Quantum free energy differences from non-equilibrium path integrals: I. Methods and numerical application

The imaginary-time path integral representation of the canonical partition function of a quantum system and non-equilibrium work fluctuation relations are combined to yield methods for computing free energy differences in quantum systems using non-equilibrium processes. The path integral representation is isomorphic to the configurational partition function of a classical field theory, to which a natural but fictitious Hamiltonian dynamics is associated. It is shown that if this system is prepared in an equilibrium state, after which a control parameter in the fictitious Hamiltonian is changed in a finite time, then formally the Jarzynski non-equilibrium work relation and the Crooks fluctuation relation are shown to hold, where work is defined as the change in the energy as given by the fictitious Hamiltonian. Since the energy diverges for the classical field theory in canonical equilibrium, two regularization methods are introduced which limit the number of degrees of freedom to be finite. The numerical applicability of the methods is demonstrated for a quartic double-well potential with varying asymmetry. A general parameter-free smoothing procedure for the work distribution functions is useful in this context.Comment: 20 pages, 4 figures. Added clarifying remarks and fixed typo

The Five Eras of Chiropractic & the future of chiropractic as seen through the eyes of a participant observer

Chiropractic has endured a turbulent history, marked by tremendous advances in areas such as education and licensing while marred by interprofessional conflict and a poor public image. The prolonged interprofessional conflict was instrumental in shaping the culture of chiropractic. These obstacles have long-since been removed although there are lingering effects from them

Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations

Alkali (Li+, Na+, K+, Rb+, and Cs+) and halide (F−, Cl−, Br−, and I−) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Åqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4PEW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells

Quantum Dynamical Rate Constant for the H + O3 Reaction Using a Six-Dimensional Double Many-Body Expansion Potential Energy Surface

We present a quantum mechanical, three-dimensional, infinite-orden-sudden-approximation study of the H + O3 atmospheric reaction using a recently reported double many-body expansion potential energy surface for ground-state HO3. The results are compared with existing experimental data and previously reported quasiclassical trajectory calculations which employed the same interaction potential. Agreement with the recommended experimental data is moderate, but encouraging when compared with the data of Clyne and Monkhouse, which extends over the range of temperatures 300 ≤ T/K ≤ 650, and with the recent measurement of Greenblatt and Wiesenfeld for T = 300 K. In comparison with the classical trajectory results, the agreement is also moderate, the differences being attributed to both methodological approximations in the quantum formalism and the problem of zero-point energy leakage in classical dynamics