Theoretical studies on intermolecular hydrogen transfer reactions

Abstract

Overview of Intermolecular Hydrogen Transfer Reactions This thesis explores various features of intermolecular hydrogen transfer reactions using theoretical methods such as ab initio calculations and analytical models. Key aspects studied include:

Tunneling effects Negative temperature dependence Violation of the principle of conservation of bond orders Principle of non-perfect synchronization Modified Bond Energy–Bond Order (BEBO) relations

These phenomena are analyzed in the light of quantum chemical energetics and mathematical models throughout Chapters 2–5.

Chapter 1: Introduction Chapter 1 provides a general introduction to hydrogen transfer reactions and the ab initio computational procedure.

Chapter 2: Tunneling in Hydrogen Transfer Reactions This chapter presents a study on tunneling of hydrogen in chemical reactions. The objective was to explain the linear behavior of log?k(T) vs. T in the low-temperature region, where k(T) is the rate constant at temperature T. For the H-transfer reaction between methyl radical and methane, ab initio calculations at the correlated second-order Møller–Plesset (MP2) level yield a potential energy surface that fits a symmetric Eckart function. Further mathematical treatment, assuming a constant density of states, leads to a simple linear relation between log?k(T) and T. Density of states was later included, and the ab initio calculations were refined with MP2 optimizations for the same reaction to evaluate accurate rate constants.

Chapter 3: Negative Temperature Dependence This chapter addresses the negative temperature dependence of rate constants in certain highly exothermic H-abstraction reactions. Potential energy surfaces for H-transfer reactions between HCN, CH?, C?H?, i-C?H?, t-C?H?? and the CN radical were traced at both Self-Consistent Field (SCF) and MP2 levels. Results reveal that there is no barrier for reactions between secondary and tertiary alkanes with CN radical at the MP2 level. Calculations also indicate high exothermicity for all these reactions. Using a collision theory model, we find that the rate of reaction is proportional to the inverse square root of temperature, suggesting a slow variation of rate constant at moderate temperatures.

Chapter 4: Bond Order, Free Valence, and Spin Density This chapter examines concepts such as bond order, free valence, valence, and spin density as defined by Mayer. The inflection point in bond order profiles was traditionally considered the transition state for chemical reactions, but our findings show this is not universally true. We propose two properties-free valence and spin density-which, on the migrating atom, rise from zero and fall to zero through a maximum from reactants to products. These maxima coincide exactly with the energy maxima, irrespective of reaction thermodynamics along the minimum energy path. Investigations at SCF and MP2 levels suggest that the principle of conservation of bond orders does not always hold due to the development of free valence or spin density on the migrating atom. Analytical equations indicate that free valence depends on the square of spin density. We also observe the non-perfect synchronization principle operating in bond rearrangements during a simple metathetic reaction: H + H? ? H? + H\text{H + H? ? H? + H}H + H? ? H? + H This suggests that the development of free valence (or spin density) on the migrating atom may cause differences in bond-forming and bond-breaking processes in open-shell metathesis reactions.

Chapter 5: Extension to BEBO Model Finally, studies using these qualitative concepts are extended to the Bond Energy–Bond Order (BEBO) model, which relates the energy of a system to exponentially raised bond orders for various H-transfer reactions. The ambiguity in assigning a value for the bond order exponent and its sign was resolved by considering multiple chemical reactions. We conclude that the bond order exponent should be greater than unity and positive to satisfy the curvature requirements at the transition state. Analytical relations were derived between:

Bond order and heat of reaction Bond distance and heat of reaction Brønsted coefficient and heat of reaction