Monte Carlo explicitly correlated methods

Solving the non-relativistic time-independent electronic Schrödinger equation is in general difficult and requires approximation. For experimental accuracy, wave-function based methods require a large set of basis functions and inclusion of instantaneous correlation through expensive correlated methods. The methods that have been developed to account for the incompleteness of the basis set, the R12/F12 methods, create high dimensional integrals that need to be separated with the resolution of the identity, are limited in their form of the correlation factor due to analytical integration, and not highly parallel scalable. The solution to these drawbacks proposed in this work is Monte Carlo (MC). The stochastic second-order many-body perturbation theory, or the MC-MP2-F12 method, was developed for highly parallel evaluation of second-order many-body perturbation theory (MP2) energies near the complete basis set (CBS) limit. Single molecule energies were on average closer to the CBS limit than the corresponding method with a much larger basis set. Many different reaction energies for small molecules were computed showing a mean error from the CBS limit result within chemical accuracy. Two different methods were used the full variational MP2-F12 correction, MC-MP2-F12($VBX$), and a non-variational approximate form only satisfied at the minimum of the MC-MP2-F12($VBX$) formula, MC-MP2-F12($V$). Despite previous assumptions, the MC-MP2-F12($V$) formula is accurate not only for absolute energies but relative energies as well. Scaling for relative errors was shown to be $O(n^{4})$ where $n$ is the number of basis functions, one order lower than the corresponding deterministic method. Due to the MC-MP2-F12($V$) and more complete MC-MP2-F12($VBX$) having the same asymptotic scaling as $n$ increases, it is generally recommended that one use the $VBX$ method for larger molecules. Various correlation factors were tested but the Slater-type geminal (STG) developed by Ten-no was confirmed to be the best. A more extensive study of different functional forms of correlation factors was conducted using the MC-MP2-F12 method with a total of 17 correlation factors in order to elucidate qualities of the correlation hole and shape. Higher-order cusp conditions, or derivatives of the wavefunction, and their properties were also studied. It was found that every correlation factor that had the best convergence to the CBS limit had a very specific shape on the range of 0 to 1.5 Bohr. Despite having vastly differing long-range behavior, the best correlation factors gave very similar energies. This was found to be due to the decoupling of electrons at long distance, and the dominance of the orbital expansion at large inter-electron distance, $r_{12}$. While the importance of satisfying the cusp condition at $r_{12}=0$ could not be determined, the study confirmed that the intermediate region is of the most importance in general. Lastly, the MC-F12 algorithm developed for MC-MP2-F12 was extended to explicitly correlated second-order Green's function theory (GF2-F12) for basis-set corrected ionization potentials (IPs). The same set of benchmark organic molecules that were studied in the original GF2-F12 study were compared to verify the usefulness of the MC algorithm. Analogous to MC-MP2-F12, the two different methods MC-GF2-F12($V$) and MC-GF2-F12($VBX$) were tested. A mean average error of 0.049 eV and 0.018 eV was achieved for the MC-GF2-F12($V$) and MC-GF2-F12($VBX$) methods respectively. System size scaling was found to be $O(n^{4})$. As a demonstration of size scalability, the first IPs of fullerenes C$_{60}$ and C$_{70}$ were corrected from HF at the MC-GF2-F12($VBX$) level. Errors of 0.37 eV and 0.05 eV from experiment were achieved for C$_{60}$ and C$_{70}$ respectively. The sources of the large error in C$_{60}$ is unknown. Further accuracy can be expected from developing the full non-diagonal frequency-dependent formalism with MC, as well as combining MC-GF2-F12 with the MC-GF3 and MC-GF4 methods

YOUNG STARS IN AN OLD BULGE: A NATURAL OUTCOME OF INTERNAL EVOLUTION IN THE MILKY WAY

The center of our disk galaxy, the Milky Way, is dominated by a boxy/peanut-shaped bulge. Numerous studies of the bulge based on stellar photometry have concluded that the bulge stars are exclusively old. The perceived lack of young stars in the bulge strongly constrains its likely formation scenarios, providing evidence that the bulge is a unique population that formed early and separately from the disk. However, recent studies of individual bulge stars using the microlensing technique have reported that they span a range of ages, emphasizing that the bulge may not be a monolithic structure. In this Letter we demonstrate that the presence of young stars that are located predominantly nearer to the plane is expected for a bulge that has formed from the disk via dynamical instabilities. Using an N-body+ smoothed particle hydrodynamics simulation of a disk galaxy forming out of gas cooling inside a dark matter halo and forming stars, we find a qualitative agreement between our model and the observations of younger metal-rich stars in the bulge. We are also able to partially resolve the apparent contradiction in the literature between results that argue for a purely old bulge population and those that show a population comprised of a range in ages; the key is where to look

Morphology of the Acromion and Scapular Spine with Special Interest in the Strength & Failure Prediction after Reverse Total Shoulder Replacement

Scapular spine fractures following a reverse arthroplasty are a significant clinical concern. This ongoing study looks at the morphology of the acromion and scapular spine with an interest in the strength and failure prediction of the bone. Digital 3D models of the scapular spine were created from cadaver CTs, then bone density and distribution data was obtained. It was found that the cortical bone was most dense just medial of the lateral angle. The cross-sectional area here was also the largest and decreased medially. This has important implications for implant fixation hardware as cortical bone --compared to cancellous bone-- is stronger, denser, and therefore a better option for fixation hardware

Distinction of disorder, classical and quantum vibrational contributions to atomic mean-square amplitudes in dielectric pentachloronitrobenzene

The solid-state molecular disorder of pentachloronitrobenzene (PCNB) and its role in causing anomalous dielectric properties are investigated. Normal coordinate analysis (NCA) of atomic mean-square displacement parameters (ADPs) is employed to distinguish disorder contributions from classical and quantum-mechanical vibrational contributions. The analysis relies on multitemperature (5-295 K) single-crystal neutron-diffraction data. Vibrational frequencies extracted from the temperature dependence of the ADPs are in good agreement with THz spectroscopic data. Aspects of the static disorder revealed by this work, primarily tilting and displacement of the molecules, are compared with corresponding results from previous, much more in-depth and time-consuming Monte Carlo simulations; their salient findings are reproduced by this work, demonstrating that the faster NCA approach provides reliable constraints for the interpretation of diffuse scattering. The dielectric properties of PCNB can thus be rationalized by an interpretation of the temperature-dependent ADPs in terms of thermal motion and molecular disorder. The use of atomic displacement parameters in the NCA approach is nonetheless hostage to reliable neutron data. The success of this study demonstrates that state-of-the-art single-crystal Laue neutron diffraction affords sufficiently fast the accurate data for this type of study. In general terms, the validation of this work opens up the field for numerous studies of solid-state molecular disorder in organic materials.Comment: Now published in Physical Review

Convolutional neural networks can decode eye movement data: A black box approach to predicting task from eye movements

Previous attempts to classify task from eye movement data have relied on model architectures designed to emulate theoretically defined cognitive processes and/or data that have been processed into aggregate (e.g., fixations, saccades) or statistical (e.g., fixation density) features. Black box convolutional neural networks (CNNs) are capable of identifying relevant features in raw and minimally processed data and images, but difficulty interpreting these model architectures has contributed to challenges in generalizing lab-trained CNNs to applied contexts. In the current study, a CNN classifier was used to classify task from two eye movement datasets (Exploratory and Confirmatory) in which participants searched, memorized, or rated indoor and outdoor scene images. The Exploratory dataset was used to tune the hyperparameters of the model, and the resulting model architecture was retrained, validated, and tested on the Confirmatory dataset. The data were formatted into timelines (i.e., x-coordinate, y-coordinate, pupil size) and minimally processed images. To further understand the informational value of each component of the eye movement data, the timeline and image datasets were broken down into subsets with one or more components systematically removed. Classification of the timeline data consistently outperformed the image data. The Memorize condition was most often confused with Search and Rate. Pupil size was the least uniquely informative component when compared with the x- and y-coordinates. The general pattern of results for the Exploratory dataset was replicated in the Confirmatory dataset. Overall, the present study provides a practical and reliable black box solution to classifying task from eye movement data