Vibrational period

Figure Al.6.8. Wavepacket interferometry. The interference contribution to the exeited-state fluoreseenee of I2 as a fiinotion of the time delay between a pair of ultrashort pulses. The interferenee eontribution is isolated by heterodyne deteetion. Note that the stnieture in the interferogram oeeurs only at multiples of 300 fs, the exeited-state vibrational period of f. it is only at these times that the wavepaeket promoted by the first pulse is baek in the Franek-Condon region. For a phase shift of 0 between the pulses the returning wavepaeket and the newly promoted wavepaeket are in phase, leading to eonstnietive interferenee (upper traee), while for a phase shift of n the two wavepaekets are out of phase, and interfere destnietively (lower traee). Reprinted from Seherer N F et 0/1991 J. Chem. Phys. 95 1487.

Eample For protein molecules with motions occurring at a frequency of about 1 cm the vibrational period is about 30 ps. Clearly, simulations of hundreds of picoseconds are necessary to probe adequately the motions of this system. 

Physically the cutting-corner trajectory implies that the particle crosses the barrier suddenly on the time scale of the slow -vibration period. In the literature this approximation is usually called sudden , frozen bath and fast flip approximation, or large curvature case. In the opposite case of small curvature (also called adiabatic and slow flip approximation), coj/coo < sin tp, which is relevant for transfer of fairly heavy masses, the MEP may be taken to a good accuracy to be the reaction path. 

Such reactions are often exothermic and the role of the third body is to carry away some of the energy released and thus stabilize the product molecule. In the absence of a collision with a third body, the highly vibrationally excited product molecule would usually decompose to its reactant molecules in the timescale of one vibrational period. Almost any molecule can act as a third body, although the rate constant may depend on the nature of the third body. In the Earth s atmosphere the most important third-body molecules are N2 and O2. 

The description of states participating in a spin-state transition as electronic isomers with discrete nuclear configurations, in particular different metal-ligand distances, requires that separate electronic and vibrational spectra of the two spin states exist. Indeed, a superposition of the individual vibrational spectra of the two states is in general observed, the relative contribution of the states being a function of temperature [41, 139, 140, 141, 142]. This observation sets a lower limit for the spin-state lifetime longer than the nuclear vibrational period, i.e.,... 

In the Landauer/Imry limit, the transport through the junction is due to elastic scattering. If the gap between the injection energy and the frontier orbital resonance is large, the Landauer/Buttiker contact time is very small, so that the charge is present on the molecule for a very short time. This means that its interaction with any vibration will be weak, because there just is not time to complete a full vibrational period before the charge has gone into the electrode sink. 

Although the curves in Figures 13-15 were developed for transient loads defined by total applied forces and inpulses, we could as easily have developed them by initially specifying an applied pressure transient loading, with its accompanying specific impulse, plus a loaded area. So, the concept certainly applies to simple structures under blast loading. The inportant inferences to be drawn from the simple- analyses are that structures respond primarily to peak overpressure if their vibration periods are much shorter than the blast duration, while they respond primarily to specific impulse if their vibration periods are much longer than the blast duration. 

Fig. 5. Pulse sequence for MR detection of vibration using a radiofrequency field gradient. A binomial 1331 radiofrequency pulse (pulse length D, interpulse delay r) is applied in-phase with the mechanical wave. Thus the vibration period 7V is equal to 4(D + r). The number of cycles can be increased to ensure a better frequency selectivity. The constant RF field gradient generated by a dedicated RF coil allows space encoding without using conventional static field gradients (from Ref. 16 with permission from Elsevier).

When the electric field strength of the incident light is ED, the induced dipole will be m, = aE0 where a is the optical polarisability. The electric field strength of radiation scattered by the induced dipole Es, depends on second derivative of m1 with respect to time. The useful experimental quantities are intensities of scattered light (Is) and incident important light (is). These are respectively proportional to Es2 and E02, averaged over a vibrational period, i.e., from time t = 0 to 10/C, where 1 is wavelength of... 

We now analyze the chemical species prevalent in water at these extreme conditions by defining instantaneous species based on the O-H bond distance. If that distance is less than a cut-off value rc, we count the atom pair as being bonded. Determining all bonds in the system gives the chemical species at each point in time. Species with lifetimes less than an O-H bond vibrational period (10 fs) are transient and do not represent bound molecules. The optimal cut-off rc between bonded and nonbonded species is given by the location of the maximum in the free energy surface.83... 

The vibrational phase v is characterised by selecting r0 at random from the interval between r0 and r0 + uR x, where x is the vibrational period of BC. 

A is a constant related to the atomic vibration period which is of the order of 10 13 s... 

We should note one situation that could lead to certain substitutions at sulfur being concerted rather than stepwise. If for some reason in a particular situation the stability of the intermediate should become so low that the lifetime of the intermediate becomes less than a vibration period, then substitution by a concerted path becomes required. Except for that special case, however, we believe that the stepwise mechanism should be employed. 

---