Accurate ab initio based multisheeted double many-body expansion potential energy surface for the three lowest electronic singlet states of H3+

The authors present diabatic and adiabatic potential energy surfaces for the three lowest electronic singlet states of H3+. The modeling of the surfaces is based on the multi-sheeted double many-body expansion method which consists of dressing the various matrix elements of the diatomics-in-molecules potential matrix with three-body terms. The avoided crossing between the two lowest states and the conical intersection between the second and the third state are accurately represented by construction.     

Recalibrated double many-body expansion potential energy surface and dynamics calculations for HN2

A single-sheeted double many-body expansion potential energy surface is reported for the lowest doublet state of HN2 by fitting additional multireference configuration interaction energies in the N...NH channel. A stratified analysis of the root-mean-squared error indicates an accuracy superior to that achieved for the previously reported form. Detailed dynamical tests are also performed for the N + NH reaction using both the quasi-classical trajectory method and the capture theory, and the results are compared with available empirical data. The vibrational resonances of the HN2 metastable radical are also calculated and compared with previous theoretical predictions.     

Ab initio-based double many-body expansion potential energy surface for the first excited triplet state of the ammonia molecule

A global single-sheeted double many-body expansion potential energy surface is reported for the first excited triplet state of NH(3). It employs an approximate cluster expansion of the molecular potential that utilizes previously reported functions of the same family for the triatomic fragments. Four-body energy terms have been calibrated from extensive accurate ab initio data so as to reproduce the main features of the title system. A new switching function formalism has been reported to approximate the true multisheeted nature of NH(3)((3)A(2) (')) potential energy surface, thus allowing the correct behavior at the NH(2)((2)A(")) + H((2)S) and NH(2)((4)A(")) + H((2)S) dissociation limits. The resulting fully six-dimensional potential energy function reproduces the correct symmetry under the permutation of identical atoms, and predicts the correct behavior at all dissociation channels while providing a realistic representation at all interatomic separations. The major attributes of the NH(3) double many-body expansion potential energy surface have also been characterized, and found to be in good agreement, both with the calculated ones from the raw ab initio energies and the theoretical results available in the literature.     

A realistic double many-body expansion potential energy surface for SO2(X1A') from a multiproperty fit to accurate ab initio energies and vibrational levels

A single-valued double many-body expansion potential energy surface (DMBE I) recently obtained for the ground electronic state of the sulfur dioxide molecule by fitting correlated ab initio energies suitably corrected by scaling the dynamical correlation energy is now refined by fitting simultaneously available spectroscopic levels up to 6886 cm(-1) above the minimum. The topographical features of the novel potential energy surface (DMBE II) are examined in detail, and the method is emphasized as a robust route to fit together state-of-the-art theoretical calculations and spectroscopic measurements using a single fully dimensional potential form.     

The double many-body expansion of potential energy surfaces from interacting 2S atoms

The double many-body expansion (DMBE ) method has been applied to the many-valued ground-state potential energy surfaces from three and four interacting ²S atoms. New forms are suggested where the degeneracy manifold of the two Riemann sheets of the potential surface can be made identical to that predicted from the London equation that is correct to first-order. Considerable flexibility can be introduced through adjustable coefficients to fit ab initio data, whereas the potential energy terms can be chosen to maintain the correct analytic properties at the conical intersection. Hence, the new forms may be used on the extrapolation of the potential energy from the lowest- to the upper-Riemann sheets. Long-range effects are semiempirically described from the general formalism of the DMBE method.     

Accurate double many-body expansion potential energy surface for ground-state HS2 based on ab initio data extrapolated to the complete basis set limit

A double many-body expansion potential energy surface is reported for the electronic ground state of HS(2) by fitting accurate multireference configuration interaction energies calculated with aug-cc-pVTdZ and aug-cc-pVQdZ basis sets upon separate extrapolation of the complete-active-space self-consistent field and dynamical correlation components of the total energy to the complete basis set limit. The major topographical features of the potential energy surface are examined in detail, and the model function is used for thermalized calculations of the rate constants for the S + SH → H + S(2) reaction at 298 and 400 K. A value of (1.44 ± 0.06) × 10(-11) cm(3) s(-1) is obtained at 298 K, providing perhaps the most reliable estimate of the rate constant known thus far for such a reaction.     

Symmetry analysis of the vibronic States in the upper conical potential (2(3)A') of triplet

The symmetry properties of the rovibronic resonance states (Slonczewski resonances) supported by an upright conical potential are investigated. These symmetry properties lead to a useful correlation between states calculated with and without consideration of the geometrical phase, which can assist in the assignment of those states. The vibronic resonance states of triplet H3(+) (2(3)A'), which had been studied by us before, have now been assigned to spectroscopic quantum numbers.     

Ab initio-based global double many-body expansion potential energy surface for the first 2A" electronic state of NO2

An ab initio-based global double many-body expansion potential energy surface is reported for the first electronic state of the NO(2)((2)A") manifold. Up to 1700 ab initio energies have been employed to map the full configuration space of the title molecule, including stationary points and asymptotic channels. The calculated grid energies have been scaled to account for the incompleteness of the basis set and truncation of the MRCI expansion and fitted analytically with a total root-mean-squared-deviation smaller than 1.0 kcal mol(-1). The lowest point of the potential energy surface corresponds to the (2)B(1) linear minimum, which is separated from the C(s) distorted minimum by a C(2v) barrier of ≈9.7 kcal mol(-1). As usual, the proposed form includes a realistic representation of long-range interactions. Preliminary work indicates its reliability for reaction dynamics.     

Repulsive double many-body expansion potential energy surface for the reactions N(4S)+H2<-->NH(X3Sigma-)+H from accurate ab initio calculations

A single-sheeted DMBE potential energy surface is reported for the reactions N(4S)+H2<-->NH(X3Sigma-)+H based on a fit to accurate multireference configuration interaction energies. These have been calculated using the aug-cc-pVQZ basis set of Dunning and the full valence complete active space wave function as reference, being semi-empirically corrected by scaling the two-body and three-body dynamical correlation energies. The topographical features of the novel global potential energy surface are examined in detail, including a conical intersection involving the two first 4A' potential energy surfaces which has been transformed into an avoided crossing in the present single-sheeted representation.     

Accurate ab initio potential energy surfaces for the 3A' and 3A' electronic states of the O(3P)+HBr system

In this work, we report the construction of potential energy surfaces for the (3)A(') and (3)A(') states of the system O((3)P) + HBr. These surfaces are based on extensive ab initio calculations employing the MRCI+Q/CBS+SO level of theory. The complete basis set energies were estimated from extrapolation of MRCI+Q/aug-cc-VnZ(-PP) (n = Q, 5) results and corrections due to spin-orbit effects obtained at the CASSCF/aug-cc-pVTZ(-PP) level of theory. These energies, calculated over a region of the configuration space relevant to the study of the reaction O((3)P) + HBr → OH + Br, were used to generate functions based on the many-body expansion. The three-body potentials were interpolated using the reproducing kernel Hilbert space method. The resulting surface for the (3)A(') electronic state contains van der Waals minima on the entrance and exit channels and a transition state 6.55 kcal/mol higher than the reactants. This barrier height was then scaled to reproduce the value of 5.01 kcal/mol, which was estimated from coupled cluster benchmark calculations performed to include high-order and core-valence correlation, as well as scalar relativistic effects. The (3)A(') surface was also scaled, based on the fact that in the collinear saddle point geometry these two electronic states are degenerate. The vibrationally adiabatic barrier heights are 3.44 kcal/mol for the (3)A(') and 4.16 kcal/mol for the (3)A(') state.     

HN2(2A') electronic manifold. II. Ab initio based double-sheeted DMBE potential energy surface via a global diabatization angle

A double-sheeted double many-body expansion potential energy surface is reported for the coupled 12A'/22A' states of HN2 by fitting about 6000 ab initio energies. All crossing seams are described to their full extent on the basis of converged results. The lowest adiabatic sheet is fitted with a rmsd of 0.8 kcal mol-1 with respect to the calculated energies up to 100 kcal mol-1 above the absolute minimum, and the topology of the first excited-state investigated with the aid of the upper adiabatic sheet. A new scheme that overcomes obstacles in previous diabatization methods for modeling global double-sheeted potential energy surfaces is also reported. The novel approach uses a global diabatization angle which allows the diabats to mimic both the crossing seams and atom-diatom dissociation limits.     

The many-body expansion of the potential energy function for elemental clusters

The many-body expansion of the potential energy function of elemental clusters is examined in general terms in regard to its convergence for microclusters and the bulk phase. The systems Be_n and Li_n are examined in detail. For Li it is clear that the many-body expansion has no low-order convergence, but it is shown that a potential of the form gives good binding energies for Li_n (3<n?9) and also a good value for the heat of atomization of the bcc crystal.     

Six-dimensional potential energy surface for H2 at Ru(0001)

The six-dimensional (6D) potential energy surface (PES) for the H(2) molecule interacting with a clean Ru(0001) surface has been computed accurately for the first time. Density functional theory (DFT) and a pseudopotential based periodic plane-wave approach have been used to calculate the electronic interactions between the molecule and the surface. Two different generalized gradient approximation (GGA) exchange-correlation functionals, PW91 and RPBE, have been adopted. Based on the DFT/GGA calculated potential energies, an analytical 6D PES has been constructed using the corrugation reducing procedure. A very accurate representation of the DFT/GGA data has been achieved, with an average error in the interpolation of about 3 meV and a maximum error not larger than about 30 meV. The top site is found to be the most reactive site for both functionals used, but PW91 predicts a higher reactivity than RPBE, with lower-energy and earlier-located dissociation barriers. The energetic corrugation displayed by the RPBE PES is larger than the PW91 PES while the geometric corrugation is smaller. The differences between the two PESs increase as the distance of the molecular center of mass to the surface decreases. A direct comparison with experimental investigations on H(2)/Ru(0001) could shed light on the suitability of these XC potentials often used in DFT calculations.     

An ab initio potential energy surface and vibrational states of MgH2(1(1)A')

A three-dimensional global potential energy surface for the ground electronic state of MgH(2) is constructed from more than 3000 ab initio points calculated using the internally contracted multireference configuration interaction method with the Davidson correction at the complete basis set limit. Low-lying vibrational energy levels of MgH(2) and MgD(2) are calculated using the Lanczos algorithm, and found to be in good agreement with known experimental band origins. The majority of the vibrational energy levels up to 8000 cm(-1) are assigned with normal mode quantum numbers. However, our results indicate a gradual transition from a normal mode regime for the stretching vibrations at low energies to a local mode regime near 7400 cm(-1), as evidenced by a decreasing energy gap between the (n(1),0,0) and (n(1)-1,0,1) vibrational states and bifurcation of the corresponding wave functions.     

Accurate one-dimensional potential energy curve of the linear (H2)2 cluster

We present a sub-0.3 K accuracy, ground-state one-dimensional potential energy curve of the metastable linear configuration of the (H(2))(2) cluster calculated exclusively with explicitly correlated Gaussian functions with shifted centers. The H(2) internuclear distance is kept at the isolated H(2) vibrational ground-state average value of 1.448 736 bohr and the intermonomer separation is varied between 2 and 100 bohrs. The analytical gradient of the energy with respect to the nonlinear parameters of the Gaussians (i.e., the exponents and the coordinates of the shifts) has been employed in the variational optimization of the wave function. Procedures for enlarging the basis set and for adjusting the centers of the Gaussians to the varying intermonomer separation have been developed and used in the calculations.     

New double many-body expansion potential energy surface for ground-state HCN from a multiproperty fit to accurate ab initio energies and rovibrational calculations

An accurate single-sheeted double many-body expansion potential energy surface has been obtained for the ground electronic state of the hydrogen cyanide molecule via a multiproperty fit to ab initio energies and rovibrational data. This includes 106 rovibrational levels and 2313 discrete points, which are fit with a rmsd of 4 cm(-1) and 2.42 kcal mol(-1), respectively, and seven zero first-derivatives that are reproduced at three stationary points. Since the potential also describes accurately the appropriate asymptotic limits at the various dissociation channels, it is commended both for the simulation of rovibrational spectra and reaction dynamics.     

A reliable new three-dimensional potential energy surface for H(2)-Kr

An improved three-dimensional potential energy surface for the H(2)-Kr system is determined from a direct fit of new infrared spectroscopic data for H(2)-Kr and D(2)-Kr to a potential energy function form based on the exchange-Coulomb model for the intermolecular interaction energy. These fits require repetitive, highly accurate simulations of the observed spectra, and both the strength of the potential energy anisotropy and the accuracy of the new data make the "secular equation perturbation theory" method used in previous analyses of H(2)-(rare gas) spectra inadequate for the present work. To address this problem, an extended version of the "iterative secular equation" method was developed which implements direct Hellmann-Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.     

Potential energy surface and quantum dynamics study of rovibrational states for HO(3) (X (2)A')

An analytic potential energy surface has been constructed by fitting to about 28 thousand energy points for the electronic ground-state (X (2)A') of HO(3). The energy points are calculated using a hybrid density functional HCTH and a large basis set aug-cc-pVTZ, i.e., a HCTH/aug-cc-pVTZ density functional theory (DFT) method. The DFT calculations show that the trans-HO(3) isomer is the global minimum with a potential well depth of 9.94 kcal mol(-1) with respect to the OH + O(2) asymptote. The equilibrium geometry of the cis-HO(3) conformer is located 1.08 kcal mol(-1) above that of the trans-HO(3) one with an isomerization barrier of 2.41 kcal mol(-1) from trans- to cis-HO(3). By using this surface, a rigorous quantum dynamics (QD) study has been carried out for computing the rovibrational energy levels of HO(3). The calculated results determine a dissociation energy of 6.15 kcal mol(-1), which is in excellent agreement with the experimental value of Lester et al. [J. Phys. Chem. A, 2007, 111, 4727.].     

A six-dimensional H(2)-H(2) potential energy surface for bound state spectroscopy

We present a six-dimensional potential energy surface for the (H(2))(2) dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer's center of mass. The surface is intended to describe accurately the bound and quasibound states of the dimers (H(2))(2), (D(2))(2), and H(2)-D(2) that correlate with H(2) or D(2) monomers in the rovibrational levels (v,j)=(0,0), (0,2), (1,0), and (1,2). We employ a close-coupled approach to compute the energies of these bound and quasibound dimer states using our potential energy surface, and compare the computed energies for infrared and Raman transitions involving these states with experimentally measured transition energies. We use four of the experimentally measured dimer transition energies to make two empirical adjustments to the ab initio potential energy surface; the adjusted surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm(-1). For 26 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. Finally, we use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.     

Calibration-quality adiabatic potential energy surfaces for H3(+) and its isotopologues

Calibration-quality ab initio adiabatic potential energy surfaces (PES) have been determined for all isotopologues of the molecular ion H(3)(+). The underlying Born-Oppenheimer electronic structure computations used optimized explicitly correlated shifted Gaussian functions. The surfaces include diagonal Born-Oppenheimer corrections computed from the accurate electronic wave functions. A fit to the 41,655 ab initio points is presented which gives a standard deviation better than 0.1 cm(-1) when restricted to the points up to 6000 cm(-1) above the first dissociation asymptote. Nuclear motion calculations utilizing this PES, called GLH3P, and an exact kinetic energy operator given in orthogonal internal coordinates are presented. The ro-vibrational transition frequencies for H(3)(+), H(2)D(+), and HD(2)(+) are compared with high resolution measurements. The most sophisticated and complete procedure employed to compute ro-vibrational energy levels, which makes explicit allowance for the inclusion of non-adiabatic effects, reproduces all the known ro-vibrational levels of the H(3)(+) isotopologues considered to better than 0.2 cm(-1). This represents a significant (order-of-magnitude) improvement compared to previous studies of transitions in the visible. Careful treatment of linear geometries is important for high frequency transitions and leads to new assignments for some of the previously observed lines. Prospects for further investigations of non-adiabatic effects in the H(3)(+) isotopologues are discussed. In short, the paper presents (a) an extremely accurate global potential energy surface of H(3)(+) resulting from high accuracy ab initio computations and global fit, (b) very accurate nuclear motion calculations of all available experimental line data up to 16,000 cm(-1), and (c) results suggest that we can predict accurately the lines of H(3)(+) towards dissociation and thus facilitate their experimental observation.