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.

Welland Canal Survey of Lands Abraham Augustine, 1837

Survey map and description of Jacob Augustine's land created by The Welland Canal Company. Included is a written description of the land along with a drawing of the land. The land surveyed is lot #26 in Humberstone.Noteable features include; canal, concession, line between Abraham and Jacob Augustine's land. The land totals 7 1/4 acres. Surveyor notes are seen in pencil on the map.

Welland Canal Survey of Lands Jacob Augustine, 1837

Survey map and description of Jacob Augustine's land created by The Welland Canal Company. Included is a written description of the land along with a drawing of the land. The land surveyed is lot #27 in Humberstone. Noteable features include; canal, concession, line between Neff and J. Augustine's land. The land totals 8 acres. Surveyor notes are seen in pencil on the map.

Application of Reptation Quantum Monte Carlo and Related Methods to LiH

This work investigates mathematical details and computational aspects of Metropolis-Hastings reptation quantum Monte Carlo and its variants, in addition to the Bounce method and its variants. The issues that concern us include the sensitivity of these algorithms' target densities to the position of the trial electron density along the reptile, time-reversal symmetry of the propagators, and the length of the reptile. We calculate the ground-state energy and one-electron properties of LiH at its equilibrium geometry for all these algorithms. The importance sampling is performed with a single-determinant large Slater-type orbitals (STO) basis set. The computer codes were written to exploit the efficiencies engineered into modern, high-performance computing software. Using the Bounce method in the calculation of non-energy-related properties, those represented by operators that do not commute with the Hamiltonian, is a novel work. We found that the unmodified Bounce gives good ground state energy and very good one-electron properties. We attribute this to its favourable time-reversal symmetry in its target density's Green's functions. Breaking this symmetry gives poorer results. Use of a short reptile in the Bounce method does not alter the quality of the results. This suggests that in future applications one can use a shorter reptile to cut down the computational time dramatically.

Letter to Mr. Henry H. Collier, 1837

Henry Haight Collier, was born in Howard, Steuben County, N. Y., November 28, 1818. His father, Richard Collier, was from Green County, in the same State. His grandfather, Isaac Collier, and his great-grandfather were originally from England. His mother, Mary Haight, was of Dutch origin. In 1835, Henry went to St. Catharines, where his elder brother, Richard Collier, resided. He spent two years at Grantham Academy, and then returned to Steuben County, to read law in Bath, with Edward Howell, and subsequently with Hammond and Campbell. Mr. Collier never opened a law office. He studied law for two years and in 1839 he went to Texas where he was connected with the State and Treasury Departments. In 1845 Mr. Collier returned to St. Catharines and opened a general store called St. Catharines Agricultural Works with his brother. The store remained open until May, 1877. He added the manufacturing of lumber in 1850, and manufacturing of agricultural implements in 1869. He built one of the first saw mills on the canal, on Lock No. 5, in St. Catharines. In July, 1877, he was appointed Collector of Customs. He became a Village Councilor for St. Paul’s Ward in 1859, and held that office from fifteen to twenty years. He was Deputy Reeve and member of the County Council for two terms. He was the Mayor of St. Catharines in 1872 and 1873. He was also Chairman of the Board of Water Commissioners of the city, during the time that the works were being built. He was a Justice of the Peace for twenty years or more. Mr. Collier was affiliated with the Reform Party and he was a Knight Templar in the Masonic fraternity and an Odd Fellow. He was also active in the Methodist Church. On June 1, 1858, he married Cornelia, daughter of Moses Cook, of "Westchester Place," St. Catharines, and had a daughter and son. Mary J. (married name: Mrs. Frank Camp) was a graduate of the Female Seminary at Hamilton, and Henry Herbert was a student in the University of Toronto. Henry H. Collier died on July 15, 1895 and is buried in Victoria Lawn Cemetery, St. Catharines, Ontario. Sources: www.accessgeneology.com "Historical Profiles from Victoria Lawn Cemetery" by Paul E. Lewis "Sincerely Lamented St. Catharines Obituaries 1817-1918" by Paul Hutchison

Letters to the Honourable John H. Dunn, 1837-1838

The recipient of the letters is John Henry Dunn who was born on St. Helena (a British territory island of volcanic origin located in the South Atlantic Ocean) in 1792 to John Charles Dunn and Elizabeth Bazette. He was married to Charlotte Roberts on May 4th, 1820 and they had 6 sons and 2 daughters. He came to Canada in 1820 in which year he became the Receiver General for Canada. He held this position until 1841.Charlotte died in 1835. In 1822 he was named to the Province’s Legislative Council. He was president of the Welland Canal Company from 1825-1833. In 1836 he was named to the executive council of Upper Canada but resigned 3 weeks later with fellow counselors when lieutenant governor Sir Francis Bond refused the advice of the council. Dunn was made the Receiver General for the newly formed Province of Canada in 1841, and was elected to represent Toronto in the legislative assembly that year. He married his second wife on March 9th, 1842. Her name was Sophie-Louise Juchereau Duchsnay. They had a son and a daughter. In 1843 he resigned, and was not re-elected in 1844. He returned to England with his family and died in London on April 21, 1854. Dunn was a supporter of the Welland Canal, St. Lawrence Canals and other public improvements. Between the passage of the Canada Trade Act and the Act of the Union he had tried to insure that projects received funding despite financial constraints. He claimed that he has saved Upper Canada from bankruptcy. His son, Alexander Roberts Dunn received the Victoria Cross for his role in the Charge of the Light Brigade at Balaclava. Dunn Street in Niagara Falls is named after John Henry Dunn. The town and township of Dunnville were also named for him. Sources: http://biographi.ca/009004-119.01-e.php?id_nbr=3889 http://www.niagarafrontier.com/cityfalls.html

Dr. Stuart D. Scott Papers, 1837-2010 (non-inclusive)

Dr. Stuart D. Scott has written extensively in the fields of prehistory and history. As an archaeologist, he has traveled to some of the most significant sites in the world, including Pompeii, Stonehenge, the Valley of the Kings, Egypt’s pyramids and the Taj Mahal. He spent nine months excavating with the Tikal Project in Guatemala before returning to the University of Arizona where he received a Ph.D. in 1963. He excavated in New Zealand as a Fulbright scholar in 1963-1964. In the fall of 1964, Dr. Scott started a long career in the Anthropology Department of the State University of New York. He taught graduate and undergraduate archaeology courses and continued his archaeological and historical research. In 1979, Scott established the Old Fort Niagara Archaeology in Progress Project at Old Fort Niagara in Youngstown, New York. For many years, he became involved with historical archaeology in western New York. It was during this work that he became interested in the Upper Canada Rebellion of 1837-1838 and its aftermath. Dr. Scott and his wife, Patricia Kay Scott, would use Christmas breaks, summer vacations, and sabbatical years to travel. They were repeatedly lured back to the South Pacific, conducting research in New Zealand, Australia and many of the Micronesian and Polynesian islands. To tell the whole story of the Rebellion and the prison exiles, they traveled extensively in Canada, the United States, England and Tasmania to collect archival research and to experience the scenes of this remarkable narrative. In 2004, Dr. Scott published To the Outskirts of Habitable Creation: Americans and Canadians Transported to Tasmania in the 1840s, which told the story of the men captured, tried, convicted, and exiled as a result of the Rebellion, also called the Patriot War. Other contributions include: • A collaboration with Dr. Charles Cazeau on the book Exploring the Unknown, Great Mysteries Reexamined published by Plenum Press in 1979 • The Patriot Game: New Yorkers and the Canadian Rebellion of 1837-1838, which appeared in New York History, Vol. 68, No.3. 1987 • A Frontier Spirit: The Life of James Gemmell published in Australiasian Canadian Studies, Vol. 25, No. 2 2007 • To the Outskirts of Habitable Creation which appeared in the Friends of the National Archives, Vol. 20, No. 1 2009 • Numerous academic journal publications • Service on conference panels • Various research papers and proposals Before retiring in 1997 and while still a resident of Buffalo, N.Y., Dr. Scott spent considerable time with Brock University President Emeritus James A. Gibson and History Professor Colin Duquemin. The three shared a love of Rebellion history. It was largely because of this connection that Brock University was chosen as the recipient of Dr. Scott’s research materials.