Article
This is related to the relative stability and lifetime of the various inter-
mediate structures. Owing to computational limitations, it is very dif-
ficult to obtain the accurate lifetimes for the intermediate structures,
which are relatively long compared to the simulation time. Instead, we
have calculated the interacting energy (ΔEb) between a water molecule
at the edge and the remaining water molecules together with the Au
substrate after optimization for various intermediate structures by
classical force field. The maximum interacting energy corresponds to
that needed to decompose the existing structure during the growth,
thus providing an estimation for the lifetime.
As shown in Extended Data Fig. 9, our calculations show that the maxi-
mum interacting energy between a water molecule at the zigzag edge and
the remaining water molecules follows ZZ3 > ZZ2 > ZZ4 > ZZ5 > ZZ6 > ZZ1.
Such a trend suggests that individual pentagon structures attached at
the zigzag edge (ZZ1) are the most stable. By contrast, zigzag-565 (ZZ4)
should have the shortest lifetime among the intermediate structures with
paired water, which explains why such a structure cannot be observed
experimentally. In addition, we note that the lifetime of the 5(6···6)5
structure at the zigzag edge increases with the number of the hexagons.
For armchair edge structures, the maximum interacting energy follows
AC4 > AC3 > AC2 > AC1. Interestingly, it was revealed that the composite
575/656 structure (AC1) is very stable. However, we cannot distinguish
between the 575/656 structure and the 5756-type edge in experiment,
because only the top layer of the 2D bilayer ice can be imaged by STM
and AFM. Such a composite 575/656 structure would greatly facilitate
the 5756-to-5656 conversion during the growth of the armchair edge
structure. Furthermore, the lifetime of the 5656-type edge decreases
rapidly as its length increases, which is consistent with experimental
results that indicate that the observed 5656-type edges are mostly short.
Data availability
The source data are available from the corresponding authors upon
reasonable request.
Code availability
The custom code and mathematical algorithms that support the find-
ings of this study are available from the corresponding authors upon
reasonable request.
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Acknowledgements We thank J.-J. Wang for discussions. This work was supported by the
National Key R&D Program under grant numbers 2016YFA0300901, 2017YFA0205003 and
2015CB856801, the National Natural Science Foundation of China under grant numbers
11888101, 11634001, 21725302 and 11525520, the Strategic Priority Research Program of the
Chinese Academy of Sciences under grant number XDB28000000, and the Beijing Municipal
Science & Technology Commission. J.S.F. and X.C.Z were supported by US National Science
Foundation (CHE-1665324). We are grateful for the computational resources provided by the
TianHe-1A and TianHe II supercomputers, by the High-performance Computing Platform of
Peking University supercomputing facility, and by the UNL Holland Computing Center.Author contributions Y.J. and E.-G.W. designed and supervised the project. R.M. and Y.T.
performed the STM/AFM measurements with J.G. and J.P.; D.C., J.C., X.-Z.L. and L.-M.X.
performed ab initio DFT calculations. C.Z., J.S.F. and X.C.Z. carried out the classical molecular-
dynamics simulations. D.C. carried out the theoretical simulations of the AFM images. R.M.,
D.C., C.Z., Y.T., J.C., X.-Z.L., X.C.Z., L.-M.X., E.-G.W., and Y.J. analysed the data. Y.J., R.M., D.C.,
L.-M.X., C.Z. and X.C.Z. wrote the manuscript with the input of all other authors. The
manuscript reflects the contributions of all authors.
Competing interests The authors declare no competing interests.Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41586-019-
1853-4.
Correspondence and requests for materials should be addressed to X.C.Z., L.-M.X., E.-G.W.
or Y.J.
Peer review information Nature thanks Miquel Salmeron and Yoshiaki Sugimoto for their
contribution to the peer review of this work.
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