# Nature of Interlayer Binding and Stacking of sp–sp ^{2} Hybridized Carbon Layers: A Quantum Monte Carlo Study

## Abstract

α-graphyne is a two-dimensional sheet of sp-sp2 hybridized carbon atoms in a honeycomb lattice. While the geometrical structure is similar to that of graphene, the hybridized triple bonds give rise to electronic structure that is different from that of graphene. Similar to graphene, α-graphyne can be stacked in bilayers with two stable configurations, but the different stackings have very different electronic structures: one is predicted to have gapless parabolic bands and the other a tunable bandgap which is attractive for applications. In order to realize applications, it is crucial to understand which stacking is more stable. This is difficult to model, as the stability is a result of weak interlayer van der Waals interactions which are not well captured by density functional theory (DFT). We have used quantum Monte Carlo simulations that accurately include van der Waals interactions to calculate the interlayer binding energy of bilayer graphyne and to determine its most stable stacking mode. Our results show that inter-layer bindings of sp- and sp2-bonded carbon networks are significantly underestimated in a Kohn-Sham DFT approach, even with an exchange-correlation potential corrected to include, in some approximation, van der Waals interactions. Finally, our quantum Monte Carlo calculations reveal that the interlayermore »

- Authors:

- Argonne National Lab. (ANL), Argonne, IL (United States). Leadership Computing Facility
- Intel Corporation, Hillsboro, OR (United States)
- Konkuk Univ., Seoul (Korea). Dept. of Physics
- Argonne National Lab. (ANL), Argonne, IL (United States). Material Science Division

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1395067

- Grant/Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Theory and Computation

- Additional Journal Information:
- Journal Volume: 13; Journal Issue: 11; Journal ID: ISSN 1549-9618

- Publisher:
- American Chemical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; Quantum Monte Carlo; Diffusion Monte Carlo; QMCPACK; Graphene; Graphyne; High Accuracy; First principle Calculations; ab-initio

### Citation Formats

```
Shin, Hyeondeok, Kim, Jeongnim, Lee, Hoonkyung, Heinonen, Olle, Benali, Anouar, and Kwon, Yongkyung.
```*Nature of Interlayer Binding and Stacking of sp–sp 2 Hybridized Carbon Layers: A Quantum Monte Carlo Study*. United States: N. p., 2017.
Web. doi:10.1021/acs.jctc.7b00747.

```
Shin, Hyeondeok, Kim, Jeongnim, Lee, Hoonkyung, Heinonen, Olle, Benali, Anouar, & Kwon, Yongkyung.
```*Nature of Interlayer Binding and Stacking of sp–sp 2 Hybridized Carbon Layers: A Quantum Monte Carlo Study*. United States. doi:10.1021/acs.jctc.7b00747.

```
Shin, Hyeondeok, Kim, Jeongnim, Lee, Hoonkyung, Heinonen, Olle, Benali, Anouar, and Kwon, Yongkyung. Wed .
"Nature of Interlayer Binding and Stacking of sp–sp 2 Hybridized Carbon Layers: A Quantum Monte Carlo Study". United States. doi:10.1021/acs.jctc.7b00747. https://www.osti.gov/servlets/purl/1395067.
```

```
@article{osti_1395067,
```

title = {Nature of Interlayer Binding and Stacking of sp–sp 2 Hybridized Carbon Layers: A Quantum Monte Carlo Study},

author = {Shin, Hyeondeok and Kim, Jeongnim and Lee, Hoonkyung and Heinonen, Olle and Benali, Anouar and Kwon, Yongkyung},

abstractNote = {α-graphyne is a two-dimensional sheet of sp-sp2 hybridized carbon atoms in a honeycomb lattice. While the geometrical structure is similar to that of graphene, the hybridized triple bonds give rise to electronic structure that is different from that of graphene. Similar to graphene, α-graphyne can be stacked in bilayers with two stable configurations, but the different stackings have very different electronic structures: one is predicted to have gapless parabolic bands and the other a tunable bandgap which is attractive for applications. In order to realize applications, it is crucial to understand which stacking is more stable. This is difficult to model, as the stability is a result of weak interlayer van der Waals interactions which are not well captured by density functional theory (DFT). We have used quantum Monte Carlo simulations that accurately include van der Waals interactions to calculate the interlayer binding energy of bilayer graphyne and to determine its most stable stacking mode. Our results show that inter-layer bindings of sp- and sp2-bonded carbon networks are significantly underestimated in a Kohn-Sham DFT approach, even with an exchange-correlation potential corrected to include, in some approximation, van der Waals interactions. Finally, our quantum Monte Carlo calculations reveal that the interlayer binding energy difference between the two stacking modes is only 0.9(4) eV/atom. From this we conclude that the two stable stacking modes of bilayer α-graphyne are almost degenerate with each other, and both will occur with about the same probability at room temperature unless there is a synthesis path that prefers one stacking over the other.},

doi = {10.1021/acs.jctc.7b00747},

journal = {Journal of Chemical Theory and Computation},

issn = {1549-9618},

number = 11,

volume = 13,

place = {United States},

year = {2017},

month = {10}

}

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