Representation Of Potential Energy Surface Research Articles

Flexible DMRG-Based Framework for Anharmonic Vibrational Calculations.

We present a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm tailored to strongly anharmonic molecules described by general, high-dimensional model representations of potential energy surfaces. For this purpose, we extend the vDMRG framework to support vibrational Hamiltonians expressed in the so-called n-mode second-quantization formalism. The resulting n-mode vDMRG method offers full flexibility with respect to both the functional form of the PES and the choice of the single-particle basis set. We leverage this framework to apply, for the first time, vDMRG based on an anharmonic modal basis set optimized with the vibrational self-consistent field algorithm on an on-the-fly constructed PES. We also extend the n-mode vDMRG framework to include excited-state-targeting algorithms in order to efficiently calculate anharmonic transition frequencies. We demonstrate the capabilities of our novel n-mode vDMRG framework for methyloxirane, a challenging molecule with 24 coupled vibrational modes.

Parametrically Managed Activation Function for Fitting a Neural Network Potential with Physical Behavior Enforced by a Low-Dimensional Potential.

Machine-learned representations of potential energy surfaces generated in the output layer of a feedforward neural network are becoming increasingly popular. One difficulty with neural network output is that it is often unreliable in regions where training data is missing or sparse. Human-designed potentials often build in proper extrapolation behavior by choice of functional form. Because machine learning is very efficient, it is desirable to learn how to add human intelligence to machine-learned potentials in a convenient way. One example is the well-understood feature of interaction potentials that they vanish when subsystems are too far separated to interact. In this article, we present a way to add a new kind of activation function to a neural network to enforce low-dimensional constraints. In particular, the activation function depends parametrically on all of the input variables. We illustrate the use of this step by showing how it can force an interaction potential to go to zero at large subsystem separations without either inputting a specific functional form for the potential or adding data to the training set in the asymptotic region of geometries where the subsystems are separated. In the process of illustrating this, we present an improved set of potential energy surfaces for the 14 lowest 3A' states of O3. The method is more general than this example, and it may be used to add other low-dimensional knowledge or lower-level knowledge to machine-learned potentials. In addition to the O3 example, we present a greater-generality method called parametrically managed diabatization by deep neural network (PM-DDNN) that is an improvement on our previously presented permutationally restrained diabatization by deep neural network (PR-DDNN).

Neural network potentials for chemistry: concepts, applications and prospects.

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Diffusion Monte Carlo with fictitious masses finds holes in potential energy surfaces

Holes are commonly associated with high-dimensional, non-parametric representations of potential energy surfaces (PESs). These are regions of the PES with large negative values. Typically these occur at highly distorted geometries of (in reality) high energy. Finding holes in a systematic and efficient way is thus an important aspect in the development of PESs. Here we propose using diffusion Monte Carlo (DMC) with artificially reduced masses to automatically and robustly sample large regions of a fit, including those at very high energies. We demonstrate this for a recent PES of methane that was obtained using energies and gradients. The DMC software with the methane potential is available for download.

Diabatization by Machine Intelligence.

Understanding nonadiabatic dynamics is important for chemical and physical processes involving multiple electronic states. Direct nonadiabatic dynamics simulations are often employed to observe such processes on a femtosecond time scale. One often needs to do the simulation on a longer time scale, but direct simulation based on electronic structure calculations of the surfaces and couplings is expensive due to the large number of electronic structure calculations needed for ensemble averaging or simulation of longer-time processes. An alternative approach is to construct an analytical representation of potential energy surfaces (PESs) and couplings, which allows for faster dynamics calculations. Diabatic representations are preferred for such purposes because of the smoothness of the surfaces and couplings and the scalar nature of the couplings. However, many diabatization procedures are complicated by the need to consider orbitals or vector coupling elements, and these can make the process very labor-intensive. To circumvent these difficulties, we here propose diabatization by a deep neural network (DDNN) based on a new architecture for a deep neural network that requires neither orbital input nor vector input. The DDNN method allows convenient and semiautomatic diabatization, and it is demonstrated here for a model problem and for producing diabatic potential energy matrices for thiophenol.

Reactive dynamics and spectroscopy of hydrogen transfer from neural network-based reactive potential energy surfaces

The ‘in silico’ exploration of chemical, physical and biological systems requires accurate and efficient energy functions to follow their nuclear dynamics at a molecular and atomistic level. Recently, machine learning tools have gained a lot of attention in the field of molecular sciences and simulations and are increasingly used to investigate the dynamics of such systems. Among the various approaches, artificial neural networks (NNs) are one promising tool to learn a representation of potential energy surfaces. This is done by formulating the problem as a mapping from a set of atomic positions x and nuclear charges Zi to a potential energy V(x). Here, a fully-dimensional, reactive neural network representation for malonaldehyde (MA), acetoacetaldehyde (AAA) and acetylacetone (AcAc) is learned. It is used to run finite-temperature molecular dynamics simulations, and to determine the infrared spectra and the hydrogen transfer rates for the three molecules. The finite-temperature infrared spectrum for MA based on the NN learned on MP2 reference data provides a realistic representation of the low-frequency modes and the H-transfer band whereas the CH vibrations are somewhat too high in frequency. For AAA it is demonstrated that the IR spectroscopy is sensitive to the position of the transferring hydrogen at either the OCH- or OCCH3 end of the molecule. For the hydrogen transfer rates it is demonstrated that the O–O vibration (at ∼250 cm−1) is a gating mode and largely determines the rate at which the hydrogen is transferred between the donor and acceptor. Finally, possibilities to further improve such NN-based potential energy surfaces are explored. They include the transferability of an NN-learned energy function across chemical species (here methylation) and transfer learning from a lower level of reference data (MP2) to a higher level of theory (pair natural orbital-LCCSD(T)).

Adsorbate-Driven Electrode Processes, Part 2: Order to Disorder Transitions

Adsorbates on metal electrodes change the step formation energies and preferred step orientations relative to those of clean electrodes. We apply previously developed approximate density functional theory potential energy surfaces from Behler-Parrinello neural networks. We investigate the adsorbate order to disorder transition on terraces and monolayer and bilayer steps. We identify how the adlattice disorders with changing adsorbate coverage for these surfaces.

Direct diabatization and analytic representation of coupled potential energy surfaces and couplings for the reactive quenching of the excited 2Σ+ state of OH by molecular hydrogen.

We have employed extended multiconfiguration quasidegenerate perturbation theory, fourfold-way diabatic molecular orbitals, and configurational uniformity to develop a global three-state diabatic representation of the potential energy surfaces and their couplings for the electronically nonadiabatic reaction OH* + H2 → H2O + H, where * denotes electronic excitation to the A 2Σ+ state. To achieve sign consistency of the computed diabatic couplings, we developed a graphics processing unit-accelerated algorithm called the cluster-growing algorithm. Having obtained consistent signs of the diabatic couplings, we fit the diabatic matrix elements (which consist of the diabatic potentials and the diabatic couplings) to analytic representations. Adiabatic potential energy surfaces are generated by diagonalizing the 3 × 3 diabatic potential energy matrix. The comparisons between the fitted and computed diabatic matrix elements and between the originally computed adiabatic potential energy surfaces and those generated from the fits indicate that the current fit is accurate enough for dynamical studies, and it may be used for quantal or semiclassical dynamics calculations.

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we implement a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work suggest a more efficient scaling of computational cost with molecular size as compared to other methods.

Toolkit for the Construction of Reproducing Kernel-Based Representations of Data: Application to Multidimensional Potential Energy Surfaces.

In the early days of computation, slow processor speeds limited the amount of data that could be generated and used for scientific purposes. In the age of big data, the limiting factor usually is the method with which large amounts of data are analyzed and useful information is extracted. A typical example from chemistry are high-level ab initio calculations for small systems, which have nowadays become feasible even if energies at many different geometries are required. Molecular dynamics simulations often require several thousand distinct trajectories to be run. Under such circumstances suitable analytical representations of potential energy surfaces (PESs) based on ab initio calculations are required to propagate the dynamics at an acceptable cost. In this work we introduce a toolkit which allows the automatic construction of multidimensional PESs from gridded ab initio data based on reproducing kernel Hilbert space (RKHS) theory. The resulting representations require no tuning of parameters and allow energy and force evaluations at ab initio quality at the same cost as empirical force fields. Although the toolkit is primarily intended for constructing multidimensional potential energy surfaces for molecular systems, it can also be used for general machine learning purposes. The software is published under the MIT license and can be downloaded, modified, and used in other projects for free.

The spherical-harmonics representation for the interaction between diatomic molecules: The general case and applications to CO[sbnd]CO and CO[sbnd]HF

The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties, specifically in van der Waals clusters, with applications also to classical and quantum molecular dynamics simulations. The technique consists in the construction (by ab initio or semiempirical methods) of the expanded potential interaction up to terms that provide the generation of a number of leading configurations sufficient to account for faithful geometrical representations. This paper reports the full general description of the method of the spherical-harmonics expansion as applied to diatomic-molecule – diatomic-molecule systems of increasing complexity: the presentation of the mathematical background is given for providing both the application to the prototypical cases considered previously (O2O2, N2N2, and N2O2 systems) and the generalization to: (i) the COCO system, where a characteristic feature is the lower symmetry order with respect to the cases studied before, requiring a larger number of expansion terms necessary to adequately represent the potential energy surface; and (ii) the COHF system, which exhibits the lowest order of symmetry among this class of aggregates and therefore the highest number of leading configurations.

Atmospheric Chemistry of Criegee Intermediates: Unimolecular Reactions and Reactions with Water.

Criegee intermediates are produced in the ozonolysis of unsaturated hydrocarbons in the troposphere, and understanding their fate is a prerequisite to modeling climate-controlling atmospheric aerosol formation. Although some experimental and theoretical rate data are available, they are incomplete and partially inconsistent, and they do not cover the tropospheric temperature range. Here, we report quantum chemical rate constants for the reactions of stabilized formaldehyde oxide (CH2OO) and acetaldehyde oxide (syn-CH3CHOO and anti-CH3CHOO) with H2O and for their unimolecular reactions. Our results are obtained by combining post-CCSD(T) electronic structure benchmarks, validated density functional theory potential energy surfaces, and multipath variational transition state theory with multidimensional tunneling, coupled-torsions anharmonicity, and high-frequency anharmonicity. We consider two different types of reaction mechanisms for the bimolecular reactions, namely, (i) addition-coupled hydrogen transfer and (ii) double hydrogen atom transfer (DHAT). First, we show that the MN15-L exchange-correlation functional has kJ/mol accuracy for the CH2OO + H2O and syn-CH3CHOO + H2O reactions. Then we show that, due to tunneling, the DHAT mechanism is especially important in the syn-CH3CHOO + H2O reaction. We show that the dominant pathways for reactions of Criegee intermediates depend on altitude. The results we obtain eliminate the discrepancy between experiment and theory under those conditions where experimental results are available, and we make predictions for the full range of temperatures and pressures encountered in the troposphere and stratosphere. The present results are an important cog in clarifying the atmospheric fate and oxidation processes of Criegee intermediates, and they also show how theoretical methods can provide reliable rate data for complex atmospheric processes.

Novel mixture model for the representation of potential energy surfaces.

We demonstrate that knowledge of chemical physics on a materials system can be automatically extracted from first-principles calculations using a data mining technique; this information can then be utilized to construct a simple empirical atomic potential model. By using unsupervised learning of the generative Gaussian mixture model, physically meaningful patterns of atomic local chemical environments can be detected automatically. Based on the obtained information regarding these atomic patterns, we propose a chemical-structure-dependent linear mixture model for estimating the atomic potential energy. Our experiments show that the proposed mixture model significantly improves the accuracy of the prediction of the potential energy surface for complex systems that possess a large diversity in their local structures.

Tensor decomposition in potential energy surface representations.

In order to reduce the operation count in vibration correlation methods, e.g., vibrational configuration interaction (VCI) theory, a tensor decomposition approach has been applied to the analytical representations of multidimensional potential energy surfaces (PESs). It is shown that a decomposition of the coefficients within the individual n-mode coupling terms in a multimode expansion of the PES is feasible and allows for convenient contractions of one-dimensional integrals with these newly determined factor matrices. Deviations in the final VCI frequencies of a set of small molecules were found to be negligible once the rank of the factors matrices is chosen appropriately. Recommendations for meaningful ranks are provided and different algorithms are discussed.

Vibrational Fingerprints of Low-Lying Pt(n)P(2n) (n = 1-5) Cluster Structures from Global Optimization Based on Density Functional Theory Potential Energy Surfaces.

Vibrational fingerprints of small Pt(n)P(2n) (n = 1-5) clusters were computed from their low-lying structures located from a global exploration of their DFT potential energy surfaces with the GSAM code. Five DFT methods were assessed from the CCSD(T) wavenumbers of PtP2 species and CCSD relative energies of Pt2P4 structures. The eight first Pt(n)P(2n) isomers found are reported. The vibrational computations reveal (i) the absence of clear signatures made by overtone or combination bands due to very weak mechanical and electrical anharmonicities and (ii) some significant and recurrent vibrational fingerprints in correlation with the different PP bonding situations in the Pt(n)P(2n) structures.

Pt–Zn Clusters on Stoichiometric MgO(100) and TiO2(110): Dramatically Different Sintering Behavior

Zn was suggested to be a promising additive to Pt in the catalysis of dehydrogenation reactions. In this work, mixed Pt–Zn clusters deposited on two simple oxides, MgO(100) and TiO2(110), were investigated. The stability of these systems against cluster sintering, one of the major mechanisms of catalyst deactivation, is simulated using a Metropolis Monte Carlo scheme under the assumption of the Ostwald ripening mechanism. Particle migration, association to and dissociation from clusters, and evaporation and redeposition of monomers were all included in the simulations. Simulations are done at several high temperatures relevant to reactions of catalytic dehydrogenation. The effect of temperature is included via both the Metropolis algorithm and the Boltzmann-weighted populations of the global and thermally accessible local minima on the density functional theory potential energy surfaces of clusters of all sizes and compositions up to tetramers. On both surfaces, clusters are shown to sinter quite rapidly. However, the resultant compositions of the clusters most resistant to sintering are quite different on the two supports. On TiO2(110), Pt and Zn appear to phase separate, preferentially forming clusters rich in just one or the other metal. On MgO(100), Pt and Zn remain well-mixed and form a range of bimetallic clusters of various compositions that appear relatively stable. However, Zn is more easily lost from MgO through evaporation. These phenomena were rationalized by several means of chemical bonding analysis.

Shape of Multireference, Equation-of-Motion Coupled-Cluster, and Density Functional Theory Potential Energy Surfaces at a Conical Intersection.

We report and characterize ground-state and excited-state potential energy profiles using a variety of electronic structure methods along a loop lying on the branching plane associated with a conical intersection (CI) of a reduced retinal model, the penta-2,4-dieniminium cation (PSB3). Whereas the performance of the equation-of-motion coupled-cluster, density functional theory, and multireference methods had been tested along the excited- and ground-state paths of PSB3 in our earlier work, the ability of these methods to correctly describe the potential energy surface shape along a CI branching plane has not yet been investigated. This is the focus of the present contribution. We find, in agreement with earlier studies by others, that standard time-dependent DFT (TDDFT) does not yield the correct two-dimensional (i.e., conical) crossing along the branching plane but rather a one-dimensional (i.e., linear) crossing along the same plane. The same type of behavior is found for SS-CASPT2(IPEA=0), SS-CASPT2(IPEA=0.25), spin-projected SF-TDDFT, EOM-SF-CCSD, and, finally, for the reference MRCISD+Q method. In contrast, we found that MRCISD, CASSCF, MS-CASPT2(IPEA=0), MS-CASPT2(IPEA=0.25), XMCQDPT2, QD-NEVPT2, non-spin-projected SF-TDDFT, and SI-SA-REKS yield the expected conical crossing. To assess the effect of the different crossing topologies (i.e., linear or conical) on the PSB3 photoisomerization efficiency, we discuss the results of 100 semiclassical trajectories computed by CASSCF and SS-CASPT2(IPEA=0.25) for a PSB3 derivative. We show that for the same initial conditions, the two methods yield similar dynamics leading to isomerization quantum yields that differ by only a few percent.

A new global and compact analytical representation of the potential energy surface of triatomic systems: application to copper nitrosyl and water

A new, general analytical representation of potential energy surfaces (PES) for triatomic molecules is developed. It is based on a novel, angular-dependent form of the Morse potential extended to two bonds. The very compact analytical form needs only a few adjustable parameters while yielding a physically sound description of the global behaviour of the interactions in the entire configuration space. As a first example, the global PES of the lowest adiabatic state of water monomer (H2O) is reviewed. Parameters were adjusted to sets of energy points obtained from ab initio calculations at the coupled cluster and multi-reference configuration interaction level of theory. Experimental vibrational band centres of levels below 5000 cm−1 are correctly reproduced to within 3 cm−1; higher lying levels are less well described than in previously determined PES representations which involved a substantially extended set of adjustable parameters. Spectroscopic and thermodynamic data as well as reaction barriers are overall qualitatively well reproduced. The representation is suitable to describe semi-quantitatively the recombination as well as the abstraction reaction in the limit of low collision energies. As a second example, the first global PES of the copper nitrosyl molecule (CuNO) is presented. The equilibrium structure with a bent Cu–N–O connectivity and the dissociation energy match the currently best known values from ab initio calculations (Krishna and Marquardt, J. Chem. Phys. 136, 244303 (2012)) and vibrational band centres agree well with previously published experimental data from matrix isolation spectroscopy for various isotopologues. A high lying metastable state with the linear connectivity N–Cu–O is predicted.

Non-adiabatic effects during the dissociative adsorption of O2 at Ag(111)? A first-principles divide and conquer study

We study the gas-surface dynamics of O2 at Ag(111) with the particular objective to unravel whether electronic non-adiabatic effects are contributing to the experimentally established inertness of the surface with respect to oxygen uptake. We employ a first-principles divide and conquer approach based on an extensive density-functional theory mapping of the adiabatic potential energy surface (PES) along the six O2 molecular degrees of freedom. Neural networks are subsequently used to interpolate these grid data to a continuous representation. The low computational cost with which forces are available from this PES representation allows then for a sufficiently large number of molecular dynamics trajectories to quantitatively determine the very low initial dissociative sticking coefficient at this surface. Already these adiabatic calculations yield dissociation probabilities close to the scattered experimental data. Our analysis shows that this low reactivity is governed by large energy barriers in excess of 1.1 eV very close to the surface. Unfortunately, these adiabatic PES characteristics render the dissociative sticking a rather insensitive quantity with respect to a potential spin or charge non-adiabaticity in the O2–Ag(111) interaction. We correspondingly attribute the remaining deviations between the computed and measured dissociation probabilities primarily to unresolved experimental issues with respect to surface imperfections.

Studying molecular quantum dynamics with the multiconfiguration time‐dependent Hartree method

AbstractThis review covers the multiconfiguration time‐dependent Hartree (MCTDH) method, which is a powerful and general algorithm for solving the time‐dependent Schrödinger equation. The formal derivation is discussed as well as applications of the method. Recent extensions of MCTDH are treated in brief, namely, MCTDHB and MCTDHF, for treating identical particles (bosons and fermions), and the very powerful multilayer (ML‐MCTDH) formalism. Compact representations of potential energy surfaces (PESs) are also discussed, as the representation of a PES becomes a major bottleneck when going to larger systems (nine or more dimensions) while employing a full‐dimensional, complicated, and nonseparable PES. As applications of MCTDH, we discuss the calculation of photoionization and photoexcitation spectra of the vibronically coupled systems butatriene and pyrazine, respectively, and the infra‐red spectrum of the Zundel cation (protonated water dimer) H5O+2. © 2011 John Wiley & Sons, Ltd.This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics