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.

Rick Bell Family fonds, 1874-1875, 1879, 1884, 1886, 1888-1889, 1896, 1898, 1909-1910, 1939, 1945, n.d.

Lewis Tyrell married Jane Gains on August 31, 1849 in Culpeper Court House, Virginia. Jane Gains was a spinster. Lewis Tyrell died September 25, 1908 at his late residence, Vine St. and Welland Ave., St. Catharines, Ont. at the age of 81 years, 5 months. Jane Tyrell died March 1, 1886, age 64 years. Their son? William C. Tyrell died January 15, 1898, by accident in Albany, NY, age 33 years, 3 months. John William Taylor married Susan Jones were married in St. Catharines, Ont. on August 10, 1851 by William Wilkinson, a Baptist minister. On August 9, 1894 Charles Henry Bell (1871-1916), son of Stephen (1835?-1876) and Susan Bell, married Mary E. Tyrell (b. 1869?) daughter of Lewis and Alice Tyrell, in St. Catharines Ontario. By 1895 the Bell’s were living in Erie, Pennsylvania where children Delbert Otto (b. 1895) and Edna Beatrice (b. 1897) were born. By 1897 the family was back in St. Catharines where children Lewis Tyrell (b. 1899), Gertrude Cora (b. 1901), Bessie Jane (b. 1902), Charles Henry (b. 1906), Richard Nelson (b. 1911) and William Willoughby (b. 1912) were born. Charles Henry Bell operated a coal and ice business on Geneva Street. In the 1901 Census for St. Catharines, the Bell family includes the lodger Charles Henry Hall. Charles Henry Hall was born ca. 1824 in Maryland, he died in St. Catharines on November 11, 1916 at the age of 92. On October 24, 1889 Charles Hall married Susan Bell (1829-1898). The 1911 Census of Canada records Charles Henry Hall residing in the same household as Charles Henry and Mary Bell. The relationship to the householder is step-father. It is likely that after Stephen Bell’s death in 1876, his widow, Susan Bell married Hall. In 1939, Richard Nelson Bell, son of Charles Henry and Mary Tyrell Bell, married Iris Sloman. Iris (b. 22 May 1912 in Biddulph Township, Middlesex, Ontario) was the daughter of Albert (son of Joseph b. 1870 and Elizabeth Sloman, b. 1872) and Josie (Josephine Ellen) Butler Sloman of London, Ont. Josie (b. 1891) was the daughter of Everett Richard and Elizabeth McCarthy (or McCarty) Butler, of Lucan Village, Middlesex North. According to the 1911 Census of Canada, Albert, a Methodist, was a porter on the railroad. His wife, Josephine, was a Roman Catholic. Residing with Albert and Josie were Sanford and Sadie Butler and Sidney Sloman, likely siblings of Albert and Josephine. The Butler family is descended from Peter Butler, a former slave, who had settled in the Wilberforce Colony in the 1830s. Rick Bell b. 1949 in Niagara Falls, Ont. is the son of Richard Nelson Bell. In 1979, after working seven years as an orderly at the St. Catharines General Hospital while also attending night school at Niagara College, Rick Bell was hired by the Thorold Fire Dept. He became the first Black professional firefighter in Niagara. He is a founding member of the St. Catharines Junior Symphony; attended the Banff School of Fine Arts in 1966 and also performed with the Lincoln & Welland Regimental Band and several other popular local groups. Upon the discovery of this rich archive in his mothers’ attic he became passionate about sharing his Black ancestry and the contributions of fugitive slaves to the heritage Niagara with local school children. He currently resides in London, Ont.

Proceedings : Grand Lodge, A.F. & A.M. of Canada in the Province of Ontario - 1939

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

Bell - Sloman Wedding Day Photo, 1939

This photograph was taken on the wedding day of Richard Nelson Bell and Iris Sloman in 1939. Pictured in the photograph, from left, are: Charles Bell, father of Richard Nelson Bell; Josephine Sloman, mother of Iris; Richard Nelson Bell; Iris Sloman Bell; Mary Bell, mother of Richard Nelson Bell; and Albert Sloman, father of Iris. This family photo was in the possession of Rick Bell, of St. Catharines, Ontario. The Sloman - Bell ancestry includes escaped Black slaves from the United States.

Richard Nelson Bell - Iris Sloman Wedding Day Photo, 1939

A black and white photograph taken in 1939 on the occasion of the marriage of Richard Nelson Bell to Iris Sloman. Pictured in the photograph, from left to right, are: Bert Sloman; Richard Nelson Bell; Iris Sloman Bell; and Helen Beatty Sloman. This photograph was in the possession of Rick Bell, the son of Richard Nelson and Iris Bell. The Bell - Sloman family descends from former Black slaves from the United States.Bert Sloman (Albert Edward Sloman) passed away in 1986 at Kitchener-Waterloo, Ontario. His wife Vera Matilda Sloman passed away January 4, 2011 at Cambridge Memorial Hospital. They had a son, Ron Sloman.

Richard and Iris Bell Wedding Day, 1939

Richard and Iris (Sloman) Bell are pictured on the grounds of unknown gardens, possibly in Niagara Falls, on their wedding day in 1939. This photo was among the family memorabilia in the possession of their son, Rick Bell, of St. Catharines.