Article pubs.acs.org/JPCC
Effect of van der Waals Interactions on the Adsorption of Olympicene Radical on Cu(111): Characteristics of Weak Physisorption versus Strong Chemisorption Handan Yildirim* and Abdelkader Kara* Department of Physics, University of Central Florida, Orlando, Florida 32816, United States ABSTRACT: We report the results of Olympicene radical (C19H11) adsorption characteristics on Cu(111) obtained within the density functional framework with and without the inclusion of self-consistent van der Waals (vdW) interactions to evaluate their effects. Our calculations suggest that the vdW interactions enhance the adsorption energies, and the degree of enhancement strongly depends on the implementation. Among the considered configurations, the highest adsorption energy calculated using PBE is found to be 0.24 eV, while those obtained with the inclusion of vdW interactions are 1.32 eV (rPW86), 1.91 eV (optPBE), 2.29 eV (optB88), and 2.65 eV (optB86b). The high energetic contribution obtained using the vdW interactions correlates with the changes in the adsorption heights (from 3.4 Å (PBE and rPW86) to 2.24 Å (optB86b)), the change in the structural integrity of Olympicene radical upon adsorption, and the changes in the surface electronic structure. Furthermore, our calculations reveal a net charge transfer of 0.39e− (the highest) from the substrate to the molecule upon inclusion of vdW interactions (opt-type functionals), while no charge transfer is found using PBE and rPW86 functionals. Upon adsorption, an interface state at about 0.6 eV below the Fermi level is observed, along with a noticeable change in the position of the d-band center and width only when the vdW interactions (opt-type) are considered. These significant changes can be considered as strong indications of a transition in the nature of bonding from the weak physisorption to strong chemisorption. Our results reveal the unavoidable importance of the self-consistent vdW interactions for an accurate description of adsorption characteristics of organic species on metal substrates, and further provide a minimal list of characteristics to be considered for distinguishing the weak physisorption from strong chemisorption.
I. INTRODUCTION Organic materials show a promising alternative for the fabrication of flexible, lightweight, low-cost, and durable electronic devices.1 Their adsorption on metal substrates and the characteristics of the interface are of technological importance. It is well established that the carrier injection barrier at the organic/metal interface is strongly related to the device performance.2 This so-called Shottky-barrier height (SBH) has been widely studied3 and is known to control the electronic transport across the metal−semiconductor interface. It was demonstrated that the SBH depends “sensitively” on the interface characteristics (atomic and electronic).3 Thus, it is important to explore the details of the interface characteristics to gain a fundamental understanding of the key issues, which ultimately affect the performance of organic materials-based devices. The adsorption characteristics of organic species on metal surfaces depend mostly on the nature of the bonding. These characteristics can help to distinguish strong chemisorption (binding energies from several hundreds of millielectronvolts to a few electronvolts) from weak physisorption (binding energies from a few millielectronvolts to few hundreds of millielectronvolts), for example. The challenge in this context is to construct a minimal list of characteristics © 2013 American Chemical Society
applicable to many adsorption systems that could help in identifying and/or classifying the nature of the bonding with the substrates. As for small molecule adsorption such as CO, H2, and CH4 on metal surfaces, the knowledge of adsorption energy alone for most cases is sufficient to distinguish between physisorption (i.e., H2 on Cu(100) and Cu(110) with the experimental binding energy of 22 meV4) and the chemisorption, such as CO adsorption on Cu(100) and (110) with the calculated adsorption energies in the order of several hundreds of millielectronvolts.5 However, for large organic molecule adsorption in which many atoms contribute to the bonding with the substrate, the simple definition used for small molecules can no longer be sufficient to classify the nature of the bonding. Additionally, upon adsorption, some large molecules experience structural changes such as bending (observed mostly for chemisorbed systems, particularly for the adsorption on transition metal surfaces) resulting in nonequivalent contribution to the adsorption energy. Furthermore, even the definition of adsorption energy per atom Received: November 17, 2012 Revised: January 24, 2013 Published: January 28, 2013 2893
dx.doi.org/10.1021/jp311361e | J. Phys. Chem. C 2013, 117, 2893−2902
The Journal of Physical Chemistry C
Article
within generalized gradient approximation (GGA) in the form of Perdew−Burker−Ernzerhof (PBE)23 and also employing the self-consistent24 van der Waals density functional (optPBE,25 optB88,25 optB86b,26 and rPW8627,28), as it is known that inclusion of vdW interactions, in general, contributes substantially to the adsorption energies. We demonstrate here that a minimal list of adsorption characteristics, although they are not novel and may not be exhaustive, can indeed be instrumental to distinguish between physisorbed and chemisorbed systems. We note that not all of the characteristics explored here may be required for classifying the nature of bonding for other molecules/metals systems, and for some other systems, they may not be complete. Nevertheless, the list combines at least the most common features that are expected to be present for distinguishing the bonding nature of organic molecule with metal substrates. Below, after a brief introduction of the computational methods, and the calculation details, we will first report the adsorption geometries, adsorption energies, and electronic structure characteristics including interface states, charge transfer, and the changes in the d-band center position and width obtained using PBE and the vdW functionals. We will then provide the discussions on the performance of these functionals, and finally summarize our findings in the Conclusion.
may no longer be relevant when large molecules are considered. Thus, it is of interest to study the nature of bonding for large molecule adsorption on metal substrates. In this work, we attempt to use a minimal list containing the geometric, energetic, and electronic structure characteristics to explore the nature of bonding for the adsorption of Olympicene radical (C19H11, the radical of the Olympicene molecule C19H12) on a close packed Cu(111) surface. For evaluating the geometric characteristics, we explore the structural modifications upon adsorption on Cu(111) surface, and determine whether there are structural changes such as bending, tilting, or both. Note that bending for some cases requires a substantial amount of energy, which may be accommodated in the presence of strong bonding. Thus, we will use bending as the first characteristic for our proposed minimal list. The second characteristic for the minimal list is the adsorption height, which is in general known to be large for weak physisorption (i.e., >3 Å), and small for strong chemisorption, in the order of ∼2 Å. The last geometric characteristic of the list is the buckling of the surface atoms that is shown to be present for chemisorbed systems.6 For chemisorption, one expects the energy levels to be affected leading to splits, shifts, and the broadening of the molecular orbitals, indicating strong hybridization with the substrate states. One of the consequences of these electronic structure changes is the appearance of interface states near the Fermi level. Thus, our test will include exploring the existence of potential interface state as a parameter in classifying the nature of bonding. Additionally, upon adsorption, the changes in the position of the d-band center (i.e., shifts toward higher and/or lower binding energies) and in the d-bandwidth will be explored, as these changes may be helpful to measure the degree of hybridization with the adsorbed species orbitals. Finally, it is expected that the electron donations and backdonations may result in a net charge transfer between the adsorbate and the substrate, implying a chemisorbed system. The proposed list of minimal characteristics is tested for the Olympicene radical (C19H11) adsorption on Cu(111) to illustrate our points, and to construct a concrete list of characteristics to distinguish physisorption from chemisorption. The Olympicene molecule (C19H12) and its radical (C19H11) have recently been synthesized, and observed experimentally using the atom field microscopy (AFM) by the research groups in the University of Warwick and the IBM-Zurich.7 The resulting AFM images of the adsorbed Olympicene radical on Cu(111) show brighter edges both at the two rings region and the edges,7 indicating that the molecule undergoes structural changes identified as the bending and tilting. We will show hereafter that our calculations well produce the experimentally observed characteristics when the vdW interactions are taken into account. Olympicene, similar to pentacene (C22H14), is suggested to be a good candidate for organic-based devices with promising electronic and optical properties. Thus, it is highly desirable to explore the atomic and electronic structures of the interface with metal surfaces for better assessing its potential. Note that the importance of an accurate inclusion of van der Waals (vdW) interactions to obtain reliable adsorption energies associated with the processes for which the standard density functional theory (DFT) schemes predict weak binding has been demonstrated with the recent advances in the field for the adsorption of many organic molecules on metal substrates.8−22 To illustrate our points for distinguishing physisorption from chemisorption, we performed calculations using both DFT
II. COMPUTATIONAL DETAILS First-principles calculations have been carried out within the periodic DFT framework, as embodied into the Vienna ab initio Simulation Package (VASP)29 version 5.2.12 to explore the adsorption characteristics of Olympicene radical on Cu(111), including adsorption geometry, adsorption energy, charge transfer, the interface electronic structure, and to evaluate the effects introduced by the vdW interactions, and the comparison of the performance of these implementations. The calculations are performed first using the GGA for comparison with those obtained by including the nonlocal interactions through the self-consistent van der Waals density functional theory (optPBE,25 optB88,25 optB86b,26 and rPW8627,28) as implemented in the VASP package.29 The interaction between the valence electrons and ionic cores is described by the projector augmented wave (PAW) method.30,31 A kinetic-energy cutoff of 400 eV is used for the wave functions, and Brillouin zone is sampled using 4 × 4 × 1 k-point meshes. The optimization of total energies for each adsorption configuration is performed using the Conjugated Gradient (CG) algorithm with the force criterion on each atom set for the convergence to be 0.02 eV/Å. The calculated Cu lattice constants are 3.635 Å, 3.648 Å, 3.626 Å, 3.598 Å, and 3.747 Å using PBE, optPBE, optB88, optB86b, and rPW86, respectively, and they are in excellent agreement with those reported elsewhere.26 The Cu(111) surface is modeled with six layers for all of the ⎡5 0⎤ vdW calculations each containing 30 Cu atoms (in a ⎢ ⎥ ⎣− 3 6 ⎦ structure), and the supercell contains a vacuum region of 23 Å separating the two surfaces. The molecule is adsorbed only on one side of the surface. Upon adsorption of the molecule, the bottom three layers of the surface are fixed, and the top three layers are allowed to relax. In all of the calculations, the molecule is brought to the surface at a distance of 3.8 Å, in a flat configuration, as is found in the gas phase. Most of the PBE calculations are performed using the four layers slab, and two 2894
dx.doi.org/10.1021/jp311361e | J. Phys. Chem. C 2013, 117, 2893−2902
The Journal of Physical Chemistry C
Article
Figure 1. Schematic description of translation (from (a) to (b)) and rotation (from (a) to (c)) for searching different adsorption configurations starting from an initial configuration. The red and pink colors represent C and H, while gray and light blue are the first and second layer Cu atoms, respectively.
Figure 2. Optimized adsorption geometries for the Olympicene radical on Cu(111). The adsorption geometries were obtained using optPBE, optB88, optB86b, and rPW86 functionals for (a) configuration 1, (b) configuration 2, (c) configuration 3, (d) configuration 4, and (e) configuration 5. The adsorption geometries obtained using PBE for (f) configuration 1, (g) configuration 2, (h) configuration 3, (i) configuration 4, (j) configuration 5, (k) configuration 6, and (l) configuration 7. Gray and light blue spheres represent the first and the second layer Cu atoms, while red and pink spheres are C and H atoms, respectively.
bottom layers are fixed upon adsorption. The convergence test with six layers slab shows that the contribution to the calculated adsorption energy is only 30 meV; hence the results of the four layers slab are sufficient. Let us note that for Olympicene radical there are no welldefined high-symmetry adsorption sites on the (111) surface. For the calculations using the vdW functionals, several adsorption geometries are obtained by performing rotations and translations starting from an initial configuration (Figure
1a), followed by full relaxation. The adsorption geometries determined by translations consist of displacing the molecule in such a way that some well-chosen C atoms (see Figure 1a, atom labeled with T is used for translation, while those R1 and R2 are for rotations) would be moved in four different ways: (i) to occupy the nearest (left) atop site; (ii) to occupy the fcc site with the rings surrounding the atop sites; (iii) to occupy the fcc sites with the rings surrounding the fcc sites; and finally (iv) to occupy the atop sites below the initial configuration. 2895
dx.doi.org/10.1021/jp311361e | J. Phys. Chem. C 2013, 117, 2893−2902
The Journal of Physical Chemistry C
Article
Table 1. Comparison of the Adsorption Energies (Ead), Adsorption Heights (Had), Tilt Angle (α), Bending (Δz), and Buckling of the First Layer Cu Atoms Obtained Using PBE and optPBE, optB88, optB86b, and rPW86 Functionals for Different Adsorption Configurationsa method
conf.
Ead (eV)
Had (Å)
α (deg)
Δz (Å)
buckling (Å)
PBE
1−7 1, 2 3 4 5 1, 2 3 4 5 1, 2 3 4 5 1 2 3 4 5
0.18−0.21 1.32, 1.32 1.31 1.29 1.30 2.29, 2.29 2.12 2.06 2.14 2.65, 2.65 2.42 2.31 2.42 1.91 1.91 1.80 1.78 1.79
3.11−3.34 3.33 (3.35) 3.34 (3.42) 3.40 (3.41) 3.39 (3.40) 2.33 (2.43) 2.46 (2.53) 2.58 (2.65) 2.37 (2.49) 2.26 (2.35) 2.23 (2.34) 2.41 (2.50) 2.29 (2.41) 2.34 (2.46) 2.43 (2.47) 2.72 (2.77) 2.86 (2.89) 2.68 (2.76)
4.7−6.0 1.9, 1.8 0.9 1.2 1.0 6.9, 6.0 5.9 3.8 5.0 4.5, 5.0 5.7 3.9 4.9 7.2 8.0 4.3 3.2 3.5
0.02−0.07 0.02, 0.01 0.02 0.02 0.03 0.08, 0.09 0.12 0.03 0.16 0.07, 0.09 0.13 0.03 0.09 0.15 0.14 0.09 0.02 0.09
0.02−0.04 0.05, 0.06 0.05 0.05 0.05 0.14, 0.14 0.12 0.13 0.19 0.13, 0.13 0.15 0.15 0.18 0.17 0.18 0.09 0.08 0.14
rPW86
optB88
optB86b
optPBE
The adsorption energy Ead is defined as Ead = −(Eolymp/surf − Esurf − Eolymp), where subscripts olymp/surf, surf, and olymp refer to the Olympicene radical on surface system, the clean substrate, and the isolated radical system, respectively. The highest adsorption energy calculated using the six layers slab for PBE is 0.24 eV.
a
rPW86 functionals. For each adsorption configuration, in Table 1, we report the corresponding adsorption energies and adsorption heights, the tilt angle, the bending, and the buckling of the first layer atoms. Note that the buckling of the deeper layers is found to be negligible. The adsorption energies corresponding to each configuration obtained using PBE are found to vary slightly from 0.18 to 0.21 eV using the four layers slab (and the largest adsorption energy obtained using the six layers slab is 0.24 eV), while the adsorption energies obtained using the vdW functionals vary from 1.29 to 1.32 eV (for rPW86), from 1.78 to 1.91 eV (for optPBE), from 2.06 to 2.29 eV (for optB88), and finally from 2.31 to 2.65 eV (for optB86b). Note that the significant enhancement in the adsorption energy upon inclusion of the vdW interactions entirely modifies the nature of bonding from the weak physisorption to strong chemisorption, except for the case of rPW86 functional, as we show hereafter. The largest enhancement in the adsorption energies is obtained using the optB86b functional, while the least is found using the rPW86 functional. This finding is in agreement with those reported in the literature for the performance of these vdW functionals derived for the adsorption of acenes on metal substrates,32,33 and in our recent calculations on the acenes, as well.34 The large difference in the calculated adsorption energies between the optB86 and rPW86 functionals can be tied to the strong repulsive nature of the latter as discussed in the literature.33 The adsorption energies calculated using the other opt-type functionals still suggest chemisorption for the nature of bonding with the calculated energies slightly varying from one implementation to another. Below, we will present further evidence to highlight the differences obtained in the adsorption energies, and the underlying origins of both geometric and electronic structure in nature. Let us now compare the changes in the adsorption geometries of the Olympicene radical upon adsorption calculated using PBE and the vdW functionals to further
As for the calculations using PBE, due to a much shallow potential energy surface, six starting configurations are used by successive 10° rotations. In addition, adsorption sites similar to those obtained with the inclusion of the vdW interactions are also considered. For all seven adsorption geometries using PBE, we find that the adsorption energies do not vary significantly from each other. Although the list of chosen adsorption geometries is not exhaustive, however, we find them to be sufficient to serve for the ultimate goal of this work. For all of the adsorption configurations considered, we calculate the corresponding adsorption energies, charge transfer, the structural changes in the molecule and the surface, and the change in the interface characteristics.
III. RESULTS AND DISCUSSION Below, we summarize the results for the adsorption of Olympicene radical on Cu(111) using PBE and those obtained with the inclusion of vdW interactions to reveal the changes introduced to the adsorption characteristics, and explore the performance of these chosen vdW functionals. In the first section, we summarize and compare the adsorption energies, the adsorption heights, and the structural changes in the molecule obtained using PBE and vdW functionals. In the following section, we discuss how the adsorption modifies the surface electronic structure, and the effects introduced by the inclusion of the vdW interactions. The net charge transfer, the changes in the position of the d-band center and d-bandwidth (as they can be used to measure the interaction strength between the molecule and the surface), and finally the appearance of a new interface state, which suggests a significant overlap between the molecule orbitals and the surface states, are reported. III.1. Adsorption Characteristics. Adsorption Geometries and Adsorption Energies. In Figure 2a−l, we plot the top view of the optimized adsorption configurations for Olympicene radical on Cu(111) using PBE, optB86b, optB88, optPBE, and 2896
dx.doi.org/10.1021/jp311361e | J. Phys. Chem. C 2013, 117, 2893−2902
The Journal of Physical Chemistry C
Article
trace the origin(s) of the significant changes in the adsorption energies introduced by the inclusion of vdW interactions. In Table 1, we present the adsorption heights for all of the configurations that seem to correlate with the strengths of the corresponding adsorption energies. Two types of adsorption heights are evaluated and reported in the table: the first is determined using the Cu surface atom with the highest zcomponent and the C atom with the lowest z-component, while the second (shown in parentheses in the table) is calculated using the averaged z-components of all of the Cu atoms at the top layer, and the lowest z-component of the C atom. The difference between the results is about 0.1 Å or less. From these results, we find that the adsorption heights vary significantly from those obtained using PBE with the inclusion of vdW interactions. Furthermore, among the vdW implementations, the largest adsorption heights are found for the rPW86 functional (from 3.33 to 3.40 Å), while the significant reduction in the adsorption heights is obtained using the optPBE (from 2.34 to 2.86 Å), optB88 (from 2.33 to 2.58 Å), and optB86b (from 2.23 to 2.41 Å) functionals. The variation obtained for the adsorption heights using the same functional results from the different configuration of the atoms associated with the adsorption geometry. Among the considered vdW functionals, the optB86b functional adsorbs the Olympicene closest to the surface, while the rPW86 functional does the opposite. Note that this finding is in agreement with the reports on the performance of this vdW functional.32,35−37 It is suggested that the rPW86 functional, due to its strong repulsive nature, leads to large adsorption heights, and most often gives inaccurate adsorption energies.33 Our results, so far, based on the adsorption energies, also suggest that this functional leads to strong physisorption for the nature of binding, which is significantly different from that found using the opt-type functionals. We will elaborate further in the text on this difference for the adsorption heights, and its consequences on the surface electronic structure, and the correlations with the calculated adsorption energies. The results also indicate that the calculated adsorption energies correlate with the adsorption heights; the closer adsorption of Olympicene radical to the surface resulted higher adsorption energy. The most commonly observed structural changes for organic species upon adsorption on metal substrates are reported to be bending (see Figure 3a), arching, and tilting (see Figure 3b). The bending occurs when the molecule is not adsorbed flat on the surface, with the edge atoms at a larger position than the central atoms, while the arching is just the opposite of bending. For tilting, one side of the molecule adsorbs closer to the surface, leaving the other side to be at a larger distance from the surface. From the optimized adsorption geometries of the Olympicene radical on Cu(111), the tilt angle and the degree of bending are calculated and summarized in the Table 1. The results suggest that the Olympicene radical undergoes an appreciable degree of tilt and bending. The degree of bending and tilting is larger for the opt-type functionals than that obtained using the rPW86 functional, while the PBE results suggest tilting; however, no bending is observed. In Figure 3d, the charge density distribution in a plane above the radical is plotted using the optB86b functional. The red colored areas in the figure are those at which the charge density is the highest in that plane. The figure reveals that tilt of the molecule results in a higher (plane) density at the 2-rings region as this region is at a larger distance from the surface than
Figure 3. Schematic view of (a) bending, (b) tilting, (c) top view of the Olympicene radical adsorbed on Cu(111), and (d) the charge distribution in a plane above the radical. The red colored areas represent higher charge density regions, which are located at larger distance to the surface. These regions also reveal the bending (edges of the three rings) and the tilting (front part of the two rings) of the radical. The tilting and bending are also reported experimentally (see ref 7). The red and pink spheres represent C and H, while gray and light blue spheres are the first and the second layer Cu atoms, respectively. Bending and tilting representations in (a) and (b) are exaggerated in the figures for clarity.
the 3-rings region (see Figure 3c,d). The figure also suggests that the molecule experiences bending identified from higher density region at the two sides of the 3-rings region (see Figure 3c,d). The comparison of the adsorption geometry obtained with that of the AFM7 suggests a very good agreement, particularly for tilting and bending features reproduced in our calculations. Note that adsorption-induced bending of organic molecules has been observed for those chemisorbed systems.6,38 In a thorough analysis of the structural changes in acenes upon adsorption, we observe this to occur systematically when molecules are adsorbed on transition metal substrates.34 Table 1 also summarizes the calculated buckling for the first layer Cu atoms upon adsorption. The degree of buckling may help to assess the interaction strength with the substrate upon adsorption. Our results suggest that the buckling of the first layer obtained using opt-type functionals varies between 0.10 and 0.19 Å (depending on the adsorption geometry), suggesting an appreciable degree of rearrangements of the first layer atoms brought by relatively strong adsorption. On the other hand, our results obtained using PBE and the rPW86 functional show almost no buckling as the Olympicene radical does not adsorb close to the surface as compared to that obtained using the opt-type functionals. This indicates that interaction with the substrate may be described as physisorption by these functionals. III.2. Interface Electronic Structure and Charge Transfer. The change in the position of the d-band center and width upon adsorption of such adsorbates as C, O, N, H, as well as small molecules NO, CO, etc., on metal substrates has been used as a measure to reveal the interaction strength, and the degree of overlap between the adsorbates and the substrates states.39 In the case of strong interaction with the substrate, it was shown that the significant changes to the substrate electronic structure could be obtained appearing as a shift in the position of surface d-band center, and the broadening/ narrowing of the surface d-bandwidth.40,41 In Figure 4a−f, we plot the total d-electronic densities of states (DOS) for the Cu surface atoms of the clean Cu(111) 2897
dx.doi.org/10.1021/jp311361e | J. Phys. Chem. C 2013, 117, 2893−2902
The Journal of Physical Chemistry C
Article
Figure 4. Total electronic densities of states (DOS) for Cu surface atom (a) of the clean Cu(111) calculated using PBE, rPW86, optPBE, optB88, and optB86b, (b) with and without the adsorption calculated using PBE, (c) with and without the adsorption obtained using rPW86, (d) with and without the adsorption obtained using optPBE, (e) with and without the adsorption obtained using optB88, and (f) with and without the adsorption obtained using optB86b functional. The DOS is calculated for the adsorption configuration 1.
and of the Olympicene radical on Cu(111) system calculated using PBE, rPW86, optPBE, optB88, and optB86b, respectively. Our goal is to reveal the changes in the surface electronic structure upon adsorption of Olympicene radical, and compare the effect of the vdW interactions brought by different implementations. This is necessary to evaluate the role and the performance of vdW interactions for accurate description of interface characteristics between the organic adsorbates and the metal substrate. In Figure 4a, we compare the DOS of the Cu surface atoms from the clean Cu(111) obtained using PBE, rPW86, optPBE, optB88, and optB86b. The figure and the calculated d-band features (see Table 2) suggest that rPW86 shows a slight difference from those obtained using the opttype functionals. Comparison of the DOS of the Cu atoms from the clean surface and those from the Olympicene radical adsorbed surface shows no significant change in the surface dband when using PBE (see Figure 4b). With the inclusion of vdW interactions using the rPW86 functional, the DOS features also show no significant change (see Figure 4c). However, the DOS calculated using the opt-type functionals (see Figure 4d− f) indicates that the surface electronic structure is modified noticeably, and that new peaks emerge, d-band positions shift, and the d-band widths are substantially modified. These observations correlate well with the small adsorption heights found using these functionals (see Table 1). Such small adsorption distances to the surface lead to stronger interaction with the surface and change the surface electronic structure. To quantify the changes in the surface electronic structure, and to determine the effect of the vdW interactions, we have calculated the changes in the position of the d-band center and d-bandwidth upon adsorption on Cu(111), and summarized the results in Table 2. For the clean surface, our results suggest that the position of the d-band center shifts toward lower binding energy and the d-bandwidth is narrowed when we use
Table 2. Comparison of the Changes in the Positions of the d-Band Center (Ed) and the d-Band Widths (Wd) With Respect to the Clean Cu(111) Surface, and the Net Charge Transfer Obtained Using PBE, optPBE, optB88, optB86b, and rPW86 Functionals method PBE PBE rPW86
optB88
optB86b
optPBE
conf. Cu(111) 1−7 Cu(111) 1, 2, 3,4 5 Cu(111) 1, 2 3 4 5 Cu(111) 1 2 3 4 5 Cu(111) 1, 2 3 4 5
Ed (eV) −2.39 −2.36 −2.22 −2.29 −2.27 −2.40 −2.52 −2.50 −2.48 −2.50 −2.40 −2.60 −2.59 −2.57 −2.57 −2.55 −2.34 −2.43 −2.43 −2.43 −2.43
to −2.31 to −2.31 to to to to
−2.65 −2.64 −2.57 −2.69
to to to to to
−2.76 −2.75 −2.80 −2.69 −2.78
to to to to
−2.57 −2.48 −2.47 −2.50
Wd (eV) 2.61 2.62 2.40 2.44−2.47 2.43−2.46 2.61 2.71−2.82 2.70−2.79 2.67−2.75 2.70−2.81 2.62 2.86−2.92 2.78−2.91 2.77−2.95 2.75−2.84 2.77−2.90 2.55 2.62−2.72 2.62−2.66 2.62−2.66 2.63−2.68
charge transfer (e−)
