Bridged and Open Carbocation Structures as a Function of the Correlation Level in ab Initio Calculations:  The 4-Methyl-2-pentyl Cation

Abstract

An investigation of the alkylation reaction of propene with the 2-propyl cation by ab initio density functional methods at the B3LYP/6-31G** level found a distorted trimethyl-1-protonated cyclopropane as an energy minimum along the reaction coordinate (intermediate) and an open ion, the 4-methyl-2-pentyl cation (1), as another energy minimum (product). In contrast, the open ion 1 was not an energy minimum in MP2/6-31G** calculations. Attempts at geometry optimizations of 1 at that level led invariably to the protonated cyclopropane structure (more symmetrical than in the previous case). The ion 1 was in fact a transition structure in the MP2/6-31G** optimizations. A coupled cluster (CCSD/6-31G**) geometry optimization showed, however, the open ion 1 as a true energy minimum. This result brings a note of caution concerning MP2 geometry optimizations of carbocations. In particular, when these calculations find small energy differences between bridged and open structures, but find only the bridged structures as energy minima, the results might be in error. What the level of calculation is at which the predicted carbocation structures can be considered definitive remains an open question.

Biosynthesis via carbocations: Theoretical studies on terpene formation

“…While the shortcomings associated with B3LYP (and other DFT methods) are well known (e.g., neglect of medium-range correlation, dispersion), 7 such methods appear to provide reasonable results for carbocation rearrangements (at least for the sorts of questions asked in the studies described below, when applied appropriately). A variety of studies have compared the B3LYP and MP2 methods in their abilities to predict carbocation geometries and potential energy surfaces for carbocation rearrangements, [16][17][18][19][20][21][22][23][24] and, although results from these methods often agree with each other, they sometimes disagree for cases where carbocations reside on relatively flat regions of a potential energy surface (i.e., where significant changes in geometry are accompanied by only small changes in energy). In fact, such disagreement can be a hint that a particular portion of an energy surface is indeed flat.…”

On the structure and dynamics of secondary n-alkyl cations

“…Note also that ten of the 11 low-energy longarm-clinal forms are also closed forms, thus demonstrating a general prevalence for closed forms on the PES in agreement with past studies. [9][10][11][12][13][14][15][16][17][18][19][20] Curiously, the lowest-energy form, with two clinal longarms, is not fully closed but open-clinal on both sides.…”

“…40 At higher accuracy, Fărcaşiu pointed out that CCSD optimizations of a branched sec-alkyl ion indicate that the preference for closed forms lies intermediate between the DFT and MP2 results. 15 Hence, this PES effect, which further lowers closed-structure energies, might cause the open and closed forms of sec-n-alkyl ions to have commensurate free energies in reality.…”

“…PCP + structures have some CCC bond angles of Ͻ90°and are commonly seen as the lowest-energy PES minima in computational studies. [9][10][11][12][13][14][15][16][17][18][19][20] Fărcaşiu and co-workers [12][13][14][15] referred to them as "bridged" structures, but we prefer calling them "closed" structures, first to avoid confusion with H-bridged structures and second to recognize their dynamical relationship with classical "open" structures. We appear to be the first to point out that closed structures are rather rare in DFT simulations at catalytic ͑ϳ800 K͒ temperatures.…”

The Rotational Barrier in Ethane: A Molecular Orbital Study

“…Additionally, the third generation mPWB95 functional was applied since recent studies in small systems have shown that it yields more reliable results than the B3LYP functional [ 39 , 40 ]. We compared the results calculated with DFT and those calculated with MP2 theory since it its known that B3LYP and MP2 give errors in opposite direction in the energy for organic molecules [ 41 ]. In addition, we compared the basis 6-31G(d,p), 6-31+G(d,p), and 6-31++G(d,p) in order to evaluate the effect of the addition of polarization and diffusion to the basis set.…”