It is shown that the quantum mechanics is capable of describing processes which have all the aspects of certain chemical reactions. It turns out that a system may change from one configuration to another when a quantum level of the one configuration has the same energy as a quantum level of the other. Among such reactions mention is made and some discussion given of the large classes of molecular rearrangements, and decompositions, including radioactive disintegration. The dependence on pressure and temperature is slightly discussed and it is indicated that the present theory quite explains the necessity of the old "activation hypothesis" of Arrhenius. The old notions should, however, be modified to take into account that it is not sufficient to have at least the "activation energy" but the molecule must be in a particular state to react. Moreover when there are several "activated" states the rate of reaction from different ones may be very different indeed. Insight is gained into the nature of certain types of catalytic action including special wall catalyses. Some features of photochemical reactions are made clear by the theory.
It is shown that the quantum mechanics is capable of describing processes which have all the aspects of certain chemical reactions. It turns out that a system may change from one configuration to another when a quantum level of the one configuration has the same energy as a quantum level of the other. Among such reactions mention is made and some discussion given of the large classes of molecular rearrangements, and decompositions, including radioactive disintegration. The dependence on pressure and temperature is slightly discussed and it is indicated that the present theory quite explains the necessity of the old "activation hypothesis" of Arrhenius. The old notions should, however, be modified to take into account that it is not sufficient to have at least the "activation energy" but the molecule must be in a particular state to react. Moreover when there are several "activated" states the rate of reaction from different ones may be very different indeed. Insight is gained into the nature of certain types of catalytic action including special wall catalyses. Some features of photochemical reactions are made clear by the theory.
The water molecule and a hydrogenic abstraction reaction are used to explore in detail some quantum entanglement features of chemical interest. We illustrate that the energetic and quantum-information approaches are necessary for a full understanding of both the geometry of the quantum probability density of molecular systems and the evolution of a chemical reaction. The energy and entanglement hypersurfaces and contour maps of these two models show different phenomena. The energy ones reveal the well-known stable geometry of the models, whereas the entanglement ones grasp the chemical capability to transform from one state system to a new one. In the water molecule the chemical reactivity is witnessed through quantum entanglement as a local minimum indicating the bond cleavage in the dissociation process of the molecule. Finally, quantum entanglement is also useful as a chemical reactivity descriptor by detecting the transition state along the intrinsic reaction path in the hypersurface of the hydrogenic abstraction reaction corresponding to a maximally entangled state.
This introductory chapter provides an overview of quantum mechanics, which is a subject of central importance in chemistry, and is by nature a mathematical theory. The chemist's approach to the understanding of matter and its chemical transformations is to take a microscopic view, connecting experimental observation with the properties of constituent molecules. However, at the microscopic level, atoms, molecules, and their constituent particles do not obey the familiar laws of mechanics that pertain to the everyday macroscopic world. For example, the existence of molecular line spectra indicates that molecules can be found only at certain well-defined energies, unlike objects at our own scale whose energy appears to be continuously variable. This book aims to explain the fundamentals of quantum mechanics from the point of view of chemistry; describe the areas of chemistry where quantum mechanics is most important; and show how quantum mechanics is applied to chemical problems.
Introduction Key features of quantum mechanics are the uncertainty principle, wave–particle duality, quantization of energies and the modification of classical probability laws. Biology is concerned with how natural systems function – from understanding how genetically coded information is replicated, to attaining a mechanistic model for complex multistep reactions. Recently researchers have been asking whether quantum mechanics, normally the domain of physics, is also needed to understand some biological processes. This field includes fascinating developments in theory and experiment, as well as multidisciplinary discussion, and the state-of-the-art is documented in this book. Erwin Schrödinger, in his famous book What is Life ? (Schrödinger, 1944), noted that quantum mechanics accounts for the stability of living things and their cellular processes because of our understanding, via quantum mechanics, of the stability and structure of molecules. The fact that quantum effects create, sometimes large, energy gaps between different states of a chemical system is also important. Such energy gaps, between electronic energy levels, enable living organisms to capture and store the energy carried from the sun by photons, and to visualize the world around them via optically induced chemical reactions. Davydov's view in Biology and Quantum Mechanics (Davydov, 1982) was that quantum mechanics is most relevant for isolated systems in pure states and therefore is of little importance for biological systems that are in statistical states at thermal equilibrium.
Bohm theory is a formulation of Quantum Mechanics that characterises the state of a quantum system according to both the wave function, as in the conventional formulation, and the coordinates (positions) of all the particles that evolve in time drawing quantum continuous trajectories. Furthermore, a statistical ensemble of all the possible trajectories, raising from the impossibility to know the initial position of all the particles, establishes the exact correspondence with the traditional Quantum Mechanics. From a computational point of view, Bohm theory has found many applications in Chemical Physics especially to develop new methodologies for solving the Schrödinger equation and to address semi-classical approximations of Quantum Mechanics. From a theoretical point of view, the most appealing feature of Bohm theory is its capability to supply a conceptual map between the quantum formalism and our representation of what a chemical system is. Chemical systems are composed of molecules, but the same idea of molecule requires a specific arrangement in the space of particles, i.e., the nuclei of the atoms. The statistical description of conventional Quantum Mechanics on the basis of wave function alone is insufficient to establish a clear correspondence with such a picture of molecules. Indeed, chemists employ usually Classical Mechanics in order to overcome this drawback of the standard quantum theory. On the other hand, if the particles position is included in the quantum formalism, as Bohm theory does, the map can be defined in a self-consistent way. In other words, Bohm theory appears to be the suitable quantum framework to represent molecules and their motion. The chemical representation of molecular systems finds a natural correspondence with a single Bohm trajectory, since it is always implicitly assumed that molecular components have specific spatial position independently of our knowledge about it. Consequently, we develop a quantum method whose fundamental assumption is that a single Bohm trajectory, i.e., a quantum molecular trajectory, describes the molecular systems and the molecular motion correctly. First of all, we examine the correspondence between a single Bohm trajectory and the conventional Quantum Mechanics, without using the ensemble of trajectories. We verify that such a correspondence exists through numerical simulations and we prove formally that the statistical properties of a single Bohm trajectory explain the probabilistic description of Quantum Mechanics. Once the consistency of this original approach has been established, we investigate the predicted properties. For instance, we take into account the constants of motion (such as the energy) corresponding to the time evolution of the coordinates and the behaviour of simple chemical systems, e.g., the vibrational motion of single molecules interacting with a resonant field. In this way, unexpected features of the molecular motion are found. Secondly, we tackle the challenge of describing many components systems (like the chemical systems in ordinary conditions). As a matter of fact, the computation of the Bohm trajectory and of the wave function is extremely demanding. However, the statistical properties of the Bohm trajectory allow the derivation of stochastic theories for examining the dynamics of open quantum systems, i.e., few molecules (or few degrees of freedom) interacting with their environment (the other molecules). One of the developed stochastic methods correlates the dynamics of the reduced density matrix, for the degrees of freedom of interest, to the evolution of the corresponding Bohm coordinates. In other words, the Bohm equation, determining the set of all the particles velocities according to the full wave function, is replaced with a stochastic one that approximates the velocity of a subset of coordinates according to the reduced density matrix. In such a way, the quantum fluctuations induced by the environment are taken into account. The advantage of this method concerns its capability of describing quantum systems, including open quantum systems, in terms of a quantum trajectory. This could allow the understanding of the molecular motion during a spectroscopical experiment. The possibility of investigating reactive systems, such as conformational changes, is particularly interesting. As a matter of fact, chemical reactions can be completely characterised only through the particles motion and we define the suit- able quantum methodology providing a self-consistent description of the molecular motion.
It is a remarkable empirical fact, known for a long time, that in certain self-organized periodic chemical reactions, such as Liesegang's or Belousov-Zhabotinsky's reactions, the product of molecular weight of precipitate, precipitation length period, and speed of precipitation is of the order of universal Planck's quantum of action h. Based on the fact that the classical and quantum diffusions are processes, which are indistinguishable in the configuration space, a quantum criterion in terms of diffusion constants has been established. This criterion enables one to find out conditions under which the quantum behavior of self-organized periodic reactions can be observed.
Abstract It has been shown in a previous paper that classical mechanics are not adequate to treat the transition of a hydrogen atom or proton across an energy barrier of the dimensions commonly met with in chemical reaction. The treatment given was based on an exact solution of the Schrödinger equation and a type of potential curve having no discontinuities in slope, but owing to the laborious nature of the computations involved, no attempt was made to investigate quantitatively the effect of variations in the heat of activation, the width of the barrier, or the mass of the particle. The present paper describes an approximate treatment leading to simple equations which can be applied directly to investigate these points. In a recent paper, Wigner has given a method of treatment applicable to any form of potential curve. His final equations are, however, only valid for the case in which the difference between the quantum mechanical and classical results can be expressed as a small correction term, and cannot be applied when there are large deviations from classical behaviour.