Vibrational spectroscopy polyatomic molecules

The goal of this book is to present in a coherent way the problems of the laser control of matter at the atomic-molecular level, namely, control of the velocity distribution of atoms and molecules (saturation Doppler-free spectroscopy) control of the absolute velocity of atoms (laser cooling) control of the orientation, position, and direction of motion of atoms (laser trapping of atoms, and atom optics) control of the coherent behavior of ultracold (quantum) gases laser-induced photoassociation of cold atoms, photoselective ionization of atoms photoselective multiphoton dissociation of simple and polyatomic molecules (vibrationally or electronically excited) multiphoton photoionization and mass spectrometry of molecules and femtosecond coherent control of the photoionization of atoms and photodissociation of molecules. 

In electronic spectroscopy of polyatomic molecules the system used for labelling vibronic transitions employs N, to indicate a transition in which vibration N is excited with v" quanta in the lower state and v quanta in the upper state. The pure electronic transition is labelled Og. The system is very similar to the rather less often used system for pure vibrational transitions described in Section 6.2.3.1. 

The starting points for many conventions in spectroscopy are the paper by R. S. Mulliken in the Journal of Chemical Physics (23, 1997, 1955) and the books of G. Herzberg. Apart from straightforward recommendations of symbols for physical quantities, which are generally adhered to, there are rather more contentious recommendations. These include the labelling of cartesian axes in discussions of molecular symmetry and the numbering of vibrations in a polyatomic molecule, which are often, but not always, used. In such cases it is important that any author make it clear what convention is being used. 

I. N. Levine (1975) Molecular Spectroscopy (John Wiley Sons, New York). A survey of the theory of rotational, vibrational, and electronic spectroscopy of diatomic and polyatomic molecules and of nuclear magnetic resonance spectroscopy. 

Approaches to Vibration-Rotation Spectroscopy for Polyatomic Molecules. 

Unlike the case of simple diatomic molecules, the reaction coordinate in polyatomic molecules does not simply correspond to the change of a particular chemical bond. Therefore, it is not yet clear for polyatomic molecules how the observed wavepacket motion is related to the reaction coordinate. Study of such a coherent vibration in ultrafast reacting system is expected to give us a clue to reveal its significance in chemical reactions. In this study, we employed two-color pump-probe spectroscopy with ultrashort pulses in the 10-fs regime, and investigated the coherent nuclear motion of solution-phase molecules that undergo photodissociation and intramolecular proton transfer in the excited state. 

The major changes in the new edition are as follows There are three new chapters. Chapter 1 is a review and summary of aspects of quantum mechanics and electronic structure relevant to molecular spectroscopy. This chapter replaces the chapter on electronic structure of polyatomic molecules that was repeated from Volume I of Quantum Chemistry. Chapter 2 is a substantially expanded presentation of matrices. Previously, matrices were covered in the last chapter. The placement of matrices early in the book allows their use throughout the book in particular, the very tedious and involved treatment of normal vibrations has been replaced by a simpler and clearer treatment using matrices. Chapter 7 covers molecular electronic spectroscopy, and contains two new sections, one on electronic spectra of polyatomic molecules, and one on photoelectron spectroscopy, together with the section on electronic spectra of diatomic molecules from the previous edition. In addition to the new material on matrices, electronic spectra of polyatomic molecules, and photoelectron... 

Microwave spectroscopy often gives more definite and precise information on the structure of polyatomic molecules than vibration-rotation and electronic spectra. For example, consider the simplest oxime formald-oxime, CH2=NOH. There are two likely structural configurations for this... 

Raman spectroscopy (Section 4.10) aids the study of the vibrations of polyatomic molecules. For a vibration to be Raman active, it must give a change in the molecular polarizability. For many molecules with some symmetry, one or more of the normal modes correspond to no change in... 

The principal reaction discussed above forms oxygen molecules in high vibrational levels of the ground state. This is chemi-excitation but is not chemiluminescence vibration-rotation transitions of homonuclear molecules are forbidden. For such cases electronic absorption spectroscopy is the required technique. For reactions in which a heteronuclear diatomic (or a polyatomic) molecule is excited these transitions are allowed. They are overtones of the molecular transitions that occur in the near infrared. These excited products emit spontaneously. The reactions are chemiluminescent, their emission spectra may be obtained and analyzed in order to deduce the detailed course of the reaction. 

As discussed in Section II, the excited-state dynamics of polyatomic molecules is dictated by the coupled flow of both charge and energy within the molecule. As such, a probe technique that is sensitive to both nuclear (vibrational) and electronic configuration is required in order to elucidate the mechanisms of such processes. Photoelectron spectroscopy provides such a technique,... 

The second problem relates to the inclusion, or otherwise, of molecular symmetry arguments. There is no avoiding the fact that an understanding of molecular symmetry presents a hurdle (although I think it is a low one) which must be surmounted if selection rules in vibrational and electronic spectroscopy of polyatomic molecules are to be understood. This book surmounts the hurdle in Chapter 4, which is devoted to molecular symmetry but which treats the subject in a non-mathematical way. For those lecturers and students who wish to leave out this chapter much of the subsequent material can be understood but, in some areas, in a less satisfying way. 

Raman Selection Rules. For polyatomic molecules a number of Stokes Raman bands are observed, each corresponding to an allowed transition between two vibrational energy levels of the molecule. (An allowed transition is one for which the intensity is not uniquely zero owing to symmetry.) As in the case of infrared spectroscopy (see Exp. 38), only the fundamental transitions (corresponding to frequencies v, V2, v, ...) are usually intense enough to be observed, although weak overtone and combination Raman bands are sometimes detected. For molecules with appreciable symmetry, some fundamental transitions may be absent in the Raman and/or infrared spectra. The essential requirement is that the transition moment F (whose square determines the intensity) be nonzero i.e.. 

Most fundamental rotation-vibration bands are located in the mid-infrared region from 4000 - 400 cm". A few vibrational bands appear in the far infrared where purely rotational spectra of light molecules with two or three atoms are also observed. This is in contrast to heavier polyatomic molecules the study of their rotational spectra is the domain of the microwave spectroscopist who employs different equipment, particularly, monochromatic tunable radiation sources. Rotational constants determined from IR-work are therefore usually less accurate than those obtained by microwave spectroscopy. 

Near-infrared absorption is therefore essentially due to combination and overtone modes of higher energy fundamentals, such as C-H, N-H, and O-H stretches, which appear as lower overtones and lower order combination modes. Since the NIR absorption of polyatomic molecules thus mainly reflects vibrational contributions from very few functional groups, NIR spectroscopy is less suitable for detailed qualitative analysis than IR, which shows all (active) fundamentals and the overtones and combination modes of low-energy vibrations. On the other hand, since the vibrational intensities of near-infrared bands are considerably lower than those of corresponding infrared bands, optical layers of reasonable size (millimeters, centimeters) may be transmitted in the NIR, even in the case of liquid samples, compared to the layers of pm size which are detected in the infrared. This has important consequences for the direct quantitative study of chemical reactions, chemical equilibria, and phase equilibria via NIR spectroscopy. 

The same ideas extend straightforwardly to deal with property surfaces describing the dependence of a molecular property on geometry, for example, the dipole moment and polarisability derivatives that control the activity of a vibrational mode in IR and Raman spectroscopy. Extension to the case of redundant internal coordinates, the typical situation for polyatomic molecules, is also straightforward. 

G. D. Carney, L. L. Sprandel, and C. W. Kern, Variational approaches to vibration-rotation spectroscopy for polyatomic molecules. Adv. Chem. Phys. 37, 305-379 (1978). 

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