`S1

Supplementary Information for

Engineering stepped edge surface structures of MoS2 sheet stacks stepped to

accelerate the hydrogen evolution reaction

Jue Hu,1 Bolong Huang,2 Chengxu Zhang,3,4 Zilong Wang,1 Yiming An,1 Dan Zhou,1

He Lin, 1 Michael K. H. Leung,3 Shihe Yang1*

1 Department of Chemistry, The Hong Kong University of Science and Technology,

Clear Water Bay, Kowloon, Hong Kong, China.

2 Department of Applied Biology and Chemical Technology, The Hong Kong

Polytechnic University, Hong Hum, Kowloon, Hong Kong, China.

3 Ability R&D Energy Research Centre, School of Energy and Environment, City

University of Hong Kong, Hong Kong, China.

4 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui, China.

*To whom correspondence should be addressed.E-mail: chsyang@ust.hk (S.Y.)

Electronic Supplementary Material (ESI) for Energy & Environmental Science.This journal is © The Royal Society of Chemistry 2017

`S2

Supplementary Notes

1. Theoretical approach................................................................................................S3

2. Theoretical calculation analyses of the se-MoS2, fe-MoS2 and single layer MoS2 (SL-

MoS2) systems .............................................................................................................S8

3. Synthetic strategy for and structure characterizations of the randomly grown MoS2

array (r-MoS2) ............................................................................................................S28

4. Morphology and chemical structure comparison of the r-MoS2, fe-MoS2 and se-MoS2

sheet arrays.................................................................................................................S29

5. Theoretical time-dependent density functional theory (TDDFT) calculated excitation

spectra analysis of se-MoS2 .......................................................................................S42

6. HER kinetics with different edge surface structures of MoS2 ...............................S44

7. Faradic efficiency of the se-MoS2 catalyst ............................................................S47

8. Electrochemical surface area analysis of different edge surface structures of MoS2

and commercial Pt/C catalysts ...................................................................................S48

9. Elucidation of turnover frequency (TOF) ..............................................................S51

10. HER stability of the stepped edge se-MoS2 catalyst............................................S53

11. Hubbard projection calculations of the se-MoS2 system .....................................S56

12. HOMO and LUMO orbitals for stepped MoS2 edge surface system (se-MoS2) .S57

13. DFT-calculated potential relaxation process to stably absorb H on the disulfide

ligands ........................................................................................................................S59

14. Volcano plot of experimentally measured exchange current density as a function of

the DFT-calculated free energy of hydrogen adsorption ...........................................S63

Tables .........................................................................................................................S64

References .................................................................................................................S66

`S3

Supplementary Figures and Discussion

1. Theoretical approach

1.1. Calculation details

In the realistic nanomaterials, the local structures of MoS2 layer systems could be very

different. The experimentally reported structures are dominantly based on the crystal

MoS2 layer. Thus, we modeled the stepped edge (se-) and flat edge (fe-) MoS2 models

using the hexagonal lattice with the same space group but with cut-off at the layer

boundary.

We used the CASTEP code to perform our DFT+U calculations.1 In this framework,

we use the rotationally invariant (Anisimov type) DFT+U functional2 and the Hubbard

U parameter self-consistently determined for the pseudized Mo 5d5 orbital by our new

linear response method.3 To stabilize the hole states that lie in the S 3p orbitals, we also

apply a self-consistently determined Hubbard U potential (method used above) to the S

3p states following the approach of Lany,4, 5 Morgan et al.,6 and Keating et al.7

Accordingly, both the d- and p-orbital electrons of the semi-core orbital based sulfides

should be considered when using DFT+U3.8-12 The geometry optimization used the

Broyden-Fletcher-Goldfarb-Shannon (BFGS) algorithm through all calculations.

The PBE functional was chosen for PBE+U calculations with a kinetic cutoff energy of

750 eV, with the valence electron states expressed in a plane-wave basis set. The

ensemble DFT (EDFT) method of Marzari et al.13 is used for convergence. Reciprocal

space integration was performed using the special k-point (¼, ¼, 0)14 with Gamma-

`S4

center-off, which was self-consistently selected for total energy minimization. With this

special k-point, the total energy is converged to less than 5.0x10-7 eV per atom. The

Hellmann-Feynman forces on the atom were converged to less than 0.001 eV/Å.

As to the pseudopotentials, we know that the norm-conserving pseudopotentials can

reflect all-electron behavior for outer shell valence electrons for |S-matrix|=1, unlike

the ultrasoft pseudopotentials.15, 16 Therefore, the non-linear core corrected norm-

conserving pseudopotential can provide a better response in DFT+U calculations,

especially for the calculations of defects.8 We note that our method actually provides

almost identical values of the U parameter for both norm-conserving and ultrasoft

pseudopotentials. This means that the obtained value has an intrinsic physical meaning

for the studied materials. Meanwhile, this will help us to reflect all-electron behavior

of the valence electrons especially for the subtle effect of the 5d electrons and outter 5s

electrons.

The Mo and S norm-conserving pseudopotentials are generated using the OPIUM code

in the Kleinman-Bylander projector form,17 and the non-linear partial core correction18

and a scalar relativistic averaging scheme19 are used to treat the spin-orbital coupling

effect. For this treatment, we actually similarly choose non-linear core correction

technique for correcting the valence-core charge density overlapping in such heavy

fermions elements, the detail discussion of such method has been presented in previous

work about the native point defect study of CeO2.8, 9 In particular, we treated the (4s,

4p, 5d, 5s) states as the valence states of the Mo atoms and the half-filled 5d5 for Mo+

is its ground state semicore electronic configuration. The RRKJ method is chosen for

`S5

the optimization of the pseudopotentials.20

Prior to ab-initio predictions of the Hubbard U on orbitals, the geometries and lattice

parameters of all MoS2 structural models were optimized using PBE functional

calculations. This procedure reduces the computational cost and ensures the reliability

of the Hubbard U value obtained by our self-consistent iterative calculations. We use

this procedure before the Hubbard U determination because DFT has been already

verified to be reliable for the structural optimization of compound solids even with 4f

or 5f orbitals,21 even with ultrasoft pseudopotentials. This may be due to the well-

developed pseudopotential technique8, 9, 21 and, more importantly, to the fact that the

electrons on semi-core orbitals have a small influence on the lattice parameters when

treated as valence electrons, as shown by the small difference of the DFT and DFT+U

calculated lattice parameter.3, 7-9, 22 Nevertheless, the U parameter must be determined

more carefully. 3, 7-9, 22

For the all of the electronic states calculations in MoS2 models, we use the self-

consistent determination for the U correction on the localized 5d orbitals to correct the

on-site Coulomb energy of the electron spurious self-energy. In previous work, we have

estalished a manner to determine the on-site electronic self-energy and related

wavefunction relaxation in the orbitals, so as to obtained an accurate orbital eivenvalues

for electronic structures.3, 10, 23 Such suggested parameter works on various types of

materials such as oxides,3, 8, 10-12 sulfides,23 oxysulfides,24 and fluorides.25 By that

method, the Hubbard U parameters on the half-filled shell of 4d5 orbitals of Mo is self-

consistently determined to be Ud=4.02 eV. To reduce the influence of the localized hole

`S6

states produced by 3p orbitals of S sites, the self-consistently determined Hubbard U

potentials is also applied on the S-3p orbitals (Up=2.89 eV), which have been reached

a consensus in many oxides materials.4-7 Thus, it is necessary to consider both self-

energy corrections on d- and p-orbitals for semi-core orbital based materials.3, 8, 9 The

detail process was referred to the previous work. With our self-consistently

determination process, the on-site Hubbard U parameters for 5d of Mo and different 3p

of S-sites are obtained respectively.

1.2. Hydrogen adsorption free energy

The hydrogen adsorption free energies were determined in the same way as HG

Nørskov et al.'s previous study, 26, 27 which is defined as

(S1)

where is the hydrogen adsorption energy, is the the difference in zero point HE ZPEE

energy, T is the temperature in Kelvin (300K in this study) and is the difference in S

entropy between H which is adsorbed and in the gas phase at 101325 Pa. A normal

mode analysis was used to determine the vibrational frequencies of the adsorbed

species, which were used to determine the zero point energy correction and the entropy.

The hydrogen adsorption energy is defined as

(S2)

where (MoS2+H) refers to hydrogen adsorbed on the MoS2 surface, (MoS2) refers to a

clean MoS2 surface, and (H2) refers to gas phase hydrogen molecule. The hydrogen

adsorption free energy was calculated at zero potential and pH = 0.HG

`S7

2. Theoretical calculation analyses of the se-MoS2, fe-MoS2 and single layer MoS2

(SL-MoS2) systems

Figure S1. PDOSs of p-orbitals of S bonding with H in both the se-MoS2 and fe-MoS2

systems.

To elucidate how the edge surface structure affects the electronic structure of the edge

states and how that in turn affects the HER kinetics at the edge sites, the atom-projected

density of states (PDOS) of atoms were calculated. There are four dominant peaks for

both se-MoS2 and fe-MoS2 systems observed from our PDOSs analysis, which focus

on p orbitals of S bonded with H at the disulfide ligand (S22-). To reduce the extended

tail states and van-hove singularities of flat energy surface in reciprocal space for our

`S8

structural models, we set the Gaussian smearing parameter as 0.4 eV in consistent with

the magnitude of general experimental x-ray photoemission spectrum instrumental

errors. We listed the positions of four dominant levels together with H (H=HOMO) and

L (L=LUMO) levels in the Table S1.

There are two peaks (level 2 and 3) and one shoulder state (level 1) in valence band.

Below the valence band maximum (VBM, where the EV=0 eV), we see that the two

distinguished peaks locate around the EV-5 eV (level 2) is the non-bonding p-orbital

levels of in-plain S sites (i.e. the long-pair 3p electronic states), acting as background

integrations of all in-plain S-3p projected orbital energy levels that collectively

influence the absorption site of disulfide ligand S22- at the edge. The positions of this

peak (level 2) has an energy difference of 0.10 eV showing that a nearly the same

contributions of the collective 3p-orbitals arise from in-plain S sites onto the disulfide

ligand S22- at the edge, except of miner difference on the electronic occupations due to

size of the plain of two different systems.

The peak around EV-7 eV (level 3) is found to be the localized p-orbitals around the

one of the S site in the disulfide ligand S22- at the edge. There shows an energetic

difference in this state as 0.11 eV from the PDOSs indicating a slight different p-

bonding state of S site binding with S (chemisorption) for both systems. Especially, the

energy interval between level 2 and 3 exhibits a scale of 0.21 eV which means the p-

bonding state get lowered of S binding with H from S22- at the top apex edge of se-

MoS2 compared to fe-MoS2 with respect to the in-plane S sites.

Another typical state below the VBM (EV=0 eV) is the shoulder state (level 1) where

`S9

locates the level of EV-2.90 eV for se-MoS2 and EV-2.51 eV for fe-MoS2, respectively.

These shoulder states are the non-bonding lone-pair p-orbitals localizing between two

S sites both with two-fold coordination. Our calculation shows the consistency with the

study by Zhuang et al., in which the S dimer (as reported in literature) at the edge

contributes the highest occupied state that close to the Fermi level (EF).28 The difference

is that our self-consistent orbital corrected p-orbital level for the edge state shows an

energy interval below the EF but still act the highest occupied p-bonding states in similar

trend to the calculation by Zhuang et al.28

We see from the PDOSs that this different arises from the different size of edge from

the layered se-MoS2 and fe-MoS2 systems, where denote the HOMO states (level H) of

both systems. The anti-bonding state of the p-orbitals (or 3p empty states) of S from the

disulfide ligand S22- at the top apex edge has an obvious shifting at the levels above the

EV=0 eV. There is one sharp peak for the fe-MoS2 system at the EV+1.90 eV, while two

peaks with a middle level at EV+2.42 eV for the se-MoS2 system. These two levels

denote their corresponding LUMO states (level L).

To reflect the general charge transfer difference of the absorbing site of H at the

disulfide ligand at the edge, we compared the energy differences of level splitting

between different states. Firstly, the bonding (level 3) and antibonding states (level 1)

of p-orbitals of S site binding with H has an interval of 9.33 eV and 8.70 eV for se-MoS2

and fe-MoS2 respectively (Table S1). An energetic contrast (0.63 eV) shows that

binding between H and S at the disulfide ligand from the top apex edge in se-MoS2

layer is stronger. Secondly, the splitting between nearby edge state to the p-antibonding

`S10

state also exhibits an interval of 5.32 eV and 4.41 eV for se-MoS2 and fe-MoS2

respectively. Such contrast of 0.91 eV is an analogue energy splitting between bonding

and antibonding states for the edge sites (two-fold coordinated S) at one single layer

from the entire se-MoS2 and fe-MoS2 systems. In this way, we can clearly observe

different contributions on the absorbing sites of H from the both normally two-fold

coordinated S sites and disulfide ligand at the edge in a single picture. The difference

between the levels shown in PDOSs shows a quantum chemical trend that why the ∆GH

lowered in se-MoS2 system. In comparison to the flat MoS2 edge surface, there is an

upshift of the anti-bonding state and meanwhile a downshift of the bonding state of the

p-states for the stepped MoS2 edge surface.

Therefore, in electronic properties, we discussed the p-orbital levels from Figure 1C

that it has larger HOMO-LUMO splitting for se-MoS2 than fe-MoS2, showing a more

charge transfer for a proton-electron exchange for H+ (proton) to bind with S22- in se-

MoS2 system. The p-bonding state of S site that binds with H after relaxation shows an

energy interval between the bonding level and p-bonding state of S sites at the in-plane

layer of MoS2, where the S binding with H is lower. This presents a contrast compared

to the states before the H absorption, and about 0.21 eV wider for se-MoS2 to combine

with H than the fe-MoS2 system. Another difference is the p-bonding state near the

HOMO level is contributed from the two-fold coordinated S sites from the edge of

layer. Such bonding state shifts to lower level in se-MoS2 with relative difference of

0.39 eV. Considering the anti-bonding state, we see the se-MoS2 has 0.52 eV higher

than the fe-MoS2 system, in physical trend that wider bonding and anti-bonding interval

`S11

has relative more stable in binding energy, in line with the above ∆GH difference by

total energy calculations. Therefore, a physical trend shows a relatively stronger

binding energy between H and S at the disulfide ligands (S22-) at the top apex edge of

se-MoS2, in consistent with the chemisorption free energy difference for se-MoS2 and

fe-MoS2 systems (i.e. ∆GH =0.02 eV and 0.05 eV, respectively).

In general view on the above, the electronic DOSs of the two systems follow the

regulation behavior of Cohen-Fritzsche-Ovshinsky model, in which overlapping band

tails states causing a Fermi level (EF) to lie near the mid-gap of host system.29 Such

similar electronic behaviors have been discussed in other solid systems from one of our

authors’ previous work.30-33 The extended tail states at the band edge arise because

some portion of short range disorder existing in the system such as the terminated

disulfide ligands (S22-) at the top apex edge. We hereby take the energy interval between

HOMO and LUMO states as 1.75 eV ~ 1.80 eV in consistent with the magnitude of

experimentally reported band gap (i.e. optical fundamental gap) for MoS2 layered

system. Our ab-initio calculations on the band structures of multi-layered, bi-layered,

and single-layered MoS2 crystal lattice show the band gaps are 1.42 eV, 1.50 eV, and

1.77 eV, respectively, based on our self-consistent orbital corrections. The band gap

value of single-layered MoS2 is consistent with the result reported by Nørskov et al that

is 1.64 eV.34

`S12

Figure S2. PDOSs of 1s orbitals of H in both the stepped edge and flat MoS2 edge

surfaces.

Figure S2 shows that the bonding state of the 1s of H in se-MoS2 system is at 6.8 eV

below the valence band maximum (VBM) while the weight-center of the anti-bonding

states is at 4.0 eV above the VBM. For the fe-MoS2, the bonding state of 1s in H is at

the 6.6 eV below the VBM while the anti-bonding state is staying at 2.6 eV above the

VBM. Meanwhile, the energy splitting between the bonding and anti-bonding states of

1s orbital of H in the two systems are 10.8 and 9.0 eV respectively. As discussed above,

the PDOS calculations demonstrated an upshift of the anti-bonding state and meanwhile

a downshift of the bonding state of 1s orbital of H in se-MoS2 system compared with

fe-MoS2 system. From the analysis of PDOSs, we see that the HOMO-LUMO splitting

`S13

has a difference and implies a contrast in charge transfer between H absorption site and

layered systems. This typically leads to a strengthened hydrogen adsorption on the

active stepped MoS2 edge sites, and thus a stronger binding energy for se-MoS2

compared with the fe-MoS2 system. The stronger H chemisorption energy for se-MoS2

compared with the fe-MoS2 system leads to a reduced H adsorption free energy (0.02

eV) on the stepped MoS2 edge surface (Figure 1C).

`S14

Figure S3. The ab-initio calculated electrostatic potential for se-MoS2 and fe-)(zV

MoS2 systems.

To illustrate the electron density distribution contrast in two systems, we further carried

out self-consistent macroscopic averaged planar electrostatic potential as proposed in

terms of following equation:

(S3)dxdyVzV )(1)( r

where is the xy-plane averaged potential and Ω is the area of the plane normal to )(zV

the z direction.

Due to different forms of layer stacking in se-MoS2 and fe-MoS2 systems, the

electrostatic potentials for electrons on the layer relative to the vacuum level shows an

energy contrast near the middle layer in our structural models. We see that the potential

level in se-MoS2 has a clear trend that it has a lower energy barrier for promoting the

electrons from the in-plane layer to the vacuum region near the edge. In another word,

`S15

the electrons can surmount shallower energy potential well from the in-plane to the

edge than the fe-MoS2, before the proton/electron exchange in HER reaction. Our

electrostatic potential plots also show that the se-MoS2 has less energy barrier in HER

reactions compared to fe-MoS2, in similar trend discussed by Zhuang et al.28

Another interesting finding is that the potential varies obviously only along the z-

direction which means the direction normal to the MoS2 layer. Our calculations shows

the energy along the direction horizontal to the layer has nearly flat energy surface as

small as 0.02 eV/Å, similar to the estimation by Bollinger et al.34 By using a novel

Fermi softness model, Zhuang et al has confirmed the high catalytic activity of the HER

reactions occurring at the low-dimensional MoS2 with S dimers terminated edges.28

This high active area has been previous highlighted by Bollinger et al. with STM

experiments and DFT calculations.34

`S16

Figure S4. Theoretical calculated Dielectric functions (A) 1 and (B) 2 spectra of

stepped edge (se-MoS2) and flat edge surface-terminated MoS2 (fe-MoS2) systems. The

insert figures are the corresponding structure and p orbital configurations.

Figure S4 compares the theoretical calculated 1 and 2 spectra between se-MoS2 and

fe-MoS2 systems. The main 2 peak in the fe-MoS2 is much stronger and lies at a lower

energy than in the se-MoS2. By Kramers-Kronig analysis, this translates into a lower

1(0) for the amorphous phase. The aforementioned electron configuration has been

originally coined as resonant bonding as early as discussed by Pauling. The pronounced

p-π electron delocalization, which characterizes resonant bonding, leads to a

significantly increased electronic sharing ability. The phenomenon of large contrast in

dielectric functions is one of the fingerprints of resonant bonding in the edge of

disulfide ligands terminated fe-MoS2 system.

`S17

Figure S5. Schematic diagram demonstrating the origin of resonant bond and its

weakened or absence cases. The p-orbitals of S sites arise from disulfide (S22-) ligands

in MoS2 system in 1-D (side-view). In the stepped se-MoS2 system, the p-orbital

alignment is weakened (A), this leads to a localization in way of further randomly

distributed directions of p-lobes (B). (C) In the fe-MoS2 system, the p-orbitals of

different S sites align in a line and turn to be delocalized (shown in dashed line) to form

a resonant bond illustrated within a green shaded area.

The S atom originally has a filled non-bonding orbital in one of 3p-orbital components,

containing paired electrons. To first simplified the model, we approximate it forms an

independent linear chain of p-states along the x direction. In overall, the p-orbitals in

`S18

se-MoS2 system are non-degenerated with discrete levels due to the weakened

possibilities of real-space overlapping in types of both ppσ and ppπ, shown in Figure

S5A. Then this will transform into a more localized form of p-orbital alignment, which

is randomly distributed at the edge as shown in Figure S5B, contributing a large reactive

area of HER through charge exchange between disulfide (S22-) ligand with H+. Whereas

in fe-MoS2 system, the p-orbitals with respect to energy will line-up and transform into

a degenerated band near the Fermi level EF resulting in a near zero band gap (e.g. 0.058

eV from our calculations based on self-energy corrected method). The bonding scenario

within such system in which a single degenerated p-band forms a two-centered bond to

the another disulfide (S22-) ligand from adjacent layer (more than allowed by the 8-N

rule) was called resonant bonding in earlier work of Pauling. This bonding is

schematically shown in Figure S5C.

This model is indeed established beyond conventional covalent bonding based 8-N rule

established in semiconductor materials. Huang and Robertson suggested that the low-

frequency electronic transition contrast arises from a loss of resonant bonding and a

loss of medium-range order in the misaligned p-π orbitals, which causes a substantial

reduction in the optical matrix element.30 In the MoS2 system, only the p-electrons can

facilitate such partially directional and covalent interaction behavior between adjacent

layers, as d-orbitals of Mo sites are strongly localized with semi-core character. It shows

that the bonding in the fe-MoS2 system has an unusual medium ranged ordered (MRO)

and long ranged ordered (LRO) p-π resonance with a large component given by the

aligned disulfide (S22-) ligands through interlayers, while weakened or absence in se-

`S19

MoS2 system due to the misaligned p-π orbitals in short ranged orders (SRO). The

weakened MRO and LRO in se-MoS2 system will increase the degree of p-electrons

localization of disulfide (S22-) ligands at the edge for better reactivity of H+ contact and

charge exchange.

We have shown that it is possible to synthesize multi-stacking layered MoS2 systems

with two different edge surface structures (stepped and flat edges). The present study

provides a new insight that we modulate the edge active sites to control the performance

of HER. This approach presented here should be applicable to more generalized

transition metal dichalcogenides catalyst, by engineering their surface structures.

The SL-MoS2 system

DFT calculations on the Gibbs free energy for H evolutions with ¼ coverage model of

sing-layer MoS2 with disulfide ligand (S22-) were carried out according to the equation

from Nøskov et al.35 The free energy without orbital corrections of Mo and S sites are

0.217091 eV and the entropy and vibrational contributions have already been taken into

account estimated by Nøskov et al (~0.29 eV).35 This shows an evidently higher energy

barrier for H to be absorbed on the single layer with S22- ligands, indicating an

underperformance of HER due to higher energy barrier.

Further with orbital corrections on Mo and S sites, especially for on-site 3p orbitals of

S22-, the interactions of S-H has been updated with more accurate calculation. The free

energy is shown to be -0.072909 eV. In the absolute magnitude, this free energy is still

larger than the ones calculated from se-MoS2 and fe-MoS2 systems. In addition, the

negative value shows its trend of overbinding capability for S22- with absorbed H in SL-

`S20

MoS2 system.

The free energy ∆GH~-0.07 eV for SL-MoS2 is the important reference here used for

comparison with our as-synthesized se- and fe- MoS2 system. Due to the expected

strong charge localization for the SL-MoS2, such lone pair electrons of S22- at the top

apex region turn to be more localized, and its capability of binding the H is showing

stronger. Thus, the too strong S-H bonding leads to a weakening of the HER for

producing the nearly free mobile H after the charge exchange between H+ and S22-.

The contrast among the free energy of H binding on the disulfide ligand of MoS2 system

is now located on the relationship between the free energy of H-binding and charge

localization. Originally, we may deduce that the single layer MoS2 similar with

disulfide ligand S22- would have better performance in HER due to its stronger

localization of the charge near the edge. But the contrast in free energy contrast seems

to be deviated from the deduction on charge localization of SL-MoS2 system.

Therefore, we follow-up this thinking and analyze this line with details, which is helpful

to find out where the essential reason is and induced this deviation.

Although, this single layer system is slightly different from the Mo-edge single layer

MoS2 with 50%S observed by Nøskov et al, the physical trend will be still similar for

our consideration. Following this stream line, we need to specify this deduction with

more details to assist our investigation.

We hereby investigated the charge transfer induced dipole moment of SL-MoS2, se-

MoS2, and fe-MoS2 systems with DFT calculation, following the method introduced

from Clark et al in Europhys. Lett. 44, 578 (1998).36 This calculation method has been

`S21

implemented within the code we are using.

The calculated the dipole moments of three systems have been shown in the following

table in terms of the magnitude of dipole and directions (kx, ky, kz). The total electrons

of the three systems used in our modeling for computation of dipole moment have been

also presented in Table S2.

From this Table S2, we see that the total dipole moment actually parallels to the surface

directions of MoS2 layer, and the component vertical to the surface is almost negligible,

as shown in the magnitude of kz, smaller than 0.01.

Note that, the absolute value of the dipole magnitude is less meaningful. However, the

relative ratio to each other among these three systems is more important. By this

calculation result, it is helpful to our further simplifications of the analysis within these

three systems, which means, the charge transfer may only occur from the in-plane to

the layer edge within the region of layer surface among SL-, se- and fe- MoS2.

We qualitatively give the equivalent charge crossover separation distance L has the

following relationship:

or, (S4)

ii

iii

q

lqL

v

LqmagnitudedipoleTotali

i

Using this L as an index, we can classify which one has the highest degree of charge

localization self-consistently with consideration of structural configuration globally.

Due to the long-ranged resonant π-orbital coupling, the L for fe-MoS2 is the largest

(~2.02, i.e. 0.42 Å), and the one for SL has similar magnitude to fe-MoS2, about 1.69,

or 0.35 Å. However, they are 2.83 and 2.36 times higher than the one calculated in se-

`S22

MoS2 (~0.15 Å), respectively. Therefore, we see that the SL-MoS2 has the smallest

magnitude of dipole but with relative longer charge transfer length, L. The fe-MoS2 has

the largest dipole which is nearly 3.6 times higher than the SL-MoS2 and 3.4 times

larger than the se-MoS2 respectively. However, the se-MoS2 has the shortest equivalent

crossover distance as deduced from the Table S2 and Eq. S4. Combined with the real

part dielectric function in zero point energy, the static dielectric constant ε1(0) smallest

oscillator strength. Thus, the se-MoS2 is found to be showing a relative stronger charge

localization character than the other two systems, SL- and fe- MoS2.

Accordingly, we would like to update our theoretical model here to analyze the HER

performance that, miss-align π-orbital resonance (small dielectric constant) plus the

stronger charge localization equipping with smaller charge transfer equivalent length L

in crafted MoS2 nanostructure system may have a better HER performance. Moreover,

from some extent, the equivalent length L also denotes the interaction range showing

that the charge localization may not localized on the top apex point in SL-MoS2. This

means the localization is surrounding the edge instead of locating at the S22-.

The non-radiative energy transfer distance by two-center resonance

Currently, as investigated from the literature, there are still not any analytic theoretical

solutions on the bonding range of π-orbital resonance. However, there are two

approximated models available to simulate such phenomenon. One is from the

discussion on the previous theoretical work on the other solid system and using the

static electronics model and using the oscillator strength imbedded within the dielectric

`S23

functions,37, 38 the other available model is the Förster resonant energy transfer (FRET)

model,39 in this way, the energy transfer efficiency contributed by the dipole-dipole

interactions of on-site valence orbitals is inversely proportional to the sixth power of

the distance between donor and acceptor sites or two dipole sites, (~R-6), indicating this

energy transfer model is extremely sensitive to small deviations of distance between

the two dipoles.40, 41

(1) For FRET energy transfer model

We derive here using a quasi-classical model:

Now we continue to estimate the non-radiative energy transfer rate (probability)

contributed by charge transfer induced dipoles.

, (S5)2gs

hexedipole

exh

gse

FRETdipole HP

where the notations of e and h denote the transferred electrons and holes formed by the

system, and the notations of gs and ex denotes the ground and excited states

respectively. If we consider different amount of charges of two centers, and to simplify

our idea, we only consider the energy transfer is between the two layer only (inter-

layer). Thus, choose a quasi-classical model to describe the interacting hamiltonian by

dipole transition, which is approximated by:

, and (S6) 3int Rk

VH geomADlayererAdipole

rr3int RrV D

layerer

where the and denotes the dipole moment and the related electrical field r layererV int

(E-field) given by gradient of the potentials Vinter-layer of the opposite dipoles. In a

geometrical shape approximation, the factor kgeom is the geometrical factor.

`S24

Therefore, the probability of energy transfer by FRET is showing between the layers

are inversely proportional to the sixth power of inter-layer distance R.

We use this model to assist our analysis that, the se-MoS2 effectively lower down or

even blockades the energy transfer through the layer with miss-aligned π-orbital

resonance through a crafted structural configuration. Therefore, the energy transfer is

constrained within the regions of the layers. Meanwhile, according to the equivalent L

we are using to index the charge transfer capability in the layer, the localization shows

a stronger feature in se-MoS2 compared to the SL-MoS2. Therefore, the se-MoS2 is

found to be a superior system in HER to the other two systems.

(2) For the dielectric function related bonding oscillator strength

In the paper, we have already introduced the dielectric function related to the electronic

properties among two different systems (i.e. se- and fe- MoS2). Here we derive the

relationship between the oscillator strength (imbedded in dielectric function) and FRET

energy transfer model.

The dielectric function is shown as:

(S7)21 i

The imaginary part , is further derived as:2

(S8)

)(')(

''

2

)(')(

'

2

'2 2emptykfullk

kkkk

emptykfullk

kkkk fm

eme

h

hh

h

The is the joint density of states that multiplicative integral of both h kk '

valence and conduction band density of states, describe the electronic inter-level

transition probability. By Kronig-Kramer relationship, the real part of dielectric

`S25

function, is described as:2

(S9)

)(')(

2'

'22

)(')(

3'

2'

2

24

12

emptykfullk kk

kk

emptykfullk kk

kk fm

em

e

hh

From the work done by Harrison and Pantelides42-45, the oscillator strength for

electronic inter-level transition is yielded from the dielectric function, show as follow:

(S10) kkkkkk mf '2

'2

' /2h

In the Eq. (S10), it is the dimensionless oscillator strength correlate the real and

imaginary part of dielectric functions, and used for describing the electronic transitions

probability and optical properties. Recall the Eq. (S5) and (S6), we found if the dipole

interaction is involved in the inter-layer electronic transition and energy transfer, the

magnitude of the oscillator strength in Eq. (S10) is shown to be .6 R

Therefore, from the preliminary analytic analysis above, we have seen that both

transition oscillator strength of bonding and energy transfer described by FRET, they

indeed share the nearly the same dipole interacting Hamiltonian. This Hamiltonian is

actually diverse proportional to the six power of the inter-layer distance R, and denoting

a high sensitivity to the distance changes or layer edge directions varied.

`S26

3. Synthetic strategy for and structure characterizations of the randomly grown

MoS2 array (r-MoS2)

Figure S6. (A) Synthesis procedure of randomly grown MoS2 array (r-MoS2) via a

conventional hydrothermal method. (B) High- and (inset) low-magnification FESEM

images of r-MoS2. (C) High- and (inset) low-magnification TEM images and (inset)

the corresponding selected-area electron diffraction (SAED) patterns of r-MoS2.

`S27

4. Morphology and chemical structure comparison of the r-MoS2, fe-MoS2 and se-

MoS2 sheet arrays

Figure S7. FESEM images for r-MoS2 (A and B), fe-MoS2 (C and D) and se-MoS2

sheet array (E and F). Scale bar in all of the images is 100 nm.

`S28

Figure S8. FESEM image and the corresponding elemental analysis of the r-MoS2: (A)

FESEM image; (B) Energy-dispersive spectroscopy (EDS) spectrum; (C) Mo profile;

and (D) S profile.

The elemental analysis as shown in Figure S8-10 reveals that the ratios of S to Mo for

r-MoS2, fe-MoS2 and se-MoS2 catalysts are all slightly larger than 2, confirming the

successful synthesis of MoS2 on carbon fiber paper surface for all of the MoS2 samples.

`S29

Figure S9. FESEM image and the corresponding elemental analysis of the fe-MoS2:

(A) FESEM image; (B) Energy-dispersive spectroscopy (EDS) spectrum; (C) Mo

profile; and (D) S profile.

`S30

Figure S10. FESEM image and the corresponding elemental analysis of the se-MoS2:

(A) FESEM image; (B) Energy-dispersive spectroscopy (EDS) spectrum; (C) Mo

profile; and (D) S profile.

`S31

Figure S11. FESEM images for microwave hydrothermal-synthesized MoS2 nanosheet

array on (A, B) Ti plate and (C, D) carbon cloth.

`S32

Figure S12. TEM images for r-MoS2 (A and B), fe-MoS2 (C and D) and se-MoS2 sheet

array (E and F).

The morphology and structural information of the as-obtained MoS2 catalysts were

`S33

further revealed by transmission electron microscopy (TEM) and energy-dispersive X-

ray spectroscopy (EDS) mapping. TEM images (Figure 2C and 3C, and Figure S6C and

S12) confirm the layer-like structure of all the r-MoS2, fe-MoS2 and se-MoS2 samples.

Besides the flower-like morphology, the circle-like nanotube formed by folding the

layers and flat-like morphology formed by piling up the layers were also observed from

the TEM images of the r-MoS2 sample (Figure S12). As shown in Figure 2D, the se-

MoS2 sample exhibits only sheets structure with the thickness of about 10 nm, which is

consistent with the thickness determined from the edges in the FESEM image (Figure

2B), confirming a vertically aligned S-Mo-S layer structure on the carbon fiber paper

substrate. In the sulfurization step of MoS2 growth, the MoS2 layer orientation is

seriously affected by the sulfurization conditions. The microwave hydrothermal

technique can provide increased reaction kinetics, rapid heating, and hence enhanced

reaction rates. Therefore, MoS2 layers which are perpendicular to the substrate were

generated for the microwave hydrothermal synthesized fe-MoS2 and se-MoS2 samples

due to the much faster sulfur diffusion along the layers through van der Waals gaps than

across the layers. It is worth noting that the crystal fringes along the edge are stepped

for the se-MoS2 sample as indexed by arrows in Figure 2 and Figure S13, while the

edges for fe-MoS2 are flat as indexed by yellow dash line in Figure 3C and Figure S12.

The uniform distribution of the Mo and S elements in MoS2 sheets demonstrated a

uniform composition of MoS2 in all of the r-MoS2, fe-MoS2 and se-MoS2 samples

(Figure S13-15).

`S34

Figure S13. Energy-dispersive spectroscopy (EDS) mapping profiles of r-MoS2. (A)

TEM image; (B) Mo profile; (C) S profile. The mapping profiles show a uniform

dispersion of Mo and S elements in r-MoS2 sample.

Figure S14. Energy-dispersive spectroscopy (EDS) mapping profiles of fe-MoS2. (A)

TEM image; (B) Mo profile; (C) S profile. The mapping profiles show a uniform

dispersion of Mo and S elements in fe-MoS2 sample.

`S35

Figure S15. Energy-dispersive spectroscopy (EDS) mapping profiles of se-MoS2. (A)

TEM image; (B) Mo profile; (C) S profile. The mapping profiles show a uniform

dispersion of Mo and S elements in se-MoS2 sample.

`S36

Figure S16. Merged selected-area electron diffraction (SAED) patterns of r-MoS2 and

se-MoS2.

The insets in Figure 2C, 3C and S6C show the corresponding selected-area electron

diffraction (SAED) patterns. The SAED patterns, as compared with the merged SAED

images in Figure S16, clarify the same polycrystalline structure for all of the r-MoS2,

fe-MoS2 and se-MoS2 catalysts, and shows strong ring patterns of (100), (103), (110)

and (200) planes of MoS2 crystal. All the diffraction peaks of r-MoS2, fe-MoS2 and se-

MoS2 catalysts were indexed to well-crystallized MoS2 (JCPDS: 75-1539,

JCPDS=Joint Committee on Powder Diffraction Standards), indicating the successful

synthesis of the MoS2 crystalline for all the MoS2 samples.

Figure S17. (A) High- and (inset) low-magnification FESEM images, (B) FESEM

images and the corresponding energy-dispersive spectroscopy (EDS) spectrum of (C)

O profile, (D) Mo profile; and (E) S profile of microwave hydrothermal-synthesized

MoS2 at the reaction time of 40 min.

`S37

Figure S18. (A-C) FESEM images, (D-F) TEM images and (G-I) schematic

illustrations of the microwave hydrothermal-synthesized MoS2 nanosheet arrays

obtained at different reaction times: 50 min (A, D, G), 90min (B, E, H) and 120 min

(C, F, I).

`S38

Figure S19. (A) AFM topographical height image and (B) the corresponding height

profile of dispersed se-MoS2; (C) AFM height image and (D) the corresponding height

profile of dispersed fe-MoS2.

The stepped edge surface-terminated structure of se-MoS2 was further confirmed by

atomic force microscopic (AFM) height images as shown in Figure 2 and Figure S19.

The height profile of the flat edge surface-terminated MoS2 (fe-MoS2) shows a smooth

decrease at the MoS2 edges. However, the height profiles of se-MoS2 exhibit several

height plats at the edges and the distance between two of the plats is about 0.65 nm

which is in good agreement with the thickness of one MoS2 layer. Thus, AFM height

`S39

images further confirmed the stepped edge surface-terminated structure of se-MoS2.

Figure S20. Absorption infrared spectra of the fe-MoS2 and se-MoS2 catalysts.

The infrared spectra of fe-MoS2 and se-MoS2 show the high intensity characteristic

bands of edge-terminated disulfide ligands at 508 and 543 cm−1 due to the ν(S―S)

vibrations.

`S40

5. Theoretical time-dependent density functional theory (TDDFT) calculated

excitation spectra analysis of se-MoS2

Figure S21. (A) The experimental UV-Vis-NIR spectra and calculated reflectivity by

TDDFT method from the range of 200-1400 nm for se-MoS2. (B) Comparison of the

experimental measured and TDDFT calculated excitation spectra within the range of

200-600 nm for se-MoS2 and fe-MoS2.

We further benchmark the optical levels with various characterization techniques

including the theoretical time-dependent density functional theory (TDDFT) method.

Experimentally, we use the reflective method to measure the optical absorption. As

shown in Figure S21A, the comparisons of the TDDFT calculated reflectivity based on

our structural model of stepped edge surface MoS2 system. It can be seen that the optical

peaks and valleys are matched very well in the range of 400 nm to 1300 nm, especially

in the near-infra-red range (NIR) of 1000-1300 nm. Such twin peaks character may be

due to the disulfide ligand (S22-) at the apex edge of the MoS2 layer. For the excitation

absorption spectra, as shown in Figure S21B, both experiment and calculation show

`S41

that the drop in absorption intensity is at about 430 nm and are in principle consistent

with each other. The broad peak shown by our calculations at the 330 nm and 530 nm

are also agreed well with experimental spectra. There is a slight difference at the 250

nm that the contrast at the valley of the absorption intensity is not obvious. This may

be due to the systematic error for high energy excitation in our TDDFT calculation.

Moreover, our calculation trend shows a good consistency that the se-MoS2 is always

superior to the fe-MoS2 in optical absorption of UV-Vis-NIR.

Therefore, as strongly confirmed by the morphology, AFM height and chemical

structure analyses, stepped (se-MoS2) and flat (fe-MoS2) edge surface-terminated MoS2

nanosheet arrays were well designed and synthesized. Figure 2A shows the schematic

illustration of the morphology for the se-MoS2 catalyst deduced from the morphology

and chemical structure analyses. The as-showed stepped edge surface-terminated

structure which can adjust the electronic structure of the MoS2 edges for H adsorption

and the vertically aligned S-Mo-S layers which ensures an ultrafast electron transport

from the CFP substrate to MoS2 edges within one S-M-S may be benefit for improving

the HER kinetics.

`S42

6. HER kinetics with different edge surface structures of MoS2

The electrocatalytic activities of the as-obtained MoS2 for HER were investigated in

0.5 M H2SO4 solution in a standard three-electrode electrochemical cell. The

polarization curves after iR correction in Figure 4A were obtained at a scan rate of 5

mV/s. The HER activity is improved in terms of onset potential when vertically aligned

MoS2 sheets were directly grown on the CFP which ensure a maximum exposure of

MoS2 active edge sites on the catalyst surface. The random growth r-MoS2 catalyst

exhibits a lowest HER catalytic activity, with an overpotential of 217 mV at the current

density of 10 mA/cm2. fe-MoS2 gives out a low overpotential of 142 mV at 10 mA/cm2.

The HER activity of the se-MoS2 is further boosted with the overpotential as low as

104 mV to reach the current density of 10 mA/cm2. Tafel slop and exchange current

density (j0), the most inherent indicators of the HER activity, were carefully estimated

by linear fitting of the polarization curves according to the Butler-Volmer equation. As

shown in Figure 4B, the Tafel plots recorded on r-MoS2, fe-MoS2, se-MoS2 and

commercial Pt/C catalysts exhibited classical Tafel behavior. The high exchange

current density of the se-MoS2 exhibits one of the best HER performance among most

of the MoS2-based materials reported to date (Table S2). After fitting the linear part at

large overpotential of the Tafel plot, the Tafel slopes of r-MoS2, fe-MoS2, se-MoS2 and

commercial Pt/C catalysts were determined to be 121, 69, 59 and 34 mV/dec,

respectively. The Tafel slope of the commercial Pt/C catalyst (34 mV/dec) agrees well

with the values in the references.27, 46

`S43

Figure S22. (A) Nyquist plots and fits of the impedance response of the vertically

aligned se-MoS2 sheet array catalyst under the overpotential from 100 mV to 200 mV

in 10 mV increment and the corresponding equivalent circuit that fits the

electrochemical impedance spectroscopy (EIS) data. (B) Nyquist plots of the r-MoS2,

fe-MoS2 and se-MoS2 catalysts at the overpotential of 200 mV.

EIS testing was conducted at specific overpotentials over a frequency range from 100

kHz to 5 mHz. Figure 4C and S22 show the Nyquist plots and the corresponding fitted

curves for the HER of se-MoS2 sample under the overpotential from 100 mV to 200

mV in 10 mV increment. A simple equivalent circuit that describes the catalytic system

is shown in Figure S22, where Rs is attributed to the uncompensated solution resistance,

constant-phase element (CPE) refers to the double-layer capacitance under HER

conditions, and Rct represents the charge transfer resistance in HER. The fit of the EIS

data can yield a charge transfer resistance. The charge-transfer Tafel slope (Figure 4C)

which can be derived from the linear fit of the plot of log Rct versus overpotential, is 56

`S44

mV/dec of the se-MoS2 catalyst. This value is very close to the Tafel slope obtain from

the voltammetric data (59 mV/dce) reflecting not only a charge transfer rate

determining step but also a quick electron transfer feature of the se-MoS2 catalyst in

HER. The Nyquist plots of r-MoS2, fe-MoS2 and se-MoS2 catalysts at the overpotential

of 200 mV show that the se-MoS2 catalyst has the smallest charge transfer resistance

(Rct) of only 2.7 Ω, indicating the ultrafast Faradaic process and thus a superior HER

kinetics. This can be attributed to the special structure of the vertically aligned MoS2

nanosheet array. The vertically aligned S-Mo-S layers ensure an ultrafast electron

transport from the CFP substrate to MoS2 edges within one S-Mo-S layer and

significantly decrease the electron transfer resistance in the hydrogen evolution

process.47, 48 In addition, the stepped edge surface-terminated structure that exposes an

abundance of active edge sites can ensure a complete interaction of active sites with

reactants and a better overall charge transfer conductivity. T

`S45

7. Faradic efficiency of the se-MoS2 catalyst

Figure S23. The amount of hydrogen theoretically calculated and experimentally

measured versus time for se-MoS2 catalyst. The Faradic efficiency for se-MoS2 was

calculated by comparing the amount of experimentally quantified hydrogen with

theoretical hydrogen production. The practical hydrogen production rate in Figure S23

agreed well with the theoretical value, revealing that an approximately 100% of Faradic

efficiency was attained.

`S46

8. Electrochemical surface area analysis of different edge surface structures of

MoS2 and commercial Pt/C catalysts

Figure S24. Cyclic voltammograms (CV) curves in the region of 0.1~0.2 V vs. RHE at

various scan rates (10~50 mV/s) for fe-MoS2 (A), se-MoS2 (B) and r-MoS2 (C)

catalysts. (D) Corresponding charging current density differences plotted against scan

rate for r-MoS2, fe-MoS2 and se-MoS2 catalysts, where Cdl is equivalent to the slope of

the fitted line.

Cdl is derived from the cyclic voltammetry curves with different scan rate in the

potential range where no faradic current was observed. The Cdl is improved by more

`S47

than 50 times when the MoS2 is directly grown on the carbon fiber paper (r-MoS2, 47.7

mF/cm2) comparing with the commercial MoS2 brushed on the carbon fiber paper

substrate (commercial MoS2, 0.9 mF/cm2 shown in Figure S25) due to the more

exposed edges on the MoS2 surface. Furthermore, it can be clearly found that the Cdl of

the fe-MoS2 (92.8 mF/cm2) and se-MoS2 (113.3 mF/cm2) is about twice higher than

that of the r-MoS2 catalyst (47.7 mF/cm2) indicating a much higher electrochemical

surface area of the vertically aligned MoS2 sheet array. The slightly larger Cdl of se-

MoS2 catalyst than fe-MoS2 may be due to the stepped edge surface of se-MoS2.

`S48

Figure S25. High- (A) and low-magnification (B) FESEM images of commercial MoS2

electrode coated on carbon fiber paper substrate. (C) Cyclic voltammograms (CV)

curves in the region of 0.1~0.2 V vs. RHE at various scan rates (10~50 mV/s) for

commercial MoS2 catalyst. (D) Corresponding charging current density differences

plotted against scan rate for commercial MoS2 catalyst, where Cdl is equivalent to the

slope of the fitted line.

`S49

9. Elucidation of turnover frequency (TOF)

The TOF is calculated using the current density (j) and the active site density (N)

according to the following equation:

(S11)2Total number of H molecules per secondTotal number of active sites per unit area 2

jTOFqN

where q is the elementary charge as 1.6×10-19, and 2 accounts for 2 electrons transfer

per one H2 molecule generation. The active sites per unit area are obtained from the

electrochemical surface area (ECSA). The ECSA of a catalyst can be calculated from

the double layer capacitance (Cdl) according equation S12:

(S12)dl

s

CECSAC

where Cs is the capacitance of the sample of an atomically smooth planar surface of

material per unit area under identical electrolyte conditions. Here we use general

specific capacitance of Cs=0.04 mF/cm2 in 0.5M H2SO4 based on typical reported

values.49 From reference50 we know that the density of HER active sites in Mo atoms

in MoS2 nanoparticles is 1.28×1014 Mo atoms per cm2. So the active Mo sites density

(NMo) is calculated according to equation S13:

(S13)Mo 19 14Mo dl2 2 1.6 10 1.28 10 ( / 0.04)

j jTOFqN C

`S50

Figure S26. Plot that displays the turnover frequency (TOF) per Mo atom of r-MoS2,

fe-MoS2 and se-MoS2 catalysts.

To further understand the intrinsic HER kinetics of the vertically aligned MoS2 sheet

array, we investigated the turnover frequency (TOF) of the MoS2 catalysts which

describes as the average activity of each HER active site, as shown in Figure S26 in

Supplementary Information using the method mentioned in references for a fair

comparison to the literatures.50, 51 The calculated TOF (Figure S26) of se-MoS2 is 1.5

H2 molecules per second at overpotential of 200 mV, which is, to the best of our

knowledge, higher than most of MoS2-based HER catalyst reported to date.

`S51

10. HER stability of the stepped edge se-MoS2 catalyst

The long-term stability of se-MoS2 catalyst was assayed by mean of

chronopotentiometry measurement (η ~ t). The process was performed at a constant

current density of -10 mA/cm2. By comparison, the stability of the commercial Pt/C

catalyst was also measured in the same condition, which underwent serious HER decay

after 18 h chronopotentiometry measurement (Figure S27).

Figure S27. Chronopotentiometry responses (η ~ t) recorded from the (A) se-MoS2

sheet array and commercial Pt/C catalysts at a constant current density of -10 mA/cm2,

and (B) se-MoS2 sheet array at a constant current density of -20 mA/cm2. (C)

Polarization curves recorded from the se-MoS2 sheet array at a scan rate of 5 mV/s

before and after the chronopotentiometry test. Inset: SEM images of the se-MoS2 sheet

`S52

array before and after chronopotentiometry test for 26 h. (D) Polarization curves

recorded from the commercial Pt/C catalyst at a scan rate of 5 mV/s before and after

the chronopotentiometry test.

Figure S28. (A) The XRD patterns, (B) Raman spectra, XPS (C) Mo 3d and (D) S 2p

spectra for the se-MoS2 catalyst before and after the chronopotentiometry test at 10

mA/cm2 for 26 hours. The standard pattern of the pristine 2H MoS2 (JCPDS 75-1539)

was also shown in A.

`S53

Figure S29. FESEM images of the se-MoS2 sheet array after chronopotentiometry test

for 26 h (A and B). (C) CV curves in the region of 0.1~0.2 V vs. RHE at various scan

rates (10~50 mV/s) for se-MoS2 after the chronopotentiometry test for 26 hours, and

the corresponding (D) charging current density differences plotted against scan rate of

se-MoS2. Cdl is equivalent to the slope of the fitted line.

`S54

11. Hubbard projection calculations of the se-MoS2 system

Figure S30. Hubbard projections of 5d and 3p orbitals of Mo (A) and S sites (B) in se-

MoS2 system.

The Hubbard projection calculations have been carried on the 5d orbitals of Mo sites

and 3p orbitals of S sites. We found the 5d orbitals from the valence states of Mo sites

are actually the open-shell which can attract the extrinsic electrons to reach even lower

energy minimum through charge density overlapping, while for the 3p orbitals of S

sites, a closed shell with self-energy counteracted in as-projected shell. This indicates

the strong Coulomb repulsive potentials in the p orbitals will evidently pushed the 3p

electrons out from the valence shell of S sites to even deeper range away from S2- ion

nuclei and provided an electron-rich flat for an easy charge-exchange (gaining an

electrons) of the proton and easily to be a freely mobile H atom, so as to free a H to the

ambient environment. Therefore, in this se-MoS2 system, the Mo sites are having less

catalytic reactivity than the S sites in hydrogen evolution reactions.

`S55

12. HOMO and LUMO orbitals for stepped MoS2 edge surface system (se-MoS2)

Figure S31. Top view (A), front view (B) and side view (C) of HOMO and LUMO

orbitals for stepped MoS2 edge surface system (se-MoS2).

We further noticed that the orbitals of HOMO states are mainly localized at the S sites

at the edge including the disulfide ligand S22-, which means the localized electrons are

mainly at the edge of se-MoS2 for charge exchange of proton. The in-plane S sites of

se-MoS2 has nearly no HOMO state orbital distribution showing a deep state far below

the VBM, in agreement with our PDOSs analysis. A higher electronic reactivity for

HER is proposed to occur at the both around the edge especially the disulfide ligand

`S56

S22-, as the HOMO state as the local charge density is covering the edge following a

gradient-like distribution among the layers of se-MoS2. The majority of LUMO states

are localized at the Mo sites at the both side edge and top apex edge, another portion of

LUMO states are localized at two-fold coordinated S sites across the layers of the se-

MoS2 system. We believe that the energetic favorable for selecting reactions of protons

is at the top apex edge of the system. This indicates the HER reactions of as-synthesized

stepped MoS2 is coming out at the disulfide ligand site where the rich reservoir of

localized p-electrons, in consistent with the combined studies of STM experiments and

DFT calculations by Bollinger et al.34

`S57

13. DFT-calculated potential relaxation process to stably absorb H on the disulfide

ligands

Figure S32. DFT-calculated potential relaxation process to stably absorb H on the

disulfide ligands. Front view of the process contact and relaxed local structures of the

(A) flat edge surface terminated MoS2 (fe-MoS2) system and (B) stepped edge surface

`S58

terminated MoS2 (se-MoS2) system to stably absorb ¼ ML hydrogen on one of the

MoS2 layers, where violet, yellow and dark cyan spheres represent H, S and Mo atoms,

respectively.

It can be seen from the Figure 5 and Figure S32 that both the stepped and flat MoS2

edge surfaces have such switching effect on the disulfide ligand (S22-) at the top apex

angle site. However, the difference is that the disulfide ligands present double-switch

in the stepped se-MoS2 system while only a local single-switch for the flat fe-MoS2

system. The structures before and after relaxation in binding with H has slight

difference in the disulfide ligands (S22-) in the layers without H absorption, but vastly

distorted in dihedral angles of S22- binding H in both se-MoS2 and fe-MoS2. We can see

from Figure 5 and Figure S31 that a switching effect occurs on the S22- bonded with H

at the top apex edge after relaxation, showing an obvious charge density

variation/redistribution nearby the top apex edge of the layer that absorbed H. We see

that the disulfide ligand (S22-) at the top apex edge of both systems has an obvious

switching effect. The difference is that the se-MoS2 has two/double S22- switching effect

after structural relaxation in bonding with H, while only one of disulfide ligands from

the layer of the fe-MoS2 has the switching effect, the other shows less deviations. This

indicates that se-MoS2 system has more local structural relaxation to release the energy

in order to reach a more stable H binding state compared with the fe-MoS2 system.

Therefore, the advantages of the stepped edge surface structure with optimized

hydrogen adsorption free energy also leads to the high HER kinetics of the se-MoS2

`S59

catalysts.

We further look at the local short range order (SRO) on the disulfide ligand binding

with H after relaxation. The S-H bond length is 1.38 Å in se-MoS2 compared to the 1.39

Å measured in fe-MoS2, only with 0.01 Å shortened. The nearby S-S bond length (of

S22-) is found to be 2.08 Å in se-MoS2 and 2.07 Å in fe-MoS2 merely with 0.01 Å

elongated. In bond angles, the S-S-H angle shows 98.8° in se-MoS2 and 97.3° in fe-

MoS2 with only a change of 1.5°. This might not explain the energetic contrast in ∆GH

through the SRO. Therefore, the medium range order (MRO) and long range order

(LRO) may be reasonable to interpret the difference. Firstly, the disulfide ligand that

binds with H in both the se-MoS2 and fe-MoS2 systems has switched approximately

85°~90° with nearly similar angles. However, the nearest disulfide ligand (nearby) in

the same layer shows that there is about 45° switching in se-MoS2 while only about 5°

switching in fe-MoS2 system, showing the second nearest S sites distortion might

support the different scaled stabilization energy. Secondly, the host lattice structures

have an obvious difference between the stepped edge surface se-MoS2 and flat edge

surface fe-MoS2 systems. This not only exhibits an energy contrast in p-bonding orbital

levels of the edges seen from the level 1 (ppπ) (discussed in Figure S1 of Supplementary

Information), but also the larger energy difference to break the bonding between S and

H for the energy between level 1 (ppπ) and 4 (ppσ*). Moreover, in Figure S4 the

imaginary part of dielectric functions (ε2) shows a joint DOSs of valence and

conduction bands denotes the excitation occurs earlier in fe-MoS2 than the se-MoS2 in

both π→σ* and σ→σ* transitions mainly for p-orbitals. This confirms the scenario of

`S60

energy splitting observed from our PDOSs analysis in Figure S1 of Supplementary

Information. The se-MoS2 has lowered and broadened π→σ* transition peak from the

ε2 spectrum presenting a trend that larger probability and loosen excitation selection

rule for p-electrons to be a hole state in proton/electron exchange in HER. It also

indicates a weakening of MRO and LRO for se-MoS2 due to a localization of p-

electrons. Accordingly, this explains in view of both electronic properties and structural

relaxation that the MoS2 has much more stability in binding with H at the stepped edge

surface.

`S61

14. Volcano plot of experimentally measured exchange current density as a

function of the DFT-calculated free energy of hydrogen adsorption

Figure S33. A volcano plot of experimentally measured exchange current density as a

function of the DFT-calculated free energy of hydrogen adsorption. The simple kinetic

model proposed by Nørskov and coworkers to explain the origin of the volcano plot

reflects the Sabatier principle.52 It can be seen that the experimental exchange current

densities of MoS2 with stepped and flat edge surfaces are close to the expected

exchange current values in the volcano plot, indicating a good correlation between the

theoretical calculation and experimental results.

`S62

Tables

Table S1. Energy positions of levels observed in p-orbital PDOSs analysis. We took

the valence band maximum (VBM) as 0 eV, which is EV=0 eV. The H and L levels are

measured through the band tail inflexion points based on Cohen-Fritzche-Ovshinsky

(CFO) model.

Unit: eV 1 (ppπ) 2 (ppσ) 3 (ppσ) 4 (ppσ*) H L

Stepped -2.90 -5.10 -6.91 2.42 -1.25 0.50

Flat -2.51 -5.20 -6.80 1.90 -1.10 0.70

Table S2. DFT calculated total effective dipole of layered MoS2 systems.

SystemMagnitude of

Dipole (Debye)

Total

Electronskx ky kz

SL-MoS2 496.309480 294.0 -0.78603 0.618188 0.000536

se-MoS2 521.118270 728.0 -0.99397 -0.10931 -0.00834

fe-MoS2 1785.417540 882.0 -0.81431 0.580428 0.000555

`S63

Table S3. HER performance of recently reported active MoS2-based catalysts in 0.5 M H2SO4 electrolyte.

Catalysts j0

(mA/cm2)η (mV) @

j=-10 mA/cm2

Tafel slope

(mV/dec)Ref.

Stepped edge surface-terminated MoS2

sheet stacks0.20 104 59 This work

MoSx-NCNT 0.033 110 40 Nano Lett. 14, 122853

Li-MoS2 0.167 116 62 ACS Nano 8, 494054

MoC-Mo2C 0.011 126 43 Chem. Sci. 7, 339955

Amorphous MoSx film / 160 40 Acc. Chem. Res.

47, 267156 MoSx/graphene

protected Ni foam / 141 42.8 Adv. Mater. 25, 75657

O-incorporated MoS2 nanosheets 0.013 190 55 J. Am. Chem. Soc.

135, 1788158

1T-MoS2 nanosheets / 187 43 J. Am. Chem. Soc. 135, 1027459

Defect-rich MoS2 0.0089 195 50 Adv. Mater. 25, 580760

Double-gyroid MoS2/FTO 0.0007 220 50 Nat. Mater. 11,

96361 MoS2/FTO / 170 40 Chem. Sci. 2,

126262 MoS2/N-doped

carbon nanoboxes / 165 /Angew. Chem.

Int. Ed. 54, 739563

MoS2/CoSe2 hybrid 0.073 68 36 Nat. Common. 6, 598264

Co-MoS3 0.011 171 56.9 Adv. Mater. 28, 9265

Fe-MoS3 0.0002 180 39 Chem. Sci. 3, 251566

Strained vacancy MoS2

/ 170 60 Nat. Mater. 15, 4827

Amorphous MoSxCly / 160 46 Energy Environ. Sci. 8, 86267

Edge-terminate MoS2 film 0.0022 400 86 Nano Lett. 13,

134168 MoS2/Graphene / 165 41 Chem. Mater. 26,

234469

Ni-Mo-S nanosheets 0.049 200 85.3Sci. Adv.

10.1126/sciadv.150025970

Mo2C/CNT 0.014 152 55.2 Energy Environ. Sci. 6, 94371

MoO3-MoS2 nanowires / 250 50 Nano Lett. 11,

416872 MoS2 with 9.4 Å interlayer spacing 0.00962 150 49 Nat. Common. 6,

749373 MoS3 particles 0.00063 265 54 Energy Environ.

Sci. 5, 613674 MoS2.7@dealloyed

nanoporous Au / 210 41 Adv. Mater. 26, 310075

MoS2(1-x)Px/CB / 120 57 Adv. Mater. 28,

`S64

142776

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