No abstract

A new method to generate spin-orbit coupled potential energy surfaces: Effective relativistic coupling by asymptotic representation J. Chem. Phys. 136, 034103 (2012); 10.1063/1.3675846Representation of the 6D potential energy surface for a diatomic molecule near a solid surfaceThe recently proposed scheme for representing multidimensional potential energy surfaces as a linear combination of products of one-dimensional functions is extended. The extensions prove to be important if one proceeds to higher dimensions. An iteration procedure is introduced which can further improve the representation. The product representation of potential energy surfaces is especially well suited to be employed within the framework of the multiconfiguration time-dependent Hartree ͑MCTDH͒ approximation. The potential representation scheme cannot only be used to represent given analytical potential energy surfaces, but also to interpolate multidimensional surfaces on given, e.g. ab initio, product grid points. The product representation method is applied to the three-dimensional S1 electronic surface of NOCl and to a six-dimensional model Coulomb potential. To check the quality of the NOCl surface representation, the photoabsorption spectrum for an excitation from the S0 to the S1 surface is computed. Weight functions are shown to be easily implemented and, in the case of the NOCl surface, allow a substantial reduction of the number of required expansion coefficients. Exploiting the underlying symmetries of the potential under consideration can further reduce the computational effort, as is shown in the example of the Coulomb potential. Finally, the NOCl S1 potential surface defined on 616 ab initio points is interpolated, as an example for the product interpolation scheme.

An efficient method was recently introduced [J. Chem. Phys. 102, 5605 (1995); 104, 7974 (1996)] to represent multidimensional potential energy surfaces as a linear combination of products of one-dimensional functions, so-called natural potentials. Weight functions were shown to be easily implemented in the product representation scheme as long as they are separable, i.e., defined as a product of one-dimensional weight functions. Here the constraint imposed by the special product form of the separable weights is removed. Nonseparable weights are emulated by dividing the potential energy surface in arbitrary regions of minor and major physical relevance and by utilizing a so-called relevant region iteration procedure. Maintaining the advantageous computational scaling properties of the product representation scheme, this relevant region iteration procedure allows the stepwise improvement of the surface representation in the regions of major relevance. The quality of the product representation in the regions of minor relevance remains nevertheless acceptable. As a consequence, the number of potential expansion coefficients can be reduced substantially. The product representation of potential energy surfaces is especially well suited to be employed within the framework of the multiconfiguration time-dependent Hartree (MCTDH) approximation. To check the performance of the proposed method the Liu–Siegbahn–Truhlar–Horowitz (LSTH) surface is represented in Jacobian coordinates, and initial-state selected reaction probabilities for the H+H2(ν=j=0)→H2+H exchange reaction are computed.

A novel modification of the flux operator formalism is introduced that combines the merits of the flux operator approach with those of complex absorbing potentials. The method is used to determine initial-state selected reaction probabilities for a broad energy range from a single appropriately chosen time-dependent wave packet. The propagation may be performed solely in the coordinates of the reagents arrangement channel. State-to-state transition probabilities can also be obtained when appropriate projectors are included. In contrast to similar methods the present one does not require the calculation of derivatives with respect to the reaction coordinate. More importantly, it avoids the need to (E,t)-Fourier transform the wave packet at every grid point on a dividing surface. The proposed formula, though completely general, is especially well suited to handle multiconfiguration time-dependent Hartree wave functions. As a check of the reliability initial-state selected reaction probabilities for the collinear H+H2→H2+H reaction are calculated and compared with (numerically) exact results. We also show that the initial wave packet may be placed close to the interaction region when its energy distribution is corrected for the mean potential energy.

The recently developed multiconfiguration time-dependent Hartree approach (MCTDH) is for the first time applied to quantum reactive scattering. State-resolved reaction probabilities for the collinear H+H2(ν=0,1)→H2(ν=0,1)+H exchange-reaction are calculated and are found to be in excellent agreement with previous results obtained by time-independent methods. To compute the reaction probabilities the initial wavepacket is propagated forward and the final wave packet backwards in time. The Fourier transform at energy E of the time-dependent overlap of both wave packets is then proportional to the S-matrix element. Complex absorbing potentials are shown to be easily implemented in the MCTDH scheme. Fixed single-particle functions are introduced which result in a decrease in computational effort. The MCTDH algorithm requires the potential energy surface to be represented in a particular form. A new scheme for representing potential energy surfaces in a MCTDH adapted form is derived. This scheme can also be used for fitting multidimensional surfaces to given data points.