Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning

Classical intermolecular potentials typically require an extensive parametrization procedure for any new compound considered. To do away with prior parametrization, we propose a combination of physics-based potentials with machine learning (ML), coined IPML, which is transferable across small neutral organic and biologically-relevant molecules. ML models provide on-the-fly predictions for environment-dependent local atomic properties: electrostatic multipole coefficients (significant error reduction compared to previously reported), the population and decay rate of valence atomic densities, and polarizabilities across conformations and chemical compositions of H, C, N, and O atoms. These parameters enable accurate calculations of intermolecular contributions---electrostatics, charge penetration, repulsion, induction/polarization, and many-body dispersion. Unlike other potentials, this model is transferable in its ability to handle new molecules and conformations without explicit prior parametrization: All local atomic properties are predicted from ML, leaving only eight global parameters---optimized once and for all across compounds. We validate IPML on various gas-phase dimers at and away from equilibrium separation, where we obtain mean absolute errors between 0.4 and 0.7 kcal/mol for several chemically and conformationally diverse datasets representative of non-covalent interactions in biologically-relevant molecules. We further focus on hydrogen-bonded complexes---essential but challenging due to their directional nature---where datasets of DNA base pairs and amino acids yield an extremely encouraging 1.4 kcal/mol error. Finally, and as a first look, we consider IPML in denser systems: water clusters, supramolecular host-guest complexes, and the benzene crystal.Comment: 15 pages, 9 figure

Motion in a Random Force Field

We consider the motion of a particle in a random isotropic force field. Assuming that the force field arises from a Poisson field in $\mathbb{R}^d$, $d \geq 4$, and the initial velocity of the particle is sufficiently large, we describe the asymptotic behavior of the particle

Force field feature extraction for ear biometrics

The overall objective in defining feature space is to reduce the dimensionality of the original pattern space, whilst maintaining discriminatory power for classification. To meet this objective in the context of ear biometrics a new force field transformation treats the image as an array of mutually attracting particles that act as the source of a Gaussian force field. Underlying the force field there is a scalar potential energy field, which in the case of an ear takes the form of a smooth surface that resembles a small mountain with a number of peaks joined by ridges. The peaks correspond to potential energy wells and to extend the analogy the ridges correspond to potential energy channels. Since the transform also turns out to be invertible, and since the surface is otherwise smooth, information theory suggests that much of the information is transferred to these features, thus confirming their efficacy. We previously described how field line feature extraction, using an algorithm similar to gradient descent, exploits the directional properties of the force field to automatically locate these channels and wells, which then form the basis of characteristic ear features. We now show how an analysis of the mechanism of this algorithmic approach leads to a closed analytical description based on the divergence of force direction, which reveals that channels and wells are really manifestations of the same phenomenon. We further show that this new operator, with its own distinct advantages, has a striking similarity to the Marr-Hildreth operator, but with the important difference that it is non-linear. As well as addressing faster implementation, invertibility, and brightness sensitivity, the technique is also validated by performing recognition on a database of ears selected from the XM2VTS face database, and by comparing the results with the more established technique of Principal Components Analysis. This confirms not only that ears do indeed appear to have potential as a biometric, but also that the new approach is well suited to their description, being robust especially in the presence of noise, and having the advantage that the ear does not need to be explicitly extracted from the background

Brownian motion in a non-homogeneous force field and photonic force microscope

The Photonic Force Microscope (PFM) is an opto-mechanical technique based on an optical trap that can be assumed to probe forces in microscopic systems. This technique has been used to measure forces in the range of pico- and femto-Newton, assessing the mechanical properties of biomolecules as well as of other microscopic systems. For a correct use of the PFM, the force field to measure has to be invariable (homogeneous) on the scale of the Brownian motion of the trapped probe. This condition implicates that the force field must be conservative, excluding the possibility of a rotational component. However, there are cases where these assumptions are not fulfilled Here, we show how to improve the PFM technique in order to be able to deal with these cases. We introduce the theory of this enhanced PFM and we propose a concrete analysis workflow to reconstruct the force field from the experimental time-series of the probe position. Furthermore, we experimentally verify some particularly important cases, namely the case of a conservative or rotational force-field

Matter-field theory of the Casimir force

A matter-field theory of the Casimir force is formulated in which the electromagnetic field and collective modes of dielectric media are treated on an equal footing. In our theory, the Casimir force is attributed to zero-point energies of the combined matter-field modes. We analyze why some of the existing theories favor the interpretation of the Casimir force as originating from zero-point energies of the electromagnetic field and others from those of the matter.Comment: 12pages, 1 Postscript figur