Steve Alexandre Ndengué

Automated construction of potential energy surfaces

ABSTRACT Methods to construct molecular potential energy surfaces through automated generation of ab initio electronic structure data are reviewed. Given a chosen method for fitting ab initio data (electronic energies represented at particular geometries) into an analytic surface, the questions of how best to select the data point locations and how to interface an electronic structure software package with fitting codes in parallel on a high-performance computing cluster are addressed. It is shown that methods based on interpolating moving least squares fitting are useful as they lend themselves to an algorithm which iteratively refines the fitted surface towards arbitrary accuracy. Several variants of the method are illustrated through examples including spectroscopic potentials for van der Waals systems, systems with high permutation symmetry, reactive systems, and systems with multiple coupled electronic states. An outlook identifying areas for future development is given. GRAPHICAL ABSTRACT

Single- and multireference electronic structure calculations for constructing potential energy surfaces

Recent developments in single and multireference electronic structure methods and the approaches suitable to generate ab initio data that may be employed in the construction of global molecular potential energy surfaces are reviewed. The most appropriate, robust, accurate and cost effective strategies are discussed in the context of various applications ranging from cold collisions and weakly interacting clusters, to large amplitude motion in covalently bound molecules, as well as reaction and photodissociation dynamics. The relationships between the types and necessary quantity of ab initio data, and representations through fitting are important, and issues related to symmetry and electronic state degeneracy are mentioned. The impacts of limitations or error in the electronic structure data are discussed in terms of how they are reflected in calculations of spectroscopy, dynamics and kinetics. This discussion includes examples such as the submerged reef feature found along the path to formation of ozone on several published potentials. For that example, a relatively small absolute error in the form of a spurious barrier has profound effects on the dynamics and rates of exchange reactions. The origin of the spurious barrier in ozone and other systems is discussed from an electronic structure standpoint. The effective use of dynamically-weighted state-averaged multireference calculations to obtain robustly convergent global surfaces is detailed.

Absorption cross section of ozone isotopologues calculated with the multiconfiguration time-dependent hartree (MCTDH) method: I. The Hartley and Huggins bands.

The absorption cross sections of 18 isotopologues of the ozone molecule have been calculated in the range of the Hartley-Huggins bands (27000-55000 cm(-1)). All 18 possible ozone isotopologues made with (16)O, (17)O, and (18)O have been considered, with emphasis on those of geophysics interest like (16)O(3) (17)O(16)O(2), (16)O(17)O(16)O, (18)O(16)O(2), and (16)O(18)O(16)O. We have used the MCTDH algorithm to propagate wavepackets. As an initial wavepacket, we took the vibrational ground state multiplied by the transition dipole moment surface. The cross sections have been obtained from the autocorrelation function of this wavepacket. Only two potential energy surfaces (PESs) and the corresponding transition dipole moment are involved in the calculation. The dissociating R state has been omitted. The calculations have been performed only for J = 0. The comparison with the experimental absorption cross sections of (16)O(3) and (18)O(3) has been performed after an empirical smoothing which mimics the rotational envelop. The isotopologue dependence of the cross sections of 18 isotopologues can be split into two energy ranges, (a) from 27000 to 32000 cm(-1), the Huggins band, which is highly structured, and (b) from 32000 to 55000 cm(-1), the main part of the cross section which has a bell shape, the Hartley band. This bell-shaped envelop has been characterized by a new analytic model depending on only four parameters, amplitude, center, width, and asymmetry. The isotopologue dependence of these parameters reveals the tiny differences between the absorption cross sections of the various isotopologues. In contrast to the smooth shape of the Hartley band, the Huggins band exhibits pronounced vibrational structures and therefore shows large isotopologue differences which may induce a significant isotopologue dependence of the ozone photodissociation rates under actinic flux.

Ozone photolysis: Strong isotopologue/isotopomer selectivity in the stratosphere

Author Institution: CTMM Institut Charles Gerhardt UMR-CNRS 5253; University of Montpellier, France; Univ. Grenoble 1 / CNRS, LIPhy UMR 5588, Grenoble, F-38041, France; Department of Information Technology, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary

Rotational Excitations in CO–CO Collisions at Low Temperature: Time-Independent and Multiconfigurational Time-Dependent Hartree Calculations

The rotational excitation in collisions between two carbon monoxide molecules was studied while combining the use of both time-independent and time-dependent formalisms. All of the calculations made use of a recently published four dimensional PES for CO dimer. Time-independent scattering calculations were performed in the lower part of the collision energy range, thus limiting the number of open channels and computational cost. The PES features a low-energy path for geared motion that appears to affect the excitation propensities in low-energy collisions. For reactants colliding without initial rotational excitation, symmetric excitations (both monomers excited equally) are strongly favored. This behavior deviates significantly from an exponential gap model based on endo- or exoergicity. Comparable time-dependent calculations were performed in an extended energy range made feasible by the lower cost of those calculations. The wave packet propagation in the time-dependent approach was performed with the multiconfiguration time-dependent hartree (MCTDH) method and analyses via the flux method, and the Tannor and Weeks approach was used to calculate the transition probabilities in the energy range up to 1000 cm(-1). We deduce from the cross sections the corresponding reaction rates for temperatures between 10 and 250 K. MCTDH was found to yield well-converged results, where the methods overlap, validating the use of MCTDH as an efficient tool to study collision processes.

Resonances of HCO Computed Using an Approach Based on the Multiconfiguration Time-Dependent Hartree Method

The improved relaxation method with a complex absorbing potential (CAP) was used to compute resonance states of the formyl radical (HCO) using the Heidelberg multi-configuration time-dependent Hartree (MCTDH) program. To benchmark this approach, the same potential energy surface as was used in three other method development studies was used here. It was found that the MCTDH-based approach was able to accurately and efficiently compute 90 resonance states up to more than 1 eV above the dissociation limit. Extremely close agreement was obtained for energies and widths (lifetimes) calculated using MCTDH compared with those reported previously for three other CAP-based approaches that separately involved filter-diagonalization, a preconditioned complex-symmetric Lanczos algorithm, and a non-Hermitian real-arithmatic Lanczos method. The high accuracy achieved in this benchmark study supports the applicability of MCTDH to the study of resonances in larger systems in which increased dimensionality makes the efficiency of MCTDH advantageous.

Vibrational energy levels of the simplest Criegee intermediate (CH2OO) from full-dimensional Lanczos, MCTDH, and MULTIMODE calculations

Accurate vibrational energy levels of the simplest Criegee intermediate (CH2OO) were determined on a recently developed ab initio based nine-dimensional potential energy surface using three quantum mechanical methods. The first is the iterative Lanczos method using a conventional basis expansion with an exact Hamiltonian. The second and more efficient method is the multi-configurational time-dependent Hartree (MCTDH) method in which the potential energy surface is refit to conform to the sums-of-products requirement of MCTDH. Finally, the energy levels were computed with a vibrational self-consistent field/virtual configuration interaction method in MULTIMODE. The low-lying levels obtained from the three methods are found to be within a few wave numbers of each other, although some larger discrepancies exist at higher levels. The calculated vibrational levels are very well represented by an anharmonic effective Hamiltonian.

The Influence of Renner-Teller Coupling between Electronic States on H+CO Inelastic Scattering

We examine the excitation of carbon monoxide from its rovibrational ground state via collisions with a hydrogen atom. Calculations employ the Multi-Configuration Time-Dependent Hartree method and treat the nonadiabatic dynamics with the inclusion of both the ground and the Renner-Teller coupled first excited electronic states. For this purpose, a new set of recently presented global HCO Potential Energy Surfaces (PESs) that cover the 0-3 eV range of energy is used. The results obtained here considering only the ground state (without the Renner-Teller coupling) are in qualitative agreement with those available in the literature. The Renner-Teller effect is known to have an important effect on the spectroscopy of the system, and its inclusion and effects on the dynamics for the processes described in this paper are fairly significant also. The results of this study indicate that for certain very particular initial conditions rather dramatic effects can be observed.

The rotational spectrum and potential energy surface of the Ar–SiO complex

The rotational spectra of five isotopic species of the Ar-SiO complex have been observed at high-spectral resolution between 8 and 18 GHz using chirped Fourier transform microwave spectroscopy and a discharge nozzle source; follow-up cavity measurements have extended these measurements to as high as 35 GHz. The spectrum of the normal species is dominated by an intense progression of a-type rotational transitions arising from increasing quanta in the Si-O stretch, in which lines up to v = 12 (∼14 500 cm-1) were identified. A structural determination by isotopic substitution and a hyperfine analysis of the Ar-Si17O spectrum both suggest that the complex is a highly fluxional prolate symmetric rotor with a vibrationally averaged structure between T-shaped and collinear in which the oxygen atom lies closer to argon than the silicon atom, much like Ar-CO. To complement the experimental studies, a full dimensional potential and a series of effective vibrationally averaged, two-dimensional potential energy surfaces of Ar + SiO have been computed at the CCSD(T)-F12b/CBS level of theory. The equilibrium structure of Ar-SiO is predicted to be T-shaped with a well depth of 152 cm-1, but the linear geometry is also a minimum, and the potential energy surface has a long, flat channel between 140 and 180°. Because the barrier between the two wells is calculated to be small (of order 5 cm-1) and well below the zero-point energy, the vibrationally averaged wavefunction is delocalized over nearly 100° of angular freedom. For this reason, Ar-SiO should exhibit large amplitude zero-point motion, in which the vibrationally excited states can be viewed as resonances with long lifetimes. Calculations of the rovibrational level pattern agree to within 2% with the transition frequencies of normal and isotopic ground state Ar-SiO, and the putative K a = ±1 levels for Ar-28SiO, suggesting that the present theoretical treatment well reproduces the salient properties of the intramolecular potential.