Pierre Valiron

Hierarchy of counterpoise corrections for N-body clusters: generalization of the Boys-Bernardi scheme

Abstract The counterpoise correction method of Boys and Bernardi is generalized for a consistent treatment of the basis set superposition error (BSSE) of three-body and higher many-body effects along the line used by White and Davidson for the three-body terms in an ice model. The BSSE-corrected energy terms are calculated recursively by using the hierarchy of one-, two-, three-body, etc. energy terms, and by recomputing each such contribution in basis sets of subclusters of increasing size. The scheme is illustrated by calculations on the He trimer at the RHF, MP2 and MP4 levels. The results suggest that properly BSSE-corrected cluster calculations may combin refined two-body interactions with approximate many-body corrections. The method might be useful in calculating potential surfaces of chemical reactions.

Quasi-classical rate coefficient calculations for the rotational (de)excitation of H2O by H2

Context. The interpretation of water line emission from existing observations and future HIFI/Herschel data requires a detailed knowledge of collisional rate coefficients. Among all relevant collisional mechanisms, the rotational (de)excitation of H 2 O by H 2 molecules is the process of most interest in interstellar space. Aims. To determine rate coefficients for rotational de-excitation among the lowest 45 para and 45 ortho rotational levels of H 2 O colliding with both para and ortho-H 2 in the temperature range 20-2000 K. Methods. Rate coefficients are calculated on a recent high-accuracy H 2 O-H 2 potential energy surface using quasi-classical trajectory calculations. Trajectories are sampled by a canonical Monte-Carlo procedure. H 2 molecules are assumed to be rotationally thermalized at the kinetic temperature. Results. By comparison with quantum calculations available for low lying levels, classical rates are found to be accurate within a factor of 1-3 for the dominant transitions, that is those with rates larger than a few 10 -12 cm 3 s -1 . Large velocity gradient modelling shows that the new rates have a significant impact on emission line fluxes and that they should be adopted in any detailed population model of water in warm and hot environments.

R12-calibrated H2O–H2 interaction: Full dimensional and vibrationally averaged potential energy surfaces

The potential energy surface of H(2)O-H(2) is of great importance for quantum chemistry as a test case for H(2)O-molecule interactions. It is also required for a detailed understanding of important astrophysical processes, namely, the collisional excitation of water, including the pumping of water masers and the formation of molecular hydrogen on icy interstellar dust grains. We have calculated the interaction for H(2)O-H(2) by performing both rigid-rotor (five-dimensional) and non-rigid-rotor (nine-dimensional) calculations using the coupled-cluster theory at the level of singles and doubles with perturbative corrections for triple excitations [CCSD(T)] with moderately large but thoroughly selected basis set. The resulting surface was further calibrated using high precision explicitly correlated CCSD(T)-R12 calculations on a subset of the rigid-rotor intermolecular geometries. The vibrationally averaged potential is presented in some details and is compared with the most recent rigid-rotor calculations. We explain, in particular, as to why vibrationally averaged rigid-rotor geometries are a better choice than equilibrium geometries. Our fit of the vibrationally averaged surface provides for the first time an accuracy of approximately 3 cm(-1) in the van der Waals minimum region of the interaction. The overall accuracy of the nine-dimensional surface and fit is lower but remains of the order of 3%-4% of the anisotropy in the domain spanned by the vibrational functions.

Improved low-temperature rate constants for rotational excitation of CO by H 2

Cross sections for the rotational (de)excitation of CO by ground state para- and ortho-H 2 are obtained using quantum scattering calculations for collision energies between 1 and 520 cm -1 . A new CO-H 2 potential energy surface is employed and its quality is assessed by comparison with explicitly correlated CCSD(T)-R12 calculations. Rate constants for rotational levels of CO up to 5 and temperatures in the range 5-70 K are deduced. The new potential is found to have a strong influence on the resonance structure of the cross sections at very low collision energies. As a result, the present rates at 10 K differ by up to 50% with those obtained by Flower (2001) on a previous, less accurate, potential energy surface.

A full nine-dimensional potential-energy surface for hydrogen molecule-water collisions

The hydrogen and water molecules are ubiquitous in the Universe. Their mutual collisions drive water masers and other line emission in various astronomical environments, notably molecular clouds and star-forming regions. We report here a full nine-dimensional interaction potential for H2O-H2 calibrated using high-accuracy, explicitly correlated wave functions. All degrees of freedom are included using a systematic procedure transferable to other small molecules of astrophysical or atmospherical relevance. As a first application, we present rate constants for the vibrational relaxation of the upsilon2 bending mode of H2O obtained from quasiclassical trajectory calculations in the temperature range of 500-4000 K. Our high-temperature (T > or = 1500 K) results are found compatible with the single experimental value at 295 K. Our rates are also significantly larger than those currently used in the astrophysical literature and will lead to a thorough reinterpretation of vibrationally excited water emission spectra from space.

The accuracy of atomization energies from explicitly correlated coupled-cluster calculations

The accuracy of atomization energies obtained from explicitly correlated coupled-cluster R12 calculations (CC-R12)—including single and double excitation operators (CCSD-R12) and a posteriori perturbative corrections for triple excitations [CCSD[T]-R12 and CCSD(T)-R12]—is studied for CH2(1A1), NH3, H2O, HF, N2, CO, and F2. The basis-set convergence with functions of high angular momentum is demonstrated. Unlike for conventional calculations, already the spdf saturation on nonhydrogen atoms and spd saturation on hydrogen are sufficient for CC-R12 calculations to provide results accurate to within 1 kJ/mol of the limit of a complete basis. Remaining small uncertainties at the CCSD[T]-R12 or CCSD(T)-R12 levels are attributed to the insufficient convergence within the coupled-cluster hierarchy towards the limit of full configuration interaction. It is shown that near the basis-set limit (as provided by CC-R12 calculations) the CCSD[T] variant of the triples correction gives, on average, results closer to the ...

Influence of a new potential energy surface on the rotational (de)excitation of H

Aims.Using a newly determined 5D potential energy surface for H2-H2O we provide an extended and revised set of rate coefficients for de-excitation of the lowest 10 para- and 10 ortho- rotational levels of H2O by collisions with para-(j=0) and ortho-H2(j=1), for kinetic temperatures from 5 K to 20 K. Methods.Our close coupling scattering calculations involve a slightly improved set of coupled channels with respect to previous calculations. In addition, we discuss the influence of several features of this new 5D interaction on the rotational excitation cross sections. Results. The new interaction potential leads to significantly different rate coefficients for collisions with para-H2 (j=0). In particular the de-excitation rate coefficient for the 110 to 101 transition is increased by up to 300% at 5 K. At 20 K this increase is 75%. Rate coefficients for collisions with ortho-H2(j=1) are modified to a lesser extent, by up to 40%. The influence of the new potential on collisions with both para-(j=0) and ortho-H2(j=1) is expected to become less pronounced at higher temperatures.

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Aims: Rate coefficients for the rotational excitation of the ten lowest levels of ortho-H_2CO by collisions with H2 molecules are computed for kinetic temperatures in the range 5-100 K. Methods: Cross sections are obtained from extensive, fully converged, quantum-mechanical scattering calculations using a highly accurate potential energy surface computed at the CCSD(T) level with a basis set extrapolation procedure. Scattering calculations are carried out for H2 molecules in both para and ortho rotational levels. Results: The present rates are shown to differ significantly from those available in the literature. Moreover, the strength of propensity rules is found to depend on the para/ortho form of H2. Radiative transfer modeling also shows that the new rates have a significant impact on H_2CO emission line fluxes and that they should be adopted in any detailed radiative transfer model of ortho-H_2CO in cold environments (T ⪉ 30 K). This paper is dedicated to the memory of our friend and colleague, Pierre Valiron, who died on 31 August 2008. Table of rate coefficients is available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/493/687

O by H

The ammonia molecule containing large amplitude inversion motion is a revealing system in examining high-order correlation effects on potential energy surfaces. Correlation contributions to the equilibrium and saddle point geometries, inversion barrier height and vibrational energy levels, including inversion splittings, have been investigated. A six-dimensional Taylor-type series expansion of the Born–Oppenheimer potential energy surface, which is scaled to different levels of theory, is used to determine vibrational energy levels and inversion splittings variationally. The electronic energies are calculated by coupled-cluster methods, combining explicitly correlated R12 theory (which includes the interelectronic coordinate in the electronic wave function) with a conventional approach including excitations up to the pentuple level. Finally, the electronic correlation contribution is scaled to the full configuration interaction limit. Corrections due to relativistic and non-Born–Oppenheimer effects are also included. Special emphasis is put on the convergence of the high-order contributions with respect to the size of the atomic basis set. To achieve an accuracy of 1 cm−1, it is essential to be at the basis set limit, include all the subtle effects and also include highly excited configurations—even up to the pentuple level in the coupled-cluster expansion.

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A second order Mo/ller–Plesset perturbation theory which is free of the basis set superposition error (BSSE) is developed based on the “Chemical Hamiltonian Approach” (CHA). The zeroth order Hamiltonian is built up on the BSSE-free (but not orthogonal and not necessarily real) canonic CHA–SCF orbitals and their orbital energies. As the exclusion of BSSE makes the problem nonHermitian, biorthogonal perturbation theory is used to obtain the first order wave function. The second order energy is, however, calculated by using the conventional Hermitian Hamiltonian, in accord with the “CHA with conventional energy” recipe. For that reason we use a generalized Hylleraas functional introduced recently; this guarantees the second order energy to be real even in the case of complex CHA–SCF orbitals. The matrix elements entering the generalized Hylleraas functional are calculated by transforming all wave functions, creation and annihilation operators to an auxiliary orthonormalized basis. The new CHA-MP2 method has ...