Department of Chemistry Faculty Publications
http://hdl.handle.net/1974/14051
2018-01-16T13:04:50ZThe vibration-rotation-tunneling levels of N2–H2O and N2–D2O
http://hdl.handle.net/1974/23827
The vibration-rotation-tunneling levels of N2–H2O and N2–D2O
Wang, Xiao-Gang; Carrington, Tucker
In this paper, we report vibration-rotation-tunneling levels of the van der Waals clusters N2–H2O and
N2–D2O computed from an ab initio potential energy surface. The only dynamical approximation
is that the monomers are rigid. We use a symmetry adapted Lanczos algorithm and an uncoupled
product basis set. The pattern of the cluster’s levels is complicated by splittings caused by H–H
exchange tunneling (larger splitting) and N–N exchange tunneling (smaller splitting). An interesting
result that emerges from our calculation is that whereas in N2–H2O, the symmetric H–H tunnelling
state is below the anti-symmetric H–H tunnelling state for both K = 0 and K = 1, the order is reversed
in N2–D2O for K = 1. The only experimental splitting measurements are the D–D exchange tunneling
splittings reported by Zhu et al. [J. Chem. Phys. 139, 214309 (2013)] for N2–D2O in the v2 = 1
region of D2O. Due to the inverted order of the split levels, they measure the sum of the K = 0 and
K = 1 tunneling splittings, which is in excellent agreement with our calculated result. Other splittings
we predict, in particular those of N2–H2O, may guide future experiments.
2015-03-30T00:00:00ZUsing an Expanding Nondirect Product Harmonic Basis with an Iterative Eigensolver to compute Vibrational Energy Levels with as Many as Seven Atoms
http://hdl.handle.net/1974/23826
Using an Expanding Nondirect Product Harmonic Basis with an Iterative Eigensolver to compute Vibrational Energy Levels with as Many as Seven Atoms
Brown, James
We demonstrate that it is possible to use a variational method to compute 50 vibrational levels of
ethylene oxide (a seven-atom molecule) with convergence errors less than 0.01 cm−1. This is done by
beginning with a small basis and expanding it to include product basis functions that are deemed to be
important. For ethylene oxide a basis with fewer than 3 × 106 functions is large enough. Because the
resulting basis has no exploitable structure we use a mapping to evaluate the matrix-vector products
required to use an iterative eigensolver. The expanded basis is compared to bases obtained from
pre-determined pruning condition. Similar calculations are presented for molecules with 3, 4, 5,
and 6 atoms. For the 6-atom molecule, CH3CH, the required expanded basis has about 106 000
functions and is about an order of magnitude smaller than bases made with a pre-determined pruning
condition.
2016-08-16T00:00:00ZVibrational Spectra of Halide-Water Dimers: Insights on Ion Hydration from Full-Dimensional Quantum Calculations on Many-Body Potential Energy Surfaces
http://hdl.handle.net/1974/23816
Vibrational Spectra of Halide-Water Dimers: Insights on Ion Hydration from Full-Dimensional Quantum Calculations on Many-Body Potential Energy Surfaces
Wang, Xiao-Gang; Carrington, Tucker; Bajaj, Pushp; Paesani, Francesco
Full-dimensional vibrational spectra are calculated for both X (H2O) and X (D2O) dimers (X = F, Cl,
Br, I) at the quantum-mechanical level. The calculations are carried out on two sets of recently developed
potential energy functions (PEFs), namely, Thole-type model energy (TTM-nrg) and many-body
energy (MB-nrg), using the symmetry-adapted Lanczos algorithm with a product basis set including
all six vibrational coordinates. Although both TTM-nrg and MB-nrg PEFs are derived from
coupled-cluster single double triple-F12 data obtained in the complete basis set limit, they differ
in how many-body effects are represented at short range. Specifically, while both models describe
long-range interactions through the combination of two-body dispersion and many-body classical electrostatics,
the relatively simple Born-Mayer functions employed in the TTM-nrg PEFs to represent
short-range interactions are replaced in the MB-nrg PEFs by permutationally invariant polynomials
to achieve chemical accuracy. For all dimers, the MB-nrg vibrational spectra are in close agreement
with the available experimental data, correctly reproducing anharmonic and nuclear quantum
effects. In contrast, the vibrational frequencies calculated with the TTM-nrg PEFs exhibit significant
deviations from the experimental values. The comparison between the TTM-nrg and MB-nrg results
thus reinforces the notion that an accurate representation of both short-range interactions associated
with electron density overlap and long-range many-body electrostatic interactions is necessary for
a correct description of hydration phenomena at the molecular level.
2017-12-30T00:00:00ZComputing Vibrational Energy Levels of CH4 With a Smolyak Collocation Method
http://hdl.handle.net/1974/23806
Computing Vibrational Energy Levels of CH4 With a Smolyak Collocation Method
Avila, Gustavo; Carrington, Tucker
In this paper, we demonstrate that it is possible to apply collocation to compute vibrational energy levels of a five-atom molecule using an exact kinetic energy operator (with cross terms and coordinate-dependent coefficients). This is made possible by using (1) a pruned basis of products of univariate functions; (2) a Smolyak grid made from nested sequences of grids for each coordinate; (3) a collocation method that obviates the need to solve a generalized eigenvalue problem; (4) an efficient sequential transformation between the (nondirect product) grid and the (nondirect product) basis representations; and (5) hierarchical univariate functions that make it possible to avoid storing large intermediate vectors. The accuracy of the method is confirmed by computing 500 vibrational energy levels of methane.
2017-12-30T00:00:00Z