Neural Network Representation of Three-State Quasidiabatic Hamiltonians Based on the Transformation Properties from a Valence Bond Model: Three Singlet States of H3.

A neural network (NN) approach was recently developed to construct accurate quasidiabatic Hamiltonians for two-state systems with conical intersections. Here, we derive the transformation properties of elements of 3 × 3 quasidiabatic Hamiltonians based on a valence bond (VB) model and extend the NN-based method to accurately diabatize the three lowest electronic singlet states of H3+, which exhibit the avoided crossing between the ground and first excited states and the conical intersection between the first and second excited states for equilateral triangle configurations (D3h). The current NN framework uses fundamental invariants (FIs) as the input vector and appropriate symmetry-adapted functions called covariant basis to account for the special symmetry of complete nuclear permutational inversion (CNPI). The resulting diabatic potential energy matrix (DPEM) can reproduce the ab initio adiabatic energies, energy gradients, and derivative couplings between adjacent states as well as the particular symmetry. The accuracy of DPEM is further validated by full-dimensional quantum dynamics calculations. The flexibility of the FI-NN approach based on the VB model shows great potential to resolve diabatization problems for many extended and multistate systems.

A fundamental invariant-neural network representation of quasi-diabatic Hamiltonians for the two lowest states of H3.

The fundamental invariant neural network (FI-NN) approach is developed to represent coupled potential energy surfaces in quasidiabatic representations with two-dimensional irreducible representations of the complete nuclear permutation and inversion (CNPI) group. The particular symmetry properties of the diabatic potential energy matrix of H3 for the 1A' and 2A' electronic states were resolved arising from the E symmetry in the D3h point group. This FI-NN framework with symmetry adaption is used to construct a new quasidiabatic representation of H3, which reproduces accurately the ab initio energies and derivative information with perfect symmetry behaviors and extremely small fitting errors. The quantum dynamics results on the new FI-NN diabatic PESs give rise to accurate oscillation patterns in the product state-resolved differential cross sections. These results strongly support the accuracy and efficiency of the FI-NN approach to construct reliable diabatic representations with complicated symmetry problems.

Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer.

We report full-dimensional, ab initio potential energy and dipole moment surfaces, denoted PES and DMS, respectively, for arbitrary numbers of water monomers. The PES is a sum of 1-, 2-, and 3-body potentials which can also be augmented by semiempirical long-range higher-body interactions. The 1-body potential is a spectroscopically accurate monomer potential, and the 2- and 3-body potentials are permutationally invariant fits to tens of thousands of CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ electronic energies, respectively. The DMS is a sum of 1- and 2-body DMS, which are covariant fits to tens of thousands MP2/aug-cc-pVTZ dipole moment data. We present the details of these new 2- and 3-body potentials and then extensive applications and tests of this PES are made to the structures, classical binding energies, and harmonic frequencies of water clusters up to the 22-mer. In addition, we report the dipole moment for these clusters at various minima and compare the results against available and new ab initio calculations.

Global potential energy surfaces for O((3)P) + H2O((1)A1) collisions.

Global analytic potential energy surfaces for O((3)P) + H(2)O((1)A(1)) collisions, including the OH + OH hydrogen abstraction and H + OOH hydrogen elimination channels, are presented. Ab initio electronic structure calculations were performed at the CASSCF + MP2 level with an O(4s3p2d1f)/H(3s2p) one electron basis set. Approximately 10(5) geometries were used to fit the three lowest triplet adiabatic states corresponding to the triply degenerate O((3)P) + H(2)O((1)A(1)) reactants. Transition state theory rate constant and total cross section calculations using classical trajectories to collision energies up to 120 kcal mol(-1) (∼11 km s(-1) collision velocity) were performed and show good agreement with experimental data. Flux-velocity contour maps are presented at selected energies for H(2)O collisional excitation, OH + OH, and H + OOH channels to further investigate the dynamics, especially the competition and distinct dynamics of the two reactive channels. There are large differences in the contributions of each of the triplet surfaces to the reactive channels, especially at higher energies. The present surfaces should support quantitative modeling of O((3)P) + H(2)O((1)A(1)) collision processes up to ∼150 kcal mol(-1).

Depression of reactivity by the collision energy in the single barrier H + CD4 -> HD + CD3 reaction.

Crossed molecular beam experiments and accurate quantum scattering calculations have been carried out for the polyatomic H + CD(4) --> HD + CD(3) reaction. Unprecedented agreement has been achieved between theory and experiments on the energy dependence of the integral cross section in a wide collision energy region that first rises and then falls considerably as the collision energy increases far over the reaction barrier for this simple hydrogen abstraction reaction. Detailed theoretical analysis shows that at collision energies far above the barrier the incoming H-atom moves so quickly that the heavier D-atom on CD(4) cannot concertedly follow it to form the HD product, resulting in the decline of reactivity with the increase of collision energy. We propose that this is also the very mechanism, operating in many abstraction reactions, which causes the differential cross section in the backward direction to decrease substantially or even vanish at collision energies far above the barrier height.

Full-dimensional, ab initio potential energy and dipole moment surfaces for water.

We report full-dimensional, ab initio potential energy (PES) and dipole moment surfaces (DMS) for water. The PES is a sum of one-, two- and three-body terms. The three-body potential is a fit, reported here, to roughly 30,000 intrinsic three-body energies obtained with second-order Møller-Plesset perturbation theory (MP2) and using the aug-cc-pVTZ basis set (avtz). The one- and two-body potentials are from an ab initio water dimer potential [Shank et al., J. Chem. Phys. 130, 144314 (2009)]. The predictive accuracy of the PES is demonstrated for the water trimer, tetramer, and hexamer by comparing the energies and harmonic frequencies obtained from the PES and new high level ab initio calculations at the respective global minima. The DMS is constructed from one- and two-body dipole moments, based on fits to MP2/avtz dipole moments. It is shown to be very accurate for the hexamer by comparison with direct calculations of the hexamer dipole. To illustrate the anharmonic character of the PES one-mode calculations of the 18 monomer fundamentals of the hexamer are reported in normal coordinates.

Ab initio calculation of the photoelectron spectra of the hydroxycarbene diradicals.

Photoelectron spectra of the cis and trans isomers of HCOH were computed using vibrational wave functions calculated by diagonalizing the Watson Hamiltonian, including up to four mode couplings. The full-dimensional CCSD(T)/cc-pVTZ potential energy surfaces were employed in the calculation. Photoionization induces significant changes in equilibrium structures, which results in long progressions in the nu(5), nu(4), and nu(3) modes. The two isomers show progressions in different modes, which leads to qualitatively distinguishable spectra. The spectra were also calculated in the double harmonic parallel-mode (i.e, neglecting Duschinsky rotation) approximation. Calculating displacements along the normal coordinates of the cation state was found to give a better approximation to the vibrational configuration interaction spectrum; this is due to the effects of Duschinsky rotations on the vibrational wave functions.

Quasiclassical trajectory calculations of the HO2 + NO reaction on a global potential energy surface.

We report quasiclassical trajectory calculations of the HO(2) + NO reaction using a new full dimensional, singlet potential energy surface (PES) which is a fit to more than 67 000 energies obtained with density functional theory-B3LYP/6-311G(d,p)-calculations. The PES is invariant with respect to permutation of like nuclei and describes all isomers of HOONO, HONO(2), saddle points connecting them and the OH + NO(2), HO(2) + NO channels. Quasiclassical trajectory calculations of cross-sections for the HO(2) + NO to form HOONO, HONO(2) and OH + NO(2) are done using this PES, for reactants in the ground vibrational state and rotational states sampled from a 300 K Boltzmann distribution. Trajectory calculations illustrate the pathway that HO(2) + NO takes to the energized HOONO complex, which dissociates to products OH + NO(2), reactants HO(2) + NO, or isomerizes to HONO(2). The association cross sections are used to obtain rate constants for formation of HOONO and HONO(2) in the high-pressure limit, and formation of products OH + NO(2) in the low-pressure limit.

Full-dimensional ab initio potential energy surface and vibrational configuration interaction calculations for vinyl.

The potential energy landscape and two permutationally invariant, full-dimensional ab initio-based potential energy surfaces (PESs) for the doublet vinyl radical, C(2)H(3), are described. The first of the two surfaces, denoted as PES/S, describes the equivalent CH(2)CH global minimum and the saddle point separating them, planar and nonplanar H-atom migration saddle points, a methylcarbyne local minimum that is due to a Jahn-Teller conical intersection, and the saddle point connecting it with the global minimum. The second PES, denoted PES/D, contains all stationary points of PES/S and in addition describes dissociation to C(2)H(2)+H fragments, including the saddle point to dissociation along a least-energy path. The surfaces are least-squares fits to electronic energies obtained with use of the spin-restricted coupled cluster singles and doubles with perturbative treatment of triples method and augmented correlation consistent polarized valence triple zeta basis sets, using permutationally invariant polynomials in "Morse variables" and a many-body expansion. PES/S is a fit to roughly 34,000 and PES/D to roughly 50,000 electronic structure energies. PES/S is used in full-dimensional, vibrational configuration interaction calculations of the vinyl zero-point energy and fundamental vibrational energies, which are compared to recent experiments.

Accurate ab initio and "hybrid" potential energy surfaces, intramolecular vibrational energies, and classical ir spectrum of the water dimer.

We report three modifications to recent ab initio, full-dimensional potential energy surfaces (PESs) for the water dimer [X. Huang et al., J. Chem. Phys. 128, 034312 (2008)]. The first modification is a refit of ab initio electronic energies to produce an accurate dissociation energy D(e). The second modification adds replacing the water monomer component of the PES with a spectroscopically accurate one and the third modification produces a hybrid potential that goes smoothly in the asymptotic region to the flexible, Thole-type model potential, version 3 dimer potential (denoted TTM3-F) [G. S. Fanourgakis and S. S. Xantheas, J. Chem. Phys. 128, 074506 (2008)]. The rigorous D(0) for these PESs, obtained using diffusion Monte Carlo calculations of the dimer zero-point energy, and an accurate zero-point energy of the monomer, range from 12.5 to 13.2 kJ/mol (2.99-3.15 kcal/mol), with the latter being the suggested benchmark value. For TTM3-F D(0) equals 16.1 kJ/mol. Vibrational calculations of monomer fundamental energies using the code MULTIMODE are reported for these PESs and the TTM3-F PES and compared to experiment. A classical molecular dynamics simulation of the infrared spectra of the water dimer and deuterated water dimer at 300 K are also reported using the ab initio dipole moment surface reported previously [X. Huang, B. J. Braams, and J. M. Bowman, J. Phys. Chem. A 110, 445 (2006)].

Accurate ab initio potential energy surface, dynamics, and thermochemistry of the F+CH4-->HF+CH3 reaction.

An accurate full-dimensional global potential energy surface (PES) for the F+CH(4)-->HF+CH(3) reaction has been developed based on 19 384 UCCSD(T)/aug-cc-pVTZ quality ab initio energy points obtained by an efficient composite method employing explicit UCCSD(T)/aug-cc-pVDZ and UMP2/aug-cc-pVXZ [X=D,T] computations. The PES contains a first-order saddle point, (CH(4)- -F)(SP), separating reactants from products, and also minima describing the van der Waals complexes, (CH(4)- - -F)(vdW) and (CH(3)- - -HF)(vdW), in the entrance and exit channels, respectively. The structures of these stationary points, as well as those of the reactants and products have been computed and the corresponding energies have been determined using basis set extrapolation techniques considering (a) electron correlation beyond the CCSD(T) level, (b) effects of the scalar relativity and the spin-orbit couplings, (c) diagonal Born-Oppenheimer corrections (DBOC), and (d) zero-point vibrational energies and thermal correction to the enthalpy at 298 K. The resulting saddle point barrier and ground state vibrationally adiabatic barrier heights (V(SP) and V(VAGS)), dissociation energy of (CH(3)- - -HF)(vdW) (D(e) and D(0)), and the reaction enthalpy (DeltaH(e) ( degrees ), DeltaH(0) ( degrees ), and DeltaH(298) ( degrees )) are (240+/-40 and 245+/-200 cm(-1)), (1070+/-10 and 460+/-50 cm(-1)), and (-10000+/-50, -11200+/-80, and -11000+/-80 cm(-1)), respectively. Variational vibrational calculations have been carried out for (CH(3)- - -HF)(vdW) in full (12) dimensions. Quasiclassical trajectory calculations of the reaction using the new PES are reported. The computed HF vibrational and rotational distributions are in excellent agreement with experiment.

Photochemical reactions of the low-lying excited states of formaldehyde: T1/S0 intersystem crossings, characteristics of the S1 and T1 potential energy surfaces, and a global T1 potential energy surface.

Accurate ab initio calculations using the multireference configuration interaction method have been performed to characterize the potential energy surfaces (PESs) of low-lying excited states (S(1) and T(1)) of formaldehyde (H(2)CO) and hydroxymethylene (HCOH) with emphasis on their isomerization, dissociation, and the possible role of the T(1) state in the nonadiabatic photodissociation of H(2)CO. Two regions on the T(1) PES are found to contribute to the nonadiabatic transition to the ground (S(0)) state. Three minima on the seam of crossing (MSXs), 80-85 kcal/mol (above the S(0) global minimum), are located in the HCOH region; they, however, are blocked by a high-energy isomerization transition state at approximately 107 kcal/mol. The other MSX discovered in the H(2)CO region is reachable with energy

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.].

Roaming is the dominant mechanism for molecular products in acetaldehyde photodissociation.

Reaction pathways that bypass the conventional saddle-point transition state (TS) are of considerable interest and importance. An example of such a pathway, termed "roaming," has been described in the photodissociation of H(2)CO. In a combined experimental and theoretical study, we show that roaming pathways are important in the 308-nm photodissociation of CH(3)CHO to CH(4) + CO. The CH(4) product is found to have extreme vibrational excitation, with the vibrational distribution peaked at approximately 95% of the total available energy. Quasiclassical trajectory calculations on full-dimensional potential energy surfaces reproduce these results and are used to infer that the major route to CH(4) + CO products is via a roaming pathway where a CH(3) fragment abstracts an H from HCO. The conventional saddle-point TS pathway to CH(4) + CO formation plays only a minor role. H-atom roaming is also observed, but this is also a minor pathway. The dominance of the CH(3) roaming mechanism is attributed to the fact that the CH(3) + HCO radical asymptote and the TS saddle-point barrier to CH(4) + CO are nearly isoenergetic. Roaming dynamics are therefore not restricted to small molecules such as H(2)CO, nor are they limited to H atoms being the roaming fragment. The observed dominance of the roaming mechanism over the conventional TS mechanism presents a significant challenge to current reaction rate theory.

"Roaming" dynamics in CH3CHO photodissociation revealed on a global potential energy surface.

We present a quasiclassical trajectory study of the photodissociation of CH3CHO to molecular and radical products, CH4 + CO and CH3 + HCO, respectively, using global ab initio-based potentials energy surfaces. The molecular products have a well-defined potential barrier transition state (TS) but the dynamics exhibit strong deviations from the TS pathway to these products. The radical products are formed via a variational TS. Calculations are reported at total energies corresponding to photolysis wavelengths of 308, 282, 264, 248 and 233 nm. The results at 308 nm focus on a comparison with experiment [Houston, P. L.; Kable, S. H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 16079] and the elucidation of the nature and extent of non-TS reaction dynamics to form the molecular products, CH4 + CO. At the other wavelengths the focus is the branching ratio of these products and the radical products, CH3 + HCO.

Accurate ab initio structure, dissociation energy, and vibrational spectroscopy of the F(-)-CH4 anion complex.

Accurate equilibrium structure, dissociation energy, global potential energy surface (PES), dipole moment surface (DMS), and the infrared vibrational spectrum in the 0-3000 cm(-1) range of the F(-)-CH4 anion complex have been obtained. The equilibrium electronic structure calculations employed second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster (CC) method up to single, double, triple, and perturbative quadruple excitations using the aug-cc-p(C)VXZ [X = 2(D), 3(T), 4(Q), and 5] correlation-consistent basis sets. The best equilibrium geometry has been obtained at the all-electron CCSD(T)/aug-cc-pCVQZ level of theory. The dissociation energy has been determined based on basis set extrapolation techniques within the focal-point analysis (FPA) approach considering (a) electron correlation beyond the all-electron CCSD(T) level, (b) relativistic effects, (c) diagonal Born-Oppenheimer corrections (DBOC), and (d) variationally computed zero-point vibrational energies. The final D(e) and D0 values are 2398 +/- 12 and 2280 +/- 20 cm(-1), respectively. The global PES and DMS have been computed at the frozen-core CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory, respectively. Variational vibrational calculations have been performed for CH4 and F(-)-CH4 employing the vibrational configuration interaction (VCI) method as implemented in Multimode.

Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface.

Quantum calculations of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcalmol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calculations of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calculated using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm(-1) in Cartesian coordinates and 22.6 cm(-1) in normal coordinates, with an uncertainty of 2-3 cm(-1). This splitting is also calculated based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calculation gives a tunneling splitting of 21-22 cm(-1). The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm(-1). These calculated tunneling splittings agree with each other to within less than the standard uncertainties obtained with the DMC method used, which are between 2 and 3 cm(-1), and agree well with the experimental values of 21.6 and 2.9 cm(-1) for the H and D transfer, respectively.

The theoretical prediction of infrared spectra of trans- and cis-hydroxycarbene calculated using full dimensional ab initio potential energy and dipole moment surfaces.

Accurate infrared spectra of the two hydroxycarbene isomers are computed by diagonalizing the Watson Hamiltonian including up to four mode couplings using full dimensional potential energy and dipole moment surfaces calculated at the CCSD(T)/cc-pVTZ (frozen core) and CCSD6-311G(**) (all electrons correlated) levels, respectively. Anharmonic corrections are found to be very important for these elusive higher-energy isomers of formaldehyde. Both the energy levels and intensities of stretching fundamentals and all overtone transitions are strongly affected by anharmonic couplings between the modes. The results for trans-HCOHHCOD are in excellent agreement with the recently reported IR spectra, which validates our predictions for the cis-isomers.

Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver.

The reduced density matrix (RDM) method, which is a variational calculation based on the second-order reduced density matrix, is applied to the ground state energies and the dipole moments for 57 different states of atoms, molecules, and to the ground state energies and the elements of 2-RDM for the Hubbard model. We explore the well-known N-representability conditions (P, Q, and G) together with the more recent and much stronger T1 and T2(') conditions. T2(') condition was recently rederived and it implies T2 condition. Using these N-representability conditions, we can usually calculate correlation energies in percentage ranging from 100% to 101%, whose accuracy is similar to CCSD(T) and even better for high spin states or anion systems where CCSD(T) fails. Highly accurate calculations are carried out by handling equality constraints and/or developing multiple precision arithmetic in the semidefinite programming (SDP) solver. Results show that handling equality constraints correctly improves the accuracy from 0.1 to 0.6 mhartree. Additionally, improvements by replacing T2 condition with T2(') condition are typically of 0.1-0.5 mhartree. The newly developed multiple precision arithmetic version of SDP solver calculates extraordinary accurate energies for the one dimensional Hubbard model and Be atom. It gives at least 16 significant digits for energies, where double precision calculations gives only two to eight digits. It also provides physically meaningful results for the Hubbard model in the high correlation limit.

Vibrational ground state properties of H(5)(+) and its isotopomers from diffusion Monte Carlo calculations.

Diffusion Monte Carlo computations, with and without importance sampling, of the zero-point properties of H(5)(+) and its isotopomers using a recent high accuracy global potential energy surface are presented. The global minimum of the potential possesses C(2v) symmetry, but the calculations predict a D(2d) geometry for zero-point averaged structure of H(5)(+) with one H atom "in the middle" between two HH diatoms. The predicted zero-point geometries of the deuterated forms have H in the middle preferred over D in the middle and for a nonsymmetric arrangement of D atoms the preferred arrangement is one which maximizes the number of D as the triatomic ion. We speculate on the consequences of these preferences in scattering of H(2)+H(3)(+) and isotopomers at low energies, such as those in the interstellar medium.