Reference Potential Energy Research Articles

Importance Sampling for Equilibrium Properties in Non-Adiabatic Systems: Application to Anomalous Interfacial Charge Transfer

Interfacial charge transfer plays a significant role in the performance of optoelectronic devices. Compared with real-time non-adiabatic dynamics simulations, statistical mechanics could obtain the equilibrium properties directly. We here present an importance sampling approach to calculate the electron distribution at general interfaces. The configuration distribution based on a series of reference potential energy surfaces is utilized to reweight the properties of interest. The high accuracy, precision, and efficiency of the new method are verified by comparing the results of different sampling approaches and non-adiabatic dynamics simulations. We find that numbers of states, electronic couplings, reorganization energies, and energetic disorders all have strong impacts on the anomalous interfacial charge transfer across a high energy barrier. In addition, based on the data computed by importance sampling in relatively small but diverse systems, we propose an effective machine learning approach to train artificial neural networks, which could predict the interfacial charge transfer in extremely large systems. Due to its high performance, our importance sampling method is promising for the statistical study of equilibrium properties in general non-adiabatic systems.

Data-Driven Many-Body Potential Energy Functions for Generic Molecules: Linear Alkanes as a Proof-of-Concept Application.

We present a generalization of the many-body energy (MB-nrg) theoretical/computational framework that enables the development of data-driven potential energy functions (PEFs) for generic covalently bonded molecules, with arbitrary quantum mechanical accuracy. The "nearsightedness of electronic matter" is exploited to define monomers as "natural building blocks" on the basis of their distinct chemical identity. The energy of generic molecules is then expressed as a sum of individual many-body energies of incrementally larger subsystems. The MB-nrg PEFs represent the low-order n-body energies, with n = 1-4, using permutationally invariant polynomials derived from electronic structure data carried out at an arbitrary quantum mechanical level of theory, while all higher-order n-body terms (n > 4) are represented by a classical many-body polarization term. As a proof-of-concept application of the general MB-nrg framework, we present MB-nrg PEFs for linear alkanes. The MB-nrg PEFs are shown to accurately reproduce reference energies, harmonic frequencies, and potential energy scans of alkanes, independently of their length. Since, by construction, the MB-nrg framework introduced here can be applied to generic covalently bonded molecules, we envision future computer simulations of complex molecular systems using data-driven MB-nrg PEFs, with arbitrary quantum mechanical accuracy.

Functional sensitivity analysis approach to retrieve the potential energy function from the quantum second virial coefficient

Intermolecular forces play a central role in theoretical chemistry and many studies focus on the establishment of accurate potential energy curves. The potential energy function can be obtained by ab initio methods, representing a direct problem. On the other hand, it can be obtained as an inverse problem dealing directly with experimental data. This work explores the inverse problem to obtain the potential energy function, for the helium system, from second virial coefficient data at low temperatures. The methodology used was the functional sensitivity analysis approach. In this methodology a new proposal to obtain the sensitivity density of the phase shift with respect to the potential energy function is presented. From the sensitivity density of the second virial coefficient the most suitable temperature range for recovering the region of the potential well can be determined (3 to 20 K). The inverse problem was addressed in a single nonlinear step. Using functional sensitivity analysis and the Tikhonov regularization an estimate of the potential energy function was optimized with an average error of 3.7% against 7.6% in the initial approximation when compared to the reference potential energy function. The calculated second virial coefficient with this new potential gives an absolute deviation between 4.2×10−4 cm3mol−1 and 0.15 cm3mol−1 against 3.6 cm3mol−1 and 29.1 cm3mol−1 in the initial approximation.

Selecting your reference potential energy in a vertically hanging spring!

When defining the gravitational potential energy of an object in a system, the reference point where you define a potential energy can be overlooked. Consider this cartoon you may have seen in Fig. 1. The cartoon is a light-hearted way to look at potential; however, it can be misleading. When considering potential energy in this situation, we examine the ball and Earth together as a system. Potential energy is due to an interaction between the object and what influences it.

Computation of the S1 ← S0 Vibronic Absorption Spectrum of Formaldehyde by Variational Gaussian Wavepacket and Semiclassical IVR Methods.

The vibronic absorption spectrum of the electric dipole forbidden and vibronically allowed S1(1 A2) ← S0(1 A1) transition of formaldehyde is calculated by Gaussian wavepacket and semiclassical methods, along with numerically exact reference calculations, using the potential energy surface of Fu, Shepler, and Bowman ( J. Am. Chem. Soc. 2011, 133, 7957). Specifically, the variational multiconfigurational Gaussian (vMCG) approach and the Herman-Kluk semiclassical initial value representation (HK-SCIVR) are compared to assess the accuracy and convergence of these methods, benchmarked against numerically exact time-dependent wavepacket propagation (TDWP) on the reference potential energy surface. The vMCG calculation is shown to converge quite well with about 100 variationally evolving Gaussian functions and using a local cubic expansion instead of the conventional local harmonic approximation. By contrast, the HK-SCIVR approach with ∼105 trajectories reproduces the vibrationally structured spectral envelope correctly but yields a strongly broadened spectrum. The comparison of the computed absorption spectrum with experiment shows that the relevant vibronic progressions are reasonably reproduced by all computations, but deviations of the order of 10-100 cm-1 occur, underscoring that both electronic structure calculations and dynamical approaches remain challenging in the calculation of typical small-molecule excited-state spectra by trajectory-based methods.

Developing accurate intramolecular force fields for conjugated systems through explicit coupling terms

The accuracy of molecular mechanics force fields (FF) reveals critical for applications where precise molecular structures along a conformational sampling are required, as in the simulation of electronic spectroscopies. This implies abandoning generalized FFs in favor of specific FFs, with non-transferable parameters able to accurately describe the targeted species. A promising strategy in this direction consists in the so-called quantum mechanically derived FFs, in which the parameters are fitted onto reference data computed through quantum chemistry. However, in order to obtain a global set of parameters able to reliably describe the reference potential energy surface in different regions of the conformational space, the complexity of the analytical expressions of the FF becomes crucial. Regarding intramolecular interactions, the functional form of standard transferable FFs is restricted to terms that depend on only one internal coordinate. It will be shown that such models may reveal insufficient to describe systems as polyenic chains, where complex electronic effects, e.g., conjugation, intrinsically couple different internal coordinates (ICs). We propose a functional form for intramolecular FFs, which includes explicit couplings between flexible dihedrals and stiff ICs (bonds and angles), being able to properly describe the geometrical changes arising not only from steric interactions, but also from conjugation effects, i.e., the change of bond orders induced by conformational changes. The parameterization of the coupled FFs is carried out by means of automated and efficient computational protocols, purposely developed in the present work. All procedures are tested and validated by generating FFs for the two smallest compounds in the polyenic series (butadiene and hexatriene).

Evaluation of the Momentum Closure Schemes in MPAS-Ocean

In order to compare and evaluate the performances of the Laplacian viscosity closure, the biharmonic viscosity closure, and the Leith closure momentum schemes in the MPAS-Ocean model, a variety of physical quantities, such as the relative reference potential energy (RPE) change, the RPE time change rate (RPETCR), the grid Reynolds number, the root mean square (RMS) of kinetic energy, and the spectra of kinetic energy and enstrophy, are calculated on the basis of results of a 3D baroclinic periodic channel. Results indicate that: 1) The RPETCR demonstrates a saturation phenomenon in baroclinic eddy tests. The critical grid Reynolds number corresponding to RPETCR saturation differs between the three closures: the largest value is in the biharmonic viscosity closure, followed by that in the Laplacian viscosity closure, and that in the Leith closure is the smallest. 2) All three closures can effectively suppress spurious dianeutral mixing by reducing the grid Reynolds number under sub-saturation conditions of the RPETCR, but they can also damage certain physical processes. Generally, the damage to the rotation process is greater than that to the advection process. 3) The dissipation in the biharmonic viscosity closure is strongly dependent on scales. Most dissipation concentrates on small scales, and the energy of small-scale eddies is often transferred to large-scale kinetic energy. The viscous dissipation in the Laplacian viscosity closure is the strongest on various scales, followed by that in the Leith closure. Note that part of the small-scale kinetic energy is also transferred to large-scale kinetic energy in the Leith closure. 4) The characteristic length scale L and the dimensionless parameter Г in the Leith closure are inherently coupled. The RPETCR is inversely proportional to the product of Г and L. When the product of Г and L is constant, both the simulated RPETCR and the inhibition of spurious dianeutral mixing are the same in all tests using the Leith closure. The dissipative scale in the Leith closure depends on the parameter L, and the dissipative intensity depends on the parameter Г. 5) Although optimal results may not be achieved by using the optimal parameters obtained from the 2D barotropic model in the 3D baroclinic simulation, the total energies are dissipative in all three closures. Dissipation is the strongest in the biharmonic viscosity closure, followed by that in the Leith closure, and that in the Laplacian viscosity closure is the weakest. Mesoscale eddies develop the fastest in the biharmonic viscosity closure after the baroclinic adjustment process finishes, and the kinetic energy reaches its maximum, which is attributed to the smallest dissipation of enstrophy in the biharmonic viscosity closure. Mesoscale eddies develop the slowest, and the kinetic energy peak value is the smallest in the Laplacian viscosity closure. Results in the Leith closure are between that in the biharmonic viscosity closure and the Laplacian viscosity closure.

Attribution of horizontal and vertical contributions to spurious mixing in an Arbitrary Lagrangian–Eulerian ocean model

We examine the separate contributions to spurious mixing from horizontal and vertical processes in an ALE ocean model, MOM6, using reference potential energy (RPE). The RPE is a global diagnostic which changes only due to mixing between density classes. We extend this diagnostic to a sub-timestep timescale in order to individually separate contributions to spurious mixing through horizontal (tracer advection) and vertical (regridding/remapping) processes within the model. We both evaluate the overall spurious mixing in MOM6 against previously published output from other models (MOM5, MITGCM and MPAS-O), and investigate impacts on the components of spurious mixing in MOM6 across a suite of test cases: a lock exchange, internal wave propagation, and a baroclinically-unstable eddying channel.The split RPE diagnostic demonstrates that the spurious mixing in a lock exchange test case is dominated by horizontal tracer advection, due to the spatial variability in the velocity field. In contrast, the vertical component of spurious mixing dominates in an internal waves test case. MOM6 performs well in this test case owing to its quasi-Lagrangian implementation of ALE. Finally, the effects of model resolution are examined in a baroclinic eddies test case. In particular, the vertical component of spurious mixing dominates as horizontal resolution increases, an important consideration as global models evolve towards higher horizontal resolutions.

Cheap but accurate calculation of chemical reaction rate constants from ab initio data, via system-specific, black-box force fields.

Building on the recently published quantum-mechanically derived force field (QMDFF) and its empirical valence bond extension, EVB-QMDFF, it is now possible to generate a reliable potential energy surface for any given elementary reaction step in an essentially black box manner. This requires a limited and pre-defined set of reference data near the reaction path and generates an accurate approximation of the reference potential energy surface, on and off the reaction path. This intermediate representation can be used to generate reaction rate data, with far better accuracy and reliability than with traditional approaches based on transition state theory (TST) or variational extensions thereof (VTST), even if those include sophisticated tunneling corrections. However, the additional expense at the reference level remains very modest. We demonstrate all this for three arbitrarily chosen example reactions.

Spurious dianeutral mixing in a global ocean model using spherical centroidal voronoi tessellations

In order to quantitatively evaluate the spurious dianeutral mixing in a global ocean model MPAS-Ocean (Model for Prediction Across Scales) using a spherical centroidal voronoi tessellations developed jointly by the National Center for Atmospheric Research and the Los Alamos National Laboratory in the United States, we choose z* vertical coordinate system in MPAS-Ocean, in which all physical mixing processes, such as convection adjustment and explicit diffusion parameter schemes, are omitted, using a linear equation of state. By calculating the Reference Potential Energy (RPE), front revolution position, time rate of RPE change, probability density function distribution and dimensionless parameter χ, from the perspectives of resolution, viscosity, Horizontal Grid Reynolds Number (HGRN), ReΔ, and momentum transmission scheme, using two ideal cases, overflow and baroclinic eddy channel, we qualitatively analyze the simulation results by comparison with the three non-isopycnal models in Ilicak et al. (2012), i.e., MITGCM, MOM, and ROMS. The results show that the spurious dianeutral mixing in the MPAS-Ocean increases over time. The spurious dianeutral transport is proportional to the HGRN directly and is reduced by increasing the lateral viscosity or using a finer resolution to control HGRN. When the HGRN is less than 10, spurious transport is reduced significantly. When using the proper viscosity closure, MPAS-Ocean performs better than MITGCM and MOM, closely to ROMS, in the 2D case without rotation, and much better than the above-mentioned three ocean models under the condition of 3D space with rotation due to the cell area difference between the hexagon cell and the quadrilateral cell with the same resolution. Both the Zalesak (1979) flux corrected transport scheme and Leith closure in MPAS-Ocean play an excellent role in reducing spurious dianeutral mixing. The performance of Leith scheme is preferable to the condition of three-dimensional baroclinic eddy.

Measurement and modeling of polarized specular neutron reflectivity in large magnetic fields.

The presence of a large applied magnetic field removes the degeneracy of the vacuum energy states for spin-up and spin-down neutrons. For polarized neutron reflectometry, this must be included in the reference potential energy of the Schrödinger equation that is used to calculate the expected scattering from a magnetic layered structure. For samples with magnetization that is purely parallel or antiparallel to the applied field which defines the quantization axis, there is no mixing of the spin states (no spin-flip scattering) and so this additional potential is constant throughout the scattering region. When there is non-collinear magnetization in the sample, however, there will be significant scattering from one spin state into the other, and the reference potentials will differ between the incoming and outgoing wavefunctions, changing the angle and intensities of the scattering. The theory of the scattering and recommended experimental practices for this type of measurement are presented, as well as an example measurement.

Understanding the structure and electronic properties of Th4+-water complexes

We present a systematic quantum chemistry study of the [Th(H2O)n]4+(n = 1 to 10) complexes to gain insight into their electronic structure and properties: the effect of the ligand distribution on the valence shells of the thorium(IV) ion is studied by means of the electron localization function (ELF) topological analysis. Particular care is given to the study of the mono-aqua complex both at its equilibrium geometry, using various tools such as energy decomposition analyses (EDA), and along its dissociation pathway. Indeed, as several electronic states cross the Th4 +-H2O0ground state along the minimum energy path, we demonstrate that the diabatic representation implemented in MOLPRO is able to generate reference potential energy surfaces that will lead to the evaluation of diabatic dissociation curves. The calculated diabatic interaction energy curve will allow for a consistent parameterization of new generation force fields dedicated to heavy metals based on quantum chemistry.

Pyrazine excited states revisited using the extended multi-state complete active space second-order perturbation method

We demonstrate that the recently developed extended multi-state complete active space second-order perturbation theory (XMS-CASPT2) [Shiozaki et al., J. Chem. Phys., 2011, 135, 081106] provides qualitatively correct potential energy surfaces for low-lying excited singlet states of pyrazine, while the potential energy surfaces of the standard MS-CASPT2 methods are ill-behaved near the crossing point of two reference potential energy surfaces. The XMS-CASPT2 method is based on the extended multi-configuration quasi-degenerate perturbation theory proposed earlier by Granovsky [J. Chem. Phys., 2011, 134, 214113]. We show that the conical intersection at the XMS-CASPT2 level can be described without artifacts if the entire method is invariant with respect to any unitary rotations of the reference functions. The photoabsorption spectra of the 1(1)B(3u) and 1(1)B(2u) states of pyrazine are simulated, based on a vibronic-coupling model Hamiltonian. The XMS-CASPT2 spectrum of the 1(1)B(3u) band is found to be comparable to the one computed by a more expensive multireference configuration interaction (MRCI) method, while the XMS-CASPT2 simulation of the 1(1)B(2u) band is slightly inferior to the MRCI one.

Quantum-dynamics study of the ${\rm H}_5^+$H5+ cluster: Full dimensional benchmark results on its vibrational states

A full-dimensional quantum dynamics study is carried out for the highly fluxional H(5)(+) cation on a recent reference potential energy surface by using the multi configuration time-dependent Hartree method. With five equivalent light atoms and shallow barriers between various low-lying stationary points on the surface, the spectroscopic characterization of H(5)(+) represents a huge challenge for accurate quantum dynamics simulations. The present calculation is the first such a study on this cation, which together with its isotope analogies are of primary importance in the interstellar chemistry. The vibrational ground state properties and several vibrationally excited states corresponding to low vibrational frequency motions, not yet directly observable by the experiment, are presented and analyzed.

A First-Principles-Based Potential for the Description of Alkaline Earth Metals

We present a set of Gupta potentials fitted against highest-level ab initio data for interactions of the alkaline earth metals: beryllium, magnesium, and calcium. Reference potential energy curves have been computed for both pure and mixed dimers with the coupled cluster method including corrections for basic set incompleteness and relativistic effects. To demonstrate their usability for the efficient description of high-dimensional complex energy landscapes, the obtained potentials have been used for the global optimization of 38- and 42-atom clusters. Both pure and mixed compositions (binary and ternary clusters) were investigated. Distinctive trends in the structure of the latter are discussed.

Spurious dianeutral mixing and the role of momentum closure

This paper examines spurious dianeutral transport within a suite of ocean models (GOLD, MITgcm, MOM, and ROMS). We quantify such transport through a global diagnostic that computes the reference potential energy, whose evolution arises solely through transport between density classes. Previous studies have focused on the importance of accurate tracer advection schemes in reducing the spurious transport and closure. The present study highlights complementary issues associated with momentum transport. Spurious dianeutral transport is shown to be directly proportional to the lateral grid Reynolds number (ReΔ), with such transport significantly reduced when ReΔ<10.Simulations with the isopycnal model GOLD provide a benchmark for the smallest level of spurious dianeutral transport realizable in our model suite. For idealized simulations with a linear equation of state, GOLD exhibits identically zero spurious dianeutral mixing, and thus maintains a constant reference potential energy when all physical mixing processes are omitted. Amongst the non-isopycnal models tested in idealized simulations, ROMS generally produces smaller spurious dianeutral mixing than MITgcm or MOM, since ROMS makes use of a higher order upwind-biased scheme for momentum transport that enforces a small ReΔ. In contrast, MITgcm and MOM both employ unbiased (centered) discretizations of momentum transport, and therefore rely on lateral friction operators to control the grid Reynolds number. We find that a lateral shear-dependent Smagorinsky viscosity provides an effective means to locally reduce ReΔ, and thus to reduce spurious dianeutral transport in MITgcm and MOM.In addition to four idealized simulations, we quantify spurious dianeutral transport in realistic global ocean climate simulations using GOLD and MOM with a realistic equation of state for seawater, both with and without mesoscale eddies in the resolved flow field. The GOLD simulations have detectable levels of spurious cabbeling from along isopycnal advective truncation errors. Significantly larger spurious dianeutral transport arises in a non-eddying MOM simulation. In an eddying MOM simulation, spurious dianeutral transport is larger still but is reduced by increasing momentum friction.

Communication: Hybrid ensembles for improved force matching

Force matching is a method for parameterizing empirical potentials in which the empirical parameters are fitted to a reference potential energy surface (PES). Typically, training data are sampled from a canonical ensemble generated with either the empirical potential or the reference PES. In this Communication, we show that sampling from either ensemble risks excluding critical regions of configuration space, leading to fitted potentials that deviate significantly from the reference PES. We present a hybrid ensemble which combines the Boltzmann probabilities of both potential surfaces into the fitting procedure, and we demonstrate that this technique improves the quality and stability of empirical potentials.

Efficiency of nested Markov chain Monte Carlo for polarizable potentials and perturbed Hamiltonians

AbstractNested Markov chain Monte Carlo is a rigorous way to enhance sampling of a given energy landscape using an auxiliary, approximate potential energy surface. Its practical efficiency mainly depends on how cheap and how different are the auxiliary potential with respect to the reference system. In this article, a combined efficiency index is proposed and assessed for two important families of energy surfaces. As illustrated for water clusters, many‐body polarizable potentials can be approximated by simplifying the polarization contribution and keeping only the two‐body terms. In small systems, neglecting polarization entirely is also acceptable. When the reference potential energy is obtained from diagonalization of a quantum mechanical Hamiltonian, a first‐order perturbation scheme can be used to estimate the energy difference occuring on a Monte Carlo move. Our results indicate that this perturbation approximation performs well provided that the number of steps between successive diagonalization is adjusted beforehand. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2342–2346, 2010

Systematic First Principles Parameterization of Force Fields for Metal−Organic Frameworks using a Genetic Algorithm Approach

A systematic strategy is proposed to derive the necessary force field parameters directly from first principles calculations of nonperiodic model systems to reproduce both the structure and curvature of the reference potential energy surface. The parameters are determined using a genetic algorithm combined with a novel fitness criterion based on a representation of structure and curvature in a set of redundant internal coordinates. Due to the efficiency of this approach it is possible to abandon the need for transferability of the parameters. The method is targeted for the application on metal-organic frameworks (MOFs), where parameters for molecular mechanics force fields are often not available, because of the wide range of possible inorganic fragments involved. The scheme is illustrated for Zn4O-based IRMOF materials on the example of MOF-5. In a "building block" approach parameters are derived for the two model systems basic zinc formate (Zn4O(O2CH)6), and dilithium terephthalate with reference data obtained from density functional theory. The resulting potential gives excellent agreement with the structure, vibrational frequencies, thermal behavior and elastic constants of the periodic MOF-5.

On the Heisenberg behaviour of magnetic coupling in the manganese dimer

The magnetic coupling in the manganese dimer has been investigated with multiconfigurational computational schemes. Whereas the perturbational approaches present severe deviations to the expected Heisenberg behaviour, variational techniques based on difference dedicated configuration interaction (DDCI) perfectly fit a Heisenberg spectrum corresponding to antiferromagnetic coupling. This shows that the study of weak magnetic coupling as in Mn 2 is at (or beyond) the limit of applicability of perturbational techniques. Potential energy curves are obtained for the six low-lying Σ states by adding the DDCI energy difference to the reference potential energy surface calculated with coupled cluster techniques for the monoconfigurational 11 Σ g + state.