Phillip S. Thomas

Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms

We propose a method for solving the vibrational Schrödinger equation with which one can compute hundreds of energy levels of seven-atom molecules using at most a few gigabytes of memory. It uses nested contractions in conjunction with the reduced-rank block power method (RRBPM) described in J. Chem. Phys. 2014, 140, 174111. Successive basis contractions are organized into a tree, the nodes of which are associated with eigenfunctions of reduced-dimension Hamiltonians. The RRBPM is used recursively to compute eigenfunctions of nodes in bases of products of reduced-dimension eigenfunctions of nodes with fewer coordinates. The corresponding vectors are tensors in what is called CP-format. The final wave functions are therefore represented in a hierarchical CP-format. Computational efficiency and accuracy are significantly improved by representing the Hamiltonian in the same hierarchical format as the wave function. We demonstrate that with this hierarchical RRBPM it is possible to compute energy levels of a 64-D coupled-oscillator model Hamiltonian and also of acetonitrile (CH3CN) and ethylene oxide (C2H4O), for which we use quartic potentials. The most accurate acetonitrile calculation uses 139 MB of memory and takes 3.2 h on a single processor. The most accurate ethylene oxide calculation uses 6.1 GB of memory and takes 14 d on 63 processors. The hierarchical RRBPM shatters the memory barrier that impedes the calculation of vibrational spectra.

Observation of the A-X electronic transitions of cyclopentyl and cyclohexyl peroxy radicals via cavity ringdown spectroscopy.

The A-X electronic absorption spectra of cyclopentyl, cyclohexyl, and cyclohexyl-d(11) peroxy radicals have been recorded at room temperature by cavity ringdown spectroscopy. By comparing the experimental spectra with predictions from ab initio and density functional calculations, we have assigned the band origins and vibrational structure of each of these species. The spectrum of cyclopentyl peroxy is interpreted primarily in terms of two overlapping gauche conformers, while that of cyclohexyl peroxy appears to be a superposition of axially and equatorially substituted gauche conformers, both based on the chair conformation of cyclohexane. Expectations from calculated Boltzmann factors indicate comparable populations for cis-conformers; however, no bands uniquely assignable to cis-conformers of either peroxy can be identified. Plausible assignments for cis-conformers are considered, and possible explanations for their absence are offered, including specifically lower oscillator strengths than for the gauche conformers. Mode mixing appears to be responsible for the appearance of multiple vibrations with COO bending character for both peroxies, particularly for cyclohexyl peroxy.

Electronic transition moment for the 0(0)(0) band of the à ← X̃ transition in the ethyl peroxy radical.

The electronic transition moment for the G-conformer of ethyl peroxy was determined from the experimentally measured value of the peak absorption cross-section and the simulation of its rovibronic spectrum using the results of the high resolution spectroscopy of this molecule. The resulting value is |μ(e)(G)| = 2.55(6) × 10(-2) Debye, which is compared to values from electronic structure calculations.

Ã-X absorption of propargyl peroxy radical (H-C≡C-CH2OO·): a cavity ring-down spectroscopic and computational study.

The Ã-X electronic absorption spectrum of propargyl peroxy radical has been recorded at room temperature by cavity ring-down spectroscopy. Electronic structure calculations predict two isomeric forms, acetylenic and allenic, with two stable conformers for each. The acetylenic trans conformer, with a band origin at 7631.8 ± 0.1 cm(-1), is definitively assigned on the basis of ab initio calculations and rotational simulations, and possible assignments for the acetylenic gauche and allenic trans forms are given. A fourth form, allenic cis, is not observed. Simulations based on calculated torsional potentials predict that the allenic trans form will have a long, poorly resolved progression in the OOCC torsional vibration, consistent with experimental observations.