Electronic and Chemical Properties of Germanene: The Crucial Role

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Electronic and Chemical Properties of Germanene: The Crucial Role of Buckling Abdulrahiman Nijamudheen, Rameswar Bhattacharjee, Snehashis Choudhury, and Ayan Datta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511488m • Publication Date (Web): 29 Jan 2015 Downloaded from http://pubs.acs.org on February 1, 2015

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The Journal of Physical Chemistry

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Electronic and Chemical Properties of Germanene: The Crucial Role of Buckling A. Nijamudheena, Rameswar Bhattacharjeea, Snehashis Choudhurya,b, and Ayan Dattaa* a

Department of Spectroscopy, Indian Association for the Cultivation of Science, 2A and 2B Raja S. C.

Mullick Road, Jadavpur – 700032, Kolkata, West Bengal, India. b

Present Address: School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853

Abstract The heavier analogues of graphene namely silicene and germanene are known to be buckled. Such buckling leads to interesting properties like direct band gap in hydrogenated germanene, known as germanane. This article shows that the sequential replacement of C by Ge in benzene leads to increasing buckling with the maximal buckling distance (d = 0.61 Å) in Ge6H6. The origin of such buckling induced lowering of symmetry (D6h → D3d) is traced to Pseudo Jahn – Teller (PJT) distortion along the b2g normal mode arising out of mixing of the non-degenerate (A1g) ground state with low lying (Δ0 = 4.36 eV) excited state of B2g symmetry. Buckling also leads to enhanced chemical reactivity of germanene towards hydrogen to form germanane. The large affinity of germanene towards hydrogenation explains the experimental synthesis of exfoliated layers of germanane by Goldberger and co-workers (ACS Nano, 2013, 7, 4414-4421). Germanene → germanane formation leads to the opening up of a large band gap making hydrogenation a chemical route to control the electronic properties in these new 2D materials. The presence of buckling in germanene leads to higher hole reorganization energies than polyaromatic hydrocarbons (PAH) of the same nuclearity. Keywords: Two Dimensional Materials; Germanene; Exfoliated layered sheets; Psuedo Jahn-Teller (PJT) Distortion; Band Gap tuning; Hydrogenation.

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Page 2 Introduction The discovery of unique electronic, mechanical, and transport properties of graphene has led to tremendous amount of research in the past decade towards the exploration of these properties for various device applications.1 Motivated by the success of graphene, there have been a large number of attempts to investigate atomically thin materials made of elements other than carbon. Some of the promising two dimensional systems that are being well explored are metal chalcogenides (MoS2, WS2, TiSe2, Bi2Te3, Sb2Te3, β-FeSe, etc.), hexagonal boron nitride, silicene, germanene, phosphorene, and various oxides.2-7 Among them, all silicon and all germanium analogues of graphene, also known as silicene and germanene, respectively are attracting interest because the current semiconductor industry is based on Si and Ge and it is predicted that these novel materials could be easily incorporated with the existing technology.8-14 Interestingly, they possess very similar electronic properties as that of graphene such as massless Dirac fermions, quantum-Hall effect, and bandgap tunability in the presence of an external electric field.15-21 Although the synthesis of free standing silicene and germanene monolayers have not been achieved yet, buckled monolayer of silicene has been realized over a number of substrates such as silver surface, diboride thin film, and iridium surface.22-24 Very recently, Li, et. al. have reported the first synthesis of germanene sheet by its successful fabrication on a Pt(111) surface.25 Dávila, et. al. have reported the formation of atomically thin germanene layer on Au(111) surface by the dry deposition of germanium on Au(111) surface.26 One remarkable breakthrough in this field was achieved by Goldberger and co–workers by preparing stable multilayers of hydrogenated germanene (germanane) through the deintercalation of CaGe2.27 From theory, it has been predicted that germanane has an excellent electron mobility and a direct


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Page 3 band gap of 1.53 eV. Later, it has been shown that replacing the H-termination by methyltermination could improve the stability of these systems significantly while retaining the excellent electronic properties.28 It is interesting to note that, in addition to the opto-electronics applications, silicene and germanene could also lead to novel chemistry.29 Unlike graphene, silicene and germanene show intrinsic buckling distortions in each of the six-membered rings throughout the honeycomb lattice. Therefore, these systems could be easily functionalized through chemical reactions and could find interesting applications such as catalysis.30-31 In this letter, we have used hybrid density functional methods to systematically study the structural and electronic properties of clusters of germanene and germanane with the size ranging from one to 25 six membered rings. The origin of buckling distortion in the hexa-germabenzene ring and extended sheets was rationalized based on the Pseudo Jahn Teller (PJT) distortion and assessed its importance with respect to their C and Si counterparts. The properties such as HOMO–LUMO gaps, hydrogenation energies, and electron and hole reorganization energies were discussed. Buckling is shown to assist hydrogenation which induces a band gap opening. Computational methods All structural calculations on GemHn and GemHn+o clusters were performed using two popular hybrid density functional theory methods namely PBE032-33 and B3PW9134 using Gaussian 09 suite of programs.35 These functionals have been successful in reproducing the structures, energies, and electronic properties of 2D nanomaterials like silicene.36-37 A triple zeta quality basis set (TZVP) was used for the calculations.38 The suitability of the cluster calculations were also verified by performing periodic DFT calculations at the PBE-D239 level in Quantum Espresso.40 Harmonic vibrational frequencies were computed to confirm that the optimized geometry is a minimum in the potential energy surface and also to calculate the force



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Page 4 constants associated with the buckling distortion. Derivative coupling (nonadiabatic coupling) vectors for the interaction of the ground state with the higher electronic states were computed at the state-averaged multiconfiguration SCF level41-42 with the TZVPP basis sets43 in MOLPRO.4445

An accurate estimate of the energy separation between the electronic states of different

symmetries as a function of the buckling distortion was obtained at the EOM-CCSD/TZVPP46 level. Results and discussions Unlike benzene, its all germanium analogue planar hexagermabenzene (Ge6H6) is a third order saddle point. Within DFT, three vibrational instabilities associated with puckering (qD3d; ω = –123.57 and 131.43 cm-1 at PBE0 and B3PW91, respectively) and doubly degenerate twisting modes47 (qC2; ω = –45.79 cm-1 and –60.16 cm-1 at PBE0 and B3PW91, respectively) exist in the planar D6h structure. Distortion along the D3d normal mode of the planar structure leads to removal of all the imaginary modes and results in a chair-like, stable Ge6H6 molecule. The puckering (buckling) distance d8-10 for Ge6H6 is 0.61 Å at PBE0 level. The buckling angle, φ (the dihedral angle or torsional angle defined for any four adjacent Ge atoms) in Ge6H6 is 48.8°. Changing the level of theory to B3PW91 has inconsequential effect on the nature of buckling (d = 0.63 Å, φ = 49.9°). To understand the structures and stability of germabenzenes,48-49 carbon atoms in benzene were replaced by one to six germanium atoms successively to form mono, di, tri, tetra, penta, and hexa substituted isomers (see Figure 1) and the geometry was fully optimized at PBE0/TZVP level of theory. Monosubstituted germabenzene retains its planarity in a good agreement with the experimental reports on germabenzene stabilized by a Tbt (2,4,6tris[bis(trimethylsilyl)methyl]phenyl) group.49 Calculated C-C (1.39 – 1.40 Å) and C-Ge (1.84 Å) bond lengths in GeC5H6 are also indicative of stabilization due to aromaticity in this


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Page 5 molecule. The calculated bond lengths are very close to the experimentally observed C-Ge (1.83 Å) and C – C (1.39 – 1.40 Å) bond lengths. Substitution of two germanium atoms leads to three isomers (see Figure 1) – 3 (ortho), 4 (meta), and 5 (para) out of which 3 is non – planar with an average buckling angle of φ = 9.6º whereas 4 and 5 remain planar. Their stability decreases in the order 3 (0.0 kcal/mol) > 4 (16.5 kcal/mol) > 5 (25.4 kcal/mol). Among the three trisubstituted isomers, only 1,3,5 – substituted isomer (6) retains the planarity (D3h symmetry) and all C–Ge bond lengths are the same in 6. However, this isomer is less stable compared to 7 and 8 by 31.1 and 9.1 kcal/mol, respectively. The degree of distortion from planarity was found to be directly proportional to the stability order with the isomers 7 and 8 are being non – planar by 17.5º and 15.0º, respectively. All tetrasubstituted isomers (9, 10, 11) are unstable in the planar geometry with the stability order of 9 (0.0 kcal/mol) > 11 (14.6 kcal/mol) > 10 (25.9 kcal/mol). As it has been expected, the most stable tetrasubstituted isomer (9) has the largest distortion from planarity (16.5°). Similarly, the penta and hexa germanium substituted benzenes 12 and 13 are non-planar by 37.1º and 48.8º, respectively. The buckling of germabenzenes on sequential substitution of C by Ge predicted here are very similar to that reported earlier for the hexasilabenzenes.50-51 While calculations at different levels of theories predicted a planar structure for GeC5H6 and similar buckling angles for Ge6H6, the structures of other CnGemH6 systems were found to be sensitive to the functional used (see Suppo Info).



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Figure 1. Optimized geometries of CnGemH6 (n + m = 6) clusters at PBE0/TZVP level.

Based on our calculations at the level of clusters and periodic 2D lattice, we find that germanene is substantially buckled. Manifestation of this effect occurs even in the smallest six membered ring Ge6H6 with a reduction in the point group symmetry from D6h to D3d. Unrestricted broken symmetry (UBS) DFT calculations at various levels show that Ge6H6 remains a closed shell molecule with negligible spin contamination (see Supp. Info.). Therefore, the origin of lowering in symmetry for such a closed shell system must be Psuedo Jahn – Teller (PJT) distortion.52-56 Consequently, the Occupied Molecular Orbital (OMO) and the Unoccupied Molecular Orbital (UMO) electronic states can rather easily undergo mixing by vibronic coupling. Similar phenomenon has been reported for the lowering of symmetry of small gold clusters in their ground state.57 One can qualitatively understand this by analysing the symmetry of the distortion mode (b2g) and representing this as a product of symmetries of the OMO and UMO. As shown in Figure 2, three possible combinations were obtained at the PBE0/TZVP level of theory for the D6h structure of Ge6H6. The interaction between the HOMO (e1g) and the LUMO + 3 (e2g) levels involves the lowest energy gap (5.05 eV) and one should expect that the interaction between these two orbitals can lead to PJT distortion in the D6h structure of Ge6H6


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Page 7 along the b2g vibrational mode. As can be seen qualitatively from the nature of the e1g orbitals (degenerate π type) and the e2g orbitals (degenerate σ* type), mixing between them is expected to break the in-plane symmetry of the molecule. This provides a chemical understanding of the origin of buckling distortion in Ge6H6. It is interesting to note that OMO-UMO gap for the case of hexasilabenzene (silicene model) is much higher (6.83 eV)54 and therefore, the PJT distortion in germanene is much more prominent compared to silicene. We therefore, anticipate that PJT distortions in germanene should be detected in experiments rather easily. As a proof of principles, additional calculations (at PBE0/TZVP level) were performed for C6H6 where the PJT effect is completely suppressed. As expected, a significantly large UMO-OMO gap (10.53 eV) found for C6H6 clearly explains its stable planar geometry. It is important to note that, the experimental realization of the CnGemH6 clusters and small germanene clusters would require them to be protected by bulky groups. However, an understanding of the reduced symmetry in the naked clusters would help to ascertain if the reduction in symmetry of experimental molecules arises from the basic physics of vibronic coupling in the Ge hexagons or from the surroundings.



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Figure 2: Possible combinations of the occupied molecular orbitals (OMO) and unoccupied orbitals (UMO) which may undergo vibronic coupling along the b2g buckling distortion mode for Ge6H6 (D6h symmetry). The OMO – UMO gaps (E) are reported in eV. To gain a better quantitative understanding of the PJT distortion in germanene, one needs to compute the vibronic coupling constant (V), primary force constant for the b2g distortion (K0), and the energies of the ground state and various electronic excited states along the distortion mode. In Figure 3 (i), the adiabatic potential energy surface (APES) cross section for the ground state and 9 excited states along the b2g distortion mode (starting from the planar geometry, along the normal mode, Q(b2g) corresponding to b2g mode) calculated at the EOM-CCSD/TZVPP level is plotted. The ground state (A1g) shows clear instability towards distortion thereby leading to a double minimum for Q (b2g) ≠ 0 and a maximum at Q (b2g) = 0. Such a double well like APES


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Page 9 cross section of the ground state is typical for PJT in the strong coupling limit between the ground state and the excited state(s) of the proper symmetry and is well-known in the literature.53 As it is shown in Figure 3(i), the ground state (Ag) and the sixth excited state (B2g) can vibronically couple along the b2g distortion mode. The gap (∆0) between these two states is 4.36 eV which is in the range for which PJT distortions in the ground state have been reported for the structures of metal clusters.57 The derivative coupling vectors between these two states (Ag and B2g states) calculated at the SA-MCSCF/TZVPP level and an animation of the vector58 are shown in Figure 3 (ii). From the norm of the vector, we calculated the vibronic coupling constant V = 2.47 eV/Å. Since only two states have the required symmetry and energy gap to undergo the PJT distortion in the ground state, we use the two-state model of interaction of diabatic states which gives the ground state effective force constant along the distortion mode KGS = K0 – V2/∆0 where K0 is the primary force constant of the diabatic potential energy surface of the undistorted molecule for the ground state. Within the DFT (PBE0/TZVP) level, we calculated KGS (b2g) = 1.37 eV/Å2 which when substituted into the previous equation leads to K0 = 0.29 eV/Å2. Within the strong coupling limit of interaction of two diabatic states which leads to permanent distortion (lowering of symmetry) in the ground state, the condition for distortion is 2V2/K0 > ∆0. Clearly, Ge6H6 satisfies this condition as 2V2/K0 = 42.08 eV > 4.36 eV (∆0). Therefore, we believe that the buckling distortion in Ge6H6 and its 2D analogue germanene arises from the PJT distortions discussed above. Following the same procedures described above for Ge6H6, we found that for C6H6, 2V2/K0 = 3.16 eV < 8.22 eV (∆0) and for Si6H6, 2V2/K0 = 5.35 eV > 3.85 eV (∆0). Hence, in C6H6 the PJT effect is completely quenched whereas in Si6H6, even though such effects lead to substantial puckering, the magnitude should be much smaller than that predicted for Ge6H6.



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Figure 3: (i) Adiabatic potential energy surface (APES) cross section for variation of the ground state energy and nine excited states with respect to the distortion along the b2g distortion mode for planar Ge6H6 (EOM-CCSD/TZVPP level at highest abelian group, D2h. ∆0 represents the vertical energy gap (in eV) at Q = 0 between the A1g state (ground state) and the B2g state (excited state). (ii) Derivative coupling vector between the A1g and the lowest B2g state calculated at SA-MCSCF/TZVPP level.


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Figure 4: Optimized geometries of GemHn systems. a and b represent the unit vectors through which the germanene fragments were extended (a = b =1 for Ge6H6 and a = b = 5 for Ge70H22). In order to understand the structural and electronic properties of germanene fragments we have modelled GemHn clusters in a systematic way by changing the unit vectors a and b from 1 to 5 as shown in Figure 4. The puckering in the germanene fragments remains consistent as going from Ge6H6 (d = 0.61 Å, φ = 48.8º) to Ge70H22 (d = 0.63 Å, φ = 49.7º). Plane wave calculations predict that the average buckling angle in the extended sheet of germanene (d = 0.69 Å, φ = 52.2º) is similar compared to that of the clusters. The buckling distortions in these



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Page 12 systems are clearly more than that reported for the respective silicenes and show good agreement with the previous experimental and theoretical studies on extended germanene sheets.8-9, 25-26 The stability for the germanene nanoflakes (shown in Figure 4) were calculated in terms of the binding energy as ΔE = E(GemHn) – (m/2) E(Ge2H2) + [(m – n)/2] E(H2) where m and n represent the number of Ge and H atoms in a germanene fragment, respectively. The global energy minimum of digermyne is known to be a double-bridged, butterfly-like geometry with C2v symmetry.59-60 Calculated Ge-Ge and Ge-H bond lengths (2.36 Å and 1.77 Å, respectively) in Ge2H2 at PBE0 level show good agreement with the high level wave function based methods. The choice of digermyne as a fractional unit was made because this is the smallest system with a Ge-Ge bond and a Ge-H bond with Ge in a tricordinated environment. As it has been expected, the binding energy per Ge atom was found to gradually increase with the size of the system from -0.67 eV in Ge6H6 to -0.87 eV in Ge70H22. Even though the calculated BE/atom is lesser than the silicon analogues by ~0.25 eV, they are indicative that larger GemHn clusters can indeed exist due to sufficient stabilization energy. However, the small clusters are expected to be stable only in the gas-phase and in oxygen free environment. Only with sufficiently large clusters, the two dimensional nature of the system emerges. Therefore, only for the ligand protected small clusters, one can envision device applications. The HOMO–LUMO gaps in the germanene nanoflakes decrease sharply on moving from the smallest system Ge6H6 with a value of 3.04 eV to the higher analogues to just 0.28 eV in Ge70H22. This trend is very much similar to that found earlier for the polyaromatic hydrocarbons (PAHs) and single layered silicon sheets.61,36 Nevertheless, the clusters of Ge have smaller HOMO–LUMO gaps than their Si and C analogues because of the presence of a large number of states near the Fermi energy in the case of germanium.


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Page 13 A fruitful approach to understand the charge transport properties in a material is to calculate its reorganization energy (λ). The reorganization energy of a system can be directly correlated with its ability to act as an electron or hole field effect transistor. Within the Marcus incoherent hopping model which is appropriate to describe conduction mechanism in molecular materials, λ describes the extent of nuclear relaxation on adding or removal of an electron which is typical in P-type and N-type field effect transistors.62-63 Therefore, we calculated the internal reorganization energies in germanene clusters using the expression λhole/electron = (E±* - E±) + (Ecation/anion* - E) where E±* is the energy of cation/anion state in the neutral geometry, E± is the energy of cation/anion state in the cation/anion geometry, Ecation/anion* is the energy of neutral state in the cation/anion geometry, and E is the energy of neutral state in the neutral geometry. Reorganization energies of the germanene clusters calculated at PBE0/TZVP level are shown in Table 1. In general, the hole reorganization energies (λhole) were found to be smaller than the electron reorganization energy (λelectron). This result is similar to that found for polyacenes61 and silicenes,36 which are known to be better hole conductors than electron conductors.



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Page 14 Table 1. The structural and electronic properties calculated for germanene fragments at the PBE0 level of theory.

GemHn

Point group (B3PW91)

Binding energy/ Ge atom (eV)

HOMO – LUMO gap (eV)

Reorganization energy (eV) (PBE0)

PBE0

B3PW91

PBE0

B3PW91

λhole

λelectron

Ge6H6

D3d

-0.71

-0.67

3.31

3.04

0.39

0.82

Ge10H8

C2h

-0.77

-0.72

2.37

2.14

0.25

0.42

Ge14H10

C2h

-0.78

-0.74

1.81

1.62

0.21

0.25

Ge18H12

C2h

-0.79

-0.75

1.46

1.29

0.17

0.16

Ge22H12

Ci

-0.84

-0.80

1.43

1.26

0.16

0.25

Ge28H14

Ci

-0.85

-0.81

1.11

0.97

0.14

0.20

Ge30H14

C2h

-0.87

-0.83

1.09

0.95

0.14

0.20

Ge34H16

Ci

-0.86

-0.82

0.89

0.76

0.16

0.22

Ge38H16

Ci

-0.88

-0.84

0.83

0.71

0.13

0.22

Ge46H18

Ci

-0.89

-0.85

0.65

0.55

0.12

0.25

Ge48H18 Ge70H22 Ge14H10 Ge16H10 Ge24H12

C2h C2h C2 C2h D3d

-0.89 -0.91 -0.79 -0.82 -0.87

-0.85 -0.87 -0.74 -0.78 -0.83

0.62 0.34 2.30 1.88 1.98

0.51 0.28 2.08 1.68 1.80

0.12 0.47 0.23 0.15 0.13

0.26 0.21 0.45 0.23 0.19

Hydrogenation of graphene and silicene has been well documented in the literature as a strong tool that allows chemical functionalization and modifies the electronic structure. Recent synthesis of hydrogenated germanene (germanane) has also shown exciting characteristics of this system.27 Here, to understand the effect of hydrogenation in the structural and electronic properties, all germanene clusters were fully saturated by hydrogen atoms (see Figure 5) and optimized their geometry at PBE0 and B3PW91 levels to calculate the energy of hydrogenation, HOMO–LUMO gaps, and reorganization energy. The heat of hydrogenation (ΔH) for a GemHn+o cluster was calculated by using the relation ΔH = H(GemHn+o) – H(GemHn) – (o/2) H(H2) where H(GemHn+o), H(GemHn), and H(H2) are the enthalpy values calculated for GemHn+o, GemHn, and H2, respectively at 298.15 K.


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Figure 5: Hydrogenation of germanene Ge70H22 to form germanane Ge70H92. The heat of hydrogenation for germanene → germanane are reported in Table 2. Even though the heat of hydrogenation per Ge atom for the smaller clusters are large due to the higher fraction of free GeH2 ends on the periphery of the rings, they quickly converge to -0.53 eV at the PBE0/TZVP level (-0.46 eV at the B3PW91/TZVP level) with increase in the size of the cluster for which the percentage of dangling bonds are small. For example, while for the smallest unit Ge6H12 the percentage of dangling GeH2 units on the periphery is 100% it reduces to only 31% for Ge70H92. Calculations on the extended sheet of germanene using plane wave PBE-D2 calculations predict the heat of hydrogenation per Ge atom to be -0.29 eV. Unlike PAHs, the hydrogenation in germanenes should not lead to significant loss of aromatic stabilization as the aromatic stabilization if any, of the six membered germanene rings are expected to be small64



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Page 16 and the intrinsic buckling of six membered rings leads to enhanced preference for hydrogenation in Ge systems. Therefore, the calculated heat of hydrogenation is clearly more than that reported for the respective PAHs. Interestingly, even though the hydrogenation enthaplies for germanene is larger than that for PAH, they are smaller than the respective Si analogues. Both silicene and germanene layers are already buckled in their ground state and hence should prefer hydrogenation and gain as a result of additional Ge-H/Si-H bonds on formation of silicane and germanane. Nevertheless, a Si-H bond (De=76.1 kcal/mol, req=1.48 Å) is known to be stronger than a Ge-H bond (De=68.9 kcal/mol, req=1.53 Å)65-66 and therefore, the heat of hydrogenation is smaller for germanene than silicene.


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Page 17 Table 2. The heat of hydrogenation values for the germanenes and the electronic properties of the germananes calculated at the PBE0 level of theory.

Heat of

Heat of

Reorganization HOMO – LUMO

hydrogenation

hydrogenation/ Ge

energy (eV) gap (eV)

GemHn+o

(eV)

atom (eV)

(PBE0)

PBE0

B3PW91

PBE0

B3PW91

PBE0

B3PW91

λhole

λelectron

Ge6H12

-3.71

-3.36

-0.62

-0.56

7.27

6.90

1.51

2.58

Ge10H18

-5.96

-5.35

-0.60

-0.53

6.10

5.77

1.01

2.05

Ge14H24

-8.27

-7.41

-0.59

-0.53

5.45

5.13

0.73

1.75

Ge18H30

-10.61

-9.47

-0.59

-0.53

5.08

4.77

0.53

1.53

Ge22H34

-12.31

-10.94

-0.56

-0.50

5.09

4.73

0.46

1.12

Ge28H42

-15.58

-13.82

-0.56

-0.49

4.77

4.44

0.35

1.13

Ge30H44

-16.46

-14.56

-0.55

-0.49

4.78

4.41

0.30

0.91

Ge34H50

-18.86

-16.70

-0.55

-0.49

4.55

4.25

0.29

0.68

Ge38H54

-20.64

-18.22

-0.54

-0.48

4.53

4.16

0.26

0.37

Ge46H64

-24.84

-21.90

-0.54

-0.48

4.35

3.98

0.23

0.32

Ge48H66

-25.89

-22.67

-0.54

-0.47

4.33

3.96

0.21

0.30

Ge70H92

-36.86

-32.41

-0.53

-0.46

4.03

3.66

0.16

0.22

Ge14H24

-8.12

-7.41

-0.58

-0.52

5.63

5.26

0.83

1.86

Ge16H26

-9.12

-9.02

-0.57

-0.56

5.54

5.16

0.71

1.50

Ge24H36

-12.98

-11.49

-0.54

-0.48

5.11

4.72

0.52

1.11

Conclusions In conclusion, we have shown that the buckling distortion in germanene arises out of PJT distortion. Such PJT distortion leads to a reduced symmetry in germanene and creates an sp3 like environment in these 2D materials. It has been predicted that all germabenzenes with a Ge-Ge bond is unstable in a planar geometry. The structural and electronic properties of the germanene



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Page 18 of 26

Page 18 and germanane clusters were critically examined starting from the smallest structural units consisting of a six membered ring to that consisting of up to 25 six membered rings. Our calculations reveal that the germanene clusters are hole conducting materials and stabilization of these clusters by protecting bulky groups can lead to their isolation and crystallization. It will be very interesting to compare the structures of the predicted clusters with those in molecular crystals like that for Ge-analogues of tetracene or pentacene. Due to the already existing sp3 like buckling in germanene, hydrogenation becomes facile which leads to an opening of band gap. Presence of a finite band gap in germanane makes it an ideal system for band gap tuning either by the application of an external electric field or via chemical functionalization.

Acknowledgements AD thanks DST, INSA, and CSIR-EMR for partial funding. RB thanks CSIR for JRF. We thank CRAY supercomputer for the MRSCF calculations. Author Information *Corresponding Author: [email protected]. Notes The authors declare no competing financial interest. Supporting Information Cartesian coordinates, energies, and harmonic frequencies for all the structures reported, additional calculations, and complete references 3, 35, 40 and 44. This information is available free of charge via the Internet at http://pubs.acs.org.


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Page 19 References 1. Novoselov, K. S.; Fal′ko, V. I.; Colombo, L.; Gellert, P. R.; Schwab, M. G.; Kim, K. A Roadmap for graphene. Nature 2012, 490, 192-200. 2.

Xu, M.; Liang, T.; Shi, M.; Chen, H. Graphene-like two-dimensional materials. Chem. Rev. 2013, 113, 3766–3798.

3. Butler, S. Z.; Hollan, S. M.; Cao, L.; Cui, Yi; Gupta, J. A.; Gutierrez, H. R.; Heinz, T. F.; Hong, S. S.; Huang, J.; Ismach, A. F., et. al. Progress, challenges, and opportunities in twodimensional materials beyond graphene ACS Nano 2013, 7, 2898–2926. 4.

Geim, A. K.; Grigorieva, I. V. Van der Waals heterostructures. Nature 2013, 499, 419-425.

5. Matte, H. S. S. R.; Gomathi, A.; Manna, A. K.; Late, D. J.; Datta, R.; Pati, S. K.; Rao, C. N. R. MoS2 and WS2 analogues of graphene Angew. Chem. Int. Ed. 2010, 49, 4059– 4062. 6. Yamijala, SRKCS.; Pati, S. K. Electronic and magnetic properties of zigzag boron-nitride nanoribbons with even and odd-line Stone-Wales (5–7 Pair) defects. J. Phys. Chem. C 2013, 117, 3580–3594. 7. Ghosh, D.; Parida, P.; Pati, S. K. Line Defects at the heterojunction of hybrid boron nitride– graphene nanoribbons. J. Mater. Chem. C 2014, 2, 392–398. 8. Cahangirov, S.; Topsakal, M.; Aktürk, E.; Șahin, H.; Ciraci, S. Two- and one-dimensional honeycomb structures of silicon and germanium. Phys. Rev. Lett. 2009, 102, 236804. 9. Șahin, H.; Cahangirov, S.; Topsakal, M.; Bekaroglu, E.; Akturk, E.; Senger, R. T.; Ciraci, S. Monolayer honeycomb structures of group-IV elements and III-V binary compounds: Firstprinciples calculations. Phys. Rev. B. 2009, 80, 155453. 10. Kaloni, T. P.; Schwingenschlögl, U. Quasi free-standing silicene in a superlattice with hexagonal boron nitride. Sci. Rep. 2013, 3, 3192.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 26

Page 20 11. Kaloni, T. P.; Gangopadhyay, S.; Singh, N.; Jones, B.; Schwingenschlögl, U. Electronic properties of Mn-decorated silicene on hexagonal boron nitride. Phys. Rev. B. 2013, 88, 235418. 12. Liu, H.; Gao, J.; Zhao, J. Silicene on substrates: A way to preserve or tune its electronic properties. J. Phys. Chem. C 2013, 117, 10353−10359. 13. Li, L.; Zhao, M. First-principles identifications of superstructures of germanene on Ag(111) surface and h-BN substrate. Phys. Chem. Chem. Phys. 2013, 15, 16853-16863. 14. Kaloni, T. P.; Schwingenschlögl, U. Weak interaction between germanene and GaAs(0001) by H intercalation: A route to exfoliation. J. Appl. Phys. 2013, 114, 184307 15. Ezawa, M. Valley-polarized metals and quantum anomalous Hall effect in silicene. Phys. Rev. Lett. 2012, 109, 055502. 16. Kaloni, T. P.; Singh, N.; Schwingenschlögl, U. Prediction of a quantum anomalous Hall state in Co-decorated silicene. Phys. Rev. B 2014, 89, 035409. 17. Kaloni, T. P. Tuning the structural, electronic, and magnetic properties of germanene by the adsorption of 3d transition metal atoms. J. Phys. Chem. C 2014, 118, 25200-25208. 18. Kara, A.; Enriquez, H.; Seitsonen, A. P.; Voon, L.; Vizzini, S.; Aufray, B.; Oughaddou, H. A review on silicene - new candidate for electronics. Surf. Sci. Rep. 2012, 67, 1–18. 19. Xu, C.; Luo, G.; Liu, Q.; Zheng, J.; Zhang, Z.; Nagase, S.; Gaoa, Z.; Lu, J. Giant magnetoresistance in silicene nanoribbons. Nanoscale, 2012, 4, 3111-3117. 20. Houssa, M.; Pourtois, G.; Afanas’ev, V. V.; Stesmans, A. Electronic properties of twodimensional hexagonal germanium. Appl. Phys. Lett. 2010, 96, 082111. 21. Ma, Y.; Dai, Y.; Lu, Y-B.; Huang, B. Effective bandgap engineering in wrinkled germanane via tiny electric field. J. Mater. Chem. C 2014, 2, 1125–1130.


Page 21 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Page 21 22. Feng, B.; Ding, Z.; Meng, S.; Yao, Y.; He, X.; Cheng, P.; Chen, L.; Wu, K. Evidence of silicene in honeycomb structures of silicon on Ag(111). Nano Lett. 2012, 12, 3507– 3511. 23. Fleurence, A.; Friedlein, R.; Ozaki, T.; Kawai, H.; Wang, Y.; Yamada-Takamura, Y. Experimental evidence for epitaxial silicene on diboride thin films. Phys. Rev. Lett. 2012, 108, 245501. 24. Vogt, P.; De Padova, P.; Quaresima, C.; Avila, J.; Frantzeskakis, E.; Asensio, M. C.; Resta, A.; Ealet, B.; Le Lay, G. Silicene: compelling experimental evidence for graphene like twodimensional silicon. Phys. Rev. Lett. 2012, 108, 155501. 25. Li, L.; Lu, S.; Pan, J.; Qin, Z.; Wang, Y.; Wang, Y.; Cao, G.; Du, S.; Gao, H. Buckled germanene formation on Pt(111). Adv. Mater. 2014, 26, 4820–4824. 26. Dávila, M. E.; Xian, L.; Cahangirov, S.; Rubio, A.; Lay, L. L. Germanene: a novel twodimensional germanium allotrope akin to graphene and silicene. New J. Phys. 2014, 16, 095002. 27. Bianco, E.; Butler, S.; Jiang, S.; Restrepo, O. D.; Windl, W.; Goldberger, J. E. Stability and exfoliation of germanane: a germanium graphane analogue. ACS Nano 2013, 7, 4414– 4421. 28. Jiang, S.; Butler, S.; Bianco, E.; Restrepo, O. D.; Windl, W.; Goldberger, J. E. Improving the stability and optical properties of germanane via one-step covalent methyl-termination. Nat. Commun. 2014, 5, 3389. 29. Jose, D.; Datta, A. Structures and chemical properties of silicene: unlike graphene. Acc. Chem. Res. 2014, 47, 593-602. 30. Li, C.; Yang, S.; Li, S-S.; Xia, J-B.; Li, J. Au-decorated silicene: design of a high-activity catalyst toward CO oxidation. J. Phys. Chem. C 2013, 117, 483-488.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 26

Page 22 31. Liu, Z.; Lou, Z.; Li, Z.; Wang, G.; Wang, Z.; Liu, Y.; Huang, B.; Xia, S.; Qin, X.; Zhang, X.; Dai, Y. GeH: A novel material as a visible-light driven photocatalyst for hydrogen evolution. Chem. Commun. 2014, 50, 11046-11048. 32. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865-3868. 33. Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: the PBE0 model. J. Chem. Phys. 1999, 110, 6158-6170. 34. Becke, A. D. Density-‐functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648-5652. 35. Frisch, M. J.; et al. Gaussian 09; Gaussian, Inc.: Wallingford, CT, 2009. 36. Jose, D.; Datta, A. Structures and electronic properties of silicene clusters: a promising material for FET and hydrogen storage. Phys. Chem. Chem. Phys. 2011, 13, 7304–7311. 37. Drummond, N. D.; Z ́lyomi, V.; Fal’ko, V. I. Electrically tunable band gap in silicene. Phys. Rev. B. 2012, 85, 075423. 38. Dunning Jr., T. H. Gaussian basis functions for use in molecular calculations. III. Contraction of (10s6p) atomic basis sets for the first-‐row atoms. J. Chem. Phys. 1971, 55, 716−723. 39. Grimme, S. Semiempirical GGA-Type Density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787-1799. 40. Giannozzi, P. et. al. QUANTUM ESPRESSO: A Modular and open-source software project for quantum simulations of materials. J. Phys. Con-dens. Matter 2009, 21, 395502. 41. Werner, H-J.; Knowles, P. J. A second order multiconfiguration SCF procedure with optimum convergence. J. Chem. Phys. 1985, 82, 5053-5063.


Page 23 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Page 23 42. Knowles, P. J.; Werner, H-J. An Efficient second-order MC SCF method for long configuration expansions. Chem. Phys. Lett. 1985, 115, 259-267. 43. Schäfer, A.; Huber, C.; Ahlrichs, R. Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829- 5835. 44. MOLPRO, version 2012.1, a package of ab initio programs, Werner, H.-J.; Knowles, P. J.; Knizia G.; Manby, F. R.; Schütz, M.; Korana, C. T.; Mitrushenkov, A.; Rauhut, G.; Shamasundan, K. R.; Adler, T. B. et al. 45. Werner, H-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: a generalpurpose quantum chemistry program package. WIREs Comput Mol Sci. 2012, 2, 242-253. 46. Stanton, J. F.; Bartlett, R. J. The equation of motion coupledcluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties. J. Chem. Phys. 1993, 98, 7029-7039. 47. Silverstein, R. M.; Webster, F. X.; Kiemle, D.; Bryce, D. L. Spectrometric Identification of Organic Compounds, 8th Edition. Wiley, 2014. 48. Tokitoh, N.; Nakata, N.; Shinohara, A.; Takeda, N.; Sasamori, T. Coordination chemistry of a kinetically stabilized germabenzene: syntheses and properties of stable η6-germabenzene complexes coordinated to transition metals. Chem. Eur. J. 2007, 13, 1856 – 1862. 49. Tokitoh, N. New progress in the chemistry of stable metallaaromatic compounds of heavier group 14 elements. Acc. Chem. Res. 2004, 37, 86-94. 50. Mohan, V.; Datta, A. Structures and electronic properties of Si-substituted benzenes and their transition-metal complexes. J. Phys. Lett. 2010, 1, 136-140. 51. Ivanov, A. S.; Boldyrev, A. I. Si6–nCnH6 (n = 0–6) Series: When do silabenzenes become planar and global minima? J. Phys. Chem. A 2012, 116, 9591– 9598.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 26

Page 24 52. Liu, Y.; Bersuker, I. B.; Garcia-Fernandez, P.; Boggs, J. E. Pseudo Jahn−Teller origin of nonplanarity and rectangular-ring structure of tetrafluorocyclobutadiene. J. Phys. Chem. A 2012, 116, 7564 – 7570. 53. Bersuker, I. B. Pseudo-Jahn-Teller effect - A two-state paradigm in formation, deformation, and transformation of molecular systems and solids. Chem. Rev. 2013, 113, 1351–1390. 54. Jose, D.; Datta, A. Understanding of the buckling distortions in silicene. J. Phys. Chem. C, 2012, 116, 24639–24648. 55. Mandal, T. K.; Jose, D.; Nijamudheen, A.; Datta, A. Structures and electronic properties of heavier congeners of disk like molecules:(Si, Ge) sulflower and (Si, Ge) olympicene. J. Phys. Chem. C, 2014, 118, 12115–12120. 56. Kozuch, S.; Hrovat, D. A.; Borden, W. T. Why is (SiO)4 calculated to be tetrahedral, whereas (CO)4 is square planar? A molecular orbital analysis. J. Am. Chem. Soc. 2013, 135, 19282−19291. 57. Soto, J. R.; Molina, B.; Castro, J. J. Nonadiabatic structure instability of planar hexagonal gold cluster cation Au7 and its spectral signature. RSC Adv. 2014, 4, 8157–8164. 58. Bally, T.; Bernhard, S.; Matzinger, S.; Roulin, J-L.;Sastry, G. N.; Truttmann, L.; Zhu, Z.; Marcinek, A.; Adamus, J.; Kaminski, R.; Gebicki. J.; Williams, F.; Chen, G-F.; Fulscher, M. P. The radical cation of syn-tricyclooctadiene and its rearrangement Products. Chem. Eur. J, 2000, 6, 858 – 868. 59. Boone, A. J.; Magers, D. H.; Leszczyński, J. Searches on the potential energy hypersurfaces of GeCH2, GeSiH2, and Ge2H2. Int. J. Quantum Chem. 1998, 70, 925-932. 60. Palágyi, Z.; Schaefer III, H. F.; Kapuy, E. Ge2H2: A molecule with a low-lying monobridged equilibrium geometry. J. Am. Chem. Soc. 1993, 115, 6901-6903.


Page 25 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Page 25 61. Ruiz-Morales, Y. HOMO-LUMO Gap as an index of molecular size and structure for polycyclic aromatic hydrocarbons (PAHs) and asphaltenes: A theoretical study. I. J. Phys. Chem. A 2002, 106, 11283-11308. 62. Datta, A.; Mohakud, S.; Pati, S. K. Electron and hole mobilities in polymorphs of benzene and naphthalene: Role of intermolecular interactions. J. Chem. Phys. 2007, 126, 144710. 63. Marcus, R. A. Electron transfer reactions in chemistry. Theory and experiment. Rev. Mod. Phys. 1993, 65, 599-610. 64. Lee, V. Y.; Sekiguchi, A. Aromaticity of group 14 organometallics: experimental aspects. Angew. Chem. Int. Ed. 2007, 46, 6596 – 6620. 65. Benson, S. W. J. III- Bond energies. Chem. Educ.. 1965, 42, 502-518. 66. Darwent, B. deB. National standard reference data series. 1979, 31, 1-48, Washington, DC.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 26

Page 26 Table of Contents (TOC):


Electronic and Chemical Properties of Germanene: The Crucial Role

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