The collision theory is unsuitable for complex molecules because it assumes the existence of molecules in the form of ideal elastic spherical particles. However, for complex molecules, in addition to translational energy, other types of molecular energy must be taken into account, for example, rotational and vibrational. According to the theory of collisions, the existence of reactions in which three or more molecules must collide is impossible. In addition, decomposition reactions of the type AB = A + B difficult to explain with this theory.
To overcome these difficulties H. Eyring in 1935. proposed the activated complex theory. Any chemical reaction or any other molecular process occurring in time (diffusion, viscous flow, etc.) consists in a continuous change in the distances between the nuclei of atoms. In this case, the configuration of the nuclei corresponding to the initial state, through some intermediate configuration - an activated complex or a transition state - turns into a final configuration. It is assumed that the activated complex is formed as an intermediate state in all chemical reactions. It is viewed as a molecule that exists only temporarily and breaks down at a certain rate. This complex is formed from such interacting molecules, the energy of which is sufficient for them to be able to come close to each other according to the scheme: reagents activated complex products. The activated complex has an intermediate structure between reactants and products. The activation energy of a reaction is the additional energy that the reacting molecules must acquire in order to form the activated complex required for the reaction to proceed.
The activation energy always represents the absorbed energy, regardless of whether the total change in it for the reaction is positive (endothermic reaction) or negative (exothermic reaction). This is shown schematically in Fig. 6.
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Figure 6. Energy scheme for the formation of an activated complex.
Activation is the communication of such an amount of energy to molecules that, when they are effectively converted, substances are formed in an activated state.
Transformation is the formation of reaction products from substances in an activated state.
If the system cannot pass through this energy barrier, chemical transformations cannot occur in it. This means that this system is chemically inactive and needs some additional energy for activation. The amount of this extra energy depends on how much energy the system already has.
The energy of the initial system cannot be less than its zero energy (ie at 0 0 K). To activate any system, it is enough to give it additional energy. This energy is called the true activation energy.
The true activation energy of an elementary chemical act is the minimum energy that the initial system must have in excess of zero energy (ie, at 0 0 K) in order for chemical transformations to occur in it. The difference between the true activation energy of the reverse and direct reactions is equal to the thermal effect of the reaction at absolute zero.
History of creation. The development of quantum mechanics led to the creation of the theory of the activated complex (transition state), proposed in 1935 by Eyring, Evans and Polanyi simultaneously. But the first basic ideas of the theory were formulated by R. Marcelin in 1915, Marcelin, Ann. Phys. , 3, 158 (1915), who died in 1915 and did not have time to develop his views
phase space The phase space of a system of reacting substances, defined by sets of s coordinates (q) and s momenta (p), is divided by the critical surface S# into regions of final and initial substances
Critical surface (potential energy surface) Near the critical surface, the following conditions are assumed: There is a certain potential (U) depending on the coordinates of the nuclei (qi) and corresponding to the adiabatic term of the system (ground electronic state). This potential determines the motion near the critical surface S#. The distribution function of the states of the system near the critical surface does not depend on time, it is given by the value of temperature and at the intersection. S# (thermodynamic equilibrium is not assumed) is in equilibrium.
The adiabatic approximation is a method for the approximate solution of problems in quantum mechanics, used to describe quantum systems in which fast and slow subsystems can be distinguished.
The basic principles of the adiabatic approximation The motion of each of the nuclei occurs in the potential (electric) field created by the remaining nuclei, and in the averaged field of all electrons of the molecules of the reacting system as a whole. The average field of electrons corresponds to some average distribution of their electric charge in space. potential (potential field) determines for each nuclear configuration the forces that act on the nuclei. the potential depends on how the nuclei of the molecule are located at each moment of time, and on what state (ground or excited) the system of electrons in the molecule is. the potential field for a given system of nuclei depends on the distances between the individual nuclei of the molecular system and can be represented graphically as a function of internuclear distances
The reaction coordinate is a quantity that characterizes the change in a polyatomic system in the process of its chemical transformation from reagents to reaction products Definition K. r. is closely related to the topography of the potential energy surface (PES) U (qi), which is a function of N internal coordinates of the system qi (i = 1, 2, . . . , N), which determine the relative position of atomic nuclei, i.e., nuclear-electronic system configuration
Reaction path Potential energy surface chem. reactions A + BC: AB + C. The cross indicates the saddle point, the dotted line indicates the reaction path - the path with minimum energy. The path consists of two branches, the bottom of the valley leading from the minimum corresponding to the reactants to the pass point, the bottom of the valley leading from the minimum corresponding to the products. K. r. is defined as the length of the arc s(q, q") on the curve of the path of the rc, counted from the starting point q" to any point q lying on this curve.
Potential energy surface Each point on the potential surface is nothing but the energy of the molecular system in a given electronic state in the absence of nuclear motion, that is, the total energy minus the kinetic energy of the nuclei
Potential energy surface cross section Potential energy surface cross section along the isomerization reaction path Reagents and products correspond to minima at a=0 and a=1 (two isomers in the case of isomerization). If the valley of the reactants or products has 2 molecular fragments with free refers. movement, the minima degenerate into horizontal asymptotics. half-line (shown by dotted line).
Basic provisions of the activated complex theory Any chemical reaction or any other molecular process occurring in time (diffusion, viscous flow) consists in a continuous change in the distances between the nuclei of atoms. the configuration of the nuclei corresponding to the initial state, through some intermediate configuration - an activated complex or a transition state - turns into a final configuration. the initial substances are in equilibrium with the activated complexes (the rate of formation of the latter is much higher than the rate of their decay), the distribution of the molecules of the reacting substances in energy due to collisions corresponds to the equilibrium distribution of Maxwell -
An example of the formation of an activated complex in the HI dissociation reaction, such an activated complex is formed due to the rearrangement of bonds between hydrogen and iodine atoms
Transition state The transition state (activated complex) can be considered as an ordinary molecule, characterized by certain thermodynamic properties, except that, in addition to the usual three degrees of freedom of translational motion of the center of gravity, it has a fourth degree of freedom of internal translational motion associated with motion along the path ( coordinates) reactions
Features of the transition state The transition state is not some intermediate compound, since it corresponds to the maximum energy along the reaction path and, therefore, it is unstable and must turn into reaction products Molecules that have reached the energy barrier turn into reaction products
Differences between the potential energy of the transition state and the molecular system A typical form of the dependence of the potential energy of the reaction system on the reaction coordinate. E 0 is the height of the potential barrier, ΔН is the thermal effect of a chemical reaction Potential curve of a diatomic molecule (dependence of the energy of a system of two atoms on the internuclear distance).
The mechanism of formation of the activated complex Let us consider in general terms the reaction A + B ←→ X** → C + D, where A and B are the starting materials; X** - transition state, or activated complex; C and D are reaction products. The reaction under consideration consists of two successive processes. The first is the transition of A and B to the activated state. The second is the breakdown of the resulting complex into products C and D.
Graphical representation of the transition state PES profile along the reaction coordinate. The overall reaction rate ω is determined by the slowest link. Here such a link is the transition of the X** complex through the "plateau". In this case, we mean not the speed of movement of the transition state in space, but the movement of a point that displays the energy of the system. We will call a transition state such a state, which is represented by points lying at the top of the potential barrier on a certain small segment δ on the reaction path
The reaction rate of the decomposition of the activated complex The reaction rate is determined by the number of decays of all transition states per unit volume per unit time: ω = c** /t. The value of t can be expressed in terms of the average velocity of the transition state and along the reaction path at the top of the barrier: t = δ/u. (XVI.28)
The basic equation of the theory of AK theory postulates a thermodynamic equilibrium between the reactants and AK, characterized by an equilibrium constant. On this basis, the rate constant of a chemical reaction k is expressed by the equations:
entropy and enthalpy of activation entropy and enthalpy of activation, represent changes in the entropy and enthalpy of the system during the transition from reagents to AA
Application of the theory Sequential calculation of the absolute reaction rates according to equation (2) consists in determining the geometric configurations of the reagents and AA (at this stage, the height of the potential barrier is also determined) and calculating for these configurations the moments of inertia and vibrational frequencies that are necessary to calculate the statistical sums and the final determination activation energy
Limitations of the theory The activated complex theory is based on two assumptions: the hypothesis of thermodynamic equilibrium between the reactants and AA. the reaction rate is identified with the rate of AA decay. Both assumptions cannot be rigorously substantiated.
Why? Only in rare cases is it correct to consider the reaction coordinate as a straight line. Usually, it is a curve in a multidimensional space of internal variables and is a complex combination of elementary movements, which is not the same in its various sections.
An example of a reaction coordinate is a continuously changing combination of two stretching vibrations. The simplest PES for the reaction A + BC -> AB + C with all three atoms A, B and C on the same straight line (angular motions are ignored). Interatomic distances r are plotted along the coordinate axes. BC and r. AB - Curves 1-5 - constant energy levels The dotted line indicates the reaction coordinate, the cross - the saddle point.
electron-nonadiabatic processes and the transmission factor Because of the curvilinearity, the reaction coordinate cannot be considered an independent degree of freedom. Her interaction with other, transverse movements leads to the exchange of energy between them. As a result, the initially equilibrium energy distribution over the transverse degrees of freedom may be disturbed and the system may return to the reactant region even after it has already passed through the AK configuration in the direction of the products. These processes take into account the transmission coefficient for reactions in which x differs significantly from unity, theory loses its meaning
Tunnel effect estimation of the transmission factor in the framework of model dynamic calculations. It is assumed that not all, but only some of the transverse degrees of freedom interact with the translational motion of the system along the reaction coordinate. They are taken into account in the quantum dynamic calculation; the remaining degrees of freedom are processed within the framework of the equilibrium theory. In such calculations, corrections for quantum tunneling are also automatically determined. Tunneling - passing between potential energy surfaces
Rice. 2. Potential energy diagram along the reaction coordinate
Rice. 1. The simplest 2-dimensional potential energy surface for
reactions A + BC → AB + C with the location of all three atoms on one straight line
Along the coordinate axes, interatomic distances r BC and r AB . Curves 1–5 are the levels of constant energy, the dashed line is the reaction coordinate, x is the saddle point.
More often, one-dimensional schemes are used, representing a cross section along the reaction coordinate (Fig. 2). In these diagrams, states A + BC and AB + C are stable minima, and the top of the potential barrier corresponds to a saddle point, or saddle point (x). The height of the potential barrier is determined by the configuration of the particles, the amount of energy required to overcome the repulsion, and some other factors. Each distance between the reacting particles corresponds to a point on the potential energy surface.
A chemical reaction is considered as a transition from a configuration of reactants to a configuration of products through the point ABC. This point (or some small segment of the reaction trajectory with length δ) is called activated complex or transitional state.
The difference E o between the energies of the initial state and the activated complex ABC is the activation energy of the elementary reaction A + BC. The reaction coordinate is the most favorable way for the reaction to proceed, requiring the least energy costs.
Starting from the works of G. Eyring, there are many approximate calculation methods for finding potential energy surfaces for adsorption and catalysis, exact approaches require complex quantum mechanical calculations in practice and are almost never used in calculating adsorption and catalysis rates.
The theory of the activated complex or the theory of the transition state (aka the theory of absolute velocities) is based on three assumptions:
1. The Maxwell-Boltzmann equilibrium between the activated complex and the reagents is observed, so their concentration can be calculated using the Maxwell-Boltzmann distribution function.
2. The reaction rate is identified with the rate of decomposition of the activated complex. The reaction proceeds with overcoming the lowest potential barrier at the point of the activated complex or near it.
3. Overcoming the potential barrier near the activated complex is described as the translational motion of the system along the reaction coordinate. The movement of the system (the course of the reaction) along the reaction coordinate is possible only in the direction of formation of the reaction products. This means that the activated complex, once it has formed, cannot be converted back into the original substances.
This property fundamentally distinguishes the activated complex, which describes the elementary act of the reaction, from the properties of intermediate products, which describe the path of chemical transformation and are detected by physical methods of investigation. The very formation of the activated complex is sufficient for the reaction to take place.
Activated complexes are the same particles or complexes of particles, differing only in a configuration with an increased energy reserve and unstable in the direction of the reaction coordinate, their average lifetime
τ # = 2πh/kT, (1)
where h and k are the Planck and Boltzmann constants, respectively.
At normal temperatures for chemical reactions τ # ≈ -13 s, i.e. close in time to one oscillation. Such times were still not available experimentally, the situation changed with the advent of femtosecond spectroscopy (femto - 10 -15), in which lasers with pulses up to 10 -14 s long were used to identify particles, i.e., less than the time of one oscillation. In 1999, for the creation of femtosecond spectroscopy, the work of A. Zivail was awarded the Nobel Prize.
Thus, an experimental opportunity arose to better understand the structure of the activated complex.
F-tion of the potential energy of atomic nuclei U from their ext. coordinates, or degrees of freedom. In a system of n cores, the number of internal degrees of freedom N = 3n - 6 (or 3n - - 5 if all nuclei are located on one straight line). The simplest two-dimensional (N = 2) PES is shown in fig. 1. The reagents and products of the district on it correspond to areas of relatively small potential energy (valleys), separated by an area of increase. energy-potential barrier. The curved line passing along the bottom of the valleys through the barrier is the reaction coordinate. One-dimensional diagrams are often used, depicting a PES section deployed along the p-tion coordinate (see Fig. 2). In these schemes, the top of the potential barrier corresponds to a saddle point, or a saddle point. The same concepts are transferred to multidimensional PES with N > 2. The states of the reactants and products are stable, they correspond to configurations (i.e., fixed values of the coordinates φ), which are minima (or valleys) on the multidimensional PES. Chem. p-tion is considered as a transition from the configuration of reactants to the configuration of products through the configuration of a saddle point along the coordinate of the p-tion. The configurations of both minima and saddle points are PES stationary points, i.e. in them U/q i = 0. 
Modern the derivation of equation (2), chemically less obvious, is based on collision theory. The rate of p-tion is identified with the rate of transition of the reacting chemical. systems through an (N - 1)-dimensional surface in the space of configurations, separating the regions of reactants and products. In collision theory, this speed is called. flow through the critical sur-st. Ur-tion in the form (2) is obtained if you hold a critical. pov-st through the saddle point is orthogonal to the coordinate of the p-tion and accept that on the critical. pov-sti energetic. the distribution of the reactants is in equilibrium. The corresponding region of the space of coordinates and momenta (phase space) is characterized by the same statistical. sum . This allows us to consider the critical pov-st as a set of AK configurations. So arr., AK is immediately defined as an object with (N - 1) ext. degrees of freedom and it is not necessary to enter its extent along the p-tion coordinate.
Application of the theory. According to the theory, the p-tion mechanism is quite determined by the configurations of the reactants and products (minima, or valleys, on the PES) and the corresponding AK (saddle points). Theoretical the calculation of these configurations by the methods of quantum chemistry would give comprehensive information about the directions and velocities of the chemical. districts. Such calculations are being intensively developed; for simple chem. systems containing 10-15 atoms, to-rye belong to the elements of the first two periods of the periodic table, they are practically realizable and quite reliable. Consistent calculation of abs. speed p-tion by ur-tion (2) is to determine the geom. configurations of reagents and AK (at this stage, the height of the potential barrier is also determined) and the calculation for these configurations of the moments of inertia and oscillations. frequencies, to-rye necessary for the calculation of statistical. sums and ending. definitions. When applied to complex p-tions, representing the practical. interest, the full and reliable implementation of such a program is laborious and often unfeasible. Therefore, the molecular constants required for calculations by equations (2) and (3) are often found empirically. methods. For stable configurations of reactants, the moments of inertia and oscillations. frequencies are usually known from spectroscopic. data, however, for AK eksperim. their determination is impossible due to the small time of his life. If follow. quantum-chem. calculation is not available, interpolation calculation schemes are used to estimate these values.
Limitations of the theory and attempts to improve it. The activated complex theory is based on two assumptions. The first is the thermodynamic hypothesis. equilibrium between reactants and AA. According to the second, the rate of p-tion is identified with the rate of decay of AK. Both assumptions cannot be rigorously substantiated. This is revealed if we consider the movement of chemical. systems along the p-tion coordinate all the way from the reactants to the products, and not just near the top of the potential barrier. Only in rare cases is it correct to consider the coordinate of the district as a straight line, as in fig. 2. Usually it is a curve in a multidimensional space ext. variables and is a complex combination of elementary movements, which is not the same in dec. their areas. For example, in fig. 1 coordinate p-tion is a continuously changing combination of two stretching vibrations.
Equilibrium distribution of energy in reagents for thermal. p-tions provided almost always; it is violated only in extremely fast processes. The problem is whether it will remain in AK. Because of the curvilinearity, the p-coordinate cannot be considered an independent degree of freedom. Her interaction with other, transverse movements leads to the exchange of energy between them. As a result, firstly, the initially equilibrium distribution of energy over the transverse degrees of freedom may be disturbed and, secondly, the system may return to the reactant region even after it has already passed through the AK configuration in the direction of the products. Finally, it must be borne in mind that, according to equations (2), (3) and (5), chem. district is considered as a classic. transition; quantum features are ignored, for example. electronic non-adiabatic processes and tunnel effect. In the early formulations of the theory, the so-called. transmission factor It was assumed that it collected the influence of the factors listed above, not taken into account in the derivation of these equations. Thus, the definition of x goes beyond the scope of the activated complex theory; moreover, for p-tions, in which x differs significantly from unity, the theory loses its meaning. However, for complex districts, the assumption does not contradict the experiment. data, and this explains the popularity of the activated complex theory.
Consistent an informal consideration of all these effects is possible only within the framework of the dynamic. calculation (see Dynamics of an elementary act). Attempts were made to take them into account separately. For example, a systematic method was proposed. clarification of the AC configuration, since the choice of a saddle point as such is based on intuitive ideas and, generally speaking, is not necessary. There may be other configurations, for which the calculation error for f-lames (2) and (3), due to the return of the system to the reactant region after passing through these configurations, is less than for the saddle point configuration. Using the formulation of the activated complex theory in terms of collision theory (see above), it can be argued that the reverse flow (from products to reagents) through the critical. pov-st corresponds to the part of the total direct flow (from reactants to products) that generates it and equal to it. The smaller this part, the more accurate the calculation of the rate of p-tion according to the activated complex theory. These considerations formed the basis of the so-called. variational definition of AK, according to Krom, the surface that minimizes the forward flow is considered critical. For her, the rate of p-tion, calculated from equations (2) and (3), is minimal. As a rule, zero energies of transverse vibrations change along the p-coordinate. This is another reason for the displacement of the AC configuration from the saddle point of the PES; it is also taken into account by the variational theory.
Means. Attention was paid to the development of methods for determining the probabilities of quantum tunneling in chem. districts. Finally, it became possible to estimate the transmission factor in the framework of the model dynamics. computing. It is assumed that with the postulate. By moving the system along the coordinate of the p-tion, not all interact, but only some of the transverse degrees of freedom. They are taken into account in the quantum dynamic. calculation; the remaining degrees of freedom are processed within the framework of the equilibrium theory. In such calculations, corrections for quantum tunneling are also automatically determined.
The improved methods for calculating abs. speeds of chem. districts require serious calculations. efforts and lack the universality of the activated complex theory.
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Use literature for the article "ACTIVATED COMPLEX THEORY": Glesston S, Leidler K., Eyring G., Theory of absolute reaction rates, trans. from English, M., 1948; Leidler K., Kinetics of organic reactions, trans. from English, M., 1966: Thermal bimolecular reactions in gases, M., 1976. M. V. Bazilevsky.
Transition state theory (activated complex)
In an attempt to eliminate the shortcomings of the theory of active collisions, scientists have proposed a new theory of chemical kinetics. This was done almost simultaneously in 1935, more than half a century after the discoveries of Arrhenius, G. Eyring (USA), on the one hand, and M. Polyani and M. G. Evans (Great Britain), on the other. They suggested that the chemical reaction between start and finish undergoes a kind of "transitional state," as Evans and Polanyi called it, during which an unstable "activated complex" (Eyring's term) is formed. The activation energy is just what is required to achieve this state, in which the probability of successful completion of the reaction is very high. Therefore, the activation energy and can be less than the breaking energy of the initial chemical bonds.
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The essence of the transition state theory (activated complex):
1) during the interaction, the reactant particles lose their kinetic energy, which turns into potential energy, and in order for the reaction to take place, it is necessary to overcome a certain barrier of potential energy;
2) the difference between the potential energy of particles and the mentioned energy barrier is the activation energy;
3) the transition state is in equilibrium with the reactants;
4) in those reactions where the activation energy is significantly lower than the breaking energy of chemical bonds, the processes of formation of new bonds and destruction of old bonds can completely or partially coincide in time.
The lifetime of the activated complex is equal to the oscillation period of one molecule (10 -13 s), so it cannot be detected experimentally and, accordingly, it cannot be isolated and studied. Therefore, it is possible to prove the truth of the theory of the transition state only with the help of calculations. And for this purpose, scientists used the most advanced technique at that time, which then experienced a rapid flowering - quantum chemistry. Even a whole trend in quantum chemistry has emerged in terms of calculating the energy of the transition state.
Theory of active collisions >>
Transition state theory (activated complex)
