Nonlinear molecules vibrational spectroscopy

Cho M, Hess C, Bonn M. 2002. Lateral interactions between adsorbed molecules Investigations of CO on Ru(OOl) using nonlinear surface vibrational spectroscopies. Phys Rev B 65 ... 

Much of the previous section dealt with two-level systems. Real molecules, however, are not two-level systems for many purposes there are only two electronic states that participate, but each of these electronic states has many states corresponding to different quantum levels for vibration and rotation. A coherent femtosecond pulse has a bandwidth which may span many vibrational levels when the pulse impinges on the molecule it excites a coherent superposition of all tliese vibrational states—a vibrational wavepacket. In this section we deal with excitation by one or two femtosecond optical pulses, as well as continuous wave excitation in section A 1.6.4 we will use the concepts developed here to understand nonlinear molecular electronic spectroscopy. 

Hyper-Raman spectroscopy is not a surface-specific technique while SFG vibrational spectroscopy can selectively probe surfaces and interfaces, although both methods are based on the second-order nonlinear process. The vibrational SFG is a combination process of IR absorption and Raman scattering and, hence, only accessible to IR/Raman-active modes, which appear only in non-centrosymmetric molecules. Conversely, the hyper-Raman process does not require such broken centrosymmetry. Energy diagrams for IR, Raman, hyper-Raman, and vibrational SFG processes are summarized in Figure 5.17. 

Vibrational modes of peroxynitrite anion observable by Raman spectroscopy. A nonlinear molecule with four atoms can have only six independent modes. These consist of three bond stretching modes, two bending modes, and torsion of the OO-NO bond, which will make peroxynitrite nonplanar. 

In our discussion the usual Born-Oppenheimer (BO) approximation will be employed. This means that we assume a standard partition of the effective Hamiltonian into an electronic and a nuclear part, as well as the factorization of the solute wavefunction into an electronic and a nuclear component. As will be clear soon, the corresponding electronic problem is the main source of specificities of QM continuum models, due to the nonlinearity of the effective electronic Hamiltonian of the solute. The QM nuclear problem, whose solution gives information on solvent effects on the nuclear structure (geometry) and properties, has less specific aspects, with respect the case of the isolated molecules. In fact, once the proper potential energy surfaces are obtained from the solution of the electronic problem, such a problem can be solved using the standard methods and approximations (mechanical harmonicity, and anharmonicity of various order) used for isolated molecules. The QM nuclear problem is mainly connected with the vibrational properties of the nuclei and the corresponding spectroscopic observables, and it will be considered in more detail in the contributions in the book dedicated to the vibrational spectroscopies (IR/Raman). This contribution will be focused on the QM electronic problem. 

Nonlinear optical infrared-visible sum frequency generation (IR-vis SFG) is a versatile surface-specific vibrational spectroscopy that meets the requirements mentioned above. SFG provides vibrational spectra of molecules adsorbed on a surface, while the molecules in the gas phase do not produce a signal. Consequently, SFG can be operated in a pressure range from UFIV to ambient conditions and still detects only the adsorbed species. A direct comparison of adsorbate structures under UFIV and elevated pressure is therefore feasible. Furthermore, SFG can be applied to molecules adsorbed on single crystals, thin films, metal foils, and supported nanoparticles (46,116-121) and is thus a promising tool to extend surface science experiments to more realistic conditions. 

A fmther step is to spectroscopically monitor adsorbed and reacting molecules on the surface of the nanoparticles under technically relevant conditions [59]. A few techniques with high-pressme capability are illustrated in Fig. 15.9b. Ambient pressure vibrational spectra of adsorbed molecules can be obtained by IR-vis SFG or PM-IRAS [51, 55, 60, 61]. Both methods can be applied from UHV to ambient pressure. Nonlinear optical SFG spectroscopy is inherently interface specific (i.e., there is no gas-phase SFG signal), and PM-IRAS allows for an accurate... 

Despite these problems of saturation of vibrational bands IR spectroscopy, described in the next subsection, has been recently shown to nevertheless remain an especially powerful method to observe H2O molecules. Special recently proposed set-ups can avoid saturation in the whole conventional IR region, thus taking full advantage of the power of IR to study H-bond networks. They are first described, before the contribution of recent time-resolved nonlinear IR spectroscopy is examined. Other methods such as NIR or Raman spectroscopy, which are intrinsically free of this saturation effects can also be used to study the HjO molecule. They are often limited to some specific problems, as they do not display the power of ordinary IR spectroscopy for the study of H-bonds or of H2O molecules and cannot consequently be considered as general methods. They are described in the last subsection of this section on vibrational spectroscopy. 

Because the central atom is not in tine with the other two, the symmetric stretching vibration produces a change in dipole momeni and is thus IR active. For example, stretching peaks at 3657 and 3766 cm (2.74 and 2.66 pm) appear in the IR spectrum for the symmetric and asymmet ric stretching vibrations of the water molecule. I here is only one component to the scissoring vibration for this nonlinear molecule because motion in the plane of the molecule constitutes a rotational degree of freedom. For water, the bending vibration causes absorption at 1595 cm (6.27 pm). The difference in behavior oflinear and nonlinear triaiomic molecules with two and three absorption bands, respectively. illustrates how IR absorption spectroscopy can sometimes be used to deduce molecular shapes. 

In the harmonic-oscillator approximation, the quantum-mechanical energy levels of a polyatomic molecule turn out to be vib 2, (v, + )hv,, where the v s are the frequencies of the normal modes of vibration of the molecule and v, is the vibrational quantum number of the ith normal mode. Each v, takes on the values 0,1,2,... independently of the values of the other vibrational quantum numbers. A linear molecule with n atoms has 3n — 5 normal modes a nonlinear molecule has 3n — 6 normal modes. (See Levine, Molecular Spectroscopy, Chapter 6 for details.)... 

Vibrational spectroscopy of molecules depends on quantum mechanics, which requires well-defined frequencies and atomic displacements known as the normal modes of vibrations of the molecules. A linear molecule with N atoms has 3N-5 normal modes, and a nonlinear molecule has 3N-6 normal modes of vibrations. Several types of motions leads to normal modes such as (i) stretching motion between two bonded atoms, (ii) bending motion between three atoms connected by two bonds, and (iii) out-of-plane deformation modes take place with changes from a planar structure to a nonplanar one. 

In this chapter, we extend our treatment of rotation in diatomic molecules to nonlinear polyatomic molecules. A traditional motivation for treating polyatomic rotations quantum mechanically is that they form a basis for experimental determination for bond lengths and bond angles in gas-phase molecules. Microwave spectroscopy, a prolific area in chemical physics since 1946, has provided the most accurate available equilibrium geometries for many polar molecules. A background in polyatomic rotations is also a prerequisite for understanding rotational fine structure in polyatomic vibrational spectra (Chapter 6). The shapes of rotational contours (i.e., unresolved rotational fine structure) in polyatomic electronic band spectra are sensitive to the relative orientations of the principal rotational axes and the electronic transition moment (Chapter 7). Rotational contour analysis has thus provided an invaluable means of assigning symmetries to the electronic states involved in such spectra. 

A technique which combines the high sensitivity of resonant laser ionization methods with the advantages of nonlinear coherent Raman spectroscopy is called IDSRS (ionization detected stimulated Raman spectroscopy). The excitation process, illustrated in Figure 5, can be briefly described as a two-step photoexcitation process followed by ion/electron detection. In the first step two intense narrow-band lasers (ct L, 0) ) are used to vibrationally excite the molecule via the stimulated Raman process. The excited molecules are then selectively ionized in a second step via a two- or multiphoton process. If there are intermediate resonant states involved (as state c in Figure 5), the method is called REMPI (resonance enhanced multi-photon ionization)-detected stimulated Raman spectroscopy. The technique allows an increase in sensitivity of over three orders of magnitude because ions can be detected with much higher sensitivity than photons. 

Similarly, the first-order expansion of the p° and a of Eq. (5.1) is, respectively, responsible for IR absorption and Raman scattering. According to the parity, one can easily understand that selection mles for hyper-Raman scattering are rather similar to those for IR [17,18]. Moreover, some of the silent modes, which are IR- and Raman-inactive vibrational modes, can be allowed in hyper-Raman scattering because of the nonlinearity. Incidentally, hyper-Raman-active modes and Raman-active modes are mutually exclusive in centrosymmetric molecules. Similar to Raman spectroscopy, hyper-Raman spectroscopy is feasible by visible excitation. Therefore, hyper-Raman spectroscopy can, in principle, be used as an alternative for IR spectroscopy, especially in IR-opaque media such as an aqueous solution [103]. Moreover, its spatial resolution, caused by the diffraction limit, is expected to be much better than IR microscopy. 

Raman spectroscopy comprises a family of spectral measurements based on inelastic optical scattering of photons at molecules or crystals. It involves vibrational measurements as well as rotational or electronic studies and nonlinear effects. Following, Raman will be used in the established but slightly inaccurate way as a synonym for the most important and most common technique of the family, linear vibrational Raman scattering. 

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