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(BQ) Part 2 book A guide to molecular mechanics and quantum chemical calculations has contents: Obtaining and interpreting atomic charges; kinetically controlled reactions, applications of graphical models, obtaining and using transition state geometries.
Chapter 15 Obtaining and Using Transition-State Geometries This chapter addresses practical issues associated with establishing, verifying and using transition-state geometries It outlines a number of practical strategies for finding transition states, and provides criteria for establishing whether or not a particular geometry actually corresponds to the transition state of interest Most of the remainder of the chapter focuses on choice of transition-state geometry, and in particular, errors introduced by using transition-state (and reactant) geometries from one model for activation energy calculations with another (“better”) model The chapter concludes with a discussion of “reactions without transition states” Introduction The usual picture of a chemical reaction is in terms of a onedimensional potential energy (or reaction coordinate) diagram transition state energy (E) reactants products reaction coordinate (R) The vertical axis corresponds to the energy of the system and the horizontal axis (the “reaction coordinate”) corresponds to the 409 Chapter 15 adf 409 3/25/03, 10:48 AM geometry of the system The starting point on the diagram (“reactants”) is an energy minimum, as is the ending point (“products”) In this diagram, the energy of the reactants is higher than that of the products (an “exothermic reaction”) although this does not need to be the case The energy of the reactants can be lower than that of the products (an “endothermic reaction”), or reactant and product energies may be the same (a “thermoneutral reaction”) either by coincidence or because the reactants and products are the same molecule (a “degenerate reaction”) Motion along the reaction coordinate is assumed to be continuous and pass through a single energy maximum (the “transition state”) According to transitionstate theory, the height of the transition state above the reactant relates to the overall rate of reaction (see Chapter 9) Reactants, products and transition state are all stationary points on the potential energy diagram In the one-dimensional case (a “reaction coordinate diagram”), this means that the derivative of the energy with respect to the reaction coordinate is zero dE = dR (1) The same must be true in dealing with a many-dimensional potential energy diagram (a “potential energy surface”).* Here all partial derivatives of the energy with respect to each of the independent geometrical coordinates (Ri) are zero ∂E = i = 1,2, 3N-6 ∂Ri (2) In the one-dimensional case, reactants and products are energy minima and characterized by a positive second energy derivative d2E dR2 (3) >0 The transition state is an energy maximum and is characterized by a negative second energy derivative * Except for linear molecules, 3N-6 coordinates are required to describe an N atom molecule 3N-5 coordinates are required to describe a linear N atom molecule Molecular symmetry may reduce the number of independent coordinates 410 Chapter 15 adf 410 3/25/03, 10:48 AM d2E (4) i = 1,2, 3N-6 (8) These correspond to equilibrium forms (reactants and products) Stationary points for which all but one of the second derivatives are 411 Chapter 15 adf 411 3/25/03, 10:48 AM positive are so-called (first-order) saddle points, and may correspond to transition states If they do, the coordinate for which the second derivative is negative is referred to as the reaction coordinate (ξp) ∂2E ∂ξp2