Tak-San Ho

A GENERAL METHOD FOR CONSTRUCTING MULTIDIMENSIONAL MOLECULAR POTENTIAL ENERGY SURFACES FROM AB INITIO CALCULATIONS

A general interpolation method for constructing smooth molecular potential energy surfaces (PES’s) from ab initio data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an a posteriori error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one‐dimensional potential energy curve of the He–He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], a two‐dimensional p...

A global H2O potential energy surface for the reaction O(1D)+H2→OH+H

A global, single‐valued ground‐state H2O potential surface for the reaction O(1D)+H2→OH+H has been constructed from a new set of accurate ab initio data using a general multidimensional interpolation method. The ab initio calculations are of the multireference, configuration interaction variety and were carried out using augmented polarized triple zeta basis sets. The multidimensional method is formulated within the framework of the reproducing kernel Hilbert space theory. The H2O potential is expressed as a many‐body sum of a single one‐body term, three two‐body terms, and a single three‐body term. The one‐body term is the dissociation energy to the three‐atom limit 2H(2S)+O(3P). The two‐body terms are two O–H and one H–H adiabatic diatomic potentials of lowest energy. Each diatomic term is obtained by interpolating a discrete set of ab initio data using a one‐dimensional, second‐order, distancelike reproducing kernel. The three‐body term is obtained by interpolating the difference of the H2O ab initio d...

POTENTIAL ENERGY SURFACE AND QUASICLASSICAL TRAJECTORY STUDIES OF THE N(2D)+H2 REACTION

We present a global potential energy surface for the 1A″ state of NH2 based on application of the reproducing kernel Hilbert space interpolation method to high quality ab initio (multireference configuration interaction) results. Extensive quasiclassical trajectory calculations are performed on this surface to study the N(2D)+H2/D2 reaction dynamics. Comparison is made with calculations on the lower level [first order configuration interaction (FOCI)] surface of Kobayashi, Takayanagi, Yokoyama, Sato, and Tsunashima (KTYST). We find a saddle point energy of 2.3 (1.9) kcal/mol for the perpendicular approach for the second order configuration interaction (SOCI) (SOCI with Davidson correction) surfaces, and a collinear stationary point energy of 5.5 (4.6) kcal/mol. The ordering of these stationary points is reversed compared to the corresponding FOCI results, and the only true reaction path on our surface is perpendicular. The primary reaction mechanism is determined to be C2v insertion to produce short lived...

Exploring the reaction dynamics of nitrogen atoms: A combined crossed beam and theoretical study of N(2D)+D2→ND+D

In the first successful reactive scattering study of nitrogen atoms, the angular and velocity distribution of the ND product from the reaction N(2D)+D2 at 5.1 and 3.8 kcal/mol collision energies has been obtained in a crossed molecular beam study with mass spectrometric detection. The center-of-mass product angular distribution is found to be nearly backward–forward symmetric, reflecting an insertion dynamics. About 30% of the total available energy goes into product translation. The experimental results were compared with those of quasiclassical trajectory calculations on an accurate potential energy surface obtained from large scale ab initio electronic structure computations. Good agreement was found between the experimental results and the theoretical predictions.

A globally smooth ab initio potential surface of the 1 A′ state for the reaction S(1D)+H2

A procedure based on the reproducing kernel Hilbert space (RKHS) interpolation method has been implemented to produce a globally smooth potential energy surface (PES) for the 1 A′ state of the S(1D)+H2 reaction from a set of accurate ab initio data, calculated at the multireference configuration interaction level with augmented polarized quadruple-zeta basis sets and arranged on a three-dimensional regular full grid in the Jacobi coordinates. The procedure includes removing a small number of questionable ab initio data points, implementing a recently developed technique for efficiently handling a partially filled grid, and adopting a sequence of regularizations for attaining additional smoothness. The resulting RKHS PES is analytic, first-order differentiable, and fast to evaluate. Quasiclassical trajectory calculations have been performed and compared with the results based on a recent hybrid PES obtained from a combination of the RKHS interpolation in the entrance channel and Murrell–Carter (MC)-type fi...

Semiclassical many-mode floquet theory

Abstract It is shown that the single-mode Floquet formalism of Shirley can be extended to a generalized many-mode Floquet theory, yielding a practical non-perturbative technique for the semiclassical treatment of the interaction of a quantum system several monochromatic oscillating fields. The theory is illustrated by a detailed study of the population dynamics of a three-level system driven by two monochromatic radiation fields.

A fast algorithm for evaluating multidimensional potential energy surfaces

A recently introduced general interpolation method based on reproducing kernel Hilbert space (RKHS) theory has been quite successful in constructing a number of potential energy surfaces. A straightforward implementation is slow when large numbers of ab initio  points are involved, since the computation time is proportional to the number of points. The algorithm introduced here precomputes and stores the sums necessary to generate the surface, allowing the surface computation time to be independent of the number of points. The method is tested on its ability to reproduce a prior global analytic fit to the potential surface for the N(2D)+H2 system based on a 7×7×7 grid of points. The RKHS interpolated surface is found to exactly reproduce the 343 points on which it is based, and has a root mean square (rms) error of 14.2 kJ mol−1 elsewhere, while the prior analytic fit has a rms error of 25.1 kJ mol−1 at the points used to fit the surface. With a 16×16×16 grid as input the RKHS surface had a rms error of 1...

Reproducing kernel Hilbert space interpolation methods as a paradigm of high dimensional model representations: Application to multidimensional potential energy surface construction

A generic high dimensional model representation (HDMR) method is presented for approximating multivariate functions in terms of functions of fewer variables and for going beyond the tensor-product formulation. Within the framework of reproducing kernel Hilbert space (RKHS) interpolation techniques, an HDMR is formulated for constructing global potential energy surfaces. The HDMR tools in conjunction with a successive multilevel decomposition technique provide efficient and accurate procedures for reducing a multidimensional interpolation problem to smaller, independent subproblems. It is shown that, when compared to the conventional tensor-product approach, the RKHS–HDMR methods can accurately produce smooth potential energy surfaces over dynamically relevant, nonrectangular regions using far fewer ab initio data points. Numerical results are given for a reduced two-level RKHS–HDMR of the C(1D)+H2 reactive system. The proposed RKHS–HDMR is intimately related to Gordon’s blending-function methods for multi...

On the importance of exchange effects in three-body interactions: The lowest quartet state of Na3

Three-body interactions in a homonuclear van der Waals bound trimer (the 1 4A2′ state of Na3) are studied spectroscopically for the first time using laser induced emission spectroscopy on a liquid helium nanodroplet coupled with ab initio calculations. The van der Waals bound, spin polarized sodium trimers are prepared via pickup by, and selective survival in, a beam of helium clusters. Laser excitation from the 1 4A2′ to the 2 4E′ state, followed by dispersion of the fluorescence emission, allows for the resolution of the structure due to the vibrational levels of the lower state and for the gathering of precise information on the three-body interatomic potential. From previous experiments on Na2 we know that the presence of the liquid helium perturbs the spectra by a very small amount [see J. Higgins et al., J. Phys. Chem. 102, 4952 (1998)]. Ab initio potential energy calculations are carried out at 42 geometries of the lowest quartet state using the coupled cluster method at the single, double, and non...

Quantum observable homotopy tracking control

This paper presents a new tracking method where the target observable O(s,T) at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s>or=0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique.