DFT calculations using periodic boundary conditions on an iron gall 3D coordination polymer of interest for cultural heritage conservation Sara Zaccaron, Renzo Ganzerla, Marco Bortoluzzi
3D structure of the coordination polymer having formula [(Fe3L3)3-]∞ -]∞ (H4L = gallic acid, 3,4,5-trihydroxybenzoic acid) proposed for iron gall inks and here visualized along the c translation vector
DFT calculations using periodic boundary conditions on an iron gall 3D coordination polymer of interest for cultural heritage conservation Sara Zaccarona*, Renzo Ganzerlaa, Marco Bortoluzzia
a
*
Department of Molecular Sciences and Nanosystems, Ca’ Foscari, University of Venice, Dorsoduro 2137, 30123 Venice, Italy e-mail:
[email protected]
Received: 2013-02-24 Accepted: 2013-03-26 Abstract: The electronic structure of a 3D iron-based coordination polymer having formula [(Fe3L3)3-]∞ (H4L = gallic acid, 3,4,5-trihydroxybenzoic acid) has been studied by applying DFT-based computational methods in combination with periodic boundary conditions and plane-waves or numerical basis sets. The model compound has been built on the basis of reported experimental structural parameters. Data regarding the ground-state spin multiplicity, the magnetic interactions among the primitive cells, the charge and spin distributions, the oxidation states, the frontier bands, the band gap, and the optical properties have been computed. Keywords: Iron, Gallic Acid, Coordination Polymers, DFT, Conservation of Cultural Heritage. DOI: 10.7361/SciCF-442 1. Introduction
Iron gall complexes are the main components of iron gall inks, which belong to the family of tannin pigments and have been the most used writing materials since the beginning of the 11th century [1]. The ancient procedure for the preparation of these inks requires three main ingredients: plant extracts rich in tannins (usually from gall nuts), vitriol (ferrous sulphate), and a binder such as arabic gum. Iron gall complexes are usually obtained in laboratory by reacting an iron(II) salt, for example iron sulphate, with gallic acid (3,4,5-trihydroxybenzoic acid) under aerobic conditions in acidulated water. However, iron gall derivatives can also be obtained starting from iron(III) salts. Molecular structures of most of the products of the reaction between tannins and iron salts are still not completely ascertained. Krekel [2] proposed the formation of dinuclear complexes of iron, such as that shown in Fig. 1, where the coordination of a conjugate base of gallic acid to formally iron(III) ions occurs through the phenate oxygen atoms. In such a model the ligands behave as chelating-bridging species. Decarboxylation after complexation is a subsequent reaction that is proposed in some cases. 58
Figure 1. Example of proposed structure for iron gall complexes.
Single-crystal X-R ay diffraction measurement have been carried out in the past by Wunderlich et al. on the product formed by the reaction of iron(III) chloride and gallic acid [3]. As far as we know, this compound is the only structurally characterized iron gall dye. This species is a 3D polymer where several iron metal ions are coordinated by the conjugate base (L) of the gallic acid (H4L). The excess of negative charge is neutralized by H3O+ cations and the formula is [Fe(H3O)(H2O)(L)]n. The iron centres have
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slightly distorted octahedral geometry with six Fe-O bonds, as shown in Fig. 2. Two oxygen atoms mutually in cis position belong to two separate carboxylic moieties and the corresponding Fe-O bond lengths are 2.006 Å. Other two L ligands are mutually cis and coordinate the metal ion, each one with two phenate-type oxygen atoms. The corresponding FeO bonds are 2.000 Å (oxygen atoms in position 3 and 5) and 2.028 Å (oxygen atoms in position 4). Each carboxylate group behaves as bridging ligand between two iron centres, while the three phenatetype oxygen atoms of every ligand chelate two metal ions. The oxygen atom in para position with respect to carboxylate acts as bridging atom, as observable in Fig. 3.
Important historical objects in libraries and archives show noticeable degradation phenomena caused by the destructive effects of metallo-gallate inks interacting with cellulose and sizing. Comparable degradation effects are known also for other substrates of interest for cultural heritage, as example wool fibres. The chemical phenomenon of corrosion caused by iron gall inks has been intensively studied for many years. Acid hydrolysis and after-effects of Fenton reactions have been blamed [4]. Unfortunately, the incomplete information actually present in literature about the electronic features of iron gall inks makes some degradation pathways still unclear. The understanding of the electronic configuration of the ground and the excited states of these inks appears of paramount interest for the synthesis of new materials and the development of methodologies useful for preservation and restoration of cultural heritage. For these reasons, in the present paper we report a computational DFT study on the electronic structure of a iron-gall 3D coordination polymer, which can be considered as a model for iron gall inks. 2. Computational details
The model compound [(Fe3L3)3-]∞ has been built on Figure 2. Octahedral coordination sphere around the iron centre the basis of the deposited X-R ay data regarding the in [Fe(H3O)(H2O)(L)]n. product of the reaction between iron(III) chloride and gallic acid [3]. The internal coordinates have not been changed with respect to the experimental values. The oxygen atoms present in the cavities of the 3D polymer (corresponding to water molecules or H3O+ cations) have been removed from the original structure and hydrogen atoms have been added to the carbon atoms in position 2 and 6 of the aromatic rings, using the following internal coordinates: C-H bond lengths = 1.082 Å; C1-C-H angle = 120°; CCOO -C1-C-H dihedral angle = 0°. The primitive cell has formula (Fe3L3)3-. The periodic boundary conditions are the same reported among the X-R ay data, Figure 3. Coordination modes of the polydentate ligand in i.e. trigonal space group (a = 8.664 Å, b = 8.664 Å, c [Fe(H3O)(H2O)(L)]n. Left: coordination of the phenate oxygen = 10.861 Å, α = 90°, β = 90°, γ = 120°), cell volume atoms; right: coordination of the carboxylate moiety. = 706.05 Å3, symmetry group P3121. Single-point unrestricted DFT calculations have been carried out using the pure GGA functional PBE The deep blue colour of iron gall species is proba- [5] in combination with a plane-waves basis set (enbly attributable to a strong electronic delocalisation ergy cutoff = 380 eV) [6]. Ultrasoft pseudopotentials among the metal ions, but no detailed study is cur- have been used to replace the electrons of the inner rently present in the literature and real oxidation spheres [7]. Initial values of 15, 13, 11 and 9 have and spin states of the iron centres are not unambig- been considered for the number of unpaired elecuously ascertained. trons in the primitive cell of [(Fe3L3)3-]∞. The optimi59
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sation of spin multiplicity during self-consistent field gap is 0.65 eV. The same band gap value has been calculations has been allowed and a SCF tolerance obtained from DFT PBE calculations based on nuof 5.0E-7 eV/atoms has been used. The sampling merical basis set. of the Brillouin zone has been carried out with the scheme of Monkhorst and Pack (shrinking factors: a = 3; b = 3; c = 2, spacing comprised between 0.044 and 0.046 Å-1 in each of the three lattice directions) [8]. Population analyses have been performed using the Mulliken [9] and Hirshfeld [10] distributions. Two sets of shrinking factors (a = 3; b = 3; c = 2 and a = 6; b = 6; c = 4) have been used for the simulation of the optical properties of the model compound and twelve empty bands have been considered in these last calculations. The results on the ground-state electronic configuration have been verified by carrying out unrestricted PBE calculations with an atom-centred doubly-numerical polarized basis set and DFT semicore pseudopots [11]. The sampling of the primi- Figure 4. 3D structure of [(Fe3L3)3-]∞, view along a vector. tive cell in the reciprocal space has been done as described above. SCF tolerance was set equal to 1.0E-6 eV/atoms. The software used for calculations based on plane-waves is CASTEP [12], while DFT PBE calculations with numerical basis set have been carried out with Dmol3 [13]. 3. Results and Discussion
Fig.s 4-6 report the 3D structure of the model structure [(Fe3L3)3-]∞, visualized along the three translation vectors. Total electron density is essentially localized on the atoms and on the C-H, C-C, C-O and Fe-O bonds. No meaningful direct covalent interaction is present among the metal centres. The most stable electronic configuration corresponds to the higher multiplicity, i.e. 15 unpaired electrons in each primitive cell. The comparison of the integral of spin density (7.50 hbar) with the integrated spin density for absolute values of spin states (7.55 hbar) indicates that ferromagnetic interaction is present among the primitive cells. The energy values of the frontier bands (planewaves calculations) indicate that the compound can be described as a semiconductor. In fact, the highest-occupied bands range from -0.05 to 0.00 eV (alpha spin) and from -0.30 to -0.29 eV (beta spin), while the lowest-unoccupied bands are comprised between 2.83 and 2.86 eV (alpha spin) and 0.65 and 0.67 eV (beta spin). Therefore, the minimum band 60
Figure 5. 3D structure of [(Fe3L3)3-]∞, view along b vector.
Figure 6. 3D structure of [(Fe3L3)3-]∞, view along c vector.
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Table 1 reports the Mulliken charge analysis and the Mulliken and Hirshfeld spin distributions. Spin density results essentially localized on the iron centres and, to a lesser extent, on the phenate and carboxylate oxygen atoms, while it is virtually absent on the carbon atoms of the aromatic ring and of the carboxylate moiety. Table 1. Mulliken and Hirshfeld charge (a.u.) and spin (hbar) distributions in the primitive cell of [(Fe3L3)3-]∞ (plane-waves basis set). Atom type(a)
Mulliken charge
Mulliken spin
Hirshfeld spin
H (6)
0.27
0.00
0.00
C1 (3)
-0.10
0.01
0.01
C2 – C6 (6)
-0.37
0.02
0.02
C3 – C5 (6)
0.17
0.00
0.01
C4 (3)
0.06
0.02
0.02
CCOO (3)
0.56
0.00
0.02
O3 – O5 (6)
-0.65
0.11
0.10
O4 (3)
-0.66
0.13
0.13
OCOO (6)
-0.62
0.06
0.06
Fe (3)
1.53
1.97
1.93(c)
(b)
posed for the electronic structure of [(Fe3L3)3-]∞. The calculated absorption spectrum, represented in Fig. 7, closely resembles the commonly reported spectra for iron gall dyes (see for example Fig. 8 [15]). In particular, besides the usual absorptions centred in the UV range, attributable to transitions inherent the gallic acid electronic structure, a very wide band centred in the red region is predicted, which is the origin of the deep blue colour of this class of compounds.
Figure 7. Simulated absorption spectrum of [(Fe3L3)3-]∞.
Number of equivalent atoms in parentheses. (b) 2.00 hbar using numerical basis set. (c) 1.93 hbar using numerical basis set. (a)
Interestingly, both Mulliken and Hirshfeld distributions agree with a spin density value for the iron centres of about 2 hbar, instead of the 2.5 hbar expected for high-spin iron(III) ions. The computed values indicate the presence of high-spin iron(II) metal ions and this hypothesis is confirmed by the quite low Mulliken charge on the iron atoms. Moreover, a more detailed study of the electronic populations shows that the electronic configuration of the metal ions is essentially d6, with five up electrons and one down electron. Therefore, the qualitative picture arising from charge and spin distributions corresponds to high-spin iron(II) metal centres (about 4 unpaired electrons) bridged by radical ligands of the type [L3-]· (about one unpaired electron, delocalised mainly among the oxygen atoms). One of the steps of the formation of the coordination polymer synthesized by Wunderlich appears therefore the one-electron reduction of the iron(III) ions by the gallic acid [14]. The simulation of the optical properties has been carried out in order to validate the model here pro61
Figure 8. Experimental absorption spectrum of an iron gall ink.
The good agreement between experimental and theoretical electronic transitions confirms the reliability of the information collected in this communication about the ground-state electronic configuration of a model for iron gall inks.
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4. Acknowledgements
The authors thank Ca’ Foscari University for financial support. We acknowledge the CINECA Awards N. HP103I3CHF (2010) and N. HP10CRPVUO (2011) for the availability of high performance computing resources. Prof. Valerio Bertolasi, University of Ferrara, is gratefully acknowledged for support. 5. References [1]
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