Machine Learning Configuration Interaction

We propose the concept of machine learning configuration interaction (MLCI) whereby an artificial neural network is trained on-the-fly to predict important new configurations in an iterative selected configuration interaction procedure. We demonstrate that the neural network can discriminate between important and unimportant configurations, that it has not been trained on, much better than by chance. MLCI is then used to find compact wavefunctions for carbon monoxide at both stretched and equilibrium geometries. We also consider the multireference problem of the water molecule with elongated bonds. Results are contrasted with those from other ways of selecting configurations: first-order perturbation, random selection and Monte Carlo configuration interaction. Compared with these other serial calculations, this prototype MLCI is competitive in its accuracy, converges in significantly fewer iterations than the stochastic approaches, and requires less time for the higher-accuracy computations.Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in The Journal of Chemical Theory and Computation, copyright American Chemical Society after peer review. To access the final edited and published work see https://pubs.acs.org/articlesonrequest/AOR-dANIFXJKzRAyR99E6hb

Exact and LDA entanglement of tailored densities in an interacting one-dimensional electron system

We calculate the `exact' potential corresponding to a one-dimensional interacting system of two electrons with a specific, tailored density. We use one-dimensional density-functional theory with a local-density approximation (LDA) on the same system and calculate densities and energies, which are compared with the `exact' ones. The `interacting-LDA system' corresponding to the LDA density is then found and its potential compared with the original one. Finally we calculate and compare the spatial entanglement of the electronic systems corresponding to the interacting-LDA and original interacting system.Comment: 7 pages, 4 figure

Financial conditions and the risks to economic growth in the United States since 1875

We explore the historical relationship between financial conditions and real economic growth for quarterly U.S. data from 1875 to 2017 with a flexible empirical copula modelling methodology. We compare specifications with both linear and non-linear dependence, and with both Gaussian and non-Gaussian marginal distributions. Our results indicate strong statistical support for models that are both non-Gaussian and nonlinear for our historical data, with considerable heterogeneity across sub-samples. We demonstrate that ignoring the contribution of financial conditions typically understates the conditional downside risks to economic growth in crises. For example, accounting for financial conditions more than doubles the probability of negative growth in the year following the 1929 stock market crash

Characterizing a configuration interaction excited state using natural transition geminals

We introduce natural transition geminals as a means to qualitatively understand a transition where double excitations are important. The first two $A_{1}$ singlet states of the CH cation are used as an initial example. We calculate these states with configuration interaction singles (CIS) and state-averaged Monte Carlo configuration interaction (SA-MCCI). For each method we compare the important natural transition geminals with the dominant natural transition orbitals. We then compare SA-MCCI and full configuration interaction (FCI) with regards to the natural transition geminals using the beryllium atom. We compare using the natural transition geminals with analyzing the important configurations in the CI expansion to give the dominant transition for the beryllium atom and the carbon dimer. Finally we calculate the natural transition geminals for two electronic excitations of formamide.Comment: 15 pages, 2 figures. Mol. Phys. (2013

Approaching exact hyperpolarizabilities via sum-over-states Monte Carlo configuration interaction

We propose using sum-over-states calculations with the compact wavefunctions of Monte Carlo configuration interaction to approach accurate values for higher-order dipole properties up to second hyperpolarizabilities in a controlled way. We apply the approach to small systems that can generally be compared with full configuration interaction (FCI) results. We consider hydrogen fluoride with a 6-31g basis and then look at results, including frequency dependent properties, in an aug-cc-pVDZ basis. We extend one calculation beyond FCI by using an aug-cc-pVTZ basis. The properties of an H$_{4}$ molecule with multireference character are calculated in an aug-cc-pVDZ basis. We then investigate this method on a strongly multireference system with a larger FCI space by modelling the properties of carbon monoxide with a stretched geometry. The behavior of the approach with increasing basis size is considered by calculating results for the neon atom using aug-cc-pVDZ to aug-cc-pVQZ. We finally test if the unusual change in polarizability between the first two states of molecular oxygen can be reproduced by this method in a 6-31g basis.Comment: 11 pages, 14 figure

Applying Monte Carlo configuration interaction to transition metal dimers: exploring the balance between static and dynamic correlation

We calculate potential curves for transition metal dimers using Monte Carlo configuration interaction (MCCI). These results, and their associated spectroscopic values, are compared with experimental and computational studies. The multireference nature of the MCCI wavefunction is quantified and we estimate the important orbitals. We initially consider the ground state of the chromium dimer. Next we calculate potential curves for Sc$_{2}$ where we contrast the lowest triplet and quintet states. We look at the molybdenum dimer where we compare non-relativistic results with the partial inclusion of relativistic effects via effective core potentials, and report results for scandium nickel.Comment: 9 pages and 8 figure

Effects of wing leading-edge deflection on low-speed aerodynamic characteristics of a low-aspect-ratio highly swept arrow-wing configuration

Static force tests were conducted in the Langley V/STOL tunnel at a Reynolds number (based on the mean aerodynamic chord) of about 2.0 x 10 to the 6th power for an angle-of-attack range from about - 10 deg to 17 deg and angles of sideslip of 0 and + or - 5 deg. Limited flow visualization studies were also conducted in order to provide a qualitative assessment of leading-edge upwash characteristics

Distributed upper-surface blowing concept

A low speed investigation was conducted in the Langley V/STOL tunnel to determine the powered lift aerodynamic performance of a distributed upper surface blown propulsive lift transport model. The model used blowing slots across the span of the wing to produce a thin jet efflux near the leading edge and at the knee of the trailing edge flap (internally blown jet flap). Results indicate that these concepts have both good propulsive related lift and low drag due to lift characteristics because of uniform spanwise propulsive thrust. The leading edge blowing concept provides low speed lift characteristics which are competitive with the flap-hinge-line blowing concept and does not require additional leading edge treatment for prevention of abrupt stall