Williamsonloomis5544

We provide an explicit route to the Lagrange multipliers of the system and identify those operators that act as the dominant constraints.Despite the fact that anisotropic particles have been introduced to describe molecular interactions for decades, they have been poorly used for polymers because of their computing time overhead and the absence of a relevant proof of their impact in this field. We first report a method using anisotropic beads for polymers, which solves the computing time issue by considering that beads keep their principal orientation alongside the mean local backbone vector of the polymer chain, avoiding the computation of torques during the dynamics. Applying this method to a polymer bulk, we study the effect of anisotropic interactions vs isotropic ones for various properties such as density, pressure, topology of the chain network, local structure, and orientational order. We show that for different classes of potentials traditionally used in molecular simulations, those backbone oriented anisotropic beads can solve numerous issues usually encountered with isotropic interactions. We conclude that the use of backbone oriented anisotropic beads is a promising approach for the development of realistic coarse-grained potentials for polymers.The σ-hole⋯σ-hole stacking interaction, an unrecognized type of noncovalent interaction, has been found to be present in large quantities in the Cambridge Structural Database. In the σ-hole⋯σ-hole stacking interaction, each of the two interacting σ-holes has the dual electron donor/electron acceptor character; when one σ-hole acts as an electron donor, the other σ-hole acts as an electron acceptor, and vice versa. The σ-hole⋯σ-hole stacking interaction is clearly different from the σ-hole bond in which the charge transfer occurs mainly from the electron donor to the σ-hole. Energy component analysis shows that the σ-hole⋯σ-hole stacking interaction is dominated by the dispersion energy, which is similar to the nature of the aromatic stacking interaction between unsaturated molecules or the σ⋯σ stacking interaction between saturated molecules.In this work, we develop the free-energy spectrum theory for thermodynamics of open quantum impurity systems that can be either fermionic or bosonic or combined. We identify two types of thermodynamic free-energy spectral functions for open quantum systems and further consider the thermodynamic limit, which supports the Gaussian-Wick description of hybrid environments. We can then relate the thermodynamic spectral functions to the local impurity properties. These could be experimentally measurable quantities, especially for the cases of quantum dots embedded in solid surfaces. Another type of input is the bare-bath coupling spectral densities, which could be accurately determined with various methods. For illustration, we consider the simplest noninteracting systems, with focus on the strikingly different characteristics between the bosonic and fermionic scenarios.We present in detail and validate an effective Monte Carlo approach for the calculation of the nuclear vibrational densities via integration of molecular eigenfunctions that we have preliminary employed to calculate the densities of the ground and the excited OH stretch vibrational states in the protonated glycine molecule [Aieta et al., Nat Commun 11, 4348 (2020)]. Here, we first validate and discuss in detail the features of the method on a benchmark water molecule. Then, we apply it to calculate on-the-fly the ab initio anharmonic nuclear densities in the correspondence of the fundamental transitions of NH and CH stretches in protonated glycine. We show how we can gain both qualitative and quantitative physical insight by inspection of different one-nucleus densities and assign a character to spectroscopic absorption peaks using the expansion of vibrational states in terms of harmonic basis functions. The visualization of the nuclear vibrations in a purely quantum picture allows us to observe and quantify the effects of anharmonicity on the molecular structure, also to exploit the effect of IR excitations on specific bonds or functional groups, beyond the harmonic approximation. We also calculate the quantum probability distribution of bond lengths, angles, and dihedrals of the molecule. Notably, we observe how in the case of one type of fundamental NH stretching, the typical harmonic nodal pattern is absent in the anharmonic distribution.Most of the methods presently available to investigate the molecular magnetic response work extremely well for the computation of properties, such as magnetizability and nuclear magnetic shielding, but they provide insufficiently accurate current density maps, in that they do not guarantee exact conservation, leading to unphysical features in maps. read more The present study starts from the results obtained by Epstein and Sambe and moves forward to generalize them. An off-diagonal hypervirial relationship, connecting the matrix elements of a given differentiable function of position f(r) to its derivatives ∇f(r), via the anticommutator ∇αf,p^α+ with the canonical momentum operator p^, has first been proven. Afterward, this relationship is applied to show that the equations proposed by Sambe to check the quality and conservation of computed electronic current densities can be obtained as particular cases of this general theorem, with a substantial gain in computational efficiency. Connections with previous work by Arrighini, Maestro, and Moccia are outlined, and the implications that hint at future work are discussed.Monte Carlo simulations were performed to study the phase behavior of equimolar mixtures of spheres and cubes having selective inter-species affinity. Such a selectivity was designed to promote the formation of the substitutionally ordered NaCl compound, the "C* phase," and to be driven not only by energetic bonds but also by entropic bonds generated by dimples on the cube facets. Nestling of the spheres in the cube indentations can promote negative nonadditive mixing and increase the C* phase packing entropy. The focus is on congruent phase behavior wherein the C* phase directly melts into, and can be conveniently accessed from, the disordered state. A specialized thermodynamic integration scheme was used to trace the coexisting curves for varying the values of the interspecies contact energy, ε*, the relative indentation size, λ, and the sphere-to-cube size ratio, ζ. By starting from a known coexistence point with ε* > 0 and λ = 0 (no indentation), it is found that increasing λ (at fixed ε* and ζ) reduces the free-energy and pressure of the C* phase at coexistence, indicative of stronger entropic bonding.