A. J. C. Varandas

A double many‐body expansion of the two lowest‐energy potential surfaces and nonadiabatic coupling for H3

We present a consistent analytic representation of the two lowest potential energy surfaces for H3 and their nonadiabatic coupling. The surfaces are fits to ab initio calculations published previously by Liu and Siegbahn and also to new ab initio calculations reported here. The analytic representations are especially designed to be valid in the vicinity of the conical intersection of the two lowest surfaces, at geometries important for the H+H2 reaction, and in the van der Waals regions.

Basis-set extrapolation of the correlation energy

A simple theoretically motivated model to extrapolate the correlation energy based on correlation-consistent polarized X-tuple basis sets is suggested. It has the form EXcor=E∞cor[1+A3 X−3(1+A4 X−1)], where EXcor is the energy for the X-tuple basis set, E∞cor and A3 are parameters to be determined from a set (Xmin−Xmax) of correlation consistent basis sets at a given level of theory, and A4 is a function of A3. Even for the simple (2,3) extrapolation scheme, the method is shown to yield energies for 33 test data sets that are more accurate than those obtained from pure correlation consistent sextuple-zeta basis sets at a much lower computational cost. Other extrapolation schemes have also been investigated, including a simple one-parameter rule EXcor=E∞cor(1–2.4X−3).

Quasiclassical trajectory calculations of the thermal rate coefficients for the reactions H(D)+O2→OH(D)+O and O+OH(D)→O2+H(D) as a function of temperature

Thermal rate coefficients are calculated for the reaction, (1), H+O2→OH+O and its reverse, (−1), O+OH→O2+H, using the quasiclassical trajectory method and the most recently reported double many‐body expansion (DMBE IV) potential energy surface for the ground electronic state of the hydroperoxyl radical. The full range of temperatures for which experimental data is available in the literature has been covered, namely, 1000≤T≤3000 K for reaction (1) and 150≤T≤3000 K for reaction (−1). The equilibrium constant has also been evaluated. In addition, calculations of the isotopic effect on the thermal rate coefficient for the deuterated reactions D+O2→OD+O and O+OD→O2+D, and equilibrium constant, are reported. The theoretical results are shown to be in good agreement with the most recent and accurate experimental measurements.

A realistic double many-body expansion (DMBE) potential energy surface for ground-state O3 from a multiproperty fit to ab initio calculations, and to experimental spectroscopic, inelastic scattering, and kinetic isotope thermal rate data

A new single-valued potential energy surface is reported for the ground electronic state of ozone from the double many-body expansion (DMBE) method. The parameters appearing in the DMBE formalism are determined from a multiproperty analysis using ab initio energies, and experimental data from spectroscopic, incomplete total scattering cross section, and kinetic thermal rate measurements. Based on this new surface, thermal rate coefficients for the 18O + 16O2 → 18O16O + 16O isotope exchange reaction are also reported over the temperature range 300 < T < 2000 K from the quasi-classical trajectory method.

Excitation function for H+O2 reaction: A study of zero‐point energy effects and rotational distributions in trajectory calculations

The excitation function of the H+O2 (v=0)→OH+O reaction has been determined from trajectory calculations using the HO2 DMBE IV potential energy surface. Reactive cross sections for thirteen translational energies, corresponding to a total of a quarter of a million trajectories, have been computed covering the range 65≤Etr/kJ mol−1≤550. Various schemes for analyzing the trajectories, three of which aim to correct approximately for the zero‐point energy problem of classical dynamics, have been investigated. One of these schemes aims to correct also for known requirements on rotational distributions, e.g., for the fact that by Hund’s rules for the coupling of angular momentum the product OH (2Π) molecule always rotates. It has been found that zero‐point energy effects and lowest‐J constraints on rotational distributions may have a crucial role, especially close to the threshold energy of reaction. Agreement with recent measurements of absolute reactive cross sections is generally satisfactory but, unlike exp...

Analytical potentials for triatomic molecules: IX. The prediction of anharmonic force constants from potential energy surfaces based on harmonic force fields and dissociation energies for SO2 and O3

Analytical potential energy functions which are valid at all dissociation limits have been derived for the ground states of SO2 and O3. The procedure involves minimizing the errors between the observed vibrational spectra and spectra calculated by a variational procedure. Good agreement is obtained between the observed and calculated spectra for both molecules. Comparisons are made between anharmonic force fields, previously determined from the spectral data, and the force fields obtained by differentiating the derived analytical functions at the equilibrium configurations.

A novel non-active model to account for the leak of zero-point energy in trajectory calculations. Application to H + O2 reaction near threshold

Abstract A novel non-active model to correct for the leak of zero-point energy in quasi-classical trajectory calculations is proposed. It consists of eliminating every trajectory that fails to satisfy the zero-point energy requirement of quantum mechanics at the end of the trajectory, and then correct the results using a unified statistical approach which takes into account the relative probabilities of the reactive and non-reactive events. The correction factor assumes a simple analytic form, adding no extra cost of the traditional quasiclassical trajectory approach. Test calculations are presented for the total reactivity of the H + O 2 reaction out of the initial vibrational—rotational state ( v,j ) = (0, 0), keeping the total angular momentum J = 0. Comparison of the results with quantum mechanical reactivities calculated on the same (DMBE IV) potential energy surface shows good agreement. A possible generalization of the model to require a local zero-point energy along the trajectory is pointed out.

Use of scaled external correlation, a double many-body expansion, and variational transition state theory to calibrate a potential energy surface for FH2

A new potential energy surface is presented for the reaction F+H2→HF+H. The regions of the surface corresponding to collinear and bent geometries in the F–H–H and H–F–H barrier regions are based on scaled external correlation (SEC) electronic structure calculations, and the F–H⋅⋅⋅H exit channel region is based on the previously developed surface No. 5. The functional form of the new surface includes dispersion forces by a double many‐body expansion (DMBE), and the surface was adjusted so that the van der Waals well in the F⋅⋅⋅H–H region agrees with available experimental predictions. We have calculated stationary point properties for the new surface as well as product–valley barrier maxima of vibrationally adiabatic potential curves for F+H2→HF(v’=3)+H,F+HD→HF(v’=3)+D, and F+D2→DF(v’=4)+D. The new surface should prove useful for studying the effect on dynamics of a low, early barrier with a wide, flat bend potential, as indicated by the best available electronic structure calculations.

Energy switching approach to potential surfaces: An accurate single‐valued function for the water molecule

A novel scheme is suggested to construct a global potential energy surface by switching between representations which are optimal for different energy regimes. The idea is illustrated for the electronic ground state of water for which we use as switched functions the many‐body expansion potential of Murrell and Carter [J. Chem. Phys. 88, 4887 (1984)] and the polynomial form of Polyansky, Jensen, and Tennyson, [J. Chem. Phys. 101, 7651 (1994)]. By also modifying the former to reproduce the Coulombic behavior at the collapsed molecular limits for vanishingly small interatomic distances and approximately account for the long range forces, the new potential energy surface has been given double many‐body expansion quality. The result is a global H2O potential energy surface which has spectroscopic accuracy and may be used for studies of reaction dynamics.

A general approach to the potential energy functions of small polyatomic systems: Molecules and van der Waals molecules

Abstract This paper is concerned with recent theoretical progresses on the determination of potentials for use in spectroscopic and gas phase scattering calculations. Emphasis is placed on the global representation of the potential surface by using the many-body expansion of the molecular potential energy. Novel developments which allow further flexibility and reliability to this method while conveying generality both for chemically stable and van der Waals molecules are described. The essential feature of the new method is to separate the (extended-) Hartree-Fock and correlation energy components of the terms of the many-body expansion. In this double many-body expansion of the molecular energy the Hartree-Fock components are, in principle, obtained from accurate SCF calculations while the correlation components are obtained semiempirically from the dispersion energy coefficients for the various separate and united atom limits and those also known for the equilibrium geometries of the subsystems. Examples are given to illustrate the method.