Schaefer and Allen have applied their focal point method to the question of the benzylic effect in the S_N2 reaction.¹ S_N2 reactions are accelerated when the attack occurs at the benzylic carbon, a well-known phenomenon yet the reason for this remains unclear. The standard textbook-like argument has been that the negative charge built up in the S_N2 transition state can be delocalized into the phenyl ring. However, solution phase Hammett studies are often U-shaped, indicating that both electron donating and withdrawing group accelerate the substitution reaction. (This is usually argued as indicative of a mechanism change from S_N2 to S_N1.)

The focal point method involves a series of very large computations where both basis set size and degree of electron correlation are systematically increased, allowing for an extrapolation to essentially infinite basis set and complete correlation energy. The energy of the transition state (relative to separated reactants) for four simple S_N2 reactions evaluated with the focal point method are listed in Table 1. The barrier for the benzylic substitutions is lower than for the methyl cases, indicative of the benzylic effect.

Table 1. Energy (kcal mol^-1) of the transition state relative to reactants.¹

To answer the question of why the benzylic substitution reactions are faster, they examined the charge distribution evaluated at B3LYP/DZP++. As seen in Table 1, this method does not accurately reproduce the activation barriers, but the errors are not terrible, and the trends are correct.

In Figure 1 are the geometries of the transition states for the reaction of fluoride with methylflouride or benzylfluoride. The NBO atomic charges show that the phenyl ring acquired very little negative charge at the transition state. Rather, the electric potential at the carbon under attack is much more revealing. The potential is significantly more positive for the benzylic carbon than the methyl carbon in both the reactant and transition states.

VC = -405.156 V	VC = -404.379 V

Figure 1. MP2/DZP++ transition states for the reaction of fluoride with methylfluoride and benzylflouride. NBO charges on F and C and the electrostatic potential in Volts.¹

They next examined the reaction of fluoride with a series of para-substituted benzylfluorides. The relation between the Hammet σ constants and the activation energy is fair (r = 0.971). But the relation between the electrostatic potential at the benzylic carbon (in either the reactant or transition state) with the activation energy is excellent (r = 0.994 or 0.998). Thus, they argue that it is the increased electrostatic potential at the benzylic carbon that accounts for the increased rate of the S_N2 reaction.

References

(1) Galabov, B.; Nikolova, V.; Wilke, J. J.; Schaefer III, H. F.; Allen, W. D., "Origin of the S_N2 Benzylic Effect," J. Am. Chem. Soc., 2008, 130, 9887-9896, DOI: 10.1021/ja802246y.

In the book I extensively discuss the singlet-triplet gap of methylene and some of the chemistry of phenylcarbene. Schleyer and Schaefer have now reported computations on the singlet-triplet gap of arylcarbenes.¹ The geometries of phenylcarbene 1, diphenylcarbene 2, 1-naphthylcarbene 3, bis(1-naphtyl)carbene 4, and 9-anthrylcarbene 5 were optimized at B3LYP/6-311+G(d,p). These geometries are shown in Figure 1.

1s	1t
2s	2t
3s	3t
4s	4s
4s	4s

Figure 1. B3LYP/6-311+G(d,p) optimized structures of singlet and triplet 1-5.

Since this functional is known to underestimate the singlet-triplet gap of carbenes, they employ an empirical correction based on the difference in this gap for methylene between the computed value (11.89 kcal mol^-1) and the experimental value (9.05 kcal mol^-1). These corrected energy gaps are listed in Table 1.

Table 1. Corrected singlet-triplet energy gaps (kcal mol^-1) at B3LYP/6-311+G(d,p).

Using the following isodesmic reactions, they estimate the stabilization of the singlet or triplet carbene afforded by the aryl substituent:

R-C-H + CH₄ → H-C-H + R-CH₃

R-C-R + CH₄ → R-C-H + R-CH₃

These isodesmic energies are listed in Table 2. For phenylcarbne, the phenyl group stabilizes the singlet more than the triple, reducing the ST gap by 6.3 kcal mol^-1. However, adding a second phenyl group (making 2) stabilizes both the singlet and triplet by about the same amount, leading to little change in the ST gap. The singlet does not get accrue the potential benefit of the second aryl group because sterics prohibit the two rings from being coplanar.

Table 2. Aryl effect for 1-5 based on the isodesmic reaction energies (kcal mol^-1)

References

(1) Woodcock, H. L.; Moran, D.; Brooks, B. R.; Schleyer, P. v. R.; Schaefer, H. F., "Carbene Stabilization by Aryl Substituents. Is Bigger Better?," J. Am. Chem. Soc., 2007, 129, 3763-3770, DOI: 10.1021/ja068899t.

InChIs

1: InChI=1/C7H6/c1-7-5-3-2-4-6-7/h1-6H

2: InChI=1/C13H10/c1-3-7-12(8-4-1)11-13-9-5-2-6-10-13/h1-10H

3: InChI=1/C11H8/c1-9-5-4-7-10-6-2-3-8-11(9)10/h1-8H

4: InChI=1/C21H14/c1-2-8-19-14-16(12-13-17(19)6-1)15-20-10-5-9-18-7-3-4-11-21(18)20/h1-14H

5: InChI=1/C15H10/c1-11-14-8-4-2-6-12(14)10-13-7-3-5-9-15(11)13/h1-10H

I mentioned “mindless chemistry” in the interview with Fritz Schaefer. This term, the title of the article by Schaefer and Schleyer,¹ refers to locating minimum energy structures through a stochastic search driven solely by a computer algorithm. No chemical rationale or intuition is used; rather, the computer simply tries a slew of different possibilities and mindlessly marches through them.

The approach employed by Schaefer and Schleyer is to use the ‘kick” algorithm of Saunders.² An arbitrary initial geometry is first selected (Saunders even suggests the case where all atoms are located at the same point!) and then a kick is applied to each atom, with random direction and displacement, to create a new geometry. An optimization is then performed with some quantum mechanical method, to produce a new structure. The kick is then applied to this new structure (or to the initial one again) to generate another geometry to start up another optimization. By doing many different “kicks” with different kick size, one can span a large swath of configuration space.

In their first “mindless chemistry” paper, Schafer and Schleyer identified some new structures of BCONS, C₆Be and C₆Be^2-.¹ In their next application,³ they explored the novel molecule periodane, which has the molecular formula LiBeBCNOF, named to reflect its make-up of one atom of every element (save neon) on the first full row of the periodic table. Krüger⁴ located the planar structure 1 (see Figure 1). But Schaefer and Schleyer, employing the “kick” algorithm located 27 structures that are lower in energy than 1, Their lowest energy structure 2 is 122 kcal mol^-1 lower than 1. They advocate for this stochastic search to gain broad understanding of the nature of the potential energy surface and then refining the search using “human logic”.

1

2

Figure 1. Optimized structures of periodane 1 and 2.

(Note – I have only provided a sketch of 2 since the supporting information for the article has not yet been posted on the Wiley web site. I will update this post with the actual structure when it becomes available.)

References

(1) Bera, P. P.; Sattelmeyer, K. W.; Saunders, M.; Schaefer, H. F.; Schleyer, P. v. R., "Mindless Chemistry," J. Phys. Chem. A, 2006, 110, 4287-4290, DOI: 10.1021/jp057107z.

(2) Saunders, M., "Stochastic Search for Isomers on a Quantum Mechanical Surface," J. Comput. Chem.. 2004, 25, 621-626, DOI: 10.1002/jcc.10407

(3) Bera, P. P.; Schleyer, P. v. R.; Schaefer, H. F., III, "Periodane: A Wealth of Structural Possibilities Revealed by the Kick Procedure," Int. J. Quantum Chem. 2007, 107, 2220-2223, DOI: 10.1002/qua.21322

(4) Krüger, T., "Periodane – An Unexpectedly Stable Molecule of Unique Composition," Int. J. Quantum Chem. 2006, 106, 1865-1869, DOI: 10.1002/qua.20948