Anharmonic Surface Research Articles

Thermodynamic and Kinetic Properties of the Lithium-Silver System.

A carbon-silver anode has recently been shown to suppress dendrite formation in all-solid-state lithium-ion batteries. The role that silver plays in enabling the reversible deposition and stripping of lithium remains unknown. Furthermore, very little is known about the thermodynamic and kinetic properties of Li x Ag1-x alloys. Here, we report on an in-depth first-principles study of phase stability and diffusion mechanisms in the Li-Ag alloy system. We identify two new intermetallic phases that are predicted to be stable in Li-rich Li x Ag1-x alloys with stoichiometries of Li3Ag and Li11Ag2. Our calculations show that the peculiar and highly anharmonic energy surface of pure Li along the Bain and Burgers paths persists upon the addition of Ag to BCC Li. This has important implications for room-temperature phase stability and mechanical properties. We have also performed a systematic study of diffusion mechanisms in the Li x Ag1-x alloy system as a function of alloy concentration x. Diffusion in alloys and intermetallics is mediated by vacancies. High vacancy formation energies are predicted in the Li x Ag1-x alloy, especially in Ag-rich FCC solid solutions. Complex diffusion mechanisms are identified in the B2 and γ-brass intermetallic phases that include two-atom hops and second-nearest neighbor hops. The migration barriers are found to decrease with increasing Li concentration, with predictions of exceptionally low migration barriers of 0.1 eV in the D03 Li3Ag phase.

Second-harmonic generation in nonlinear plasmonic lattices enhanced by quantum emitter gain medium.

We report on a theoretical study of second-harmonic generation (SHG) in plasmonic nanostructures interacting with two-level quantum emitters (QEs) under incoherent energy pump. We generalize the driven-dissipative Tavis-Cummings model by introducing the anharmonic surface plasmon-polariton (SPP) mode coupled to QEs and examine physical properties of corresponding SPP-QE polariton states. Our calculations of the SHG efficiency for strong QE-SPP coupling demonstrate orders of magnitude enhancement facilitated by the polariton gain. We further discuss time-domain numerical simulations of SHG in a square lattice comprising Ag nanopillars coupled to QEs utilizing a fully vectorial nonperturbative nonlinear hydrodynamic model for conduction electrons coupled to Maxwell-Bloch equations for QEs. The simulations support the idea of gain enhanced SHG and show orders of magnitude increase in the SHG efficiency as the QEs are tuned in resonance with the lattice plasmon mode and brought above the population inversion threshold by incoherent pumping. By varying pump frequency and tuning QEs to a localized plasmon mode, we demonstrate further enhancement of the SHG efficiency facilitated by strong local electric fields. The incident light polarization dependence of the SHG is examined and related to the symmetries of participating plasmon modes.

Isotopic-Perturbation NMR Study of Hydrogen-Bond Symmetry in Solution: Temperature Dependence and Comparison of OHO and ODO Hydrogen Bonds.

Is a hydrogen bond symmetric, with the hydrogen centered between two donor atoms, or is it asymmetric, with the hydrogen closer to one but jumping to the other? The NMR method of isotopic perturbation has been used to distinguish these. Previous evidence from isotope shifts implies that a wide variety of dicarboxylate monanions are asymmetric, present as a rapidly equilibrating mixture of tautomers. However, calculations of hydrogen trajectories across an anharmonic potential-energy surface could reproduce the observed isotope shifts in a phthalate monoanion. Therefore, it was concluded that those isotope shifts are instead consistent with isotope-induced desymmetrization on a symmetric potential-energy surface. To distinguish between these two interpretations, the 18O-induced isotope effects on the 13C NMR chemical shifts of cyclohexene-1,2-dicarboxylate monoanion in chloroform-d and on the 19F NMR chemical shifts of difluoromaleate monoanion in D2O have been investigated. In both cases the isotope effects are larger at lower temperature and also with deuterium in the hydrogen bond. It is concluded that these behaviors are consistent with the perturbation of an equilibrium between asymmetric tautomers and inconsistent with isotope-induced desymmetrization on a symmetric potential-energy surface.

Effects of tunnelling and asymmetry for system-bath models of electron transfer.

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of the Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.

An assessment of mean-field mixed semiclassical approaches: Equilibrium populations and algorithm stability.

We study several recent mean-field semiclassical dynamics methods, focusing on the ability to recover detailed balance for long time (equilibrium) populations. We focus especially on Miller and Cotton's [J. Phys. Chem. A 117, 7190 (2013)] suggestion to include both zero point electronic energy and windowing on top of Ehrenfest dynamics. We investigate three regimes: harmonic surfaces with weak electronic coupling, harmonic surfaces with strong electronic coupling, and anharmonic surfaces with weak electronic coupling. In most cases, recent additions to Ehrenfest dynamics are a strong improvement upon mean-fieldtheory. However, for methods that include zero point electronic energy, we show that anharmonic potential energy surfaces often lead to numerical instabilities, as caused by negative populations and forces. We also show that, though the effect of negative forces can appear hidden in harmonic systems, the resulting equilibrium limits do remain dependent on any windowing and zero point energy parameters.

Anharmonic Surface Interactions for Biomolecular Screening and Characterization

The acoustic response of conventional mechanical oscillators, such as a piezoelectric crystal, is predominantly harmonic at modest amplitudes. However, here, we observe from the electrical response that significant motional anharmonicity is introduced in the presence of attached analyte. Experiments were conducted with streptavidin-coated polystyrene microbeads of various sizes attached to a quartz crystal resonator via specific and nonspecific molecular tethers in liquid. Quantitative analysis reveals that the deviation of odd Fourier harmonics of the response caused by introduction of microbeads as a function of oscillation amplitude presents a unique signature of the molecular tether. Hence, the described anharmonic detection technique (ADT) based on this function allows screening of biomolecules and provides an additional level of selectivity in receptor-based detection that is often associated with nonspecific interactions. We also propose methods to extract mechanical force-extension characteristics of the molecular tether and activation energy using this technique.

Suppression of eddies in films over topography

We study inertial film flow down undulated inclines. With increasing Reynolds number, eddies are formed in the troughs of the bottom undulation. Further increase leads to a diminution of the eddies until they vanish completely. At even higher Reynolds numbers, they reappear yielding an eddy-free window of Reynolds numbers. Within this window, the free-surface shape changes abruptly. The change comes along with a sudden decrease in the mean film thickness and an abrupt transition of the surface shape type from anharmonic with a strong indentation to harmonic. The anharmonic surface shape shows typical features of a hydraulic jump, which vanishes during the transition. We find that the eddies disappear at Reynolds numbers where the first harmonic of the free-surface contour is sufficiently strong regardless of the exact surface shape. Numerical calculations are in good agreement with the experimental findings.

Systematic Study of Anharmonic Features in a Principal Component Analysis of Gramicidin A

We use principal component analysis (PCA) to detect functionally interesting collective motions in molecular-dynamics simulations of membrane-bound gramicidin A. We examine the statistical and structural properties of all PCA eigenvectors and eigenvalues for the backbone and side-chain atoms. All eigenvalue spectra show two distinct power-law scaling regimes, quantitatively separating large from small covariance motions. Time trajectories of the largest PCs converge to Gaussian distributions at long timescales, but groups of small-covariance PCs, which are usually ignored as noise, have subdiffusive distributions. These non-Gaussian distributions imply anharmonic motions on the free-energy surface. We characterize the anharmonic components of motion by analyzing the mean-square displacement for all PCs. The subdiffusive components reveal picosecond-scale oscillations in the mean-square displacement at frequencies consistent with infrared measurements. In this regime, the slowest backbone mode exhibits tilting of the peptide planes, which allows carbonyl oxygen atoms to provide surrogate solvation for water and cation transport in the channel lumen. Higher-frequency modes are also apparent, and we describe their vibrational spectra. Our findings expand the utility of PCA for quantifying the essential features of motion on the anharmonic free-energy surface made accessible by atomistic molecular-dynamics simulations.

Structural Prediction and Phase Transformation Mechanisms in Calcium at High Pressure

High-pressure phase transformations of Ca are studied using the metadynamics method to explore the anharmonic free-energy surface, together with a genetic algorithm structural search method to identify lowest enthalpy structures. Disagreement between theory and experiment regarding the structure of Ca in the pressure range 32-119 GPa is partially resolved by the demonstration of different phase transition behavior at 300 K from that at low temperatures. A new lowest enthalpy I4(1)/amd structure is obtained with both methods with an estimated superconducting critical temperature in agreement with experiment.

Spectroscopic properties of trichlorofluoromethane CCl3F calculated by density functional theory

Density functional theory is used to generate local potential energy surfaces in normal coordinates for several chlorine isotopomers of trichlorofluoromethane (CCl(3)F, CFC11). An examination of predicted structures suggested that the PBE0 functional would be suitable. Anharmonic surfaces around the equilibrium geometries are reported, as determined by energies, gradients, and second derivatives. Vibrational levels for fundamentals, overtones and combination bands are reported, as well as harmonic frequencies, anharmonic constants, rotational constants, isotope shifts, and infrared intensities. These are compared with experimental information.

Applying the vibronic coupling model Hamiltonian to the photoelectron spectrum of cyclobutadiene

The vibronic coupling model Hamiltonian has been set up to provide global potential energy surfaces for the lowest three singlet states of the neutral molecule and the doubly-degenerate ground state of the radical cation. Both systems are dominated by non-adiabatic coupling between the states, and the model is able to describe the anharmonic adiabatic surfaces using simple coupled diabatic states. The model is fitted to electronic structure calculations at the CASSCF level. To test the model, the photoelectron spectrum is calculated and compared to experiment. It is found that while the simple model is able to reproduce qualitatively the known topology of the potential energy surfaces, it is unable to accurately reproduce the photoelectron spectrum. It is concluded that this is due to inaccuracies in the electronic structure calculations.

Direct Observation of Anharmonic Coupling in the Time Domain with Femtosecond Stimulated Raman Scattering

Off-resonant impulsive Raman excitation is used to initiate nonstationary nuclear motion in low-frequency vibrational modes of deuterio-chloroform. Femtosecond time-resolved stimulated Raman probing of the high-frequency C-D stretch reveals additional vibrational sidebands that arise as a result of anharmonic coupling between the impulsively excited low-frequency and the probed high-frequency vibrations. These experiments illustrate the detailed molecular information on anharmonic and reactive surfaces available from multidimensional femtosecond stimulated Raman techniques.

The internal coordinate path Hamiltonian; application to methanol and malonaldehyde

The internal coordinate path Hamiltonian is introduced for the study of the vibrations of molecules which have one large amplitude motion. The Hamiltonian is represented in terms of a one path coordinate and 3N—7 normal coordinates. The variational method is used to solve the Schrödinger equation. The molecules studied are methanol and malonaldehyde. For methanol the internal coordinate is a dihedral angle, for malonaldehyde it is the difference in the distances between the migrating hydrogen and the neighbouring oxygen atoms. For methanol there is little coupling between the path and the normal coordinates and so no complications were encountered in the calculations which used harmonic surfaces generated by density functional and Møller—Plesset theory. Fundamental frequencies were predicted. Malonaldehyde is a different story. There is substantial coupling between the path coordinate and several of the normal coordinates. This introduces many complications: an anharmonic surface is essential and large variational configuration interaction calculations are essential for convergence. Furthermore, because the Coriolis terms require the evaluation of derivatives of both the nuclear coordinates and the normal coordinate eigenvectors along the path, great care must be taken with these numerical procedures. B3LYP predicts too low a transition state which overemphasizes the large Coriolis terms near the transition state. This may be one of the reasons why our fundamental vibrations are in poor agreement with observation. It is most encouraging that the tunnelling splitting is 58 cm−1 (obs. 21.56 cm−1), obtained with our quartic density functional surface.

Role of Surface Intramolecular Dynamics in the Efficiency of Energy Transfer in Ne Atom Collisions with a n-Hexylthiolate Self-Assembled Monolayer

The energy-transfer dynamics associated with Ne atom collisions with a n-hexylthiolate self-assembled monolayer (SAM) surface at 20 kcal/mol collision energy are studied in chemical dynamics simulations by using both harmonic/separable and anharmonic/coupled surface models and by considering a SAM in both its classical potential energy minimum and containing a 293 K energy distribution. For the anharmonic surface, excitation of higher-energy potential energy minima arising from different intermolecular conformations of the alkyl chains and intramolecular vibrational energy redistribution (IVR) between the surface modes during the collision enhance the energy transfer from Ne atom translation to the surface. IVR is efficient for the alkyl chain's torsional modes and intramolecular chain-bending modes and occurs on the time scale of the Ne atom collisions. It does not occur during the collisions for other modes, such as the higher-frequency intrachain CCC bends. This IVR between surface modes, during the co...

Generation of harmonics and chaos in the dynamics of anharmonic surfaces

Effective equations of motion of a surface atom placed in an anharmonic surface potential are derived for three kinds of substrates (i) continuous dispersionless, (ii) discrete with nearest neighbours harmonic interactions, and (iii) a substrate showing a strong spatial dispersion. The resulting equations of motion are differential equations in the case (i) and Volterra Integro-Differential Equations (VIDE) in the cases (ii) and (iii). Examples of non-linear surface response to phonons coming from the bulk are given for the dispersionless substrate.

Time Dependent Coupled Cluster Approach to Resonance Raman Excitation Profiles from General Anharmonic Surfaces

A time dependent coupled cluster approach to the calculation of Resonance Raman excitation profiles on general anharmonic surfaces is presented. The vibrational wave functions on the ground electronic surface are obtained by the coupled cluster method (CCM). It is shown that the propagation of the vibrational ground state on the upper surface is equivalent to propagation of the vacuum state by an effective hamiltonian generated by the similarity transformation of the vibrational hamiltonian of that surface by the CCM wave operator of the lower surface up to a normalization constant. This time propagation is carried out by the time-dependent coupled cluster method in a time dependent frame. Numerical studies are presented to asses the validity of the approach.

An analytical model for the study of anharmonic dynamics in surfaces

An exact analytic formulation is presented for the dynamics of anharmonic low index surfaces of fcc crystals, based on an anharmonic pair potential coupling the first and second surface layers. This yields a general analytic expression for helium specular scattering at thermal energies in low index surfaces. The theoretical results are in agreement, in particular, with experimental data for Cu(1 0 0). The mean square displacements for surface layer sites are calculated as a function of temperature in this approach, and found to be in agreement with the results of the molecular dynamics simulation for Cu(1 0 0). The anharmonic pair potential strength is evaluated. The analytic formulation for the thermal attenuation of helium specular scattering in anharmonic surfaces, should make possible the selective access to the scattered intensities from other quasi-elastic surface processes notably at high temperature.

A Hamiltonian with a Subset of Normal Modes for Studying Mode-Specific Energy Transfer in Intermolecular Collisions

A Hamiltonian is described in which some degrees of freedom are represented by normal modes and the remainder retain their complete couplings and anharmonicities. The classical equations of motion for this Hamiltonian may be efficiently integrated in Cartesian coordinates. This Hamiltonian is used to study the mode specificity of energy transfer in Ne-atom collisions with alkanethiolate chains and a monolayer of n-hexyl thiolate chains self-assembled on Au{111}. The intermolecular and intramolecular degrees of freedom for these chain and self-assembled monolayer (SAM) systems are represented by normal modes. Collinear collisions with n-hexyl and n-octadecyl thiolate chains show that only one mode is excited at low collision energies. Mode specificity is also observed in Ne-atom collisions with the SAM. As expected from the adiabatic/impulsive model of T → V energy transfer, higher frequency modes of the chains and monolayer are excited as the Ne-atom translational energy is increased. A comparison, between this normal mode model and an anharmonic surface model, suggests it is efficient energy transfer to highly anharmonic modes of the surface which give rise to the Boltzmann component in the translational energy distribution of the scattered Ne atoms.

Infrared spectrum of HXeI revisited: anharmonic vibrational calculations and matrix isolation experiments

Anharmonic correlation-corrected vibrational self-consistent-field (CC–VSCF) calculations are reported for the neutral HXeI molecule. Fundamental, overtone and combination frequencies and their absorption intensities are computed, and compared with previous and new experimental data from FTIR matrix isolation measurements. Agreement between experiment and calculations extend the identification of the HXeI molecule, and the calculations prove useful in aiding assignment of new observed transitions. The results show that especially the Xe–H bond of HXeI is highly anharmonic. While the agreement between theory and experiment is useful for assignment, quantitative discrepancies still remain due to the deficiency of MP2 theory to describe the highly anharmonic surface.

Harmonics generation and chaos in scattering of phonons from anharmonic surfaces

The effective equations of motion for a surface atom in an anharmonic surface potential have been derived for dispersionless one-dimensional substrates. The system is equivalent to a non-linear damped oscillator (Duffing oscillator) with the forcing term depending on the form of the incident wave. Efficiency of harmonics generation, phonon reflection coefficients, effective local density of states, regions of chaotic motion and windows of periodic motion have been comparatively evaluated for the system subject to an oscillating external force and to the irradiation by a monochromatic phonon coming from the bulk. Comparison of the resonant desorption of the surface atom within a given time interval has been made for the same example of anharmonic surface potential in both types of perturbation.