Nine-dimensional Potential Energy Surface Research Articles

Bending Relaxation of H2 O by Collision with Para- and Ortho-H2.

We extend our recent theoretical work on the bending relaxation of H2 O in collisions with H2 by including the three water modes of vibration coupled with rotation, as well as the rotation of H2 . Our full quantum close-coupling method (excluding the H2 vibration) is combined with a high-accuracy nine-dimensional potential energy surface. The collisions of para-H2 O and ortho-H2 O with the two spin modifications of H2 are considered and compared for several initial states of H2 O. The convergence of the results as a function of the size of the rotational basis set of the two colliders is discussed. In particular, near-resonant energy transfer between H2 O and H2 is found to control the vibrational relaxation process, with a dominant contribution of transitions with = , and being respectively the H2 initial and final rotational quantum numbers. Finally, the calculated value of the H2 O bending relaxation rate coefficient at 295 K is found to be in excellent agreement with its experimental estimate.

HDO-CO Complex: D-Bonded and H-Bonded Isomers and Intra- and Intermolecular Rovibrational States from Full-Dimensional and Fully Coupled Quantum Calculations.

We report full-dimensional and fully coupled quantum bound-state calculations of the J = 0, 1 intra- and intermolecular rovibrational states of the isotopically asymmetric HDO-CO complex. They are performed on the ab initio nine-dimensional (9D) potential energy surface (PES) [Liu, Y.; Li, J. Phys. Chem. Chem. Phys. 2019, 21, 24101]. The present study complements our earlier theoretical investigation of the 9D rovibrational level structure of the H2O-CO and D2O-CO complexes [Felker, P. M.; Bačić, Z. J. Chem. Phys. 2020, 153, 074107]. What distinguishes HDO-CO is that, unlike the two isotopically symmetric isotopologues, it does not display hydrogen-interchange tunneling but has two distinct isomers, the lower-energy D-bonded HOD-CO and the higher-energy H-bonded DOH-CO. The highly efficient methodology employed in the present calculations derives from our earlier study referenced above, taking into account the lower symmetry of HDO-CO. The full 9D rovibrational Hamiltonian is partitioned into three reduced-dimension Hamiltonians: the 5D rigid-monomer intermolecular vibrational Hamiltonian and two intramolecular vibrational Hamiltonians, one for the HDO monomer (3D) and another for the CO monomer (1D), and a 9D remainder term. The reduced-dimension Hamiltonians are diagonalized separately, and small portions of their low-energy eigenstates are incorporated in the compact final 9D product contracted basis covering all internal, intra- and intermolecular degrees of freedom of the complex. The 9D rovibrational Hamiltonian is diagonalized in this fully contracted basis. The calculations show that the eigenstates belonging to the D-bonded and H-bonded isomers, designated as D and H, respectively, are easy to identify, owing to the near-complete localization of their wave functions in either of the two minima on the PES. The computed intramolecular vibrational frequencies of the two monomers are either blue- or red-shifted, depending on the mode. The excitations of the intramolecular vibrational modes affect the energies of the low-lying D and H intermolecular vibrational states in the respective intramolecular manifolds. Comparison is made with the experimental data available in the literature.

H2O-CO and D2O-CO complexes: Intra- and intermolecular rovibrational states from full-dimensional and fully coupled quantum calculations.

We present efficient yet rigorous, full-dimensional quantum bound-state calculations of the fully coupled J = 0 and one intra- and intermolecular rovibrational levels of H2O-CO and D2O-CO complexes. The new ab initio nine-dimensional (9D) potential energy surface (PES) [Y. Liu and J. Li, Phys. Chem. Chem. Phys. 21, 24101 (2019)] is employed. In the spirit of the recently introduced general procedure [P. M. Felker and Z. Bačić, J. Chem. Phys. 151, 024305 (2019)], the 9D rovibrational Hamiltonian is partitioned into a 5D (rigid-monomer) intermolecular Hamiltonian, two intramolecular vibrational Hamiltonians-one for the water monomer (3D) and another for the CO monomer (1D), and a 9D remainder term. The low-energy eigenstates of the three reduced-dimension Hamiltonians are used to build up the 9D product contracted basis, in which the matrix of the full rovibrational Hamiltonian is diagonalized. In line with the findings of our earlier study referenced above, the 5D intermolecular eigenstates included in the 9D bases extend up to at most 230 cm-1 above the lowest-energy state of the given parity, much less than the intramolecular fundamentals of the two complexes that span the range of energies from about 1200 cm-1 to 3800 cm-1. The resulting Hamiltonian matrices are small for the 9D quantum problem considered, ≈ 10 000 for J = 0 and 13 500 for J = 1 calculations, allowing for direct diagonalization. The 9D calculations permit exploring a number of features of the rovibrational level structure of H2O-CO and D2O-CO that are beyond the quantum 5D rigid-monomer treatments reported to date. These include the differences in the magnitudes of the hydrogen-exchange tunneling splittings computed in 9D and 5D, the sensitivity of the tunneling splittings to the intramolecular vibrational excitation, the frequency shifts of the intramolecular vibrational modes, which, depending on the mode, can be either blue- or redshifts, and the effects of the excitation of the intramolecular fundamentals on the low-lying intermolecular eigenstates. Also examined is the extent of the eigenstate delocalization over the two minima on the PES. Whenever possible, a comparison is made with the experimental data in the literature.

Ro-vibrational spectra of the simplest deuterated criegee intermediate CD2OO

Criegee intermediates are of significance in the atmospheric chemistry. In this work, the ro-vibrational spectra of the simplest deuterated Criegee intermediate, CD2OO, were studied by a vibrational self-consistent field/virtual configuration interaction (VSCF/VCI) method based on a nine-dimensional accurate potential energy surface and dipole surface for its ground electronic state. The calculated fundamental vibrational frequencies and rotational constants are in excellent agreement with the available experimental results. These data are useful for further spectroscopic studies of CD2OO. Especially, the rotational constants for excited vibrational levels are essential for experimental spectral assignments. However, the infrared intensities from different resources, including the current computation, the experiment, and previous calculations at the NEVPT2 and B3LYP levels, deviate significantly.

Effects of surface motion and electron-hole pair excitations in CO2 dissociation and scattering on Ni(100).

The energy transfer between different channels is an important aspect in chemical reactions at surfaces. We investigate here in detail the energy transfer dynamics in a prototypical system, i.e., reactive and nonreactive scattering of CO2 on Ni(100), which is related to heterogeneous catalytic processes with Ni-based catalysts for CO2 reduction. On the basis of our earlier nine-dimensional potential energy surface for CO2/Ni(100), dynamical calculations have been done using the generalized Langevin oscillator (GLO) model combined with local density friction approximation (LDFA), in which the former accounts for the surface motion and the latter accounts for the low-energy electron-hole pair (EHP) excitation. In spite of its simplicity, it is found that the GLO model yields quite satisfactory results, including the significant energy loss and product energy disposal, trapping, and steering dynamics, all of which agree well with the ab initio molecular dynamics ones where many surface atoms are explicitly involved with high computational cost. However, the GLO model fails to describe the reactivity enhancement due to the lattice motion because it intrinsically does not incorporate the variance of barrier height on the surface atom displacement. On the other hand, in LDFA, the energy transferred to EHPs is found to play a minor role and barely alter the dynamics, except for slightly reducing the dissociation probabilities. In addition, vibrational state-selected dissociative sticking probabilities are calculated and previously observed strong mode specificity is confirmed. Our work suggests that further improvement of the GLO model is needed to consider the lattice-induced barrier lowering.

Water dissociating on rigid Ni(100): A quantum dynamics study on a full-dimensional potential energy surface.

We constructed a nine-dimensional (9D) potential energy surface (PES) for the dissociative chemisorption of H2O on a rigid Ni(100) surface using the neural network method based on roughly 110 000 energies obtained from extensive density functional theory (DFT) calculations. The resulting PES is accurate and smooth, based on the small fitting errors and the good agreement between the fitted PES and the direct DFT calculations. Time dependent wave packet calculations also showed that the PES is very well converged with respect to the fitting procedure. The dissociation probabilities of H2O initially in the ground rovibrational state from 9D quantum dynamics calculations are quite different from the site-specific results from the seven-dimensional (7D) calculations, indicating the importance of full-dimensional quantum dynamics to quantitatively characterize this gas-surface reaction. It is found that the validity of the site-averaging approximation with exact potential holds well, where the site-averaging dissociation probability over 15 fixed impact sites obtained from 7D quantum dynamics calculations can accurately approximate the 9D dissociation probability for H2O in the ground rovibrational state.

Ab Initio Molecular Dynamics Study of Dissociative Chemisorption and Scattering of CO2 on Ni(100): Reactivity, Energy Transfer, Steering Dynamics, and Lattice Effects

The dissociative chemisorption of polyatomic molecules on metal surfaces has attracted much interest in recent years due to their industrial and fundamental importance. Comparing with extensively studied systems such as methane and water, however, dissociative chemisorption of CO2, which is important for CO2 activation, has so far received scant attention. We recently reported vibrational enhancement of the dissociative chemisorption of CO2 on a rigid Ni(100) surface using a nine-dimensional potential energy surface (PES) based on a large number of density functional theory calculations. However, that PES is incapable of describing the lattice motion and energy transfer between this heavy molecule and the surface. To overcome these limitations, we present here ab initio molecular dynamics results for CO2 scattering and dissociation. In addition to formation of adsorbed O and CO, CO2 is found to have a large trapping probability in a chemisorption well, along with a substantial amount of energy loss to sur...

Full-Dimensional Potential Energy and Dipole Moment Surfaces of GeH4 Molecule and Accurate First-Principle Rotationally Resolved Intensity Predictions in the Infrared.

Nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) of the germane molecule are constructed using extended ab initio CCSD(T) calculations at 19 882 points. PES analytical representation is determined as an expansion in nonlinear symmetry adapted products of orthogonal and internal coordinates involving 340 parameters up to eighth order. Minor empirical refinement of the equilibrium geometry and of four quadratic parameters of the PES computed at the CCSD(T)/aug-cc-pVQZ-DK level of the theory yielded the accuracy below 1 cm-1 for all experimentally known vibrational band centers of five stable isotopologues of 70GeH4, 72GeH4, 73GeH4, 74GeH4, and 76GeH4 up to 8300 cm-1. The optimized equilibrium bond re = 1.517 594 Å is very close to best ab initio values. Rotational energies up to J = 15 are calculated using potential expansion in normal coordinate tensors with maximum errors of 0.004 and 0.0006 cm-1 for 74GeH4 and 76GeH4. The DMS analytical representation is determined through an expansion in symmetry-adapted products of internal nonlinear coordinates involving 967 parameters up to the sixth order. Vibration-rotation line intensities of five stable germane isotopologues were calculated from purely ab initio DMS using nuclear motion variational calculations with a full account of the tetrahedral symmetry of the molecules. For the first time a good overall agreement of main absorption features with experimental rotationally resolved Pacific Northwest National Laboratory spectra was achieved in the entire range of 700-5300 cm-1. It was found that very accurate description of state-dependent isotopic shifts is mandatory to correctly describe complex patterns of observed spectra at natural isotopic abundance resulting from the superposition of five stable isotopologues. The data obtained in this work will be made available through the TheoReTS information system.

A highly accurate ab initio potential energy surface for methane.

A new nine-dimensional potential energy surface (PES) for methane has been generated using state-of-the-art ab initio theory. The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set limit and incorporates a range of higher-level additive energy corrections. These include core-valence electron correlation, higher-order coupled cluster terms beyond perturbative triples, scalar relativistic effects, and the diagonal Born-Oppenheimer correction. Sub-wavenumber accuracy is achieved for the majority of experimentally known vibrational energy levels with the four fundamentals of (12)CH4 reproduced with a root-mean-square error of 0.70 cm(-1). The computed ab initio equilibrium C-H bond length is in excellent agreement with previous values despite pure rotational energies displaying minor systematic errors as J (rotational excitation) increases. It is shown that these errors can be significantly reduced by adjusting the equilibrium geometry. The PES represents the most accurate ab initio surface to date and will serve as a good starting point for empirical refinement.

Quantum dynamics of water dissociative chemisorption on rigid Ni(111): An approximate nine-dimensional treatment.

The quantum dynamics of water dissociative chemisorption on the rigid Ni(111) surface is investigated using a recently developed nine-dimensional potential energy surface. The quantum dynamical model includes explicitly seven degrees of freedom of D2O at fixed surface sites, and the final results were obtained with a site-averaging model. The mode specificity in the site-specific results is reported and analyzed. Finally, the approximate sticking probabilities for various vibrationally excited states of D2O are obtained considering surface lattice effects and formally all nine degrees of freedom. The comparison with experiment reveals the inaccuracy of the density functional theory and suggests the need to improve the potential energy surface.

Full-Dimensional Quantum Calculations of Vibrational Levels of NH4(+) and Isotopomers on An Accurate Ab Initio Potential Energy Surface.

Vibrational energy levels of the ammonium cation (NH4(+)) and its deuterated isotopomers are calculated using a numerically exact kinetic energy operator on a recently developed nine-dimensional permutation invariant semiglobal potential energy surface fitted to a large number of high-level ab initio points. Like CH4, the vibrational levels of NH4(+) and ND4(+) exhibit a polyad structure, characterized by a collective quantum number P = 2(v1 + v3) + v2 + v4. The low-lying vibrational levels of all isotopomers are assigned and the agreement with available experimental data is better than 1 cm(-1).

Communication: Enhanced dissociative chemisorption of CO2 via vibrational excitation.

A fully coupled global nine-dimensional potential energy surface for the dissociative chemisorption of CO2 on Ni(100) is constructed from ∼18,000 density functional points. It reveals a complex reaction pathway dominated by two near iso-energetic transition states. The dissociation probabilities obtained by quasi-classical trajectories on the potential energy surface reproduced experimental trends, and indicate that vibrational excitations of CO2 significantly promote the dissociation. Using the sudden vector projection model, the behavior of the reactivity is rationalized by couplings with the reaction coordinate at each transition state. These results offer plausible rationalization for the observed enhancement of CO2 dissociation in non-thermal plasmas by metal surfaces.

A seven-dimensional quantum dynamics study of the dissociative chemisorption of H2O on Cu(111): effects of azimuthal angles and azimuthal angle-averaging.

We report the first seven-dimensional quantum dynamics study for the dissociative chemisorption of H2O on Cu(111) using the time-dependent wave-packet approach, based on an accurate nine-dimensional potential energy surface (PES), which is newly developed by neural network fitting to ∼80 000 density functional theory points. This seven-dimensional quantum model allows the examination of the influence of azimuthal angles and also the investigation of the quantitative relationship between the seven-dimensional (7D) dissociation probabilities and those results calculated by the six-dimensional (6D) model with the flat surface approximation. The reactivity strongly depends on the azimuthal rotations due to different barrier heights. Very large differences are seen between the 7D dissociation probabilities and the 6D results with fixed azimuthal angles, at different fixed sites of impact, indicating that the 6D model by neglecting the azimuthal rotation can introduce substantial errors in calculating dissociation probabilities and the 7D quantum dynamics is essential to investigate the dissociation process. A new azimuthal angle-averaging approach is proposed that the 7D dissociation probability can be well reproduced by averaging 6D results over 18 azimuthal angles, in particular in low kinetic energy regions.

A global potential energy surface and dipole moment surface for silane.

A new nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) for silane have been generated using high-level ab initio theory. The PES, CBS-F12(HL), reproduces all four fundamental term values for (28)SiH4 with sub-wavenumber accuracy, resulting in an overall root-mean-square error of 0.63 cm(-1). The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set limit, and incorporates a range of higher-level additive energy corrections to account for core-valence electron correlation, higher-order coupled cluster terms, and scalar relativistic effects. Systematic errors in computed intra-band rotational energy levels are reduced by empirically refining the equilibrium geometry. The resultant Si-H bond length is in excellent agreement with previous experimental and theoretical values. Vibrational transition moments, absolute line intensities of the ν3 band, and the infrared spectrum for (28)SiH4 including states up to J = 20 and vibrational band origins up to 5000 cm(-1) are calculated and compared with available experimental results. The DMS tends to marginally overestimate the strength of line intensities. Despite this, band shape and structure across the spectrum are well reproduced and show good agreement with experiment. We thus recommend the PES and DMS for future use.

Quantum and classical dynamics of water dissociation on Ni(111): A test of the site-averaging model in dissociative chemisorption of polyatomic molecules.

Recently, we reported the first highly accurate nine-dimensional global potential energy surface (PES) for water interacting with a rigid Ni(111) surface, built on a large number of density functional theory points [B. Jiang and H. Guo, Phys. Rev. Lett. 114, 166101 (2015)]. Here, we investigate site-specific reaction probabilities on this PES using a quasi-seven-dimensional quantum dynamical model. It is shown that the site-specific reactivity is largely controlled by the topography of the PES instead of the barrier height alone, underscoring the importance of multidimensional dynamics. In addition, the full-dimensional dissociation probability is estimated by averaging fixed-site reaction probabilities with appropriate weights. To validate this model and gain insights into the dynamics, additional quasi-classical trajectory calculations in both full and reduced dimensions have also been performed and important dynamical factors such as the steering effect are discussed.

Vibrational energy levels of the simplest Criegee intermediate (CH2OO) from full-dimensional Lanczos, MCTDH, and MULTIMODE calculations.

Accurate vibrational energy levels of the simplest Criegee intermediate (CH2OO) were determined on a recently developed ab initio based nine-dimensional potential energy surface using three quantum mechanical methods. The first is the iterative Lanczos method using a conventional basis expansion with an exact Hamiltonian. The second and more efficient method is the multi-configurational time-dependent Hartree (MCTDH) method in which the potential energy surface is refit to conform to the sums-of-products requirement of MCTDH. Finally, the energy levels were computed with a vibrational self-consistent field/virtual configuration interaction method in MULTIMODE. The low-lying levels obtained from the three methods are found to be within a few wave numbers of each other, although some larger discrepancies exist at higher levels. The calculated vibrational levels are very well represented by an anharmonic effective Hamiltonian.

Dynamics of water dissociative chemisorption on Ni(111): effects of impact sites and incident angles.

The dissociative chemisorption of water on rigid Ni(111) is investigated using a quasiclassical trajectory method on a nine-dimensional global potential energy surface based on a faithful permutation invariant fit of ∼25 000 density functional theory points. This full-dimensional model not only confirms the validity of our earlier reduced-dimensional model with 6 degrees of freedom, but also allows the examination of the influence of impact sites and incident angles. It is shown that the reactivity depends on the site of impact in a complex fashion controlled by the topography of the potential energy surface rather than the barrier height alone. In addition, the reaction is promoted by momenta both parallel and perpendicular to the surface, as predicted by the recently proposed sudden vector projection model.

Near spectroscopically accurate ab initio potential energy surface for NH4(+) and variational calculations of low-lying vibrational levels.

A nine-dimensional potential energy surface (PES) for the ammonium cation has been constructed by fitting ∼30 000 AE-CCSD(T)-F12a/cc-pCVTZ-F12 points up to 32 262 cm(-1) (4.0 eV) from the minimum. The fitting using the permutation invariant polynomial-neural network method has high fidelity, with a root-mean-square error of merely 2.34 cm(-1). The low-lying vibrational energy levels of NH4(+) have been determined quantum mechanically using both Jacobi and normal coordinates, and the fundamental frequencies are in excellent agreement with available experimental data.

A nine-dimensional global potential energy surface for NH4(X2A1) and kinetics studies on the H + NH3↔ H2+ NH2reaction

Extensive ab initio calculations of the stationary points in the NH4(X(2)A1) system are reported using both coupled cluster and multi-reference configuration interaction methods. In addition, more than 100 000 points are generated over a large configuration space and energy range (6 eV) using the explicitly correlated unrestricted coupled cluster method with single, double, and perturbative triple excitations with the augmented correlation-consistent polarized triple zeta basis set (UCCSD(T)-F12a/aug-cc-pVTZ). Using the recently proposed permutation-invariant polynomial neural network (PIP-NN) method, these points are accurately fit to an analytical form with a total root mean squared error (RMSE) of 3.4 meV (0.08 kcal mol(-1)). Both the abstraction and exchange channels as well as the metastable ammonium radical (NH4) are included in this potential energy surface. Transition-state theory and quasi-classical trajectory calculations have been performed to obtain the rate constants for the abstraction reaction and its reverse. Comparison with available experimental results is satisfactory, providing supporting evidence for the accuracy of the potential.

A new accurate and full dimensional potential energy surface of H5+ based on a triatomics-in-molecules analytic functional form

In this work a reliable full nine-dimensional potential energy surface for studying the dynamics of H(5)(+) is constructed, which is completely symmetric under any permutation of the nuclei. For this purpose, we develop a triatoms-in-molecules method as an extension of the more common diatoms-in-molecules one, which allows a very accurate description of the asymptotic regions by including correctly the charge-induced dipole and quadrupole interactions. Moreover, this treatment provides a semiquantitative description of all the topological features of the global potential compared with coupled cluster results. In particular, the hop of the proton between two H(2) fragments produces a double well in the potential. This resonant structure involving the five atoms produces a stabilization, lowering the barrier, and the triatoms-in-molecules yields to a barrier significantly higher than the ab initio results. Therefore, to improve the triatomics-in-molecules potential surface, two five-body terms are added, which are fitted to more than 110,000 coupled-cluster ab initio points. The global potential energy surface thus obtained in this work has an overall root mean square error of 0.079 kcal/mol for energies below 27 kcal/mol above the global well. The features of the potential are described and compared with previous available surfaces.