Department of Chemistry Faculty Publicationshttp://hdl.handle.net/1974/140512018-05-26T18:07:46Z2018-05-26T18:07:46ZUsing Multi-Dimensional Smolyak Interpolation to Make a Sum-of-Products-PotentialAvila, GustavoCarrington, Tuckerhttp://hdl.handle.net/1974/238312018-01-17T08:21:01Z2015-07-27T00:00:00ZUsing Multi-Dimensional Smolyak Interpolation to Make a Sum-of-Products-Potential
Avila, Gustavo; Carrington, Tucker
We propose a new method for obtaining potential energy surfaces in sum-of-products (SOP) form.
If the number of terms is small enough, a SOP potential surface significantly reduces the cost
of quantum dynamics calculations by obviating the need to do multidimensional integrals by
quadrature. The method is based on a Smolyak interpolation technique and uses polynomial-like
or spectral basis functions and 1D Lagrange-type functions. When written in terms of the basis
functions from which the Lagrange-type functions are built, the Smolyak interpolant has only a
modest number of terms. The ideas are tested for HONO (nitrous acid).
2015-07-27T00:00:00ZA Multi-Dimensional Smolyak Collocation Method in Curvilinear Coordinates for Computing Vibrational SpectraAvila, GustavoCarrington, Tuckerhttp://hdl.handle.net/1974/238302018-01-17T08:20:59Z2015-12-02T00:00:00ZA Multi-Dimensional Smolyak Collocation Method in Curvilinear Coordinates for Computing Vibrational Spectra
Avila, Gustavo; Carrington, Tucker
In this paper, we improve the collocation method for computing vibrational spectra that was
presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative
eigensolver, energy levels and wavefunctions are determined from values of the potential on a
Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector
labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis
indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably.
Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate
integrals of coordinate dependent coefficients of differential operators. The ideas are tested by
computing energy levels of HONO using a KEO in bond coordinates
2015-12-02T00:00:00ZThe He2 - OCS complex: comparison between theory andOliaee, J. NoroozMoazzen-Ahmadi, N.McKellar, A.R.W.Wang, Xiao-GangCarrington, Tuckerhttp://hdl.handle.net/1974/238292018-01-17T08:20:55Z2017-10-31T00:00:00ZThe He2 - OCS complex: comparison between theory and
Oliaee, J. Norooz; Moazzen-Ahmadi, N.; McKellar, A.R.W.; Wang, Xiao-Gang; Carrington, Tucker
OCS is an ideal probe for quantum solvation effects in cold helium clusters. He2-OCS is
the “second step” in going from a single OCS molecule to a large doped superfluid helium
cluster. Here assignment of the spectrum of He2-OCS is significantly extended to higher values
of J, K, and vt (the low frequency torsional vibration). The observation of a new infrared band,
OCS n1 + n3, taken together with the known n1 band, enables assignments to be verified by
comparing ground state combination differences. Relatively straightforward scaling of
previously calculated theoretical energy levels gives a remarkably good fit to experiment.
2017-10-31T00:00:00ZThe Vibration-Rotation-Tunneling Levels of N2–H2O and N2–D2OWang, Xiao-GangCarrington, Tuckerhttp://hdl.handle.net/1974/238272018-01-17T14:14:58Z2015-03-30T00:00:00ZThe 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.
2015-03-30T00:00:00Z