⇦Chinese Physics Letters, 2020, Vol. 37, No. 11, Article code 117301 Quasi-One-Dimensional Free-Electron-Like States Selected by Intermolecular Hydrogen Bonds at the Glycine/Cu(100) Interface Linwei Zhou (周霖蔚)1†, Chen-Guang Wang (王晨光)1†, Zhixin Hu (胡智鑫)2, Xianghua Kong (孔祥华)1,3, Zhong-Yi Lu (卢仲毅)1, Hong Guo (郭鸿)3, and Wei Ji (季威)1* Affiliations 1Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China 2Center for Joint Quantum Studies and Department of Physics, Institute of Science, Tianjin University, Tianjin 300350, China 3Centre for the Physics of Materials and Department of Physics, McGill University, 3600 University Street, Montreal, QC, H3A 2T8, Canada Received 1 September 2020; accepted 23 September 2020; published online 8 November 2020 Supported by the National Natural Science Foundation of China (Grant Nos. 11622437, 11804247, 61674171, and 11974422), the Fundamental Research Funds for the Central Universities of China and the Research Funds of Renmin University of China (Grant Nos. 19XNQ025 and 19XNH066), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB30000000).
†Linwei Zhou and Chen-Guang Wang contributed equally to this work.
*Corresponding author. Email: wji@ruc.edu.cn Citation Text: Zhou L W, Wang C G, Hu Z X, Kong X H and Lu Z Y et al. 2020 Chin. Phys. Lett. 37 117301    Abstract We carry out ab initio density functional theory calculations to study manipulation of electronic structures of self-assembled molecular nanostructures on metal surfaces by investigating the geometric and electronic properties of glycine molecules on Cu(100). It is shown that a glycine monolayer on Cu(100) forms a two-dimensional hydrogen-bonding network between the carboxyl and amino groups of glycine using a first principles atomistic calculation on the basis of a recently found structure. This network includes at least two hydrogen-bonding chains oriented roughly perpendicular to each other. Through molecule–metal electronic hybridization, these two chains selectively hybridized with the two isotropic degenerate Cu(100) surface states, leading to two anisotropic quasi-one-dimensional surface states. Electrons occupying these two states can near-freely move from a molecule to its adjacent molecules directly through the intermolecular hydrogen bonds, rather than mediated by the substrate. This results in the experimentally observed anisotropic free-electron-like behavior. Our results suggest that hydrogen-bonding chains are likely candidates for charge conductors. DOI:10.1088/0256-307X/37/11/117301 PACS:73.20.At, 73.22.-f, 73.63.-b © 2020 Chinese Physics Society Article Text Hydrogen bonds (HBs) have been a hot research topic since their discovery roughly a hundred years ago due to the paramount roles they play in chemistry, physics, material science and many other aspects.[1–6] An HB was thought to be of an electrostatic nature where protons and anions alternately appear and bind together through Coulomb attraction, which implies that HB is, most likely, electric inert and electrons cannot freely flow through HBs. However, this understanding of HBs has been shifted in past decades. Especially in the recent years, direct proofs were obtained from non-contact atomic force microscopic (nc-AFM) measurements[6–8] and combined density functional theory (DFT) calculations.[6,7] All these results suggest that the intermolecular HB is of a covalent characteristic, which indicates that the electrons forming HBs are more delocalized than those for ionic bonds. In addition, the presence of a metal substrate may lead to the electrons of HBs even more delocalized, owing to likely electronic hybridizations between HBs and substrate surface states or to effectively applied in-plane pressure as, for example, recently revealed in BPPA adsorbed on Au(111).[7,9] The influence of charge delocalization in hydrogen bonds to the electronic structures of self-assembled systems would be a very interesting question yet to be answered, although artificial creation and manipulation of electronic states at surfaces were extensively investigated in past years.[10–14] Manipulation of electronic structures of self-assembled molecular nanostructures on metal surfaces has been an interesting research field.[15–20] Despite the multitude of possibilities and complications originating from chemical details of the molecular self-assembled nanostructures, simple but interesting and important electronic behaviors do emerge. For instance, it was experimentally found that self-assembled glycine molecules on the Cu(100) surface show a nearly free-electron-like (FEL) behavior.[16] One of its striking differences from all previously known molecular FEL behaviors[15,18,19] lies in the reported anisotropic effective masses for holes in the glycine monolayer. Such a behavior was detected for unoccupied states near the Fermi level on glycine islands only. Therefore, it is unlikely to come from image-states[19] and seems not to be surface-mediated.[18,21] How is it even possible that an anisotropic molecular FEL behavior emerges by sitting on an isotropic substrate? In this study, we carry out $ab$-initio density functional theory calculations to address the above concern by investigating the geometric and electronic properties of glycine molecules on Cu(100). It is found that the self-assembled glycine molecules form two nearly perpendicular hydrogen-bonding chains in their $p(2 \times 4)$ molecular islands grown on Cu(100), wherein direct inter-molecular electronic interactions take place through hydrogen bonds in both chains. Two the Cu(100) surface states, with different effective masses, are selectively and directionally hybridized with these two perpendicular and distinctly different hydrogen-bonding chains, respectively, resulting in two different electron velocities detected in two different directions inside a glycine overlayer. Methods. Our calculations were carried out using the density functional theory (DFT), the generalized gradient approximation (GGA) for exchange potential,[22] the projector augmented wave method[23] and a plane wave basis set as implemented in the Vienna ab initio simulation package (VASP).[24] Dispersion forces in all calculations were considered at the vdW-DF[25,26] level with the optPBE functional for exchange (optPBE-vdW)[27] and double-checked with the optB88-vdW functional,[27] which were suggested to be suitable for modeling energetic and structural properties of metal-organic interfaces.[9,28] A slab geometry consisting of six layers of Cu atoms and a $2 \times 4$ supercell separated by a 10-layer vacuum region were employed to model the Cu(100) surface. The glycine molecules were put on only one side of the Cu slab and a dipole-correction was applied. A $k$-mesh of $8 \times 4 \times 1$ was used for the surface Brillouin sampling in both structural relaxation and total energy DFT iteration. We verified the convergence of the $k$-mesh by a larger one of $12 \times 6 \times 1$ ($16 \times 8 \times 1$ for checking band-structure convergence). The energy cutoff for the plane waves was up to 400 eV. All the parameters were well checked to ensure a total energy convergence to less than 1 meV per atom. In structural relaxation, all atoms except the bottom three layers of Cu were fully relaxed until the net force on every atom was less than 0.02 eV/Å. The $k$-resolved local partial density of states ($k$R-LPDOS) offers a way to combine the $k$-resolution and the local-resolution of density of states. A very accurate and fully converged charge density of the system was first calculated. Continuing from the previously converged charge density, local partial DOSs were calculated separately at a series of $k$-points in the non-self-consistent manner. This non-self-consistent run not only keeps the correct charge density (and wavefunction) of the previously converged self-consistent run, but also outputs the corresponding LPDOS at different $k$-points. As for the fitting of effective mass, 20 $k$-points, evenly distributed within 0.012 Å$^{-1}$ (0.04 $G$–$Y$ or 0.02 $G$–$X$), were used to fit a parabolic curve with the second-order least square method. Results and Discussion. After a glycine molecule adsorbs on Cu(100), its O–H bond dissociates and the H atom desorbs at room temperature.[16] Figure 1(a) shows the atomic structure of a glycine overlayer in a previously determined structure.[29] The electronic band structures of this overlayer are shown in Fig. 1(b)–1(e). Figure 1(b) plots the hybridized states composed of Cu $p$-states and molecular $p$-states in both the $[\bar{1}10]$ and [110] directions. We also mark the fitted experimental values[16] using blue and red ribbons, respectively. The energies of these two ribbons are shifted upward by 0.02 eV for better illustration of the theory–experiment comparison. This small shift is essentially within the energetic resolution of DFT calculations and STS measurements. Other states in the same energy window are plotted in Figs. 1(c) and 1(d) for directions $[\bar{1}10]$ and [110], while Fig. 1(e) gathers all states appearing in this energy range.
cpl-37-11-117301-fig1.png
Fig. 1. (a) Atomic structure corresponding to the observed $p(2 \times 4)$ superstructure, in which the O–O lines are roughly parallel to the [$\bar{1}$10] direction (longer edge of the supercell). (b)–(e) Calculated band structures (half-filled circles) of the atomic structure in (a). All hybridized $p$-states are shown in (b), other states in [$\bar{1}$10] and [110] directions are shown in (c) and (d), while all calculated data are summarized in (e). The $k$-lattice of the $p$($2 \times 4$) supercell is shown in the inset of (b). The energy in (b)–(e) refers to the Fermi energy. Red down-half-filled and blue up-half-filled circles represent calculated eigenvalues along [$\bar{1}$10] and [110] directions, respectively. Shadows in (b) were fitted from experimental measurements (red and blue for the [$\bar{1}$10] and [110] directions, respectively).
Several key features were observed in order. First, at 0.12 and 0.14 eV, there are two almost degenerate bands denoted: band 1 (BD-1) and band 2 (BD-2) in Fig. 1(b). Away from $k \sim 0$, BD-1 always has a lower energy compared with BD-2 and it thus has a larger effective mass. From the calculated band structure, BD-1 and BD-2 can be found in both the $[\bar{1}10]$ and [110] directions although the corresponding eigenvalues in these two directions have a difference of a few meV. Both BD-1 and BD-2 show parabolic band dispersions, consistent with the two FEL bands observed in the measurements.[16] In particular, BD-1 agrees reasonably well with the measured data along $[\bar{1}10]$ and BD-2 well matches those along [110]. Our calculations show that both the bands are hybridized states originating from the two degenerate surface states of Cu(100) and frontier molecular orbitals of the glycine molecules. The effective masses of BD-1 and BD-2 were found to be 0.62–0.09$ m_{\rm e}$ and 0.062–0.001$ m_{\rm e}$, respectively. These values are quantitatively consistent with the measured value of 0.60$m_{\rm e}$ and 0.06$m_{\rm e} $.[16] Two sets of surface states of Cu(100) were observed in Figs. 1(c) and 1(d), in which we use a slab model for modeling the Cu surface where only one surface was covered by glycine molecules and the other side was a pristine surface. Given the quantitatively consistent band structure and the associated atomic structure, the origin of the FEL electronic structures was unraveled by analyzing partial density of states (PDOS) of the glycine monolayer. Figure 2 plots a local PDOS (LPDOS) of Cu, O, C and N atoms in an energy window from $-0.3$ to 0.7 eV, which shows the origin of hybridized electronic states BD-1 and BD-2. The peak sitting at 0.13–0.14 eV above the Fermi level includes contributions of the two nearly degenerate BD-1 and BD-2 states, which cannot be found in bulk Cu atoms, comprised of hybridized $p$-states of Cu (orange line) and the $p$ states originating from glycine, e.g., from the O (red line) and N (blue line) atoms. There are other three peaks residing at 0.4–0.6 eV. The two sitting at 0.46 and 0.48 eV are Cu bulk states originating from its $d$ and $d$–$p$ orbitals, respectively, while the one at 0.53 eV is an O $p$ state hybridizing with Cu $p$ and $d$ states, which is a localized state not distributing on N atoms. In addition, the predominant Cu 3$d$ contribution indicates that the two bulk states are rather localized compared with states BD-1 and $-2$. Another bulk state, nearly not hybridizing with the molecules, locates at $-0.22$ eV, hybridized with few molecular components. Therefore, the delocalized BD-1 and BD-2 states are most likely responsible for the anisotropy.
cpl-37-11-117301-fig2.png
Fig. 2. Projected density of states (PDOS) at the $\varGamma$ point for Cu 4$p$ (orange), 3$d$ (black), its adjacent O 2$p$ (red) and N 2$p$ (blue).
cpl-37-11-117301-fig3.png
Fig. 3. Projected density of states at different $k$-points for a first-layer Cu atom (a), its adjacent O (b) and N (c) atoms, the red circle (d) and blue square (e) H atoms marked in Fig. 1(a), respectively. Each curve represents the DOS projected on a certain atom for electronic states of a certain $k$-point along the $G$–$X$ ([110]) or $G$–$Y$ ([$\bar{1}$10]) direction. The selected $k$-points run along the $G$–$Y$ direction from the $G$ ($\varGamma$) to the 0.4$Y$ point and along the $G$–$X$ direction from the $G$ to the 0.2$X$ point for the upper and lower panels, respectively. In the $k$-space, the length of 0.4 $G$–$Y$ vector equals the length of the 0.2 $G$–$X$ vector, which roughly equals 0.12 Å$^{-1}$. In this energy range there are some unmentioned bulk states, especially in the Cu atom (a). They show fake anisotropy due to their different slope, which is generated by the band folding in the $p(2\times 4)$ supercell.
We next discuss the $k$-resolved LPDOS ($k$R-LPDOS), which not only inherits the advantages of LPDOS analysis but also offers key electronic information in the $k$-space. We went through the top layer Cu atoms and all representative atoms of the glycine molecule. Figure 3 shows the $k$R-LPDOSs ($s$-states for H and $p$-states for the others) of those atoms, i.e., a surface Cu atom (a), the carboxylic O atom right over the Cu atom (b), the N atom (c), the H atom marked by the red circle (H_ani, d) and the blue square (H_iso, e) in Fig. 1(a). Different curves correspond to different $k$-values along the $G$–$Y$ (upper) or $G$–$X$ (lower) direction. According to the $k$R-LPDOS of Cu [$p$-states, Fig. 3(a)], both BD-1 and BD-2 are clearly identified in each direction. In terms of the O and N atoms [Figs. 3(b) and 3(c)], their $p$ states largely hybridized with the $p$-, $d$- and $s$-states of Cu so that their $k$R-LPDOSs are rather isotropic, namely the $k$R-LPDOS peaks of BD-1 and $-2$ for the $G$–$X$ and $G$–$Y$ directions of the O or N atom develops in essentially the same way as those of the Cu atom. Such behavior, however, differs in the H_ani case. Figure 3(d) shows an anisotropic character along the two directions in the $k$-space that BD-1 (BD-2) is solely observable in the $G$–$Y$ ($G$–$X$) direction, which only appears for this particular H atom (see Fig. S1 in the Supplementary Material) and does not present in other H atoms, e.g., H_is shown in Fig. 3(e). The band dispersions in both the $G$–$X$ ([110]) and $G$–$Y$ ([$\bar{1}$10]) directions were found to be totally consistent with either the band structure calculation of this work or the previous experiments.[16] The anisotropic $k$R-LPDOS dispersion relation found for H_ani in the $k$-space suggests that this H atom plays a crucial role for the formation of the anisotropic FEL behavior in glycine/Cu(100).
cpl-37-11-117301-fig4.png
Fig. 4. Real space distributions of bands BD-1 [(a)–(d)] and BD-2 [(e)–(h)]; at a point in the $G$–$X$ direction [(a), (b), (e), (f)] and another point in the $G$–$Y$ direction [(c), (d), (g), (h)]. Colors in all isosurface plots are adopted only to stand out vertical difference of isosurfaces. Here (a), (c) (e) and (g) are top views of the real space distributions of states BD-1 and BD-2 with isosurface set at 0.004$e$/Å$^{3}$. This relatively large isosurface value makes the information from Cu surface stand out. Also, (b), (d), (f) and (h) are top views of the states BD-1 [(b), (d)] and BD-2 [(f), (h)] in comparison to atomic structure models. The isosurface value for these four panels is 0.0001$e$/Å$^{3}$, which provides much more information concerning glycine molecules. Illustration of two hydrogen-bonding chains by red and blue dashed-ellipses (i). The H atoms highlighted by black circles are H_ani atoms.
Figures 4(a)–4(d) plot the top views of the spatial distributions of the wavefunction norms of state BD-1 at two points in $G$–$X$ [Figs. 4(a) and 4(b)] and $G$–$Y$ [Figs. 4(c) and 4(d)] directions, respectively, to illustrate the paramount role that the H atom plays in the real space. State BD-2 is visualized in Figs. 4(e)–4(h) with the same scheme. Figures 4(a), 4(c), 4(e) and 4(g) show the visualized BD-1 and BD-2 in the $G$–$X$ and $G$–$Y$ directions, respectively, with a rather large isosurface value ($4\times 10^{-3} e$/Å$^{3}$). Therefore, only the features close to the Cu surface are clearly seen in these plots without loss of generality. It is very interesting that these visualized wavefunction norms show a degree of quasi-one-dimensional (Q1D) characteristics. Here, we use Fig. 4(a) as an example. It shows several pipelines extending parallel to the [110] direction. In comparison with the atomic structure shown in Fig. 4(b), the pipelines are over the interstitial region of surficial Cu atoms and some connections between the pipelines are observable on top of the Cu atoms. These features suggest the delocalized nature of BD-1 and BD-2 again. These components contributed by Cu surface atoms are Q1D in BD-1 and BD-2, a previous work[30] thus attributed the anisotropic behavior solely to the role of surface state with an improper structure.[29] Here, we emphasize that those surface states are “isotropic” in both the $k$-space and the real space, and the anisotropy is determined by the hydrogen bond networks. The wavefunction norm of BD-1 at a $k$ point within the $G$–$X$ vector [Fig. 4(a)] exhibits a Q1D feature with the 1D direction parallel to the [110] direction, corresponding to the $G$–$X$ direction in the $k$-space. It indicates that the pipelines visualized in the norm are “parallel” to the corresponding real-space vectors of the $k$-vectors. If the plotted $k$ point is in the $G$–$Y$ direction [Fig. 4(c)], the same conclusion claimed for the $G$–$X$ direction still holds its validity. Similar results also apply to BD-2. The only difference lies in that those pipelines are not parallel but are perpendicular to the associated directions of the $k$-vectors in BD-2. These findings keep most of the isotropic Cu surface characteristic (see Fig. S2 in the Supplementary Material), together with the $k$R-LPDOS results, essentially ruling out the responsibility for the anisotropic FEL behavior from the Cu surface states. We thus focus on the molecular side for the visualized wavefunction norms of BD-1 and BD-2. The norm contours, with an isosurface value of $1\times 10^{-4} e$/Å$^{3}$, of BD-1 in the $G$–$X$ and $G$–$Y$ directions are depicted in Figs. 4(b) and 4(d), respectively, together with the glycine/Cu(100)-$p$($2 \times 4$) atomic structures shown on their right sides. We plot the wavefunction norms of BD-2 with the same scheme in Figs. 4(f) and 4(h). The wavefunction norm of BD-1 along $G$–$X$ looks very similar to that of BD-2 along $G$–$Y$, in analogue to the cases of the Cu surface components of BD-1 and BD-2, e.g., Figs. 4(a)–4(g) and Figs. 4(c)–4(e). A key difference is, however, found between the Cu and molecular cases. In particular, BD-1 in the $G$–$X$ direction is a rather localized state for the molecular case, in which only one appreciable overlap between two adjacent molecules is observable within the two adjacent O atoms (highlighted in blue dashed ellipse) while both Cu wavefunctions are highly delocalized. In contrast, state BD-1 in the $G$–$Y$ direction, as shown in Fig. 4(d), is delocalized so that several overlaps are found between adjacent molecules (indicated by red dashed-ellipses). In short, the molecular component of BD-1 is anisotropic, namely localized along the [110] direction but delocalized along [$\bar{1}$10], which is distinctly different from those contributed from the Cu surface where both directions are delocalized. A similar observation, but with inverse directions, is made for BD-2 that the glycine component is delocalized along the [110] direction but localized along [$\bar{1}$10]. According to the real-space atomic structures, the inter(intra)-molecular hydrogen bonds should correspond to these overlaps. A remarkable finding is that a few hydrogen bonds appear to form two zig-zag hydrogen-bonding chains [Fig. 4(i)]. One is orientated parallel to the [$\bar{1}$10] direction [corresponding to $G$–$Y$ in the $k$-space, Figs. 4(d) and 4(i), in red] and the other is parallel to the [110] direction [$G$–$X$ in the $k$-space, Figs. 4(f) and 4(i), in blue]. Therefore, this anisotropy of delocalization is, most likely, responsible for the experimentally observed anisotropic FEL behavior, which is a result of the hydrogen-bond-induced direct wavefunction overlap in a particular direction, consistent with the $k$R-LPDOS of the H_ani atom. The hydrogen-bonding chains are formed by O, N, and H atoms. It is necessary to unveil the reason why the N and O atoms do not exhibit anisotropy in the $k$R-LPDOS. We find that N and O atoms strongly hybridize with the two degenerate isotropic surface states of Cu(100). Such a strong hybridization gives rise to the two almost isotropic FEL hybridized states [see Figs. 3(b) and 3(c)] and the band folding of substrate states does not account for the anisotropy. The H_ani atom is unique in that it has no direct interaction with the Cu surface states but does have inter (intra)-molecular electronic interactions through different hydrogen-bonding chains in the two different directions. The arrangement of the hydrogen-bond networks is highlighted in Fig. 4(i) to illustrate the intermolecular interactions. These two chains are orientated parallel to the [$\bar{1}$10] (red ellipses) and [110] (blue ellipses) directions, respectively. Very impressively, the H_ani atom is involved in both chains and is the only nodal point of these two chains. This good consistency confirms our findings of the anisotropic FEL behavior and the hydrogen-bonding chains again. Other states, such as hybridized $d$–$p$ states, lack delocalized characteristics and thereby cannot span several H atoms to form an FEL state. In light of this, only BD-1 and BD-2 exhibit electronic anisotropy as detected by the STM experiment.[16] In conclusion, we have found that the glycine overlayer adsorbed on Cu(100) forms two quasi-one-dimensional hydrogen-bonding chains. These two chains are approximately perpendicular to each other and joint at the H_ani atom. Molecular states of glycine hybridize with two degenerate isotropic surface states of Cu(100), forming two ideally isotropic hybridized surface-like anti-bonding states. These two states are interfacial states and are fully delocalized at the glycine-Cu interface. However, the localization of these two states is governed solely by the glycine formed hydrogen bond chains in which each chain allows delocalization in only one of the two states among the glycine molecules. This thus results in the experimentally observed anisotropic FEL behavior with different electron effective masses in the two directions. This mechanism was found to be responsible for the FEL electron motion being distinct from other mechanisms, e.g., the substrate-mediated FEL electron motion mechanism[18] or interfacial state mechanism formed between the metal surface states and molecular $\pi$ state,[21] in PTCDA/Ag(111). Although the PTCDA[31] and glycine overlayers both contain COO groups, the O-Metal bonding is a rather localized sigma bond in the present case while the PTCDA case is of a delocalized $\pi$ characteristic. In short, the newly unveiled mechanism indicates that hydrogen bonds can act as ``channels`` to delocalize electrons, making the whole system exhibit free-electron-like characteristics in specific directions. Although the conductive monolayer overlayer may not be directly resulted from the hydrogen bond networks, they do actively participate in forming the interfacial free-electron-like states and largely determine their properties, e.g., effective masses. This result refreshes the understanding of hydrogen bonds, especially for the role in carrying near-freely moved carriers at metal-organic interfaces. Hydrogen bonds are of crucial importance and of high flexibility in building nanostructures. We believe this work may stimulate substantially following studies in terms of delocalized electronic states in artificially made nanostructures. Calculations were performed at the Physics Lab of High-Performance Computing of Renmin University of China and the Shanghai Supercomputer Center. 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