Explicit factorization of external coordinates in constrained Statistical Mechanics models

If a macromolecule is described by curvilinear coordinates or rigid constraints are imposed, the equilibrium probability density that must be sampled in Monte Carlo simulations includes the determinants of different mass-metric tensors. In this work, we explicitly write the determinant of the mass-metric tensor G and of the reduced mass-metric tensor g, for any molecule, general internal coordinates and arbitrary constraints, as a product of two functions; one depending only on the external coordinates that describe the overall translation and rotation of the system, and the other only on the internal coordinates. This work extends previous results in the literature, proving with full generality that one may integrate out the external coordinates and perform Monte Carlo simulations in the internal conformational space of macromolecules. In addition, we give a general mathematical argument showing that the factorization is a consequence of the symmetries of the metric tensors involved. Finally, the determinant of the mass-metric tensor G is computed explicitly in a set of curvilinear coordinates specially well-suited for general branched molecules.Comment: 22 pages, 2 figures, LaTeX, AMSTeX. v2: Introduccion slightly extended. Version in arXiv is slightly larger than the published on

Generalized Gradient Approximation Made Thermal

Using the methodology of conditional-probability density functional theory, and several mild assumptions, we calculate the temperature-dependence of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). This numerically-defined thermal GGA reduces to the local approximation in the uniform limit and PBE at zero temperature, and can be fit reasonably accurately (within 8%) assuming the temperature-dependent enhancement is independent of the gradient. This locally thermal PBE satisfies both the coordinate-scaled correlation inequality and the concavity condition, which we prove for finite temperatures. The temperature dependence differs markedly from existing thermal GGA's.Comment: 6 pages, 5 figure

Quantum mechanical calculation of the effects of stiff and rigid constraints in the conformational equilibrium of the Alanine dipeptide

If constraints are imposed on a macromolecule, two inequivalent classical models may be used: the stiff and the rigid one. This work studies the effects of such constraints on the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2 without any simplifying assumption. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of all the correcting terms to the naive CED based in the Potential Energy Surface (PES) that appear when the constraints are considered. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.Comment: 37 pages, 4 figures, LaTeX, BibTeX, AMSTe

Resistance and Resurgence Through Being: How Urban Indigenous Youth are Practicing Cultural Safety and Connectedness in Southern Ontario

Within what is currently known a Canada, Indigenous individuals have come to be the youngest and fastest growing segment of the population and largely reside in cities. However, the resources and literature that surround urban Indigenous youth do not mirror these changes well. This thesis centres on the stories and experiences of cultural safety and connectedness for urban Indigenous youth living in the Waterloo and Wellington Regions of Southern Ontario, Canada. Photovoice and community visioning exercises were utilized to collect stories and creative expressions of experiences and desires with participants. The youth participants shared avenues that they are taking to feel culturally safe and connected; internal and external factors that help and hinder these processes; and what an ideal Indigenous place looks and feels like. Through these accounts, it became evident that Indigenous youth are actively asserting their presence through being and contributing to realized Indigenous futurities

Correlation energy of the uniform gas determined by ground state conditional probability density functional theory

Conditional-probability density functional theory (CP-DFT) is a formally exact method for finding correlation energies from Kohn-Sham DFT without evaluating an explicit energy functional. We present details on how to generate accurate exchange-correlation energies for the ground-state uniform gas. We also use the exchange hole in a CP antiparallel spin calculation to extract the high-density limit. We give a highly accurate analytic solution to the Thomas-Fermi model for this problem, showing its performance relative to Kohn-Sham and may be useful at high temperatures. We explore several approximations to the CP potential. Results are compared to accurate parameterizations for both exchange-correlation energies and holes.Comment: Corrected typos, minor changes in text and notation for clarity and continuity with other work, results unchange

Effects of topological solitons on autocorrelation functions for chains of coupled torsional oscillators

©1983 American Institute of PhysicsThe electronic version of this article is the complete one and can be found online at: http://link.aip.org/link/?JCPSA6/78/6914/1DOI:10.1063/1.444640Brownian dynamics computer simulations were performed on chains of coupled torsional oscillators. The purpose was to observe the changes in autocorrelation functions, related to typical experimental measurements, caused by the introduction of topological solitons or kinks into the system. We considered three model systems: a chain of coupled torsional oscillators, a chain of coupled torsional oscillators with additional onefold rotational potentials acting on each oscillator, and a chain of coupled torsional oscillators with additional threefold rotational potentials. These models are of interest because of their application to torsional motions in polymeric systems, and, in particular, the system with onefold rotational potentials has been studied extensively as the sine–Gordon chain. We present simulation results for three autocorrelation functions of these three systems both with and without topological solitons