Polyatomic molecules vibrational

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

The representation as a two-dimensional potential energy diagram is simple for diatomic molecules. But for polyatomic molecules, vibrational motion is more complex. If the vibrations are assumed to be simple harmonic, the net vibrational motion of TV-atomic molecule can be resolved into 3TV-6 components termed normal modes of ibrations (3TV-5 for... 

Beyond Diatomic Molecules Polyatomic Molecule Vibrational Dynamics... 

CSA calculations can be performed of rotational excitation cross sections for atom-asymmetric top collisions quite easily at low collision energies. To date, the only application of the CSA to an atom-polyatomic molecule vibrational-rotational problem has been to He+CO2(01 0,j 00 0,j )[27] and some of these calculations are described in Section HI. 

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 the case of polyatomic molecules, one may consider separately the accommodation coefficients for translational and for vibrational energy. Values of the latter, civ, are discussed by Nilsson and Rabinovitch [7]. 

The above three sources are a classic and comprehensive treatment of rotation, vibration, and electronic spectra of diatomic and polyatomic molecules. 

Pack R T 1976 Simple theory of diffuse vibrational structure in continuous UV spectra of polyatomic molecules. I. Collinear photodissociation of symmetric triatomics J. Chem. Phys. 65 4765... 

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. 

Haarhoff P C 1963 The density of vibrational energy levels of polyatomic molecules Mol. Phys. 7 101-17... 

As in classical mechanics, the outcome of time-dependent quantum dynamics and, in particular, the occurrence of IVR in polyatomic molecules, depends both on the Flamiltonian and the initial conditions, i.e. the initial quantum mechanical state I /(tQ)). We focus here on the time-dependent aspects of IVR, and in this case such initial conditions always correspond to the preparation, at a time of superposition states of molecular (spectroscopic) eigenstates involving at least two distinct vibrational energy levels. Strictly, IVR occurs if these levels involve at least two distinct... 

Weitz E and Flynn G W 1981 Vibrational energy flow in the ground electronic states of polyatomic molecules Adv. Chem. Rhys. 47 185-235... 

Orr B J and Smith I W M 1987 Collision-induced vibrational energy transfer in small polyatomic molecules J. Rhys. Chem. 91 6106-19... 

Hippier H, Troe J and Wendelken H J 1983 Collisional deactivation of vibrationally highly excited polyatomic molecules. II. Direct observations for excited toluene J. Chem. Phys. 78 6709... 

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

The selection rule for vibronic states is then straightforward. It is obtained by exactly the same procedure as described above for the electronic selection rules. In particular, the lowest vibrational level of the ground electronic state of most stable polyatomic molecules will be totally synnnetric. Transitions originating in that vibronic level must go to an excited state vibronic level whose synnnetry is the same as one of the coordinates, v, y, or z. 

McCoy A B and Siebert E L 1996 Canonical Van VIeck pertubation theory and its applications to studies of highly vibrationally excited states of polyatomic molecules Dynemics of Moiecuies end Chemicei Reections ed R E Wyatt and J Z H Zhang (New York Dekker) p 151... 

The most powerful teclmique for studying VER in polyatomic molecules is the IR-Raman method. Initial IR-Raman studies of a few systems appeared more than 20 years ago [16], but recently the teclmique has taken on new life with newer ultrafast lasers such as Ti sapphire [39]. With more sensitive IR-Raman systems based on these lasers, it has become possible to monitor VER by probing virtually every vibration of a polyatomic molecule, as illustrated by recent studies of chlorofonn [40], acetonitrile [41, 42] (see example C3.5.6.6 below) and nitromethane [39, 43]. 

In diatomic VER, the frequency Q is often much greater than so VER requires a high-order multiphonon process (see example C3.5.6.1). Because polyatomic molecules have several vibrations ranging from higher to lower frequencies, only lower-order phonon processes are ordinarily needed [34]- The usual practice is to expand the interaction Hamiltonian > in equation (03.5.2) in powers of nonnal coordinates [34, 631,... 

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