Accurate analytic He–H2 potential energy surface from a greatly expanded set of ab initio energies

The interaction potential energy surface (PES) of H4 is of great importance for quantum chemistry as a test case for molecule–molecule interactions. It is also required for a detailed understanding of certain astrophysical processes, namely collisional excitation and dissociation of H2 in molecular clouds, at densities too low to be accessible experimentally. The 6101 ab initio H4 energies reported in 1991 by Boothroyd et al. demonstrated large inaccuracies in analytic H4 surfaces available at that time. Some undesirable features remained in the more accurate H4 surfaces fitted to these energies by Keogh and by Aguado et al., due in part to the relatively sparse coverage of the six-dimensional H4 conformation space afforded by the 6101 ab initio energies. To improve the coverage, 42 079 new ab initio H4 energies were calculated, using Buenker’s multiple reference (single and) double excitation configuration interaction program. Here the lowest excited states were computed as well as the ground state, and energies for the original 6101 conformations were recomputed. The ab initio energies have an estimated rms “random” error of ∼0.5 millihartree and a systematic error of ∼1 millihartree (0.6 kcal/mol). A new analytical H4 PES was fitted to these 48 180 ab initio energies (and to an additional 13 367 points generated at large separations), yielding a significant improvement over previous H4 surfaces. This new PES has an rms error of 1.43 millihartree relative to these 48 180 ab initio energies (the fitting procedure used a reduced weight for high energies, yielding a weighted rms error of 1.15 millihartree for these 48 180 ab initio energies). For the 39 064 ab initio energies that lie below twice the H2 dissociation energy, the new PES has an rms error of 0.95 millihartree. These rms errors are comparable to the estimated error in the ab initio energies themselves. The new PES also fits the van der Waals well to an accuracy of about 5%. For relatively compact conformations (energies higher than the H2 dissociation energy), the conical intersection between the ground state and the first excited state is the largest source of error in the analytic surface. The position of this conical intersection forms a somewhat complicated three-dimensional hypersurface in the six-dimensional conformation space of H4. A large portion of the position of the conical intersection has been mapped out, but trying to include the conical intersection explicitly in an analytic surface is beyond the scope of the present paper.

The interaction potential energy surface (PES) of H4 is of great importance for quantum chemistry, as a test case for molecule–molecule interactions. It is also required for a detailed understanding of certain astrophysical processes, namely, collisional excitation and dissociation of H2 in molecular clouds, at densities too low to be accessible experimentally. Accurate ab initio energies were computed for 6046 conformations of H4, using a multiple reference (single and) double excitation configuration interaction (MRD-CI) program. Both systematic and ‘‘random’’ errors were estimated to have an rms size of 0.6 mhartree, for a total rms error of about 0.9 mhartree (or 0.55 kcal/mol) in the final ab initio energy values. It proved possible to include in a self-consistent way ab initio energies calculated by Schwenke, bringing the number of H4 conformations to 6101. Ab initio energies were also computed for 404 conformations of H3; adding ab initio energies calculated by other authors yielded a total of 772 conformations of H3. (The H3 results, and an improved analytic PES for H3, are reported elsewhere.) Ab initio energies are tabulated in this paper only for a sample of H4 conformations; a full list of all 6101 conformations of H4 (and 772 conformations of H3 ) is available from Physics Auxiliary Publication Service (PAPS), or from the authors. The best existing analytic PESs for H4 are shown to be accurate only for pairs of H2 molecules with intermolecular separations greater than about 3 bohr (1.6 Å). High energy collisions (such as might lead to direct collisional dissociation) cannot be well represented by such surfaces. A more general analytic PES for H4 is required, which will be accurate for compact (high-energy) conformations and for conformations that cannot be subdivided into a pair of H2 molecules. Work in progress on devising such a surface (fitted to the 6101 conformations of this work) will be reported in a forthcoming paper.

Classical trajectories have been used to compute rates for the unimolecular reaction H2CN-->H+HCN on a fitted ab initio potential energy surface (PES). The ab initio energies were obtained from CCSD(T)/aug-cc-pvtz electronic structure calculations. The ab initio energies were fitted by the interpolating moving least-squares (IMLS) method. This work continues the development of the IMLS method for producing ab initio PESs for use in molecular dynamics simulations of many-atom systems. A dual-level scheme was used in which the preliminary selection of data points was done using a low-level theory and the points used for fitting the final PES were obtained at the desired higher level of theory. Classical trajectories were used on various low-level IMLS fits to tune the fit to the unimolecular reaction under study. Procedures for efficiently picking data points, selecting basis functions, and defining cutoff limits to exclude distant points were investigated. The accuracy of the fitted PES was assessed by comparing interpolated values of quantities to the corresponding ab initio values. With as little as 330 ab initio points classical trajectory rate constants were converged to 5%-10% and the rms error over the six-dimensional region sampled by the trajectories was a few tenths of a kcal/mol.

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.

Potential energy surface of interaction of two diatomic molecules for air flows simulation at intermediate temperatures

An accurate three-dimensional potential energy surface (PES) for the interaction of rigid H2 with Si is developed using the single and double excitation coupled cluster theory with noniterative treatment of triple excitations [CCSD (T)]. Mixed basis sets, aug-cc-pCVTZ for the Si atom and aug-cc-pVTZ for the H atom with midbond functions are used. We first fit the calculated single point energies to an analytic two-dimensional potential model at a fixed r H–H = 2.19a 0 value. The computations involve 198 ab initio points on the PES. The characteristics of the fitted PES are compared with those of previous surfaces. Our theoretical results in this work with an average absolute error of 0.3425 % and a maximum error less than 4.0072 % compared with the ab initio values calculated.

In this work we report an ab initio intermolecular potential energy surface and theoretical spectroscopic studies for Xe-H(2)O complex. The ab initio energies are calculated with CCSD(T) method and large basis sets (aug-cc-pVQZ for H and O and aug-cc-pVQZ-PP for Xe) augmented by a {3s3p2d2f1g} set of bond functions. This potential energy surface has a global minimum corresponding to a planar and nearly linear hydrogen bonded configuration with a well depth of 192.5 cm(-1) at intermolecular distance of 4.0 A, which is consistent with the previous determined potential by Wen and Jager [J. Phys. Chem. A 110, 7560 (2006)]. The bound state calculations have been performed for the complex by approximating the water molecule as a rigid rotor. The theoretical rotational transition frequencies, isotopic shifts, nuclear quadrupole coupling constants, and structure parameters are in good agreement with the experimental observed values. The wavefunctions are analyzed to understand the dynamics of the ground and the first excited states.

An accurate, ab initio potential energy surface (PES) is reported for CH3OH including the bound region as well as the barrierless dissociation to CH3+OH. The surface is a linear least-squares fit to a total of 45,199 ab initio energies, most of which were computed using CCSD(T)-F12b/aug-cc-pVDZ theory and a small number using CASPT2/aug-cc-pVDZ theory. The latter set was done in the multi-reference region of the PES in order to obtain a realistic description of the OH–CH3 interaction in the near asymptotic region. The geometries and harmonic frequencies of the stationary points agree very well with direct CCSD(T)-F12b calculations. The three-fold barrier to internal rotation of CH3OH is also accurately described by the PES. The zero-point energies of methanol and CH3+OH are determined by Diffusion Monte Carlo calculations. The D0 dissociation energy is 90.1 kcal/mol, in very good agreement with the recent IUPAC evaluation [Ruscic et al., J. Phys. Chem. Ref. Data 34, 573 (2005)] result of 90.25 kcal/mol.

In evaluating some low temperature (T&amp;lt;1000 K) thermal rate coefficients for inelastic rotational excitation of H2 by H atoms, Sun and Dalgarno have found a marked sensitivity to the potential energy surface adopted for the calculations. We have investigated the origin of the discrepancies between previous H3 potential energy surfaces and have developed a refined surface which addresses these concerns. New quasiclassical trajectory calculations of cross sections for low energy rotational excitation are reported. The refined surface is based on 8701 ab initio energies, most newly computed for this purpose. It has the same functional form as our earlier (BKMP) surface, but since the fit of the parameters is more fully constrained than for any previous surface it is a more accurate representation. The refined surface matches the ab initio energies with an overall rms error of 0.27 mEh (i.e., 0.17 kcal/mol) and a maximum absolute deviation of 6.2 mEh (for a very compact high energy equilateral triangle conformation). For ‘‘noncompact’’ conformations (no interatomic distance smaller than 1.15 bohr), the rms error is 0.18 mEh and the maximum absolute deviation is 1.7 mEh. The refined surface is compared critically to four previous surfaces, including the DMBE surface of Varandas et al., in several respects: Legendre expansion coefficients; the interaction region for low energy rotational excitation; near the collinear saddle point; near conical intersections of the ground and first excited state surfaces; the van der Waals well; and compact geometries. We have also compared new first excited state ab initio energies for 1809 conformations with corresponding predictions from the DMBE surface.

This study address the adequacy of ab initio pair interaction energy potentials for the prediction of macroscopic properties. Recently, Bukowski et al. [J. Phys. Chem. A 103, 7322 (1999)] performed a comprehensive study of the potential energy surfaces for several pairs of molecules using symmetry-adapted perturbation theory. These ab initio energies were then fit to an appropriate site–site potential form. In an attempt to bridge the gap between ab initio interaction energy information and macroscopic properties prediction, we performed Gibbs ensemble Monte Carlo (GEMC) simulations using their developed pair potentials for acetonitrile and methanol. The simulations results show that the phase behavior of acetonitrile is well described by just the pair interaction potential. For methanol, on the other hand, pair interactions are insufficient to properly predict its vapor-liquid phase behavior, and its saturated liquid density. We also explored simplified forms for representing the ab initio interaction energies by refitting a selected range of the data to a site–site Lennard-Jones and to a modified Buckingham (exponential-6) potentials plus Coulombic interactions. These were also used in GEMC simulations in order to evaluate the quality and computational efficiency of these different potential forms. It was found that the phase behavior prediction for acetonitrile and methanol are highly dependent on the details of the interaction potentials developed.

We compute a new potential energy surface (PES) for the study of the inelastic collisions between N2H(+) and H2 molecules. A preliminary study of the reactivity of N2H(+) with H2 shows that neglecting reactive channels in collisional excitation studies is certainly valid at low temperatures. The four dimensional (4D) N2H(+)-H2 PES is obtained from electronic structure calculations using the coupled cluster with single, double, and perturbative triple excitation level of theory. The atoms are described by the augmented correlation consistent triple zeta basis set. Both molecules were treated as rigid rotors. The potential energy surface exhibits a well depth of ≃2530 cm(-1). Considering this very deep well, it appears that converged scattering calculations that take into account the rotational structure of both N2H(+) and H2 should be very difficult to carry out. To overcome this difficulty, the "adiabatic-hindered-rotor" treatment, which allows para-H2(j = 0) to be treated as if it were spherical, was used in order to reduce the scattering calculations to a 2D problem. The validity of this approach is checked and we find that cross sections and rate coefficients computed from the adiabatic reduced surface are in very good agreement with the full 4D calculations.

Potential energy surfaces for interactions of H2O with H2, N2 and O2: A hyperspherical harmonics representation, and a minimal model for the H2O–rare-gas-atom systems

An algorithm for constructing a quasidiabatic, coupled electronic state Hamiltonian, in a localized region of nuclear coordinate space, suitable for determining bound state spectra, is generalized to determine a nonlocal Hamiltonian capable of describing, for example, multichannel nonadiabatic photodissociation. For N(state) coupled electronic states, the Hamiltonian, H(d), is a symmetric N(state) x N(state) matrix whose elements are polynomials involving: decaying exponentials exp(-ar(i,j) (n)) n=1,2, where r(i,j)=R(i)-R(j), r(i,j)=|r(i,j)|, R(j) locates the jth nucleus; and scaled dot-cross product coordinates, proportional to r(i,j) x r(i,k) *r(i,l). The constructed Hamiltonian is constrained to reproduce, exactly, the ab initio data, energies, gradients, and derivative coupling at selected points, or nodes, in nuclear coordinate space. The remainder of the ab initio data is approximated in a least-squares sense using a normal equations approach. The fitting procedure includes a damping term that precludes oscillations due to the nodal constraints or local excesses of parameters. To illustrate the potential of the fitting procedure an H(d) is constructed, with the full nuclear permutation-inversion symmetry, which describes portions of the 1,2 (1)A potential energy surfaces of NH(3), including the minimum energy point on the 1,2 (1)A seam of conical intersection and the NH(2)+H asymptote. Ab initio data at 239 nuclear configurations was used in the construction which was tested at 48 additional nuclear configurations. While the energy range on the ground and excited potential energy surface is each individually approximately 45,000 cm(-1), the root mean square error for the energies at all points is only 93.6 cm(-1). The location and local conical topography of the minimum energy conical intersection is exactly reproduced. The derivative couplings are shown to be well reproduced, justifying the attribute quasidiabatic.

Molecular anions have recently been detected in the interstellar and circumstellar media. Accurate modeling of their abundance requires calculations of collisional data with the most abundant species that are usually He atoms and H2 molecules. In this paper, we focus on the collisional excitation of the first observed molecular anion, C6H(-), by He and H2. Theoretical calculations of collisional cross sections rely generally on ab initio interaction potential energy surfaces (PESs). Hence, we present here the first PESs for the C6H(-)-H2 and C6H(-)-He van der Waals systems. The ab initio energy data for the surfaces were computed at the explicitly correlated coupled cluster with single, double, and scaled perturbative triple excitations level of theory. The method of interpolating moving least squares was used to construct 4D and 2D analytical PESs from these data. Both surfaces are characterized by deep wells and large anisotropies. Analytical models of the PESs were used in scattering calculations to obtain cross sections for low-lying rotational transitions. As could have been anticipated, important differences exist between the He and H2 cross sections. Conversely, no significant differences exist between the collisions of C6H(-) with the two species of H2 (para- and ortho-H2). We expect that these new data will help in accurately determining the abundance of the C6H(-) anions in space.

We present a 3D isotropic ab initio three-body (para-H2)3 interaction potential energy surface (PES). The electronic structure calculations are carried out at the correlated coupled-cluster theory level, with single, double, and perturbative triple excitations. The calculations use an augmented correlation-consistent triple zeta basis set and a supplementary midbond function. We construct the PES using the reproducing-kernel Hilbert space toolkit [O. T. Unke and M. Meuwly, J. Chem. Inf. Model. 57, 1923 (2017)] with phenomenological and empirical adjustments to account for short-range and long-range behaviors. The (para-H2)3 interaction energies deviate drastically from the Axilrod-Teller-Muto (ATM) potential at short intermolecular separations. We find that the configuration of three para-H2 molecules at the corners of an equilateral triangle is responsible for the majority of the (para-H2)3 interaction energy contribution in a hexagonal-close-packed lattice. In cases where two para-H2 molecules are close to one another while the third is far away, the (para-H2)3 interaction PES takes the form of a modified version of the ATM potential. We expect the combination of this PES together with a first-principles para-H2-para-H2 adiabatic hindered rotor potential to outperform a widely used effective pair potential for condensed many-body systems of para-H2.