Instantaneous normal modes

Goodyear G and Stratt R M 1996 The short-time intramoleoular dynamios of solutes in liquids. I. An instantaneous-normal-mode theory for friotion J. Chem. Phys. 105 10050-71... 

Cao, J., Voth, G.A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties. J. Chem. Phys. 100 (1994) 5093-5105 II Dynamical properties. J. Chem. Phys. 100 (1994) 5106-5117 III. Phase space formalism and nalysis of centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6157-6167 IV. Algorithms for centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6168-6183 V. Quantum instantaneous normal mode theory of liquids. J. Chem. Phys. 101 (1994) 6184 6192. 

To render the KP theory feasible for many-body systems with N particles, we make the approximation of independent instantaneous normal mode (INM) coordinates [qx° 3N for a given configuration xo 3W [12, 13], Hence the multidimensional V effectively reduces to 3N one-dimensional potentials along each normal mode coordinate. Note that INM are naturally decoupled through the 2nd order Taylor expansion. The INM approximation has also been used elsewhere. This approximation is particularly suited for the KP theory because of the exponential decaying property of the Gaussian convolution integrals in Eq. (4-26). The total effective centroid potential for N nuclei can be simplified as ... 

The effective frequencies that characterize solvent response can be characterized more quantitatively from several points of view, including generalized Langevin theory [367-372], Brownian oscillators [373, 374], and instantaneous normal modes [375],... 

Filter-Diagonalization to Extract Instantaneous Normal Modes. 

E. Poliak Instantaneous normal modes are reasonable for short times. For long times, one may try to use a generalized Langevin equation representation. Sometimes it will work but sometimes not. When yes and when not is not well understood for liquids. 

Prof. Fleming, the expressions you are using for the nonlinear response function may be derived using the second-order cumulant expansion and do not require the use of the instantaneous normal-mode model. The relevant information (the spectral density) is related to the two-time correlation function of the electronic gap (for resonant spectroscopy) and of the electronic polarizability (for off-resonant spectroscopy). You may choose to interpret the Fourier components of the spectral density as instantaneous oscillators, but this is not necessary. The instantaneous normal mode provides a physical picture whose validity needs to be verified. Does it give new predictions beyond the second-order cumulant approach The main difficulty with this model is that the modes only exist for a time scale comparable to their frequencies. In glasses, they live much longer and the picture may be more justified than in liquids. 

G. R. Fleming Prof. Mukamel s first point is correct. The value of the instantaneous normal-mode approach is to provide a molecu-... 

A more mechanistic approach, Instantaneous Normal Mode (INM) theory [122], can be used to characterize the collective modes of a liquid. Ribeiro and Madden [123] applied this theory to a series of fused salts, including both noncoordinating and coordinating species. They found that the INM analysis provided a good estimate of the diffusion constants for noncoordinating fused salts. For coordinating ions, however, the situation was complicated by the existence of transient, quasimolecular species. While a more detailed analysis is possible [124], the spectrum becomes sufficiently complicated that it would be difficult to characterize specific motions in the system. 

B. The Instantaneous Vibrational Friction and the Instantaneous Normal Modes of the Solvent... 

Our instantaneous-normal-mode theory of vibrational energy relaxation suggests a rather interesting physical picture. The solvent surrounding our... 

Figure 2 Normalized instantaneous-normal-mode spectra for high-density supercritical Ar. The overall density of states (DOS) is contrasted with three different INM influence spectra for a diatomic solute for rotational friction, vibrational friction, and (nonpolar) solvation dynamics. Only the spectrum of modes for vibrational friction is of direct relevance to this chapter, but the other influence spectra show the strong similarities in the instantaneous solvent dynamics associated with different kinds of solute relaxation.

Keyes T. J Phys Chem A 101 2921, 1997. A somewhat different approach toward instantaneous normal modes. 

In the case of nonlinear polarizability coupling, the ratio of the cascaded to direct fifth-order response can be expressed in terms of the ratio of the first and second derivative of the polarizability [Equation (32)]. Using instantaneous normal mode simulations, Murry et al. (40) have calculated the relative ratios of a 11 and at2> for 5000 intermolecular modes in CS2. Although their results show this ratio to be somewhat randomly... 

The two most widely implemented numerical integration techniques within MD are the Verlet algorithm and the use of instantaneous normal mode coordinates. The Verlet algorithm begins by writing the Taylor expansion for a coordinate at time t+ Af and f- Af ... 

These instantaneous normal modes show a number of useful properties. 

In this contribution the concept of instantaneous normal modes is applied to three molecular liquid systems, carbon monoxide at 80 K and carbon disulphide at ambient temperature and two different densities. The systems were chosen in this way because pairs of them show similarities either in structural or in dynamical properties. The systems and their simulation are described in the following section. Subsequently two different types of molecular coordinates are used cis input to normal mode calculations, external, i.e. translational and rotational coordinates, and internal, i.e. vibrational coordinates of strongly infrared active modes, respectively. The normal mode spectra are related quantitatively to molecular properties and to those of liquid structure and dynamics. Finally a synthesis of both calculations is attempted on qualitative grounds aiming at the treatment of vibrational dephcising effects. 

III. Instantaneous normal mode spectra for translational and rotational... 

For the calculation of the normal mode spectra external and internal coordinates were assumed to be dynamically decoupled. Translational and rotational coordinates were extracted from the trajectories while all vibrational coordinates were set to zero. Dynamical matrices were set up for 50 configurations generated by molecular dynamics simulation. Long-range Coulombic interactions were treated using the Ewald summation technique. In Figure 2 the instantaneous normal mode spectra are depicted while in Table 3 some of their integral properties are compiled. 

---