At 1.3 nN, the NDEs improve product selec-
tivity by fourfold forUin comparison to the
statistical outcome. The apparent enhance-
ment on selectivity is much smaller (<10%)
forAandD, because ofAbeing a kinetic trap
and an already preferred product channel on
the FMPES andDhaving a relatively low dy-
namic contribution (Fig. 4B).
The isomer-dependent dynamic responses
result from a varying degree of openness in the
exit reaction channels along the dihedral coor-
dinate, which is further determined by reactant
stereochemistry (fig. S92). The 120° ridge on
the FMPES blocks the majority of dynamic
exit coming fromD, leaving behind a narrow
and risen gorge (Df= 3°) for its thermal exit
(Fig. 4A). In contrast, the exit channel forA
is wider (Df= 45°), whereas forUthere is a
modest constriction (Df= 35°). We used an
additive model to relate dynamic population
(f) and the relative configuration of stereo-
centers on the cyclobutane rings. Mathemat-
ically, we found that the stereochemistry along
the pulling direction plays a primary role in
promoting dynamic trajectories, with trans
configuration much better than cis; the stereo-
chemistry orthogonal to the force is secondary,
with cis better than trans. This rule allowed us
to rank the tendency to undergo dynamic ring
opening for all possible cyclobutane stereo-
isomers (fig. S93).
The force-induced NDE is expressed as a
linear hybridization of dynamic and thermal
extremes with a force-dependent partition
(Fig. 4E). The dynamic regime is stereospe-
cific by definition, and the selectivity of product
isomers in the thermal regime was assumed to
be statistical. This statistical (transition state
theory, TST) stereoselectivity (STST) was ob-
tained from equilibrium product distributions
calculated by solving the system of rate equa-
tions of the activation-isomerization reaction
network (Fig. 4E, right box, and fig. S94). The
rate constant for each rate equation was cal-
culated by TST (table S14). The force-dependent
nonstatistical stereoselectivity (SNDE), defined
as the ratio between direct stereoisomeric pro-
duct and all isomerization products, is predict-
able from the statistical stereoselectivity,STST,
and the dynamic fraction,f:
SNDE¼STSTþf
1 fðÞ 1When the dynamic fraction increases from
0 to 1, theSNDEgoes from its thermal value,
STST(f= 0), to being a stereospecific trans-
formation in the limit whenf→1(tableS15).
This model reproduces the observed dynamic
selectivity without the need to run full long
MD simulations.
The hybrid NDE framework reveals that
there is not necessarily a simple connection
between the intermediate’s stability and the
dynamic selectivity of mechanochemical reac-
tions. Although the stereoconvergent ring
opening of the ester-substituted cyclobutane
has been observed and attributed to its long-
living intermediate ( 28 ), our study suggests
that a long-lived intermediate need not be
destined for lower stereoselectivity. Indeed,
we have improved the product stereoselec-
tivity of the ester derivatives compared to the
reported literature values. Similarly, the alkyl
D-isomer displayed high stereoselectivity under
all experimental conditions despite its longest
diradical lifetime as shown by radical quench-
ing experiments with 4-hydroxyl TEMPO (table
S17). Rather, stereoselectivity can be affected
dynamically for a short-lived intermediate: for
example, by a neighboring product channel
serving as a dynamic sink to draw the trespass-
ing trajectories into an irreversible path, sim-
ilar to the formation of (E,Z)-bisalkene from
theU-isomer.
We envision that external force is an exper-
imental method for controlling nonstatistical
dynamics and steering reaction trajectories
away from constraints imposed by potential
energy surfaces. The hybrid framework will
offer ability to probe and understand the dy-
namic effects of mechanochemical phenomena
in polymeric materials. The ability to control
dynamics and stereochemistry of mechano-
chemical reactions may be helpful for program-
ming properties of next-generation polymeric
materials whose life cycles will go beyond the
single-use paradigm.REFERENCES AND NOTES- B. K. Carpenter,J. Am. Chem. Soc. 117 , 6336– 6344
(1995). - S. C. Ammal, H. Yamataka, M. Aida, M. Dupuis,Science 299 ,
1555 – 1557 (2003). - Y. Nieves-Quinones, D. A. Singleton,J. Am. Chem. Soc. 138 ,
15167 – 15176 (2016). - C. Doubleday, C. P. Suhrada, K. N. Houk,J. Am. Chem. Soc.
128 , 90–94 (2006). - F. F. Crim,Proc. Natl. Acad. Sci. U.S.A. 105 , 12654– 12661
(2008). - J. Rehbein, B. K. Carpenter,Phys. Chem. Chem. Phys. 13 ,
20906 – 20922 (2011). - J. Rehbein, B. Wulff,Tetrahedron Lett. 56 , 6931– 6943
(2015). - S. R. Hare, D. J. Tantillo,Pure Appl. Chem. 89 , 679– 698
(2017). - Y. J. Hong, D. J. Tantillo,Nat. Chem. 6 , 104– 111
(2014). - J. Wang, B. L. Feringa,Science 331 , 1429– 1432
(2011). - C. J. Brown, F. D. Toste, R. G. Bergman, K. N. Raymond,
Chem. Rev. 115 , 3012–3035 (2015). - A. C. Aragonèset al.,Nature 531 , 88–91 (2016).
- W. Mtangiet al.,J. Am. Chem. Soc. 139 , 2794– 2798
(2017). - M.T.Ong,J.Leiding,H.Tao,A.M.Virshup,
T. J. Martínez,J. Am. Chem. Soc. 131 , 6377– 6379
(2009). - P. Dopieralskiet al.,Nat. Chem. 5 , 685– 691
(2013). - C. R. Hickenbothet al.,Nature 446 , 423– 427
(2007). - A. E. M. Beedleet al.,Nat. Commun. 9 , 3155
(2018).
18. M. E. McFadden, M. J. Robb,J. Am. Chem. Soc. 141 ,
11388 – 11392 (2019).
19. J. M. Lenhardtet al.,Science 329 , 1057– 1060
(2010).
20. Z. Chenet al.,Nat. Chem. 12 , 302–309 (2020).
21. R. Nixon, G. De Bo,Nat. Chem. 12 , 826– 831
(2020).
22. M. Wollenhaupt, C. Schran, M. Krupička, D. Marx,
ChemPhysChem 19 , 837–847 (2018).
23. E. Fischer, R. Gleiter,Tetrahedron Lett. 26 , 5289– 5290
(1985).
24. S. Pedersen, J. L. Herek, A. H. Zewail,Science 266 , 1359– 1364
(1994).
25. M. J. Krygeret al.,J. Am. Chem. Soc. 132 , 4558– 4559
(2010).
26.H.M.Klukovich,Z.S.Kean,S.T.Iacono,
S. L. Craig,J. Am. Chem. Soc. 133 , 17882– 17888
(2011).
27. Z. Chenet al.,Science 357 , 475–479 (2017).
28.Z.S.Kean,Z.Niu,G.B.Hewage,A.L.Rheingold,
S. L. Craig,J. Am. Chem. Soc. 135 , 13598– 13604
(2013).
29. I. Tabushi, K. Yamamura, Z. Yoshida,J. Am. Chem. Soc. 94 ,
787 – 792 (1972).
30.I.M.Klein,C.C.Husic,D.P.Kovács,N.J.Choquette,
M. J. Robb,J. Am. Chem. Soc. 142 , 16364– 16381
(2020).
31. P. A. May, J. S. Moore,Chem. Soc. Rev. 42 , 7497– 7506
(2013).
32. M. J. Kryger, A. M. Munaretto, J. S. Moore,J. Am. Chem. Soc.
133 , 18992–18998 (2011).
33. J. M. Lenhardt, A. L. Black Ramirez, B. Lee,
T. B. Kouznetsova, S. L. Craig,Macromolecules 48 ,
6396 – 6403 (2015).
34. B. K. Carpenter,Chem. Rev. 113 , 7265–7286 (2013).
35. D. R. Glowacki, S. P. Marsden, M. J. Pilling,J. Am. Chem. Soc.
131 , 13896–13897 (2009).
ACKNOWLEDGMENTS
Y.L. thanks J. Fu and X. Zhu for the helpful discussions. We
thank O. Davydovich and D. Loudermilk for figure designs, and
the SCS NMR Lab for its technical support.Funding:This
work was supported by the National Science Foundation
(NSF-CMMI-19-33932). T.J.M. and S.H. thank the Army
Research Office (W911NF-15-1-0525) for financial support.
J.M. thanks the Dr.-Leni-Schöninger foundation and the
Deutsche Forschungsgemeinschaft (no. 419817859) for financial
support. This work used the XStream computational resource
supported by the National Science Foundation Major Research
Instrumentation program (ACI-1429830).Author
contributions:Y.L. conceived this work and performed
synthesis and sonication experiments; S.H. performed dynamic
simulations to construct the energy surfaces and reaction
momenta; J.M. calculated the paths and the rate constants;
Y.L., J.M., and S.H. interpreted the data and built the hybrid
model; Y.J. assisted in the synthesis and sonication
instrumentation; Q.W. assisted in polymer characterizations;
T.W. performed x-ray structural analysis; T.J.M. and J.S.M.
supervised the project; Y.L., T.J.M., and J.S.M. wrote the
manuscript with input from all authors.Competing interests:
The authors declare no competing interests.Data and
materials availability:Crystallographic data are available free
of charge from the Cambridge Crystallographic Data Centre
under reference CCDC nos. 2051124, 2051125, and 2051126.
All other data supporting the findings of this study are
presented in the main text or supplementary materials.SUPPLEMENTARY MATERIALS
science.sciencemag.org/content/373/6551/208/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S100
Tables S1 to S17
References ( 36 – 62 )
Movies S1 to S5
Structures29 March 2021; accepted 3 June 2021
10.1126/science.abi7609212 9JULY2021•VOL 373 ISSUE 6551 sciencemag.org SCIENCE
RESEARCH | REPORTS