High dimensional anharmonic potential energy surfaces: The case of methane

Decomposing anharmonicity and mode-coupling from matrix effects in the IR spectra of matrix-isolated carbon dioxide and methane

A combined experimental and computational approach revealed similarities and differences in the vibrational signature of matrix-isolated carbon dioxide and methane.

Methane dissociation on Ni(111): A fifteen-dimensional potential energy surface using neural network method

In the present work, we develop a highly accurate, fifteen-dimensional potential energy surface (PES) of CH4 interacting on a rigid flat Ni(111) surface with the methodology of neural network (NN) fit to a database consisted of about 194 208 ab initio density functional theory (DFT) energy points. Some careful tests of the accuracy of the fitting PES are given through the descriptions of the fitting quality, vibrational spectrum of CH4 in vacuum, transition state (TS) geometries as well as the activation barriers. Using a 25-60-60-1 NN structure, we obtain one of the best PESs with the least root mean square errors: 10.11 meV for the entrance region and 17.00 meV for the interaction and product regions. Our PES can reproduce the DFT results very well in particular for the important TS structures. Furthermore, we present the sticking probability S0 of ground state CH4 at the experimental surface temperature using some sudden approximations by Jackson's group. An in-depth explanation is given for the underestimated sticking probability.

Neural network iterative diagonalization method to solve eigenvalue problems in quantum mechanics

The neural network iterative diagonalization structure for computing the eigenstates of complex symmetric or Hermitian matrices.

Vibrational Activation of Methane Chemisorption: The Role of Symmetry

Quantum state-resolved reactivity measurements probe the role of vibrational symmetry on the vibrational activation of the dissociative chemisorption of CH4 on Pt(111). IR-IR double resonance excitation in a molecular beam is used to prepare CH4 in all three different vibrational symmetry components A1, E, and F2 of the 2ν3 antisymmetric stretch overtone vibration. Methyl dissociation products chemisorbed on the cold Pt(111) surface are detected via reflection absorption infrared spectroscopy (RAIRS). We observe similar reactivity for CH4 prepared in the A1 and F2 sublevels but up to a factor of 2 lower reactivity for excitation of the E sublevel. It is suggested that differences in the localization of the C-H stretch amplitudes for the three states at the transition state leads to the observed difference in reactivity rather than state-specific vibrational energy transfer to electronic excitation of the metal.

The VMFCI method: a flexible tool for solving the molecular vibration problem

The present article introduces a general variational scheme to find approximate solutions of the spectral problem for the molecular vibration Hamiltonian. It is called the "vibrational mean field configuration interaction" (VMFCI) method, and consists in performing vibrational configuration interactions (VCI) for selected modes in the mean field of the others. The same partition of modes can be iterated until self-consistency, generalizing the vibrational self-consistent field (VSCF) method. As in contracted-mode methods, a hierarchy of partitions can be built to ultimately contract all the modes together. So, the VMFCI method extends the traditional variational approaches and can be included in existing vibrational codes based on the latter approaches. The flexibility and efficiency of this new method are demonstrated on several molecules of atmospheric interest.

Highly accurate potential-energy and dipole moment surfaces for vibrational state calculations of methane

Full-dimensional ab initio potential-energy surface (PES) and dipole moment surface are constructed for a methane molecule at the CCSD(T)/cc-pVTZ and MP2/cc-pVTZ levels of theory, respectively, by the modified Shepard interpolation method based on the fourth-order Taylor expansion [MSI(4th)]. The reference points for the interpolation have been set in the coupling region of CH symmetric and antisymmetric stretching modes so as to reproduce the vibrational energy levels related to CH stretching vibrations. The vibrational configuration-interaction calculations have been performed to obtain the energy levels and the absorption intensities up to 9000 cm(-1) with the use of MSI(4th)-PES. The calculated fundamental frequencies and low-lying vibrational energy levels show that MSI(4th) is superior to the widely employed quartic force field, giving a better agreement with the experimental values. The absorption bands of overtones as well as combination bands, which are caused by purely anharmonic effects, have been obtained up to 9000 cm(-1). Strongly coupled states with visible intensity have been found in the 6500-9000 cm(-1) region where the experimental data are still lacking.

Effects of C–H stretch excitation on the H+CH4 reaction

We have investigated the effects of C-H stretching excitation on the H+CH4-->CH3+H2 reaction dynamics using the photo-LOC technique. The CH3 product vibrational state and angular distribution are measured for the reaction of fast H atoms with methane excited in either the antisymmetric stretching fundamental (nu3=1) or first overtone (nu3=2) with a center-of-mass collision energy of Ecoll ranging from 1.52 to 2.20 eV. We find that vibrational excitation of the nu3=1 mode enhances the overall reaction cross section by a factor of 3.0+/-1.5 for Ecoll=1.52 eV, and this enhancement factor is approximately constant over the 1.52-2.20-eV collision energy range. A local-mode description of the CH4 stretching vibration, in which the C-H oscillators are uncoupled, is used to describe the observed state distributions. In this model, the interaction of the incident H atom with either a stretched or an unstretched C-H oscillator determines the vibrational state of the CH3 product. We also compare these results to the similar quantities obtained previously for the Cl+CH4-->CH3+HCl reaction at Ecoll=0.16 eV [Z. H. Kim, H. A. Bechtel, and R. N. Zare, J. Chem. Phys. 117, 3232 (2002); H. A. Bechtel, J. P. Camden, D. J. A. Brown, and R. N. Zare, ibid. 120, 5096 (2004)] in an attempt to elucidate the differences in reactivity for the same initially prepared vibration.

Comparative study of C-H stretch and bend vibrations in methane activation on Ni(100) and Ni(111)

State-resolved measurements on clean Ni(100) and Ni(111) surfaces quantify the reactivity of CH4 excited to v = 3 of the nu4 bend vibration. A comparison with prior data reveals that 3nu4 is significantly less effective than the nu3 C-H stretch at promoting dissociative chemisorption, even though 3nu4 contains 30% more energy. These results contradict statistical theories of gas-surface reactivity, provide clear evidence for vibrational mode specificity in a gas-surface reaction, and point to a central role for C-H stretching motion along the reaction path to dissociative chemisorption.

Effect of bending and torsional mode excitation on the reaction Cl+CH4→HCl+CH3

A beam containing CH(4), Cl(2), and He is expanded into a vacuum chamber where CH(4) is prepared via infrared excitation in a combination band consisting of one quantum of excitation each in the bending and torsional modes (nu(2)+nu(4)). The reaction is initiated by fast Cl atoms generated by photolysis of Cl(2) at 355 nm, and the resulting CH(3) and HCl products are detected in a state-specific manner using resonance-enhanced multiphoton ionization (REMPI). By comparing the relative amplitudes of the action spectra of Cl+CH(4)(nu(2)+nu(4)) and Cl+CH(4)(nu(3)) reactions, we determine that the nu(2)+nu(4) mode-driven reaction is at least 15% as reactive as the nu(3) (antisymmetric stretch) mode-driven reaction. The REMPI spectrum of the CH(3) products shows no propensity toward the formation of umbrella bend mode excited methyl radical, CH(3)(nu(2)=1), which is in sharp distinction to the theoretical expectation based on adiabatic correlations between CH(4) and CH(3). The rotational distribution of HCl(v=1) products from the Cl+CH(4)(nu(2)+nu(4)) reaction is hotter than the corresponding distribution from the Cl+CH(4)(nu(3)) reaction, even though the total energies of the two reactions are the same within 4%. An explanation for this enhanced rotational excitation of the HCl product from the Cl+CH(4)(nu(2)+nu(4)) reaction is offered in terms of the projection of the bending motion of the CH(4) reagent onto the rotational motion of the HCl product. The angular distributions of the HCl(nu=0) products from the Cl+CH(4)(nu(2)+nu(4)) reaction are backward scattered, which is in qualitative agreement with theoretical calculation. Overall, nonadiabatic product vibrational correlation and mode specificity of the reaction indicate that either the bending mode or the torsional mode or both modes are strongly coupled to the reaction coordinate.

Converged quantum dynamics calculations of vibrational energies of CH4 and CH3D using an ab initio potential

Exact variational calculations of vibrational energies of CH4 and CH3D are carried out using a two-layer Lanczos algorithm based on the ab initio potential energy surface of D. W. Schwenke and H. Partridge, Spectrochim. Acta, Part A 57, 887 (2001). The convergence of the calculated vibrational energies is discussed in detail. In addition, we report all well converged vibrational energy levels up to 6600 cm(-1) for CH4, and those up to 5000 cm(-1) for CH3D, respectively. These results clearly outperform previous theoretical calculations. And a comparison with experimental results available is also made.

Contracted basis Lanczos methods for computing numerically exact rovibrational levels of methane

We present a numerically exact calculation of rovibrational levels of a five-atom molecule. Two contracted basis Lanczos strategies are proposed. The first and preferred strategy is a two-stage contraction. Products of eigenfunctions of a four-dimensional (4D) stretch problem and eigenfunctions of 5D bend-rotation problems, one for each K, are used as basis functions for computing eigenfunctions and eigenvalues (for each K) of the Hamiltonian without the Coriolis coupling term, denoted H0. Finally, energy levels of the full Hamiltonian are calculated in a basis of the eigenfunctions of H0. The second strategy is a one-stage contraction in which energy levels of the full Hamiltonian are computed in the product contracted basis (without first computing eigenfunctions of H0). The two-stage contraction strategy, albeit more complicated, has the crucial advantage that it is trivial to parallelize the calculation so that the CPU and memory costs are independent of J. For the one-stage contraction strategy the CPU and memory costs of the difficult part of the calculation scale linearly with J. We use the polar coordinates associated with orthogonal Radau vectors and spherical harmonic type rovibrational basis functions. A parity-adapted rovibrational basis suitable for a five-atom molecule is proposed and employed to obtain bend-rotation eigenfunctions in the first step of both contraction methods. The effectiveness of the two methods is demonstrated by calculating a large number of converged J = 1 rovibrational levels of methane using a global potential energy surface.

Fast vibrational self-consistent field calculations through a reduced mode–mode coupling scheme

We present a new methodology to perform fast correlation-corrected vibrational self-consistent field (CC-VSCF) calculations using ab initio potential energy points calculated on the fly. Our method is based on the replacement of all-electron basis sets with a pseudo-potential basis for heavy atoms, and on an efficient reduction of the number of pair-coupling elements used in the CC-VSCF procedure. The method is applied to several test systems: H2O, NH3, and CH4, where it proves to be efficient, providing a speedup factor of 2 compared to a standard CC-VSCF calculation. We also apply our technique to the simulation of the vibrational spectrum of ethane and show that very accurate results can be obtained with a substantial speedup for this system.

The anharmonic potential energy surface of methyl fluoride

A large experimental spectroscopic data set sensitive to the cubic anharmonic potential energy surface (PES) of methyl fluoride has been compiled from the literature for six symmetric and asymmetric top isotopomers of methyl fluoride: 12CH3F, 13CH3FF, 12CD3F, 13CD3F, 12CHD2F and 12CH2DF. This empirical data set has been used to critically assess the best available literature ab initio cubic force field and various 'improved' theoretical force fields. A perturbation-resonance approach to the calculation of the observables from the force constants has been utilized and existing PESs were found to reproduce the data poorly. The careful treatment required for the correct theoretical reproduction of empirical spectroscopic constants arising from highly correlated least-squares fits to the original data is discussed. A new fit to the data has been performed (optimising 19 of the 38 cubic force constants) resulting in a much improved PES. The latter has been used to predict currently unknown spectroscopic constants for the least well-characterised isotopomer 12CH2DF. The prospects for a future empirical determination of the complete cubic force field of methyl fluoride are discussed and new data most likely to yield new information on the PES identified.

Towards accurate ab initio predictions of the vibrational spectrum of methane

We have carried out extensive ab initio calculations of the electronic structure of methane, and these results are used to compute vibrational energy levels. We include basis set extrapolations, core-valence correlation, relativistic effects, and Born-Oppenheimer breakdown terms in our calculations. Our ab initio predictions of the lowest lying levels are superb.

A perturbative calculation of the rovibrational energy levels of methane

The rovibrational energy levels of methane are determined from a quartic ab initio potential energy force field where the expansion coordinates are the Morse coordinates for the stretches and extension coordinates for the bends. Energies are calculated using canonical Van Vleck perturbation theory. Results are obtained for both rotation-vibration Hamiltonians expressed as functions of curvilinear and rectilinear normal coordinates. Second, fourth, and sixth order curvilinear results are compared with experimental results, and fourth order results for the rectilinear and curvilinear Hamiltonian are compared to each other. The calculated rovibrational levels are in good agreement with the experimental values for low J levels. The calculated rotational level splittings are in even better agreement with the experiment. In particular, the ground state tetrahedral splittings, which are as small as 10(-4) cm(-1), are well reproduced by our calculations at sixth order.

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.