Tracking the light-driven layer stacking of graphene oxide
Supplementary materials
Masaki Hada1,2*†, Satoshi Ohmura3†, Yuki Yamamoto1†, Yoshiya Kishibe1, Wataru
Yajima1, Ryo Shikata1, Tomohiro Iguchi4, Keishi Akada1, Shoji Yoshida1, Jun-ichi
Fujita1, Shin-ya Koshihara5, Yuta Nishina4,6*
1

Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan.

2

Tsukuba Research Center for Energy Materials Science (TREMS), University ofTsukuba, Tsukuba 305-8573, Japan.
3

Faculty of Engineering, Hiroshima Institute of Technology, Hiroshima 731-5193, Japan.

4

Graduate School of Natural Science and Technology, Okayama University, Okayama

700-8530, Japan.
5

School of Science, Tokyo Institute of Technology, Tokyo 152-8551, Japan.

6

Research Core for Interdisciplinary Sciences, Okayama University, Okayama 700-8530,Japan.

*Emails:hada.masaki.fm@u.tsukuba.ac.jp (Masaki Hada),
nisina-y@cc.okayama-u.ac.jp (Yuta Nishina)†These authors equally contributed.

S1

Supplementary Note 1 (Note S1)
We performed population analysis by expanding the electronic wave functions in theatomic-orbital basis setsS1,S2. Here, we describe a formulation of the population analysis
based on a plane-wave basis set with ultrasoft pseudopotentials. Note that a generalizationof the formulation to the projector-augmented-wave method is straightforward.
To project the self-consistent wave functions 𝜓𝑛 (𝒓) of the nth electronic stateobtained with the plane-wave basis into the subspace generated by the atomic basis {𝜙𝜇 },the projection operator 𝑃̂ is defined asS3–S5,−1 ⟨𝜙(S1)𝑃̂ = ∑|𝜙𝜇 ⟩ 𝑆𝜇𝜈
𝜈 |𝑠̂ ,𝜇,𝜈where(S2)𝑆𝜇𝜈 = ⟨𝜙𝜇 |𝑠̂ |𝜙𝜈 ⟩and𝑠̂ = 1 + ∑ 𝑞𝜇𝜈 |𝛽𝜇 ⟩⟨𝛽𝜈 |(S3)𝜇,𝜈

with 𝛽𝜇 and 𝑞𝜇𝜈 being the localized functions and the augmentation charges,
respectively, in the ultrasoft pseudopotential.S6
By operating 𝑃̂ on 𝜓𝑛 (𝒓), the projected wave functions 𝜒𝑛 (𝒓) are obtained as|𝜒𝑛 ⟩ = 𝑃̂|𝜓𝑛 ⟩ = ∑|𝜙𝜇 ⟩𝐶𝜇𝑛 .
(S4)
𝜇where−1 ⟨𝜙 |𝑠̂ |𝐶𝜇𝑛 = ∑ 𝑆𝜇𝜈
𝜓𝑛 ⟩.
𝜈

(S5)

𝜈Generally, 𝜒𝑛 (𝒓) are not orthogonalized; 𝑅𝑛𝑚 = ⟨𝜒𝑛 |𝑠̂ |𝜒𝑚 ⟩ ≠ 𝛿𝑛𝑚 ,To ensure charge conservation, the dual of 𝜒𝑛 (𝒓) is introduced as,−1|𝜒 𝑛 ⟩ = ∑|𝜒𝑚 ⟩𝑅𝑚𝑛= ∑|𝜙𝜇 ⟩𝐶𝜇𝑛𝑚(S6)𝜇where−1𝐶𝜇𝑛 = ∑ 𝐶𝜇𝑚 𝑅𝑚𝑛(S7)

𝑚so that⟨𝜒 𝑛 |𝑠̂ |𝜒𝑚 ⟩ = 𝛿𝑛𝑚 .

(S8)
(𝑛)

For the nth electronic state, the partial gross atomic population 𝑁𝜇associated(𝑛)with the μth atomic basis function and the partial bond-overlap population 𝑂𝜇𝜈
associated with the 𝜇th and νth atomic basis functions are defined as

S2

(𝑛)

𝑁𝜇= ∑ 𝐶 𝜈𝑛 𝑆𝜈𝜇 𝐶𝜇𝑛(S9)𝜈and1(𝑛)𝑂𝜇𝜈 = (𝐶𝜇𝑛 𝑆𝜇𝜈 𝐶𝜈𝑛 + 𝐶 𝜈𝑛 𝑆𝜈𝜇 𝐶𝜇𝑛 ),2(S10)respectively.
(𝑛)
By summing 𝑁𝜇 , the gross atomic population Ni for the ith atom is obtained as follows:(𝑛)𝑁𝑖 = ∑ ∑ 𝑓𝑛 𝑁𝜇 ,(S11)𝑛 𝜇∈𝑖where 𝑓𝑛 is the electronic occupation number of the nth electronic state.
The gross charge of the ith atom 𝑄𝑖 is given by
𝑄𝑖 = 𝑍𝑖 − 𝑁𝑖 ,where 𝑍𝑖 is the total number of valence electrons of a free neutral atom.

S3(S12)

Supplementary Figure 1 (Figure S1). Raman spectra of graphene oxide without (a) andafter (b) UV photoirradiation at an incident fluence of 4 mJ/cm2. In both spectra, D, G,2D, and D+G peaks are observed as indicated in the figure; however, the difference
between these spectra is hardly observable due to the incomplete recovery of the grapheneframework. The peak at a Raman shift of ~1000 cm–1 is derived from the Si substrate.

S4

Supplementary Figure 2 (Figure S2). Randomly oriented 25-graphene model structures
for the calculation of the electron diffraction patterns.

S5Supplementary Figure 3 (Figure S3). (a) The model GO layer based on an 8 × 8 graphene
supercell (128 carbon atoms) with epoxy-functional group oxygen. (b) The modelgraphene layer based on an 8 × 8 graphene supercell. The upper and lower layers of themodel GO bilayer are (a) and (b). One side length of the supercell is 19.712 Å.

S6Supplementary Figure 4 (Figure S4). (a–d) Highest occupied molecular orbitals(HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of the bilayer graphenemodels in detail. The HOMOs and LUMOs surrounded by black and red circles are thecorresponding orbitals of the graphene model shown in the main text.

S7

Supplementary Figure 5 (Figure S5). Potential energy as a function of dC-O for AB
stacking and AA stacking. Structural optimization is not performed in each dC-O. The
origin of the axis representing energy is taken to be the energy at distance = 1.5 Å of eachsystem. Since a large dC-O is unstable, energy increased with increasing dC-O for all thestacking patterns. However, the increasing ratio of AB stacking is smaller when dC-O
exceeds 2.4 Å. This result originates from the conflict between the destabilization of GOand stacking stabilization, which indicates that the removal of epoxy-oxygen enhancesAB stacking.

S8

Supplementary Figure 6 (Figure S6). The effects of hydroxyl-functional groups aroundthe epoxy-functional group on the basal plane of GO. (a) One of the potential structuresof the model GO bilayer with an epoxy-functional group with the presence of twohydroxyl-functional groups. (b) The potential energy with sliding the upper layer of themodel GO bilayer. The potential energy removing the epoxy-oxygen shows a steep local
minimum around the position of the AB stacking.

S9

Supplementary Figure 7 (Figure S7). (a) One of the potential structures of the model GOtrilayer with an epoxy-functional group. (b) The potential energy with sliding theuppermost layer of the model GO trilayer. The potential energy removing the epoxyoxygen shows a steep local minimum around the position of the AB stacking.

S10

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