How the Number of Layers and Relative Position Modulate the

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How Number of Layers and Relative Position Modulate the Interlayer Electron Transfer in #-Stacked 2D Materials Alessandro Biancardi, Claudiu Caraiani, Wai-Lun Chan, and Marco Caricato J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b00194 • Publication Date (Web): 12 Mar 2017 Downloaded from http://pubs.acs.org on March 13, 2017

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The Journal of Physical Chemistry Letters

How Number of Layers and Relative Position Modulate the Interlayer Electron Transfer in π-Stacked 2D Materials Alessandro Biancardi,† Claudiu Caraiani,‡,¶ Wai-Lun Chan,‡ and Marco Caricato∗,† †Department of Chemistry, The University of Kansas, 1251 Wescoe Hall Dr., KS 66045-7582 ‡Department of Physics, The University of Kansas, 1251 Wescoe Hall Dr., KS 66045-7582 ¶Horia Hulubei National Institute For Physics And Nuclear Engineering, RO-077125, Magurele, Romania E-mail: [email protected] Phone: +1 785-864-6509

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Abstract Understanding the interfacial electron transfer (IET) between 2D layers is central to technological applications. We present a first-principles study of the IET between a zinc phthalocyanine film and few-layer graphene, by using our recent method for the calculation of the electronic coupling in periodic systems. The ultimate goal is the development of a predictive in silico approach for designing new 2D materials. We find the IET critically dependent on the number of layers, and their stacking orientation. In agreement with experiment, the IET to single-layer graphene is shown to be faster than that to double-layer graphene due to interference effects between layers. We predict that additional graphene layers increase the number of IET pathways, eventually leading to a faster rate. These results shed new light on the subtle interplay between structure and IET, which may lead to more effective “bottom up” design strategies for these materials.

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Interfacial electron transfer (IET) from adsorbed molecules and biomolecules to few-layers graphene (FLG) has generated great interest in recent years because of the promising applications of these materials. 1–5 FLG materials are two-dimensional (2D) systems composed of a few single-atom-thick “honeycomb” lattices of carbon atoms, and recent research has focused on how their electronic properties evolve as a function of the number of layers. 6–8 The impressive progress in experimental techniques for synthesis and manipulation of graphene, e.g. control of the number of graphene layers, 9–12 functionalization with organic and inorganic molecules, 13,14 or combination with two-dimensional layers of other materials, 15 has made possible the accurate tuning of its properties. However, in spite of extensive efforts, a general microscopic understanding of the interplay between 2D structure and interlayer transfer is still unsatisfying. Insights from theoretical simulations are therefore of utmost importance for the development of “bottom up” design strategies. 16–18 A key ingredient for understanding these systems and design new materials is the development of accurate methods for the calculation of the IET rates between layers. Even though explicit quantum dynamical descriptions are in principle desirable, 19–23 e.g. combining molecular dynamics and time-dependent density functional theory calculations, they may not always be computationally feasible nor necessary. On the other hand, the availability of cheaper and more approximate approaches is crucial for the development of fast in silico screening to design 2D materials with desired characteristics. These approaches are usually based on the calculation of electronic couplings (J), whose square modulus is proportional to the rate transfer via Marcus formula: 24,25 |J|2 k= ~

r

(∆E − λ)2 π exp − λkB T 4λkB T

!

(1)

where ∆E is the difference between the site energies, and λ is the reorganization energy. In the case of systems with similar ∆E and λ, |J|2 is already sufficient to obtain the correct transfer ratio between them, eliminating the need to evaluate λ. This is a reasonable

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assumption in the context of this work, and we will limit the following discussion to |J|2 . The calculation of the electronic coupling has been pioneered by Bredas and co-workers 26,27 in the context of isolated molecular dimers, and two of us recently extended this method to periodic solids within the Γ-point approximation. 28 In this extension, the coupling is obtained from the off-diagonal elements of the reconstructed Fock/Kohn-Sham matrix in the basis of the periodic orbitals of the donor (D) and acceptor (A) fragments, namely:

FijDA =

X

l

Γ

A φD iΓ |φlΓ εl φlΓ |φjΓ

(2)

A and φ |φ where φD |φ lΓ lΓ jΓ are the Γ-point overlaps between fragment (D/A) and superiΓ system orbitals, and εΓi are the Γ-point orbital energies for the supersystem. In the case of

non-orthonormal fragment orbitals, a further orthogonalization is required. 28 In the case of degenerate donor states, the effective coupling is obtained as an average over the number of donor states (ND ): ND X NA DA 2 1 X F |J| = ND i=1 j=1 ij 2

(3)

A remarkable example of the fine interaction between donor and acceptor layers in FLG is the change in IET rate from a film of zinc phthalocyanine (ZnPc) to a single- or AB-stacked double-layer graphene (SLG or DLG, respectively), which was recently studied by two of the present authors. 29 Time-resolved two-photon photoemission (TR-TPPE) spectroscopy was used to measure the IET rates between ZnPc films and graphene layer(s). The rates were determined by integration of the TR-TPPE spectra over the energy range mainly associated with the lowest singlet excited state of the ZnPc film. 29 The integrated intensity as a function of time showed that the transfer from a 0.5 nm ZnPc film (consistent with a single-layer of ZnPc film) to SLG is about 2 times slower compared to graphite. This can be intuitively associated with the lower density of states (DOS) of the single-layer graphene compared to graphite. However, it was also found that the IET to AB-stacked graphene double-layer was slower than both SLG and graphite. This behavior was qualitatively attributed to the 4


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electronic structure modifications created by the graphene interlayer interaction as described by a simple tight-binding model. However, in this work we show that these observations can only be quantitatively explained with first-principles computational modeling. Indeed, the ET between neighboring layers is regulated by the nature of the overlapping orbitals and their relative position/orientation. Our results shed light on the IET modulation moving from ZnPc over SLG to ZnPc over DLG, and allow us to rationalize this modulation in terms of orbital overlap between the ZnPc film and graphene. Predictions on three- and four-layer graphene indicate that new pathways for IET are created with more layers, as long as the interlayer orientation is favorable. Although the rate with three/four layers is still slower than with SLG, our results clearly show a rate increase compared to DLG that may eventually lead to the faster rate measured in graphite. Simulations with more layers would be necessary to reach that regime, but these are beyond current capabilities with accurate quantum mechanical methods. Finally, our simulations also investigate the effect of the intermolecular interaction between two ZnPc layers on the IET, which cannot be readily studied experimentally. These simulations show that the electron is mostly localized in the interlayer region of ZnPc film, and the IET rate to graphene is significantly reduced.

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Figure 1: Top view of the unit cell for ZnPc over SLG and DLG at sites A, B, and C. X and Y represent the translation vectors. The red lines are a guide for the eye and they cross at the position of the Zn atom in site A. The relative rotation between ZnPc and graphene layer(s) is 10◦ . 30,31 For DLG, the layers are in the AB-stacked configuration at a distance of 3.36 Å. 32 Following Gopakumar, Hamalainen, and co-workers 30,31 we chose three adsorption sites for ZnPc over SLG and DLG: A, where Zn is aligned with the center of a graphene ring; B and C, where Zn is aligned with a carbon atom (Figure 1). Sites B and C are not equivalent, albeit isoenergetic, because the presence of ZnPc reduces the symmetry of the graphene lattice. In a similar system on SLG, the B and C adsorption sites were found more stable than A by ∼9 kcal/mol, via first-principles calculations using a plane wave basis set, the localdensity approximation (LDA) and vdW-DF corrections. 33 However, it is unlikely that ZnPc and graphene maintain the same relative positions in the actual material because the two crystals have different in-plane symmetry and are incommensurate. 31 In fact, a distribution of relative orientations should be expected.

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Figure 2: DOS for the single-layer ZnPc on SLG and DLG. The vertical dotted red line is a guide for the eye to indicate Ef . As shown in Figure 2, the overall structure of the DOS of SLG and DLG is similar, with main differences occurring around the van Hove maxima 34 and above 8 eV. In all cases, Ef is in the range -4.2 – -4.3 eV, (see also Table S1 of the supporting information, SI) in agreement with previous experimental and computational results. 34–37 The presence of the ZnPc layer(s) creates additional peaks around Ef , which are involved in the photoinduced electron transfer studied in this work (see also Figure S2 of the SI). However, the DOS alone offers no explanation about the IET modulation moving from SLG to DLG, thus requiring the inspection of electronic coupling and corresponding orbitals. In order to simplify the notation, we will call the layer orbitals involved in the IET: fn Hfn m and Lm , where H and L refer to the highest occupied and lowest unoccupied orbitals,

respectively, the superscript fn refers to the n-th fragment, and the subscript m refers to a particular orbital on that fragment. We drop the superscript when referring to the supersystem orbitals, which are numbered in order of increasing energy. The layer orbitals involved in the IET, |J|2 , and the energy diagrams are shown in Figure 3. In all cases, the transfer involves two almost degenerate orbitals around 1 eV above Ef 7



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Figure 3: Mean |J|2 for the IET for the single-layer ZnPc over SLG or DLG at sites A, B, and C, together with the corresponding orbital isodensity surfaces and Γ-point energy level f1 schemes. |J|2 refers to the transfer to the Lf1 1 and L2 orbitals localized on graphene. The green levels refer to the orbitals localized on ZnPc, while the gray ones refer to the orbitals localized on graphene. due to the ZnPc layer, and two almost degenerate orbitals close to Ef due to SLG. Two additional almost degenerate states are also created around 0.4 eV above Ef in the DLG case, in agreement with the experimental results of Ref. 38. The calculated mean |J|2 refers to the transfer from the ZnPc layer orbitals to the lowest pair of unoccupied layer orbitals close to Ef , consistently with the experimental conditions reported in Ref. 29. The results showed in Figure 3 are in agreement with experiment: |J|2 is larger with SLG than with DLG in most cases. For ZnPc adsorbed on sites B and C on both SLG and DLG, the calculated |J|2 SLG/DLG ratio is 1.4, in perfect agreement with the experimental ratio of 1.4. 29 Conversely, for ZnPc adsorbed on site A on both SLG and DLG the ratio is 2.9. Only in the case of ZnPc adsorbed on sites B and C for SLG and on site A for DLG, the calculated ratio is 0.8. As discussed above, the most likely scenario is a distribution of adsorption sites, so that the coupling for SLG is on average larger than for DLG. This somewhat surprising rate decrease requires an explicit analysis of the contributions to Eq. 2. We focus on the terms with the largest contribution, i.e. six supersystem orbitals for SLG (H1 , H2 , L1 -L4 ), and ten supersystem orbitals for DLG (H1 -H4 , L1 -L6 ). The individual

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|FijDA |2 are reported in Table S2 of the SI, and the corresponding main terms that contribute to the summation in Eq. 2 are reported in Tables S3-S4 for SLG and DLG, respectively. For f1 −3 conformation A, the largest coupling is Lf2 eV2 for SLG, and 2 →L1 , with values of 19 · 10

4.5 · 10−3 eV2 for DLG. The main contributions to the sum in Eq. 2 for SLG are (in eV)

f1

f1

f1 f2 f2 L1 |H1 εH1 H1 | Lf2 2 = −0.50, L1 |H2 εH2 H2 | L2 = −0.11, and L1 |L4 εL4 L4 | L2 =

f1

f2 f2 0.34 for SLG; Lf1 1 |L2 εL2 L2 | L2 = −0.30, and L1 |L6 εL6 L6 | L2 = 0.16 are the main

contributions for DLG. Thus, even if for DLG more supersystem orbitals contribute to the sum, their overall values are smaller than for SLG. Also, the orbital energies of the dominant terms are basically the same for SLG and DLG (Tables S3 and S4), thus the rate decrease for DLG seems to be due to the smaller overlap between fragment and supersystem orbitals. This is a result of the different orbital pattern in DLG, consisting of considerably more localized orbital lobes than in SLG (Figure 3). The situation is similar for conformation f1 −3 eV2 , while for DLG all of the B, where the largest coupling is Lf2 2 →L2 in SLG: 3.7 · 10

couplings are very small. In the SLG case, the most important terms in the sum in Eq. 2

f1

f2 f2 are Lf1 2 |L2 εL2 L2 | L2 = 0.17 and L2 |L4 εL4 L4 | L2 = −0.14, while for DLG all of the

values are small. As for conformation A, the supersystem orbital energies εΓl are very similar

between SLG and DLG, and the difference is mainly due to the value of the supersystemgraphene fragment overlap. For conformation C the situation is slightly different: the largest f1 coupling is Lf2 2 →L2 as for conformation B, but this time its value is the same for both SLG f1 −3 and DLG: 5.2 · 10−3 eV2 . DLG also has a significant contribution from Lf2 1 →L1 : 2.1 · 10

eV2 . This coupling is small for SLG: 0.2 · 10−3 eV2 . Thus, for C, |J|2 is slightly larger for DLG than for SLG: 2.0 · 10−3 eV2 and 1.5 · 10−3 eV2 , respectively. The largest contributions

f1

f1 f2 f2 f1 for the Lf2 2 →L2 coupling are L2 |L2 εL2 L2 | L2 = 0.34 and L2 |L4 εL4 L4 | L2 = −0.19

f1

f2 f2 for SLG, and they are Lf1 2 |L2 εL2 L2 | L2 = 0.26 and L2 |L6 εL6 L6 | L2 = −0.19 for DLG. In this case, since the values are closer in magnitude, the fact the DLG has more

contributing supersystem orbitals leads to an equal value of the coupling with SLG. For f1 the Lf2 1 →L1 coupling, the cancellation due to the opposite sign of the various terms favors

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DLG over SLG. Although |J|2 is larger for DLG than for SLG in the C conformation, this is isoenergetic with the B conformation, as discussed above, and thus the coupling is averaged between the two (Figure 3), leading to an overall decrease of |J|2 passing from the SLG to the DLG system.

Figure 4: Mean |J|2 for IET for the single-layer ZnPc over TLG and QLG at sites A, B, and C, together with the Γ-point energy level schemes. |J|2 refers to the transfer to the lowest set of unoccupied orbitals localized on graphene. Another issue to address is the IET increase when the ZnPc film is deposited on bulk graphene. We investigate this increase by considering three- and four-layer graphene (TLG and QLG, respectively). For TLG, we consider two stacking configurations: ABA and ABC, while for QLG we only consider the ABAB configuration, as shown in Figure 4 together with the corresponding |J|2 . As shown in the figure, adding more graphene layers increases the number of energy levels above Ef . For TLG(ABA) and for QLG, the repetition of AB stacked layers increases the number of states at the Fermi level, which are the ones that contribute to the IET process. In this case, |J|2 increases compared to that for DLG, although it is still smaller than for SLG. For TLG(ABC), the extra states are considerably above the Fermi level, and do not contribute to the transfer so that |J|2 is comparable to DLG. These results suggest that including more and more layers with the proper relative configuration (ABAB...) does increase the value of |J|2 , and correspondingly of the IET rate, until it 10


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becomes larger than that for SLG. It would be interesting to determine how many layers of graphene are necessary to reach the transition point. Unfortunately, a first-principles calculation beyond four layers is presently prohibitive, and it was shown that even with eight layers the electronic distribution of bulk graphene is not reproduced. 11 Thus, we leave this investigation for future work. The experiments in Ref. 29 also investigated the photophysics of a thick layer of ZnPc (up to 10 nm) on graphene. Although the experiment could not probe what happens at the ZnPc-graphene interface, we want to explore how adding ZnPc layers may affect the IET to graphene. Hence, we performed calculations with a double-layer of ZnPc (shown as 2ZnPC) on SLG and DLG. To the best of our knowledge, no experimental information about the structure of multiple ZnPc layers is available, thus we considered three possible relative conformations between the ZnPc layers: one perfectly-stacked and two translated conformations, all with an interlayer distance of 3.36Å. In the translated configurations, the second layer is moved in the x direction by either 3.69Å (similar to Ref. 39), or by 7.38Å, i.e. half of the lattice vector in the x direction. Since the trends for all three conformations are similar, here we only discuss the perfectly-stacked configuration. The results for 2ZnPc are shown in Figure 5 (the corresponding individual |J|2 for all three configurations are reported in Tables S5 and S6 of the SI). Even though in the double-layer the IET occurs from either of two almost degenerate states, we assume that the intermolecular relaxation within the ZnPc is fast, thus limiting the IET process to the lowest pair of orbitals. Note that |J|2 for the second-lowest pair of orbitals has similar numerical values. A comparison of |J|2 between ZnPc and 2ZnPc (see Figures 3 and 5) shows a decrease in value for the latter by a factor of 2. The |J|2 values for the translated ZnPc double-layer are equivalent to those for the stacked double-layer, as evident from Tables S5 and S6 of the SI. For the IET to SLG and DLG, the same considerations discussed above for the single-layer ZnPc basically also apply for the case of double-layer ZnPc. The |J|2 decrease is due to the fact that in 2ZnPc the fragment orbitals are mostly localized in between the ZnPc double-layer, thus decreasing the

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Figure 5: Mean |J|2 for the IET for the fully overlapped double-layer ZnPc over SLG or DLG at sites A, B, and C, together with the corresponding orbital isodensity surfaces and f1 Γ-point energy level schemes. |J|2 refers to the transfer to Lf1 1 and L2 orbitals localized on graphene. orbital density at the interface with graphene, as shown in Figure 5. This is in qualitative agreement with measurements for the 10 nm thick ZnPc film, 29 where probing the first 2 nm of this layer showed a long-lived ZnPc excited state. It is reasonable to assume that adding further layers beyond the two tested here would create states that are also delocalized across the ZnPc layers, thus further reducing the relative amount of electron density at the interface between ZnPc and graphene, and consequently decreasing the IET rate. We presented the application of a new theoretical approach for predicting the interfacial IET between 2D layers. We studied the IET modulation between a film of ZnPc and graphene as a function of both number of layers and relative position. The results are in line with the experimental trends, thus confirming the validity of the computational model. We show that in addition to the well known orientation dependence, 40–42 the relative position (conformations A, B and C) between the donor and acceptor layers also influences the IET rates as a result of the state mixing. We rationalized the IET changes in terms of the overlap between the supersystem and fragment layer orbitals. We also show that the number and relative orientation of the acceptor layers determine how many acceptor states are available for the IET transfer. This type of analysis may then be employed to study other 2D mate-

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rials, and provide accurate predictions for the development of “bottom up” design strategies in materials design.

Computational Methods All DFT calculations were performed with a development version of the GAUSSIAN suite of programs, 43 using a screened exchange hybrid density functional, HSE06, 44–49 , the 631G(d,p) basis set, and a uniform mesh with 8 × 6 irreducible k-points. HSE06 is a rangeseparated hybrid functional with exact exchange in the short-range, specifically developed for PBC as a good compromise between accuracy and computational cost. The couplings were calculated by using an in-house post-processing code. The ground state geometry of the isolated ZnPc was optimized using the same aforementioned level of theory, whereas the graphene layer(s) were built using the experimental graphite distances, i.e. fixing the C-C distance and the inter-layer distance to 1.42Å, 50 and 3.36Å, 32,51,52 respectively. The orbital isodensity surfaces were generated by using an isodensity value of 0.01 e/Bohr3 .

Acknowledgement C. C. and W. L. C. acknowledge support from US National Science Foundation, grant DMR1351716. A. B. and M. C. gratefully acknowledge partial support from the National Science Foundation under Grant No. OIA-1539105 and from the University of Kansas startup funds.

Supporting Information The Supporting Information reports: the HOCO energies, the band gap for all the graphenebased systems discussed in the article, the values of the individual contribution to the electronic couplings, the corresponding isodensity surface of the corresponding orbitals, the density of states, and all of the unit cell geometries. 13



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How the Number of Layers and Relative Position Modulate the

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