Electronic Properties of Water in Liquid Environment. A Sequential QM/MM Study Using the Free Energy Gradient Method

There is a continuous search for theoretical methods that are able to describe the effects of the liquid environment on molecular systems. Different methods emphasize different aspects, and the treatment of both the local and bulk properties is still a great challenge. In this work, the electronic properties of a water molecule in liquid environment is studied by performing a relaxation of the geometry and electronic distribution using the free energy gradient method. This is made using a series of steps in each of which we run a purely molecular mechanical (MM) Monte Carlo Metropolis simulation of liquid water and subsequently perform a quantum mechanical/molecular mechanical (QM/MM) calculation of the ensemble averages of the charge distribution, atomic forces, and second derivatives. The MP2/aug-cc-pV5Z level is used to describe the electronic properties of the QM water. B3LYP with specially designed basis functions are used for the magnetic properties. Very good agreement is found for the local properties of water, such as geometry, vibrational frequencies, dipole moment, dipole polarizability, chemical shift, and spin-spin coupling constants. The very good performance of the free energy method combined with a QM/MM approach along with the possible limitations are briefly discussed.

A simple analysis of the influence of the solvent-induced electronic polarization on the N-15 magnetic shielding of pyridine in water

Electronic polarization induced by the interaction of a reference molecule with a liquid environment is expected to affect the magnetic shielding constants. Understanding this effect using realistic theoretical models is important for proper use of nuclear magnetic resonance in molecular characterization. In this work, we consider the pyridine molecule in water as a model system to briefly investigate this aspect. Thus, Monte Carlo simulations and quantum mechanics calculations based on the B3LYP/6-311++G (d,p) are used to analyze different aspects of the solvent effects on the N-15 magnetic shielding constant of pyridine in water. This includes in special the geometry relaxation and the electronic polarization of the solute by the solvent. The polarization effect is found to be very important, but, as expected for pyridine, the geometry relaxation contribution is essentially negligible. Using an average electrostatic model of the solvent, the magnetic shielding constant is calculated as -58.7 ppm, in good agreement with the experimental value of -56.3 ppm. The explicit inclusion of hydrogen-bonded water molecules embedded in the electrostatic field of the remaining solvent molecules gives the value of -61.8 ppm.

Calculations of the spectral shifts and line profiles of alkaline earth atoms in liquid helium environment

Liquid configurations generated by Metropolis Monte Carlo simulations are used in time-dependent density functional theory calculations of the spectral line shifts and line profiles of the lowest lying excitation of the alkaline earth atoms, Be, Mg, Ca, Sr and Ba embedded in liquid helium. The results are in very good agreement with the available experimental data. Special attention is given to the calculated spectroscopic shift and the associated line broadening. The analysis specifies the inhomogeneous broadening of the three separate contributions due to the splitting of the s -> p transition of the alkaline earth atom in the liquid environment. (C) 2012 Elsevier B. V. All rights reserved.

Stochastic quantization of the spherical model and supersymmetry.

In this work, we reported some results about the stochastic quantization of the spherical model. We started by reviewing some basic aspects of this method with emphasis in the connection between the Langevin equation and the supersymmetric quantum mechanics, aiming at the application of the corresponding connection to the spherical model. An intuitive idea is that when applied to the spherical model this gives rise to a supersymmetric version that is identified with one studied in Phys. Rev. E 85, 061109, (2012). Before investigating in detail this aspect, we studied the stochastic quantization of the mean spherical model that is simpler to implement than the one with the strict constraint. We also highlight some points concerning more traditional methods discussed in the literature like canonical and path integral quantization. To produce a supersymmetric version, grounded in the Nicolai map, we investigated the stochastic quantization of the strict spherical model. We showed in fact that the result of this process is an off-shell supersymmetric extension of the quantum spherical model (with the precise supersymmetric constraint structure). That analysis establishes a connection between the classical model and its supersymmetric quantum counterpart. The supersymmetric version in this way constructed is a more natural one and gives further support and motivations to investigate similar connections in other models of the literature.

Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

On the renormalization flow representation of field theory and some applications

In this thesis we discuss a representation of quantum mechanics and quantum and statistical field theory based on a functional renormalization flow equation for the one-particle-irreducible average effective action, and we employ it to get information on some specific systems.

Planck stars: theory and phenomenology

General Relativity (GR) is one of the greatest scientific achievements of the 20th century along with quantum theory. Despite the elegance and the accordance with experimental tests, these two theories appear to be utterly incompatible at fundamental level. Black holes provide a perfect stage to point out these difficulties. Indeed, classical GR fails to describe Nature at small radii, because nothing prevents quantum mechanics from affecting the high curvature zone, and because classical GR becomes ill-defined at r = 0 anyway. Rovelli and Haggard have recently proposed a scenario where a negative quantum pressure at the Planck scales stops and reverts the gravitational collapse, leading to an effective “bounce” and explosion, thus resolving the central singularity. This scenario, called Black Hole Fireworks, has been proposed in a semiclassical framework. The purpose of this thesis is twofold: - Compute the bouncing time by means of a pure quantum computation based on Loop Quantum Gravity; - Extend the known theory to a more realistic scenario, in which the rotation is taken into account by means of the Newman-Janis Algorithm.

Accurate Predictions of Water Cluster Formation, (H2O)n=2-10

An efficient mixed molecular dynamics/quantum mechanics model has been applied to the water cluster system. The use of the MP2 method and correlation consistent basis sets, with appropriate correction for BSSE, allows for the accurate calculation of electronic and free energies for the formation of clusters of 2−10 water molecules. This approach reveals new low energy conformers for (H2O)n=7,9,10. The water heptamer conformers comprise five different structural motifs ranging from a three-dimensional prism to a quasi-planar book structure. A prism-like structure is favored energetically at low temperatures, but a chair-like structure is the global Gibbs free energy minimum past 200 K. The water nonamers exhibit less complexity with all the low energy structures shaped like a prism. The decamer has 30 conformers that are within 2 kcal/mol of the Gibbs free energy minimum structure at 298 K. These structures are categorized into four conformer classes, and a pentagonal prism is the most stable structure from 0 to 320 K. Results can be used as benchmark values for empirical water models and density functionals, and the method can be applied to larger water clusters.

Using the Franck-Hertz Experiment To Illustrate Quantization Energy States of the Neon Atom by Electron Impact

na provide students with motivation for the study of quantum mechanics. That microscopic matter exists in quantized states can be demonstrated with modem versions of historic experiments: atomic line spectra (I), resonance potentials, and blackbody radiation. The resonance potentials of mercury were discovered by Franck and Hertz in 1914 (2). Their experiment consisted of bombarding atoms by electrons, and detecting the kinetic energy loss of the scattered electrons (3). Prior to the Franck-Hertz experiment, spectroscopic work bv Balmer and Rvdbere revealed that atoms emitted radiatibn at discrete ekergiis. The Franck-Hertz experiment showed directly that auantized enerm levels in an atom are real, not jist optiEal artifacts. atom can be raised to excited states by inelastic collisions with electrons as well as lowered from excited states by emission of photons. The classic Franck-Hertz experiment is carried out with mercury (4-7). Here we present an experiment for the study of resonance potentials using neon.

Atmospheric Implications for Formation of Clusters of Ammonium and 1−10 Water Molecules

A mixed molecular dynamics/quantum mechanics model has been applied to the ammonium/water clustering system. The use of the high level MP2 calculation method and correlated basis sets, such as aug-cc-pVDZ and aug-cc-pVTZ, lends confidence in the accuracy of the extrapolated energies. These calculations provide electronic and free energies for the formation of clusters of ammonium and 1−10 water molecules at two different temperatures. Structures and thermodynamic values are in good agreement with previous experimental and theoretical results. The estimated concentration of these clusters in the troposphere was calculated using atmospheric amounts of ammonium and water. Results show the favorability of forming these clusters and implications for ion-induced nucleation in the atmosphere.

Accurate Predictions of Water Cluster Formation, (H2O)n=2−10

An efficient mixed molecular dynamics/quantum mechanics model has been applied to the water cluster system. The use of the MP2 method and correlation consistent basis sets, with appropriate correction for BSSE, allows for the accurate calculation of electronic and free energies for the formation of clusters of 2−10 water molecules. This approach reveals new low energy conformers for (H2O)n=7,9,10. The water heptamer conformers comprise five different structural motifs ranging from a three-dimensional prism to a quasi-planar book structure. A prism-like structure is favored energetically at low temperatures, but a chair-like structure is the global Gibbs free energy minimum past 200 K. The water nonamers exhibit less complexity with all the low energy structures shaped like a prism. The decamer has 30 conformers that are within 2 kcal/mol of the Gibbs free energy minimum structure at 298 K. These structures are categorized into four conformer classes, and a pentagonal prism is the most stable structure from 0 to 320 K. Results can be used as benchmark values for empirical water models and density functionals, and the method can be applied to larger water clusters.

Minimal assumption derivation of a weak Clauser-Horne inequality

According to Bell's theorem a large class of hidden-variable models obeying Bell's notion of local causality (LC) conflict with the predictions of quantum mechanics. Recently, a Bell-type theorem has been proven using a weaker notion of LC, yet assuming the existence of perfectly correlated event types. Here we present a similar Bell-type theorem without this latter assumption. The derived inequality differs from the Clauser-Horne inequality by some small correction terms, which render it less constraining.

Modern charge density studies: the entanglement of experiment and theory

This tutorial review article is intended to provide a general guidance to a reader interested to learn about the methodologies to obtain accurate electron density mapping in molecules and crystalline solids, from theory or from experiment, and to carry out a sensible interpretation of the results, for chemical, biochemical or materials science applications. The review mainly focuses on X-ray diffraction techniques and refinement of experimental models, in particular multipolar models. Neutron diffraction, which was widely used in the past to fix accurate positions of atoms, is now used for more specific purposes. The review illustrates three principal analyses of the experimental or theoretical electron density, based on quantum chemical, semi-empirical or empirical interpretation schemes, such as the quantum theory of atoms in molecules, the semi-classical evaluation of interaction energies and the Hirshfeld analysis. In particular, it is shown that a simple topological analysis based on a partition of the electron density cannot alone reveal the whole nature of chemical bonding. More information based on the pair density is necessary. A connection between quantum mechanics and observable quantities is given in order to provide the physical grounds to explain the observations and to justify the interpretations.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Solvation-Driven Charge Transfer and Localization in Metal Complexes

In any physicochemical process in liquids, the dynamical response of the solvent to the solutes out of equilibrium plays a crucial role in the rates and products: the solvent molecules react to the changes in volume and electron density of the solutes to minimize the free energy of the solution, thus modulating the activation barriers and stabilizing (or destabilizing) intermediate states. In charge transfer (CT) processes in polar solvents, the response of the solvent always assists the formation of charge separation states by stabilizing the energy of the localized charges. A deep understanding of the solvation mechanisms and time scales is therefore essential for a correct description of any photochemical process in dense phase and for designing molecular devices based on photosensitizers with CT excited states. In the last two decades, with the advent of ultrafast time-resolved spectroscopies, microscopic models describing the relevant case of polar solvation (where both the solvent and the solute molecules have a permanent electric dipole and the mutual interaction is mainly dipole−dipole) have dramatically progressed. Regardless of the details of each model, they all assume that the effect of the electrostatic fields of the solvent molecules on the internal electronic dynamics of the solute are perturbative and that the solvent−solute coupling is mainly an electrostatic interaction between the constant permanent dipoles of the solute and the solvent molecules. This well-established picture has proven to quantitatively rationalize spectroscopic effects of environmental and electric dynamics (time-resolved Stokes shifts, inhomogeneous broadening, etc.). However, recent computational and experimental studies, including ours, have shown that further improvement is required. Indeed, in the last years we investigated several molecular complexes exhibiting photoexcited CT states, and we found that the current description of the formation and stabilization of CT states in an important group of molecules such as transition metal complexes is inaccurate. In particular, we proved that the solvent molecules are not just spectators of intramolecular electron density redistribution but significantly modulate it. Our results solicit further development of quantum mechanics computational methods to treat the solute and (at least) the closest solvent molecules including the nonperturbative treatment of the effects of local electrostatics and direct solvent−solute interactions to describe the dynamical changes of the solute excited states during the solvent response.