Understanding molecular representations in machine learning: The role of uniqueness and target similarity

The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Based on the postulates of quantum mechanics, we introduce a hierarchy of representations which meet uniqueness and target similarity criteria. To systematically control target similarity, we rely on interatomic many body expansions, as implemented in universal force-fields, including Bonding, Angular, and higher order terms (BA). Addition of higher order contributions systematically increases similarity to the true potential energy and predictive accuracy of the resulting ML models. We report numerical evidence for the performance of BAML models trained on molecular properties pre-calculated at electron-correlated and density functional theory level of theory for thousands of small organic molecules. Properties studied include enthalpies and free energies of atomization, heatcapacity, zero-point vibrational energies, dipole-moment, polarizability, HOMO/LUMO energies and gap, ionization potential, electron affinity, and electronic excitations. After training, BAML predicts energies or electronic properties of out-of-sample molecules with unprecedented accuracy and speed

Toward transferable interatomic van der Waals interactions without electrons: The role of multipole electrostatics and many-body dispersion

We estimate polarizabilities of atoms in molecules without electron density, using a Voronoi tesselation approach instead of conventional density partitioning schemes. The resulting atomic dispersion coefficients are calculated, as well as many-body dispersion effects on intermolecular potential energies. We also estimate contributions from multipole electrostatics and compare them to dispersion. We assess the performance of the resulting intermolecular interaction model from dispersion and electrostatics for more than 1,300 neutral and charged, small organic molecular dimers. Applications to water clusters, the benzene crystal, the anti-cancer drug ellipticine---intercalated between two Watson-Crick DNA base pairs, as well as six macro-molecular host-guest complexes highlight the potential of this method and help to identify points of future improvement. The mean absolute error made by the combination of static electrostatics with many-body dispersion reduces at larger distances, while it plateaus for two-body dispersion, in conflict with the common assumption that the simple $1/R^6$ correction will yield proper dissociative tails. Overall, the method achieves an accuracy well within conventional molecular force fields while exhibiting a simple parametrization protocol.Comment: 13 pages, 8 figure

Noncommutative Field Theories and Gravity

We show that after the Seiberg-Witten map is performed the action for noncommutative field theories can be regarded as a coupling to a field dependent gravitational background. This gravitational background depends only on the gauge field. Charged and uncharged fields couple to different backgrounds and we find that uncharged fields couple more strongly than the charged ones. We also show that the background is that of a gravitational plane wave. A massless particle in this background has a velocity which differs from the velocity of light and we find that the deviation is larger in the uncharged case. This shows that noncommutative field theories can be seen as ordinary theories in a gravitational background produced by the gauge field with a charge dependent gravitational coupling.Comment: 8 pages. v2 and v3: minor corrections, added reference

Theoretical Analysis of STM Experiments at Rutile TiO_2 Surfaces

A first-principles atomic orbital-based electronic structure method is used to investigate the low index surfaces of rutile Titanium Dioxide. The method is relatively cheap in computational terms, making it attractive for the study of oxide surfaces, many of which undergo large reconstructions, and may be governed by the presence of Oxygen vacancy defects. Calculated surface charge densities are presented for low-index surfaces of TiO$_2$, and the relation of these results to experimental STM images is discussed. Atomic resolution images at these surfaces tend to be produced at positive bias, probing states which largely consist of unoccupied Ti 3$d$ bands, with a small contribution from O 2$p$. These experiments are particularly interesting since the O atoms tend to sit up to 1 angstrom above the Ti atoms, so providing a play-off between electronic and geometric structure in image formation.Comment: 9 pages, Revtex, 3 postscript figures, accepted by Surf. Scienc

Systematic review of the use of granulocyte-macrophage colony-stimulating factor in patients with advanced melanoma.

Several immunomodulatory checkpoint inhibitors have been approved for the treatment of patients with advanced melanoma, including ipilimumab, nivolumab and pembrolizumab. Talimogene laherparepvec is the first oncolytic virus to gain regulatory approval in the USA; it is also approved in Europe. Talimogene laherparepvec expresses granulocyte-macrophage colony-stimulating factor (GM-CSF), and with other GM-CSF-expressing oncolytic viruses in development, understanding the clinical relevance of this cytokine in treating advanced melanoma is important. Results of trials of GM-CSF in melanoma have been mixed, and while GM-CSF has the potential to promote anti-tumor responses, some preclinical data suggest that GM-CSF may sometimes promote tumor growth. GM-CSF has not been approved as a melanoma treatment. We undertook a systematic literature review of studies of GM-CSF in patients with advanced melanoma (stage IIIB-IV). Of the 503 articles identified, 26 studies met the eligibility criteria. Most studies investigated the use of GM-CSF in combination with another treatment, such as peptide vaccines or chemotherapy, or as an adjuvant to surgery. Some clinical benefit was reported in patients who received GM-CSF as an adjuvant to surgery, or in combination with other treatments. In general, outcomes for patients receiving peptide vaccines were not improved with the addition of GM-CSF. GM-CSF may be a valuable therapeutic adjuvant; however, further studies are needed, particularly head-to-head comparisons, to confirm the optimal dosing regimen and clinical effectiveness in patients with advanced melanoma

Scrambling and Gate Effects in Realistic Quantum Dots

We evaluate the magnitude of two important mesoscopic effects using a realistic model of typical quantum dots. ``Scrambling'' and ``gate effect'' are defined as the change in the single-particle spectrum due to added electrons or gate-induced shape deformation, respectively. These two effects are investigated systematically in both the self-consistent Kohn-Sham (KS) theory and a Fermi liquid-like Strutinsky approach. We find that the genuine scrambling effect is small because the potential here is smooth. In the KS theory, a key point is the implicit inclusion of residual interactions in the spectrum; these dominate and make scrambling appear larger. Finally, the gate effect is comparable in the two cases and, while small, is able to cause gate-induced spin transitions.Comment: 5 pages, 3 figure

Theoretical study of molecular electronic excitations and optical transitions of C60

We report results on ab initio calculations of excited states of the fullerene molecule by using configuration interaction (CI) approach with singly excited determinants (SCI). We have used both the experimental geometry and the one optimized by the density functional method and worked with basis sets at the cc-pVTZ and aug-cc-pVTZ level. Contrary to the early SCI semiempirical calculations, we find that two lowest $^1 T_{1u} \leftarrow {}^1 A_g$ electron optical lines are situated at relatively high energies of ~5.8 eV (214 nm) and ~6.3 eV (197 nm). These two lines originate from two $^1 T_{1u} \leftarrow {}^1 A_g$ transitions: from HOMO to (LUMO+1) ($6h_u \to 3t_{1g}$) and from (HOMO--1) to LUMO ($10h_g \to 7t_{1u}$). The lowest molecular excitation, which is the $1 ^3 T_{2g}$ level, is found at ~2.5 eV. Inclusion of doubly excited determinants (SDCI) leads only to minor corrections to this picture. We discuss possible assignment of absorption bands at energies smaller than 5.8 eV (or $\lambda$ larger than 214 nm).Comment: 6 pages, 1 figure, 9 Table

The noncommutative degenerate electron gas

The quantum dynamics of nonrelativistic single particle systems involving noncommutative coordinates, usually referred to as noncommutative quantum mechanics, has lately been the object of several investigations. In this note we pursue these studies for the case of multi-particle systems. We use as a prototype the degenerate electron gas whose dynamics is well known in the commutative limit. Our central aim here is to understand qualitatively, rather than quantitatively, the main modifications induced by the presence of noncommutative coordinates. We shall first see that the noncommutativity modifies the exchange correlation energy while preserving the electric neutrality of the model. By employing time-independent perturbation theory together with the Seiberg-Witten map we show, afterwards, that the ionization potential is modified by the noncommutativity. It also turns out that the noncommutative parameter acts as a reference temperature. Hence, the noncommutativity lifts the degeneracy of the zero temperature electron gas.Comment: 11 pages, to appear in J. Phys. A: Math. Ge

Main-belt Asteroids in the K2 Uranus Field

We present the K2 light curves of a large sample of untargeted main-belt asteroids (MBAs) detected with the Kepler Space Telescope. The asteroids were observed within the Uranus superstamp, a relatively large, continuous field with a low stellar background designed to cover the planet Uranus and its moons during Campaign 8 of the K2 mission. The superstamp offered the possibility of obtaining precise, uninterrupted light curves of a large number of MBAs and thus determining unambiguous rotation rates for them. We obtained photometry for 608 MBAs, and were able to determine or estimate rotation rates for 90 targets, of which 86 had no known values before. In an additional 16 targets we detected incomplete cycles and/or eclipse-like events. We found the median rotation rate to be significantly longer than that of the ground-based observations, indicating that the latter are biased toward shorter rotation rates. Our study highlights the need and benefits of further continuous photometry of asteroids