Ralph Jaquet

Explicitly correlated potential energy surface of , including relativistic and adiabatic corrections

After a short historical account of the theory of the ion, two ab initio methods are reviewed that allow the computation of the ground-state potential energy surface (PES) of in the Born–Oppenheimer (BO) approximation, with microhartree or even sub-microhartree accuracy, namely the R12 method and the method of explicitly correlated Gaussians. The BO-PES is improved by the inclusion of relativistic effects and adiabatic corrections. It is discussed how non-adiabatic effects on rotation and vibration can be simulated by corrections to the moving nuclear masses. The importance of the appropriate analytic fit to the computed points of the PES for the subsequent computation of the rovibronic spectrum is addressed. Some recent extensions of the computed PES in the energy region above the barrier to linearity are reviewed. This involves a large set of input geometries and the correct treatment of the dissociation asymptotics, including the coupling with the first excited singlet state. Some comments on this state as well as on the lowest triplet state of are made. The paper ends with a few remarks on the ion .

First-principles rovibrational analysis of the H3+-molecule.

The fitting of highly accurate potential energy points and of the diagonal adiabatic coupling for H3+ using different functional forms is presented. A recently derived analytical potential based on 69 points has been extended to give a highly reliable form of the topology of the surface far beyond the barrier to linearity. Rovibrational frequencies have been derived and are compared with experiment. Detailed information about the experimentally observed rovibrational transitions near 1.25 microm will be given. The computed transition frequencies reproduce experimental transitions within a tenth up to a few hundredths of a wavenumber, if a simulation of non-adiabatic effects is taken into account.

The influence of non-adiabaticity on the nuclear motion in the H3+ molecule

Abstract The rovibrational spectrum of H 3 + has been analyzed by taking into account that non-adiabatic couplings can be simulated by using atomic masses for vibrational and nuclear masses for rotational motion. This results in computed transition frequencies that reproduce experiment in most cases by a factor of 10 better than the original results including only adiabatic corrections. The deviation from experiment is in the range of a few hundredths of a wavenumber.

Rovibrational energy levels and transitions for H3 + computed from a new highly accurate potential energy surface

Bound rovibrational levels and selected transitions have been calculated for H3 + using a new potential energy surface (PES) computed by the CISD-R12-method. The present PES has an error of approximately 1 cm-1 in the relevant region around the minimum. This results in computed frequencies that reproduce experiment with a standard deviation of <0·31 cm-1 using nuclear masses for the motion of the three nuclei. In order to test non-Born-Oppenheimer effects different mass ratio definitions between nuclei and electrons have been analysed.

Investigations with the finite element method on the Cyber 205

We are trying to investigate systematically the application of the finite element method (FEM) for solving the Schrödinger equation. The present paper is devoted to the calculation of vibrational transition probabilities for the collinear reactive system A + BC (i.e. H+H2 and their isotopes). The calculations are fully two-dimensional and the results are compared with earlier FEM calculations and conventional basis set expansion methods using the the R-matrix or S-matrix propagation.We made extensive analysis of FEM on the vector-computer Cyber 205 and developed a vector code for the efficient use in two dimensions, so that in the near future applications even in three dimensions will be possible.For the hydrogen exchange reactions we investigated the following isotope combinations: (a) H + H2, b) H + DH, D + HD and H + MuH (symmetric reaction), (c) D + HH, H + DD and Mu + DD (asymmetric reaction). We calculated the transition probabilities for up to five open vibrational channels and found excellent agreement with known “exact” values.

Investigations with the finite element method. II. The collinear F + H2 reaction

Abstract We are investigating systematically the use of the finite element method (FEM) for solving the Schrodinger equation. The present work is devoted to the calculation of vibrational transition probabilities for the collinear reactive system F + H 2 . The calculations are fully two-dimensional and the results are compared with the conventional basis set expansion methods using the R -matrix or S -matrix propagation. Extensive analysis of FEM on the vector computer Cyber 205 was made and a vector code for the efficient use in two dimensions was developed, so that in the near future applications even in three dimensions will be possible. The details of our FEM calculations are the following: The integration area was discretized into triangles where quadratic polynomials for the local wavefunction were defined. Convergent results can be reached with this simple ansatz with roughly 10000 grid points.

The reaction Ne+H 2 + (v=0, 1, 2, 3, 4)→NeH++H: 3D potential energy surface and quasiclassical trajectory calculations

A three-dimensional potential energy surface for the endoergic reaction Ne+H2+→NeH++H in the2A′ ground state of the system NeH2+ has been calculated by quantum chemical ab initio methods (CEPA approximation). The calculated points on this surface were fitted to an analytic ansatz in terms of an extended LEPS functional form augmented by a correction function. The latter was expanded in polynomials in inverse powers of the internuclear distances. This analytic form was used for quasiclassical trajectory calculations of reactive cross sections. In agreement with experimental investigations a strong vibrational enhancement is observed, i.e. the reaction is markedly favored if the necessary reaction energy is supplied as vibrational energy of H2+ rather than as relative translational energy. Other properties of the reaction dynamics such as the backward to forward scattering ratio, the lifetime of the collision complex NeH2+, and final rotational and vibrational state distributions are also discussed on the basis of the quasiclassical trajectory calculations.

Application of the finite element method to eigenvalue problems I. One dimensional calculations using optimized elements

Abstract The finite element method (FEM) is used for solving the Schrodinger equation in one dimension. Simple model potentials are selected to compare analytical and numerical results. Within FEM, polynomials up to eighth order are used. A much higher accuracy of the eigenvalues could be achieved, if the size of the elements was adjusted to the node structure of the solution.

Using a nondirect product basis to compute J > 0 rovibrational states of H3(+).

We have used a Lanczos algorithm with a nondirect product basis to compute energy levels of H3(+) with J values as large as 46. Energy levels computed on the potential surface of M. Pavanello, et al. (J. Chem. Phys. 2012, 136, 184303) agree well with previous calculations for low J values.

Reactive scattering for different isotopologues of the H3(-) system: comparison of different potential energy surfaces.

Reaction probabilities and cross sections for the ion-neutral molecule collision H(-) + H2 and its different isotopologues are presented. Quasi-classical trajectory, time-independent, and time-dependent quantum calculations are compared with experimental results. In the calculations, three different ab initio potentials have been used to clarify their applicability.