Amrendra Vijay

Adsorption of gold on stoichiometric and reduced rutile TiO2 (110) surfaces

We present a density functional study of reduced and stoichiometric rutile TiO2 (110) surfaces, and of binding of gold monomers and dimers to them. On the stoichiometric TiO2 surface, a Au atom binds to either a five-coordinated Ti atom on the basal plane, or atop a bridging oxygen atom. The two sites have nearly the same binding energy, suggesting diffusion of Au across unreduced regions of TiO2 (110) will be fast. The reduction of the rutile surface, by removal of bridging oxygen atoms, causes a charge redistribution in the system, which extends far from the vacancy site. A Au atom binds strongly to the reduced surfaces: the greater the degree of reduction the stronger the binding. On all reduced surfaces, the preferred binding sites are the vacant bridging oxygen sites. Less stable is the binding to a nearby five-coordinated Ti atom. The binding of Au2 on the reduced surfaces follows a similar pattern. Specifically, if two adjacent vacant sites are available, the optimal structure involves the dimer “d...

Structure of the (001) surface of γ alumina

Using density functional theory, we have studied the structure and energetics of the (001) face of γ alumina. Our results address several experimental issues: (1) When the face with tetrahedral aluminum is exposed in the bulk-terminated system, the surface reconstructs extensively, leading to exposure of the higher-density layer. When only a few layers are present, this reconstruction may even lead to the collapse of the system into a different structure. (2) We find that the lowest energy is obtained if the vacant spinel sites lie on octahedral positions. We also find that vacancies are less preferred on the surface than in the bulk. (3) Migration to and from the surface of vacant spinel sites, by hopping of Al atoms between octahedral and tetrahedral cation sites has a rather high barrier. This suggests the vacancy distribution may not reach equilibrium if the material is not annealed carefully during preparation.

A polynomial expansion of the quantum propagator, the Green’s function, and the spectral density operator

One of the methods for calculating time propagators in quantum mechanics uses an expansion of e−iĤt/ℏ in a sum of orthogonal polynomial. Equations involving Chebychev, Legendre, Laguerre, and Hermite polynomials have been used so far. We propose a new formula, in which the propagator is expressed as a sum in which each term is a Gegenbauer polynomial multiplied with a Bessel function. The equations used in previous work can be obtained from ours by giving specific values to a parameter. The expression allows analytic continuation from imaginary to real time, transforming thus results obtained by evaluating thermal averages into results pertaining to the time evolution of the system. Starting from the expression for the time propagator we derive equations for the Green’s function and the density of states. To perform computations one needs to calculate how the polynomial in the Hamiltonian operator acts on a wave function. The high order polynomials can be obtained from the lower ordered ones through a thr...

Semiclassical wave packet calculations on ion–molecule reactions: Studies on B+(3Pu)+H2 reaction

We present the investigations of nonadiabatic scattering processes (reactive as well charge-transfer) occurring in B++H2 reaction in the gas phase on the triplet electronic surfaces utilizing a mixed quantum-classical approach to scattering of three particle systems in hyperspherical coordinates. The time-dependent Schrodinger equation is solved in diabatic representation using wave packet propagation method on a grid in two quantum dimensions. The potential-energy surfaces have been obtained using the valence-bond diatomics-in-molecule approach.

A Lorentzian function based spectral filter for calculating the energy of excited bound states in quantum mechanics

In this paper, we study a Lorentzian function based spectral filter suitable for computing highly excited bound states of a quantum system. Using this filter, we have derived an expression for spectral intensities and also implemented a filter diagonalization scheme. We have used a Chebyshev polynomial based series expansion of the filter operator, and this allows us to accomplish a partial resummation of the double series analytically when computing the necessary matrix elements; this saves considerable computational effort. The exponential damping term in the Lorentzian provides a convenient control over the resolution of the computed spectrum in the spectral intensity plot. As a numerical test, we have computed eigenvalues and spectral intensities of a model Hamiltonian in an arbitrary energy window. For situations where eigenvalues are distributed nonuniformly we suggest a computational protocol, which judiciously combines the spectral intensity information with the filter diagonalization method. This protocol is efficient only with the Lorentzian filter studied here.

Anomalies in the equilibrium and nonequilibrium properties of correlated ions in complex molecular environments

Emergent statistical attributes, and therefore the equations of state, of an assembly of interacting charge carriers embedded within a complex molecular environment frequently exhibit a variety of anomalies, particularly in the high-density (equivalently, the concentration) regime, which are not well understood, because they do not fall under the low-concentration phenomenologies of Debye-Hückel-Onsager and Poisson-Nernst-Planck, including their variants. To go beyond, we here use physical concepts and mathematical tools from quantum scattering theory, transport theory with the Stosszahlansatz of Boltzmann, and classical electrodynamics (Lorentz gauge) and obtain analytical expressions both for the average and the frequency-wave vector-dependent longitudinal and transverse current densities, diffusion coefficient, and the charge density, and therefore the analytical expressions for (a) the chemical potential, activity coefficient, and the equivalent conductivity for strong electrolytes and (b) the current-voltage characteristics for ion-transport processes in complex molecular environments. Using a method analogous to the notion of Debye length and thence the electrical double layer, we here identify a pair of characteristic length scales (longitudinal and the transverse), which, being wave vector and frequency dependent, manifestly exhibit nontrivial fluctuations in space-time. As a unifying theme, we advance a quantity (inverse length dimension), g_{scat}^{(a)}, which embodies all dynamical interactions, through various quantum scattering lengths, relevant to molecular species a, and the analytical behavior which helps us to rationalize the properties of strong electrolytes, including anomalies, in all concentration regimes. As an example, the behavior of g_{scat}^{(a)} in the high-concentration regime explains the anomalous increase of the Debye length with concentration, as seen in a recent experiment on electrolyte solutions. We also put forth an extension of the standard diffusion equation, which manifestly incorporates the effects arising from the underlying microscopic collisions among constituent molecular species. Furthermore, we show a nontrivial connection between the current-voltage characteristics of electrolyte solutions and the Landauers approach to electrical conduction in mesoscopic solids and thereby establish a definite conceptual bridge between the two disjoint subjects. For numerical insight, we present results on the aqueous solution of KCl as an example of strong electrolyte, and the transport (conduction as well as diffusion) of K^{+} ions in water, as an example of ion transport across the voltage-gated channels in biological cells.

Normal and Anomalous Diffusion: An Analytical Study Based on Quantum Collision Dynamics and Boltzmann Transport Theory.

Diffusion, an emergent nonequilibrium transport phenomenon, is a nontrivial manifestation of the correlation between the microscopic dynamics of individual molecules and their statistical behavior observed in experiments. We present a thorough investigation of this viewpoint using the mathematical tools of quantum scattering, within the framework of Boltzmann transport theory. In particular, we ask: (a) How and when does a normal diffusive transport become anomalous? (b) What physical attribute of the system is conceptually useful to faithfully rationalize large variations in the coefficient of normal diffusion, observed particularly within the dynamical environment of biological cells? To characterize the diffusive transport, we introduce, analogous to continuous phase transitions, the curvature of the mean square displacement as an order parameter and use the notion of quantum scattering length, which measures the effective interactions between the diffusing molecules and the surrounding, to define a tuning variable, η. We show that the curvature signature conveniently differentiates the normal diffusion regime from the superdiffusion and subdiffusion regimes and the critical point, η = ηc, unambiguously determines the coefficient of normal diffusion. To solve the Boltzmann equation analytically, we use a quantum mechanical expression for the scattering amplitude in the Boltzmann collision term and obtain a general expression for the effective linear collision operator, useful for a variety of transport studies. We also demonstrate that the scattering length is a useful dynamical characteristic to rationalize experimental observations on diffusive transport in complex systems. We assess the numerical accuracy of the present work with representative experimental results on diffusion processes in biological systems. Furthermore, we advance the idea of temperature-dependent effective voltage (of the order of 1 μV or less in a biological environment, for example) as a dynamical cause of the perpetual molecular movement, which eventually manifests as an ordered motion, called the diffusion.