Na2 Vibrating in the Double-Well Potential of State 2 1Σu+ (JM = 00): A Pulsating "Quantum Bubble" with Antagonistic Electronic Flux.

The theory of concerted electronic and nuclear flux densities associated with the vibration and dissociation of a multielectron nonrotating homonuclear diatomic molecule (or ion) in an electronic state 2S+1Σg,u+ (JM = 00) is presented. The electronic population density, nuclear probability density, and nuclear flux density are isotropic. A theorem of Barth , presented in this issue, shows that the electronic flux density (EFD) is also isotropic. Hence, the evolving system appears as a pulsating, or exploding, "quantum bubble". Application of the theory to Na2 vibrating in the double-minimum potential of the 2 1Σu+ (JM = 00) excited state reveals that the EFD consists of two antagonistic components. One arises from electrons that flow essentially coherently with the nuclei. The other, which is oppositely directed (i.e., antagonistic) and more intense, is due to the transition in electronic structure from "Rydberg" to "ionic" type as the nuclei traverse the potential barrier between inner and outer potential wells. This "transition" component of the EFD rises and falls sharply as the nuclei cross the barrier.

Beyond the Born-Oppenheimer approximation: a treatment of electronic flux density in electronically adiabatic molecular processes.

Intuition suggests that a molecular system in the electronic ground state Φ0 should exhibit an electronic flux density (EFD) in response to the motion of its nuclei. If that state is described by the Born-Oppenheimer approximation (BOA), however, a straightforward calculation of the EFD yields zero, since the electrons are in a stationary state, regardless of the state of the nuclear motion. Here an alternative pathway to a nonzero EFD from a knowledge of only the BOA ground-state wave function is proposed. Via perturbation theory a complete set of approximate vibronic eigenfunctions of the whole Hamiltonian is generated. If the complete non-BOA wave function is expressed in the basis of these vibronic eigenfunctions, the ground-state contribution to the EFD is found to involve a summation over excited states. Evaluation of this sum through the so-called "average excitation energy approximation" produces a nonzero EFD. An explicit formula for the EFD for the prototypical system, namely, oriented H2+ vibrating in the electronic ground state, is derived.

Computation of the electronic flux density in the Born-Oppenheimer approximation.

A molecule in the electronic ground state described in the Born­Oppenheimer approximation (BOA) by the wave function ΨBO = Φ0χ0 (where Φ0 is the time-independent electronic energy eigenfunction and χ0 is a time-dependent nuclear wave packet) exhibits a nonzero nuclear flux density, whereas it always displays zero electronic flux density (EFD), because the electrons are in a stationary state. A hierarchical approach to the computation of the EFD within the context of the BOA, which utilizes only standard techniques of quantum chemistry (to obtain Φ0) and quantum dynamics (to describe the evolution of χ0 on the ground-state potential energy surface), provides a resolution of this puzzling, nonintuitive result. The procedure is applied to H2(+) oriented parallel with the z-axis and vibrating in the ground state (2)Σg(+). First, Φ0 and χ0 are combined by the coupled-channels technique to give the normally dominant z-component of the EFD. Imposition of the constraints of electronic continuity, cylindrical symmetry of Φ0 and two boundary conditions on the EFD through a scaling procedure yields an improved z-component, which is then used to compute the complementary orthogonal ρ-component. The resulting EFD agrees with its highly accurate counterpart furnished by a non-BOA treatment of the system.

Quasi-classical theory of electronic flux density in electronically adiabatic molecular processes.

The standard Born-Oppenheimer (BO) description of electronically adiabatic molecular processes predicts a vanishing electronic flux density (EFD). A previously proposed "coupled-channels" theory permits the extraction of the EFD from the BO wave function for one-electron diatomic systems, but attempts at generalization to many-electron polyatomic systems are frustrated by technical barriers. An alternative "quasi-classical" approach, which eliminates the explicit quantum dynamics of the electrons within a classical framework, yet retains the quantum character of the nuclear motion, appears capable of yielding EFDs for arbitrarily complex systems. Quasi-classical formulas for the EFD in simple systems agree with corresponding coupled-channels formulas. Results of the application of the new quasi-classical formula for the EFD to a model triatomic system indicate the potential of the quasi-classical scheme to elucidate the dynamical role of electrons in electronically adiabatic processes in more complex multiparticle systems.

Coupled-channels quantum theory of electronic flux density in electronically adiabatic processes: application to the hydrogen molecule ion.

This article presents the results of the first quantum simulations of the electronic flux density (j(e)) by the "coupled-channels" (CC) theory, the fundamentals of which are presented in the previous article [Diestler, D. J. J. Phys. Chem. A 2012, DOI: 10.1021/jp207843z]. The principal advantage of the CC scheme is that it employs exclusively standard methods of quantum chemistry and quantum dynamics within the framework of the Born-Oppenheimer approximation (BOA). The CC theory goes beyond the BOA in that it yields a nonzero j(e) for electronically adiabatic processes, in contradistinction to the BOA itself, which always gives j(e) = 0. The CC is applied to oriented H(2)(+) vibrating in the electronic ground state ((2)Σ(g)(+)), for which the nuclear and electronic flux densities evolve on a common time scale of about 22 fs per vibrational period. The system is chosen as a touchstone for the CC theory, because it is the only one for which highly accurate flux densities have been calculated numerically without invoking the BOA [Barth et al, Chem. Phys. Lett. 2009, 481, 118]. Good agreement between CC and accurate results supports the CC approach, another advantage of which is that it allows a transparent interpretation of the temporal and spatial properties of j(e).

Coupled-channels quantum theory of electronic flux density in electronically adiabatic processes: fundamentals.

The Born-Oppenheimer (BO) description of electronically adiabatic molecular processes predicts a vanishing electronic flux density (j(e)), =1/2∫dR[Δ(b) (x;R) - Δ(a) (x;R)] even though the electrons certainly move in response to the movement of the nuclei. This article, the first of a pair, proposes a quantum-mechanical "coupled-channels" (CC) theory that allows the approximate extraction of j(e) from the electronically adiabatic BO wave function . The CC theory is detailed for H(2)(+), in which case j(e) can be resolved into components associated with two channels α (=a,b), each of which corresponds to the "collision" of an "internal" atom α (proton a or b plus electron) with the other nucleus ß (proton b or a). The dynamical role of the electron, which accommodates itself instantaneously to the motion of the nuclei, is submerged in effective electronic probability (population) densities, Δ(α), associated with each channel (α). The Δ(α) densities are determined by the (time-independent) BO electronic energy eigenfunction, which depends parametrically on the configuration of the nuclei, the motion of which is governed by the usual BO nuclear Schrödinger equation. Intuitively appealing formal expressions for the electronic flux density are derived for H(2)(+).

Statistical thermodynamics of the stability of multivalent ligand-receptor complexes.

Multivalent ligands can form ligand-receptor complexes that are orders of magnitude more stable than their monovalent counterparts. A theory of this "enhancement effect" based on fundamental principles of statistical thermodynamics is presented. A key finding is a simple analytical expression that provides clear and direct insight into the mechanism by which the enhanced stability of the multivalent ligand-receptor complex can be achieved. The theory explains experimental data on the activation of ion channels in the membranes of cells by polymer-linked divalent ligands.

Hybrid atomistic-coarse-grained treatment of multiscale processes in heterogeneous materials: a self-consistent-field approach.

A treatment of multiscale quasistatic processes that combines an atomistic description of microscopic heterogeneous ("near") regions of a material with a coarse-grained (quasicontinuum) description of macroscopic homogeneous ("far") regions is presented. The hybrid description yields a reduced system consisting of the original atoms of the near regions plus pseudoatoms (nodes of the coarse-graining mesh) of the far regions, which interact through an effective many-body potential energy V(eff) that depends on the thermodynamic state. The approximate nature of V(eff) gives rise to "ghost forces," which are reflected in spurious heterogeneities close to interfaces between near and far regions. The impact of ghost forces, which afflict all previous hybrid schemes, is greatly diminished by a self-consistent-field hybrid atomistic-coarse-grained (SCF-HACG) methodology. Tests of the SCF-HACG technique on a fully three-dimensional prototypal model [Lennard-Jones (12,6) crystal] yield thermomechanical properties (e.g., local stress) in good agreement with "exact" properties computed in the fully atomistic limit. The SCF-HACG method is also successfully used to characterize the grain boundary in a Lennard-Jones bicrystal.

Coarse-grained free-energy-functional treatment of quasistatic multiscale processes in heterogeneous materials.

A new treatment of quasistatic (reversible) multiscale processes in heterogeneous materials at nonzero temperature is presented. The system is coarse grained by means of a finite-element mesh. The coarse-grained free-energy functional (of the positions of the nodes of the mesh) appropriate to the thermodynamic-state variables controlled in the relevant process is minimized. Tests of the new procedure on a Lennard-Jonesium crystal yield thermomechanical properties in good agreement with the "exact" atomistic results.

An extension of the quasicontinuum treatment of multiscale solid systems to nonzero temperature.

Covering the solid lattice with a finite-element mesh produces a coarse-grained system of mesh nodes as pseudoatoms interacting through an effective potential energy that depends implicitly on the thermodynamic state. Use of the pseudoatomic Hamiltonian in a Monte Carlo simulation of the two-dimensional Lennard-Jones crystal yields equilibrium thermomechanical properties (e.g., isotropic stress) in excellent agreement with "exact" fully atomistic results.

Hybrid atomistic-coarse-grained treatment of thin-film lubrication. II.

A new hybrid atomistic-coarse-grained (HACG) treatment of reversible processes in multiple-scale systems involving fluid-solid interfaces was tested through isothermal-isobaric Monte Carlo simulations of the quasistatic shearing of a model two-dimensional lubricated contact comprising two planar Lennard-Jones solid substrates that sandwich a softer Lennard-Jones film. Shear-stress profiles (plots of shear stress T(yx) versus lateral displacement of the substrates) obtained by the HACG technique, which combines an atomistic description of the interfacial region with a continuum description of regions well removed from the interface, are compared with "exact" profiles (obtained by treating the whole system at the atomic scale) for a selection of thermodynamic states that correspond to systematic variations of temperature, load (normal stress), film-substrate coupling strength, and film thickness. The HACG profiles are in excellent agreement overall with the exact ones. The HACG scheme provides a reliable description of quasistatic shearing under a wide range of conditions. It is demonstrated that the elastic response of the remote regions of the substrates can have a significant impact on the static friction profile (plot of maximum magnitude of T(yx) versus load).

Hybrid atomistic-coarse-grained treatment of thin-film lubrication. I.

A technique that melds an atomistic description of the interfacial region with a coarse-grained description of the far regions of the solid substrates is presented and applied to a two-dimensional model contact consisting of planar solid substrates separated by a monolayer fluid film. The hybrid method yields results in excellent agreement with the "exact" (i.e., fully atomistic) results. The importance of a proper accounting for the elastic response of the substrates, which is reliably and efficiently accomplished through coarse-graining of the far regions, is demonstrated.

Role of nanoscopic liquid bridges in static friction.

Interpretations of recent experiments on the effects of humidity on friction hypothesize that liquid-water bridges can span nanoscopic gaps at the interface between the sliding surfaces. By means of a lattice-gas model the mechanisms by which such bridges may engender static friction at a single ideal nanoscopic contact were studied. The model contact consists of a simple (spherically symmetric) fluid constrained between two plane-parallel substrates decorated with weakly and strongly attractive stripes that alternate periodically in one transverse direction. In analogy with the experiments the shear yield stress (yield strength) tau(s) of the contact was computed as a function of the chemical potential mu of the fluid (the analog of humidity). The influence of other thermodynamic state variables, such as temperature and distance between the substrates, and of the relative strength of the stripes on the yield-strength curves (i.e., tau(s) versus mu) was explored. Some intriguing correlations between experiment and theory are observed.

On the thermodynamic stability of confined thin films under shear.

Thin films of monatomic fluid constrained between two plane-parallel structured solid walls have been modeled by Monte Carlo simulation under conditions (fixed temperature, chemical potential, and normal stress or load) prevailing in high-precision measurements of surface forces. Several states of the film, corresponding to different numbers of layers of fluid parallel with the walls, are generally consistent with these conditions, but only one is thermodynamically stable; the others are metastable. When the walls are properly aligned, epitaxial solid phases are stable. These melt under shear, eventually becoming metastable, whereupon a drainage (or imbibition) transition occurs, leading to a stable phase with fewer (or more) layers.

Shear forces in molecularly thin films.

Monte Carlo and molecular dynamics methods have been used to study the shearing behavior of an atomic fluid between two plane-parallel solid surfaces having the face-centered cubic (100) structure. A distorted, face-centered cubic solid can form epitaxially between surfaces that are separated by distances of one to five atomic diameters. Under these conditions a critical stress must be overcome to initiate sliding of the surfaces over one another at fixed separation, temperature, and chemical potential. As sliding begins, a layer of solid exits the space between the surfaces and the remaining layers become fluid.