The Instantaneous Normal Modes of Liquids

We use ring-polymer-molecular-dynamics (RPMD) techniques and the semi-empirical q-TIP4P/F water model to investigate the relationship between hydrogen bond connectivity and the characteristics of nuclear position fluctuations, including explicit incorporation of quantum effects, for the energetically low lying isomers of the prototype cluster [H 2 O] 8 at T = 50 K and at 150 K. Our results reveal that tunneling and zero-point energy effects lead to sensible increments in the magnitudes of the fluctuations of intra and intermolecular distances. The degree of proton spatial delocalization is found to map logically with the hydrogen-bond connectivity pattern of the cluster. Dangling hydrogen bonds exhibit the largest extent of spatial delocalization and participate in shorter intramolecular O-H bonds. Combined effects from quantum and polarization fluctuations on the resulting individual dipole moments are also examined. From the dynamical side, we analyze the characteristics of the infrared absorption spectrum. The incorporation of nuclear quantum fluctuations promotes red shifts and sensible broadening relative to the classical profile, bringing the simulation results in much more satisfactory agreement with direct experimental information in the mid and high frequency range of the stretching band. While RPMD predictions overestimate the peak position of the low frequency shoulder, the overall agreement with that reported using an accurate, parameterized, many-body potential is reasonable, and far superior to that one obtains by implementing a partially adiabatic centroid molecular dynamics approach. Quantum effects on the collective dynamics, as reported by instantaneous normal modes, are also discussed. © 2013 AIP Publishing LLC.

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“…Within this context, the analysis of the instantaneous normal modes 65 (INM) is also instructive. In the top panel of Fig.…”

Section: Time Dependent Resultsmentioning

confidence: 99%

Nuclear quantum effects on the structure and the dynamics of [H2O]8 at low temperatures

Videla

Rossky

Laría

2013

The Journal of Chemical Physics

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“…Note that INM are naturally decoupled through the 2nd order Taylor expansion. The approximation of decoupling the INM coordinates has also been used elsewhere [159,160]. This approximation is particularly suited for the KP theory because of the exponential decaying property of the Gaussian convolution integrals in Eq.…”

Section: Automated Integration-free Path-integral (Aif-pi) Methodsmentioning

confidence: 99%

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Wong

2014

Commun. comput. phys.

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Abstract. Feynman's path integral reformulates the quantum Schrödinger differential equation to be an integral equation. It has been being widely used to compute internuclear quantum-statistical effects on many-body molecular systems. In this Review, the molecular Schrödinger equation will first be introduced, together with the BornOppenheimer approximation that decouples electronic and internuclear motions. Some effective semiclassical potentials, e.g., centroid potential, which are all formulated in terms of Feynman's path integral, will be discussed and compared. These semiclassical potentials can be used to directly calculate the quantum canonical partition function without individual Schrödinger's energy eigenvalues. As a result, path integrations are conventionally performed with Monte Carlo and molecular dynamics sampling techniques. To complement these techniques, we will examine how Kleinert's variational perturbation (KP) theory can provide a complete theoretical foundation for developing non-sampling/non-stochastic methods to systematically calculate centroid potential. To enable the powerful KP theory to be practical for many-body molecular systems, we have proposed a new path-integral method: automated integrationfree path-integral (AIF-PI) method. Due to the integration-free and computationally inexpensive characteristics of our AIF-PI method, we have used it to perform ab initio path-integral calculations of kinetic isotope effects on proton-transfer and RNA-related phosphoryl-transfer chemical reactions. The computational procedure of using our AIF-PI method, along with the features of our new centroid path-integral theory at the minimum of the absolute-zero energy (AMAZE), are also highlighted in this review.

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“…In the former case it is often possible to analyze the Hessian in the stationary points of the free-energy, having therefore important information on the shape and stability of the thermodynamic states [7]. In liquids, on the other hand, the Hessian of the potential energy is the key object in the context of the instantaneous normal modes approach [11,12], where the average spectrum of the Hessian is directly connected to many physical observables of the system. In particular, it has been argued that there exists a deep relation between the diffusion properties of a liquid and the negative unstable eigenvalues of the average Hessian [12].…”

Section: Introductionmentioning

confidence: 99%

Index distribution of random matrices with an application to disordered systems

2000

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We compute the distribution of the number of negative eigenvalues (the index) for an ensemble of Gaussian random matrices, by means of the replica method. This calculation has important applications in the context of statistical mechanics of disordered systems, where the second derivative of the potential energy (the Hessian) is a random matrix whose negative eigenvalues measure the degree of instability of the energy surface. An analysis of the probability distribution of the Hessian index is therefore relevant for a geometric characterization of the energy landscape in disordered systems. The approach we use here is particularly suitable for this purpose, since it addresses the problem without any a priori assumption on the random matrix ensemble and can be naturally extended to more realistic, non-Gaussian distributions.

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The Instantaneous Normal Modes of Liquids

Cited by 375 publications

References 73 publications

Nuclear quantum effects on the structure and the dynamics of [H2O]8 at low temperatures

Nuclear quantum effects on the structure and the dynamics of [H2O]8 at low temperatures

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Index distribution of random matrices with an application to disordered systems

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