@article{kwon_curtin_morrow_kelley_jakubikova_2023, title={Adaptive basis sets for practical quantum computing}, volume={4}, ISSN={["1097-461X"]}, url={https://doi.org/10.1002/qua.27123}, DOI={10.1002/qua.27123}, abstractNote={AbstractElectronic structure calculations on small systems such as H2, H2O, LiH, and BeH2 with chemical accuracy are still a challenge for the current generation of noisy intermediate‐scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allows one to keep the number of qubits employed in the calculations at a minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provides an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H2 molecule, in which exponents and contraction coefficients depend on the HH distance, and apply it to the generation of H2 potential energy surface on IBM‐Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double‐zeta basis sets, thus allowing one to perform double‐zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner.}, journal={INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY}, author={Kwon, Hyuk-Yong and Curtin, Gregory M. M. and Morrow, Zachary and Kelley, C. T. and Jakubikova, Elena}, year={2023}, month={Apr} }
@article{morrow_kwon_kelley_jakubikova_2021, title={Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation}, volume={17}, ISSN={["1549-9626"]}, url={https://doi.org/10.1021/acs.jctc.1c00569}, DOI={10.1021/acs.jctc.1c00569}, abstractNote={The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in modern chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as stable conformers (local minima) and transition states (first-order saddle points) connected by a minimum-energy path. Our group has previously produced surrogate reduced-dimensional PESs using sparse interpolation along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. These surrogates used a single interpolation basis, either polynomials or trigonometric functions, in every dimension. However, relevant molecular dynamics (MD) simulations often involve some combination of both periodic and nonperiodic coordinates. Using a trigonometric basis on nonperiodic coordinates, such as bond lengths, leads to inaccuracies near the domain boundary. Conversely, polynomial interpolation on the periodic coordinates does not enforce the periodicity of the surrogate PES gradient, leading to nonconservation of total energy even in a microcanonical ensemble. In this work, we present an interpolation method that uses trigonometric interpolation on the periodic reaction coordinates and polynomial interpolation on the nonperiodic coordinates. We apply this method to MD simulations of possible isomerization pathways of azomethane between cis and trans conformers. This method is the only known interpolative method that appropriately conserves total energy in systems with both periodic and nonperiodic reaction coordinates. In addition, compared to all-polynomial interpolation, the mixed basis requires fewer electronic structure calculations to obtain a given level of accuracy, is an order of magnitude faster, and is freely available on GitHub.}, number={9}, journal={JOURNAL OF CHEMICAL THEORY AND COMPUTATION}, publisher={American Chemical Society (ACS)}, author={Morrow, Zachary and Kwon, Hyuk-Yong and Kelley, C. T. and Jakubikova, Elena}, year={2021}, month={Sep}, pages={5673–5683} }
@article{kwon_morrow_kelley_jakubikova_2021, title={Interpolation Methods for Molecular Potential Energy Surface Construction}, volume={125}, ISSN={["1520-5215"]}, url={https://doi.org/10.1021/acs.jpca.1c06812}, DOI={10.1021/acs.jpca.1c06812}, abstractNote={The concept of a potential energy surface (PES) is one of the most important concepts in modern chemistry. A PES represents the relationship between the chemical system's energy and its geometry (i.e., atom positions) and can provide useful information about the system's chemical properties and reactivity. Construction of accurate PESs with high-level theoretical methodologies, such as density functional theory, is still challenging due to a steep increase in the computational cost with the increase of the system size. Thus, over the past few decades, many different mathematical approaches have been applied to the problem of the cost-efficient PES construction. This article serves as a short overview of interpolative methods for the PES construction, including global polynomial interpolation, trigonometric interpolation, modified Shepard interpolation, interpolative moving least-squares, and the automated PES construction derived from these.}, number={45}, journal={JOURNAL OF PHYSICAL CHEMISTRY A}, publisher={American Chemical Society (ACS)}, author={Kwon, Hyuk-Yong and Morrow, Zachary and Kelley, C. T. and Jakubikova, Elena}, year={2021}, month={Nov}, pages={9725–9735} }
@article{morrow_kwon_kelley_jakubikova_2021, title={Reduced-dimensional surface hopping with offline-online computations}, volume={8}, ISSN={["1463-9084"]}, url={https://doi.org/10.1039/D1CP03446D}, DOI={10.1039/D1CP03446D}, abstractNote={We simulate the photodissociation of azomethane with a fewest-switches surface hopping method on reduced-dimensional potential energy surfaces constructed with sparse grid interpolation.}, journal={PHYSICAL CHEMISTRY CHEMICAL PHYSICS}, publisher={Royal Society of Chemistry (RSC)}, author={Morrow, Zachary and Kwon, Hyuk-Yong and Kelley, C. T. and Jakubikova, Elena}, year={2021}, month={Aug} }
@article{morrow_stoyanov_2020, title={A METHOD FOR DIMENSIONALLY ADAPTIVE SPARSE TRIGONOMETRIC INTERPOLATION OF PERIODIC FUNCTIONS}, volume={42}, ISSN={["1095-7197"]}, url={https://doi.org/10.1137/19M1283483}, DOI={10.1137/19M1283483}, abstractNote={We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical "best" convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.}, number={4}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Morrow, Zachary and Stoyanov, Miroslav}, year={2020}, pages={A2436–A2460} }
@article{morrow_liu_kelley_jakubikova_2019, title={Approximating Periodic Potential Energy Surfaces with Sparse Trigonometric Interpolation}, volume={123}, ISSN={1520-6106 1520-5207}, url={http://dx.doi.org/10.1021/acs.jpcb.9b08210}, DOI={10.1021/acs.jpcb.9b08210}, abstractNote={The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in computational chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as local minima, maxima, and transition states. Construction of full-dimensional PESs for molecules with more than ten atoms is computationally expensive and often not feasible. Previous work in our group used sparse interpolation with polynomial basis functions to construct a surrogate reduced-dimensional PESs along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. However, polynomial interpolation does not preserve the periodicity of the PES gradient with respect to angular components of geometry, such as torsion angles, which can lead to nonphysical phenomena. In this work, we construct a surrogate PES using trigonometric basis functions, for a system where the selected reaction coordinates all correspond to the torsion angles, resulting in a periodically repeating PES. We find that a trigonometric interpolation basis not only guarantees periodicity of the gradient, but also results in slightly lower approximation error than polynomial interpolation.}, number={45}, journal={The Journal of Physical Chemistry B}, publisher={American Chemical Society (ACS)}, author={Morrow, Zack and Liu, Chang and Kelley, C. T. and Jakubikova, Elena}, year={2019}, month={Oct}, pages={9677–9684} }