Construction Of Potential Energy Surfaces Research Articles

Construction of molecular reactive potential energy surfaces based on neural networks

In this article, recent developments in construction of potential energy surfaces using neural networks are reviewed. Based on the previous studies, a systematical method is proposed for iteratively selecting new molecular conformations. The problem for data sampling is now fully resolved under strict standards. A series of potential energy surfaces have been constructed based on highly accurate ab initio energies, using this data selecting scheme and combined with several fitting methods as well as extensive dynamics calculations. Highly reliable dynamics results can be obtained from these surfaces.

Automated construction of potential energy surfaces

ABSTRACTMethods to construct molecular potential energy surfaces through automated generation of ab initio electronic structure data are reviewed. Given a chosen method for fitting ab initio data (electronic energies represented at particular geometries) into an analytic surface, the questions of how best to select the data point locations and how to interface an electronic structure software package with fitting codes in parallel on a high-performance computing cluster are addressed. It is shown that methods based on interpolating moving least squares fitting are useful as they lend themselves to an algorithm which iteratively refines the fitted surface towards arbitrary accuracy. Several variants of the method are illustrated through examples including spectroscopic potentials for van der Waals systems, systems with high permutation symmetry, reactive systems, and systems with multiple coupled electronic states. An outlook identifying areas for future development is given.

Multistate density function theory and the construction of diabatic and adiabatic potential energy surfaces

A multistate density function theory( MSDFT) based on valence bond theory was introduced. As an application,the MSDFT method was illustrated by the bond dissociation of H2 and the proton transfer between HNO3 and a water molecule. In the dissociation of H2,the MSDFT method yields a correct behavior as the two H atoms stretch to infinity,and gives a potential well in accord with second-order perturbation using complete active space( CASPT2). For the proton transfer process of HNO3,MSDFT can be used to yield both diabatic and adiabatic potential energy curves as a function of the proton transfer reaction coordinate. For the reaction barrier height,the inclusion of an ionic state in a three-state model can significantly improve the accuracy in barrier height in comparison with the high-level results.

The PyPES library of high quality semi-global potential energy surfaces.

In this article, we present a Python-based library of high quality semi-global potential energy surfaces for 50 polyatomic molecules with up to six atoms. We anticipate that these surfaces will find widespread application in the testing of new potential energy surface construction algorithms and nuclear ro-vibrational structure theories. To this end, we provide the ability to generate the energy derivatives required for Taylor series expansions to sixth order about any point on the potential energy surface in a range of common coordinate systems, including curvilinear internal, Cartesian, and normal mode coordinates. The PyPES package, along with FORTRAN, C, MATLAB and Mathematica wrappers, is available at http://sourceforge.net/projects/pypes-lib.

Advances in atomic-scale tribological mechanisms of solid interfaces

It is important to explain the triboligical mechanism of solid interfaces at the atomic scale. Theoretical models developments involving atomic-scale tribology and the most classical first-principles theory for atomic-scale friction have been described. The construction of potential energy surface based on first-principle calculation is found extremely useful to unveil the tribological mechanism for atomic-scale solid sheets. Furthermore, atomic-scale tribological mechanisms exploring achievements for metals interfaces, tribo-chemisty, carbon-based solid lubrication material and 2h-MoS2 have also been reviewed.

A fast hybrid method for constructing multidimensional potential energy surfaces from ab initio calculations: A new global analytic PES of NH2 system

A hybrid fitting scheme is proposed for the construction of global analytic ab initio potential energy surfaces (PESs) by means of applying reproducing kernel Hilbert space (RKHS) interpolation and cubic spline interpolation onto different dimensions of the molecular configuration space. In addition to inheriting most advantages of the pure RKHS method, this scheme offers the following extra benefits: short initiation time and enhanced stability and accuracy. We also propose a fast algorithm for the scheme allowing the PES computation time to be independent of the number of ab initio points. We have constructed an adiabatic PES of N(2D)+H2→NH+H reactive system from more than twenty thousand ab initio points using this scheme. The accurate quantum dynamics results calculated on the constructed PES demonstrate high accuracy and efficiency of this new scheme.

An implementation of the Levenberg–Marquardt algorithm for simultaneous-energy-gradient fitting using two-layer feed-forward neural networks

We present in this study a new and robust algorithm for feed-forward neural network (NN) fitting. This method is developed for the application in potential energy surface (PES) construction, in which simultaneous energy-gradient fitting is implemented using the well-established Levenberg–Marquardt (LM) algorithm. Three fitting examples are demonstrated, which include the vibrational PES of H2O, reactive PESs of O3 and ClOOCl. In the three testing cases, our new LM implementation has been shown to work very efficiently. Not only increasing fitting accuracy, it also offers two other advantages: less training iterations are utilized and less data points are required for fitting.

Perimetric coordinate system in potential energy surfaces, spline interpolations, and the study of triatomic reaction dynamics

Two applications of the perimetric coordinates to triatomic potential energy surfaces are explored. The first is the depiction of level surfaces, providing a global visualization of the potential energy surface. In this representation, the relation among the stationary points and the dissociation channels are easily seen. These level surfaces are shown to be the natural generalization of the well-known two-dimensional level curves of restricted potential energy surfaces; they also allow us to understand the relation of the two-dimensional graphs with the global potential energy surface. Case studies for [Cl, H2], [H, O, Cl] and [O3] potential energy surfaces are discussed in detail. The second application of the perimetric coordinates is the construction of global potential energy surfaces by means of cubic splines, thus avoiding the restrictions related to the triangular inequality. The procedure is straightforward, and a careful analysis of the influence of the interpolation knots on the quality of the potential energy surface was carried out. The potential energy surfaces constructed by such procedure were able to reproduce known dynamical features of the following chemical reactions: Cl + H2 → H + HCl, F + HD → HF(DH) + D(H) and O(1D) + HCl → Cl + OH (H + OCl).

Dissociative chemisorption dynamics of small molecules on metal surfaces

Much progress has been achieved for both experimental and theoretical studies on the dissociative chemisorption of molecules on surfaces. Quantum state-resolved experimental data has provided unprecedented details for these fundamental steps in heterogeneous catalysis, while the quantitative dynamics is still not fully understood in theory. An in-depth understanding of experimental observations relies on accurate dynamical calculations, in which the potential energy surface and adequate quantum mechanical implementation are desired. This article summarizes the current methodologies on the construction of potential energy surfaces and the quantum mechanical treatments, some of which are promising for future applications. The challenges in this field are also addressed.

Quantum effects in the abstraction reaction by H atoms of primary and secondary hydrogens in n-C4H10: a test of a new potential energy surface construction method

Recently, von Horsten et al. suggested an efficient method to construct two dimensional potential energy surfaces (PESs) for use in quantum scattering simulations, in which they utilised the minimum energy path (MEP) and assumed harmonic behaviour of the PES near the MEP. In the same paper, the authors applied this method to various H-abstraction reactions from C1-C3 alkane molecules. In this work we demonstrate an alternative PES construction method, and apply it to the more challenging H-abstraction from n-C(4)H(10) reactions. The geometry optimizations and frequency calculations are done at the MP2/cc-pVTZ level of theory, while the energies are calculated with the CCSD(T) method with the same basis set. The calculations give adiabatic energy barrier heights of 45.9 kJ mol(-1) and 34.4 kJ mol(-1) for the primary and secondary hydrogens in n-C(4)H(10). When compared to purely classical transition state theory, quantum scattering calculations show that quantum tunnelling and zero-point effects have large contributions at low temperatures, typically below 500 K. The branching ratio study suggests that the abstraction of secondary hydrogen in n-C(4)H(10) dominates the overall reaction rate at low temperatures. The rate constants for the two abstraction channels become more comparable as the temperature increases.

Quasi-Classical Trajectory Study of the N(2D) + H2(X1ΣG+) → NH(X3Σ–) + H(2S) Reaction Based on an Analytical Potential Energy Surface

Using the multireference configuration interaction method with the Davidson correction and a large orbital basis set (aug-cc-pV5Z), we obtain an energy grid that includes 17,500 points for the construction of a new analytical potential energy surface (APES) for the N((2)D) + H(2)(X(1)Σ(g)(+)) → NH(X(3)Σ(-)) + H((2)S) reaction. The APES, which contains 145 parameters and is represented with a many-body expansion and a new switch function, is fitted from the ab initio energies using an adaptive nonlinear least-squares algorithm. The geometric characteristics of the reported APES in the literature and those of our APES are also compared. On the basis of the APES that we obtained, reaction cross sections are computed by means of quasi-classical trajectory calculations and compared with the experimental and theoretical values available in the literature.

Neural network potentials for metals and oxides – First applications to copper clusters at zinc oxide

AbstractThe development of reliable interatomic potentials for large‐scale molecular dynamics (MD) simulations of chemical processes at surfaces and interfaces is a formidable challenge because a wide range of atomic environments and very different types of bonding can be present. In recent years interatomic potentials based on artificial neural networks (NNs) have emerged offering an unbiased approach to the construction of potential energy surfaces (PESs) for systems that are difficult to describe by conventional potentials. Here, we review the basic properties of NN potentials and describe their construction for materials like metals and oxides. The accuracy and efficiency are demonstrated using copper and zinc oxide as benchmark systems. First results for a potential of the combined ternary CuZnO system aiming at the description of oxide‐supported copper clusters are reported.magnified imageModel of a copper cluster at the ZnO($10\overline {1} 0$) surface.

On the quantum theory of molecules

Transition state theory was introduced in 1930s to account for chemical reactions. Central to this theory is the idea of a potential energy surface (PES). It was assumed that such a surface could be constructed using eigensolutions of the Schrödinger equation for the molecular (Coulomb) Hamiltonian but at that time such calculations were not possible. Nowadays quantum mechanical ab initio electronic structure calculations are routine and from their results PESs can be constructed which are believed to approximate those assumed derivable from the eigensolutions. It is argued here that this belief is unfounded. It is suggested that the potential energy surface construction is more appropriately regarded as a legitimate and effective modification of quantum mechanics for chemical purposes.

Ab initio chemical kinetics for the ClOO + NO reaction: Effects of temperature and pressure on product branching formation

The kinetics and mechanism for the reaction of ClOO with NO have been investigated by ab initio molecular orbital theory calculations based on the CCSD(T)/6-311+G(3df)//PW91PW91∕6-311+G(3df) method, employed to evaluate the energetics for the construction of potential energy surfaces and prediction of reaction rate constants. The results show that the reaction can produce two key low energy products ClNO + (3)O(2) via the direct triplet abstraction path and ClO + NO(2) via the association and decomposition mechanism through long-lived singlet pc-ClOONO and ClONO(2) intermediates. The yield of ClNO + O(2) ((1)△) from any of the singlet intermediates was found to be negligible because of their high barriers and tight transition states. As both key reactions initially occur barrierlessly, their rate constants were evaluated with a canonical variational approach in our transition state theory and Rice-Ramspergen-Kassel-Marcus/master equation calculations. The rate constants for ClNO + (3)O(2) and ClO + NO(2) production from ClOO + NO can be given by 2.66 × 10(-16) T(1.91) exp(341/T) (200-700 K) and 1.48 × 10(-24) T(3.99) exp(1711/T) (200-600 K), respectively, independent of pressure below atmospheric pressure. The predicted total rate constant and the yields of ClNO and NO(2) in the temperature range of 200-700 K at 10-760 Torr pressure are in close agreement with available experimental results.

ChemInform Abstract: Accurate Calculations of Reaction Rates: Predictive Theory Based on a Rigorous Quantum Transition State Concept

AbstractReview: 135 refs.

Accurate ab initio potential energy surfaces for the 3A′′ and 3A′ electronic states of the O(3P)+HBr system

In this work, we report the construction of potential energy surfaces for the (3)A('') and (3)A(') states of the system O((3)P) + HBr. These surfaces are based on extensive ab initio calculations employing the MRCI+Q/CBS+SO level of theory. The complete basis set energies were estimated from extrapolation of MRCI+Q/aug-cc-VnZ(-PP) (n = Q, 5) results and corrections due to spin-orbit effects obtained at the CASSCF/aug-cc-pVTZ(-PP) level of theory. These energies, calculated over a region of the configuration space relevant to the study of the reaction O((3)P) + HBr → OH + Br, were used to generate functions based on the many-body expansion. The three-body potentials were interpolated using the reproducing kernel Hilbert space method. The resulting surface for the (3)A('') electronic state contains van der Waals minima on the entrance and exit channels and a transition state 6.55 kcal/mol higher than the reactants. This barrier height was then scaled to reproduce the value of 5.01 kcal/mol, which was estimated from coupled cluster benchmark calculations performed to include high-order and core-valence correlation, as well as scalar relativistic effects. The (3)A(') surface was also scaled, based on the fact that in the collinear saddle point geometry these two electronic states are degenerate. The vibrationally adiabatic barrier heights are 3.44 kcal/mol for the (3)A('') and 4.16 kcal/mol for the (3)A(') state.

Accuracy of Low-level Surface in Hierarchical Construction of Potential Energy Surface

The effects of low-level PES on the overall accuracy of the final surface constructed by using hierarchical construction were investigated with the constructions of a number of global surfaces for the H3 system at UHF (UMP2, DFT-B3LYP, UCCSD(T))/vtz, and UCCSD(T)/avqz levels of theory. The total reaction probabilities for the H+H2 reaction calculated on these surfaces revealed that the accuracy of UCCSD(T)/avqz surface is very close to the well-known BKMP2 surface, while the UCCSD(T)/vtz PES has a slightly higher barrier. In contrast, the low-level theories (UHF, UMP2, DFT-B3LYP) with vtz basis set can only provide a qualitative description of this simplest reaction despite the fact that they are widely used to study reactions in complex systems. On the other hand, although these theories are not accurate on describing the reaction, they can be used to provide the low-level PESs for hierarchical construction of the UCCSD(T)/avqz PES with the number of UCCSD(T)/avqz energies substantially reduced.

ChemInform Abstract: Potential Energy Surfaces for Metal‐Assisted Chemical Reactions

AbstractReview: 92 refs.

Accurate multimode vibrational calculations using a B-spline basis: theory, tests and application to dioxirane and diazirinone

The use of B-spline basis sets is explored in the context of a vibrational program for automatic potential energy surface (PES) construction and multimode anharmonic vibrational wave function calculation. Results are compared with calculations using localized Gaussians and harmonic oscillator basis functions. Potential energy surfaces are constructed in an iterative fashion using a recently developed adaptive density-guided approach. The basis set requirements for an accurate representation of the vibrational wave functions are met by both B-spline basis sets as well as the well-known distributed Gaussian basis sets. Furthermore, the property of minimal support of the B-spline functions makes the use of B-spline basis more advantageous compared to harmonic oscillator basis functions, when combined with the adaptive procedure for PES construction used in this work. The methodology is tested for model potentials and water and subsequently applied to study vibrational states of dioxirane and diazirinone. The latter have proven to be elusive to experimental characterization and high level vibrational calculations based on accurate PES may offer a guidance for the experimental work.

Quasi-classical Trajectory Study of the Ne + H2+ → NeH+ + H Reaction Based on Global Potential Energy Surface

Using the multireference configuration interaction method with a Davidson correction and a large orbital basis set (aug-cc-pVQZ), we obtain an energy grid that includes 32 038 points for the construction of a new analytical potential energy surface (APES) for the Ne + H(2)(+) → NeH(+) + H reaction. The APES is represented as a many-body expansion containing 142 parameters, which are fitted from 31 000 ab initio energies using an adaptive nonlinear least-squares algorithm. The geometric characteristics of the reported APES and the one presented here are also compared. On the basis of the APES we obtained, reaction cross sections are computed by means of quasi-classical trajectory (QCT) calculations and compared with the experimental and theoretical data in the literature.