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

A COMPUTATIONAL INVESTIGATION OF c-C3_{3}H2_{2}...HX(X = F, Cl, Br) H-BONDED COMPLEXES

Author Institution: Centre for Research in Molecular Modeling \& Department of Chemistry and Biochemistry, Concordia University, Montreal, QC, CanadaCyclopropenylidene (c-C$_{3}$H$_{2}$) is of significant importance in interstellar chemistry and synthetic chemistry (e.g., transition metal and organic catalysis). Because of its peculiar structure, c-C$_{3}$H$_{2}$ can act as a hydrogen-bond donor or acceptor. In order to gain insight into this feature, the ground-state potential energy surfaces of singlet c-C$_{3}$H$_{2}$ complexed with hydrogen halides HX (X = F, Cl, Br) have been explored extensively by density-functional theory (B3LYP) and {\it{ab initio}} quantum chemistry (MP2) with a variety of basis sets, cc-pVxZ and aug-cc-pVxZ (x = D, T). The complexes characterized have the carbenic end of c-C$_{3}$H$_{2}$ H-bonded to HX, with some proton transfer occurring, the extent of which follows the order HF < HCl < HBr. Accompanying the complex formation are the dipole moment enhancement, the charge transfer, red shifts of the HX vibrational stretching frequencies together with the significant enhancement of band intensity and concomitant HX bond elongation. The nature of H-bonding in these complexes has been explored, based on energy decomposition schemes and the Bader's quantum theory of atoms-in-molecules, with the conclusion that c-C$_{3}$H$_{2}$ is a strong H-bond acceptor with respect to the hydrogen halides

First-Principles Excited-State Molecular Dynamics Simulations: Application to Cluster Photochemistry

Computer simulations of the real time-evolution of complex chemical systems in their electronically excited states, resulting for example from photoexcitation, represent many challenges for modern computational chemistry. In this contribution, we discuss the application of first-principles molecular dynamics simulations of the excited state dynamics of clusters made up of a halide ion and a number of solvent (water) molecules. The number of difficulties encountered in such simulations is outlined, and preliminary results are reported and discussed in connection with available experimental data. A brief outlook for the future development of the current research is also given in light of recent progress in high-performance computing. La simulation sur ordinateur de la dynamique de systèmes chimiques complexes et de leur états électroniques excités, résultant par exemple d'une photoexcitation, présente un défi de taille pour la chimie numérique moderne. Dans ce travail, nous décrivons une simulation de dynamique moléculaire des états excités d'amas comportant un ion halogène entouré d'un certain nombre de molécules de solvant (eau). On décrit les difficultés généralement rencontrées dans de telles simulations, et on discute de résultats préliminaires en relation avec les données expérimentales disponibles. Une brève perspective des développements futurs pressentis est donnée, à la lumière des progrès récents dans le domaine du calcul de haute performance

A computational study of the 1,3-dipolar cycloaddition reaction mechanism for nitrilimines

The [3+2] and [1+2] cycloaddition pathways between ethene and a series of 13 nitrilimines (R1CNNR2) have been examined by density functional theory [PBE0/6-311++G(2df,pd)] calculations. All reactions have low barriers ranging from 14.14 (R1 = CH3, R2 = H) to 1.01 (R1 = R2 = F) kcal mol–1, and large reaction exothermicities consistent with the transient nature of nitrilimines. The [3+2] and [1+2] transition-state structures are very similar, mainly differing in the relative orientation of their fragments and the newly forming C—C bond distance, and exhibit only minor deviations from the structures of the reactants. Both reaction pathways are concerted and asynchronous, but the [1+2] reaction has a greater degree of asynchronicity. Examination of the frontier molecular orbitals reveals that both the [3+2] and [1+2] barrier heights are related to two sets of orbital interactions, with the interaction between the lowest unoccupied molecular orbital π of nitrilimine and the highest occupied molecular orbital of ethene in common. The second interaction in both cases is carbene-like. A relationship between the weights of the 1,3-dipolar resonance contribution in the various nitrilimines and the corresponding [3+2] barrier heights was not found, but a good correlation could be found between the [1+2] barrier heights and both the 1,3-dipolar and carbene contributions. Inspection of the potential energy surface in the vicinity of the two transition states for the reaction between unsubstituted nitrilimine and ethene suggests that the observed [3+2] product is a result of an initial carbene-like approach of the two fragments followed by a ridge bifurcation that leads to the [3+2] product minimum

Effects of Cholesterol on the Thermodynamics and Kinetics of Passive Transport of Water through Lipid Membranes

While it has long been known that cholesterol reduces the permeability of biological membranes to water, the exact mechanism by which cholesterol influences transmembrane permeation is still unclear. The thermodynamic and kinetic contributions to the transport of water across mixed DPPC/cholesterol bilayers of different composition are thus examined by molecular dynamics simulations. Our analyses show that cholesterol decreases transmembrane permeability to water mainly by altering the thermodynamics of water transport. In particular, the free-energy barrier to permeation is magnified in the dense bilayer interior and the partitioning of water is significantly lowered. The changes are observed to correlate quantitatively well with the cholesterol-dependent density and thickness of the bilayers. In contrast, diffusion coefficients are relatively insensitive to cholesterol concentration, except in the sparsely populated center of the bilayer. Diffusion of water in cholesterol-containing bilayers appears to be related to changes in the free area in the middle of the bilayer and to the solute cross-sectional area in the denser hydrophobic regions. Overall, cholesterol is found to have an inhibitory effect on the permeation of water at all concentrations investigated, although bilayers containing cholesterol concentrations up to 20 mol % display a more dramatic dependence on cholesterol content than at higher concentrations. Our results show that it is possible to quantitatively reproduce the relative effects of cholesterol on lipid bilayer permeability from molecular dynamics simulations