Investigating Intermolecular Interactions in Crystalline Aspirin Using CDFT

Drugs today are widely administered in their crystalline form, namely via tablets and capsules. The crystal structure of a drug molecule affects important drug qualities such as solubility, bioavailability, shelf life, and compaction properties. In order to form a basis for crystal structure prediction, it is necessary to first understand how intermolecular interactions cause molecules to pack in certain ways. Being able to predict and perhaps even control a drug molecule’s crystal structure will lead to the development of higher quality drugs that perform more consistently. Scientists and engineers do not fully understand the reasons for a molecule assuming a certain crystal structure. Current methods show that many energetically favorable conformations of a specific molecule are possible, but only a small handful of those are actually observed. Aspirin forms I and II were used as the drug molecules of choice for this study. Employing conceptual density functional theory allowed for the calculation of energy, as well as Fukui functions based on charge densities. CRYSTAL09 was used to optimize coordinates and to conduct single point calculations for neutral and charged aspirin for both the crystal and single molecules. Contacts between molecules were found using Mercury and OpenDX. Mapping charge density, Fukui functions, and electrostatic potential were mapped on a molecule’s Hirshfeld surface allowed for the visualization of interactions between molecules in a crystal cell. This was achieved using IBM’s OpenDX. Future work will involve calculating the energies of individual interactions in order to determine how influential they are on crystal structure

Investigation of Major Intermolecular Interactions in 7,8-dihydrobenzo(k)phenanthridin-6(5H)-one Crystal Using Quantum Calculations and Crystallographic Visualization Programs

Currently, tablets and capsules are the most common ways of delivering drugs. The active pharmaceutical ingredients and excipients used to make those tablets and capsules are in their crystalline form generally. However, a single molecule can form multiple different crystal structures because of different packing arrangements of the molecules. These different crystal structures have identical chemical composition but different properties such as solubility, density, stability, etc. This phenomenon is called polymorphism. Occurrence of polymorphism could be a disaster for both patients and pharmaceutical companies, as the drug could lose its efficacy due to changes in properties. Studying intermolecular interactions in crystals can give us a better understanding of how and why molecules pack together in a certain way. In this research, 7,8-dihydrobenzo(k)phenanthridin-6(5H)-one is the molecule investigated. Its crystal data files were obtained from the Cambridge Crystallographic Data Centre. A crystallographic visualization program called Mercury was used to observe all contact modes and measure distances between atoms. Quantum calculations were performed using Density Functional Theory. Then, Fukui functions and electrostatic potentials for both the crystal and the molecule were calculated. These properties were mapped on the molecule’s Hirshfeld surface and on molecular slices using OpenDX software to help visualize intermolecular interactions. Comparison between crystals and molecules was performed to observe how these properties change when molecules form crystals. These mapped properties were helpful to analyze major intermolecular interactions, but further analysis on other compounds is needed in order to fully explain molecular packing in crystals and predict crystal structures

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms. In this paper, we propose a novel neural-ODE based method that uses spectral expansions in space to learn spatiotemporal DEs. The major advantage of our spectral neural DE learning approach is that it does not rely on spatial discretization, thus allowing the target spatiotemporal equations to contain long range, nonlocal spatial interactions that act on unbounded spatial domains. Our spectral approach is shown to be as accurate as some of the latest machine learning approaches for learning PDEs operating on bounded domains. By developing a spectral framework for learning both PDEs and integro-differential equations, we extend machine learning methods to apply to unbounded DEs and a larger class of problems.Comment: 21 pages, 5 figure

The asymptotic concentration approach combined with isogeometric analysis for topology optimization of two-dimensional linear elasticity structures

We propose an asymptotic concentration approach combined with isogeometric analysis (IGA) for the topology optimization of two-dimensional (2D) linear elasticity structures under the commonly-used framework of the solid isotropic materials and penalty (SIMP) model. Based on the SIMP framework, the B-splines are used as basis functions to describe geometric model in structural finite element analysis, which closely combines geometric modeling with structural analysis. Isogeometric analysis is utilized to define the geometric characteristics of the 2D linear elasticity structures, which can greatly improve the calculation accuracy. In addition, to eliminate the gray-scale intervals usually caused by the intermediate density in the SIMP approach, we utilize the asymptotic concentration method to concentrate the intermediate density values on either 0 or 1 gradually. Consequently, the intermediate densities representing gray-scale intervals in topology optimization results are sufficiently eliminated by virtue of the asymptotic concentration method. The effectiveness and applicability of the proposed method are illustrated by several typical examples