Isothermal and adiabatic elastic constants from virial fluctuations.

We derive expressions for classical isothermal and adiabatic elastic constants for periodic systems with the boundary contributions included explicitly. The potential-dependent part of these expressions is written in terms of potential energies of atomic groups that make up the total potential energy. It is shown that in the thermodynamic limit, the Born term, which depends on the second derivatives of potential energy, can be expressed exactly in terms of equilibrium averages that involve two types of atomic-group virials. As a result, the new form of the Born term involves only first derivatives of either atomic-group or total potential energies. The derived elastic constant expressions involving the two forms of the Born terms are tested and compared using molecular-dynamics simulations of crystalline argon and silicon. For both materials, the elastic constants obtained using the two forms of the Born term are in good agreement. In particular, the new form of the Born term converges to the same value as the original Born term but at a slower rate. The results for silicon also agree well with the results from the previous molecular-dynamics studies.

A theoretical study of the relaxation of a phenyl group chemisorbed to an RDX freestanding thin film.

Energy relaxation from an excited phenyl group chemisorbed to the surface of a crystalline thin film of α-1,3,5-trinitro-1,3,5-triazacyclohexane (α-RDX) at 298 K and 1 atm is simulated using molecular dynamics. Two schemes are used to excite the phenyl group. In the first scheme, the excitation energy is added instantaneously as kinetic energy by rescaling momenta of the 11 atoms in the phenyl group. In the second scheme, the phenyl group is equilibrated at a higher temperature in the presence of static RDX geometries representative of the 298 K thin film. An analytical model based on ballistic phonon transport that requires only the harmonic part of the total Hamiltonian and includes no adjustable parameters is shown to predict, essentially quantitatively, the short-time dynamics of the kinetic energy relaxation (∼200 fs). The dynamics of the phenyl group for times longer than about 6 ps follows exponential decay and agrees qualitatively with the dynamics described by a master equation. Long-time heat propagation within the bulk of the crystal film is consistent with the heat equation.

Obtaining the Hessian from the force covariance matrix: Application to crystalline explosives PETN and RDX.

We show that for solids the effective Hessian matrix, averaged over the canonical ensemble, can be calculated from the force covariance matrix. This effective Hessian reduces to the standard Hessian as the temperature approaches zero, while at finite temperatures it implicitly includes anharmonic corrections. As a case study, we calculate the effective Hessians and the corresponding normal mode eigenvectors and frequencies for the crystalline organic explosives pentaerythritol tetranitrate and α-1,3,5-trinitro-1,3,5-triazacyclohexane. The resulting normal mode frequencies are compared to those obtained by diagonalizing the standard Hessian matrix of second derivatives in Cartesian displacements about the potential energy minimum. Effects of temperature and statistical noise on the effective Hessians and normal mode frequencies are discussed.

Calculation of anharmonic couplings and THz linewidths in crystalline PETN.

We have developed a method for calculating the cubic anharmonic couplings in molecular crystals for normal modes with the zero wave vector in the framework of classical mechanics, and have applied it, combined with perturbation theory, to obtain the linewidths of all infrared absorption lines of crystalline pentaerythritol tetranitrate in the terahertz region (<100 cm(-1)). Contributions of the up- and down-conversion processes to the total linewidth were calculated. The computed linewidths are in qualitative agreement with experimental data and the results of molecular dynamics simulations. Quantum corrections to the linewidths in the terahertz region are shown to be negligible.

Molecular dynamics study of the pressure-dependent terahertz infrared absorption spectrum of α- and γ-RDX.

Terahertz infrared absorption spectra of the α and γ polymorphs of 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) were predicted using two different theoretical approaches based on molecular dynamics simulations. The thermodynamic conditions studied were T = 298 K and hydrostatic pressures P = 0.0, 1.0, and 2.0 GPa for α-RDX and P = 3.0, 5.2, and 7.0 GPa for γ-RDX. The spectra obtained using the two methods are similar but not identical. In the case of α-RDX for pressure P = 0.0 GPa both spectra agree reasonably well with experimental data. The predicted spectra for α-RDX exhibit red-shifting (mode softening) of the main absorption peak with increasing pressure while for γ-RDX the spectra exhibit overall blue-shifting with increasing pressure.

Terahertz spectrum and normal-mode relaxation in pentaerythritol tetranitrate: effect of changes in bond-stretching force-field terms.

Terahertz (THz) active normal-mode relaxation in crystalline pentaerythritol tetranitrate (PETN) was studied using classical molecular dynamics simulations for energy and density conditions corresponding to room temperature and atmospheric pressure. Two modifications to the fully flexible non-reactive force field due to Borodin et al. [J. Phys. Chem. B 112, 734 (2008)] used in a previous study of THz-active normal-mode relaxation in PETN [J. Chem. Phys. 134, 014513 (2011)] were considered to assess the sensitivity of the earlier predictions to details of the covalent bond-stretching terms in the force field. In the first modification the harmonic bond-stretching potential was replaced with the Morse potential to study the effect of bond anharmonicity on the THz-region mode relaxation. In the second modification the C-H and nitro-group N-O bond lengths were constrained to constant values to mimic lower quantum occupation numbers for those high-frequency modes. The results for relaxation times of the initially excited modes were found to be insensitive to either force-field modification. Overall time scales for energy transfer to other modes in the system were essentially unaffected by the force-field modifications, whereas the detailed pathways by which the energy transfer occurs are more complicated for the Morse potential than for the harmonic-bond and fixed-bond cases. Terahertz infrared absorption spectra constructed using calculated normal-mode frequencies, transition dipoles, and relaxation times for THz-active modes were compared to the spectra obtained from the Fourier transform of the dipole-dipole time autocorrelation function (DDACF). Results from the two approaches are in near agreement with each other and with experimental results in terms of main peak positions. Both theoretical methods yield narrower peaks than observed experimentally and in addition predict a weaker peak at ω ∼ 50 cm(-1) that is weak or absent experimentally. Peaks obtained using the DDACF approach are broader than those obtained from the normal-mode relaxation method.

Terahertz normal mode relaxation in pentaerythritol tetranitrate.

Normal vibrational modes for a three-dimensional defect-free crystal of the high explosive pentaerythritol tetranitrate were obtained in the framework of classical mechanics using a previously published unreactive potential-energy surface [J. Phys. Chem. B 112, 734 (2008)]. Using these results the vibrational density of states was obtained for the entire vibrational frequency range. Relaxation of selectively excited terahertz-active modes was studied using isochoric-isoergic (NVE) molecular dynamics simulations for energy and density conditions corresponding to room temperature and atmospheric pressure. Dependence of the relaxation time on the initial modal excitation was considered for five excitation energies between 10 and 500 kT and shown to be relatively weak. The terahertz absorption spectrum was constructed directly using linewidths obtained from the relaxation times of the excited modes for the case of 10 kT excitation. The spectrum shows reasonably good agreement with experimental results. Dynamics of redistribution of the excited mode energy among the other normal modes was also studied. The results indicate that, for the four terahertz-active initially excited modes considered, there is a small subset of zero wave vector (k = 0) modes that preferentially absorb the energy on a few-picosecond time scale. The majority of the excitation energy, however, is transferred nonspecifically to the bath modes of the system.

Energy and charge-transfer dynamics using projected modes.

For electron-phonon Hamiltonians with the couplings linear in the phonon operators, we construct a class of unitary transformations that separate the normal modes into two groups. The modes in the first group interact with the electronic degrees of freedom directly. The modes in the second group interact directly only with the modes in the first group but not with the electronic system. These transformations can be carried out independently for different types of phonon modes, e.g., high- versus low-frequency phonon bands. This construction generalizes recently introduced transformations for systems exhibiting a conical intersection topology. The separation of the normal modes into several groups allows one to develop new approximation schemes. We apply one of such schemes to study electronic relaxation at a semiconducting polymer interface.

Correlation functions in quantized Hamilton dynamics and quantal cumulant dynamics.

Quantized Hamilton dynamics (QHD) [O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 113, 6557 (2000)] and quantal cumulant dynamics (QCD) [Shigeta et al., J. Chem. Phys. 125, 244102 (2006)] are used to obtain a semiclassical description of two-time correlation functions (CFs). Generally, lower-order CFs couple to higher-order CFs. The infinite hierarchy is terminated by a closure, which neglects higher-order irreducible correlators and provides an efficient approximation to quantum mechanics. The approach is illustrated with a simple nonlinear system, for which the real part of the classical CF continues a perfect oscillation and the imaginary part is identically zero. At little computational expense, the second-order QHD/QCD approximation reproduces the real and imaginary parts of the quantum-mechanical CF.

Dissipation of classical energy in nonlinear quantum systems.

We show using two simple nonlinear quantum systems that the infinite set of quantum dynamical variables, as introduced in quantized Hamilton dynamics [O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 113, 6557 (2000)], behave as a thermostat with respect to the finite number of classical variables. The coherent classical component of the evolution decays by coupling to the chaotic quantum reservoir. The classical energy, understood as the part of system energy expressible through the average values of coordinates and momenta, is transferred to the quantum energy expressible through the higher moments of coordinates and momenta and other quantum variables. At long times, the classical variables reach equilibrium, and the classical energy fluctuates around the equilibrium value. These phenomena are illustrated with the exactly solvable Jaynes-Cummings model and a nonlinear oscillator.

Time-convolutionless master equation for mesoscopic electron-phonon systems.

The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number of normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers.

Exactly solvable approximating models for Rabi Hamiltonian dynamics.

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonalizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges.

Competing elimination and substitution reactions of simple acyclic disulfides.

MP2/aug-cc-pVDZ and B3LYP/cc-pVDZ calculations of the reactions of CH3SSR (R = H or CH3) with fluoride, hydroxide or allyl anion in the gas-phase were performed to determine the mechanism for both elimination and substitution reactions. The elimination reactions were shown to follow the E2 mechanism. The substitution reactions with hydroxide and fluoride proceed by the addition-elimination mechanism, but those with allyl anion proceed by the SN2 mechanism. The elimination reactions with F- and HO- are preferred to the substitution reactions, while allyl anion prefers the substitution route.

Quantum transport in chains with noisy off-diagonal couplings.

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time evolution of the system reduces to the [Lindblad, Commun. Math. Phys. 48, 119 (1976)] equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfies discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.

Fermi-Pasta-Ulam beta lattice: Peierls equation and anomalous heat conductivity.

The Peierls equation is considered for the Fermi-Pasta-Ulam beta lattice. Explicit form of the linearized collision operator is obtained. Using this form the decay rate of the normal-mode energy as a function of wave vector k is estimated to be proportional to k(5/3). This leads to the t(-3/5) long-time behavior of the current correlation function, and, therefore, to the divergent coefficient of heat conductivity. These results are in good agreement with the results of recent computer simulations. Compared to the results obtained through the mode coupling theory our estimations give the same k dependence of the decay rate but a different temperature dependence. Using our estimations we argue that adding a harmonic on-site potential to the Fermi-Pasta-Ulam beta lattice may lead to finite heat conductivity in this model.

Damped harmonic oscillator: pure states of the bath and exact master equations.

Time evolution of a harmonic oscillator linearly coupled to a heat bath is compared for three classes of initial states for the bath modes-grand canonical ensemble, number states, and coherent states. It is shown that for a wide class of number states the behavior of the oscillator is similar to the case of the equilibrium bath. If the bath modes are initially in coherent states, then the variances of the oscillator coordinate and momentum, as well as its entanglement to the bath, asymptotically approach the same values as for the oscillator at zero temperature and the average coordinate and momentum show a Brownian-like behavior. We derive an exact master equation for the characteristic function of the oscillator valid for arbitrary factorized initial conditions. In the case of the equilibrium bath this equation reduces to an equation of the Hu-Paz-Zhang type, while for the coherent states bath it leads to an exact stochastic master equation with a multiplicative noise.