Effective Harmonic Potential Research Articles

Anharmonicity in bcc refractory elements: A detailed ab initio analysis

Explicit anharmonicity, defined as the vibrational contribution beyond the quasiharmonic approximation, is qualitatively different between the group V and group VI bcc refractory elements. Group V elements show a small and mostly negative anharmonic entropy, whereas group VI elements have a large positive anharmonic entropy, strongly increasing with temperature. Here, we explain this difference utilizing highly accurate anharmonic free energies and entropies from ab initio calculations for Nb and Ta (group V), and Mo and W (group VI). The numerically calculated entropies are in agreement with prior experimental data. The difference in behavior between the two sets of elements arises not from their high-temperature behavior but rather from the $0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ quasiharmonic reference state. We understand this by analyzing the $0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and the high-temperature phonon density of states and the electronic density of states. The qualitative difference disappears when the anharmonicity is instead referenced with a high-temperature effective harmonic potential. However, even for an optimized effective harmonic reference, the remaining effective anharmonicity is significant. The reason is that the anharmonicity in the bcc systems---carried by asymmetric distributions in the nearest neighbors---can never be accounted for by a harmonically restricted potential.

Effects of magnetic field on the evolution of the wave function of a charged particle with an angular momentum

We have calculated the effect of a magnetic field on the evolution of angular momentum eigenfunctions of a charged particle. An additional harmonic potential is supplemented to trap the wave packet. We find the probability density of the wave function is oscillating in the radial direction with a time period determined by the strength of the effective harmonic potential. When the magnetic field is along the z direction, if the initial wave function is an eigenfunction of , the probability density of the particle remains axis-symmetric. While for the case of an eigenfunction of , it is anisotropic in the x−y plane and rotates with a time period inverse proportional to the strength of the external magnetic field. We also extend the results in a phenomenological way to the case with an external magnetic field that varies harmonically in time.

Thermally active nanoparticle clusters enslaved by engineered domain wall traps

The stable assembly of fluctuating nanoparticle clusters on a surface represents a technological challenge of widespread interest for both fundamental and applied research. Here we demonstrate a technique to stably confine in two dimensions clusters of interacting nanoparticles via size-tunable, virtual magnetic traps. We use cylindrical Bloch walls arranged to form a triangular lattice of ferromagnetic domains within an epitaxially grown ferrite garnet film. At each domain, the magnetic stray field generates an effective harmonic potential with a field tunable stiffness. The experiments are combined with theory to show that the magnetic confinement is effectively harmonic and pairwise interactions are of dipolar nature, leading to central, strictly repulsive forces. For clusters of magnetic nanoparticles, the stationary collective states arise from the competition between repulsion, confinement and the tendency to fill the central potential well. Using a numerical simulation model as a quantitative map between the experiments and theory we explore the field-induced crystallization process for larger clusters and unveil the existence of three different dynamical regimes. The present method provides a model platform for investigations of the collective phenomena emerging when strongly confined nanoparticle clusters are forced to move in an idealized, harmonic-like potential.

Comb of high‐Q Resonances in a Compact Photonic Cavity (Laser Photonics Rev. 11(6)/2017)

Through a suitable design, the intricate nature of multiple photon scattering in a nano-patterned structure is described by the archetypal model of the quantum harmonic oscillator. An effective harmonic potential confines the light in spectrally equi-spaced resonances with Hermite-Gauss envelopes. Extremely strong nonlinear interactions and ultra-low power threshold for parametric oscillation are predicted, owing to the very small size of the resonator. (Picture: Sylvain Combrié et al., article number 1700099, in this issue)

Modeling single molecule junction mechanics as a probe of interface bonding

Using the atomic force microscope based break junction approach, applicable to metal point contacts and single molecule junctions, measurements can be repeated thousands of times resulting in rich data sets characterizing the properties of an ensemble of nanoscale junction structures. This paper focuses on the relationship between the measured force extension characteristics including bond rupture and the properties of the interface bonds in the junction. A set of exemplary model junction structures has been analyzed using density functional theory based calculations to simulate the adiabatic potential surface that governs the junction elongation. The junction structures include representative molecules that bond to the electrodes through amine, methylsulfide, and pyridine links. The force extension characteristics are shown to be most effectively analyzed in a scaled form with maximum sustainable force and the distance between the force zero and force maximum as scale factors. Widely used, two parameter models for chemical bond potential energy versus bond length are found to be nearly identical in scaled form. Furthermore, they fit well to the present calculations of N–Au and S–Au donor-acceptor bonds, provided no other degrees of freedom are allowed to relax. Examination of the reduced problem of a single interface, but including relaxation of atoms proximal to the interface bond, shows that a single-bond potential form renormalized by an effective harmonic potential in series fits well to the calculated results. This allows relatively accurate extraction of the interface bond energy. Analysis of full junction models shows cooperative effects that go beyond the mechanical series inclusion of the second bond in the junction, the spectator bond that does not rupture. Calculations for a series of diaminoalkanes as a function of molecule length indicate that the most important cooperative effect is due to the interactions between the dipoles induced by the donor-acceptor bond formation at the junction interfaces. The force extension characteristic of longer molecules such as diaminooctane, where the dipole interaction effects drop to a negligible level, accurately fit to the renormalized single-bond potential form. The results suggest that measured force extension characteristics for single molecule junctions could be analyzed with a modified potential form that accounts for the energy stored in deformable mechanical components in series.

Configurational entropy: an improvement of the quasiharmonic approximation using configurational temperature

One challenge in computational biophysics and biology is to develop methodologies able to estimate accurately the configurational entropy of macromolecules. Among many methods, the quasiharmonic approximation (QH) is most widely used as it is simple in both theory and implementation. However, it has been shown that this method becomes inaccurate by overestimating entropy for systems with rugged free energy landscapes. Here, we propose a simple method to improve the QH approximation, i.e., to reduce QH entropy. We approximate the potential energy landscape of the system by an effective harmonic potential, and request that this potential must produce exactly the configurational temperature of the system. Due to this constraint, the force constants associated with the effective harmonic potential are increased, or equivalently, entropy of motion governed by this effective harmonic potential is reduced. We also introduce the effective configurational temperature concept which can be used as an indicator to check the anharmonicity of the free energy landscape. To validate the new method we compare it with the recently developed expansion approximate method by calculating entropy of one simple model system and two peptides with 3 and 16 amino acids either in gas phase or in explicit solvent. We show that the new method appears to be a good choice in practice as it is a compromise between accuracy and computational speed. A modification of the expansion approximate method is also introduced and advantages are discussed in some detail.

Diffusive motion ofC60on a graphene sheet

The motion of a C60 molecule over a graphene sheet at finite temperature is investigated both theoretically and computationally. We show that a graphene sheet generates a van der Waals laterally periodic potential, which directly influences the motion of external objects in its proximity. The translational motion of a C60 molecule near a graphene sheet is found to be diffusive in the lateral directions, while in the perpendicular direction, the motion may be described as diffusion in an effective harmonic potential which is determined from the distribution function of the position of the C60 molecule. We also examine the rotational diffusion of C60 and show that its motion over the graphene sheet is not a rolling motion.

Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals

In analogy to the Wannier equation for localized electronic impurity states in crystalline materials, a wave equation for the envelope of the resonant optical modes of local defects within two-dimensional periodic dielectric structures is derived. In the case of degenerate satellite extrema, this is generalized to a set of coupled Wannier-like equations for a multienvelope system. The localized Wannier envelope solutions are then used in conjunction with a group theoretical symmetry analysis to determine an approximate form for donor and acceptor modes in a hexagonal photonic crystal. For an effective harmonic potential formed by varying the filling fraction of the lattice, the localized resonant modes are explicitly calculated using the Wannier equation and symmetry analysis, and a comparison to exact numerically computed modes is presented.

Confined Diffusion Without Fences of a G-Protein-Coupled Receptor as Revealed by Single Particle Tracking

Single particle tracking is a powerful tool for probing the organization and dynamics of the plasma membrane constituents. We used this technique to study the μ-opioid receptor belonging to the large family of the G-protein-coupled receptors involved with other partners in a signal transduction pathway. The specific labeling of the receptor coupled to a T7-tag at its N-terminus, stably expressed in fibroblastic cells, was achieved by colloidal gold coupled to a monoclonal anti T7-tag antibody. The lateral movements of the particles were followed by nanovideomicroscopy at 40 ms time resolution during 2 min with a spatial precision of 15 nm. The receptors were found to have either a slow or directed diffusion mode (10%) or a walking confined diffusion mode (90%) composed of a long-term random diffusion and a short-term confined diffusion, and corresponding to a diffusion confined within a domain that itself diffuses. The results indicate that the confinement is due to an effective harmonic potential generated by long-range attraction between the membrane proteins. A simple model for interacting membrane proteins diffusion is proposed that explains the variations with the domain size of the short-term and long-term diffusion coefficients.

Liquid-like and solid-like motions in proteins

Recent analyses of molecular dynamics simulations of hydrated C-phycocyanin suggest that the internal single-particle dynamics of this protein can be decomposed into four almost decoupled motion types: (1) diffusion of residues (beads) in an effective harmonic potential, (2) corresponding vibrations in a local potential well, (3) purely rotational rigid side-chain diffusion, and (4) residue deformations. Each residue bead is represented by the corresponding C α carbon atom on the main chain. The effective harmonic residue potential can be imagined as the envelope of many local wells which are separated by small energy barriers. The residue friction matrix is assumed diagonal and the individual friction constants can be related to the density of the surrounding atoms. In this article we show that our model can be applied to lysozyme in solution as well, the only difference being that the side-chain deformations are more important and seem to be strongly correlated with the side-chain rotations. Comparing the simulated coherent scattering function of C-phycocyanin to a neutron spin-echo spectrum we show that our model can also describe collective motions in proteins at the residue level.

An effective harmonic potential for aluminophosphate molecular sieves: application to AlPO 4-5

In view of the simulation of the structural and vibrational behaviour of aluminophosphate molecular sieves and its long time scale influence on diffusive and reactive processes, an effective harmonic potential has been developed. The model was applied to the microporous aluminophosphate AlPO 4-5. The simulated structural properties and the vibrational spectrum agree unexpectedly well with the experimental data and give suggestions for the interpretation of some features of the AlPO 4-5 structure.

Harmonicity in slow protein dynamics

The slow dynamics of proteins around its native folded state is usually described by diffusion in a strongly anharmonic potential. In this paper, we try to understand the form and origin of the anharmonicities, with the principal aim of gaining a better understanding of the principal motion types, but also in order to develop more efficient numerical methods for simulating neutron scattering spectra of large proteins. First, we decompose a molecular dynamics (MD) trajectory of 1.5 ns for a C-phycocyanin dimer surrounded by a layer of water into three contributions that we expect to be independent: the global motion of the residues, the rigid-body motion of the sidechains relative to the backbone, and the internal deformations of the sidechains. We show that they are indeed almost independent by verifying the factorization of the incoherent intermediate scattering function. Then, we show that the global residue motions, which include all large-scale backbone motions, can be reproduced by a simple harmonic model which contains two contributions: a short-time vibrational term, described by a standard normal mode calculation in a local minimum, and a long-time diffusive term, described by Brownian motion in an effective harmonic potential. The potential and the friction constants were fitted to the MD data. The major anharmonic contribution to the incoherent intermediate scattering function comes from the rigid-body diffusion of the sidechains. This model can be used to calculate scattering functions for large proteins and for long-time scales very efficiently, and thus provides a useful complement to MD simulations, which are best suited for detailed studies on smaller systems or for shorter time scales.

REMPI in a focusing rf-quadrupole: a new source for mass-, energy-, and state-selected ions

Abstract Using resonance enhanced multiphoton ionization (REMPI), ions are created in a small volume centred on the axis of an rf-quadrupole. The pulsed beam of neutral molecular precursors is injected coaxially. This combination leads to high collection efficiency without the need of strong electrostatic extraction fields. The quadrupole is operated in the adiabatic limit. Therefore, the influence of the oscillatory rf-field on the ion trajectories can be described by an effective harmonic potential, which has focusing properties. Using these energy and mass dependent focusing properties, a primary H2 + beam of well-defined kinetic energy (< 5 meV (fwhm) at a mean of 50 meV) is prepared. In a typical case of multiphoton ionization of polyatomic molecules using C2H2, suppression of fragment ions by more than a factor of 10 is achieved, without losing the narrow kinetic energy spread of the parent ion beam.

Vortex pair production and decay of a two-dimensional supercurrent by a quantum-field-theory approach.

We investigate the phenomenon of the decay of a supercurrent through homogeneous nucleation of vortex-antivortex pairs in a two-dimensional (2D) like superconductor or superfluid by means of a quantum electrodynamic formulation for the decay of the 2D vacuum. The case in which both externally driven current and Magnus force are present is treated exactly, taking the vortex activation energy and its inertial mass as independent parameters. Quantum dissipation is included through the formulation introduced by Caldeira and Leggett. The most relevant consequence of quantum dissipation is the elimination of the threshold for vortex production due to the Magnus force. In the dissipation-dominated case, corresponding formally to the limit of zero intertial mass, an exact formula for the pair production rate is given. If however the inertial mass is strictly zero we find that vortex production is inhibited by a quantum effect related to the Magnus force. The possibility of including vortex pinning is investigated by means of an effective harmonic potential. While an additional term in the vortex activation energy can account for the effect of a finite barrier in the direction perpendicular to the current, pinning along the current depresses the role of the Magnus force in the dissipation-dominated dynamics, except for the above-mentioned quantum effect. A possible description of vortex nucleation due to the combined effects of temperature and externally driven currents is also presented along with an evaluation of the resulting voltage drop.