Papers by Tucker Carrington
The Journal of Chemical Physics
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The Journal of Physical Chemistry A, 2015
The anharmonic vibrational spectrum of UF6 is computed in full dimensionality directly from ab in... more The anharmonic vibrational spectrum of UF6 is computed in full dimensionality directly from ab initio data, i.e., bypassing the construction of a potential energy surface (PES). The vibrational Schrödinger equation is solved by fitting parameters of an adaptable basis using a modified version of the rectangular collocation algorithm of Manzhos and Carrington ( J. Chem. Phys . 2013 , 139 , 051101 ). The basis functions are products of parametrized Hermite polynomials that impose approximate nodal structure. The Schrödinger equation is solved in normal coordinates. The results show that anharmonicity and coupling do noticeably affect the vibrational transitions, shifting them by several cm(-1). Although UF6 has 15 coordinates, we compute hundreds of levels with fewer than 1000 basis functions and about 50 000 ab initio points. It is the efficiency of the basis that makes it possible to forego a PES.
The Journal of chemical physics, Jan 28, 2015
We propose a new method for obtaining potential energy surfaces in sum-of-products (SOP) form. If... more 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).
The Journal of chemical physics, Jan 28, 2015
Although phase-space localized Gaussians are themselves poor basis functions, they can be used to... more Although phase-space localized Gaussians are themselves poor basis functions, they can be used to effectively contract a discrete variable representation basis [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. 109, 070402 (2012)]. This works despite the fact that elements of the Hamiltonian and overlap matrices labelled by discarded Gaussians are not small. By formulating the matrix problem as a regular (i.e., not a generalized) matrix eigenvalue problem, we show that it is possible to use an iterative eigensolver to compute vibrational energy levels in the Gaussian basis.
Lecture Notes in Computer Science, 2010
ABSTRACT
Journal of the Chemical Society, Faraday Transactions 2, 1988
ABSTRACT
International Journal of Quantum Chemistry, 2014
Development and applications of neural network (NN)-based approaches for representing potential e... more Development and applications of neural network (NN)-based approaches for representing potential energy surfaces (PES) of bound and reactive molecular systems are reviewed. Specifically, it is shown that when the density of ab initio points is low, NNs-based potentials with multibody or multimode structure are advantageous for representing high-dimensional PESs. Importantly, with an appropriate choice of the neuron activation function, PESs in the sum-of-products form are naturally obtained, thus addressing a bottleneck problem in quantum dynamics. The use of NN committees is also analyzed and it is shown that while they are able to reduce the fitting error, the reduction is limited by the nonrandom nature of the fitting error. The approaches described here are expected to be directly applicable in other areas of science and engineering where a functional form needs to be constructed in an unbiased way from sparse data.
Molecular Physics, 2015
ABSTRACT A data-set of nearly 100,000 symmetry unique multi-configurational ab initio points for ... more ABSTRACT A data-set of nearly 100,000 symmetry unique multi-configurational ab initio points for methane were generated at the (AE)-MRCI-F12(Q)/CVQZ-F12 level, including energies beyond 30,000 cm−1 above the minimum and fit into potential energy surfaces (PESs) by several permutation invariant schemes. A multi-expansion interpolative fit combining interpolating moving least squares (IMLS) fitting and permutation invariant polynomials (PIP) was able to fit the complete data-set to a root-mean-square deviation of 1.0 cm−1 and thus was used to benchmark the other fitting methods. The other fitting methods include a single PIP expansion and two neural network (NN) based approaches, one of which combines NN with PIP. Full-dimensional variational vibrational calculations using a contracted-iterative method (and a Lanczos eigensolver) were used to assess the spectroscopic accuracy of the electronic structure method. The results show that the NN-based fitting approaches are able to fit the data-set remarkably accurately with the PIP-NN method producing levels in remarkably close agreement with the PIP-IMLS benchmark. The (AE)-MRCI-F12(Q)/CVQZ-F12 electronic structure method produces vibrational levels of near spectroscopic accuracy and a superb equilibrium geometry. The levels are systematically slightly too high, beginning at ∼ 1-2 cm−1 above the fundamentals and becoming correspondingly higher for overtones. The PES is therefore suitable for small ab initio or empirical corrections and since it is based on a multi-reference method, can be extended to represent dynamically relevant dissociation channels.
The journal of physical chemistry. A, Jan 15, 2013
The spectrum of CO dimer was investigated by solving the rovibrational Schrödinger equation on a ... more The spectrum of CO dimer was investigated by solving the rovibrational Schrödinger equation on a new potential energy surface constructed from coupled-cluster ab initio points. The Schrödinger equation was solved with a Lanczos algorithm. Several 4D (rigid monomer) global ab initio potential energy surfaces (PESs) were made using a previously reported interpolating moving least-squares (IMLS) fitting procedure specialized to describe the interaction of two linear fragments. The potential has two nonpolar minima giving rise to a complicated set of energy level stacks, which are very sensitive to the shapes and relative depths of the two wells. Although the CO dimer has defied previous attempts at an accurate purely ab initio description our best surface yields results in good agreement with experiment. Root-mean-square (rms) fitting errors of less than 0.1 cm(-1) were obtained for each of the fits using 2226 ab initio data at different levels. This allowed direct assessment of the qu...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
We criticize a paper by Vijay and Wyatt [Phys. Rev. E 63, 4351 (2000)], in which the authors sugg... more We criticize a paper by Vijay and Wyatt [Phys. Rev. E 63, 4351 (2000)], in which the authors suggest that energy levels computed, from the same set of matrix-vector products, with the filter diagonalization method (FDM) and the Fourier spectral analysis using the same Chebyshev correlation function are of comparable accuracy. We explain why the FDM is superior and demonstrate it numerically, using the same test matrix as that employed in the above paper. We also compare the FDM with the Lanczos method, another commonly used iterative technique for computing eigenvalues. We find that eigenvalues in a low-density region near the middle of the spectrum converge more quickly with the FDM, but that the Lanczos method requires fewer matrix-vector products to converge all the eigenvalues.
Wiley Interdisciplinary Reviews: Computational Molecular Science, 2011
The Journal of Physical Chemistry A, 2014
Anharmonic vibrational spectroscopy calculations using MP2 and B3LYP computed potential surfaces ... more Anharmonic vibrational spectroscopy calculations using MP2 and B3LYP computed potential surfaces are carried out for a series of molecules, and frequencies and intensities are compared with those from experiment. The vibrational self-consistent field with second-order perturbation correction (VSCF-PT2) is used in computing the spectra. The test calculations have been performed for the molecules HNO 3 , C 2 H 4 , C 2 H 4 O, H 2 SO 4 , CH 3 COOH, glycine, and alanine. Both MP2 and B3LYP give results in good accord with experimental frequencies, though, on the whole, MP2 gives very slightly better agreement. A statistical analysis of deviations in frequencies from experiment is carried out that gives interesting insights. The most probable percentage deviation from experimental frequencies is about −2% (to the red of the experiment) for B3LYP and +2% (to the blue of the experiment) for MP2. There is a higher probability for relatively large percentage deviations when B3LYP is used. The calculated intensities are also found to be in good accord with experiment, but the percentage deviations are much larger than those for frequencies. The results show that both MP2 and B3LYP potentials, used in VSCF-PT2 calculations, account well for anharmonic effects in the spectroscopy of molecules of the types considered.
ABSTRACT Recent experimental studies of vdWs systems including those by Moazzen-Ahmadi and McKell... more ABSTRACT Recent experimental studies of vdWs systems including those by Moazzen-Ahmadi and McKellar,1,2 as well as microwave studies by Minei and Novick3,4 have observed previously unknown stable polar isomers for systems such as (NNO)2 and (OCS)2. The multi-welled floppy nature of the PESs and the small barriers between minima place stringent requirements on the PES for a successful theoretical description of these states. An automated method of generating accurate PESs for vdW systems has been developed and is demonstrated here.5,6 A limited number of ab initio data at the explicitly correlated CCSD(T)-F12b level are interpolated into analytic PESs with negligible fitting error. High-accuracy PESs were developed for a number of systems including (NNO)2, (OCS)2, (CO)2, CO2:CS2 and (NH3)2. Using the PESs, the rovibrational Schrödinger equation is solved with a symmetry-adapted Lanczos algorithm and an uncoupled product basis set. All inter-monomer coordinates are included in the calculations. Calculated transition frequencies are in very close agreement with experiment. References (1) M. Dehghani, M. Afshari, Z. Abusara, N. Moazzen-Ahmadi, A. R. W. McKellar, J. Chem. Phys. 126, 164310 (2007). (2) M. Dehghani, M. Afshari, Z. Abusara, N. Moazzen-Ahmadi, A. R. W. McKellar, J. Chem. Phys. 126, 071102 (2007). (3) N. R. Walker, R. Nicholas, A. J. Minei, S. E. Novick, A. C. Legon, J. Mol. Spec. 251, 153 (2008). (4) A. J. Minei and S. E. Novick, J. Chem. Phys. 126, 101101 (2007). (5) R. Dawes, X.-G. Wang, A. W. Jasper, T. Carrington Jr., J. Chem. Phys. 133, 134304 (2010). (6) X.-G. Wang, T. Carrington Jr., R. Dawes and A. W. Jasper, J. Mol. Spec. 268, 53 (2011).
Handbook of High-resolution Spectroscopy, 2011
ABSTRACT I shall discuss a new method for fitting a potential function (or in fact any function) ... more ABSTRACT I shall discuss a new method for fitting a potential function (or in fact any function) to multidimensional data. The algorithm uses a representation in terms of lower-dimensional component functions of optimized coordinates. It permits dimensionality reduction. Neural networks are used to construct the component functions.
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Papers by Tucker Carrington