Subscriber access provided by UNIVERSITÁ DEGLI STUDI DI TORINO
Communication
Computational Evidence for Heavy-Atom Tunneling in the Bergman Cyclization of a 10-Membered Ring Enediyne Edyta M. Greer, Christopher V. Cosgriff, and Charles E. Doubleday J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/ja402445a • Publication Date (Web): 21 Jun 2013 Downloaded from http://pubs.acs.org on June 22, 2013
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Journal of the American Chemical Society is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Journal of the American Chemical Society
Computational Evidence for Heavy-Atom Tunneling in the Bergman Cyclization of a 10-Membered Ring Enediyne Edyta M. Greer,*,† Christopher V. Cosgriff,† and Charles Doubleday*,‡ †
Department of Natural Sciences, Baruch College of the City University of New York, 17 Lexington Ave., New York, NY 10010; ‡Department of Chemistry, Columbia University, 3000 Broadway, MC 3142, New York, NY 10027
Supporting Information Placeholder
ABSTRACT: DFT and CASSCF calculations for the cyclization of (3Z)-cyclodec-3-en-1,5-diyne have been carried out to investigate heavy-atom tunneling. At 37° C, tunneling is computed to enhance the rate by 38-40% over the transition state theory rate. Intramolecular 12 13 C/ C kinetic isotope effects are predicted to be substantial, with steep temperature dependence. These results are discussed in relation to recent experiment findings that show heavy atom tunneling at moderate temperatures. The calculations point to the possibility of a simple computational test for the likelihood of heavyatom tunneling using standard quantum chemistry information.
The 10-membered cyclic (3Z)-cyclodec-3-en-1,5diyne 1 is a structure present in a family of antitumor antibiotics,1 whose mechanism of action involves Bergman cyclization2 to form biradical 2 (Scheme 1). We felt that tunneling could contribute to this reaction, since the C1-C6 distance required to traverse the barrier must decrease near the transition state to a range similar to that of other reactions in which carbon tunneling is important.3 One manifestation of tunneling is a curved Arrhenius plot of ln k vs 1/T, for rate constant k and temperature T. In Nicolaou’s study of the cyclization of 1,4 the Arrhenius plot over 310-343 K is linear with activation energy Ea = 23.8 kcal/mol. This limited temperature range gives no information on tunneling. A more sensitive experimental criterion for tunneling is the intramolecular 12C/13C kinetic isotope effect (KIE), as recently shown by Borden, Singleton, and coworkers.3b If biradical trapping to form 3 is much faster than ring opening of 2, the KIE reflects the cyclization step. Here we have computed rate constants and intramolecular 12 13 C/ C KIEs including tunneling over 200 - 343 K. To get an accurate DFT description, we modified BLYP/6-31G(d)5 by fitting local and nonlocal exchange and correlation contributions to experimental4,6,7 and computational data.8 The fitting set included energies
and computed geometries of stationary points for cyclization of (Z)-hex-3-en-1,5-diyne,6,7,8 and the experimental barrier for cyclization of 1.4 Details are given in the SI. The modified functional is called mBLYP. Since the electronic configuration changes from a closed shell reactant to a singlet biradical product, mBLYP was used with unrestricted SCF and a broken spin initial guess. Scheme 1. Bergman cyclization of 3-cyclodecen-1,5diyne 2
1 10
3
9
4
8 5
6
7
1
H-donor
2
3
After locating stationary points (Figure 1), however, we found that mBLYP by itself is not suitable for tunneling calculations. Although mBLYP closely approximates the observed barrier, the vibrational zero point energy (ZPE) along the intrinsic reaction coordinate (IRC) changes discontinuously by 0.3 kcal/mol at the point at which the electronic configuration changes from closed to open shell. Every DFT we examined (BLYP, B3LYP, BPW91, M06-2X) has this characteristic. Therefore, we reoptimized stationary points with 10,10-CASSCF/6-31G(d) and corrected the energies with mBLYP/6-31G(d) and CCSD(T)/cc-pVTZ. ZPE was taken from CASSCF frequencies scaled by 0.91 to match mBLYP ZPE. mBLYP//CASSCF (Figure 1 energies in bold type) gives close agreement with the experimental barrier. CCSD(T)//CASSCF (upper number adjacent to mBLYP//CASSCF) gives too high a barrier by 2 kcal/mol, and CASSCF (lower adjacent energy) overestimates the barrier by 14 kcal/mol. In Figure 1, two enediyne minima, 1a and 1b, undergo cyclization via saddle points TSa and TSb, to give biradical products 2a and 2b. The IRC for the 1a-TSa-2a path preserves the C2 point group throughout. On the reactant side of TSb (Cs) the IRC leads through a valley-
ACS Paragon Plus Environment
Journal of the American Chemical Society
ridge inflection (VRI) to racemic 1b (C1) via TSc, the
+,'&!"&$
(#"1
$")(
'()*+,-./0123452
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 6
saddle point for enantiomeric interconversion of 1b.
#67# 97; >7#
-"(
-"(
%;7: #979
+,3 ./"/0
1"/
$"#4
!"(#
('&!"&$
!"#!
$'&!"%$
(%&!"#$ $%&!"#$
Figure 1. Stationary points for Bergman cyclization of 1a and 1b (point group in parentheses). Geometries were optimized by 10,10-CASSCF/6-31G(d). Energies (kcal/mol) are relative to 1a and include CASSCF vibrational zero-point energy scaled by 0.91. Energies in bold type are corrected by mBLYP/6-31G(d). In the adjacent pair of energies, the top is CCSD(T)/cc-pVTZ, bottom is CASSCF. C1-C6 distances are in Å. In TSa and TSb, these distances correspond to the maximum in the mBLYP//CASSCF IRC as described in the SI. Tunneling calculations were carried out using Polyrate,9 with the Gaussrate10 interface to Gaussian 09.11 To include CASSCF using Gamess,12 Gaussrate was modified to read and write Gamess files. The three levels of theory in Figure 1 were used in the tunneling calculations. Multidimensional tunneling probabilities were computed with the small curvature tunneling (SCT)13 option in Polyrate. In this method, frequencies are computed along the IRC to define the vibrationally adiabatic ground state curve, VaG, which is the IRC plus the ZPE. In the SCT method, VaG is the tunneling path. In the tunneling calculations, IRC and VaG curves passing through TSa and TSb were computed by CASSCF with frequencies scaled by 0.91. IRC energies were corrected by mBLYP//CASSCF and CCSD(T)// CASSCF (called mBLYP and CCSD(T) below), based on the VTST-ISPE method in Polyrate (variational transition state theory with interpolated single point energies). This was done by calculating mBLYP and CCSD(T) energies at 20 points along the CASSCF IRC and interpolating the full IRC at the more accurate level based on these points. VaG curves were then constructed by adding CASSCF ZPEs to the higher level interpolated IRC curves. Details are described in the SI. Tunneling calculations were carried out for cyclization of 1a and 1b with CASSCF and mBLYP, and for 1a with CCSD(T). Polyrate computes kCVT, the rate constant without tunneling, using canonical variational transition state theory (CVT). The SCT tunneling calculation gives κSCT, the SCT transmission coefficient, and the rate constant including SCT tunneling is given by kCVT+SCT = κSCT kCVT.14
Figure 2 shows the energy regions of the mBLYP and CASSCF VaG curves over which tunneling contributes to κSCT for cyclization of 1a at 310 K. The color intensity of each energy slice is proportional to its contribution to the Boltzmann-weighted integral over transmission probabilities to give κSCT - 1. At 310 K, tunneling is computed to have a substantial effect on the rate, with κSCT values of 1.40 (mBLYP) and 1.73 (CASSCF). CCSD(T) gives κSCT = 1.38 at 310 K, and its VaG curve is nearly superimposable on the mBLYP curve in Figure 2 (see SI). The much higher κSCT for CASSCF is due to its narrower VaG curve than mBLYP and CCSD(T), which may be the result of the large CASSCF barrier.15 The information in Figure 2 is useful for a reaction like the Bergman cyclization, whose barrier is both high and wide. The wide barrier prevents tunneling at low energies. Tunneling contributes to the rate only within a specific energy range near the top of the barrier where the barrier is sufficiently narrow. Figure 2 allows one to identify that energy range, and the barrier widths over that range, to understand how thermally activated tunneling affects rates and kinetic isotope effects as a function of temperature. Three differences between mBLYP and CASSCF stand out in Figure 2: the mBLYP curve is wider, tunneling contributes to κSCT over a much smaller energy range with mBLYP, and κSCT is smaller for mBLYP. In terms of the horizontal scales, the contribution of tunneling to κSCT in both curves is largely confined to energies at which the C1-C6 distance (top scale) changes by < 0.2 Å (or s changes by < 0.6 Å-amu1/2, bottom scale) from one side of the barrier to the other. The larger value of
ACS Paragon Plus Environment
Page 3 of 6
κSCT computed by CASSCF is the result of a larger energy range over which the width is appropriately narrow: 2.2 kcal/mol for CASSCF vs 1.5 kcal/mol for mBLYP. The essential information of Figure 2 is that κSCT is sensitive to the energy range over which the barrier is narrow enough for tunneling to contribute to the rate. ;$!;'#
