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Atomic Structure and Magnetic Nature of Copper Hydroxide Acetate Fan Yang,† Mauro Boero,*,‡,§ and Carlo Massobrio‡ Institute of Nanoscience and Nanotechnology, Huazhong Normal UniVersity, Wuhan 430079, People’s Republic of China; Institut de Physique et Chimie des Mate´riaux de Strasbourg, UMR 7504 CNRS and UniVersity of Strasbourg, 23, rue du Loess, BP43, F-67034 Strasbourg cedex 2 France; and Japan AdVanced Institute of Science and Technology, 1-1 Asahidai, Nomi-shi, Ishikawa 923-1292, Japan and CREST, Japan Science and Technology Agency, Sanban-cho, Tokyo 102-0075, Japan ReceiVed: May 12, 2010; ReVised Manuscript ReceiVed: October 4, 2010
By using density-functional theory in the framework of first-principles molecular dynamics, we carry out a dynamical annealing to identify the stable structures of copper hydroxide acetate Cu2(OH)3(CH3COO) · H2O, a fundamental compound in the field of hybrid organic-inorganic materials, for which accurate crystallographic data are not available. For the total spin value S ) 0, we obtain a large set of stable structures having very close sets of coordinates and differing in the spatial distribution of the spin densities. Only some of these structures (∼20%) feature spin topologies consistent with the in-plane ferromagnetic character experimentally established. An electron localization analysis through the electron localization function ELF shows that the different atomic and molecular units composing the systems (Cu2(OH)3(CH3COO)-, OH- and H2O) can be associated with different localization basins and connect to each other through noncovalent interactions. The relationship between the appearance of sizable spin densities on specific O atoms and the magnitude of the spin densities on the neighboring Cu atoms is also discussed. 1. Introduction Copper hydroxide acetate Cu2(OH)3(CH3COO) · H2O belongs to the family of Cu2(OH)3X transition metal layered compounds, where X is an exchangeable anion.1 This system can be considered as a precursor of a whole class of hybrid organicinorganic materials, those made of transition metal inorganic sheets characterized by interlayer spacing increasing with increasing length of the alkyl chain. Cu2(OH)3(CH3COO) · H2O consists of two-dimensional triangular arrays of CuII ions kept separated by CH3COO- spacers.2 In analogy with copper hydroxonitrate, Cu2(NO3)(OH)3, copper hydroxide acetate can be viewed as derived from the parent compound Cu2(OH)4 by replacing one-fourth of the OH- anions with CH3COO- acetate ion units. The value of the interlayer distance results from the spatial arrangement taken by the inserted species in between the inorganic layers.2 Interest in Cu2(OH)3X systems stems from their tunable magnetic properties, strongly dependent on the nature of the interlayer organic spacers. By comparing the magnetic behavior of Cu2(NO3)(OH)3 and Cu2(OH)3(CH3COO) · H2O, it appears that both compounds exhibit antiferromagnetic (AF) interlayer interactions. However, replacement of the NO3by the CH3COO- acetate ion units results in the appearance of weak ferromagnetic (F) intralayer interactions, contrary to the global AF intralayer character shown by Cu2(NO3)(OH)3.2 Density functional theory is well suited to provide insight into the bonding properties and the magnetic behavior of transition metal layered compounds. By focusing on the Cu2(OH)3X family, a convincing example has been provided
by the case of Cu2(NO3)(OH)3, for which an accurate set of crystallographic data for the atomic positions was a priori available.3 Electronic localization properties and spin topology were first described by making use of gradient corrected DFT functionals. In a further step, hybrid DFT/Hartree-Fock functionals were used to calculate exchange coupling constants and extract the temperature behavior of the magnetic susceptibility.4 The application of the same strategy to the case of copper hydroxide acetate is unfeasible, since a structural determination of comparable accuracy is not yet available. An X-ray powder diffraction study of Cu2(OH)3(CH3COO) · H2O has led to a plausible structural characterization.5 In particular, this analysis has highlighted the role of water molecules in between the layers, prone to be easily and reversibly removed by moderate heating. However, due to the lack of synthesized single crystal of suitable quality, the set of atomic coordinates is incomplete. These pieces of evidence suggest that the determination of the atomic structure is a prerequisite to any analysis of bonding and magnetic properties of this hybrid organic-inorganic material. In this work, we achieve two main goals. First, we determine the atomic structure of copper hydroxide acetate by structural optimization. Structural minima are found via a simulated annealing within the framework of first principles molecular dynamics. Then we characterize the bonding properties and the local spin topology by using the electron localization function (ELF) and a spin density topology analysis, respectively, both combined with a visual inspection of their spatial distributions. 2. Computational Methods
* To whom correspondence should be addressed. E-mail: boero@ ipcms.u-strasbg.fr. † Institute of Nanoscience and Nanotechnology, Huazhong Normal University. ‡ Institut de Physique et Chimie des Mate´riaux de Strasbourg, UMR 7504 CNRS and University of Strasbourg. § Japan Advanced Institute of Science and Technology.
We employ the first-principles molecular dynamics as coded in the CPMD package.6,7 Our calculations are performed in the Kohn-Sham density functional8 (DFT) framework with a generalized gradient approximation due to Becke9 for the exchange energy and Lee, Yang, and Parr10 (LYP) for the
10.1021/jp1043249 2010 American Chemical Society Published on Web 11/09/2010
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correlation energy. The valence electrons (including the 3d electrons of each Cu atom) are treated explicitly, whereas normconserving pseudopotentials generated following the scheme of Trouiller and Martins11 are used to account for the core-valence interaction. Nonlinear core corrections12 have been included in the case of Cu. Most of our calculations were performed on a system made of 72 atoms (8 Cu, 24 O, 8 C, and 32 H) in a periodically repeated simulation box, hereafter referred to as Nat72. The lattice parameters a ) 5.6025 Å, b ) 6.1120 Å, c ) 18.747 Å, and β ) 91°012, and symmetry group P21/m, are those determined by Masciocchi and co-workers5 in their X-ray powder diffraction study. Size effects on the interatomic distances and on the energy difference between distinct spin topologies were checked by considering a larger simulation box, made of 288 atoms (32 Cu, 96 O, 32 C, and 128 H), hereafter referred to as Nat288. By this choice, we doubled the 72 atoms box in the x and y directions, by leaving it unchanged along the z direction. In this case the simulation cell dimensions are Lx ) 11.205 Å, Ly ) 12.224 Å, Lz ) 18.747 Å. We recall that the structural measurements performed in ref 5 could not identify, within the acetate groups, the positions of both C and O atoms, thus no conclusive assignment to either one of the two species could be done. Moreover, as usual in X-ray crystallography, no information on the positions of the H atoms is available. Therefore, a complete initial set of coordinates was constructed by using a phenomenological molecular force field MMFF9413 approach as follows. First, we made a plausible choice for the positions of the C and O atoms compatible with the stereochemistry of acetate groups. Then, we did several structural optimizations to assign coordinates to the missing H atoms within a trial-and-error procedure. This provides a suitable initial arrangement including all the 72 atoms composing the unit cell, well suited to be adequately optimized by using firstprinciples methods. The wave functions are expanded at the Γ point of the supercell in a plane wave basis set with an energy cutoff of 90 Ry. In order to produce a set of distinct electronic and structural ground states, differing in the local values of the spin densities on the atoms (i.e., the spin topology), we assigned different initial random values to the fictitious electronic degrees of freedom, i.e., the coefficients of the Fourier plane-wave (PW) expansion ci(g), g being the reciprocal lattice vectors of the periodic cell and i the electronic state index. For each one of these choices, the electronic structure is relaxed to its ground state by minimization of the total energy with respect to the coefficients of the PW expansion. We stress that the PW scheme, as implemented in the standard version of current first-principles molecular codes, does not allow to assign a specific spin topology, its distribution in space becoming available only at the end of the electronic relaxation. Optimization of the structural geometries is carried out by means of first-principle molecular dynamics with a damping factor. This acts on the ionic velocities and allows for an efficient search of the minimum energy configuration, taken to be achieved when the residual forces on the atoms are smaller than 0.001 hartree/au. By using the above procedure and focusing on Nat72, we performed 53 structural optimizations corresponding to an equivalent number of initial random values for the electronic degrees of freedom. In all of these calculations the total spin multiplicity 2S+1 was set equal to 1 (S ) 0), this choice being consistent with the bulk antiferromagnetism of this compound.2 In addition, the ferromagnetic case (total spin multiplicity equal to 9, S ) 4) was also considered for Nat72.
Yang et al. For Nat288, we did two structural optimizations with S ) 0 after selection of two distinct initial sets of ci(g). To obtain the values of the spin densities (termed R and β hereafter for the up- and down-spin components, respectively) on the atoms, each eigenstate R and β is projected onto an atomic basis set. For each atom, the sum of the square of the corresponding projections provides the spin densities R and β. An insight into the electronic structure of Cu2(OH)3(CH3COO) · H2O can be achieved by using the electron localization function14,15 (ELF) η(r) which is defined as follows:
η(r) )
1 1 + (D/Dh)2
(1)
N
D)
1 1 |∇F(r)| 2 |∇ψi(r)| 2 2 i)1 8 F(r)
(2)
3 (3π2)2/3[F(r)]5/3 10
(3)
∑
Dh )
where, in our case, the Ψi(r) are the N Kohn-Sham occupied orbitals, this definition not accounting for the spin states, and F(r) the total electron density as provided by DFT. The investigation of the nature of bonding via the ELF involves the identification of the ELF maxima (the attractors), which separate disconnected localization regions. By lowering η(r) from its upper-bound value of 1 (0 e η(r) e 1), we are able to follow the evolution of the bonding patterns. This amounts to the interconnection of all different localization basins by a decrease of η(r) to lower values.15,16 One may want to employ the ELF to identify covalent and ionic bonding since, in the first case, significant η(r) . 0 regions exist between atomic cores. 3. Results and Discussion 3.1. Energetics of the Configurations and Exchange Coupling Constant. Analysis of the spin topologies for the 53 structural optimizations performed at a global spin S ) 0 reveals that the spatial distribution of the spin densities can be grouped in two classes. To the first class belong those spin configurations (41 of them) indicative of an in-plane antiferromagnetic character (partial spin Σ ) 0 on each single layer, termed AFin hereafter). Conversely, to the second class belong 12 spin configurations characterized by finite nonzero partial spin on each layer, Σ * 0, referred to as F-in hereafter. It is worth stressing that with the symbol S (S ) 0 or S ) 4) we denote the total spin state on the whole system, while, for the S ) 0 case, Σ denotes the spin of a single layer and Σ ) 0 and Σ * 0 refer to the AF-in and F-in intralayer magnetic characters, respectively. As shown in Figure 1 (relative to the AF-in cases) and in Figure 2 (relative to the F-in case), the energy differences separating distinct spin topologies within each class are quite small, namely 0.15 eV for AF-in and 0.20 eV for F-in at most. Note that 8 and 4 non equivalent topologies have been reported in Figure 1 and Figure 2, respectively, resulting from a total number of attempts of 41 (AF-in) and 12 (F-in). We found that the total energy of the entire 72 atoms periodic system in the ground state AF-in structure is lower by 0.50 eV than its F-in counterpart. In turn, this same total energy for the ferromagnetic case is higher by 0.9 eV with respect to the F-in one, leading to E(S ) 0, AF-in) < E(S ) 0, F-in) < E(S ) 4). This trend is confirmed by the total energies (per unit cell of 72 atoms) of the two structures optimized with Nat288 (see Figure 3). In this
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Figure 2. Optimized structures of Cu2(OH)3(CH3COO) · H2O seen along the [010] direction (xz plane) for Nat72, total spin S ) 0. Each configuration corresponds to a given spin topology for the in-plane Σ * 0 case. The atoms color code is identical to Figure 1. The ground state configuration is the one on the top of the left column and isosurfaces of spin densities are shown at (0.03 e/Å3.
Figure 1. Optimized structures of Cu2(OH)3(CH3COO) · H2O seen along the [010] direction (xz plane) for Nat72, total spin S ) 0. Each configuration corresponds to a given spin topology for the in-plane Σ ) 0 case. Cu atoms are brown, mostly covered by the spin density isosurfaces green (R spin states) and yellow (β spin states), O atoms are red, C atoms are blue, and H atoms are white. The ground state configuration is the one on the top of the left column. Isosurfaces of spin densities are shown at (0.03 e/Å3.
Figure 3. Optimized structures of Cu2(OH)3(CH3COO) · H2O seen along the [010] direction (xz plane) for Nat288, total spin S ) 0. Panel (a): optimized configuration leading to an in-plane Σ * 0 spin topology. Panel (b): optimized configuration leading to a in-plane Σ ) 0 spin topology. Isosurfaces of spin densities are shown at (0.03 e/Å3.
case we found that E(S ) 0, AF-in) is lower by 0.4 eV than E(S ) 0, F-in). On the basis of experimental evidence, the magnetic behavior of the F-in structure is the one most compatible with the measured trend of the magnetic susceptibility.2 It remains to be established whether this discrepancy with the experimental results could be cured by resorting to the use of hybrid DFT/ Hartree-Fock functionals.17,18 These functionals are well-known to yield accurate energetics in the case of most molecular magnetic materials at the cost of an increased computational effort.19 From the energy difference between different realizations of the same macroscopic magnetic behavior (see Figure 1 for the AF-in case and Figure 2 for the F-in case) one can extract an estimate of the exchange coupling constant. This can be done in the framework of an Ising spin Hamiltonian approximation, in which the magnetic centers located on the Cu atoms interact through a law of the kind H ) |J| SASB, Sk being a two value (1/2, -1/2) spin variable located on the k ) A and k ) B magnetic centers. The energetic cost ∆E ) 0.019 eV separating
the two lowest spin configurations (Figure 1) can be readily associated with the pair of spin needed to convert one spin configuration into the other (see the lower rows of Cu atoms on the top of Figure 1, left and right images). Accordingly, one obtains ∆E ) |J| ∼ 150 cm-1. We have to remark that this value is larger than the one extracted from the temperature behavior of the magnetic susceptibility (of the order of 30-60 cm-1 as reported in ref.20), by confirming the overestimate of the exchange coupling constants calculated within the BLYP exchange-correlation functional.19 3.2. Structural Properties. As shown in Table 1, the interatomic distances in the various molecular groups (OH-, CH3COO- and H2O) replicate quite regularly within the cell, the standard deviations being quite small. This holds true also when considering the different spin topologies found for Nat72 (S ) 0 AF-in, S ) 0 F-in, and S ) 4), as well as the two cases studied for Nat288. Indeed, the variations of the distances found among the different magnetic cases and/or different system sizes lie within the given standard deviations. For a few structures,
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TABLE 1: Interatomic Distances (in Å) of the Optimized Cu2(OH)3(CH3COO) · H2Oa
TABLE 3: Interatomic Cu-O Distances (in Å) of the Optimized Cu2(OH)3(CH3COO) · H2O for S ) 4a
O-H (O, H ∈ H2O) 0.98 (
