Reaction mechanisms potential energy surfaces

Computations can be carried out on systems in the gas phase or in solution, and in their ground state or in an excited state. Gaussian can serve as a powerful tool for exploring areas of chemical interest like substituent effects, reaction mechanisms, potential energy surfaces, and excitation energies. 

Nucleophilicity and leaving group ability 211 Effect of solvation on the gas-phase reaction 212 Mechanism of the gas-phase SN2 reaction 213 Potential energy surfaces for gas-phase SN2 reactions 214 Recent theoretical developments 218 Some examples of gas-phase SN2 reactions involving positive ions 220 Nucleophilic displacement reactions by negative ions in carbonyl systems 222 General features 222... 

In the last section, we discussed the use of QC calculations to elucidate reaction mechanisms. First-principle atomistic calculations offer valuable information on how reactions happen by providing detailed PES for various reaction pathways. Potential energy surfaces can also be obtained as a function of electrode potential (for example see Refs. [16, 18, 33, 38]). However, these calculations do not provide information on the complex reaction kinetics that occur on timescales and lengthscales of electrochemical experiments. Mesoscale lattice models can be used to address this issue. For example, in Refs. [25, 51, 52] kinetic Monte Carlo (KMC) simulations were used to simulate voltammetry transients in the timescale of seconds to model Pt(l 11) and Pt(lOO) surfaces containing up to 256x256 atoms. These models can be developed based on insights obtained from first-principle QC calculations and experiments. Theory and/or experiments can be used to parameterize these models. For example, rate theories [22, 24, 53, 54] can be applied on detailed potential energy surfaces from accurate QC calculations to calculate electrochemical rate constants. On the other hand, approximate rate constants for some reactions can be obtained from experiments (for example see Refs. [25, 26]). This chapter describes the later approach. 

Chakraborty A, Zhao Y, Lin H, Tiuhlm DG (2006) Combined valence bond-molecular mechanics potential-energy surface tmd direct dynamics study of rate constants and kinetic isotope effects for the H + C2H6 reaction. J Chem Phys 124 044315... 

In direct contrast to simulations of physical properties dominated by inter-particle forces, the second problem class (class B) concerns interactions among intramolecular and inter-molecular degrees of freedom in an event which produces a chemical change in the participants. Severely limited by the need for an accurate quantum mechanical potential energy surface, simulations in this area typically involve classical trajectory (i.e., MD) calculations for the simplest chemical reactions... 

Figure Al.6.10. (a) Schematic representation of the three potential energy surfaces of ICN in the Zewail experiments, (b) Theoretical quantum mechanical simulations for the reaction ICN ICN [I--------------...

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

Molecular mechanics methods are not generally applicable to structures very far from equilibrium, such as transition structures. Calculations that use algebraic expressions to describe the reaction path and transition structure are usually semiclassical algorithms. These calculations use an energy expression fitted to an ah initio potential energy surface for that exact reaction, rather than using the same parameters for every molecule. Semiclassical calculations are discussed further in Chapter 19. 

HyperChem can calculate transition structures with either semi-empirical quantum mechanics methods or the ab initio quantum mechanics method. A transition state search finds the maximum energy along a reaction coordinate on a potential energy surface. It locates the first-order saddle point that is, the structure with only one imaginary frequency, having one negative eigenvalue. 

Reality suggests that a quantum dynamics rather than classical dynamics computation on the surface would be desirable, but much of chemistry is expected to be explainable with classical mechanics only, having derived a potential energy surface with quantum mechanics. This is because we are now only interested in the motion of atoms rather than electrons. Since atoms are much heavier than electrons it is possible to treat their motion classically. Quantum scattering approaches for small systems are available now, but most chemical phenomena is still treated by a classical approach. A chemical reaction or interaction is a classical trajectory on a potential surface. Such treatments leave out phenomena such as tunneling but are still the state of the art in much of computational chemistry. 

Consider a reactant molecule in which one atom is replaced by its isotope, for example, protium (H) by deuterium (D) or tritium (T), C by C, etc. The only change that has been made is in the mass of the nucleus, so that to a very good approximation the electronic structures of the two molecules are the same. This means that reaction will take place on the same potential energy surface for both molecules. Nevertheless, isotopic substitution can result in a rate change as a consequence of quantum effects. A rate change resulting from an isotopic substitution is called a kinetic isotope effect. Such effects can provide valuable insights into reaction mechanism. 

After 28 years the perepoxide quasi-intermediate was supported by a two-step no intermediate mechanism [71, 72]. The minimum energy path on the potential energy surface of the reaction between singlet molecular oxygen ( A and dg-teramethylethylene reaches a vaUey-ridge inflection point and then bifurcates leading to the two final products [73]. 

Figure 14. Classical trajectories for the H + H2(v = l,j = 0) reaction representing a 1-TS (a-d) and a 2-TS reaction path (e-h). Both trajectories lead to H2(v = 2,/ = 5,k = 0) products and the same scattering angle, 0 = 50°. (a-c) 1-TS trajectory in Cartesian coordinates. The positions of the atoms (Ha, solid circles Hb, open circles He, dotted circles) are plotted at constant time intervals of 4.1 fs on top of snapshots of the potential energy surface in a space-fixed frame centered at the reactant HbHc molecule. The location of the conical intersection is indicated by crosses (x). (d) 1-TS trajectory in hyperspherical coordinates (cf. Fig. 1) showing the different H - - H2 arrangements (open diamonds) at the same time intervals as panels (a-c) the potential energy contours are for a fixed hyperradius of p = 4.0 a.u. (e-h) As above for the 2-TS trajectory. Note that the 1-TS trajectory is deflected to the nearside (deflection angle 0 = +50°), whereas the 2-TS trajectory proceeds via an insertion mechanism and is deflected to the farside (0 = —50°).

Figure 6. Initial rovibrational state specified reaction probabilities. Solid line exact quantum mechanical numerical solution. Solid line with solid square generalized TSH with use of the nonadiabatic coupling vector. Solid line with open circle generalized TSH with use of Hessian. Sur= 1(2) means the ground (excited) potential energy surface. Taken from Ref. [51].

For both statistical and dynamical pathway branching, trajectory calculations are an indispensable tool, providing qualitative insight into the mechanisms and quantitative predictions of the branching ratios. For systems beyond four or five atoms, direct dynamics calculations will continue to play the leading theoretical role. In any case, predictions of reaction mechanisms based on examinations of the potential energy surface and/or statistical calculations based on stationary point properties should be viewed with caution. 

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