Using an iterative eigensolver and intertwined rank reduction to compute vibrational spectra of molecules with more than a dozen atoms: Uracil and naphthalene.

We use a direct product basis, basis vectors computed by evaluating matrix-vector products, and rank reduction to calculate vibrational energy levels of uracil and naphthalene, with 12 and 18 atoms, respectively. A matrix representing the Hamiltonian in the direct product basis and vectors with as many components as there are direct product basis functions are neither calculated nor stored. We also introduce an improvement of the Hierarchical Intertwined Reduced-Rank Block Power Method (HI-RRBPM), proposed previously in Thomas and Carrington, Jr. [J. Chem. Phys. 146, 204110 (2017)]. It decreases the memory cost of the HI-RRBPM and enables one to compute vibrational spectra of molecules with over a dozen atoms with a typical desktop computer.

An intertwined method for making low-rank, sum-of-product basis functions that makes it possible to compute vibrational spectra of molecules with more than 10 atoms.

We propose a method for solving the vibrational Schrödinger equation with which one can compute spectra for molecules with more than ten atoms. It uses sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. By doing a sequence of partial optimizations, in each of which the factors in a SOP basis function for a single coordinate are optimized, the rank of the basis functions is reduced as matrix-vector products are computed. This is better than using an alternating least squares method to reduce the rank, as is done in the reduced-rank block power method. Partial optimization is better because it speeds up the calculation by about an order of magnitude and allows one to significantly reduce the memory cost. We demonstrate the effectiveness of the new method by computing vibrational spectra of two molecules, ethylene oxide (C2H4O) and cyclopentadiene (C5H6), with 7 and 11 atoms, respectively.

Rotational effects on the dissociation dynamics of CHD3 on Pt(111).

Dissociation of methane on metal surfaces is of high practical and fundamental interest. Therefore there is currently a big push aimed at determining the simplest dynamical model that allows the reaction dynamics to be described with quantitative accuracy using quantum dynamics. Using five-dimensional quantum dynamical and full-dimensional ab initio molecular dynamics calculations, we show that the CD3 umbrella axis of CHD3 must reorient before the molecule reaches the barrier for C-H cleavage to occur in reaction on Pt(111). This rules out the application of the rotationally sudden approximation, as explicitly shown through a comparison with calculations using this approximation. Further, we suggest that the observed umbrella swing should strongly affect the sensitivity of C-H cleavage to the initial alignment of the molecule relative to the surface as found experimentally for closely related systems. We find very large differences in reactivity for molecules pre-excited to different rotational states, particularly if these states are associated with different orientations of the C-H bond.

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.

Chebyshev high-dimensional model representation (Chebyshev-HDMR) potentials: application to reactive scattering of H2 from Pt(111) and Cu(111) surfaces.

Gas phase and surface reactions involving polyatomic molecules are of central importance to chemical physics, and require accurately fit potential energy surfaces describing the interaction in their systems. Here, we propose a method for generating a High Dimensional Model Representation (HDMR) of a multidimensional potential energy surface (PES) and apply it to reactive molecule-surface scattering problems. In the HDMR treatment, all N degrees of freedom (DOF) of an N-dimensional PES are represented but only n < N are explicitly coupled. The HDMR is obtained from Chebyshev polynomial expansions for each degree of freedom, where expansion coefficients are efficiently evaluated using discrete cosine transform (DCT) algorithms and properties of Chebyshev polynomials. HDMR surfaces constructed for the reactive scattering of H2 from Pt(111) and Cu(111) are used in quantum dynamics simulations; the resultant state-resolved reaction and scattering probabilities are compared to those from simulations using full (6D) PESs and n-mode PESs from previous work. The results are encouraging, and suggest that this method may be applicable to "late barrier" reactive systems for which the previously-used n-mode representation fails.

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.

Dialkynyl carbene derivatives: generation and characterization of triplet tert-butylpentadiynylidene (t-Bu-C≡C-C̈-C≡C-H) and dimethylpentadiynylidene (Me-C≡C-C̈-C≡C-Me).

Triplet carbenes t-butylpentadiynylidene (t-BuC(5)H, 1a) and dimethylpentadiynylidene (MeC(5)Me, 1b) have been produced photochemically from their corresponding diazo compound precursors and studied spectroscopically in cryogenic matrices (N(2) or Ar) at 10 K. The infrared, electronic absorption, and electron paramagnetic resonance spectra of these species exhibit numerous similarities to the spectra of pentadiynylidene (HC(5)H) and methylpentadiynylidene (MeC(5)H) recorded previously. EPR spectra yield zero-field splitting parameters that are typical for triplet carbenes with axial symmetry (t-BuC(5)H, 1a: |D/hc| = 0.61 cm(-1), |E/hc| ∼ 0 cm(-1); MeC(5)Me, 1b: |D/hc| = 0.62 cm(-1), |E/hc| ∼ 0 cm(-1)). Electronic spectra are characterized by weak absorptions (T(1) ← T(0)) in the near-UV and visible region (350-430 nm) with extended vibronic progressions. The electronic transitions of several -C(5)- carbenes are compared, and an apparent dependence of the transition wavelength on the level of alkyl substitution of the carbon chain is found. Chemical trapping of triplet 1a in an O(2)-doped matrix affords carbonyl oxides derived predominantly from attack at C-3. Both t-BuC(5)H (1a) and MeC(5)Me (1b) undergo photochemical rearrangement upon UV irradiation.

The A-X absorption of vinoxy radical revisited: normal and Herzberg-Teller bands observed via cavity ringdown spectroscopy.

The A-X electronic absorption spectrum of vinoxy radical has been investigated using room temperature cavity ringdown spectroscopy. Analysis of the observed bands on the basis of computed vibrational frequencies and rotational envelopes reveals that two distinct types of features are present with comparable intensities. The first type corresponds to "normal" allowed electronic transitions to the origin and symmetric vibrations in the A state. The second type is interpreted in terms of excitations to asymmetric A state vibrations, which are only vibronically allowed by Herzberg-Teller coupling to the B state. Results of electronic structure calculations indicate that the magnitude of the Herzberg-Teller coupling is appropriate to produce vibronically induced transitions with intensities comparable to those of the normal bands.

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.

Spectroscopy and photochemistry of triplet methylpentadiynylidene (Me-C[triple bond]C-:C-C[triple bond]C-H).

Triplet carbene methylpentadiynylidene, MeC(5)H (1), was investigated in cryogenic matrices by IR, UV/vis, and EPR spectroscopy. Broadband irradiation (lambda > 497 nm) of the isomeric diazo compounds, 1-diazo-hexa-2,4-diyne (2) or 2-diazo-hexa-3,5-diyne (3), generates triplet carbene 1. EPR spectra yield zero-field splitting parameters (|D/hc| = 0.62 cm(-1), |E/hc| < 0.0006 cm(-1)), which are typical for a triplet carbene with axial symmetry. The electronic spectrum of triplet 1 is characterized by a weak absorption in the near-UV and visible region (350-430 nm) with vibronic progressions corresponding to excitations of the acetylenic stretching and the terminal C[triple bond]C-H bending modes. Chemical trapping of triplet 1 in an O(2)-doped matrix affords carbonyl oxides derived predominantly from attack at C-3. Upon irradiation at lambda > 399 nm, triplet 1 undergoes photochemical 1,2-hydrogen migration to form hex-1-ene-3,5-diyne (6).

Reactive carbon-chain molecules: synthesis of 1-diazo-2,4-pentadiyne and spectroscopic characterization of triplet pentadiynylidene (H-C[triple bond]C-:C-C[triple bond]C-H).

1-Diazo-2,4-pentadiyne (6a), along with both monodeuterio isotopomers 6b and 6c, has been synthesized via a route that proceeds through diacetylene, 2,4-pentadiynal, and 2,4-pentadiynal tosylhydrazone. Photolysis of diazo compounds 6a-c (lambda > 444 nm; Ar or N2, 10 K) generates triplet carbenes HC5H (1) and HC5D (1-d), which have been characterized by IR, EPR, and UV/vis spectroscopy. Although many resonance structures contribute to the resonance hybrid for this highly unsaturated carbon-chain molecule, experiment and theory reveal that the structure is best depicted in terms of the dominant resonance contributor of penta-1,4-diyn-3-ylidene (diethynylcarbene, H-C[triple bond]C-:C-C[triple bond]C-H). Theory predicts an axially symmetric (D(infinity h)) structure and a triplet electronic ground state for 1 (CCSD(T)/ANO). Experimental IR frequencies and isotope shifts are in good agreement with computed values. The triplet EPR spectrum of 1 (absolute value(D/hc) = 0.6157 cm(-1), absolute value(E/hc) = 0.0006 cm(-1)) is consistent with an axially symmetric structure, and the Curie law behavior confirms that the triplet state is the ground state. The electronic absorption spectrum of 1 exhibits a weak transition near 400 nm with extensive vibronic coupling. Chemical trapping of triplet HC5H (1) in an O2-doped matrix affords the carbonyl oxide 16 derived exclusively from attack at the central carbon.