Simulations of solvation in a Brownian dipole lattice

Lone Pair Rotational Dynamics in Solids

Traditional classifications of crystalline phases focus on nuclear degrees of freedom. Through the examination of both electronic and nuclear structure, we introduce the concept of an electronic plastic crystal. Such a material is classified by crystalline nuclear structure, while localized electronic degrees of freedom-here lone pairs-exhibit orientational motion at finite temperatures. This orientational motion is an emergent phenomenon arising from the coupling between electronic structure and polarization fluctuations generated by collective motions, such as phonons. Using ab initio molecular dynamics simulations, we predict the existence of electronic plastic crystal motion in halogen crystals and halide perovskites, and suggest that such motion may be found in a broad range of solids with lone pair electrons. Such fluctuations in the charge density should be observable, in principle, via synchrotron scattering.

Rotational dynamics in a crystalline molecular gyroscope by variable-temperature 13C NMR, 2H NMR, X-ray diffraction, and force field calculations

A combination of solid-state 13C CPMAS NMR, 2H NMR, X-ray-determined anisotropic displacement parameters (ADPs), and molecular mechanics calculations were used to analyze the rotational dynamics of 1,4-bis[3,3,3-tris(m-methoxyphenyl)propynyl]benzene (3A), a structure that emulates a gyroscope with a p-phenylene group acting as a rotator and two m-methoxy-substituted trityl groups acting as a stator. The line shape analysis of VT 13C CPMAS and broad-band 2H NMR data were in remarkable agreement with each other, with rotational barriers of 11.3 and 11.5 kcal/mol, respectively. The barriers obtained by analysis of ADPs obtained by single-crystal X-ray diffraction at 100 and 200 K, assuming a sinusoidal potential, were 10.3 and 10.1 kcal, respectively. A similar analysis of an X-ray structure solved from data acquired at 300 K suggested a barrier of only 8.0 kcal/mol. Finally, a rotational potential calculated with a finite cluster model using molecular mechanics revealed a symmetric but nonsinusoidal potential that accounts relatively well for the X-ray-derived values and the NMR experimental results. It is speculated that the discrepancy between the barriers derived from low and high-temperature X-ray data may be due to an increase in anharmonicity, or to disorder, at the higher temperature values.

Free energy landscapes of electron transfer system in dipolar environment below and above the rotational freezing temperature

Electron transfer reaction in a polar solvent is modeled by a solute dipole surrounded by dipolar molecules with simple rotational dynamics posted on the three-dimensional distorted lattice sites. The interaction energy between the solute and solvent dipoles as a reaction coordinate is adopted and free energy landscapes are calculated by generating all possible states for a 26 dipolar system and by employing Wang-Landau sampling algorithm for a 92 dipolar system. For temperatures higher than the energy scale of dipole-dipole interactions, the free energy landscapes for the small reaction coordinate region have quadratic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] whereas for the large reaction coordinate region, the landscapes exhibit a nonquadratic shape. When the temperature drops, small notched structures appear on the free energy profiles because of the frustrated interactions among dipoles. The formation of notched structure is analyzed with statistical approach and it is shown that the amplitude of notched structure depend upon the segment size of the reaction coordinate and is characterized by the interaction energy among the dipoles. Using simulated free energy landscapes, the authors calculate the reaction rates as a function of the energy gap for various temperatures. At high temperature, the reactions rates follow a bell shaped (inverted parabolic) energy gap law in the small energy gap regions, while it becomes steeper than the parabolic shape in a large energy gap regions due to the nonquadratic shape of the free energy landscape. The peak position of parabola also changes as the function of temperature. At low temperature, the profile of the reaction rates is no longer smooth because of the many local minima of the free energy landscape.

Free energy landscape analysis of two-dimensional dipolar solvent model at temperatures below and above the rotational freezing point

Ionic solvation in a polar solvent is modeled by a central charge surrounded by dipolar molecules posted on two-dimensional distorted lattice sites with simple rotational dynamics. Density of states is calculated by applying the Wang-Landau algorithm to both the energy and polarization states. The free energy landscapes of solvent molecules as a function of polarization are depicted to explore the competition between the thermal fluctuation and solvation energy. Without a central charge, for temperatures higher than the energy scale of the dipole-dipole interactions, the energy landscape for the small polarization region exhibits a parabolic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] for electron transfer reaction, while there is an additional quartic contribution to the landscape for the large polarization region. When the temperature drops, the simulated free energy landscapes are no longer smooth due to the presence of multiple local minima arising from the frustrated interaction among the dipoles. The parabolic contribution becomes negligible and the energy landscape becomes quartic in shape. For a strong central charge, the energy landscape exhibits an asymmetric profile due to the contributions of linear and cubic terms that arise from the charge-dipole interactions.

Basis set study of classical rotor lattice dynamics

The reorientational relaxation of molecular systems is important in many phenomenon and applications. In this paper, we explore the reorientational relaxation of a model Brownian rotor lattice system with short range interactions in both the high and low temperature regimes. In this study, we use a basis set expansion to capture collective motions of the system. The single particle basis set is used in the high temperature regime, while the spin wave basis is used in the low temperature regime. The equations of motion derived in this approach are analogous to the generalized Langevin equation, but the equations render flexibility by allowing nonequilibrium initial conditions. This calculation shows that the choice of projection operators in the generalized Langevin equation (GLE) approach corresponds to defining a specific inner-product space, and this inner-product space should be chosen to reveal the important physics of the problem. The basis set approach corresponds to an inner-product and projection operator that maintain the orthogonality of the spherical harmonics and provide a convenient platform for analyzing GLE expansions. The results compare favorably with numerical simulations, and the formalism is easily extended to more complex systems.

Mechanistic analysis of the observed linear free energy relationships in p21ras and related systems

Previous studies of the GTPase reaction catalyzed by p21ras have indicated that the logarithm of the observed reaction rate and the pKa of the bound GTP are correlated by the Brønsted relationship log(kcat) = beta pKa + A. While most of the Ras mutants display a Brønsted slope beta of 2.1, a small set of oncogenic mutants exhibit a beta of > > 1. On the other hand, it was found that the corresponding Brønsted slope for the GTPase reaction of p21ras in the presence of GTPase Activating Protein (GAP) is about beta = 4.9. The present work explores the basis for such linear free energy relationships (LFERs) in general and applies these concepts to p21ras and related systems. It is demonstrated that the optimal way to analyze LFER is by using Marcus type parabolas that represent the reactant, intermediate, and product state of the reaction in a relevant energy diagram. The observed LFER is used to analyze the actual free energy surface and reaction path of the intrinsic GTPase reaction in p21ras. From this, a model reaction profile can be constructed that explains how a LFER can arise and also how the different observed Brønsted coefficients can be rationalized. This analysis is augmented by solvent isotope effect studies. It is pointed out that the overall activation barrier reflects the energy of the proton transfer (PT) step, although this step does not include the actual transition state of the hydrolysis reaction. The proposed GTP as a base mechanism is compared to a recently proposed reaction scheme where Gln61 serves as a proton shuttle in a concerted mechanism. It is shown by unique energy considerations that the concerted mechanism is unlikely. Other alternative mechanisms are also considered, and their consistency with the observed LFER and other factors is discussed. Finally, we analyze the observed LFER for the GTPase reaction of p21ras in the presence of GAP and discuss its relevance for the mechanism of GAP activation.