Abstract The classical concept of molecular structure (namely, a set of atoms with a well‐defined geometrical arrangement in space) originated well before the advent of quantum theory, and, contrary to widespread views, these two conceptual schemes (classical molecular structure and quantum theory) are not easy to reconcile. We begin with a preliminary discussion of molecular structure in terms of space and time correlations in the framework of quantum theory. Then we summarize the salient features of some critical views raised‐during recent years (essentially by Woolley) concerning the concept of molecular structure. The essential claim of this viewpoint is that “molecular structure” is not an intrinsic attribute of an isolated molecule, and appears rather as an effect of the environment (other molecules? vacuum electromagnetic field, according to quantum electrodynamics?). Afterwards, we discuss these issues in detail: we show that it is necessary to distinguish between a “quantum” or “potential” structure (which may be deduced in a straightforward way from the quantum treatment of the molecule), and the “classical” molecular structure (according to which the molecule is considered as a set of rotating and vibrating material points, corresponding to the atoms); we briefly discuss some aspects of the Born–Oppenheimer approximation. From our discussion, we deduce that the “classical structure” concept is indeed non‐trivial from a purely quantum‐mechanical point of view; in actual fact, it is related to the problem of the “classical limit” of quantum mechanics, and it appears that, at the present time, none of these classical concepts and behaviours is convincingly derivable from a strict quantum mechanical basis. Finally, we consider these same problems from the point of view of stochastic electrodynamics (SED), which is one of the stochastic models for microphysics proposed so far as a possible alternative or extension of usual quantum theory. In the framework of such a theory, the “classical limit” and, in particular, the “classical molecular structure” no longer poses a problem, but aside from these satisfactory qualitative aspects, several quantitative failures of SED prevent us from accepting it, at least in its present state, as a genuine physical alternative to quantum theory. We therefore conclude that “classical molecular structure”, and classical concepts in general, remain an open problem in the framework of present‐day quantum physics.
Abstract The classical concept of molecular structure (namely, a set of atoms with a well‐defined geometrical arrangement in space) originated well before the advent of quantum theory, and, contrary to widespread views, these two conceptual schemes (classical molecular structure and quantum theory) are not easy to reconcile. We begin with a preliminary discussion of molecular structure in terms of space and time correlations in the framework of quantum theory. Then we summarize the salient features of some critical views raised‐during recent years (essentially by Woolley) concerning the concept of molecular structure. The essential claim of this viewpoint is that “molecular structure” is not an intrinsic attribute of an isolated molecule, and appears rather as an effect of the environment (other molecules? vacuum electromagnetic field, according to quantum electrodynamics?). Afterwards, we discuss these issues in detail: we show that it is necessary to distinguish between a “quantum” or “potential” structure (which may be deduced in a straightforward way from the quantum treatment of the molecule), and the “classical” molecular structure (according to which the molecule is considered as a set of rotating and vibrating material points, corresponding to the atoms); we briefly discuss some aspects of the Born–Oppenheimer approximation. From our discussion, we deduce that the “classical structure” concept is indeed non‐trivial from a purely quantum‐mechanical point of view; in actual fact, it is related to the problem of the “classical limit” of quantum mechanics, and it appears that, at the present time, none of these classical concepts and behaviours is convincingly derivable from a strict quantum mechanical basis. Finally, we consider these same problems from the point of view of stochastic electrodynamics (SED), which is one of the stochastic models for microphysics proposed so far as a possible alternative or extension of usual quantum theory. In the framework of such a theory, the “classical limit” and, in particular, the “classical molecular structure” no longer poses a problem, but aside from these satisfactory qualitative aspects, several quantitative failures of SED prevent us from accepting it, at least in its present state, as a genuine physical alternative to quantum theory. We therefore conclude that “classical molecular structure”, and classical concepts in general, remain an open problem in the framework of present‐day quantum physics.
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.
Conceptual and formal problems Many of the problems surrounding the interpretation of quantum mechanics stem from the absence of a sufficiently general and physically transparent analysis of the connection with the domain in which classical concepts are assumed to apply. It is the purpose of this chapter to describe with the aid of a few examples how the quantum potential approach provides a context within which the conceptual and formal issues raised by this problem may be clarified. A key question is to explain how the state or context dependence which is so characteristic of the quantum domain turns into state independence at a certain level, characterized as ‘classical’. To illustrate one aspect of the conceptual problem we recall that in Bohr's interpretation the validity of classical concepts is already presupposed since, it is suggested, it is only in terms of these that one can unambiguously communicate the results of experiments in the quantum domain. Thus, classical physics must be considered as prior to quantum mechanics and the latter is a generalization of the former in that it provides a new set of laws governing the application of classical concepts. According to this view, any procedure by which classical mechanics is recovered from quantum mechanics as a mathematical limit can only be a demonstration of consistency with the already postulated epistemological relation between the two theories and not as a ‘derivation’ of classical mechanics from quantum mechanics (George, Prigogine & Rosenfeld, 1972).
Molecular structure (MS) has been treated as a convention or an epiphenomenon by physicists and quantum chemists interpreting the mathematical formalism of quantum mechanics as the essential reality criterion in the submicroscopic world (R2 world). This paper argues that, (a) even in the R2 world there is a class of entities which are real per se, even though they cannot be separated from their material support, and MS may belong to that class; (b) MS actualizes a particular molecule from the many potentialities of a given set of nuclei and electrons, all present in the same Schrödinger equation; (c) MS is a fact established in the XIXth century, albeit as a result of circumstantial evidence (because of its belonging to the R2 world); (d) the fact that MS is known, as all objects of the atomic world, in terms of analogies with macroscopic models, is not valid grounds for questioning its reality; (e) MS is a set of topological as well as geometrical relations. All along the discussion, observability according to Bohr, Heisenberg, Feynman is taken as the essential criterion of reality in the R2 world. On its basis, quantum mechanics is by no means in conflict with the reality of molecular structure and shape. On the other hand, the question of the minimum lifetime required for a MS proper to exist should be left open, pending a detailed analysis of measurement techniques.
Quantum mechanics was developed as a response to the inability of the classical theories of mechanics and electromagnetism to provide a satisfactory explanation of some of the properties of electromagnetic radiation and of atomic structure. As a result, a theory has emerged whose basic principles can be used to explain not only the structure and properties of atoms, molecules and solids, but also those of nuclei and of “elementary” particles such as the proton and neutron. Although there are still many features of the physics of such systems that are not fully understood, there are presently no indications that the fundamental ideas of quantum mechanics are incorrect. In order to achieve this success, quantum mechanics has been built on a foundation that contains a number of concepts that are fundamentally different from those of classical physics and which have radically altered our view of the way the physical universe operates. This book aims to elucidate and discuss the conceptual basis of the subject as well as explaining its success in describing the behaviour of atomic and subatomic systems.
An attempt is made to refine the classical concept of molecular structure in the light of quantum theory. It is argued that a definite molecular structure can only be associated with quantum states that are intrinsically time-dependent and therefore need not manifest the full symmetry implied by the relativity principle; conversely if a molecule is definitely observed in an eigenstate of its associated molecular Schrödinger equation, a molecular structure description is inappropriate. The theme of the article is illustrated with examples drawn from spectroscopy, dielectric phenomena, electron scattering, stereoisomerism and optical activity.
Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence of molecular structure cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our understanding of a molecule in isolation, as well as of chemistry’s relation to quantum physics.