Catalysis quantum-mechanical theory

The existing phenomenological theories of catalysis bear approximately the same relation to the electron theory as the theory of the chemical bond, which was prevalent in the last century and which made use of valence signs (and dealt only with these signs), bears to the modern quantum-mechanical theory of the chemical bond which has given the old valence signs physical content, thereby disclosing the physical nature of the chemical forces. 

The complete theory of catalysis, which would start with the isolated reaction participants, was not available until now because of the lack of adequate knowledge of the participants themselves (even the complete theory of the isolated participants, starting from the first principles, is still lacking). However, in analogy with the homogeneous chemical reactions one can expect that the quantum chemical approach, based on the semiempirical quantum mechanical methods, could be a prospective one. 

At present (beginning from 1948) the electron theory is being developed on a modern, more advanced theoretical basis. In the U.S.S.R. the initiator of this new electronic quantum-mechanical trend in catalysis is S. Z. Roginsky (Moscow), from whose laboratory a whole series of experimental and theoretical works has issued. Electronic phenomena in catalysis are also dealt with in a number of papers by A. N. Terenin and his school (Leningrad), V. I. Lyashenko and co-workers (Kiev), S. Y. Pshezhetsky and I. A. Myasnikov (Moscow), and others. 

PHYSICAL CHEMISTRY. Application of the concepts and laws of physics to chemical phenomena in order to describe in quantitative (mathematical) terms a vast amount of empirical (observational) information. A selection of only the most important concepts of physical chemistiy would include the electron wave equation and the quantum mechanical interpretation of atomic and molecular structure, the study of the subatomic fundamental particles of matter. Application of thermodynamics to heats of formation of compounds and the heats of chemical reaction, the theory of rate processes and chemical equilibria, orbital theory and chemical bonding. surface chemistry (including catalysis and finely divided particles) die principles of electrochemistry and ionization. Although physical chemistry is closely related to both inorganic and organic chemistry, it is considered a separate discipline. See also Inorganic Chemistry and Organic Chemistry. 

From its inception, the combined Quantum Mechanics/Molecular Mechanics (QM/MM) method [1-3] has played an important roll in the explicit modeling of solvent [4], Whereas Molecular Mechanics (MM) methods on their own are generally only able to describe the effect of solvent on classical properties, QM/MM methods allow one to examine the effect of the solvent on solute properties that require a quantum mechanical (QM) description. In most cases, the solute, sometimes together with a few solvent molecules, is treated at the QM level of theory. The solvent molecules, except for those included in the QM region, are then treated with an MM force field. The resulting potential can be explored using Monte Carlo (MC) or Molecular Dynamics (MD) simulations. Besides the modeling of solvent, QM/MM methods have been particularly successful in the study of biochemical systems [5] and catalysis [6],... 

Quantum dynamics effects for hydride transfer in enzyme catalysis have been analyzed by Alhambra et. al., 2000. This process is simulated using canonically variational transition-states for overbarrier dynamics and optimized multidimensional paths for tunneling. A system is divided into a primary zone (substrate-enzyme-coenzyme), which is embedded in a secondary zone (substrate-enzyme-coenzyme-solvent). The potential energy surface of the first zone is treated by quantum mechanical electronic structure methods, and protein, coenzyme, and solvent atoms by molecular mechanical force fields. The theory allows the calculation of Schaad-Swain exponents for primary (aprim) and secondary (asec) KIE... 

Part I presents the state of the art of the theory of catalysis and electrocatalysis at clusters and nanoparticles. This section provides the current frame of modeling of the interaction of clusters with substrates as well as catalytic and electrocatalytic kinetics on clusters and nanoparticles, including ab initio quantum mechanical calculations, and epitomizes recent advances in understanding the relation between electronic structure and catalytic/electrocatalytic activity. 

Warshel and Chu [42] and Hwang et al. [60] were the first to calculate the contribution of tunneling and other nuclear quantum effects to PT in solution and enzyme catalysis, respectively. Since then, and in particular in the past few years, there has been a significant increase in simulations of quantum mechanical-nuclear effects in enzyme and in solution reactions [16]. The approaches used range from the quantized classical path (QCP) (for example. Refs. [4, 58, 95]), the centroid path integral approach [54, 55], and variational transition state theory [96], to the molecular dynamics with quantum transition (MDQT) surface hopping method [31] and density matrix evolution [97-99]. Most studies of enzymatic reactions did not yet examine the reference water reaction, and thus could only evaluate the quantum mechanical contribution to the enzyme rate constant, rather than the corresponding catalytic effect. However, studies that explored the actual catalytic contributions (for example. Refs. [4, 58, 95]) concluded that the quantum mechanical contributions are similar for the reaction in the enzyme and in solution, and thus, do not contribute to catalysis. 

In the following three sections we shall discuss four applications of quantum mechanics to miscellaneous problems, selected from the very large number of applications which have been made. These are the van der Waals attraction between molecules (Sec. 47), the symmetry properties of molecular wave functions (Sec. 48), statistical quantum mechanics, including the theory of the dielectric constant of a diatomic dipole gas (Sec. 49), and the energy of activation of chemical reactions (Sec. 50). With reluctance we omit mention of many other important applications, such as to the theories of the radioactive decomposition of nuclei, the structure of metals, the diffraction of electrons by gas molecules and crystals, electrode reactions in electrolysis, and heterogeneous catalysis. 

Soon after the multiplet theory had appeared, Polanyi 34) advanced his theory of catalysis. It is based on quantum-mechanical assumptions, and conclusions from it are very similar to what the multiplet theory suggests and can virtually be interpreted by the index (I.l). The intermediate state according to Polanyi s theory is such a state at which the bonds A—B and C—D are completely broken, and the atoms A, B, C, and D are chemically bound with the valencies of the surface (Fig. 4). Polanyi points out (3<5), and with good reason, that the states (a)... 

The application of the theory of absolute reaction rates (36) to catalysis turns out to be closest to the multiplet theory. The former was applied for the first time by Temkin (58) with a simplifying assumption that the sum of the partition functions of the particles on the surface equals unity. Let us note the results (36) that are near to the multiplet theory. The theory of absolute reaction rates, based on quantum mechanics and statistics, proved that in the case of adsorption, the attraction of the two-atom molecules (of hydrogen) to two atoms of the catalyst (carbon or nickel) is energetically more favorable than to one atom. It demonstrates that on solid surfaces the true energy of activation must be small and that for the endothermic process it must be nearly equal to the heat of the latter. As in the multiplet theory, the theory considers the new bonds as beginning to be formed before the old ones are broken. The theory deals with the real arrangement of atoms and with the mutual energy of their valence electrons. 

Rate constants can be estimated by means of transition-state theory. In principle all thermodynamic data can be deduced from the partion function. The molecular data necessary for the calculation of the partion function can be either obtained from quantum mechanical calculations or spectroscopic data. Many of those data can be found in tables (e.g. JANAF). A very powerful tool to study the kinetics of reactions in heterogeneous catalysis is the dynamic Monte-Carlo approach (DMC), sometimes called kinetic Monte-Carlo (KMC). Starting from a paper by Ziff et al. [16], several investigations were executed by this method. Lombardo and Bell [17] review many of these simulations. The solution of the problem of the relation between a Monte-Carlo step and real time has been advanced considerably by Jansen [18,19] and Lukkien et al. [20] (see also Jansen and Lukkien [21]). First principle quantum chemical methods have advanced to the stage where they can now offer quantitative predictions of structure and energetics for adsorbates on surfaces. Cluster and periodic density functional quantum chemical methods are used to analyze chemisorption and catalytic surface reactivity [see e.g. 24,25]. 

The goal of quantum mechanical methods is to predict the structure, energy and properties for an A-particle system, where N refers to both the electrons and the nuclei. The energy of the system is a direct function of the exact position of all of the atoms and the forces that act upon the electrons and the nuclei of each atom. In order to calculate the electronic states of the system and their energy levels, quantum mechanical methods attempt to solve Schrodinger s equation. While most of the work that is relevant to catalysis deals with the solution of the time-independent Schrodinger equation, more recent advances in the development of time-dependent density functional theory will be discussed owing to its relevance to excited-state predictions. 

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