Hans O. Karlsson

Photodissociation of Bromobenzene, Dibromobenzene, and 1,3,5-Tribromobenzene

Quantum chemical calculations have been performed on the ground state and several low-lying excited states of bromobenzene, ortho-, meta-, and para-dibromobenzene, and 1,3,5-tribromobenzene using high-level ab initio and hybrid density-functional methods. Experimental observations of ultrafast predissociation in these molecules are clarified from extensive theoretical information about all low-energy potential-energy curves together with symmetry arguments. The intriguing observation that o- and m-dibromobenzene have two ultrafast predissociation channels while bromobenzene, p-dibromobenzene, and 1,3,5-tribromobenzene only have one such channel is explained from the calculated potential-energy curves. These show that the lowering of point-group symmetry from C2v to Cs along the main photodissociation reaction coordinate, which only occurs in o- and m-dibromobenzene, opens up a new predissociation channel. Dynamical quantum simulations based on the calculated potential-energy curves are used to estimate the coupling strength at the intersystem crossing point in bromobenzene.

Accurate time propagation for the Schrödinger equation with an explicitly time-dependent Hamiltonian

Several different numerical propagation techniques for explicitly time-dependent Hamiltonians are discussed and compared, with the focus on models of pump-probe experiments. The quality of the rotating wave approximation is analyzed analytically, and we point out under which circumstances the modeling becomes inaccurate. For calculations with the fully time-dependent Hamiltonian, we show that for multistate systems, with either time or space dependence in the interstate coupling, the fourth order truncated Magnus expansion can be reformulated so that no commutators appear. Our results show that the split-operator method should only be used when low accuracy is acceptable. For accurate and efficient time stepping, the Magnus-Lanczos approach appears to be the best choice.

Theoretical calculation of photodetachment intensities for H3O

We have calculated total and arrangement‐selected photodetachment intensities for the H3O− anion (and its deuterated form, D3O−) using a Green’s function in a discrete variable representation with absorbing boundary conditions. A multiply‐shifted quasiminimal residual method is used to obtain the Green’s function for many energies at once. We present spectra obtained by explicitly treating two and four degrees of freedom. Comparison with experiment indicates that the bending angles in the anion and neutral are more similar than in the current potential energy surfaces. The calculated spectra are also consistent with the suggestion that the barrier should be ‘‘earlier.’’

The quasi‐minimal residual algorithm applied to complex symmetric linear systems in quantum reactive scattering

The solution of systems of linear equations Ax=b with complex symmetric coefficient matrix A of size N, typically appearing in quantum-reactive scattering problems, is discussed. The quasiminimal residual (QMR) method is introduced to solve the complex symmetric linear system and is compared to the generalized minimal residual (GMRES) method. The methods are applied to two different chemical problems: the initial state-selected reaction probability for the H-2+OH-->H +H2O reaction, and the cumulative reaction probability for the isomerization of ketene, both with N>10(4). It is shown that the QMR method behaves more favorably, i.e., converges faster, than the GMRES for large N, especially when high accuracy is needed

Accurate resonances and effective absorption of flux using smooth exterior scaling

A general coordinate transformation is used to derive smooth exterior scaling (SES). Different complex paths are discussed and it is also shown how to derive a complex absorbing potential (CAP) from the SES. Accurate resonance values are computed both for short range and long range potentials. It is shown that the SES absorbs outgoing flux very effectively. The approximation of not scaling the potential and its relation to CAPs is discussed. It is emphasized that the SES can be implemented as easy as CAPs for grid methods.

Global error control of the time-propagation for the Schrödinger equation with a time-dependent Hamiltonian

Global error control of the time-propagation for the Schrodinger equation with a time-dependent Hamiltonian

Cross correlation functions Cnm(E) via Lanczos algorithms without diagonalization

It is shown how the quasiminimal residual algorithm (QMR), based on the Lanczos algorithm, can be modified to compute cross-correlation functions Cnm(E)=〈Ψn|(E−H)−1|Ψm〉 without any diagonalization by recursively updating a small number of scalars. Only three Lanczos vectors need to be stored. Several left-hand side vectors 〈Ψn| and multiple shifts E can be considered simultaneously. The new method is termed the quasiminimal recursive residue generation method (QM-RRGM) and is applied to the collinear H+H2 problem to illustrate its convergence behavior. The properties of two different formulations of the Lanczos algorithm, the usual three-term and a coupled two-term recursion, are also discussed. The QM-RRGM exhibits smooth convergence behavior, and it is shown that the stopping criteria used in the QMR algorithm can also be used for computing correlation functions.

Internal symmetry and selection rules in resonant inelastic soft x-ray scattering

Resonant inelastic soft x-ray scattering spectra excited at the dissociative 1 sigma(g) -> 3 sigma(u) resonance in gas-phase O(2) are presented and discussed in terms of state-of-the-art molecul ...

Exterior complex dilation for grid methods: Application to the cumulative reaction probability

Exterior complex dilation (ECD) is introduced for the discrete variable representation (DVR) via a general coordinate mapping. The procedure leads to a computationally efficient and easily implemented approach for imposing outgoing boundary conditions, comparable with absorbing potentials in terms of minimizing the grid and parameters used. ECD relies on a rigorous mathematical framework in contrast to absorbing potentials. The DVR-ECD approach is illustrated by computation of the cumulative reaction probability for the H+H2 reaction in one and two dimensions.

A perfectly matched layer applied to a reactive scattering problem

The perfectly matched layer (PML) technique is applied to a reactive scattering problem for accurate domain truncation. A two-dimensional model for dissociative adsorbtion and associative desorption of H(2) from a flat surface is considered, using a finite difference spatial discretization and the Arnoldi method for time-propagation. We compare the performance of the PML to that of a monomial complex absorbing potential, a transmission-free complex absorbing potential, and to exterior complex scaling. In particular, the reflection properties due to the numerical treatment are investigated. We conclude that the PML is accurate and efficient, especially if high accuracy is of significance. Moreover, we demonstrate that the errors from the PML can be controlled at a desired accuracy, enabling efficient numerical simulations.