Archive for the 'Borden' Category

The unusual PES of (CO)3

As recently explicated by Wang and Borden using NIPE spectroscopy and computations, the potential energy surface of cyclopropyl-1,2,3-trione 1 is remarkably complex.1 (U)CCSD(T)//aug-cc-pVTZ computations of the D3h singlet (the 1A1’ state shown in Figure 1) is actually a hilltop, possessing two imaginary frequencies. Distorting the structure as indicated by these imaginary frequencies and then optimizing the structure leads directly to dissociation to three CO molecules. Thus, (CO)3 does not exist as a stable minima on the singlet surface.

The D3h triplet (the 3E” state shown in Figure 1) is not a critical point on the surface; due to the Jahn-Teller effect is distorts into two different states: the 3B1 state which is a local energy minimum, and the 3A2 state which is a transition state between the symmetry-related 3B1 states.

So, this implies the possibility of a very interesting NIPE experiment. If the radical anion (CO)3-.
loses an electron and goes to the singlet surface, it lands at a hilltop(!) and should have a very short lifetime. If it goes to the triplet surface, it lands at either a transition state (3A2) and again should have a short lifetime, or it can land at the 3B1 state and perhaps have some lifetime before it dissociates by losing one CO molecule.






Figure 1. (U)CCSD(T)//aug-cc-pVTZ optimized geometries of 1 and its radical anion.

The NIPE spectrum identifies three transitions. By comparing the energies of the electron loss seen in the experiment with the computations, along with calculating the Franck-Condon factors using the computed geometries and vibrational frequencies, the lowest energy transition is to the 1A1’ state, and the second transition is part of the vibrational progression also to the 1A1’ state. This is the first identification of vibrational frequencies associated with a hilltop structure. The third transition is to the 3A2 state. No transition to the 3B1 state is found due to the large geometric difference between the radical anion and the 3B1 state; the Franck-Condon factors are zero due to no overlap of their wavefunctions.

Once again, the power of the symbiotic relationship between experiment and computation is amply demonstrated in this paper.


(1) Chen, B.; Hrovat, D. A.; West, R.; Deng, S. H. M.; Wang, X.-B.; Borden, W. T. "The Negative Ion Photoelectron Spectrum of Cyclopropane-1,2,3-Trione Radical Anion, (CO)3•– — A Joint Experimental and Computational Study," J. Am. Chem. Soc. 2014, 136, 12345-12354, DOI: 10.1021/ja505582k.


1: InChI=1S/C3O3/c4-1-2(5)3(1)6

Borden Steven Bachrach 21 Oct 2014 No Comments

Another example of tunneling control

The notion of tunneling control has been a topic of interest within this blog a number of times. As developed by Schreiner and Allen,1,2 tunneling control is a third means for predicting (or directing) the outcome of a reaction, alongside the more traditionally recognized kinetic and thermodynamic control. Tunneling control occurs when tunneling through a higher barrier is preferred over tunneling through a lower barrier.

Kozuch and Borden propose another example of tunneling control, this time in the rearrangement of the noradamantyl carbene 1.3 This carbene can undergo a 1,2-carbon shift, driven by strain relief to form the alkene 2. The alternative as a 1,2-hydrogen shift that produces the alkene 3.

These two reaction pathways were explored using B3LYP/6-31G(d,p) computations coupled with canonical variational theory and small curvature tunneling corrections. Structures of the reactant 1 and the two transition states leading to the two products 2 and 3 are shown in Figure 1. The activation barrier at 300 K is 5.4 kcal mol-1 leading to 2 and 8.6 kcal mol-1 leading to 3. Tunneling is expected to be much more important for the hydrogen shift than for the carbon shift, but even including tunneling, the rate to form 2 is much faster than the rate to form 3 at 300 K.


TS 1→2


TS 1→3


Figure 1. B3LYP/6 optimized structures of 1-3 and the transition states leading to 2 and 3.

The situation is reversed however at cryogenic temperatures (< 20 K). Tunneling is now the only route for the reactions to occur, and the rate for formation of 3 is dramatically greater than the rate of formation of 2, which is inhibited by the movement of the much heavier carbon atom. Perdeuteration of the methyl group of 1, which drastically slows the rate of tunneling in the path to 3, nonetheless still favors this pathway (forming d3-3) over formation of d3-2. Thus, at low temperatures the formation of 3 is the preferred product, a manifestation of tunneling control.

Kozuch and Borden end their paper with a hope that an experimentalist will examine this interesting case. I concur!


(1) Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D. "Methylhydroxycarbene: Tunneling Control of a Chemical Reaction," Science 2011, 332, 1300-1303, DOI: 10.1126/science.1203761.

(2) Ley, D.; Gerbig, D.; Schreiner, P. R. "Tunnelling control of chemical reactions – the organic chemist’s perspective," Org. Biomol. Chem. 2012, 10, 3781-3790, DOI: 10.1039/C2OB07170C.

(3) Kozuch, S.; Zhang, X.; Hrovat, D. A.; Borden, W. T. "Calculations on Tunneling in the Reactions of Noradamantyl Carbenes," J. Am. Chem. Soc. 2013, 135, 17274-17277, DOI: 10.1021/ja409176u.


1: InChI=1S/C11H16/c1-2-11-6-8-3-9(7-11)5-10(11)4-8/h8-10H,3-7H2,1H3

2: InChI=1S/C11H16/c1-7-10-3-8-2-9(5-10)6-11(7)4-8/h8-10H,2-6H2,1H3

3: InChI=1S/C11H16/c1-2-11-6-8-3-9(7-11)5-10(11)4-8/h2,8-10H,1,3-7H2

Borden &Tunneling Steven Bachrach 27 Jan 2014 No Comments

Unusual carbene ground states

The singlet and triplet carbene is the topic of Chapter 4, especially sections 1 and 2. The ground state of methylene is the triplet, with one electron in the σ-orbital and one electron in the π-orbital, with the spins aligned. The lowest singlet state places the pair of electrons in the σ-orbital, and this state is about 9 kcal mol-1 higher in energy than the triplet. The next lowest singlet state has one electron in each of the σ- and π-orbitals, with the spins aligned. The singlet state with both electrons in the π-orbital is the highest of these four states, some 60 kcal mol-1 above the ground state triplet.

Hoffmann and Borden now pose the question “Can the doubly occupied π carbene (1A10π2) be the ground state with appropriate substitution?” The answer they find is yes!1

The trick is to find a combination of substituents that will raise the energy of the σ-orbital and lower the energy of the π-orbital. The latter effect can be enhanced if the π-orbital can be a part of an aromatic (6e-) ring.

Two of the best possibilities for identifying a ground state 1A10π2 carbene are 1 and 2. The CASSCF/6-31G(d) optimized geometries of these two are shown in Figure 1. In 1, the nitrogen lone pairs act to destabilize the σ-orbital, while the aldehyde group acts as a withdrawing group to stabilize the π-orbital. The result is that the 1A10π6 state of 1 is predicted to be about 8 kcal mol-1 more stable than the triplet state, as per CASPT2 and CCSD(T) computations.



An ever greater effect is predicted for 2. Here the nitrogen lone pairs adjacent to the carbene act to destabilize the σ-orbital. The empty π-orbital on B lowers the energy of the carbene π-orbital by making it part of the 6-electron aromatic ring. The 1A10π6 state of 2 is predicted to be about 25 kcal mol-1 more stable than its triplet state!



Figure 1. CASSCF/6-31G(d) optimized geometries of the 1A10π6 states of 1 and 2.


(1) Chen, B.; Rogachev, A. Y.; Hrovat, D. A.; Hoffmann, R.; Borden, W. T. "How to
Make the σ0π2 Singlet the Ground State of Carbenes," J. Am. Chem. Soc. 2013, 135, 13954-13964, DOI: 10.1021/ja407116e.


1: InChI=1S/C5H2N2O2/c8-1-4-5(2-9)7-3-6-4/h1-2H

2: InChI=1S/C3H3BN2/c1-4-2-6-3-5-1/h1-2,4H

Borden &carbenes Steven Bachrach 14 Oct 2013 4 Comments

Interacting bis-allyl diradicals

Interacting bis-allyl radicals are the topic of a computational study by Gleiter and Borden.1 The new twist is to have the two allyl groups interact through a cyclobutyl, cyclopentyl or cyclohexyl ring, as in 1-3.

The degree of interaction of the radical electrons is evaluated with a number of metrics. First, the singlet-triplet energy gap is computed at CASSCF(6,6)/6-31G(d) and UB3LYP/6-31G(d). A larger gap is suggestive of strong interaction between the two allyl radicals. Next, the <S2> value of the UB3LYP wavefunction will be 0 for a pure singlet, which occurs when the radicals are strongly interacting. A value near 1 suggests an electron localized into each allyl fragment. Lastly, the natural orbital occupation numbers (NOON) of the two highest lying orbitals would be 2 and 0 for the pure interacting state and each would be 1 for the non-interacting state. The B3LYP/6-31G(d) optimized geometries of 1-3 are shown in Figure 1. The values of each metric are listed in Table 1.




Figure 1. B3LYP/6-31G(d) optimized geometries of 1-3.

Table 1. Metrics for evaluating the allyl interaction in 1-3.










1.62, 0.38





1.31, 0.69





1.20, 0.80

The different metrics are all consistent. The allyl radicals are strongly interacting in 1, with a low lying singlet state. The interaction is significantly lessened in 2 and smaller still in 3. The authors argue these differences in terms of the molecular orbital interactions between the allyl fragments and the central ring fragment.


(1) Lovitt, C. F.; Dong, H.; Hrovat, D. A.; Gleiter, R.; Borden, W. T., "Through-Bond Interactions in the Diradical Intermediates Formed in the Rearrangements of Bicyclo[n.m.0]alkatetraenes," J. Am. Chem. Soc., 2010, 132, 14617-14624, DOI: ja106329t


1: InChI=1/C10H10/c1-3-7-9-5-2-6-10(7)8(9)4-1/h1-10H

2: InChI=1/C11H12/c1-3-8-7-9-4-2-6-11(8)10(9)5-1/h1-6,8-11H,7H2

3: InChI=1/C12H14/c1-3-9-7-12-6-2-5-11(9)8-10(12)4-1/h1-6,9-12H,7-8H2

Borden &diradicals Steven Bachrach 04 Jan 2011 2 Comments

Heavy-atom tunneling confirmed

Borden predicted measurable heavy-atom isotope effects in the ring opening of cyclopropylcarbinyl radical. In my blog post on this paper, I concluded with the line:

Borden hopes that experimentalists will reinvestigate this
problem (and hopefully confirm his predictions).

Well, in a recent paper where Borden collaborates with Singleton, these predictions are confirmed!1

There is a sizable kinetic isotope effect for breaking the ring bond to a 12C over a bond to a 13C atom, up to 16% at -100 °C. The KIE predicted without including tunneling are dramatically below the experimental values, but incorporation of tunneling in the computated KIEs match up with experiment with an error no greater that 0.7%. The Arrhenius plot of ln KIE vs. 1/T shows enhanced isotope effects when tunneling is included, very nice agreement between the experimental and tunneling-corrected KIEs and curvature – all indicative of heavy atom tunneling. Lastly, the ring open product (1-butene) is the observed major product (62%) at -100 °C; the minor product is methylcyclopropane. In the absence of heavy-atom tunneling, 1-butene would be the minor product (28%).


(1) Gonzalez-James, O. M.; Zhang, X.; Datta, A.; Hrovat, D. A.; Borden, W. T.; Singleton, D. A. J. Am. Chem. Soc., 2010, 132, 12548-12549, DOI: 10.1021/ja1055593.


Cyclopropylcarbonyl radical: InChI=1/C4H7/c1-4-2-3-4/h4H,1-3H2

1-butene: InChI=1/C4H8/c1-3-4-2/h3H,1,4H2,2H3

Borden &Singleton &Tunneling Steven Bachrach 22 Oct 2010 1 Comment

Inverse isotope effect

Following up on his previous studies of isotope effects on the ring opening of cyclopropylcarbinyl radical 1 to give 2 (see my previous post), Borden now reports on its kinetic isotope effect (KIE).1

Using the small-curvature tunneling approximation along with structures and frequencies computed at B3LYP/6-31G(d), he finds a negligible KIE at C1, consistent with little motion of C1 in the transition vector. The KIE for substitution at C4 is large (k(12C/14C)=5.46), also consistent with its large motion in the transition vector. What is surprising is the KIE for deuterium substitution at C1: 0.37. This is a large inverse isotope effect!

Analysis of the vibrational frequencies that involve the C1 hydrogens provides an explanation. In going to the TS for the ring opening, both the torsional motion about the C1-C2 bond (making the double bond) and the pyramidal motion increase in frequency. This leads to a higher activation barrier for H than D, and the inverse isotope effect.


(1) Zhang, X.; Datta, A.; Hrovat, D. A.; Borden, W. T., “Calculations Predict a Large Inverse H/D Kinetic Isotope Effect on the Rate of Tunneling in the Ring Opening of Cyclopropylcarbinyl Radical,” J. Am. Chem. Soc., 2009, 131, 16002-16003, DOI: 10.1021/ja907406q.

Borden &Tunneling Steven Bachrach 04 Jan 2010 3 Comments

Oxyallyl diradical

The longstanding unknown oxyallyl diradical (1) singlet-triplet gap has now been addressed with a very nice photoelectron spectroscopy study by Lineberger with interpretation greatly aided by computations provided by Hrovat and Borden.1

The photoelectron detachment spectrum of oxyallyl radical anion shows 5 major peaks, one at 1.942 eV and a series of four peaks starting at 1.997 eV separated by 405 cm-1.

B3LYP/6-311++G(d,p) computations indicate that the energy for electron detachment from the radical anion to triplet oxyallyl diradical is 1.979 eV. (The structure of triplet 1 is shown in Figure 1.) Further, the computed vibrational frequency of the C-C-C bend is 408 cm-1. These computations suggest that the four peak sequence represents a vibrational progression in the C-C-C bend of the triplet oxyallyl diradical.



Figure 1. Structures of the singlet and triplet oxyallyl diradical 1.1

CASPT2 computations on singlet oxyallayl diradical indicate that it lies in a very shallow well, lower than the zero-point energy. (This structure is shown in Figure 1.) In fact, the singlet diradical can collapse without a barrier to cyclopropanone. Interestingly, the C-O stretching frequency of 1 is computed to be 1731 cm-1, and close inspection of the photoelectron spectrum does show a progression of this magnitude originating from peak A. Therefore, both the singlet and triplet states of 1 are identified and their gap is extraordinarily small – the singlet is only 0.055 eV lower in energy than the triplet.


(1) Ichino, T.; Villano, S. M.; Gianola, A. J.; Goebbert, D. J.; Velarde, L.; Sanov, A.; Blanksby, S. J.; Zhou, X.; Hrovat, D. A.; Borden, W. T.; Lineberger, W. C., "The Lowest Singlet and Triplet States of the Oxyallyl Diradical," Angew. Chem. Int. Ed., 2009, 48, 8509-8511, DOI: 10.1002/anie.200904417

Borden &diradicals Steven Bachrach 07 Dec 2009 No Comments

Non-Kekule Triplet Diradical

I missed this when it came out, but Quast, Sander and Borden have made the very interesting non-Kekule diradical 1.1


The EPR spectra shows the characteristic six-line signal, with zero-field splitting parameters consistent with related triplet diradicals. The Curie-Weiss plot is linear from 4.6 to 22.9 K. These data suggest a triplet ground state. CASSCF(14,14)/6-31G* computations indicate that the triplet lies 8.5 kcal mol-1 below the singlet. The optimized triplet geometry is shown in Figure 1. The triplet ground state is consistent with the Borden-Davidson rules for radicals.2


Figure 1. CASSCF(14,14)/6-31G* optimized structure of triplet 1.


(1) Quast, H.; Nudling, W.; Klemm, G.; Kirschfeld, A.; Neuhaus, P.; Sander, W.; Hrovat, D. A.; Borden, W. T., "A Perimidine-Derived Non-Kekule Triplet Diradical," J. Org. Chem. 2008, 73, 4956-4961, DOI: 10.1021/jo800589y.

(2) Borden, W. T.; Davidson, E. R., "Effects of electron repulsion in conjugated hydrocarbon diradicals," J. Am. Chem. Soc. 1977, 99, 4587-4594, DOI: 10.1021/ja00456a010.


1: InChI=1/C20H27N3/c1-19(2,3)13-8-12-9-14(20(4,5)6)11-16-17(12)15(10-13)22-18(21-7)23-16/h8-11H,1-7H3,(H2,21,22,23)/f/h22-23H

Borden &diradicals Steven Bachrach 26 Feb 2009 No Comments

Heavy atom tunneling

Wes Borden has been exploring reactions where tunneling is operational. These studies have been inspired by Bill Doering’s1 statement regarding tunneling in 1,5-sigmatropic shifts: “The tunneling effect is likely, in the opinion of some, to remain relegated to the virtual world of calculations”. Borden’s first two papers dealt with the kinetic isotope effects for the [1,5]-H shift in 1,3-cyclopentadiene and 5-methyl-1,3-cyclopentadiene.2,3

His latest article examines carbon tunneling,4 which, due to the much heavier mass of the carbon nucleus relative to a proton, is likely to play a minimal role at best. Borden looked at the ring opening of cyclopropylcarbinyl radical 1 to 3-butene-1-yl radical 2, passing through transition state TS1-2. The B3LYP/6-31G(d) optimized structures are shown in Figure 1.







Figure 1. B3LYP/6-31G(d) optimized geometries of 1, 2, and TS1-2.4

The predicted rate of the reaction at 298 K using canonical variational transition state theory is increased by about 50% when small-curvature tunneling is included. This predicted rate is a bit smaller than the experimental value. Experiments also shows a linear Arrhenius plot, and Borden’s calculations agree until one reaches very low temperatures. Below 150 K the Arrhenius curve begins to deviate from linearity, and below 20 K the curve is flat – the rate is no longer temperature dependent! Thus, at cryogenic temperatures, the tunneling rate far exceeds traditional crossing of the variational barrier. Borden hopes that experimentalists will reinvestigate this problem (and hopefully confirm his predictions).


(1) Doering, W. v. E.; Zhao, X., "Effect on Kinetics by Deuterium in the 1,5-Hydrogen Shift of a Cisoid-Locked 1,3(Z)-Pentadiene, 2-Methyl-10-methylenebicyclo<[4.4.0]dec-1-ene: Evidence for Tunneling?," J. Am. Chem. Soc., 2006, 128, 9080-9085, DOI: 10.1021/ja057377v.

(2) Shelton, G. R.; Hrovat, D. A.; Borden, W. T., "Tunneling in the 1,5-Hydrogen Shift Reactions of 1,3-Cyclopentadiene and 5-Methyl-1,3-Cyclopentadiene," J. Am. Chem. Soc., 2007, 129, 164-168, DOI: 10.1021/ja0664279.

(3) Shelton, G. R.; Hrovat, D. A.; Borden, W. T., "Calculations of the Effect of Tunneling on the Swain-Schaad Exponents (SSEs) for the 1,5-Hydrogen Shift in 5-Methyl-1,3-cyclopentadiene. Can SSEs Be Used to Diagnose the Occurrence of Tunneling?," J. Am. Chem. Soc., 2007, 129, 16115-16118, DOI: 10.1021/ja076132a.

(4) Datta, A.; Hrovat, D. A.; Borden, W. T., "Calculations Predict Rapid Tunneling by Carbon from the Vibrational Ground State in the Ring Opening of Cyclopropylcarbinyl Radical at Cryogenic Temperatures," J. Am. Chem. Soc., 2008, 130, 6684-6685, DOI: 10.1021/ja801089p.


1: InChI=1/C4H7/c1-4-2-3-4/h4H,1-3H2

2: InChI=1/C4H7/c1-3-4-2/h3H,1-2,4H2

Borden &DFT &Tunneling Steven Bachrach 17 Jun 2008 2 Comments