Dynamics polyatomic

Even with these complications due to anliannonicity, tlie vibrating diatomic molecule is a relatively simple mechanical system. In polyatomics, the problem is fiindamentally more complicated with the presence of more than two atoms. The anliannonicity leads to many extremely interestmg effects in tlie internal molecular motion, including the possibility of chaotic dynamics. 

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... 

Flowever, in order to deliver on its promise and maximize its impact on the broader field of chemistry, the methodology of reaction dynamics must be extended toward more complex reactions involving polyatomic molecules and radicals for which even the primary products may not be known. There certainly have been examples of this notably the crossed molecular beams work by Lee [59] on the reactions of O atoms with a series of hydrocarbons. In such cases the spectroscopy of the products is often too complicated to investigate using laser-based techniques, but the recent marriage of intense syncluotron radiation light sources with state-of-the-art scattering instruments holds considerable promise for the elucidation of the bimolecular and photodissociation dynamics of these more complex species. 

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... 

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

Schinke R and Huber J R 1993 Photodissociation dynamics of polyatomic molecules. The relationship between potential energy surfaces and the breaking of molecular bonds J. Rhys. Chem. 97 3463... 

Nesbitt D J 1990 Dynamics of Polyatomic van der Waals Oomplexes ed N Halberstadt and K C Janda (New York Plenum) pp 461-70... 

The reaction of an atom with a diatomic molecule is the prototype of a chemical reaction. As the dynamics of a number of atom-diatom reactions are being understood in detail, attention is now being turned to the study of the dynamics of reactions involving larger molecules. The reaction of Cl atoms with small aliphatic hydrocarbons is an example of the type of polyatomic reactions which are now being studied [M, 72, 73]. 

Zhang J Z H 1999 The semirigid vibrating rotor target model for quantum polyatomic reaction dynamics J. 

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

To use direct dynamics for the study of non-adiabatic systems it is necessary to be able to efficiently and accurately calculate electronic wave functions for excited states. In recent years, density functional theory (DFT) has been gaining ground over traditional Hartree-Fock based SCF calculations for the treatment of the ground state of large molecules. Recent advances mean that so-called time-dependent DFT methods are now also being applied to excited states. Even so, at present, the best general methods for the treatment of the photochemistry of polyatomic organic molecules are MCSCF methods, of which the CASSCF method is particularly powerful. 

The first study in which a full CASSCE treatment was used for the non-adiabatic dynamics of a polyatomic system was a study on a model of the retinal chromophore [86]. The cis-trans photoisomerization of retinal is the primary event in vision, but despite much study the mechanism for this process is still unclear. The minimal model for retinal is l-cis-CjH NHj, which had been studied in an earlier quantum chemisti7 study [230]. There, it had been established that a conical intersection exists between the Si and So states with the cis-trans defining torsion angle at approximately a = 80° (cis is at 0°). Two... 

In many cases the dynamical system consists of fast degrees of freedom, labeled x, and slow degrees of freedom, labeled y. An example is that of a fluid containing polyatomic molecules. The internal vibrations of the molecules are often very fast compared to their translational and orientational motions. Although this and other systems, like proteins, have already been treated using RESPA,[17, 34, 22, 23, 24, 25, 26] another example, and the one we focus on here, is that of a system of very light particles (of mass m) dissolved in a bath of very heavy particles (mass M).[14] The positions of the heavy particles are denoted y and the positions of the light particles rire denoted by X. In this case the total Liouvillian of the system is ... 

New Methods in Quantum Molecular Dynamics of Large Polyatomic Systems... 

P. Jungwirth and R. B. Gerber. Quantum dynamics of large polyatomic systems using a classically based separable potential method. J. Chem. Phys., 102 6046-6056, 1995. 

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. 

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