Vibrational anharmonicity dynamics

In the hydrate lattice structure, the water molecules are largely restricted from translation or rotation, but they do vibrate anharmonically about a fixed position. This anharmonicity provides a mechanism for the scattering of phonons (which normally transmit energy) providing a lower thermal conductivity. Tse et al. (1983, 1984) and Tse and Klein (1987) used molecular dynamics to show that frequencies of the guest molecule translational and rotational energies are similar to those of the low-frequency lattice (acoustic) modes. Tse and White (1988) indicate that a resonant coupling explains the low thermal conductivity. 

The first vibrational-anharmonicity term of Equation 18 has been found to dominate over nonlinear coupling in the specific case of N2, [73] and Oxtoby has argued that this term will dominate in general. [72] However, several theories have looked at dephasing due to the second, nonlinear coupling term of Equation 18. [71,74-76] Under reasonable approximations and with a steeply repulsive V, the anharmonic term also produces frequency shifts proportional to the solvent force on the vibrator, just as in Equation 19. [72] Again the issue returns to an accurate treatment of the solvent dynamics and the nature of the solvent-solute coupling. 

Several fundamental questions have been raised by these investigations and hopefully will be answered in the near future. One set of questions concerns the role of inertial dynamics coupled by short-range forces. A clear example of this type of process has not yet been unambiguously identified. An important question is whether this type of dephasing is dominated by vibrational anharmonicity or by nonlinear coupling. In the case of vibrational anharmonicity, the degree of coherence in the inertial dynamics... 

E.E.Nikitin and M.Ya.Ovchinnikova, Role of anharmonic dynamics in vibrational relaxation of impurity molecules in solids, ZhimnEksp. Teor.Fiz. 78,1551 (1980)... 

Many MD studies on the kinetic processes of proteins have revealed the existence of a specific pathway of energy flow [6-10]. In this chapter, for the purpose of studying anharmonic dynamics, we propose two models in which protein motions are assumed to be described by perturbed harmonic oscillators [11-13]. These models are based on the success of the harmonic/quasiharmonic model in the description of the equilibrium properties of proteins. Firstly, we consider vibrational energy transfer between normal modes, based on the Lagrangian [11,12] ... 

The methods of Nonlinear Dynamics(8) can be applied to gain new theoretical insight into the underlying dynamics in terms of the molecular phase space structure. In particular, the existence of low order Fermi resonances between vibrationally anharmonic local (or normal) modes or between bending vibrations and rotations, can cause dramatic changes in phase space structure, manifest in the breakdown... 

In this chapter, our goal is to present theoretical methods applied to gas phase vibrational spectroscopy. This is reviewed in Sect. 3 where we present harmonic and anharmonic spectra calculations, with special emphasis on dynamical approaches to anharmonic spectroscopy. In particular, we present the many reasons and advantages of dynamical anharmonic theoretical spectroscopy over harmonic/ anharmonic non-dynamical methods in Sect. 3.1. Illustrations taken from our work on dynamical theoretical spectroscopy are then presented in Sects. 4-6 in relation to action spectroscopy experiments. All examples presented here are conducted either in relation to finite temperature IR-MPD and IR-PD experiments, or to cold IR-MPD experiments. Beyond the conformational dynamics provided by the finite temperature trajectories, the chosen examples illustrate how the dynamical spectra manage to capture vibrational anharmonicities of different origins, of different strengths, in various domains of the vibrations from 100 to 4,000 cm and on various molecular systems. Other comprehensive reviews on theoretical anharmonic spectroscopy can be found in [7-9]. 

The third example presented in Sect. 6 illustrates our preliminary theoretical dynamical spectra in the far-IR domain below 1,000 cm, where vibrational anharmonicities arising from mode-couplings and delocalized motions have been captured with great accuracy on a model phenylalanine neutral di-peptide, in relation to cold IR-MPD experiments. 

Advantages and disadvantages of these theoretical methods over the dynamical method in accounting for vibrational anharmonicities can be roughly summarized as follows. 

All investigations presented in Sects. 4-6 have employed Bom-Oppenheimer dynamics (BOMD). We apply no scaling factor of any kind to the vibrations extracted from the dynamics. The sampling of vibrational anharmonicities, i.e., potential energy surface, dipole anharmonicities, mode couplings, anharmonic... 

The above examples of Ala H peptides demonstrate that dynamical spectra are capable of capturing the dynamical behavior of the N-H" - 0=C H-bonds and their vibrational anharmonicities with remarkable accuracy, thus providing definitive assignments of the protonated alanine peptide structures produced in the gas phase. We now turn to the vibrational spectroscopy of even more challenging molecular systems, ionic clusters, displaying large vibrational anharmonicities. Details of our combined IR-PD experimental and theoretical dynamical investigations can be fotmd in [37, 65], where the structures of CP-(Methanol)i 2 and C1 NMA(H20) =o-2 clusters (NMA = A-methy 1-acetamide) have been unraveled... 

Among the main theoretical methods of investigation of the dynamic properties of macromolecules are molecular dynamics (MD) simulations and harmonic analysis. MD simulation is a technique in which the classical equation of motion for all atoms of a molecule is integrated over a finite period of time. Harmonic analysis is a direct way of analyzing vibrational motions. Harmonicity of the potential function is a basic assumption in the normal mode approximation used in harmonic analysis. This is known to be inadequate in the case of biological macromolecules, such as proteins, because anharmonic effects, which MD has shown to be important in protein motion, are neglected [1, 2, 3]. 

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

The book thus embraces an extended study on a variety of issues within the theory of orientational ordering and phase transitions in two-dimensional systems as well as the theory of anharmonic vibrations in low-dimensional crystals and dynamic subsystems interacting with a phonon thermostat. For the sake of readability, the main theoretical approaches involved are either presented in separate sections of the corresponding chapters or thoroughly scrutinized in appendices. The latter contain the basic formulae of the theory of local and resonance states for a system of bound harmonic oscillators (Appendix 1), the theory of thermally activated reorientations and tunnel relaxation of orientational... 

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