The application of modern quantum chemical methods to the simulation of chemical reactions makes it obvious that the Copenhagen picture of quantum mechanics cannot be maintained. In ab-initio molecular dynamics methods, any kind of matter is described by applying the Schrödinger equation to the electronic structure and using classical Newton dynamics for the motion of the atomic nuclei. By lots of calculations on this basis, it has become obvious that this concept is superior to a quantum chemical description of nuclear motion. The nuclei move according to Newton's laws in a perfectly local and deterministic way while the surrounding electronic cloud determines bonding and antibonding interactions between the atoms. The resulting theory is a deterministic formulation of quantum mechanics which is free from paradoxa and is able to explain complex phenomena like photochemistry. An obvious consequence is that molecules like ammonia can have a permanent dipole moment in spectroscopic measurements, while consistent application of traditional quantum mechanics predicts a higher symmetry as is outlined in the paper.
The application of modern quantum chemical methods to the simulation of chemical reactions makes it obvious that the Copenhagen picture of quantum mechanics cannot be maintained. In ab-initio molecular dynamics methods, any kind of matter is described by applying the Schrödinger equation to the electronic structure and using classical Newton dynamics for the motion of the atomic nuclei. By lots of calculations on this basis, it has become obvious that this concept is superior to a quantum chemical description of nuclear motion. The nuclei move according to Newton's laws in a perfectly local and deterministic way while the surrounding electronic cloud determines bonding and antibonding interactions between the atoms. The resulting theory is a deterministic formulation of quantum mechanics which is free from paradoxa and is able to explain complex phenomena like photochemistry. An obvious consequence is that molecules like ammonia can have a permanent dipole moment in spectroscopic measurements, while consistent application of traditional quantum mechanics predicts a higher symmetry as is outlined in the paper.
Abstract To be accepted by the community, the claim that nuclear motion has to be treated classically must be tested for all kinds of phenomena. For the moment we claim that in a quantum chemical calculation, a classical description of nuclear motion is superior to the use of the Schrödinger equation, and investigate how far we get with this statement. In the present paper we address the question what nuclear quantum statistics means in this context. We will show that the Maxwell–Boltzmann velocity distribution evolves quickly in any molecular dynamics simulation and this guarantees the physically correct behavior of molecular systems. Using first‐principles molecular dynamics simulations, or more precisely Car–Parrinello molecular dynamics, we investigate what this means for Bose‐Einstein condensates and for Cooper pairs. It turns out that our approach can explain all relevant phenomena. As a consequence, we can introduce a deterministic formulation of quantum mechanics and can get rid of all the paradoxa in traditional quantum mechanics. The basic idea is to treat electrons and nuclei differently.
Quantum mechanics is perceived as a theory that is difficult to understand with strange philosophical consequences. This is due to the Copenhagen interpretation of quantum mechanics. On the basis of the knowledge accumulated in modern computer simulations of many-particle problems, a different approach is presented that is purely deterministic. To arrive at this simpler picture, it is sufficient to treat nuclear motion classically. It is argued that this is justified by the different nature of nuclear motion compared to electronic structure, which must be described quantum-mechanically. The underlying approximation leads directly to the theory that is mainly used nowadays to simulate chemical reactions. As a result, electronic structure develops with time without any wavefunction collapse.
Abstract: We present a fully classical and deterministic framework for chemistry that does not rely on any of the postulates of quantum mechanics.Matter is described as a continuous, fluid‑like medium whose evolution is governed by the classical equations of hydrodynamics.In this picture, atoms, molecules, chemical bonds, spectra, and reaction rates all emerge naturally from the motion and interaction of this fluid, without requiring Planck’s constant or any other quantum concept.The theory provides a self‑consistent account of chemical phenomena and yields testable predictions.
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.
Despite the quantum nature of molecules, classical mechanics is often employed to describe molecular motions that play a fundamental role in a wide range of phenomena including chemical reactions. This is due to the need of assigning well-defined positions to the atomic nuclei during the time evolution of the system in order to describe unambiguously the molecular motions, whereas quantum mechanics provides information on probabilistic nature only. One would like to employ a quantum molecular trajectory that defines rigorously the instantaneous nuclear positions and, simultaneously, guarantees the conservation of all quantum mechanics predictions unlike the classical trajectory. We argue that such a quantum molecular trajectory can be formally defined and we prove that it corresponds to a single Bohm trajectory. Our analysis establishes a clear correspondence between the statistical properties of the trajectory and the quantum expectation values. The obvious and undeniable benefit is that of dealing with a quantum methodology fully characterizing the molecular motions without any reference to classical mechanics.
When we are presented with apparently bizarre properties of microsystems governed by quantum mechanics (as in our discussion of the double-slit experiment in the previous chapter), we naturally ask whether it might be possible to find another theory, or at least another story to go with the equations, that would make more sense to us. We might seek a theory and a view of fundamental physical processes that would accord more with our classically based, everyday common sense. This typically takes the form of the question of the possibility of the existence of a more detailed description of atomic processes than that afforded by the wave function (that is, by the Copenhagen interpretation of the previous chapter). In this chapter we discuss some of the central interpretive problems of the Copenhagen version of quantum mechanics. Then, in the next two chapters, we look at the severe, general restrictions that are placed on any such completion of quantum mechanics and at one particular extension of quantum mechanics. First, though, we begin here with the struggle that ensued over the status of causality in quantum theory. THE COMPLETENESS OF QUANTUM MECHANICS Although the Heisenberg uncertainty principle (Section 20.4) and the lack of absolute predictive power are an inherent feature of quantum mechanics, there have been attempts to preserve an in principle completely deterministic structure for physics. Even classically, in a macroscopic sample of gas there are so many molecules that it would be hopeless, as a practical matter, to predict the future locations of all these molecules from Newton's laws of motion.