SFG

Kumar A, Fairley G R G and Meath W J 1985 Dipole properties, dispersion energy coefficients and integrated oscillator strengths for SFg J. Chem. Phys. 83 70... 

Recently, in situ studies of catalytic surface chemical reactions at high pressures have been undertaken [46, 47]. These studies employed sum frequency generation (SFG) and STM in order to probe the surfaces as the reactions are occurring under conditions similar to those employed for industrial catalysis (SFG is a laser-based teclmique that is described in section A 1.7.5.5 and section BT22). These studies have shown that the highly stable adsorbate sites that are probed under vacuum conditions are not necessarily tlie same sites that are active in high-pressure catalysis. Instead, less stable sites that are only occupied at high pressures are often responsible for catalysis. Because the active... 

Figure A2.5.25. Coexistence-curve diameters as functions of reduced temperature for Ne, N2, C2H4, and SFg. Dashed lines indicate linear fits to the data far from the critical point. Reproduced from [19] Pestak M W, Goldstein R E, Chan M H W, de Bniyn J R, Balzarini D A and Ashcroft N W 1987 Phys. Rev. B 36 599, figure 3. Copyright (1987) by the American Physical Society.

Viggiano A A, Morris R A and Paulson J F 1994 Effects of f and SFg vibrational energy on the rate constant for charge transfer between and SFg int. J. Mass Spectrom. ion Processes 135 31-7... 

Two notable in situ teelmiques are at the forefront of the surfaee seienee of eatalysis STM and SFG. STM is used to investigate surfaee stmetnres while SFG is used to investigate surfaee reaetion intemiediates. The... 

These effects correspond, respectively, to the processes of sum-frequency generation (SFG), SFIG and optical rectification. 

The second-order nonlinear optical processes of SHG and SFG are described correspondingly by second-order perturbation theory. In this case, two photons at the drivmg frequency or frequencies are destroyed and a photon at the SH or SF is created. This is accomplished tlnough a succession of tlnee real or virtual transitions, as shown in figure Bl.5.4. These transitions start from an occupied initial energy eigenstate g), pass tlnough intennediate states n ) and n) and return to the initial state g). A fiill calculation of the second-order response for the case of SFG yields [37]... 

Figure Bl.5.4 Quantum mechanical scheme for the SFG process witii ground state g) and excited states n ) and n).

The focus of the present chapter is the application of second-order nonlinear optics to probe surfaces and interfaces. In this section, we outline the phenomenological or macroscopic theory of SHG and SFG at the interface of centrosymmetric media. This situation corresponds, as discussed previously, to one in which the relevant nonlinear response is forbidden in the bulk media, but allowed at the interface. 

In this equation as well as in the succeeding discussions, we have suppressed, for notational simplicity, the pemuitation or degeneracy factor of two, required for SFG. 

Table Bl.5.1 Independent non-vanishing elements of the nonlinear susceptibility, for an interface in the Ay-plane for various syimnetry classes. When mirror planes are present, at least one of them is perpendicular to they-axis. For SFIG, elements related by the pennutation of the last two elements are omitted. For SFG, these elements are generally distinct any syimnetry constraints are indicated in parentheses. The temis enclosed in parentheses are antisymmetric elements present only for SFG. (After [71])...

In tills section, we provide a brief overview of some experimental issues relevant m perfomiing surface SHG and SFG measurements. 

SFIG or SFG from a medium that has a strong response in a separate detection anu. By this means, one may fiilly compensate for variations not only in pulse energy, but also in the temporal and spatial substructure of the laser pulses. Some experiments may require measurement of the phase of the nonlinear signal [57]. 

We now consider the signal strengths from surface SFIG/SFG measurements. For this purpose, we may recast... 

The basic physical quantities that define the material for SHG or SFG processes are the nonlinear susceptibility elements consider how one may detemiine these quantities experimentally. For... 

Given the interest and importance of chiral molecules, there has been considerable activity in investigating die corresponding chiral surfaces [, and 70]. From the point of view of perfomiing surface and interface spectroscopy with nonlinear optics, we must first examhie the nonlinear response of tlie bulk liquid. Clearly, a chiral liquid lacks inversion synnnetry. As such, it may be expected to have a strong (dipole-allowed) second-order nonlinear response. This is indeed true in the general case of SFG [71]. For SHG, however, the pemiutation synnnetry for the last two indices of the nonlinear susceptibility tensor combined with the... 

A quantity of interest in many studies of surfaees and interfaees is tire eoneentration of adsorbed atomie or moleeular speeies. The SHG/SFG teelmique has been found to be a usefid probe of adsorbate density for a wide range of interfaees. The surfaee sensitivity afforded by the method is illustrated by the results of figure Bl.5.9 [72]. These data show the dramatie ehange in SH response from a elean surfaee of silieon upon adsorption of a fraetion of a monolayer of atomie hydrogen. 

The SHG/SFG technique is not restricted to interface spectroscopy of the delocalized electronic states of solids. It is also a powerful tool for spectroscopy of electronic transitions in molecules. Figure Bl.5.13 presents such an example for a monolayer of the R-enantiomer of the molecule 2,2 -dihydroxyl-l,l -binaphthyl, (R)-BN, at the air/water interface [ ]. The spectra reveal two-photon resonance features near wavelengths of 332 and 340 mu that are assigned to the two lowest exciton-split transitions in the naphtli-2-ol... 

Consequently, m order for a vibrational mode to be observed in infrared-visible SFG, the molecule in its adsorbed state has to be both IR [(dp/dg,) 0] and Raman [ AaJAQ ) 0] active. 

Figure Bl.5.14 Possible lineshapes for an SFG resonance as a fiinction of the infrared frequency cojj. The measured SFG signal is proportional to + A/(cojj - + iF)P. Assuming both and F are real and...

We now present one of the many examples of interfacial vibrational spectroscopy using SFG. Figure Bl.5.15 shows the surface vibrational spectrum of the water/air interface at a temperature of 40 °C [83]. Notice that... 

Figure Bl.5.15 SFG spectrum for the water/air interface at 40 °C using the ssp polarization combination (s-, s- and p-polarized sum-frequency signal, visible input and infrared input beams, respectively). The peaks correspond to OH stretching modes. (After [ ].)...

The SHG and SFG teclmiques are also suitable for studying dynamical processes occurring on slower time scales. Indeed, many valuable studies of adsorption, desorption, difhision and other surface processes have been perfomied on time scales of milliseconds to seconds. 

In a typical time-resolved SHG (SFG) experiment using femtosecond to picosecond laser systems, two (tlnee) input laser beams are necessary. The pulse from one of the lasers, usually called the pump laser, induces the... 

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