High-dimensional ab initio potential energy surfaces for reaction dynamics calculations

There has been great progress in the development of potential energy surfaces (PESs) for reaction dynamics that are fits to ab initio energies. The fitting techniques described here explicitly represent the invariance of the PES with respect to all permutations of like atoms. A review of a subset of dynamics calculations using such PESs (currently 16 such PESs exist) is then given. Bimolecular reactions of current interest to the community, namely, H + CH(4) and F + CH(4), are focused on. Unimolecular reactions are then reviewed, with a focus on the photodissociation dynamics of H(2)CO and CH(3)CHO, where so-called "roaming" pathways have been discovered. The challenges for electronically non-adiabatic reactions, and associated PESs, are presented with a focus on the OH* + H(2) reaction. Finally, some thoughts on future directions and challenges are given.     

CVRQD ab initio ground-state adiabatic potential energy surfaces for the water molecule

The high accuracy ab initio adiabatic potential energy surfaces (PESs) of the ground electronic state of the water molecule, determined originally by Polyansky et al. [Science 299, 539 (2003)] and called CVRQD, are extended and carefully characterized and analyzed. The CVRQD potential energy surfaces are obtained from extrapolation to the complete basis set of nearly full configuration interaction valence-only electronic structure computations, augmented by core, relativistic, quantum electrodynamics, and diagonal Born-Oppenheimer corrections. We also report ab initio calculations of several quantities characterizing the CVRQD PESs, including equilibrium and vibrationally averaged (0 K) structures, harmonic and anharmonic force fields, harmonic vibrational frequencies, vibrational fundamentals, and zero-point energies. They can be considered as the best ab initio estimates of these quantities available today. Results of first-principles computations on the rovibrational energy levels of several isotopologues of the water molecule are also presented, based on the CVRQD PESs and the use of variational nuclear motion calculations employing an exact kinetic energy operator given in orthogonal internal coordinates. The variational nuclear motion calculations also include a simplified treatment of nonadiabatic effects. This sophisticated procedure to compute rovibrational energy levels reproduces all the known rovibrational levels of the water isotopologues considered, H(2) (16)O, H(2) (17)O, H(2) (18)O, and D(2) (16)O, to better than 1 cm(-1) on average. Finally, prospects for further improvement of the ground-state adiabatic ab initio PESs of water are discussed.     

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.     

Correlation energy and dispersion interaction in the ab initio potential energy curve of the neon dimer

A close approximation to the empirical potential energy curve of the neon dimer is obtained by coupled-cluster singles plus doubles plus noniterative triples calculations by using nonaugmented correlation-consistent basis sets without counterpoise corrections and complementing them by three-term extrapolations to the complete basis set limit. The potential energy is resolved into a self-consistent-field Hartree-Fock contribution and a correlation contribution. The latter is shown to decay in the long-range region in accordance with the empirical dispersion expansion.     

High-level ab initio potential energy surfaces and vibrational energies of H2CS

Six-dimensional (6D) potential energy surfaces (PESs) of H(2)CS have been generated ab initio using the recently proposed explicitly correlated (F12) singles and doubles coupled cluster method including a perturbational estimate of connected triple excitations, CCSD(T)-F12b [T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)] in conjunction with F12-optimized correlation consistent basis sets. Core-electron correlation, high-order correlation, scalar relativistic, and diagonal Born-Oppenheimer terms were included as additive high-level (HL) corrections. The resulting 6D PESs were represented by analytical functions which were used in variational calculations of the vibrational term values below 5000 cm(-1). The best PESs obtained with and without the HL corrections, VQZ-F12(*HL) and VQZ-F12?, reproduce the fundamental vibrational wavenumbers with mean absolute deviations of 1.13 and 1.22 cm(-1), respectively. A detailed analysis of the effects of the HL corrections shows how the VQZ-F12 results benefit from error cancellation. The present purely ab initio PESs will be useful as starting points for empirical refinements towards an accurate "spectroscopic" PES of H(2)CS.     

Finding minimum energy reaction paths on ab initio potential energy surfaces using the fast marching method

The fast marching method (FMM) for determining minimum-cost paths has been extended to compute the minimum-energy reaction coordinates in chemical reactions. This was accomplished by building an interface between FMM and the Gaussian program. We demonstrate the new method using an S _N 2 reaction, the isomerization of HSCN to HNCS, and a gas-phase rearrangement reaction of relevance in mass spectrometry.     

Valence- and dipole-bound anions of the thymine-water complex: ab initio characterization of the potential energy surfaces

The potential energy surfaces of the neutral and anionic thymine-water complexes are investigated using high-level ab initio calculations. Both dipole-bound (DB) and valence-bound (VB) anionic forms are considered. Four minima and three first-order stationary points are located, and binding energies are computed. All minima, for both anions, are found to be vertically and adiabatically stable. The binding energies are much higher for valence-bound than for dipole-bound anions. Adiabatic electron affinities are in the 66-287 meV range for VB anions and the 4-60 meV range for DB anions, and vertical detachment energies are in the 698-977 meV and 10-70 meV range for VB and DB anions, respectively. For cases where literature data are available, the computed values are in good agreement with previous experimental and theoretical studies. It is observed that electron attachment modifies the shape of the potential energy surfaces of the systems, especially for the valence-bound anions. Moreover, for both anions the size of the energy barrier between the two lowest energy minima is strongly reduced, rendering the coexistence of different structures more probable.     

Comment on ab initio ground state potential energy surfaces for anions of polar molecules

A new and simple proof is given of the theorem that ab initio Born—Oppenheimer energy calculations for any polar molecule having an electric dipole moment μ > 1.625 debye must yield a positive electron affinity.     

Vibrational spectrum of BiH3: Six-dimensional variational calculations on high-level ab initio potential energy surfaces

We report a theoretical study of the ground electronic state of BiH₃. The potential energy surface (PES) is obtained from coupled cluster CCSD(T) calculations with a large basis set (289 contracted Gaussian functions). The previously available quartic force field (P4) is extended by adding the dominant quintic and sextic stretching terms to yield improved potential functions in symmetry coordinates (P6) and Morse-type coordinates (M4). Second-order rovibrational perturbation calculations on the P4-PES and full variational calculations on the P6-PES and M4-PES yield almost identical vibrational term values which is rationalized by considering the local mode behavior of BiH₃ and the Morse-type character of the M4-PES. The remaining deviations between the computed and observed vibrational term values must thus be caused by imperfections in the CCSD(T) surface. A refinement of this ab initio surface by a restrained fit to experimental data allows an essentially perfect reproduction of the observed vibrational term values. Variational calculations on this refined surface provide predictions for several overtone and combination bands that have not yet been observed. Dedicated to Hermann Stoll on the occasion of his 60th birthday     

Vibrational energy levels for CH4 from an ab initio potential

Many areas of astronomy and astrophysics require an accurate high temperature spectrum of methane (CH4). The goal of the present research is to determine an accurate ab initio potential energy surface (PES) for CH4. As a first step towards this goal, we have determined a PES including up to octic terms. We compare our results with experiment and to a PES based on a quartic expansion. Our octic PES gives good agreement with experiment for all levels, while the quartic PES only for the lower levels.     

Comment on ab initio ground state potential energy surfaces for anions of polar molecules

Within the context of the Born-Oppenheimer approximation all molecules with dipole moments greater than 1.625 D have stable anions. The applicability of the Hartree-Fock approximation to describe the stability of such anions is discussed. It is concluded that correlation effects are relatively more important for molecules such as HF and HCN than the more polar alkali halides.     

Aromaticity: an ab initio evaluation of the properly cyclic delocalization energy and the pi-delocalization energy distortivity of benzene

A complete active space self-consistent field (CASSCF) calculation of the pi system of a conjugated molecule enables one to define optimal valence pi and pi* molecular orbitals (MOs). One may define from them a set of atom-centered orthogonal pi orbitals, one per carbon atom, and the resulting upper multiplet is used to define the pi-electron delocalization energy. This quantity is confirmed to be slightly distortive, i.e., to prefer bond-alternated geometries. One may also define strongly localized bond MOs corresponding to a Kekule structure and then perturb the associated strongly localized single determinant under the effect of the delocalization between the bonds and of the electronic correlation. The third order of perturbation introduces the contribution of the cyclic circulation of the electrons around the benzene ring, i.e. the aromatic energy contribution. Its value is about 1.5 eV. It is antidistortive, but remains important under bond alternation. The cyclic correlation effects are of minor importance.     

Interpolating moving least-squares methods for fitting potential energy surfaces: computing high-density potential energy surface data from low-density ab initio data points

A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs.     

An interaction potential between an alanine zwitterion and a water molecule based on ab initio calculations

Interaction energies between an alanine zwitterion and a water molecule at 150 different positions and orientations have been calculated using the ab initio method with the minimal basis set and employing the counterpoise method to eliminate the basis set superposition error. Dispersion energies are estimated using the Slater–Kirkwood formula. Out of a total of 150 computed interaction energies, 140 whose SCF interaction energies are below 5 kcal/mol have been fitted with a summation of atom-atom pair potentials in the form of the Lennard–Jones potential plus an electrostatic term. The standard deviation for this fitting is 0.49 kcal/mol. A sampling scheme regarding geometrical configurations is presented. Twenty rays are uniformly drawn from the origin of coordinates, a floatable division with equal ratios is made along each ray, and one of 60 orientations is randomly taken as the orientation of a water molecule. A nonlinear fitting method is used with a restriction on the sign change of fitting coefficients.     

Three-state trajectory surface hopping studies of the photodissociation dynamics of formaldehyde on ab initio potential energy surfaces

Full-dimensional, three-state, surface hopping calculations of the photodissociation dynamics of formaldehyde are reported on ab initio potential energy surfaces (PESs) for electronic states S(1), T(1), and S(0). This is the first such study initiated on S(1) with ab initio-calculated spin-orbit couplings among the three states. We employ previous PESs for S(0) and T(1), and a new PES for S(1), which we describe here, as well as new spin-orbit couplings. The time-dependent electronic state populations and the branching ratio of radical products produced from S(0) and T(1) states and that of total radical products and molecular products at three total energies are calculated. Details of the surface hopping dynamics are described, and a novel pathway for isomerization on T(1) via S(0) is reported. Final translational energy distributions of H + HCO products from S(0) and T(1) are also reported as well as the translational energy distribution and final rovibrational distributions of H(2) products from the molecular channel. The present results are compared to previous trajectory calculations initiated from the global minimum of S(0). The roaming pathway leading to low rotational distribution of CO and high vibrational population of H(2) is observed in the present calculations.     

Global analytical potential energy surfaces for HO2(X2A") based on high-level ab initio calculations

Two global analytical potential energy surfaces for the HO2(X2A") system have been developed by fitting approximately 15,000 ab initio points at the icMRCI+Qaug-cc-pVQZ level of theory, using the reproducing kernel Hilbert space method. One analytical potential is designed to give a very accurate representation of the low energy range that determines the vibrational spectrum, while the other attempts to provide a fast and uniformly accurate potential function for reaction dynamics. The quality of the fitted potential functions is confirmed by good agreement of the (J=0) HO2 vibrational spectrum and (J=0) quantum reaction probability for the H+O2(ji=0,nui=0) reaction with those obtained using the spline fitted potential. Quasiclassical trajectory calculations carried out on the new potential energy surface provided the reaction probability with a zero impact parameter (b=0), which is in reasonably good agreement with the J=0 quantum results.     

Photoionization-induced dynamics of ammonia: ab initio potential energy surfaces and time-dependent wave packet calculations for the ammonia cation

An analytical anharmonic six-dimensional three-sheeted potential energy surface for the ground and first excited states of the ammonia cation has been developed which is tailored to model the ultrafast photoinduced dynamics. Selected ab initio cuts, obtained by multireference configuration interaction calculations, have been used to determine the parameters of a diabatic representation for this Jahn-Teller and pseudo-Jahn-Teller system. The model includes higher-order coupling terms both for the Jahn-Teller and for the pseudo-Jahn-Teller matrix elements. The relaxation to the ground state is possible via dynamical pseudo-Jahn-Teller couplings involving the asymmetric bending and stretching coordinates. The photoelectron spectrum of NH3 and the internal conversion dynamics of NH3+ have been determined by wave packet propagation calculations employing the multiconfigurational time-dependent Hartree method. Three different time scales are found in the dynamics calculations for the second absorption band. The ultrafast Jahn-Teller dynamics of the two excited states occurs on a 5 fs time scale. The major part of the internal conversion to the ground state takes place within a short time scale of 20 fs. This fast internal conversion is, however, incomplete and the remaining excited state population does not decay completely even within 100 fs.     

Torsional eigenvalues of the water trimer on several ab initio potential surfaces

Eigenvalues corresponding to the three torsional degrees of freedom were calculated for the water trimer and its deuterated isotopomer in four sets of calculations involving different potential energy surfaces. The four potential surfaces were developed in this work by reparametrization of the CKL function against four sets of ab initio energies calculated with and without counterpoise correction. Transition frequencies corresponding to the low-frequency torsional motions of the trimer were calculated and then compared with those found from experiment to assess the accuracy of each potential energy surface. Although reparametrization of the CKL function to a set of counterpoise-corrected energies yielded transition energies that are in qualitative agreement with those from experiment, reparametrization to another set of counterpoise-corrected energies resulted in highly inaccurate values of the transition energy. As a consequence, our results demonstrate that caution must be exercised in the implementation of the counterpoise method as it does not always lead to more accurate ab initio calculations. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 233–252, 1998