Model Potential Energy Surfaces Research Articles

Structure and stability of Na+Xen clusters

The structure and stability features of Na+Xe n (n ≤ 54) clusters are theoretically investigated via model potential energy surfaces (PES) and unconstrained global optimization. The potential energy is described in terms of pair-additive potentials including polarization parametrized from accurate ab initio data on Na+Xe, complemented by three-body contributions describing the interaction between the dipoles induced by the sodium ion on the rare gas atoms. We show that the three-body contributions stabilize the linear or planar structures versus more compact shapes for n< 4. At larger sizes, the growth around the square antisprism (SA) or capped square antisprism (CSA) core is favored while icosahedral pattern based isomers exist but not as the lowest ones. A transition in the metal ion coordination from 8 (square antiprism) to 12 (icosahedron) is seen to occur near n = 50. The results are discussed and analyzed in view of existing accurate ab initio calculations on Na+Xe2 and comparisons with similar metal-ion clusters.

Quest for Inexpensive Hydrogen Isotopic Fractionation: Do We Need 2D Quantum Confining in Porous Materials or Are Rough Surfaces Enough? The Case of Ammonia Nanoclusters.

We study the adsorption energetics and quantum properties of the molecular hydrogen isotopes H2, D2, and T2 onto the surface of rigid ammonia nanoclusters with quantum simulations and accurate model potential energy surfaces (PES). A highly efficient diffusion Monte Carlo (DMC) algorithm for rigid rotors allowed us to accurately define zero-point adsorption energies for the three isotopes, as well as the degree of translational and rotational delocalization that each affords on the surface. From the data emerges that the quantum adsorption energy (Eads) of T2 can be up to twice the one of H2 at 0 K, suggesting the possibility of exploiting some form of solid ammonia to selectivity separate hydrogen isotopes at low temperatures (≃20 K). This is discussed by focusing on the structural motif that may be more effective for the task. The analysis of the contributions to Eads, however, surprisingly indicates that the average kinetic energy (Ekin) and rotation energy (Erotkin) of T2 can also be, respectively, 2 times and 20 times higher than those of H2; this finding markedly deviates from what is predicted for hydrogen molecules inside carbon nanotubes (CNT) or metallic-organic frameworks (MOF), where Ekin and Erotkin is higher for H2 due to the unavoidable effects of confinement and hindrance to its rotational motion. The rationale for these differences is provided by the geometrical distributions for the rigid rotors, which reveal an increasingly stronger coupling between rotational and translational degrees of freedom upon increasing the isotopic mass. This effect has never been observed before on adsorbing surfaces (e.g., graphite) and is induced by a strongly anisotropic and anharmonic bowl-like potential experienced by the rotors.

Vibronic Coupling Explains the Different Shape of Electronic Circular Dichroism and of Circularly Polarized Luminescence Spectra of Hexahelicenes

We present the simulation of the absorption (ABS), electronic circular dichroism (ECD), emission (EMI), and circularly polarized luminescence (CPL) spectra for the weak electronic transition between the ground (S0) and the lowest excited state (S1) of hexahelicene, 2-methylhexahelicene, 2-bromohexahelicene, and 5-azahexahelicene. Vibronic contributions have been computed at zero Kelvin and at room temperature in harmonic approximation including Duschinsky effects and accounting for both Franck-Condon and Herzberg-Teller contributions. Our results nicely capture the effects of the different substituents on the experimental spectra. They also show that HT effects dominate the shape of ECD and CPL spectra where they even induce changes of signs; HT effects are also relevant in ABS and EMI, tuning the relative intensities of the different vibronic bands. HT effects are the main reason for the differences in the line shapes of ABS and ECD and of EMI and CPL spectra and for the mirror-symmetry breaking between ABS and EMI and between ECD and CPL spectra. In order to check the robustness of our results, given also that few examples of calculations of vibronic CPL spectra exist, we adopted both adiabatic and vertical approaches to define the model potential energy surfaces of the (S0) and the (S1) states; moreover we expanded the electric and magnetic dipole transition moments around both the S0 and S1 equilibrium geometries.

Ternary fission of superheavy elements

Ternary fission of superheavy nuclei is studied within the three-cluster model potential energy surfaces (PESs). Due to shell effects, the stability of superheavy nuclei has been predicted to be associated with $Z=114$, 120, and 126 for protons and $N=184$ for neutrons. Taking some representative nuclei we have extended the ternary fission studies to superheavy nuclei. We adopted two minimization procedures to minimize the potential and considered different arrangements of the fragments. The PES from one-dimensional minimization reveals a strong cluster region favoring various ternary breakups for an arrangement in which the lightest fragment is kept at the center. The PES obtained from two-dimensional minimization reveals strong preference of ternary fragmentation in the true ternary fission region. Though the dominant decay mode of superheavy nuclei is $\ensuremath{\alpha}$ decay, the $\ensuremath{\alpha}$-accompanied ternary breakup is found to be a nonfavorable one. Further, the prominent ternary combinations are found to be associated with the neutron magic number.

Simultaneous estimation of free energies and rates using forward flux sampling and mean first passage times.

In this work, a method is proposed to simultaneously compute the transition rate constant and the free energy profile of a rare event along an order parameter connecting two well-defined regions of phase space. The method employs a forward flux sampling technique in combination with a mean first passage time approach to estimate the steady state probability and mean first passage times. These quantities are fitted to a Markovian model that allows the estimation of the free energy along the chosen order parameter. The proposed technique is first validated with two test systems (an Ising model and a model potential energy surface) and then used to study the solid-phase homogeneous nucleation of selected polyhedral particles.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape.

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values.

Adsorption and diffusion of Ru adatoms on Ru(0001)-supported graphene: Large-scale first-principles calculations.

Large-scale first-principles density functional theory calculations are performed to investigate the adsorption and diffusion of Ru adatoms on monolayer graphene (G) supported on Ru(0001). The G sheet exhibits a periodic moiré-cell superstructure due to lattice mismatch. Within a moiré cell, there are three distinct regions: fcc, hcp, and mound, in which the C6-ring center is above a fcc site, a hcp site, and a surface Ru atom of Ru(0001), respectively. The adsorption energy of a Ru adatom is evaluated at specific sites in these distinct regions. We find the strongest binding at an adsorption site above a C atom in the fcc region, next strongest in the hcp region, then the fcc-hcp boundary (ridge) between these regions, and the weakest binding in the mound region. Behavior is similar to that observed from small-unit-cell calculations of Habenicht et al. [Top. Catal. 57, 69 (2014)], which differ from previous large-scale calculations. We determine the minimum-energy path for local diffusion near the center of the fcc region and obtain a local diffusion barrier of ∼0.48 eV. We also estimate a significantly lower local diffusion barrier in the ridge region. These barriers and information on the adsorption energy variation facilitate development of a realistic model for the global potential energy surface for Ru adatoms. This in turn enables simulation studies elucidating diffusion-mediated directed-assembly of Ru nanoclusters during deposition of Ru on G/Ru(0001).

A complete description of tunnelling using direct quantum dynamics simulation: Salicylaldimine proton transfer.

We demonstrate here conclusively that the variational multiconfiguration Gaussian (vMCG) method converges to the grid based full quantum dynamics multiconfiguration time-dependent Hartree result for a tunnelling problem in many dimensions, using the intramolecular proton transfer in salicylaldimine as a model system. The 13-dimensional model potential energy surface was obtained from Hartree Fock energies with the 6-31G* basis set and the expectation value of the flux operator along the transition mode was used as a benchmark characteristic. As well as showing excellent convergence of the vMCG method on the model surface using a local harmonic approximation and a moderate number of basis functions, we show that the direct dynamics version of the vMCG also performs very well, usually needs the same number of Gaussians to converge, and converges to exact results if those are obtained on an accurately fitted surface. Finally, we make an important observation that the width of the Gaussian basis functions must be chosen very carefully to obtain accurate results with the use of the frozen-width approximation.

Including Tunneling in Non-Born-Oppenheimer Simulations.

For electronically nonadiabatic processes in all but the simplest systems, the most practical multidimensional simulation method is a semiclassical approximation in which a trajectory or the center of a wave packet follows a classical path governed by an effective potential energy function. Here, we show how such simulations can be made more realistic by including tunneling by the army ants tunneling method. We illustrate the theory by calculations with model potential energy surfaces; one model study is in the adiabatic limit, and the other one has nonadiabatic transitions between two electronic states during the tunneling event. The army ants tunneling algorithm is used to efficiently sample tunneling events in the trajectories in both cases. This work makes it possible to simulate complex nonadiabatic chemical processes by efficiently including the important quantum effect of tunneling.

3D Printing of Molecular Potential Energy Surface Models

Additive manufacturing, commonly known as 3D printing, is gaining popularity in a variety of applications and has recently become routinely available. Today, 3D printing services are not only found in engineering design labs and through online companies, but also in university libraries offering student access. In addition, affordable options for home hobbyists have already been introduced. Here, we demonstrate the use of 3D printing to generate plastic models of molecular potential energy surfaces useful for understanding molecular structure and reactivity.

Developing an approach for first-principles catalyst design: application to carbon-capture catalysis

An approach to catalyst design is presented in which local potential energy surface models are first built to elucidate design principles and then used to identify larger scaffold motifs that match the target geometries. Carbon sequestration via hydration is used as the model reaction, and three- and four-coordinate sp(2) or sp(3) nitrogen-ligand motifs are considered for Zn(II) metals. The comparison of binding, activation and product release energies over a large range of interaction distances and angles suggests that four-coordinate short Zn(II)-Nsp(3) bond distances favor a rapid turnover for CO2 hydration. This design strategy is then confirmed by computationally characterizing the reactivity of a known mimic over a range of metal-nitrogen bond lengths. A search of existing catalysts in a chemical database reveals structures that match the target geometry from model calculations, and subsequent calculations have identified these structures as potentially effective for CO2 hydration and sequestration.

Infinite swapping in curved spaces

We develop an extension of the infinite swapping and partial infinite swapping techniques [N. Plattner, J. D. Doll, P. Dupuis, H. Wang, Y. Liu, and J. E. Gubernatis, J. Chem. Phys. 135, 134111 (2011)] to curved spaces. Furthermore, we test the performance of infinite swapping and partial infinite swapping in a series of flat spaces characterized by the same potential energy surface model. We develop a second order variational algorithm for general curved spaces without the extended Lagrangian formalism to include holonomic constraints. We test the new methods by carrying out NVT classical ensemble simulations on a set of multidimensional toroids mapped by stereographic projections and characterized by a potential energy surface built from a linear combination of decoupled double wells shaped purposely to create rare events over a range of temperatures.

Advanced Potential Energy Surfaces for Condensed Phase Simulation

Computational modeling at the atomistic and mesoscopic levels has undergone dramatic development in the past 10 years to meet the challenge of adequately accounting for the many-body nature of intermolecular interactions. At the heart of this challenge is the ability to identify the strengths and specific limitations of pairwise-additive interactions, to improve classical models to explicitly account for many-body effects, and consequently to enhance their ability to describe a wider range of reference data and build confidence in their predictive capacity. However, the corresponding computational cost of these advanced classical models increases significantly enough that statistical convergence of condensed phase observables becomes more difficult to achieve. Here we review a hierarchy of potential energy surface models used in molecular simulations for systems with many degrees of freedom that best meet the trade-off between accuracy and computational speed in order to define a sweet spot for a given scientific problem of interest.

Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points

We study reaction dynamics on a model potential energy surface exhibiting post-transition state bifurcation in the vicinity of a valley ridge inflection (VRI) point. We compute fractional yields of products reached after the VRI region is traversed, both with and without dissipation. It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics. Moreover, when dissipative effects are incorporated, the product ratio depends in a complicated and highly non-monotonic fashion on the dissipation parameter. Dynamics in the vicinity of the VRI point itself play essentially no role in determining the product ratio, except in the highly dissipative regime.

Crossed-beam and reduced dimensionality studies of the state-to-state integral cross sections of the Cl + HCD3(v) → HCl(v′) + CD3 reaction

The state-to-state integral cross sections of the Cl+HCD3(v)→HCl(v′)+CD3 reaction have been studied experimentally and theoretically. Reactions involving both Cl(2P3/2) and Cl(2P1/2) were analysed. In the experiment, a time-sliced velocity imaging detection method under crossed-beam condition was used. For theoretical study, a multiple potential energy surface model is employed. A combined reduced dimensionality quantum dynamics and quantum chemistry method is used with explicit treatment of spin–orbit coupling. Good agreement between experiment and theory is obtained, especially for the energy threshold dependence of the cross sections.

Tunneling splittings in vibronic energy levels of CH 3F+X̃2E studied by high resolution photoelectron spectroscopy and ab initio calculation

The energy levels of CH3F(+) (X(2)E), which show strong vibronic coupling effect (Jahn-Teller effect), have been measured up to 3500 cm(-1) above the ground vibrational state using one-photon zero-kinetic energy photoelectron spectroscopic method. Theoretical calculations have also been performed to calculate the spin-vibronic energy levels using a diabatic model and ab initio adiabatic potential energy surfaces (APESs) including the energy gradients and derivative couplings between the APESs. The calculations showed that the tunneling splittings of the vibrational energy levels occur due to the deep potential energy wells formed by the Jahn-Teller deformation. The calculated spin-vibronic energy levels are in good agreement with the experimental data. For example, the energy splitting for the first excited vibrational energy level is calculated as 111 cm(-1) that is confirmed by the experimental value. The experimental spectrum was assigned based on the fundamental vibrational modes calculated at the energy minimum. The fundamental vibrational modes related to the H-C-F bending, H-C-H bending, C-F stretching, and C-H stretching vibrations have been observed.

Quantum-State Resolved Bimolecular Collisions of Velocity-Controlled OH with NO Radicals

Whereas atom-molecule collisions have been studied with complete quantum-state resolution, interactions between two state-selected molecules have proven much harder to probe. Here, we report the measurement of state-resolved inelastic scattering cross sections for collisions between two open-shell molecules that are both prepared in a single quantum state. Stark-decelerated hydroxyl (OH) radicals were scattered with hexapole-focused nitric oxide (NO) radicals in a crossed-beam configuration. Rotationally and spin-orbit inelastic scattering cross sections were measured on an absolute scale for collision energies between 70 and 300 cm(-1). These cross sections show fair agreement with quantum coupled-channels calculations using a set of coupled model potential energy surfaces based on ab initio calculations for the long-range nonadiabatic interactions and a simplistic short-range interaction. This comparison reveals the crucial role of electrostatic forces in complex molecular collision processes.

Theoretical Studies of Dynamic Interactions in Excited States of Hydrogen-Bonded Systems

Theoretical model for vibrational interactions in the hydrogen-bonded benzoic acid dimer is presented. The model takes into account anharmonic-type couplings between the high-frequency O–H and the low-frequency O⋯O stretching vibrations in two hydrogen bonds, resonance interactions between two hydrogen bonds in the dimer, and Fermi resonance between the O–H stretching fundamental and the first overtone of the O–H in-plane bending vibrations. The model is used for theoretical simulation of the O–H stretching IR absorption bands of benzoic acid dimers in the gas phase in the first excited singlet state. Ab initio CIS and CIS(D)/CIS/6-311++G(d,p) calculations have been carried out in the à state of tropolone. The grids of potential energy surfaces along the coordinates of the tunneling vibration and the low-frequency coupled vibration have been calculated. Two-dimensional model potentials have been fitted to the calculated potential energy surfaces. The tunneling splittings for vibrationally excited states have been calculated and compared with the available experimental data. The model potential energy surfaces give good estimation of the tunneling splittings in the vibrationally ground and excited states of tropolone, and explain monotonic decrease in tunneling splittings with the excitation of low-frequency out-of-plane modes and increase of the tunneling splittings with the excitation of low-frequency planar modes.

An Efficient and Accurate Formalism for the Treatment of Large Amplitude Intramolecular Motion

We propose a general approach to describe large amplitude motions (LAM) with multiple degrees of freedom (DOF) in molecules or reaction intermediates, which is useful for the computation of thermochemical or kinetic data. The kinetic part of the LAM Lagrangian is derived using a Z-matrix internal coordinate representation within a new numerical procedure. This derivation is exact for a classical system, and the uncertainties on the prediction of observable quantities largely arise from uncertainties on the LAM potential energy surface (PES) itself. In order to rigorously account for these uncertainties, we present an approach based on Bayesian theory to infer a parametrized physical model of the PES using ab initio calculations. This framework allows for quantification of uncertainties associated with a PES model as well as the forward propagation of these uncertainties to the quantity of interest. A selection and generalization of some treatments accounting for the coupling of the LAM with other internal or external DOF are also presented. Finally, we discuss and validate the approach with two applications: the calculation of the partition function of 1,3-butadiene and the calculation of the high-pressure reaction rate of the CH3 + H → CH4 recombination.

Jahn–Teller effect in [formula omitted]: A combined photoelectron spectroscopic measurement and ab initio theoretical study

The energy levels of CD3Cl+(X∼2E) showing strong spin-vibronic coupling effect (Jahn–Teller effect) have been measured up to 2200cm−1 above the ground vibrational state using one-photon zero-kinetic energy (ZEKE) photoelectron spectroscopic method. The ionization energy of CD3Cl was determined as 91221.5±3cm−1 or 11.3100±0.0004eV. The fundamental vibrational energy levels of CD3 deform (υ5), CD3 rock (υ6) and symmetric CD3 umbrella (υ2) vibrations have been obtained from the spectra. Theoretical calculations have been performed to calculate the spin-vibronic energy levels using a diabatic model and ab initio adiabatic potential energy surfaces, which include multimode vibronic interactions. The spin-vibronic structure of CD3Cl+ is mainly determined by the linear vibronic coupling and the mode coupling among υ5, υ6 and symmetric C–Cl stretching vibrations (υ3).