Direct variational calculations where the Born-Oppenheimer approximation is not assumed are done for all rovibrational states of the D2 molecule corresponding to first excited rotational level (the N = 1 states). All-particle explicitly correlated Gaussian basis functions are used in the calculations. The exponential parameters of the Gaussians are optimized with the aid of analytically calculated energy gradient determined with respect to these parameters. The results allow to determine the ortho-para spin isomerization energies as a function of the vibrational quantum number.
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http://dx.doi.org/10.1063/1.4919417 | DOI Listing |
Genetic prediction of complex traits, enabled by large-scale genomic studies, has created new measures to understand individual genetic predisposition. Polygenic Risk Scores (PRS) offer a way to aggregate information across the genome, enabling personalized risk prediction for complex traits and diseases. However, conventional PRS calculation methods that rely on linear models are limited in their ability to capture complex patterns and interaction effects in high-dimensional genomic data.
View Article and Find Full Text PDFJ Chem Theory Comput
January 2025
Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, P.R. China.
Milestoning is an efficient method for calculating rare event kinetics by constructing a continuous-time kinetic network that connects the reactant and product states. Its accuracy depends on both the quality of the underlying force fields and the trajectory sampling. The sampling error can be effectively controlled through various methods.
View Article and Find Full Text PDFJ Chem Phys
January 2025
Microsoft Research AI for Science, 21 Station Road, Cambridge CB1 2FB, United Kingdom.
Variational ab initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows, in principle, straightforward extraction of any other observable of interest, besides the energy, but, in practice, this extraction is often technically difficult and computationally impractical. Here, we consider the electron density as a central observable in quantum chemistry and introduce a novel method to obtain accurate densities from real-space many-electron wave functions by representing the density with a neural network that captures known asymptotic properties and is trained from the wave function by score matching and noise-contrastive estimation.
View Article and Find Full Text PDFMath Program
July 2024
Department of Mathematics and Computer Science, Philipps-Universität Marburg, 35032 Marburg, Germany.
As a starting point of our research, we show that, for a fixed order , each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order 1), satisfies stationarity conditions in terms of a coderivative construction of order , or is asymptotically stationary with respect to a critical direction as well as order in a certain sense. By ruling out the latter case with a constraint qualification not stronger than directional metric subregularity, we end up with new necessary optimality conditions comprising a mixture of limiting variational tools of orders 1 and . These abstract findings are carved out for the broad class of geometric constraints and , and visualized by examples from complementarity-constrained and nonlinear semidefinite optimization.
View Article and Find Full Text PDFJ Chem Phys
January 2025
Theoretical and Computational Physics Section, Raja Ramanna Centre for Advanced Technology, Indore 452013, India.
The orbital-free density functional theory (OF-DFT) based method is a convenient tool to carry out electronic structure calculations scaling almost linearly with the number of electrons. However, the main impediment in the application of this method is the unavailability of the accurate form for the non-interacting kinetic energy functional in terms of electron density. The Pauli kinetic energy functional is the unknown part of the kinetic energy functional, and the corresponding Pauli potential appears in the governing Euler equation.
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