Expectation values of single-particle operators in the random phase approximation ground state.

We developed a method for computing matrix elements of single-particle operators in the correlated random phase approximation ground state. Working with the explicit random phase approximation ground state wavefunction, we derived a practically useful and simple expression for a molecular property in terms of random phase approximation amplitudes. The theory is illustrated by the calculation of molecular dipole moments for a set of representative molecules.

Chiral selectivity of amino acid adsorption on chiral surfaces--the case of alanine on Pt.

We study the binding pattern of the amino acid alanine on the naturally chiral Pt surfaces Pt(531), Pt(321), and Pt(643). These surfaces are all vicinal to the {111} direction but have different local environments of their kink sites and are thus a model for realistic roughened Pt surfaces. Alanine has only a single methyl group attached to its chiral center, which makes the number of possible binding conformations computationally tractable. Additionally, only the amine and carboxyl group are expected to interact strongly with the Pt substrate. On Pt(531), we study the molecule in its pristine as well as its deprotonated form and find that the deprotonated one is more stable by 0.47 eV. Therefore, we study the molecule in its deprotonated form on Pt(321) and Pt(643). As expected, the oxygen and nitrogen atoms of the deprotonated molecule provide a local binding "tripod" and the most stable adsorption configurations optimize the interaction of this "tripod" with undercoordinated surface atoms. However, the interaction of the methyl group plays an important role: it induces significant chiral selectivity of about 60 meV on all surfaces. Hereby, the L-enantiomer adsorbs preferentially to the Pt(321)(S) and Pt(643)(S) surfaces, while the D-enantiomer is more stable on Pt(531)(S). The binding energies increase with increasing surface density of kink sites, i.e., they are largest for Pt(531)(S) and smallest for Pt(643)(S).

Adsorption and ring-opening of lactide on the chiral metal surface Pt(321)(S) studied by density functional theory.

We study the adsorption and ring-opening of lactide on the naturally chiral metal surface Pt(321)(S). Lactide is a precursor for polylactic acid ring-opening polymerization, and Pt is a well known catalyst surface. We study, here, the energetics of the ring-opening of lactide on a surface that has a high density of kink atoms. These sites are expected to be present on a realistic Pt surface and show enhanced catalytic activity. The use of a naturally chiral surface also enables us to study potential chiral selectivity effects of the reaction at the same time. Using density functional theory with a functional that includes the van der Waals forces in a first-principles manner, we find modest adsorption energies of around 1.4 eV for the pristine molecule and different ring-opened states. The energy barrier to be overcome in the ring-opening reaction is found to be very small at 0.32 eV and 0.30 eV for LL- and its chiral partner DD-lactide, respectively. These energies are much smaller than the activation energy for a dehydrogenation reaction of 0.78 eV. Our results thus indicate that (a) ring-opening reactions of lactide on Pt(321) can be expected already at very low temperatures, and Pt might be a very effective catalyst for this reaction; (b) the ring-opening reaction rate shows noticeable enantioselectivity.

Enantioselectivity of (321) chiral noble metal surfaces: a density functional theory study of lactate adsorption.

The adsorption of the chiral molecule lactate on the intrinsically chiral noble metal surfaces Pt(321), Au(321), and Ag(321) is studied by density functional theory calculations. We use the oPBE-vdW functional which includes van der Waals forces on an ab initio level. It is shown that the molecule binds via its carboxyl and the hydroxyl oxygen atoms to the surface. The binding energy is larger on Pt(321) and Ag(321) than on Au(321). An analysis of the contributions to the binding energy of the different molecular functional groups reveals that the deprotonated carboxyl group contributes most to the binding energy, with a much smaller contribution of the hydroxyl group. The Pt(321) surface shows considerable enantioselectivity of 0.06 eV. On Au(321) and Ag(321) it is much smaller if not vanishing. The chiral selectivity of the Pt(321) surface can be explained by two factors. First, it derives from the difference in van der Waals attraction of L- and D-lactate to the surface that we trace to differences in the binding energy of the methyl group. Second, the multi-point binding pattern for lactate on the Pt(321) surface is sterically more sensitive to surface chirality and also leads to large binding energy contributions of the hydroxyl group. We also calculate the charge transfer to the molecule and the work function to gauge changes in electronic structure of the adsorbed molecule. The work function is lowered by 0.8 eV on Pt(321) with much smaller changes on Au(321) and Ag(321).

Adsorption of lactic acid on chiral Pt surfaces--a density functional theory study.

The adsorption of the chiral molecule lactic acid on chiral Pt surfaces is studied by density functional theory calculations. First, we study the adsorption of L-lactic acid on the flat Pt(111) surface. Using the optimed PBE - van der Waals (oPBE-vdW) functional, which includes van der Waals forces on an ab initio level, it is shown that the molecule has two binding sites, a carboxyl and the hydroxyl oxygen atoms. Since real chiral surfaces are (i) known to undergo thermal roughening that alters the distribution of kinks and step edges but not the overall chirality and (ii) kink sites and edge sites are usually the energetically most favored adsorption sites, we focus on two surfaces that allow qualitative sampling of the most probable adsorption sites. We hereby consider chiral surfaces exhibiting (111) facets, in particular, Pt(321) and Pt(643). The binding sites are either both on kink sites-which is the case for Pt(321) or on one kink site-as on Pt(643). The binding energy of the molecule on the chiral surfaces is much higher than on the Pt(111) surface. We show that the carboxyl group interacts more strongly than the hydroxyl group with the kink sites. The results indicate the possible existence of very small chiral selectivities of the order of 20 meV for the Pt(321) and Pt(643) surfaces. L-lactic acid is more stable on Pt(321)(S) than D-lactic acid, while the chiral selectivity is inverted on Pt(643)(S). The most stable adsorption configurations of L- and D-lactic acid are similar for Pt(321) but differ for Pt(643). We explore the impact of the different adsorption geometries on the work function, which is important for field ion microscopy.

Nonequilibrium perturbation theory in Liouville-Fock space for inelastic electron transport.

We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville-Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron-vibronic and electron-electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Green's function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.

Stability analysis of multiple nonequilibrium fixed points in self-consistent electron transport calculations.

We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary, nonlinear kinetic equation for single-particle density matrix. We obtain the stability matrix by linearizing the kinetic equation around the fixed points and analyze the real part of its spectrum to assess the asymptotic time behavior of the fixed points. We derive expressions for the stability matrices within Hartree-Fock and linear response adiabatic time-dependent density functional theory. The stability analysis of multiple fixed points is performed within the nonequilibrium Hartree-Fock approximation for the electron transport through a molecule with a spin-degenerate single level with local Coulomb interaction.

Kramers problem for nonequilibrium current-induced chemical reactions.

We discuss the use of tunneling electron current to control and catalyze chemical reactions. Assuming the separation of time scales for electronic and nuclear dynamics we employ Langevin equation for a reaction coordinate. The Langevin equation contains nonconservative current-induced forces and gives nonequilibrium, effective potential energy surface for current-carrying molecular systems. The current-induced forces are computed via Keldysh nonequilibrium Green's functions. Once a nonequilibrium, current-depended potential energy surface is defined, the chemical reaction is modeled as an escape of a Brownian particle from the potential well. We demonstrate that the barrier between the reactant and the product states can be controlled by the bias voltage. When the molecule is asymmetrically coupled to the electrodes, the reaction can be catalyzed or stopped depending on the polarity of the tunneling current.

Second-order post-Hartree-Fock perturbation theory for the electron current.

Based on the super-fermion representation of quantum kinetic equations we develop nonequilibrium, post-Hartree-Fock many-body perturbation theory for the current through a region of interacting electrons. We apply the theory to out of equilibrium Anderson model and discuss practical implementation of the approach. Our calculations show that nonequilibrium electronic correlations may produce significant quantitative and qualitative corrections to mean-field electronic transport properties.

Super-fermion representation of quantum kinetic equations for the electron transport problem.

We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-hermitian liouvillian in super-Fock space. We transform the liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree-Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.

Calculation of semiclassical free energy differences along nonequilibrium classical trajectories.

We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in variant Planck's over 2pi(2) along classically generated trajectories. The results are formulated in terms of purely classical Hamiltonians and trajectories, so that semiclassical partition functions can be computed, e.g., via classical molecular dynamics simulations. The Hamiltonians, however, contain additional potential-energy terms, which are proportional to variant Planck's over 2pi(2) and are temperature-dependent. We discuss the influence of quantum interference on the nonequilibrium work and problems with unambiguous definition of the semiclassical work operator.

Nonequilibrium Fock space for the electron transport problem.

Based on the formalism of thermofield dynamics we propose a concept of nonequilibrium Fock space and nonequilibrium quasiparticles for quantum many-body system in nonequilibrium steady state. We develop a general theory as well as demonstrate the utility of the approach on the example of electron transport through the interacting region. The proposed approach is compatible with advanced quantum chemical methods of electronic structure calculations such as coupled cluster theory and configuration interaction.

Asymptotic nonequilibrium steady-state operators.

We present a method for the calculation of asymptotic operators for nonequilibrium steady-state quantum systems. The asymptotic steady-state operator is obtained by averaging the corresponding operator in Heisenberg representation over infinitely long time. Several examples are considered to demonstrate the utility of our method. The results obtained within our approach are compared to those obtained within the Schwinger-Keldysh nonequilibrium Green's functions.

Microscopic origin of the jump diffusion model.

The present paper is aimed at studying the microscopic origin of the jump diffusion. Starting from the N-body Liouville equation and making only the assumption that molecular reorientation is overdamped, we derive and solve the new (hereafter generalized diffusion) equation. This is the most general equation which governs orientational relaxation of an equilibrium molecular ensemble in the hindered rotation limit and in the long time limit. The generalized diffusion equation is an extension of the small-angle diffusion equation beyond the impact approximation. We establish the conditions under which the generalized diffusion equation can be identified with the jump diffusion equation, and also discuss the similarities and differences between the two approaches.

Unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems.

We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total Hamiltonian into the system part, the bath part, and their coupling. We rederive many equalities which are available in the literature and obtain a number of new equalities for nonequilibrium classical and quantum systems. Our results can be useful for determining partition functions and (generalized) free energies through simulations or measurements performed on nonequilibrium systems.

Directed motion and useful work from an isotropic nonequilibrium distribution.

We demonstrate that a gas of classical particles trapped in an external asymmetric potential undergoes a quasiperiodic motion, if the temperature of its initial velocity distribution TNE differs from the equilibrium temperature Teq. The magnitude of the effect is determined by the value of TNE-Teq, and the direction of the motion is determined by the sign of this expression. The "loading" and "unloading" of the gas particles change directions of their motion, thereby creating a possibility of shuttle-like motion. The system works as a Carnot engine where the heat flow between kinetic and potential parts of the nonequilibrium distribution produces the useful work.

Calculations of canonical averages from the grand canonical ensemble.

Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble provides an appropriate physical description but it is often much easier to perform the calculations in the corresponding grand canonical ensemble. We present a method to compute averages in the canonical ensemble based on calculations of the expectation values in the grand canonical ensemble. The number of particles, which is fixed in the canonical ensemble, is not necessarily the same as the average number of particles in the grand canonical ensemble.

Manifestation of nonequilibrium initial conditions in molecular rotation: the generalized J-diffusion model.

In order to adequately describe molecular rotation far from equilibrium, we have generalized the J-diffusion model by allowing the rotational relaxation rate to be angular momentum dependent. The calculated nonequilibrium rotational correlation functions (CFs) are shown to decay much slower than their equilibrium counterparts, and orientational CFs of hot molecules exhibit coherent behavior, which persists for several rotational periods. As distinct from the results of standard theories, rotational and orientational CFs are found to dependent strongly on the nonequilibrium preparation of the molecular ensemble. We predict the Arrhenius energy dependence of rotational relaxation times and violation of the Hubbard relations for orientational relaxation times. The standard and generalized J-diffusion models are shown to be almost indistinguishable under equilibrium conditions. Far from equilibrium, their predictions may differ dramatically.

Velocity dependence of friction and Kramers relaxation rates.

We study the influence of the velocity dependence of friction on the escape rate of a Brownian particle from the deep potential well (Eb>>kBT, Eb is the barrier height, kB is the Boltzmann constant, and T is the bath temperature). The bath-induced relaxation is treated within the Rayleigh model (a heavy particle of mass M in the bath of light particles of mass m<

Angular momentum dependent friction slows down rotational relaxation under nonequilibrium conditions.

It has recently been shown that relaxation of the rotational energy of hot nonequilibrium photofragments (i) slows down significantly with the increase of their initial rotational temperature and (ii) differs dramatically from the relaxation of the equilibrium rotational energy correlation function, manifesting thereby the breakdown of the linear response description [A. C. Moskun et al., Science 311, 1907 (2006)]. We demonstrate that this phenomenon may be caused by the angular momentum dependence of rotational friction. We have developed the generalized Fokker-Planck equation whose rotational friction depends upon angular momentum algebraically. The calculated rotational correlation functions correspond well to their counterparts obtained via molecular dynamics simulations in a broad range of initial nonequilibrium conditions. It is suggested that the angular momentum dependence of friction should be taken into account while describing rotational relaxation far from equilibrium.