ИСТИНА

A direct quantum mechanical description of chemical reactions (i.e. transformations of substances) will be suggested for several basic models of chemistry, and the consequences will be discussed. Typical applications of quantum mechanics in chemistry (quantum chemistry) are reductionist and indirect: redistribution of bonds between atoms is modeled in microscopic many-particle quantum system, whereas measurable macroscopic effects (thermal data, rate of reaction, etc.) are calculated using classical statistical thermodynamics. Meantime, many qualitative theories of chemistry allow for a direct introduction of quantum formalism. The very basic scheme of chemical transformation of reagents {ai} into products {bj} (1) a1 + a2 + a3 + …  b1 + b2 + b3 + … usually focuses on a few key reagents and goal products ignoring a huge number of minor components (admixtures in reagents, intermediates, by-products, etc.). A more realistic picture, related to contemporary combinatorial chemistry, represents a reaction as a distribution of reagents F(a1,a2,…ai,…) transformed into distribution of products (b1,b2,…,bj,…) in a multidimensional stoichiometry space of all compounds allowed by sorts and number of atoms in a system. With a transforming operator R = || Rij || (1) turns into (1a) (b1,b2,…,bj,…) = R F(a1,a2,…ai…), which fits better to quantum formalism. Multi-component distributions of reagents and products thus correspond to ‘wave functions’ whereas the goal product(s) {bk} play a role of eigenvectors of the ‘reaction operator’ R. Another ‘pre-quantum’ qualitative scheme of theoretical chemistry is a frontier orbital concept. In a common version, it states that a result of chemical reaction (e.g. addition or substitution at the particular atom in a substrate moiety) is guided by the wave function of valence electrons of the substrate. Taken literally, this statement is incorrect: an attacking fragment of several atoms, i.e. ‘heavy’ atomic nuclei held together by interatomic bonds, is assumed to follow ‘light’ electrons. Nevertheless, frontier orbital schemes work well in prediction of reaction paths. In fact, these schemes indirectly suggest that distributions of ‘heavy’ attacking particles near a substrate correspond to wave functions. Substitution of hydrogen atoms for chlorine in paraffine hydrocarbons CnH2n+2 will be discussed in more detail [1]. In physical chemistry, transformation of reagents to products is usually represented by movement of a point along reaction profile over a potential barrier. Classical movement of the point, forced by thermal energy, reflects the energetic effect of reaction H=EA–EB and exponential dependence k~exp(–E0/RT) of the rate constant k on inverse temperature (Figure 1). If the moving point is a quantum particle, the model immediately gives such fundamental chemical phenomena as reverse reaction and chemical equilibrium at any temperature (reflection of a quantum particle), and the existence of unstable intermediates (quasi-bound states above barrier) together with negative exponential probability of a particle with E<E0 to penetrate a barrier (quantum tunneling). A number of theoretical models of chemistry are really suitable for ‘quantization’, pointing to inherently quantum nature of chemical phenomena. E0 Figure 1 A lot of quantum-like models in modern economic and social sciences [2] (as well as in chemistry) draw to fundamental problems of mechanics per se, including the possibility of mechanical modeling of real world. The grounds of quantum theory may look ‘hard to understand’ and ‘counterintuitive’ (as noted in many textbooks) due to some logical misfit in their postulates. We believe that the ‘mainstream’ quantum theory incorporates the essentially classical principle: a precise correspondence of theoretical model to physical reality. This principle, absent in Bohmian mechanics, demands a ‘literal’ imaging of individual quantum system (instead of ensemble) by a quantum model, creating misunderstanding and paradoxes. A big advantage of Bohmian mechanics is a possibility to use fractal trajectories in description of a quantum system’s dynamics. It permits a system to be at particular trajectory’s point at any moment of time without precise fixing its point in a next moment. The ‘average’ (convergent in probability) derivatives of a fractal function allow for simultaneous measurements of conjugate variables (proven in experiments with atomic beams [3]). Fractal trajectories are experimentally observed, e.g. as time series of financial data. Fractal phase trajectories, whose outlier points are intermixed, help to understand inter-state transitions in a quantum system (Figure 2). Since all experimentally registered trajectories, as sets of points, are essentially fractal, re-determination of the place of quantum mechanics (and, generally, of mechanics in its quantum and relativistic version) in modeling physical world, is needed. Basing on various, partially conflicting sources, we may characterize mechanics as mathematical modeling with the restrictions posed by most fundamental properties of Nature (position, velocity, inertia, potentials and forces). Taken mechanics, as a framework of a physical theory, in its general quantum and relativistic version, we arrive to a theorem. Any phenomenon of the real world may be approximated by a mechanical model that reproduces one, or several, of its measurable parameters at any pre-determined accuracy level. Application of mechanics as empirical tool to construct ‘locally precise’ models for all observed phenomena allows to circumvent a bunch of quasi-philosophical problems of scale (in dimensions, velocities, etc.) that a system must fit for its quantum or relativistic modeling to be correct. In fact, most quasy-mechanical theories in economics, control science, or finance, are assumed to use classical mechanics, whereas from our viewpoint, a particular classical character of such models has to be proven. This sort of a generalized mechanistic theory may provide new insight into unusual features of human-made objects (e.g. networks) and their dynamics. References 1. Y.L.Slovokhotov. Quantum mechanics from chemical viewpoint. Rossijskij khimicheskij zhurnal (Russian Chemical Jourmal), 1998, v. 42 N3, p.p. 5–17 (in Russian) 2. A.Khrennikov. Ubiquitous Quantum Structure: From Psychology to Finance. Berlin; Heidelberg; New York, NY: Springer (2010). 3. C.H.Kurtsiefer, T.Pfau, J.Mlynek, Measurement of the Wigner function of an ensemble of helium atoms, Nature. 1997, v. 386, p. 150-153 Figure 2