Using C3v symmetry with polyspherical coordinates for methane

Toward a Comprehensive Understanding of Mode-Specific Dynamics of Polyatomic Reactions: A Full-Dimensional Quantum Dynamics Study of the H + NH3 Reaction

Mode specificity not only sheds light on reaction dynamics but also opens the door for chemical reaction control. This work reports a state-of-the-art full-dimensional quantum dynamics study on the prototypical hydrogen abstraction reaction of hydrogen with ammonia, which serves as a benchmark for advancing our fundamental understanding of polyatomic reaction dynamics. By taking advantage of the (3 + 1) Radau-Jacobi coordinates, the bond-specific probabilities are resolved with the reactant NH₃ initiated from either a non-degenerate or degenerate stretching vibrational state. The observed different atom-specific abstraction probabilities from individual states of the degenerate pair are rationalized in the local mode representation according to the different vibrational energy deposited in each N-H bond. It is verified that the three H atoms in NH₃ have the same abstraction probability as that from the degenerate pair and the linear combination of the degenerate pair gives the same reaction probability. In addition, the symmetric and asymmetric stretching modes of the reactant NH₃ have comparable efficacies on driving the reaction.

Using nondirect product Wigner D basis functions and the symmetry-adapted Lanczos algorithm to compute the ro-vibrational spectrum of CH4-H2O

By doing calculations on the methane-water van der Waals complex, we demonstrate that highly converged energy levels and wavefunctions can be obtained using Wigner D basis functions and the Symmetry-Adapted Lanczos (SAL) method. The Wigner D basis is a nondirect product basis and, therefore, efficient when the kinetic energy operator has accessible singularities. The SAL method makes it possible to exploit symmetry to label energy levels and reduce the cost of the calculation, without explicitly using symmetry-adapted basis functions. Line strengths are computed, and new bands are identified. In particular, we find unusually strong transitions between states associated with the isomers of the global minimum and the secondary minimum.

Full-dimensional quantum mechanical calculations of the reaction probability of the H + CH4 reaction based on a mixed Jacobi and Radau description

A full-dimensional time-dependent wave packet study using mixed polyspherical Jacobi and Radau coordinates for the title reaction has been reported. The non-reactive moiety CH₃ has been described using three Radau vectors, whereas two Jacobi vectors have been used for the bond breaking/formation process. A potential-optimized discrete variable representation basis has been employed to describe the vibrational coordinates of the reagent CH₄. About one hundred billion basis functions have been necessary to achieve converged results. The reaction probabilities for some initial vibrational states are given. A comparison between the present approach and other methods, including reduced and full-dimensional ones, is also presented.

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.

General internal coordinate gradient vectors and the vibrational kinetic energy operator of centrally-connected penta-atomic systems. Part I

New internal coordinate gradients, s-vectors, are derived using geometric algebra. The internal coordinates are based on a completely general description of the molecular geometry in terms of internal vectors. The internal coordinate gradients allow kinetic energy operators to be easily expressed in terms of orthogonal or non-orthogonal coordinate systems. Using this approach, a new exact vibrational kinetic energy operator for centrally-connected penta-atomic systems is derived for an internal polyspherical coordinate system based on orthogonal internal vectors. Difficulties associated with the well known coordinate redundancy in centrally-connected penta-atomic systems are discussed and overcome.

Improving the calculation of rovibrational spectra of five-atom molecules with three identical atoms by using a C3υ(G6) symmetry-adapted grid: Applied to CH3D and CHD3

In this paper we report two improvements on the approach we have used to compute rovibrational levels of methane and apply the new ideas to calculate rovibrational levels of two methane isotopomers CH3D and CHD3. Both improvements make the bend calculation better. The first improvement is a G6-invariant (or C3upsilon-invariant) grid which is designed such that each point on the grid is mapped to another point on the grid by any of the G6 operations. The second improvement is the use of fast Fourier transform (FFT) to compute the bend potential matrix-vector products. The FFT matrix-vector product is about three and ten times faster than the previous sequential summation method for the J=0 and J>0 cases, respectively. The calculated J=1 rovibrational levels of CH3D and CHD3 on the Schwenke and Partridge [Spectrochim. Acta, Part A 57, 887 (2001)] ab initio potential are in good agreement (within 6 cm(-1) for the levels up to 3000 cm(-1)) with the experimental data. The agreement is even better (within 0.1 cm(-1) for the levels up to 6000 cm(-1)) if the associated J=0 energies are subtracted.

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.