Ralph Jaquet

Bio: Ralph Jaquet is an academic researcher from Folkwang University of the Arts. The author has contributed to research in topics: Potential energy surface & Adiabatic process. The author has an hindex of 17, co-authored 48 publications receiving 954 citations. Previous affiliations of Ralph Jaquet include University of Siegen.

Sub-microhartree accuracy potential energy surface for H3+ including adiabatic and relativistic effects. I. Calculation of the potential points

Abstract: Sixty-nine points of the Born–Oppenheimer (BO) potential energy surface (PES) for the ground state of H3+ have been computed using explicitly correlated Gaussian wave functions with optimized nonlinear parameters. The calculated points have an absolute error of about 0.02 cm−1 (0.1 microhartree), i.e., they are by at least one order of magnitude more accurate than ever reported. Similarly accurate adiabatic and relativistic corrections have also been evaluated by means of the Born–Handy formula and by direct perturbation theory (DPT), respectively.

Potential energy surface of the H+3 ground state in the neighborhood of the minimum with microhartree accuracy and vibrational frequencies derived from it

Abstract: The potential energy surface (PES) of the H+3 ground state is computed by means of the single and double excitation configuration interaction with an explicit linear r12 term in the wave function (CISD‐R12) developed recently by the present authors, with a nearly saturated basis set. The points of the PES suggested by Meyer, Botschwina, and Burton (MBB) were chosen and the fitting procedure of the same authors was followed. The present PES has both on an absolute and a relative scale (i.e., relative to the minimum) an error of a few microhartrees (μEh) in the relevant region, an accuracy that has never before been achieved in a quantum chemical calculation for a triatomic molecule. From the fit the vibrational term values for the fundamental bands and some overtones of H+3, H2D+, HD+2, and D+3 were computed by means of the TRIATOM package of Tennyson and Miller. The computed frequencies are in better agreement with experiment (maximum error ∼0.5 cm−1) than those of all previous ab initio calculations (wit...

Sub-microhartree accuracy potential energy surface for H3 + including adiabatic and relativistic effects. II. Rovibrational analysis for H3 + and D3 +

Abstract: The 69 potential energy points of H3+ computed by Cencek et al. [J. Chem. Phys., 108, 2831 (1998), preceding paper] have been fitted to an analytical potential energy surface (PES). Rovibrational frequencies have been derived for the symmetric H3+ and D3+ isotopomers. A comparison with experiment shows residual discrepancies of a few tenths of cm−1 which can be ascribed mainly to nonadiabatic effects.

Toward spectroscopic accuracy of ab initio calculations of vibrational frequencies and related quantities: a case study of the HF molecule

Abstract: Calculations at various coupled-cluster (CC) levels with and without the inclusion of linear rij-dependent terms are performed for the HF molecule in its ground state with a systematic variation of basis sets. The main emphasis is on spectroscopic properties such as the equilibrium distance re and the harmonic vibration frequency ωe. Especially with the R12 methods (including linear rij-dependent terms), convergence to the basis set limit is reached. However, the results (at the basis set limit) are rather sensitive to the level of the treatment of electron correlation. The best results are found for the CCSDT1-R12 and CCSD[T]-R12 methods (CCSD[T] was previously called CCSD+T(CCSD)), while CCSD(T) overestimates ωe by ≈6 cm−1. The good agreement of conventional CCSD(T) with experiment for basis sets far from saturation (e.g. truncated at g-functions) is probably the result of a compensation of errors. The contribution of core-correlation is non-negligible and must be included (effect on ωe≈5 cm−1). Relativistic effects are also important (23 cm−1), while adiabatic effects are much smaller (<1cm−1) and non-adiabatic effects on ωe can be simulated in replacing nuclear by atomic masses; for rotation nuclear masses appear to be the better choice, at least for hydrides. From a potential curve based on calculations with the CCSDT1-R12 method with relativistic corrections, the IR spectrum is computed quantum-mechanically. Both the band heads and the rotational structures of the observed spectra are reproduced with a relative error of ≈10−4 for the three isotopomers HF, DF, and TF.

Fit of the potential energy surface for the reaction Ne+H2+→NeH++H using three different functional forms

Abstract: Three different functional forms are fit to a calculated coupled electron pair approach potential energy surface for the reaction Ne+H2+→NeH++H. Minimum energy pathways and stationary points of the various fits are discussed.

Theory and Experiment

Abstract: This paper studies the impact of ambiguity and ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitudes toward ambiguity are heterogeneous across the population, just as attitudes toward risk are heterogeneous across the population, but that heterogeneity of attitudes toward ambiguity has different implications than heterogeneity of attitudes toward risk. In particular, when some state probabilities are not known, agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This suggests a different cross-section of portfolio choices, a wider range of state price/probability ratios and different rankings of state price/probability ratios than would be predicted if state probabilities were known. Experiments confirm all of these suggestions. Our findings contradict the claim that investors who have cognitive biases do not affect prices because they are infra-marginal: ambiguity averse investors have an indirect effect on prices because they change the per-capita amount of risk that is to be shared among the marginal investors. Our experimental data also suggest a positive correlation between risk aversion and ambiguity aversion that might explain the “value effect” in historical data.

Explicitly correlated electrons in molecules.

Abstract: Explicitly Correlated Electrons in Molecules Christof H€attig, Wim Klopper,* Andreas K€ohn, and David P. Tew Lehrstuhl f€ur Theoretische Chemie, Ruhr-Universit€at Bochum, D-44780 Bochum, Germany Abteilung f€ur Theoretische Chemie, Institut f€ur Physikalische Chemie, Karlsruher Institut f€ur Technologie, KIT-Campus S€ud, Postfach 6980, D-76049 Karlsruhe, Germany Institut f€ur Physikalische Chemie, Johannes Gutenberg-Universit€at Mainz, D-55099 Mainz, Germany School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom

A general method for constructing multidimensional molecular potential energy surfaces from ab initio calculations

Abstract: 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 potential energy surface of the HeCO van der Waals molecule using recent ab initio calculations by Tao et al. [J. Chem. Phys. 101, 8680 (1994)], and a three‐dimensional potential energy surface of the H+3 molecular ion using highly accurate ab initio calculations of Rohse et al. [J. Chem. Phys. 101, 2231 (1994)]. In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by Rohse et al. using a low order polynomial fitting procedure.

Universal Gaussian basis sets for an optimum representation of Rydberg and continuum wavefunctions

Abstract: A universal Gaussian basis set concept for the calculation of Rydberg and continuum states by pure L2 methods is presented It is based on the generation of optimised sequences of Gaussian exponents by maximising the overlap with a series of Slater-type functions characterised by a constant exponent and a variable principal quantum number In this way linear combinations of Gaussian basis functions can be found which are ideally suited to imitate Laguerre-Slater functions It is thus possible to obtain optimum representations of Rydberg orbitals or of complete orthonormal systems of Laguerre functions playing an important role in the L2 expansion of continuum functions The basis sets are tested with the hydrogen atom The effectiveness of the basis is illustrated by the calculation of quantum defects associated with the s, p and d Rydberg series of the alkali metal atoms Li and Na The phaseshifts determined in the ionisation continuat of these systems nicely fit the series below the ionisation limit as is finally demonstrated by an Edlen plot

Effect of Coriolis coupling in chemical reaction dynamics

Abstract: It is essential to evaluate the role of Coriolis coupling effect in molecular reaction dynamics. Here we consider Coriolis coupling effect in quantum reactive scattering calculations in the context of both adiabaticity and nonadiabaticity, with particular emphasis on examining the role of Coriolis coupling effect in reaction dynamics of triatomic molecular systems. We present the results of our own calculations by the time-dependent quantum wave packet approach for H + D2 and F(2P3/2,2P1/2) + H2 as well as for the ion–molecule collisions of He + H2+, D− + H2, H− + D2, and D+ + H2, after reviewing in detail other related research efforts on this issue.