Polyatomic molecules coupling

The question of non-classical manifestations is particularly important in view of the chaos that we have seen is present in the classical dynamics of a multimode system, such as a polyatomic molecule, with more than one resonance coupling. Chaotic classical dynamics is expected to introduce its own peculiarities into quantum spectra [29, 77]. In Fl20, we noted that chaotic regions of phase space are readily seen in the classical dynamics corresponding to the spectroscopic Flamiltonian. Flow important are the effects of chaos in the observed spectrum, and in the wavefiinctions of tire molecule In FI2O, there were some states whose wavefiinctions appeared very disordered, in the region of the... 

For a RRKM calculation without any approximations, the complete vibrational/rotational Flamiltonian for the imimolecular system is used to calculate the reactant density and transition state s sum of states. No approximations are made regarding the coupling between vibration and rotation. Flowever, for many molecules the exact nature of the coupling between vibration and rotation is uncertain, particularly at high energies, and a model in which rotation and vibration are assumed separable is widely used to calculate the quantum RRKM k(E,J) [4,16]. To illustrate this model, first consider a linear polyatomic molecule which decomposes via a linear transition state. The rotational energy for tire reactant is assumed to be that for a rigid rotor, i.e. 

Bhuiyan L B and Hase W L 1983 Sum and density of states for enharmonic polyatomic molecules. Effect of bend-stretch coupling J. Chem. Phys. 78 5052-8... 

Quack M 1990 Spectra and dynamics of coupled vibrations in polyatomic molecules Ann. Rev. Phys. Chem. 41 839-74... 

D. Perturbative Treatment of Vibration-Rotation Coupling III. Rotation of Polyatomic Molecules... 

Treating the full internal nuclear-motion dynamics of a polyatomic molecule is complicated. It is conventional to examine the rotational movement of a hypothetical "rigid" molecule as well as the vibrational motion of a non-rotating molecule, and to then treat the rotation-vibration couplings using perturbation theory. 

This chapter deals mainly with (multi)hyphenated techniques comprising wet sample preparation steps (e.g. SFE, SPE) and/or separation techniques (GC, SFC, HPLC, SEC, TLC, CE). Other hyphenated techniques involve thermal-spectroscopic and gas or heat extraction methods (TG, TD, HS, Py, LD, etc.). Also, spectroscopic couplings (e.g. LIBS-LIF) are of interest. Hyphenation of UV spectroscopy and mass spectrometry forms the family of laser mass-spectrometric (LAMS) methods, such as REMPI-ToFMS and MALDI-ToFMS. In REMPI-ToFMS the connecting element between UV spectroscopy and mass spectrometry is laser-induced REMPI ionisation. An intermediate state of the molecule of interest is selectively excited by absorption of a laser photon (the wavelength of a tuneable laser is set in resonance with the transition). The excited molecules are subsequently ionised by absorption of an additional laser photon. Therefore the ionisation selectivity is introduced by the resonance absorption of the first photon, i.e. by UV spectroscopy. However, conventional UV spectra of polyatomic molecules exhibit relatively broad and continuous spectral features, allowing only a medium selectivity. Supersonic jet cooling of the sample molecules (to 5-50 K) reduces the line width of their... 

Polyatomic molecules provide a still richer environment for studying phase control, where coupling between different dissociation channels can occur. Indeed, one of the original motivations for studying coherent control was to develop a means for bond-selective chemistry [25]. The first example of bond-selective two-pathway interference is the dissociation of dimethyl-sulfide to yield either H or CH3 fragments [74]. The peak in Fig. 11 is indicative of a resonance embedded in an elastic continuum (case 4). 

The eigenvalue problem was introduced in Section 7.3, where its importance in quantum mechanics was stressed. It arises also in many classical applications involving coupled oscillators. The matrix treatment of the vibrations of polyatomic molecules provides the quantitative basis for the interpretation of their infrared and Raman spectra. This problem will be addressed tridre specifically in Chapter 9. 

In this chapter, the diverse coupling constants and MEC components identified in the combined electronic-nuclear approach to equilibrium states in molecules and reactants are explored. The reactivity implications of these derivative descriptors of the interaction between the electronic and geometric aspects of the molecular structure will be commented upon within both the EP and EF perspectives. We begin this analysis with a brief survey of the basic concepts and relations of the generalized compliant description of molecular systems, which simultaneously involves the electronic and nuclear degrees-of-freedom. Illustrative numerical data of these derivative properties for selected polyatomic molecules, taken from the recent computational analysis (Nalewajski et al., 2008), will also be discussed from the point of view of their possible applications as reactivity criteria and interpreted as manifestations of the LeChatelier-Braun principle of thermodynamics (Callen, 1962). 

The formulation of the preceding section is very general. We are interested, however, in rotations and vibrations of polyatomic molecules. We therefore discuss now specific applications of the algebraic method beginning with the simple case of one-dimensional coupled oscillators, presented in Section 3.3 in the Schrodinger picture. In the algebraic theory, as mentioned, one associates to each coordinate, x, and related momentum, px = — iti d/dx, an algebra. For... 

The entire approach presupposes the separation of electronic degrees of freedom. As already noted, for the higher electronic states of polyatomic molecules, there can be important couplings with both spectroscopic and dynamic implications. The vibronic spectroscopy of benzene is reviewed by Ziegler and Hudson (1982). 

When it comes to polyatomic molecules, there are two problems that complicate the issue, as already discussed in Note 1 of Chapter 3. One is the separation of the overall rotation of the molecule (Jellinek and Li, 1989). The other is that, depending on the choice of internal coordinates, certain coupling terms can be assigned to be kinetic or potential terms. A simple and familiar case is a linear triatomic, when one uses bond coordinates versus Jacobi coordinates. The case for Fermi coupling for a bending motion is discussed in Sibert, Hynes, and Reinhardt (1983). 

Most diatomic molecules have a force constant in the range 10 to 10 N m h A common tool for the calculation of Kp in diatomic molecules (often extended to couples of atoms in polyatomic molecules) is Badger s rule ... 

For a non-linear polyatomic molecule, again with the centrifugal couplings to the vibrations evaluated at the equilibrium geometry, the following terms form the rotational part of the nuclear-motion kinetic energy ... 

Vibrational states can be described in terms of the normal mode (NM) [50, 51] or the local mode (LM) [37, 52, 53] model. In the former, vibrations in polyatomic molecules are treated as infinitesimal displacements of the nuclei in a harmonic potential, a picture that naturally includes the coupling among the bonds in a molecule. The general formula for the energies of the vibrational levels in a polyatomic molecule is given by [54]... 

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