In this paper we propose a possible explanation of the fact that certain molecules exhibiting symmetric configurations are localized in one of them, instead of being delocalized as predicted by a naive application of quantum mechanics. Our mechanism is based upon the instability, in the semiclassical regime, of delocalized states under small perturbations (among which we consider the reaction field due to the environment). This mechanism predicts, for example, a different behavior for ${\mathrm{NH}}_{3}$ and ${\mathrm{AsH}}_{3}$ (delocalized ground state in the former case, localized ground state in the latter case), and similar to the case of ${\mathrm{AsH}}_{3}$ we expect localized states in the case of optical isomers, in agreement with the empirical evidence. Possible consequences concerning the understanding of the ``classical limit'' in general are briefly outlined.
In this paper we propose a possible explanation of the fact that certain molecules exhibiting symmetric configurations are localized in one of them, instead of being delocalized as predicted by a naive application of quantum mechanics. Our mechanism is based upon the instability, in the semiclassical regime, of delocalized states under small perturbations (among which we consider the reaction field due to the environment). This mechanism predicts, for example, a different behavior for NH3 and AsH3 (delocalized ground state in the former case, localized ground state in the latter case), and similar to the case of AsH3 we expect localized states in the case of optical isomers, in agreement with the empirical evidence. Possible consequences concerning the understanding of the ``classical limit'' in general are briefly outlined.
We propose a model to describe a gas of pyramidal molecules interacting via dipole-dipole interactions. A cooperative effect induced by the interaction modifies the tunneling properties between the classical equilibrium configurations of the single molecule. The model suggests that, for sufficiently high gas density, the molecules become localized in these classical configurations. On this basis it is possible to explain the shift and the disappearance of the inversion line observed upon increase of the pressure in a gas of ammonia or deuterated ammonia. The same mechanism also accounts for the presence of stable optical activity of certain pyramidal molecules. We discuss the concept of environment induced superselection rule which has been invoked in connection with this problem.
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.
In the case of tunneling in chemical reactions [see figure1.1(c)], the total energy of reagents cannot be generally considered to be small; treating it as the first-order term of h¯ as was successfully done in Chapters 6 and 7 does not lead to any sensible semiclassical theory. The semiclassical mechanics requires (1) construction of Lagrange manifolds, (2) determination of amultidimensional caustic surface, and (3) connection of wave functions between classically allowed and forbidden regions [59]. Unfortunately, these problems have not yet been solved mathematically. As was discussed in Section 3.1, in the framework of the ordinary WKB approach we can construct Lagrange manifolds and caustics in the case of two dimensions and the connection problem can be treated relatively well by assuming the local separability. Extension of this method to higher dimensions, however, cannot be practical. The complexvalued (complex coordinate and/or momentum) WKB theory has been devised, as briefly explained there, but cannot be simply extended to multidimensions (see, for instance, [15]). This formidable task can hardly be accomplished mainly because of the complexity of the Lagrange manifold and the fact that analytical properties of any realistic potential energy surfaces extended into the complex-valued coordinate space cannot be guaranteed. The use of a complex trajectory was nicely materialized by the double-ended complex trajectory in the classical S-matrix theory [206], in which the quantized boundary conditions are satisfied at both (initial and final) ends. Unfortunately, this method turned out not to be practically useful, because finding such trajectories is also a formidable task in a multidimensional complex coordinate (and/or momentum) space. We can, however, make a break through the difficulty of detecting caustics in multidimensional space. An efficient way of doing that has been devised along classical trajectory [47]. This is not a trivial task at all, since it is not possible to find caustics in high-dimensional space by just shooting classical trajectories. Since the caustics can be found along each classical trajectory, chemical dynamics with tunneling effects incorporated can now be treated by the on-the-fly method. In this subsection, this method is explained.
We study in the framework of the Schrodinger equation the effect of intermolecular interactions on the tunneling racemization of the active molecule. The active molecule is assumed as a two-level system and the left-right isomerism is viewed in terms of a double-bottomed harmonic potential well. The active molecule is assumed to be embedded in a gas, liquid or solid, submitted to a perturbing potential U created by the molecules of the sample. In our model we take into account the difference of energy E due to the weak interactions between the left (L) and right (R) configurations. We have shown that when E is equal to zero the system cannot be optically stable: the optical activity tends asymptotically to zero in the case of dilute gases or compressed gases and liquids or oscillates periodically around zero when the molecules are isolated or submitted to a static potential. Only when E is different of zero the system can be optically stable depending on the strength parameters of the potential U and on the magnitude of the spontaneous tunneling.
We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces decoherence and suppression of tunnelling. These features are necessary ingredients for classicality, but we believe that classicality also implies that quantum delocalized states spontaneously evolve into localized ones. We then show that this evolution takes place only when both noise and non linearity in the equations are present.
The probability, P ( t ), of the irreversible dissipation into a continuous spectrum of an initially ( t = 0) localized (Ψ o ) nonstationary state acquires, as time increases, 'memory' due to the lower energy bound of the spectrum, and eventually follows a nonexponential decay (NED). Regardless of the degree of dependence on energy, the magnitude of this deviation from exponential decay depends on the degree of proximity to threshold, and on whether the theory employs a real energy distribution, one form of which is g ( E ) ≡ ⟨Ψ o |δ( H − E )|Ψ o ⟩, or a complex energy distribution, G ( E ) ≡ ⟨Ψ o |( H − E + i0)|Ψ o ⟩. It is the latter that is physically consistent, since it originates from the singularity at t = 0, which breaks the S -matrix unitarity, in accordance with the non-Hermitian character of decaying states. In order to test the quantum mechanical theory, we carried out semiclassical path integral calculations of the P ( t ) for an isolated narrow tunnelling state, whereby the truncated Fourier transform of a semiclassical Green function, G sc ( E ), is obtained. The results are in agreement with the analytic results of quantum mechanics when energy and time asymmetry are taken into account. It is shown that the analytic structure of G sc ( E ) is [ D regular + D pole ], where D pole is a finite sum over complex poles, which are the complex eigenvalues, W n , that the potential can support. The W n are given by E n + Δ n − (i/2)Γ n , where E n are the real eigenvalues of the corresponding bound potential, Γ n are the energy widths and Δ n are the energy shifts, both expressed in terms of computable semiclassical quantities. The spherical harmonic oscillator (SHO) with and without angular momentum, and unstable ground states of diatomic molecules, are treated as particular cases. The exact spectrum of the SHO is recovered only when the Kramers–Langer semiclassical expression for the centrifugal potential is used, thereby bypassing the difficulty of the singularity at r = 0. The spectrum from the use of the quantal form l ( l + 1) reduces to that of l ( l + 1/2) 2 in the limit of large l , i.e., for orbits far from r = 0. Using previously computed energies and widths for the vibrational levels of He 2 2+ 1σ g 2 1 Σ g + , the application of two formulae for P ( t ), one derived from a Lorentzian real energy distribution and the other from the corresponding complex energy distribution, shows that, for the lowest level, in the former case NED starts after about 193 lifetimes, and in the latter after about 102 lifetimes. The fact that this difference is large should have consequences for the deeper understanding of irreversibility at the quantum level.