Atomic motion

Cohen-Tannoud]i C 1991 Atomic motion in laser light Fundamental Systems in Quantum Optics ed J Dalibard et al (Oxford Elsevier)... 

Lagaiiy M G 1993 Atom motion on surfaces Physics Today 46 24... 

Phonons are nomial modes of vibration of a low-temperatnre solid, where the atomic motions around the equilibrium lattice can be approximated by hannonic vibrations. The coupled atomic vibrations can be diagonalized into uncoupled nonnal modes (phonons) if a hannonic approximation is made. In the simplest analysis of the contribution of phonons to the average internal energy and heat capacity one makes two assumptions (i) the frequency of an elastic wave is independent of the strain amplitude and (ii) the velocities of all elastic waves are equal and independent of the frequency, direction of propagation and the direction of polarization. These two assumptions are used below for all the modes and leads to the famous Debye model. 

As reactants transfonn to products in a chemical reaction, reactant bonds are broken and refomied for the products. Different theoretical models are used to describe this process ranging from time-dependent classical or quantum dynamics [1,2], in which the motions of individual atoms are propagated, to models based on the postidates of statistical mechanics [3], The validity of the latter models depends on whether statistical mechanical treatments represent the actual nature of the atomic motions during the chemical reaction. Such a statistical mechanical description has been widely used in imimolecular kinetics [4] and appears to be an accurate model for many reactions. It is particularly instructive to discuss statistical models for unimolecular reactions, since the model may be fomuilated at the elementary microcanonical level and then averaged to obtain the canonical model. 

As in any field, it is usefiil to clarify tenninology. Tliroughout this section an atom more specifically refers to its nuclear centre. Also, for most of the section the /)= 1 convention is used. Finally, it should be noted that in the literature the label quantum molecular dynamics is also sometimes used for a purely classical description of atomic motion under the potential created by tlie electronic distribution. 

The atom will therefore experience a net restoring force pushing it back to the origin. If the light beams are red detuned F, then the Doppler shift of the atomic motion will introduce a velocity-dependent tenn to the restoring force such that, for small displacements and velocities, the total restoring force can be expressed as the sum of a tenn linear in velocity and a tenn linear in displacement. 

Dalibard J and Cohen-Tannoudji C 1985 Dressed-atom approach to atomic motion in laser light the dipole force revisited J.Opt.Soc.Am. B 21707-20... 

Cook R J 1979 Atomic motion in resonant radiation an application of Earnshaw s theorem Phys.Rev. 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

Fig. 10. Conformational flooding accelerates conformational transitions and makes them accessible for MD simulations. Top left snapshots of the protein backbone of BPTI during a 500 ps-MD simulation. Bottom left a projection of the conformational coordinates contributing most to the atomic motions shows that, on that MD time scale, the system remains in its initial configuration (CS 1). Top right Conformational flooding forces the system into new conformations after crossing high energy barriers (CS 2, CS 3,. . . ). Bottom right The projection visualizes the new conformations they remain stable, even when the applied flooding potentials (dashed contour lines) is switched off.

A checkmark indicates the active vibra tion (only one vibration can be displayed at a time) Atom motions are exagger ated to make them easier to see... 

SpartanView can display atom motions that occur during a conformational change or chemical reaction... 

Electron-transfer reactions appear to be inherently capable of producing excited products when sufficient energy is released (154—157). This abiUty may be related to the speed of electron transfer, which is fast relative to atomic motion, so that vibrational excitation is inhibited (158). 

The idea of having two distinct quasi-Fermi levels or chemical potentials within the same volume of material, first emphasized by Shockley (1), has deeper implications than the somewhat similar concept of two distinct effective temperatures in the same block of material. The latter can occur, for example, when nuclear spins are weakly coupled to atomic motion (see Magnetic spin resonance). Quasi-Fermi level separations are often labeled as Im p Fermi s name spelled backwards. 

The X-ray and neutron scattering processes provide relatively direct spatial information on atomic motions via detennination of the wave vector transferred between the photon/neutron and the sample this is a Fourier transfonn relationship between wave vectors in reciprocal space and position vectors in real space. Neutrons, by virtue of the possibility of resolving their energy transfers, can also give infonnation on the time dependence of the motions involved. 

Figure 9 Fit of an incoherent neutron scattering structure factor, S(Q, O)), computed for iipid H atom motion in the piane of the biiayer in a simuiation of a DPPC biiayer, by the sum of an eiastic iine, a naiTow Lorentzian with width T , and a broad Lorentzian with width T2, convoiuted with a Gaussian resoiution function with AE = 0.050 meV.

Display water as a ball-and-spoke model. How many different vibrations are there Explain. One after the other, animate these vibrations. For each, record the vibrational frequency and provide a description of the atomic motions. What appears to be easier (lower frequency), motions primarily associated with bond stretching or with angle bending ... 

It should be realized that unlike the study of equilibrium thermodynamics for which a model is often mapped onto Ising system, elementary mechanism of atomic motion plays a deterministic role in the kinetic study. In an actual alloy system, diffusion of an atomic species is mainly driven by vacancy mechanism. The incorporation of the vacancy mechanism into PPM formalism, however, is not readily achieved, since the abundant freedom of microscopic path of atomic movement demands intractable number of variational parameters. The present study is, therefore, limited to a simple spin kinetics, known as Glauber dynamics [14] for which flipping events at fixed lattice points drive the phase transition. Hence, the present study for a spin system is regarded as a precursor to an alloy kinetics. The limitation of the model is critically examined and pointed out in the subsequent sections. 

The harmonic normal mode description is quite useful for approximated evaluation of various molecular properties. For example, one can use this description in a convenient way to evaluate the average thermal atomic motion. This is done by using the normal mode vector Ls in eq. (4.12), which can be written as... 

The comparison reveals that in addition to the activity of individual atoms, the next-neighbor interaction and collective atomic motion must play an important role in creating friction. This mechanism can be investigated more efficiently via the Frenkel-Kontorova model. 

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