On the Helly Number for Hyperplane Transversals to Unit Balls

We prove two results about the Hadwiger problem of finding the Helly number for line transversals of disjoint unit disks in the plane, and about its higher-dimensional generalization to hyperplane transversals of unit balls in d -dimensional Euclidean space. These consist of (a) a proof of the fact that the Helly number remains 5 even for arbitrarily large sets of disjoint unit disks—thus correcting a 40-year-old error; and (b) a lower bound of d+3 on the Helly number for hyperplane transversals to suitably separated families of unit balls in R ^d . Received January 25, 1999, and in revised form July 7, 1999.     

MolE8: finding DFT potential energy surface minima values from force-field optimised organic molecules with new machine learning representations

The use of machine learning techniques in computational chemistry has gained significant momentum since large molecular databases are now readily available. Predictions of molecular properties using machine learning have advantages over the traditional quantum mechanics calculations because they can be cheaper computationally without losing the accuracy. We present a new extrapolatable and explainable molecular representation based on bonds, angles and dihedrals that can be used to train machine learning models. The trained models can accurately predict the electronic energy and the free energy of small organic molecules with atom types C, H N and O, with a mean absolute error of 1.2 kcal mol⁻¹. The models can be extrapolated to larger organic molecules with an average error of less than 3.7 kcal mol⁻¹ for 10 or fewer heavy atoms, which represent a chemical space two orders of magnitude larger. The rapid energy predictions of multiple molecules, up to 7 times faster than previous ML models of similar accuracy, has been achieved by sampling geometries around the potential energy surface minima. Therefore, the input geometries do not have to be located precisely on the minima and we show that accurate density functional theory energy predictions can be made from force-field optimised geometries with a mean absolute error 2.5 kcal mol⁻¹.

New representations and machine learning calculate DFT minima from force field geometries.     

DP4-AI automated NMR data analysis: straight from spectrometer to structure

A robust system for automatic processing and assignment of raw ¹³C and ¹H NMR data DP4-AI has been developed and integrated into our computational organic molecule structure elucidation workflow. Starting from a molecular structure with undefined stereochemistry or other structural uncertainty, this system allows for completely automated structure elucidation. Methods for NMR peak picking using objective model selection and algorithms for matching the calculated ¹³C and ¹H NMR shifts to peaks in noisy experimental NMR data were developed. DP4-AI achieved a 60-fold increase in processing speed, and near-elimination of the need for scientist time, when rigorously evaluated using a challenging test set of molecules. DP4-AI represents a leap forward in NMR structure elucidation and a step-change in the functionality of DP4. It enables high-throughput analyses of databases and large sets of molecules, which were previously impossible, and paves the way for the discovery of new structural information through machine learning. This new functionality has been coupled with an intuitive GUI and is available as open-source software at https://github.com/KristapsE/DP4-AI.

A robust system for automatic processing and assignment of raw ¹³C and ¹H NMR data DP4-AI has been developed and integrated into our computational organic molecule structure elucidation workflow.     

Atmospheric reactions of chloroethenes with the OH radical

The kinetics and products of the homogeneous gas-phase reactions of the OH radical with the chloroethenes were investigated at 298 ± 2 K and atmospheric pressure. Using a relative rate technique and ethane as a scavenger for the chlorine atoms produced in these OH radical reactions, rate constants (in units of 10^?12 cm³ molecule^?1s^?1) of 8.11 ± 0.24, 2.38 ± 0.14, and 1.80 ± 0.03 were obtained for 1,1-dichloroethene, cis-1, 2-dichloroethene and trans-1,2-dichloroethene, respectively. Under these conditions, the major products observed by long pathlength FT-IR absorption spectroscopy were HCHO and HC(O)Cl from vinyl chloride; HC(O)Cl from cis- and trans-1,2-dichloroethene; HCHO and COCl₂ from 1,1-dichloroethene; HC(O)Cl and COCl₂ from trichloroethene; and COCl₂ from tetrachloroethene. In the absence of a Cl atom scavenger, significant yields of the chloroacetyl chlorides, CH_xCl_3?xC(O)Cl, were observed from 1,1-dichloro-, trichloro- and tetrachloroethene, indicating that these products resulted from reactions involving chlorine atoms. The yields of all of these products are reported and the mechanisms of these gas-phase reactions discussed. In addition, OH radical reaction rate constants were redetermined, in the presence of a Cl atom scavenger, for cis- and trans-1,3-dichloropropene and 3-chloro-2-chloromethyl-1-propene, being (in units of 10^?12 cm³ molecule^?1 s^?1) 8.45 ± 0.41, 14.4 ± 0.8, and 33.5 ± 3.0, respectively.     

Modifying a branched surface to carry a foliation

We consider C¹ nonsingular flows on a closed 3-manifold under which there is no transverse disk that flows continuously back into its own interior. We provide an algorithm for modifying any branched surface transverse to such a flow ? that terminates in a branched surface carrying a foliation F precisely when F is transverse to ?. As a corollary, we find branched surfaces that do not carry foliations but that lift to ones that do.     

The contribution of quantum mechanical tunneling to the 1,2-hydrogen rearrangement of methylbromocarbene

The rate constants for the 1,2-hydrogen rearrangement of methyl- and methyl-d₃-bromocarbene have been determined as a function of temperature. The Arrhenius plots are curved, and the intermolecular isotope effect is small and may increase with increasing temperature. We believe that although the rearrangement proceeds classically at high temperatures, as suggested by theory, quantum mechanical tunneling contributes significantly to the reaction at low temperatures. Alternative explanations are presented and discussed.     

ESR study of some asymmetric-triazine copper(II) complexes having high antiviral activity

Electron paramagnetic resonance (EPR) spectroscopy and molecular dynamics calculations have been used to compare the chemical environments of Cu(II) in three substituted asymmetric-triazine (as-triazine) complexes with a closely related complex that was reported previously to have Superoxide dismutase (SOD) and antiviral activities. The structure most strongly associated with the biological activity appears to be planar with two 6-membered chelate rings having 2N2O coordination around the copper atom.     

A generalization of the variation diminishing property

For totally positive matrices, a new variation diminishing property on the sign of consecutive minors is obtained. this property is used to show shape preserving properties of curves generated by totally positive bases and, in particular, of B-spline curves. Partially supported by DGICYT PS93-0310.     

Clustering behavior of finite variance partial sum processes

Summary Clustering rates in Strassen's functional law of the iterated logarithm are determined for finite variance partial sum processes in one dimension. A general characterization of these rates, similar to one recently obtained for onedimensional Brownian motion, shows that relatively mild moment conditions on a partial sum process lead to high order clustering rates at certain points of the Strassen set.Supported in part by NSF Grant DMS-92-07248     

Adsorption of CO on a pseudomorphic palladium monolayer on Mo(110)

Adsorption of CO on a Pd monolayer (ML) supported on Mo(110) has been studied using low energy electron diffraction (LEED), temperature programmed desorption (TPD), and high resolution electron energy loss spectroscopy (HREELS). Three ordered CO substructures denoted as are observed with LEED. The binding energy of C0 on the 1.0 ML Pd/Mo(110) surface is reduced by 12 kcal/mol relative to the Pd(111) surface, consistent with previous results for supported palladium monolayers on other substrates. Two vibrational states of C0 are observed near 1950 and 2050 cm⁻¹, with the feature at the lower wavenumber having the smaller binding energy.