Sergei Manzhos

A random-sampling high dimensional model representation neural network for building potential energy surfaces

We combine the high dimensional model representation (HDMR) idea of Rabitz and co-workers [J. Phys. Chem. 110, 2474 (2006)] with neural network (NN) fits to obtain an effective means of building multidimensional potentials. We verify that it is possible to determine an accurate many-dimensional potential by doing low dimensional fits. The final potential is a sum of terms each of which depends on a subset of the coordinates. This form facilitates quantum dynamics calculations. We use NNs to represent HDMR component functions that minimize error mode term by mode term. This NN procedure makes it possible to construct high-order component functions which in turn enable us to determine a good potential. It is shown that the number of available potential points determines the order of the HDMR which should be used.

Using neural networks to represent potential surfaces as sums of products

By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.

Using neural networks, optimized coordinates, and high-dimensional model representations to obtain a vinyl bromide potential surface

We demonstrate that it is possible to obtain good potentials using high-dimensional model representations (HDMRs) fitted with neural networks (NNs) from data in 12 dimensions and 15 dimensions. The HDMR represents the potential as a sum of lower-dimensional functions and our NN-based approach makes it possible to obtain all of these functions from one set of fitting points. To reduce the number of terms in the HDMR, we use optimized redundant coordinates. By using exponential neurons, one obtains a potential in sum-of-products form, which greatly facilitates quantum dynamics calculations. A 12-dimensional (reference) potential surface for vinyl bromide is first refitted to show that it can be represented as a sum of two-dimensional functions. To fit 3d functions of the original coordinates, to improve the potential, a huge amount of data would be required. Redundant coordinates avoid this problem. They enable us to bypass the combinatorial explosion of the number of terms which plagues all HDMR and multimode-type methods. We also fit to a set of approximately 70,000 ab initio points for vinyl bromide in 15 dimensions [M. Malshe et al., J. Chem. Phys. 127, 134105 (2007)] and show that it is possible to obtain a surface in sum-of-products form of quality similar to the quality of the full-dimensional fit. Although we obtain a full-dimensional surface, we limit the cost of the fitting by building it from fits of six-dimensional functions, each of which requires only a small NN.

Using redundant coordinates to represent potential energy surfaces with lower-dimensional functions.

We propose a method for fitting potential energy surfaces with a sum of component functions of lower dimensionality. This form facilitates quantum dynamics calculations. We show that it is possible to reduce the dimensionality of the component functions by introducing new and redundant coordinates obtained with linear transformations. The transformations are obtained from a neural network. Different coordinates are used for different component functions and the new coordinates are determined as the potential is fitted. The quality of the fits and the generality of the method are illustrated by fitting reference potential surfaces of hydrogen peroxide and of the reaction OH+H(2)-->H(2)O+H.

A Comparative Computational Study of Structures, Diffusion, and Dopant Interactions between Li and Na Insertion into Si

We present a comparative computational study of sodiated vs lithiated bulk Si, including the effects of Li–Li and Na–Na interactions on dopant mobility. Both Na and Li prefer to act as interstitial defects located at the tetragonal sites of the Si matrix. The migration barrier between tetragonal sites is 0.54 eV larger for Na than for Li, which is expected to result in a drastically lower diffusion rate. The interdopant interactions reduce the barrier for Li and Na diffusion by 0.16 and 0.28 eV, respectively, providing ab initio evidence that finite ion concentrations may improve the battery charge/discharge rate.

Photofragment image analysis using the Onion-Peeling Algorithm☆

With the growing popularity of the velocity map imaging technique, a need for the analysis of photoion and photoelectron images arose. Here, a computer program is presented that allows for the analysis of cylindrically symmetric images. It permits the inversion of the projection of the 3D charged particle distribution using the Onion Peeling Algorithm. Further analysis includes the determination of radial and angular distributions, from which velocity distributions and spatial anisotropy parameters are obtained. Identification and quantification of the different photolysis channels is therefore straightforward. In addition, the program features geometry correction, centering, and multi-Gaussian fitting routines, as well as a user-friendly graphical interface and the possibility of generating synthetic images using either the fitted or user-defined parameters.

Controlling Na diffusion by rational design of Si-based layered architectures

By means of density functional theory, we systematically investigate the insertion and diffusion of Na and Li in layered Si materials (polysilane and H-passivated silicene), in comparison with bulk Si. It is found that Na binding and mobility can be significantly facilitated in layered Si structures. In contrast to the Si bulk, where Na insertion is energetically unfavorable, Na storage can be achieved in polysilane and silicene. The energy barrier for Na diffusion is reduced from 1.06 eV in the Si bulk to 0.41 eV in polysilane. The improvements in binding energetics and in the activation energy for Na diffusion are attributed to the large surface area and available free volume for the large Na cation. Based on these results, we suggest that polysilane may be a promising anode material for Na-ion and Li-ion batteries with high charge-discharge rates.

Explicitly correlated MRCI-F12 potential energy surfaces for methane fit with several permutation invariant schemes and full-dimensional vibrational calculations

A data-set of nearly 100,000 symmetry unique multi-configurational ab initio points for methane were generated at the (AE)-MRCI-F12(Q)/CVQZ-F12 level, including energies beyond 30,000 cm−1 above the minimum and fit into potential energy surfaces (PESs) by several permutation invariant schemes. A multi-expansion interpolative fit combining interpolating moving least squares (IMLS) fitting and permutation invariant polynomials (PIP) was able to fit the complete data-set to a root-mean-square deviation of 1.0 cm−1 and thus was used to benchmark the other fitting methods. The other fitting methods include a single PIP expansion and two neural network (NN) based approaches, one of which combines NN with PIP. Full-dimensional variational vibrational calculations using a contracted-iterative method (and a Lanczos eigensolver) were used to assess the spectroscopic accuracy of the electronic structure method. The results show that the NN-based fitting approaches are able to fit the data-set remarkably accurately with the PIP–NN method producing levels in remarkably close agreement with the PIP–IMLS benchmark. The (AE)-MRCI-F12(Q)/CVQZ-F12 electronic structure method produces vibrational levels of near spectroscopic accuracy and a superb equilibrium geometry. The levels are systematically slightly too high, beginning at ∼ 1–2 cm−1 above the fundamentals and becoming correspondingly higher for overtones. The PES is therefore suitable for small ab initio or empirical corrections and since it is based on a multi-reference method, can be extended to represent dynamically relevant dissociation channels.

Superexcited state reconstruction of HCl using photoelectron and photoion imaging

The velocity-map imaging technique was used to record photoelectron and photofragment ion images of HCl following two-photon excitation of the E Sigma(+)(0+), V 1Sigma(+)(0+) (nu=9,10,11) states and subsequent ionization. The images allowed us to determine the branching ratios between autoionization and dissociation channels for the different intermediate states. These branching ratios can be explained on the basis of intermediate state electron configurations, since the configuration largely prohibits direct ionization in a one-electron process, and competition between autoionization and dissociation into H* (n=2)+Cl and H+Cl*(4s,4p,3d) is observed. From a fit to the vibrationally resolved photoelectron spectrum of HCl+ it is apparent that a single superexcited state acts as a gateway to autoionization and dissociation into H+Cl*(4s). Potential reconstruction of the superexcited state to autoionization was undertaken and from a comparison of different autoionization models it appears most likely that the gateway state is a purely repulsive and low-n Rydberg state with a (4Pi) ion core.

Fitting sparse multidimensional data with low-dimensional terms

An algorithm that fits a continuous function to sparse multidimensional data is presented. The algorithm uses a representation in terms of lower-dimensional component functions of coordinates defined in an automated way and also permits dimensionality reduction. Neural networks are used to construct the component functions.