Variational Monte Carlo study of core-valence separation schemes for first-row atoms and positive ions /

All-electron partitioning of wave functions into products ^core^vai of core and valence parts in orbital space results in the loss of core-valence antisymmetry, uncorrelation of motion of core and valence electrons, and core-valence overlap. These effects are studied with the variational Monte Carlo method using appropriately designed wave functions for the first-row atoms and positive ions. It is shown that the loss of antisymmetry with respect to interchange of core and valence electrons is a dominant effect which increases rapidly through the row, while the effect of core-valence uncorrelation is generally smaller. Orthogonality of the core and valence parts partially substitutes the exclusion principle and is absolutely necessary for meaningful calculations with partitioned wave functions. Core-valence overlap may lead to nonsensical values of the total energy. It has been found that even relatively crude core-valence partitioned wave functions generally can estimate ionization potentials with better accuracy than that of the traditional, non-partitioned ones, provided that they achieve maximum separation (independence) of core and valence shells accompanied by high internal flexibility of ^core and Wvai- Our best core-valence partitioned wave function of that kind estimates the IP's with an accuracy comparable to the most accurate theoretical determinations in the literature.

Diffusion Monte Carlo study of electronic properties for H and Be atoms /

We examined three different algorithms used in diffusion Monte Carlo (DMC) to study their precisions and accuracies in predicting properties of isolated atoms, which are H atom ground state, Be atom ground state and H atom first excited state. All three algorithms — basic DMC, minimal stochastic reconfiguration DMC, and pure DMC, each with future-walking, are successfully impletmented in ground state energy and simple moments calculations with satisfactory results. Pure diffusion Monte Carlo with future-walking algorithm is proven to be the simplest approach with the least variance. Polarizabilities for Be atom ground state and H atom first excited state are not satisfactorily estimated in the infinitesimal differentiation approach. Likewise, an approach using the finite field approximation with an unperturbed wavefunction for the latter system also fails. However, accurate estimations for the a-polarizabilities are obtained by using wavefunctions that come from the time-independent perturbation theory. This suggests the flaw in our approach to polarizability estimation for these difficult cases rests with our having assumed the trial function is unaffected by infinitesimal perturbations in the Hamiltonian.

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.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Optimization of trial wave functions for use in quantum Monte Carlo with application to LiH

Methods for both partial and full optimization of wavefunction parameters are explored, and these are applied to the LiH molecule. A partial optimization can be easily performed with little difficulty. But to perform a full optimization we must avoid a wrong minimum, and deal with linear-dependency, time step-dependency and ensemble-dependency problems. Five basis sets are examined. The optimized wavefunction with a 3-function set gives a variational energy of -7.998 + 0.005 a.u., which is comparable to that (-7.990 + 0.003) 1 of Reynold's unoptimized \fin ( a double-~ set of eight functions). The optimized wavefunction with a double~ plus 3dz2 set gives ari energy of -8.052 + 0.003 a.u., which is comparable with the fixed-node energy (-8.059 + 0.004)1 of the \fin. The optimized double-~ function itself gives an energy of -8.049 + 0.002 a.u. Each number above was obtained on a Bourrghs 7900 mainframe computer with 14 -15 hrs CPU time.

Quantum Monte Carlo : some theoretical and numerical studies

In Part I, theoretical derivations for Variational Monte Carlo calculations are compared with results from a numerical calculation of He; both indicate that minimization of the ratio estimate of Evar , denoted EMC ' provides different optimal variational parameters than does minimization of the variance of E MC • Similar derivations for Diffusion Monte Carlo calculations provide a theoretical justification for empirical observations made by other workers. In Part II, Importance sampling in prolate spheroidal coordinates allows Monte Carlo calculations to be made of E for the vdW molecule var He2' using a simplifying partitioning of the Hamiltonian and both an HF-SCF and an explicitly correlated wavefunction. Improvements are suggested which would permit the extension of the computational precision to the point where an estimate of the interaction energy could be made~

Variational Monte Carlo estimation of the dissociation energy of CuH using correlated sampling

A new approach to treating large Z systems by quantum Monte Carlo has been developed. It naturally leads to notion of the 'valence energy'. Possibilities of the new approach has been explored by optimizing the wave function for CuH and Cu and computing dissociation energy and dipole moment of CuH using variational Monte Carlo. The dissociation energy obtained is about 40% smaller than the experimental value; the method is comparable with SCF and simple pseudopotential calculations. The dipole moment differs from the best theoretical estimate by about 50% what is again comparable with other methods (Complete Active Space SCF and pseudopotential methods).

Quantum Monte Carlo study of electrostatic polarizabilities of H and He atoms /

The infinitesimal differential quantum Monte Carlo (QMC) technique is used to estimate electrostatic polarizabilities of the H and He atoms up to the sixth order in the electric field perturbation. All 542 different QMC estimators of the nonzero atomic polarizabilities are derived and used in order to decrease the statistical error and to obtain the maximum efficiency of the simulations. We are confident that the estimates are "exact" (free of systematic error): the two atoms are nodeless systems, hence no fixed-node error is introduced. Furthermore, we develope and use techniques which eliminate systematic error inherent when extrapolating our results to zero time-step and large stack-size. The QMC results are consistent with published accurate values obtained using perturbation methods. The precision is found to be related to the number of perturbations, varying from 2 to 4 significant digits.

Exact property estimation from diffusion Monte Carlo with minimal stochastic reconfiguration /

Our objective is to develop a diffusion Monte Carlo (DMC) algorithm to estimate the exact expectation values, ($o|^|^o), of multiplicative operators, such as polarizabilities and high-order hyperpolarizabilities, for isolated atoms and molecules. The existing forward-walking pure diffusion Monte Carlo (FW-PDMC) algorithm which attempts this has a serious bias. On the other hand, the DMC algorithm with minimal stochastic reconfiguration provides unbiased estimates of the energies, but the expectation values ($o|^|^) are contaminated by ^, an user specified, approximate wave function, when A does not commute with the Hamiltonian. We modified the latter algorithm to obtain the exact expectation values for these operators, while at the same time eliminating the bias. To compare the efficiency of FW-PDMC and the modified DMC algorithms we calculated simple properties of the H atom, such as various functions of coordinates and polarizabilities. Using three non-exact wave functions, one of moderate quality and the others very crude, in each case the results are within statistical error of the exact values.

A. S. Whiting Manufacturing Company Limited, minute book, 1872-1909.

The Cedar Dale Scythe Works was the second manufacturing company that A.S. Whiting had established in Oshawa, the first being the Oshawa Manufacturing Co. in 1852. The Oshawa Manufacturing Co. was eventually taken over by the Joseph Hall Works in 1857. In 1862, the Cedar Dale Works was built after being in a rented space in the Hall Works for two years, building scythes and hoes. With the building of the firm, the village of Cedar Dale was established. In 1867, the firm became Whiting and Cowan when John Cowan bought into the company. After the death of Whiting in 1867, his son-in-law, R.S. Hamlin headed the company. By 1872, it became the A.S. Whiting Manufacturing Co. when Cowan withdrew from the business. Before Whiting’s death, the company had been profitable but due to new machinery being developed, hand tools were becoming obsolete and the business only lasted for a few more years (source: Oshawa Community Museum and Archives Web site).

Collective Labour Agreement between the Public Utilities Commission of the City of St. Catharines and Local 556, The International Brotherhood of Electrical Workers, 1952

In 1952, Local 556 of The International Brotherhood of Electrical Workers negotiated a contract with The Public Utilities Commission of the City of St. Catharines. The contract was to be in effect from July 1952 to September 1953. The document is unsigned.

Edward Mirynech fonds, 1913-1914, 1946, 1952-1957, 1959-1960, 1965-1982, n.d.

Edward Mirynech joined the faculty at Brock University in 1964 as assistant professor of Geology. Edward Mirynech, the son of John and Katherine Mirynech, grew up in St. Catharines, attended Connaught Public School and received his formal education at the University of Toronto. Dr. Mirynech played several critical roles in the early development of the University. In addition to teaching, Dr. Mirynech was also the acting director of the athletics department, a coach for many of the early rowing, hockey and basketball teams and served the University as marshall for the sod turning ceremony for the new DeCew campus in 1965. Dr. Mirynech was instrumental in the founding of the physical education, geography and geological sciences programs. He served as acting chairman in 1968 when the department of geological sciences enrolled its first students. Part of the unique teaching program was the annual field trips to locations such as the Belleville area, extended summer teaching programs held in Trinidad-Tobago and the following year in Iceland. In 1972, the first graduation ceremony ever to be held in the Arctic, at Pond Inlet, NWT, made national news. Three geology students, on a study trip to the Arctic, received their degrees during a special ceremony. Dr. Mirynech was among the faculty team in Pond Inlet, NWT, representing Brock University. Dr. Mirynech retired from teaching in 1985, and passed away in 2004.

Gideon Sundback fonds, 1942, 1952, 1985-1986, 1991, 2004, n.d.

Gideon Sundback was born in Stockholm, Sweden in 1880. He was educated as an engineer and settled in the United States in 1905. While working for the Universal Fastener Company, New Jersey in 1913 he developed and patented a “separable fastener”, which improved on an earlier version of what today is known as the zipper. He later moved his family to Meadville, Pennsylvania and sought a Canadian location for the production of his new invention. He settled on St. Catharines as it was an easy commute from his Pennsylvania home and opened The Lightning Fastener Company on Niagara Street. Sundback died on June 21, 1954 and is interred in Meadville, Pennsylvania. The plant continued to operate, but with increased foreign competition the manufacture of the zipper declined. The plant closed in 1981. Source: The St. Catharines Standard, July 3, 2004 Harold Fox was a noted lawyer, academic, businessman, author and a leading authority on intellectual property. He was engaged by Gideon Sunback and the Lightening Fastening Company to combat patent infringements by Colonial Fastener in the 1930s. The relationship continued when Fox was asked to become the managing director of the company, which he did until 1949. Fox lived in St. Catharines at his home “Foxcroft” until his death in 1969. Source: http://thefoxfund.com/harold.htm (November 2, 2009)

Office of the City Clerk, St. Catharines Records, 1928-1974, n.d.

The site of present-day St. Catharines was settled by 3000 United Empire Loyalists at the end of the 18th century. From 1790, the settlement (then known as "The Twelve") grew as an agricultural community. St. Catharines was once referred to Shipman's Corners after Paul Shipman, owner of a tavern that was an important stagecoach transfer point. In 1815, leading businessman William Hamilton Merritt abandoned his wharf at Queenston and set up another at Shipman's Corners. He became involved in the construction and operation of several lumber and gristmills along Twelve Mile Creek. Shipman's Corners soon became the principal milling site of the eastern Niagara Peninsula. At about the same time, Merritt began to develop the salt springs that were discovered along the river which subsequently gave the village a reputation as a health resort. By this time St. Catharines was the official name of the village; the origin of the name remains obscure, but is thought to be named after Catharine Askin Robertson Hamilton, wife of the Hon. Robert Hamilton, a prominent businessman. Merritt devised a canal scheme from Lake Erie to Lake Ontario that would provide a more reliable water supply for the mills while at the same time function as a canal. He formed the Welland Canal Company, and construction took place from 1824 to 1829. The canal and the mills made St. Catharines the most important industrial centre in Niagara. By 1845, St. Catharines was incorporated as a town, with the town limits extending in 1854. Administrative and political functions were added to St. Catharines in 1862 when it became the county seat of Lincoln. In 1871, construction began on the third Welland Canal, which attracted additional population to the town. As a consequence of continual growth, the town limits were again extended. St. Catharines attained city status in 1876 with its larger population and area. Manufacturing became increasingly important in St. Catharines in the early 1900s with the abundance of hydro-electric power, and its location on important land and water routes. The large increase in population after the 1900s was mainly due to the continued industrialization and urbanization of the northern part of the city and the related expansion of business activity. The fourth Welland Canal was opened in 1932 as the third canal could no longer accommodate the larger ships. The post war years and the automobile brought great change to the urban form of St. Catharines. St. Catharines began to spread its boundaries in all directions with land being added five times during the 1950s. The Town of Merritton, Village of Port Dalhousie and Grantham Township were all incorporated as part of St. Catharines in 1961. In 1970 the Province of Ontario implemented a regional approach to deal with such issues as planning, pollution, transportation and services. As a result, Louth Township on the west side of the city was amalgamated, extending the city's boundary to Fifteen Mile Creek. With its current population of 131,989, St. Catharines has become the dominant centre of the Niagara region. Source: City of St. Catharines website http://www.stcatharines.ca/en/governin/HistoryOfTheCity.asp (January 27, 2011)

Proceedings : Grand Lodge, A.F. & A.M. of Canada in the Province of Ontario - 1872

On spine : The Grand Lodge of Canada in the Province of Ontario.