@article{nance_kelley_2015, title={A Sparse Interpolation Algorithm for Dynamical Simulations in Computational Chemistry}, volume={37}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/140965284}, DOI={10.1137/140965284}, abstractNote={In this paper we present a new implementation of Smolyak's sparse grid interpolation algorithm designed for dynamical simulations. The implementation is motivated by an application to quantum chemistry where the goal is to simulate photo-induced molecular transformations. A molecule conforms to a geometry that minimizes its potential energy, and many molecules have multiple potential energy minima. These geometries correspond to local minima of the molecule's potential energy surface, and one can simulate how a molecule transitions from one geometry to another by following the steepest descent path, or reaction path, on potential energy surfaces. Molecular vibrations and thermal fluctuations cause randomness in dynamics, so one must follow several paths simultaneously to more accurately simulate possible reaction paths. Current algorithms for reaction path following are too computationally burdensome for molecules of moderate size, but Smolyak's interpolation algorithm offers a cheap surrogate for potenti...}, number={5}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Nance, J. and Kelley, C. T.}, year={2015}, month={Jan}, pages={S137–S156} }
 @article{nance_bowman_mukherjee_kelley_jakubikova_2015, title={Insights into the Spin-State Transitions in [Fe(tpy)2]2+: Importance of the Terpyridine Rocking Motion}, volume={54}, ISSN={0020-1669 1520-510X}, url={http://dx.doi.org/10.1021/acs.inorgchem.5b01747}, DOI={10.1021/acs.inorgchem.5b01747}, abstractNote={Iron(II) polypyridine complexes have the potential for numerous applications on a global scale, such as sensitizers, sensors, and molecular memory. The excited-state properties of these systems, particularly the intersystem crossing (ISC) rates, are sensitive to the choice of ligands and can be significantly altered depending on the coordination environment. We employ density functional theory and Smolyak's sparse grid interpolation algorithm to construct potential energy surfaces (PESs) for the photophysically relevant states ((1)A, (3,5)MC, and (1,3)MLCT) of the [Fe(tpy)2](2+) (tpy = 2,2':6',2"-terpyridine) complex, with the goal of obtaining a deeper understanding of the ground- and excited-state electronic structure of this system. The three dimensions that define our adiabatic PESs consist of equatorial and axial metal-ligand bond length distortions and a terpyridine ligand "rocking angle", which has not previously been investigated. The intersection crossing seams and minimum energy crossing points (MECPs) between surfaces are also determined. Overall, we find that the PESs of all electronic excited states investigated are characterized by low-energy valleys along the tpy rocking-angle coordinate. This results in the presence of large low-energy areas around the MECPs on the intersection seams of different electronic states and indicates that inclusion of this third coordinate is crucial for an adequate description of the PESs and surface crossing seams of the [Fe(tpy)2](2+) complex. Finally, we suggest that tuning the energetics of the tpy ligand rocking motion could provide a way to control the ISC process in this complex.}, number={23}, journal={Inorganic Chemistry}, publisher={American Chemical Society (ACS)}, author={Nance, James and Bowman, David N. and Mukherjee, Sriparna and Kelley, C. T. and Jakubikova, Elena}, year={2015}, month={Nov}, pages={11259–11268} }
 @article{nance_jakubikova_kelley_2014, title={Reaction Path Following with Sparse Interpolation}, volume={10}, ISSN={1549-9618 1549-9626}, url={http://dx.doi.org/10.1021/ct5004669}, DOI={10.1021/ct5004669}, abstractNote={Computing the potential energy of an N-atom molecule is an expensive optimization process of 3N - 6 molecular coordinates, so following reaction pathways as a function of all 3N - 6 coordinates is unfeasible for large molecules. In this paper, we present a method that isolates d < 3N - 6 molecular coordinates and continuously follows reaction paths on d-dimensional potential energy surfaces approximated by a Smolyak's sparse grid interpolation algorithm.1 Compared to dense grids, sparse grids efficiently improve the ratio of invested storage and computing time to approximation accuracy and thus allow one to increase the number of coordinates d in molecular reaction path following simulations. Furthermore, evaluation of the interpolant is much less expensive than the evaluation of the actual energy function, so our technique offers a computationally efficient way to simulate reaction paths on ground and excited state potential energy surfaces. To demonstrate the capabilities of our method, we present simulation results for the isomerization of 2-butene with two, three, and six degrees of freedom.}, number={8}, journal={Journal of Chemical Theory and Computation}, publisher={American Chemical Society (ACS)}, author={Nance, James and Jakubikova, Elena and Kelley, C. T.}, year={2014}, month={Jul}, pages={2942–2949} }