Ab initio study of the magnetic exchange coupling constants of a structural model of the oxygen evolving center in photosystem II: II [CaMnIII 3 Mn (µ4 -O)L3 Cl2 (O2 CMe)1.2 (H2 O)1.5 -
(MeOH)0.3 ]Cl0.8 ·5MeOH Heike Fliegla∗ , Karin Finka† , Wim Kloppera,b , Christopher E. Ansonc , Annie K. Powella,c and Rodolphe Cl´eracd,e a
Institute of Nanotechnology, Forschungszentrum Karlsruhe, P.O. Box 3640, D–76021 Karlsruhe, Germany
b
Lehrstuhl f¨ ur Theoretische Chemie, Institut f¨ ur Physikalische Chemie, Universit¨at Karlsruhe (TH), D–76128 Karlsruhe, Germany c
Institut f¨ ur Anorganische Chemie,
Universit¨at Karlsruhe (TH), D–76128 Karlsruhe, Germany d
CNRS, UPR 8641, Centre de Recherche Paul Pascal (CRPP) Equipe ”Mat´eriaux
Mol´eculaires Magn´etiques” 115 avenue du Dr. Albert Schweitzer, Pessac, F-33600, France e
Universit´e de Bordeaux, UPR 8641, Pessac, F-33600, France (Dated: October 31, 2008)
∗ †
Email:
[email protected] Email:
[email protected]
1
Abstract A new structural model for the oxygen evolving center in photosystem II was recently synthesized and characterized by Hewitt et al. [Chem. Commun. 2006, 2650]. A simplified Heisenberg model Hamiltonian with only two independent constants was applied to extract the magnetic spincoupling constants Jij of the mixed valent Mn4 system. In the present study, all six possible coupling constants are calculated by ab initio methods in order to obtain a detailed understanding of the magnetic behavior of the system. The broken symmetry approach of Noodleman is applied using density functional theory (DFT). Two different approaches are compared. On the one hand, the coupling constants are obtained from calculations on eight different determinants which describe the high-spin state as well as different broken-symmetry states of the tetranuclear cluster. On the other hand, a pair approach that permits a direct calculation of the individual coupling constants is used. For the pair approach, the coupling constants are also obtained from modified CASCI (Complete Active Space Configuration Interaction) calculations. With the different sets of coupling constants, the full Heisenberg Hamiltonian of the four center problem is used to calculate the magnetic susceptibilities, which are then compared with the experimental values.
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I.
INTRODUCTION
In nature, the photo-induced oxidation of water to dioxygen 2H2 O → O2 + 4e− + 4H+ is efficiently catalyzed by a manganese/calcium complex (Mn4 Ca), which is part of the multi-protein photosystem II (PS II) assembly.[1] Already in 1970, Kok and coworkers[2] proposed a possible mechanism for the water-splitting reaction, cycling the manganese atoms through different oxidation states Si (i = 0, 1, 2, 3 or 4). However, the mechanism of the water-splitting reaction and the structure of the oxygen evolving center (OEC) of PS II are still under debate.[3–5] Regarding the literature, neither the structure of the OEC nor the oxidation states of the four manganese atoms in the different Si states of the Kok cycle are absolutely clear. A serious problem lies in the identification of the structure of the reactive center. Xray absorption spectroscopy (XAS) has been applied successfully, but the interference with the protein environment of PS II and possible damage to the structure by high-energy radiation make a clear assignment difficult. A detailed investigation of a small model cluster, where the structure and the oxidation states of the manganese atoms are well known, could assist in understanding the spectra of the native system and help to identify the several possible oxidation states of the manganese atoms in the different Si states of the Kok cycle. Investigating the magnetism of such a small model system could also give insight into the question whether magnetic properties play an important role in the catalytic process or not. In 2006, Hewitt et al .[6] succeeded to synthesize a set of model clusters, following the cubane-like structural motive that was proposed by Ferreira et al.[3] One of these model II clusters, [CaMnIII 3 Mn (µ4 -O)L3 Cl2 (O2 CMe)1.2 (H2 O)1.5 -(MeOH )0.3 ]Cl0.8 ·5MeOH (structure
1 of Ref.6, see Figure 1) serves as a possible model for the S0 Kok state and yields a S =
1 2
ground state, which is in nice agreement with an EPR study of Messinger et al.[7]
L denotes a Schiff-base ligand, which is obtained from the condensation of o-vanillin and 2-hydroxypropylamine. An investigation of the magnetic behavior of this model system was performed using a simplified model Heisenberg Hamiltonian, in which the values of the six possible coupling constants Jij of the Mn4 system were restricted by the approximations visualized in Figure 2 to avoid overparametrization in the fitting procedure.[6] First, according to the literature[6], the coupling through the central oxygen atom was considered to be negligible, thus J12 and J23 were set to zero. Second, the coupling between similarly bridged 3
centers was considered to be identical, therefore J14 , J24 , and J34 were restricted to the same value. Finally, the coupling between the Mn centers 1 and 3 by the CH3 COO− group was considered to be large and antiferromagnetic (J13 < 0). In the present work, we investigate whether these approximations can be justified by ab initio calculations. There are in general two approaches to obtain exchange coupling constants by quantum chemical calculations. On the one hand, the different electronic states of the system can be directly calculated by multi-reference wavefunction-based methods. With these methods, dynamic electron correlation effects can be included and the calculated wavefunctions are eigenfunctions of the Hamiltonian of the molecule as well as of Sˆ2 . Unfortunately, applications of multireference based methods are restricted to relatively small systems.[8] They are not applicable to a system such as the present Mn4 Ca cluster because the effort increases exponentially with the number of magnetic centers. A way out of this problem may be the pairwise calculation of J values, however. As has been shown by Illas an coworkers,[9] for example, the coupling constants of a system with more than two centers can be obtained from independent calculations on systems with two magnetic centers. On the other hand, density functional theory (DFT) using the broken symmetry (BS) approach of Noodleman [10, 11] is widely used to obtain coupling constants. This method can be used on relatively large systems. A recent example is the treatment of a Mn19 cluster by Ruiz et al.[12] In the DFT-BS approach, the high-spin Kohn–Sham (KS) determinant is usually well described, and the exchange coupling constants can be obtained from the difference between the energy of the high-spin state and the energy of broken-symmetry KS determinants, in which the spins of the localized magnetic orbitals [13] are changed from α to β on some of the centers. Unfortunately, this Noodleman treatment must be regarded with care, since the broken symmetry KS determinants are in general not eigenfunctions of Sˆ2 . For a detailed discussion on the proper use of DFT for the extraction of exchange coupling constants, see for instance Refs.14–16 . Alternatively, the constrained DFT approach[16, 17] can be applied, which directly derives the Ising configurations of the system from the density response. The BS approach has successfully been used in such cases where the local electronic states at the metal centers are spatially nondegenerate. In other cases, it can be necessary to include spin–orbit coupling into the calculations.[18, 19] Mn3+ is a d4 system and in Oh symmetry the 4
ground state would be a 4 T2g state. This state is split by the surrounding external ligand field. We have performed Complete-Active-Space Self-Consistent-Field (CASSCF) calculations on mononuclear model complexes to assure that the local ground state can be described by a single determinant and spin–orbit coupling has not to be taken into account. In the present study, the BS approach of Noodlemann is applied using DFT and the Ising approximation, which is considered to provide a reasonable mapping [20, 21] onto the Heisenberg model. The investigation of the magnetic behavior of the model system is extended to the calculation of all six possible exchange coupling constants. In addition, a pair approach that permits a direct calculation of Jij is applied, and furthermore, the coupling constants are obtained by modified Complete-Active-Space Configuration-Interaction (CASCI) calculations [19] for the pair approach. Both approaches are directly compared with experimental values for the magnetic susceptibilities, which are computationally accessible through a Boltzmann average.[13] Finally, a fitting procedure was performed, using the conjugate-gradient method of Polak–Ribiere.[22] The ab initio Jij values were taken as the starting points for the minimization procedure, leading so far to the best available estimates of the couplings of the present system.
II.
THEORY A.
Exchange coupling constants
The Heisenberg–Dirac–Van-Vleck (HDV) Hamiltonian is defined as ˆ HDV = −2 H
N X
ˆi · S ˆj , Jij S
(1)
i
