), with position vectors Ro, and r respectively, defined in the center of mass (rotating) body-fixed coordinate system, in a classical field E(f) of the form Eof t) cos cot). The full semiclassical length gauge Hamiltonian is written, for a system of electrons and nuclei, as [4]... 

If the molecule has dynamic motions on the timescale of the EPR experiment, this motion will lead to relaxation effects on the EPR line. Depending on the timescale and size of these motions, these effects may be observable directly in the cw-EPR spectrum or indirectly by pulsed EPR measurements of the relaxation times. In many cases, different dynamics may simultaneously contribute to the relaxation behavior of the electron spin system, as, for example, vibrational and rotational motion, conformational dynamics, phonon coupling to the frozen solvent, and nuclear spin dynamics. In these cases, it will be difficult to obtain specific information from these relaxation measurements. On the other hand, it is possible to highlight a specific time-scale window by the selection of pulse sequences and microwave frequencies that can lead, in favourable cases, to a direct relation between measured relaxation times and interesting molecular dynamics at the paramagnetic site. In these cases, very interesting molecular dynamical aspects of electron-transfer, catalytic, or photo-reactions, unobservable by other structural methods, can be studied directly by pulse-EPR techniques. 

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