Separation of Ground State and Transition State Effects in Intramolecular and Enzymatic Reactions. 2. A Theoretical Study of the Formation of Transition States in Cyclic Anhydride Formation

Abstract

Ab initio gas phase calculations at the RHF/6-31+G(d) level have been used to define the geometries of the transition states for the intramolecular displacement reactions with monophenyl esters of glutaric (I), succinic (II), and 3,6-endoxo-Δ4-tetrahydrophthalic (III) acids to provide the corresponding anhydrides plus phenolate. As determined experimentally, the rate determining step was found to involve transition states in which phenoxide is departing. Intrinsic reaction coordinate (IRC) calculations from transition state toward reactant and product sides provided intramolecular ion−molecule complexes (IIMC) of I and II and the tetrahedral intermediate of III and the product ion−molecule complexes (IMC) of the phenoxide and anhydride of I, II, and III. Vibrational frequency calculations were performed for all stationary states. Single point calculations using an electron correlation method and different solvation methods were performed on optimized reactant side gas phase geometries. The transition states formed from I, II, and III are essentially identical in bond lengths (ester carbon to leaving phenoxide 1.77, 1.79, or 1.80 Å; carbonyl oxygen to ester carbon 1.20 or 1.21 Å; nucleophilic oxygen to ester carbon 1.44 or 1.43 Å; and α-carbon to ester carbon 1.52 or 1.53 Å) and angles (characterized by the attacking oxygen, ester carbon, and leaving oxygen 97.8°, 97.3°, 96.7°; attacking oxygen, ester carbon, and ester carbonyl oxygen 117.0°, 117.4°, 113.7°). Transition state stabilization as a result of restricting low frequency vibrations is determined by comparing the frequencies of the IIMC (and tetrahedral intermediate) to the corresponding TS. The total number of frequencies does not change in going from the IIMC (or TI) to the TS for each ester. For those frequencies lower than 1000 cm-1, the number of frequencies remains constant. On comparing the ratio between the number of frequencies below 1000 cm-1 and the total number of frequencies in the transition states formed from I, II, and III, we find 0.49, 0.51, and 0.55, respectively. By the criteria of superimposable TS structures and lack of evidence for frequency changes in the TS in the direction of increasing rate, we conclude that the rate ratios of ∼230-fold in comparing I/II and II/III reside in ground state phenomena. This conclusion is supported by the geometries of IIMC and TS structures. Gas phase reaction coordinates and derived enthalpy and entropy values are provided and discussed. Conversion of ground state intramolecular anion ester complexes (IIMC) of esters I and II to their respective TSs involves a decrease in computed ΔH⧧ while ΔS⧧ remains invariant. In a previous investigation, the formation of ground state conformations (NACs) of geometry that allows entrance to the IIMC and then TS was found to be related to ΔH° rather than ΔS°. The importance of these findings to a general concept of entropy driven kinetic processes is discussed.