Histogram filtering as a tool in variational Monte Carlo optimization

Optimization of wave functions in quantum Monte Carlo is a difficult task because the statistical uncertainty inherent to the technique makes the absolute determination of the global minimum difficult. To optimize these wave functions we generate a large number of possible minima using many independently generated Monte Carlo ensembles and perform a conjugate gradient optimization. Then we construct histograms of the resulting nominally optimal parameter sets and "filter" them to identify which parameter sets "go together" to generate a local minimum. We follow with correlated-sampling verification runs to find the global minimum. We illustrate this technique for variance and variational energy optimization for a variety of wave functions for small systellls. For such optimized wave functions we calculate the variational energy and variance as well as various non-differential properties. The optimizations are either on par with or superior to determinations in the literature. Furthermore, we show that this technique is sufficiently robust that for molecules one may determine the optimal geometry at tIle same time as one optimizes the variational energy.

Approximate cost of completing the railway from Port Dalhousie to St. Catharines and an estimate of the cost of the piers at Port Dalhousie signed by William Hamilton Merritt

Approximate cost of completing the railway from Port Dalhousie to St. Catharines and an estimate of the cost of the piers at Port Dalhousie signed by William Hamilton Merritt (5 pages, handwritten), July 8, 1854.

Approximate estimate of the cost of completing the Port Dalhousie Railway to the Grand Central Railway Station at Lock 12

Approximate estimate of the cost of completing the Port Dalhousie Railway to the Grand Central Railway Station at Lock 12. This document is badly torn and burned but most of the text is legible, July 14, 1854.

Approximate estimate of the cost of constructing and completing the Port Dalhousie and Thorold Railway to St. Catharines

Approximate estimate of the cost of constructing and completing the Port Dalhousie and Thorold Railway to St. Catharines signed by S.D. Woodruff (2 pages, handwritten), Jan. 8, 1855.

Approximate estimate of the cost of extending the Port Dalhousie and Thorold Railway from Geneva Street to the Great Western Railway Station at Lock no. 12

Approximate estimate of the cost of extending the Port Dalhousie and Thorold Railway from Geneva Street to the Great Western Railway Station at Lock no. 12 (2 copies) [one appears to be a rough copy] (2 pages, handwritten), Feb. 2, 1855.

Memorandum respecting differences between the approximate and the final estimate

Memorandum respecting differences between the approximate and the final estimate (3 ¼ pages, handwritten), n.d.

Second copy of the memorandum respecting differences between the approximate and final estimate but this one has “memorandum of extras of Brown and McDonall contract” written on the outer page

Second copy of the memorandum respecting differences between the approximate and final estimate but this one has “memorandum of extras of Brown and McDonall contract” written on the outer page (3 pages, handwritten), n.d.

Approximate estimate of the cost of macadamizing, grading, bridging and putting in culverts from Hurst’s Bridge above Thorold to Port Robinson

Approximate estimate of the cost of macadamizing, grading, bridging and putting in culverts from Hurst’s Bridge above Thorold to Port Robinson (2 pages, handwritten), n.d.

Chart of approximate quantity of excavation in slides in the deep cut

Chart of approximate quantity of excavation in slides in the deep cut, July 1, 1848.

Photograph - Young girl, Martha. Approximate age 6-9 years old. Ambrotype?

Young girl, Martha. Approximate age 6-9 years old. Ambrotype? Ca. 1850s? Brass matting with brass border. Wooden case. Photograph very faded. 8.5mm x 9.5mm (yellow sticker with “x” on front of case).