VER

Devos, A., G. Heinrich, P. Truffinet and F. Villette (1990), La longue route vers la conversion profonde . Petrole et Techniques (Revue de TAssociatiou Frangaise des Techniciens du Petrole), No. 357, p. 27. 

STM has not as yet proved to be easily applicable to the area of ultrafast surface phenomena. Nevertheless, some success has been achieved in the direct observation of dynamic processes with a larger timescale. Kitamura et al [23], using a high-temperature STM to scan single lines repeatedly and to display the results as a time-ver.sn.s-position pseudoimage, were able to follow the difflision of atomic-scale vacancies on a heated Si(OOl) surface in real time. They were able to show that vacancy diffusion proceeds exclusively in one dimension, along the dimer row. 

Watson P R, Van Hove M A and Hermann K 1999 NIST Surface Structure Database Ver. 3.0 (Gaithersburg, MD NIST Standard Reference Data Program)... 

Yarkony D R (ed) 1995 Modern Electronic Structure Theory R ver Edge, NJ World Scientific)... 

VER occurs as a result of fluctuating forces exerted by the bath on the system at the system s oscillation frequency O [5]. Fluctuating dynamical forces are characterized by a force-force correlation function. The Fourier transfonn of this force correlation function at Q, denoted n(n), characterizes the quantum mechanical frequency-dependent friction exerted on the system by the bath [5, 8]. 

Condensed phase vibrational or vibronic lineshapes (vibronic transitions create vibrational excitations of electronic excited states) rarely provide infonnation about VER (see example C3.5.6.4). Experimental measurements of VER need much more than just the vibrational spectmm. The earliest VER measurements in condensed phases were ultrasonic attenuation studies of liquids [15], which provided an overall relaxation time for slowly (>10 ns) relaxing small molecule liquids. 

Major breakthroughs in early ultrafast VER measurements were made in 1972 by Laubereau et al [22], who used picosecond lasers in an SRS pump-incoherent anti-Stokes Raman probe configuration, to study VER of C-H... 

The simplest condensed phase VER system is a dilute solution of a diatomic in an atomic (e.g. Ar or Xe) liquid or crystal. Other simple systems include neat diatomic liquids or crystals, or a diatomic molecule bound to a surface. A major step up in complexity occurs with poly atomics, with several vibrations on the same molecule. This feature guarantees enonnous qualitative differences between diatomic and polyatomic VER, and casts doubt on the likelihood of understanding poly atomics by studying diatomics alone. 

Diatomic molecules have only one vibrational mode, but VER mechanisms are paradoxically quite complex (see examples C3.5.6.1 and C3.5.6.2). Consequently there is an enonnous variability in VER lifetimes, which may range from 56 s (liquid N2 [18]) to 1 ps (e.g. XeF in Ar [25]), and a high level of sensitivity to environment. A remarkable feature of simpler systems is spontaneous concentration and localization of vibrational energy due to anhannonicity. Collisional up-pumping processes such as... 

VER of diatomic molecules bound to surfaces [28] was first studied by Eieilweil and co-workers [29], who used... 

The most powerful teclmique for studying VER in polyatomic molecules is the IR-Raman method. Initial IR-Raman studies of a few systems appeared more than 20 years ago [16], but recently the teclmique has taken on new life with newer ultrafast lasers such as Ti sapphire [39]. With more sensitive IR-Raman systems based on these lasers, it has become possible to monitor VER by probing virtually every vibration of a polyatomic molecule, as illustrated by recent studies of chlorofonn [40], acetonitrile [41, 42] (see example C3.5.6.6 below) and nitromethane [39, 43]. 

Consider an excited condensed-phase quantum oscillator Q, witli reduced mass p and nonnal coordinate q j. The batli exerts fluctuating forces on the oscillator. These fluctuating forces induce VER. The quantum mechanical Hamiltonian is [M, M]... 

Equation (C3.5.2 ) is a function of batli coordinates only. The VER rate constant is proportional to tire Fourier transfonn, at tire oscillator frequency Q, of tire batli force-correlation function. This Fourier transfonn is proportional as well to tire frequency-dependent friction q(n) mentioned previously. For example, tire rate constant for VER of tire Emdamental (v = 1) to tire ground (v = 0) state of an oscillator witli frequency D is [54]... 

Equation (C3.5.3) shows tire VER lifetime can be detennined if tire quantum mechanical force-correlation Emotion is computed. However, it is at present impossible to compute tliis Emotion accurately for complex systems. It is straightforward to compute tire classical force-correlation Emotion using classical molecular dynamics (MD) simulations. Witli tire classical force-correlation function, a quantum correction factor Q is needed 5,... 

In diatomic VER, the frequency Q is often much greater than so VER requires a high-order multiphonon process (see example C3.5.6.1). Because polyatomic molecules have several vibrations ranging from higher to lower frequencies, only lower-order phonon processes are ordinarily needed [34]- The usual practice is to expand the interaction Hamiltonian > in equation (03.5.2) in powers of nonnal coordinates [34, 631,... 

Figure C3.5.2. VER transitions involved in the decay of vibration Q by cubic and quartic anhannonic coupling (from [M])- Transitions involving discrete vibrations are represented by arrows. Transitions involving phonons (continuous energy states) are represented by wiggly arrows. In (a), the transition denoted (i) is the ladder down-conversion process, where D is annihilated and a lower-energy vibration cu and a phonon co are created.

In rare gas crystals [77] and liquids [78], diatomic molecule vibrational and vibronic relaxation have been studied. In crystals, VER occurs by multiphonon emission. Everything else held constant, the VER rate should decrease exponentially with the number of emitted phonons (exponential gap law) [79, 80] The number of emitted phonons scales as, and should be close to, the ratio O/mQ, where is the Debye frequency. A possible complication is the perturbation of the local phonon density of states by the diatomic molecule guest [77]. 

The VER lifetime of liquid O2 is 280 ms at 70 K [82]. Predicting such a slow rate from theory is a fonnidable challenge taken up by Skinner and co-workers [54] in a recent paper. The fundamental frequency of O2 is 1552... 

VER in liquid O 2 is far too slow to be studied directly by nonequilibrium simulations. The force-correlation function, equation (C3.5.2), was computed from an equilibrium simulation of rigid O2. The VER rate constant given in equation (C3.5.3) is proportional to the Fourier transfonn of the force-correlation function at the Oj frequency. Fiowever, there are two significant practical difficulties. First, the Fourier transfonn, denoted [Pg.3041]

Figure C3.5.6 compares the result of this ansatz to the numerical result from the Wiener-Kliintchine theorem. They agree well and the ansatz exliibits the expected exponential energy-gap law (VER rate decreases exponentially with Q). The ansatz was used to detennine the VER rate with no quantum correction Q= 1), with the Bader-Beme hannonic correction [61] and with a correction based [83, M] on Egelstaff s method [62]. The Egelstaff corrected results were within a factor of five of experiment, whereas other corrections were off by orders of magnitude. This calculation represents the present state of the art in computing VER rates in such difficult systems, inasmuch as the authors used only a model potential and no adjustable parameters. However the ansatz procedure is clearly not extendible to polyatomic molecules or to diatomic molecules in polyatomic solvents.

Figure C3.5.6. The computed Fourier transfonn at frequency co, of tire classical mechanical force-force correlation function for liquid O2 at 70 K from [M]- The VER rate is proportional to the value of ( " at tire O2...

A) no VER and no dephasing. (B) VER is faster tiian a vibrationai period. Once tire vibrationai ground state is reached, tire wavepacket begins to osciiiate coherentiy. (C) The VER rate is comparabie to a vibrationai period so some coherence is seen in botii excited and ground states. (D) Dephasing is faster tiian VER. 

Figure C3.5.8. Computed frequency-dependent friction (inverseiy proportionai to tire VER iifetime T ) from a ciassicai moiecuiar dynamics simuiation of rigid Hgl moiecuies in etiianoi soiution, from [90]. The Hgl vibrationai...

VER rates cannot be predicted from vibrationai iineshapes aione [5] except for a few exceptionai cases [2, 91]. The most detaiied deconstmction of vibrationai iineshapes to date is tire work of Payer and co-workers [92], who studied W(CO)g in giass-fonning iiquids inciuding 2-metiiyi pentane (2MP = 80 K). The tripiy degenerate... 

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