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.

Decew Campus Site

Dr. Deeks and Dr. Gibson touring the recently acquired Decew Campus site along a stretch of Merrittville Highway in early 1964. The Sanatorium can be seen in the background.

Decew Campus Site

Dr. Deeks and Dr. Gibson examining the sign at the Decew Campus site along the stretch of Merrittville Highway just north of St. Davids Road. This photo was taken in March of 1964.

Master Plan Layout

The original Master Plan of 1964 called for the campus to stretch out 1 1/4 miles across the escarpment with arts buildings west of the tower and science buildings to the east. This plan laid out the development of Brock for the next 10 or 11 years by which time enrollment was expected to be near 8000 students.

Tower and Pedestrian Mall

The original Master Plan of 1964 called for the campus to stretch out 1 1/4 miles across the escarpment with arts buildings west of the tower and science buildings to the east. This plan laid out the development of Brock for the next 10 or 11 years by which time enrollment was expected to be near 8000 students. Pictured here is the tower and university centre. The view is looking east towards a cluster of science buildings and residences in the background.

Amphitheatre and Tower

The original Master Plan of 1964 called for the campus to stretch out 1 1/4 miles across the escarpment with arts buildings west of the tower and science buildings to the east. This plan laid out the development of Brock for the next 10 or 11 years by which time enrollment was expected to be near 8000 students. Pictured here is the tower and behind it, in the lower left portion of the picture, the planned outdoor amphitheatre. This view is from the edge of the escarpment facing southward or southeast.

Brock University Tower

The original Master Plan of 1964 called for the campus to stretch out 1 1/4 miles across the escarpment with arts buildings west of the tower and science buildings to the east. This plan laid out the development of Brock for the next 10 or 11 years by which time enrollment was expected to be near 8000 students. Pictured here is the tower and main entrance to the university. To the left is a planned administration building. The original plans also called for a miniature canal running between the boulevard at the entrance which would then pass through an underground system and open up into a waterfall at the brink of the escarpment behind the tower.

Investigation of molecular polarizabilities and derivatives in halomethanes

The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.

NMR studies of the exchange reactions of CH3CN.BX3 with excess CH3CN /|nJoseph Fogelman. -- 260 St. Catharines, Ont. : [s. n.],

Exchange reactions between molecular complexes and excess acid or base are well known and have been extensively surveyed in the literature(l). Since the exchange mechanism will, in some way involve the breaking of the labile donor-acceptor bond, it follows that a discussion of the factors relating to bonding in molecular complexes will be relevant. In general, a strong Lewis base and a strong Lewis acid form a stable adduct provided that certain stereochemical requirements are met. A strong Lewis base has the following characteristics (1),(2) (i) high electron density at the donor site. (ii) a non-bonded electron pair which has a low ionization potential (iii) electron donating substituents at the donor atom site. (iv) facile approach of the site of the Lewis base to the acceptor site as dictated by the steric hindrance of the substituents. Examples of typical Lewis bases are ethers, nitriles, ketones, alcohols, amines and phosphines. For a strong Lewis acid, the following properties are important:( i) low electron density at the acceptor site. (ii) electron withdrawing substituents. (iii) substituents which do not interfere with the close approach of the Lewis base. (iv) availability of a vacant orbital capable of accepting the lone electron pair of the donor atom. Examples of Lewis acids are the group III and IV halides such (M=B, AI, Ga, In) and MX4 - (M=Si, Ge, Sn, Pb). The relative bond strengths of molecular complexes have been investigated by:- (i) (ii) (iii) (iv) (v] (vi) dipole moment measurements (3). shifts of the carbonyl peaks in the IIIR. (4) ,(5), (6) .. NMR chemical shift data (4),(7),(8),(9). D.V. and visible spectrophotometric shifts (10),(11). equilibrium constant data (12), (13). heats of dissociation and heats of reactions (l~), (16), (17), (18), (19). Many experiments have bben carried out on boron trihalides in order to determine their relative acid strengths. Using pyridine, nitrobenzene, acetonitrile and trimethylamine as reference Lewis bases, it was found that the acid strength varied in order:RBx3 > BC1 3 >BF 3 • For the acetonitrile-boron trihalide and trimethylamine boron trihalide complexes in nitrobenzene, an-NMR study (7) showed that the shift to lower field was. greatest for the BB~3 adduct ~n~ smallest for the BF 3 which is in agreement with the acid strengths. If electronegativities of the substituents were the only important effect, and since c~ Br ,one would expect the electron density at the boron nucleus to vary as BF3stretch, Drago (22) et al have proposed that the angular di~tortion of the X-B-X bonds from sp2 (12 ) to sp3 (10 hybridization is proportional to the amount of charge transferred, i.e. to the nature of the base, and they have rejected the earlier concept of reorganization energy in explaining the formation of the adduct bond (19).

Active isolated stretching : an investigation of the mechanical mechanisms

The Active Isolated Stretching (AIS) technique proposes that by contracting a muscle (agonist) the opposite muscle (antagonist) will relax through reciprocal inhibition and lengthen without increasing muscle tension (Mattes, 2000). The clinical effectiveness of AIS has been reported but its mechanism of action has not been investigated at the tissue level. Proposed mechanisms for increased range of motion (ROM) include mechanical or neural changes, or an increased stretch tolerance. The purpose of the study was to investigate changes in mechanical properties, i.e. stiffness, of skeletal muscle in response to acute and long-term AIS stretching for the hamstring muscle group. Recreationally active university-aged students (female n=8, male n=2) classified as having tight hamstrings, by a knee extension test, volunteered for the study. All stretch procedures were performed on the right leg, with the left leg serving as a control. Each subject was assessed twice: at an initial session and after completing a 6-week AIS hamstring stretch training program. For both test sessions active knee extension (ROM) to a position of "light irritation", passive resisted torque and stiffness were determined before and after completion of the AIS technique (2x10 reps). Data were collected using a Biodex System 3 Pro (Biodex Medical Systems, NY, USA) isokinetic dynamometer. Surface electromyography (EMG) was used to monitor vastus lateralis (VL) and hamstring muscle activity during the stretching movements. Between test sessions, 2x10 reps of the AIS bent knee hamstring stretch were performed daily for 6-weeks.

St. Lawrence Seaway Authority fonds, 1984-1991, n.d.

The St. Lawrence Seaway is a system of locks, canals and channels. Construction of the seaway began in 1954 and it opened on April 25th, 1959. It consists of a 189 mile (306 kilometer) stretch of the seaway between Montreal and Lake Ontario. The Seaway is considered to be an engineering feat with 7 locks in the Montreal – Lake Ontario section which lift vessels to 246 feet (75 meters) above sea level. The 28 mile (44 kilometer) Welland Canal is the fourth version of a link between Lake Ontario and Lake Erie. Today there are 8 Canadian locks which lift ships 326 feet (100 meters) over the Niagara Escarpment. The St. Lawrence Seaway Authority is a Canadian Government Crown Corporation which is financially self-sufficient. It depends on the tolls charged to the users of the Seaway for its revenue and operating expenses.