Conference-ISSS-6-Density Functional Theory Calculation for Magnetism of Fe-Phthalocyanine Molecules on Au ( 111 )

We investigated the electronic and magnetic states of Fe-phthalocyanine (FePc) molecules adsorbed on Au(111) using density functional theory. Comparing two exchange correlation functionals with and without +U correction, we found that the electronic configuration and magnetic moment of FePc in the gas phase are well reproduced by local density approximation (LDA) + U method. For FePc on Au(111), the residual magnetic moments of the molecule calculated by LDA and LDA+U are different, which originates from the difference in charge transfer described by two methods. We also found that the magnetic moment for the bridge configuration is smaller than that for the ontop configuration reflecting the local symmetry. [DOI: 10.1380/ejssnt.2012.38]


I. INTRODUCTION
The adsorption of molecules at metal surfaces has long attracted much attention because the bonding interactions between the molecule and the surface strongly influence the characteristics of the molecule such as geometrical structure, charge state, and magnetism.It is crucial to uncover the underlying mechanisms on how the couplings at the molecule-metal interface affect these characteristics from both fundamental and industrial points of view.Magnetic molecules adsorbed on metal surface offer the opportunity to consider the effect of the interface couplings on the spin degree of freedom.One of the intriguing phenomena brought about by the coupling of magnetic molecule with metal surface is the Kondo effect [1,2].Recently, several works about the adsorption of magnetic molecules at metal surfaces have reported on the formation of the characteristic ground state from the Kondo effect, Yosida-Kondo singlet.The Yosida-Kondo singlet appears as a sharp peak or dip near the Fermi level in the scanning tunneling spectroscopy (STS) spectra [3][4][5].
Here we focus on Fe-phthalocyanine (FePc) molecule on Au(111).To understand the magnetism of FePc on Au(111), it is crucial to unveil the geometric and electronic configurations of FePc on Au(111) and their correlation with the magnetism.However, this is challenging because of the complexity in magnetism of the FePc molecule.The magnetism of FePc has long been controversial both theoretically and experimentally [6][7][8][9][10][11][12][13][14][15][16].It has been widely accepted that FePc in the gas phase takes spin triplet (S = 1) derived from the electronic configuration of (3d) 6 .However, regarding the multiplet state of S = 1, a series of experimental and theoretical investigations have showed inconsistent results.The recent X-ray Absorption Spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) works [9][10][11] indicate that the plausible multiplet state is 3 E g state represented by (d z 2 ) 1 (d xy ) 2 (d π ) 3 , where d zx and d yz orbitals are described as d π .The previous density functional theory (DFT) calculations show that the exchange correlation functional strongly affects the electron filling of d-orbitals [14][15][16].In addition, DFT+U has recently achieved improvement in the treatment of electron correlation effect in d-electron systems [17,18].Thus, it would be beneficial to compare the DFT calculation results for FePc using typical exchange correlation functionals, such as local density approximation (LDA), generalized gradient approximation (GGA) with and without +U correction.From this point of view, we carried out the DFT calculation for (i) the gas phase FePc molecule using LDA, LDA+U, GGA, and GGA+U, (ii) FePc on Au(111) using LDA and LDA+U.

II. METHODS
The DFT calculations were performed by the plane-wave-based Vienna Ab initio Simulation Package (VASP) [19,20] with the projected augmented wave (PAW) method [21].The exchange and correlation were described at the level of LDA and GGA.We used the exchange-correlation functional determined by Ceperly and Alder [22] and parameterized by Perdew and Zunger [23] for LDA.For GGA, we used the exchange-correlation functional determined by Perdew-Burke-Ernzerhof [24].For DFT+U, we employed the method by Dudarev et al. [18].The adsorption of FePc on the Au substrate was modeled by (8×8) supercell, which consists of a FePc on a 3-layer Au slab and a vacuum of ∼15.6 Å thick along the surface normal.The atoms of the bottommost Au layer were fixed at their ideal bulk positions during the structure optimization.The positions of atoms in FePc and the top two layers of Au slab were optimized without any constraint until the forces on individual atoms were less than 0.02 eV/ Å.Because of the large size of the supercell, the Brillouin zone was sampled with a k-point only at Γ point.

A. Suitable exchange correlation functional for gas phase FePc molecule
Figure 1 shows the local density of states (LDOS) projected on Fe d-orbitals calculated for FePc in the gas phase by using LDA, LDA+U, GGA, and GGA+U.In the +U calculations, the on-site electron-electron interaction is corrected by the effective on-site Coulomb and exchange interaction parameter, U and J.According to the Dudarev method, only the difference between U and J is meaningful.We found that the U − J = 1.0 to 4.0 eV provides similar results on the filling of the d-orbitals.Thus, here we use U = 2.0 eV and J = 1.0 eV.The total magnetic moment of ∼2µ B was obtained commonly by the four methods.However, the electronic configurations are quite different.The LDA calculation without +U correction does not reproduce the electronic configuration of ( A striking difference appears in the electronic configuration in LDA and GGA calculation.The possible origins of this discrepancy are the difference in optimized structures and characteristics of exchange correlation functional.First, we compare the optimized structures obtained by GGA and LDA.We found that the FePc molecule keeps D 4h symmetry after structural optimization in both GGA and LDA calculation, although the bond lengths in the FePc molecule differ in GGA and LDA calculation results.We summarized typical bond lengths in the FePc molecule in Table I  dicated in Fig. 2. To clarify whether the optimized structures or characteristics of exchange correlation functional are essential to electronic configuration, we performed the LDOS calculation by LDA with the structure optimized by GGA.As shown in Fig. 3, obtained LDOS is almost the same as the LDA calculation results in Fig. 1.This indicates that the characteristic of exchange correlation functional is more dominant in electronic configuration than structural difference.From these results, we concluded that the choice of exchange-correlation functional is essential to reproduce the electronic configuration in FePc molecule, and LDA+U is the most suitable to treat the magnetism of FePc molecule.

B. Electronic states of FePc on Au(111)comparison between LDA and LDA+U
First, we determine the stable adsorption structure.The candidates of adsorption sites on Au(111) are ontop, bridge, hcp-hollow and fcc-hollow sites.We performed structural optimization calculations for each adsorption site with several molecular orientations using LDA and LDA+U.The stability of the FePc molecule at each ad-  sorption site can be estimated by the value of adsorption energy E ad , which is defined as where, E sub is the total energy of Au(111) substrate, E mol is the total energy of isolated FePc molecule and E tot is the total energy of the FePc on Au(111).We found that the adsorption at the hcp-hollow site is less favorable than at the ontop site by 48 meV (LDA) and 42 meV (LDA+U), and much less at fcc-hollow site.From these reasons, we limit our discussions to the ontop and bridge adsorption configurations hereafter.Figure 4 shows the stable adsorption structures of the ontop and bridge configurations.In the ontop site, the FePc molecule adsorbs with its mirror plane rotated by 15 degrees from the [11 2] direction of Au(111).In the bridge site, the mirror plane is parallel to the [11 2] direction.Table II summarizes the results calculated for each adsorption configuration.It clearly shows that the overall tendency in adsorption energy is similar in LDA and LDA+U results, and that the ontop configuration is more stable than the bridge configuration.This is consistent with the previous results by STM [5].
The remarkable difference between LDA and LDA+U appears in magnetic moment.In the LDA, the magnetic moment decreases drastically and becomes nearly half of that for the gas phase FePc.On the contrary, in LDA+U, the magnetic moment is close to that of the gas http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/)

e-Journal of Surface Science and Nanotechnology
Volume 10 (2012)  phase FePc.The plausible origin of larger decrease in the magnetic moment for the former is the disadvantages in LDA, which causes the overestimation of the admoleculesubstrate bond strength and the underestimation of the on-site electron-electron interaction [17,25].As shown in Table II, the adsorption energy calculated by LDA is greater than that by LDA+U.The Bader analysis for the number of electrons at the Fe atom (Table III) indicates that the adsorption on Au(111) causes the charge transfer from Au(111) to FePc molecule both in the LDA and LDA+U calculations.The differential charge distribution shows that the charge transfer mainly occurs between the Fe d-orbitals and Au(111) for both ontop and bridge configurations (Fig. 5).The charge transfer shown in Fig. 5 is different between LDA and LDA+U.In LDA+U, a clear charge decrease region with a cross form appears around the Fe atom.Meanwhile, the charge decrease region around the Fe atom is ambiguous.To obtain more detailed insight on the charge transfer, we calculated the LDOS of Fe d-orbitals.calculated by using LDA and LDA+U, respectively.In both methods, the Fe d z 2 orbital obtains electrons from Au(111).However, the direction of the charge transfer for the d π orbitals by LDA is opposite to that by LDA+U.In LDA, d π orbitals obtain electrons from Au(111) similarly to the d z 2 orbital, whereas the d π orbitals donate electrons to Au(111) in LDA+U.This difference in charge transfer in d π orbitals provides different magnetic moments obtained by two methods.We concluded that the disadvantages of the LDA treatment causes the overestimation of charge transfer between the Fe atom and Au(111), which results in the underestimation of the residual magnetic moments.This indicates that the LDA+U is more suitable than LDA for the description of the magnetism of FePc on Au(111).
Another interesting point is that the residual magnetic moment depends on the adsorption site.In the ontop site, the residual magnetic moment is larger than that in the bridge site.This can be explained by the LDOS of d zx and d yz orbitals.In the ontop site, the peaks associated with the d zx and d yz orbitals almost overlap and the degeneracy in d zx and d yz orbitals in the isolated FePc survives on Au(111).However, these peaks are separated by ∼100 meV in the bridge configuration and the degeneracy is lifted.In addition, the width of the d zx orbital is broader than that of d yz orbital.These features observed for the ontop and bridge configurations can be understood by the bonding nature and the local symmetry.
As shown in the differential charge distribution (Fig. 5), a bond forms only between the Fe atom and the Au atom beneath for the ontop configuration.Because this bond extends perpendicularly to the surface, it preserves the symmetry within the molecular plane.Thus, the local potential around the Fe atom in the ontop configuration keeps the 4-fold symmetry similar to the gas phase FePc molecule.On the contrary, the bonds form between the Fe atom and the two nearest-neighbor Au atoms in the bridge configuration.Thus, the symmetry of the local potential around the Fe atom reduces to the 2-fold symmetry in the bridge configuration.The difference in the peak width between d zx and d yz orbitals in the bridge configuration can be explained by the different coupling strength of these orbitals with the nearest-neighboring Au atoms.The d zx orbital extends its lobes along [11 2] direction and is strongly coupled with the Au atoms while the d yz orbital extends in the direction orthogonal to the [11 2] direction, resulting in the weaker coupling.The stronger coupling of d zx orbital leads to the larger charge transfer from Au(111) to the d zx orbital, which quenches the magnetic moment of Fe.
Finally, we comment on the relation of these results with the site specificity of the Kondo signature.It is known that the orbital degeneracy strongly affects the Kondo temperature.Our results show that the degeneracy of d zx and d yz orbital differs at the ontop and bridge site, which is the promising origin of the site specificity.http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology

IV. CONCLUSION
We carried out the DFT calculations for the gas phase FePc molecule and FePc adsorbed on Au(111) and compared the electronic configurations and magnetic moment calculated by exchange correlation functionals with and without +U correction.We found that the magnetic state in the gas phase FePc molecule is well reproduced by LDA+U.For FePc on Au(111), the residual magnetic moments calculated by LDA and LDA+U differ from each other, which originates in the difference in the charge transfer between FePc and Au(111).We also found that the magnetic moment of FePc in the bridge configuration is smaller than that in the ontop configuration because of the local symmetry.

FIG. 1 :
FIG. 1: Comparison of the local density of states (LDOS) projected on the Fe d-orbitals in an FePc molecule in gas phase calculated by A) LDA, B) LDA+U (U = 2.0 eV and J = 1.0 eV), C) GGA, and D) GGA+U (U = 2.0 eV and J = 1.0 eV) calculations.The LDOSs of dzx and dyz overlap each other reflecting the D 4h symmetry of the molecule.
[9][10][11] because the d xy , d π and d z 2 orbitals are distributed near the Fermi energy, resulting in the different configuration.In contrast, the LDA+U calculation separates them reasonably to reproduce the (d z 2 ) 1 (d π ) 3 (d xy ) 2 configuration.On the other hand, both GGA and GGA+U methods yield the similar configuration described approximately as (d z 2 ) 1 (d xy ) 1 (d π ) 4 .

FIG. 3 :
FIG. 3: The local density of states (LDOS) projected on the Fe d-orbitals in an FePc molecule in gas phase calculated by LDA with the structure optimized by GGA.

FIG. 6 :
FIG.6:The local density of states (LDOS) projected on Fe dzx, dyz and d z 2 orbitals calculated for FePc in the ontop and bridge site of Au(111) using LDA.The dashed and dotted black lines show the LDOS of dπ and d z 2 orbitals calculated for FePc in the gas phase, respectively.

FIG. 7 :
FIG. 7:The local density of states (LDOS) projected on Fe dzx, dyz and d z 2 orbitals calculated for FePc in the ontop and bridge sites of Au(111) using LDA+U.The dashed and dotted black lines show the LDOS of dπ and d z 2 orbitals calculated for FePc in the gas phase, respectively.
. The positions of each atom in Table I are in-

TABLE I :
Typical bond length in FePc molecule in LDA and GGA structural optimization calculations.The positions of each atom are indicated in Fig. 2.

TABLE II :
The adsorption energy and the magnetic moment calculated for FePc on Au(111) by LDA and LDA+U methods.

TABLE III :
Number of electrons in the Fe atom obtained from Bader analysis.