Free energy of spin-crossover complexes calculated with density functional methods

Quantum Chemical Study of Three Polymorphs of the Mononuclear Spin-Transition Complex [Fe(DPPA)(NCS)2]

The calculations of the high spin (HS) and low spin (LS) states of the [Fe(II)(DPPA)(NCS)(2)] complex have been performed at three experimentally observed geometries corresponding to three synthesized polymorphs with different spin-transition behavior. The structure optimization leads to a single molecular structure, suggesting that the existence of three geometries is not an intrinsic phenomenon but is induced by the crystal lattice. The structural difference between three forms can be reproduced by introducing the Madelung field of the crystal lattice. However, the calculations show that the differences in magnetic behavior of the three polymorphs cannot be attributed only to variations of the energy gap between two spin states.

Assessment of Density Functionals for the High-Spin/Low-Spin Energy Difference in the Low-Spin Iron(II) Tris(2,2′-bipyridine) Complex

In the iron(II) low-spin complex [Fe(bpy)3]2+, the zero-point energy difference between the 5T2g(t4(2g)e2g) high-spin and the 1A(1g)(t(6)2g) low-spin states, Delta(E)0HL, is estimated to lie in the range of 2500-5000 cm(-1). This estimate is based on the low-temperature dynamics of the high-spin-->low-spin relaxation following the light-induced population of the high-spin state and on the assumption that the bond-length difference between the two states Delta(r)HL is equal to the average value of approximately 0.2 A, as found experimentally for the spin-crossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the low-spin-state optimised geometries are found to be in very good agreement with the experimental X-ray structure of the complex and the predicted high-spin geometries are all very close to one another for a whole series of common GGA (PB86, PW91, PBE, RPBE) and hybrid (B3LYP, B3LYP*, PBE1PBE) functionals. This confirmation of the structural assumption underlying the estimation of Delta(E)0HL from experimental relaxation rate constants permits us to use this value to assess the ability of the density functionals for the calculation of the energy difference between the HS and LS states. Since the different functionals give values from -1000 to 12000 cm(-1), the comparison of the calculated values with the experimental estimate thus provides a stringent criterion for the performance of a given functional. Based on this comparison the RPBE and B3LYP* functionals give the best agreement with experiment.

Comparison of density functionals for differences between the high- (T2g5) and low- (A1g1) spin states of iron(II) compounds. IV. Results for the ferrous complexes [Fe(L)(‘NHS4’)]

Previous work testing density functionals for use in calculating high-spin-low-spin energy differences, deltaE(HL), for iron(II) spin-crossover transitions has tended to conclude that only properly reparametrized hybrid functionals can predict deltaE(HL) since it seems to depend critically on a correct description of the electron pairing energy governed by the exchange term. Exceptions to this rule are the previous three papers (I, II, and III in the present series of papers) where it was found that modern generalized gradient approximations (GGAs) and meta-GGAs could do as well as hybrid functionals, if not better, for this type of problem. In the present paper, we extend these previous studies to five more molecules which are too large to treat with high-quality ab initio calculations, namely, the series [Fe(L)('NHS(4)')], where NHS(4)=2.2'-bis(2-mercaptophenylthio)diethylamine dianion, and L=NH(3), N(2)H(4), PMe(3), CO, and NO(+). Since we know of no reliable experimental estimate of deltaE(HL), we content ourselves with a comparison against the experimentally determined ground-state spin symmetry including, in so far as possible, finite-temperature effects. Together with the results of Papers I, II, and III, this paper provides a test of a large number of functionals against the high-spin/low-spin properties of a diverse set of Fe(II) compounds, making it possible to draw some particularly interesting conclusions. Trends among different classes of functionals are discussed and it is pointed out that there is at least one functional, namely, the OLYP generalized gradient approximation, which is able to give a reasonably good description of the delicate spin energetics of Fe(II) coordination compounds without resorting to hybrid functionals which require the relatively more expensive calculation of a Hartree-Fock-type exchange term.

Computational Exploration of the Catalytic Mechanism of Dopamine β-Monooxygenase: Modeling of Its Mononuclear Copper Active Sites

Dopamine hydroxylation by the copper-superoxo, -hydroperoxo, and -oxo species of dopamine beta-monooxygenase (DBM) is investigated using theoretical calculations to identify the active species in its reaction and to reveal the key functions of the surrounding amino acid residues in substrate binding. A 3D model of rat DBM is constructed by homology modeling using the crystal structure of peptidylglycine alpha-hydroxylating monooxygenase (PHM) with a high sequence identity of 30% as a template. In the constructed 3D model, the CuA site in domain 1 is coordinated by three histidine residues, His265, His266, and His336, while the CuB site in domain 2 is coordinated by two histidine residues, His415 and His417, and by a methionine residue, Met490. The three Glu268, Glu369, and Tyr494 residues are suggested to play an important role in the substrate binding at the active site of DBM to enable the stereospecific hydrogen-atom abstraction. Quantum mechanical/molecular mechanical (QM/MM) calculations are performed to determine the structure of the copper-superoxo, -hydroperoxo, and -oxo species in the whole-enzyme model with about 4700 atoms. The reactivity of the three oxidants is evaluated in terms of density-functional-theory calculations with small models extracted from the QM region of the whole-enzyme model.

High-spin to low-spin relaxation kinetics in the [Fe(TRIM)2]Cl2 complex

A quasi-quantitative photo-induced low-spin (LS)-->high-spin (HS) conversion of FeII ions has been observed in the [Fe(TRIM)2]Cl2 complex by irradiating the sample with blue light (488 nm) at 10 K. The time dependence of the HS-->LS relaxation has been studied between 10 K and 44 K by means of magnetic susceptibility measurements. These relaxation curves could be satisfactorily fitted by mono-exponential decays including tunnelling effect except for temperatures below 30 K. The introduction of a distribution of vibrational frequencies into this model improved significantly the fits in the low-temperature range and gave a good agreement with the experimental data in the whole temperature range suggesting a multi-rate relaxation process in this complex.

The performance of nonhybrid density functionals for calculating the structures and spin states of Fe(II) and Fe(III) complexes

The local density approximation and a range of nonhybrid gradient corrected density functionals (PW91, BLYP, PBE, revPBE, RPBE) have been assessed with respect to the prediction of geometries and spin-state energy preferences for a range of homoleptic Fe(II)L6 and Fe(III)L6 complexes, where L = Cl-, CN-, NH3, pyridine, imidazole, H2O, O=CH2 and tetrahydrofuran. While the qualitative spin-state energies from in vacuo structure optimizations are reasonable the geometries are relatively poorly treated, especially for [FeCl6]3-/4-. Structural results for all the complexes are significantly improved by including environmental effects. The best compromise between structural and spin-state predictive accuracy was obtained for the RPBE functional in combination with the COSMO solvation approach. This approach systematically overestimates the energetic preference for a low spin state, which is partly due to the well-known effect of the lack of exact exchange in nonhybrid functionals and partly due to the larger solvation stabilization of low-spin complexes that have shorter bond lengths and thus smaller molecular volumes than their high-spin partners. Calculations on low spin [Fe(bipy)3]2+ and [Fe(phen)3]2+ and their ortho methyl substituted analogs, which are high spin at room temperature but cross over to low spin at low temperature, suggest the RPBE/COSMO combination generates low spin states which are too stable by approximately 13 kcal mol(-1).

A theoretical study of spin states in Ni-S4 complexes and models of the [NiFe] hydrogenase active site

We have applied density functional theory, using both pure (BP86) and hybrid (B3LYP and B3LYP*) functionals, to investigate structural parameters and reaction energies for nickel(II)-sulfur coordination compounds, as well as for small cluster models of the Ni-SI and Ni-R redox state of [NiFe] hydrogenases. Results obtained investigating experimentally well-characterized complexes show that BP86 is well suited to describe the structural features of this class of compounds. However, the singlet-triplet energy splitting and even the computed ground state are strongly dependent on the applied functional. Results for the cluster models of [NiFe] hydrogenases lead to the conclusion that in the reduced protein structures characterized by X-ray diffraction a hydride bridges the two metal centres. The energy splitting of the singlet and triplet states in Ni-R and Ni-SI models is calculated to be very small and may be overcome at room temperature to allow a spin crossover. Moreover, the relative stability of the Ni-SI and Ni-R structures adopted in the present investigation is fully compatible with their involvement in the reversible heterolytic cleavage of H(2).

Vibrational study of the Fe(phen)2(NCS)2 spin-crossover complex by density-functional calculations

The geometries and vibrational frequencies of an iron(II) spin-crossover complex Fe(phen)2(NCS)2 in the low- and high-spin states have been calculated using DFT (BP86 functional with 6-311G* + Wachters + f, 6-31G* and LANL2DZ basis sets). A redundancy-free set of internal coordinates has been defined and used to obtain a valence force field. The use of the symmetry coordinates of a perfect octahedron as internal coordinates for the FeN6 framework of the complex has enabled the description of the stretching-bending couplings. A comparison of the force constants of free ligands with the corresponding constants of the two spin states has provided a basis for the discussion of the changes in electronic charge distribution in the complex. By use of the generalized harmonic mode scrambling, it is shown that in the low-lying normal vibrations of the complex, the ligands participate as almost rigid units. Energies of these modes are close to the oscillators describing the interaction of the complex with the surrounding molecules in the solid phase.

Cooperative Spin Crossover and Order−Disorder Phenomena in a Mononuclear Compound [Fe(DAPP)(abpt)](ClO4)2 [DAPP = [Bis(3-aminopropyl)(2-pyridylmethyl)amine], abpt = 4-Amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole]

The synthesis and detailed characterization of the new spin crossover mononuclear complex [Fe(II)(DAPP)(abpt)](ClO(4))(2), where DAPP = [bis(3-aminopropyl)(2-pyridylmethyl)amine] and abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole, are reported. Variable-temperature magnetic susceptibility measurements and Mössbauer spectroscopy have revealed the occurrence of an abrupt spin transition with a hysteresis loop. The hysteresis width derived from magnetic susceptibility measurements is 10 K, the transition being centered at T(c) downward arrow = 171 K for decreasing and T(c) upward arrow = 181 K for increasing temperatures. The crystal structure was resolved in the high-spin (293 and 183 K) and low-spin (123 K) states. Both spin-state structures belong to the monoclinic space group P2(1)/n (Z = 4). The thermal spin transition is accompanied by the shortening of the mean Fe-N distances by 0.177 A. The two main structural characteristics of [Fe(DAPP)(abpt)](ClO(4))(2) are a branched network of intermolecular links in the crystal lattice and the occurrence of two types of order-disorder transitions (in the DAPP ligand and in the perchlorate anions) accompanying the thermal spin change. These features are discussed relative to the magnetic properties of the complex. The electronic structure calculations show that the structural disorder in the DAPP ligand modulates the energy gap between the HS and LS states. In line with previous studies, the order-disorder phenomena and the spin transition in [Fe(DAPP)(abpt)](ClO(4))(2) are found to be interrelated.

Theoretical Studies of the Complex [(BPMEN)Fe(II)(NCCH3)2]2+, Precursor of Non-Heme Iron Catalysts for Olefin Epoxidation and Cis-Dihydroxylation

The density functional theory (DFT) was applied to elucidate the electronic structure of the BPMEN [N,N'-bis(6-R-2-pyridylmethyl)-1,2-diaminoethane] iron complex, [(BPMEN)Fe(NCCH3)2](2+), a precursor of catalysts that catalyze the stereospecific olefin oxidation. The low-lying high and low spin states of complex 1 (R=H) are nearly degenerate with a slight preference for the high spin state. For complexes with substituents (R) at the 6-positions of two pyridine rings of BPMEN, the ground state is the high spin (HS) state, with the low spin (LS) state higher in energy by 9.5, 5.3, 8.5, 6.3, and 5.1 kcal/mol for complexes 2 (R=CH3), 3 (R=SiH3), 4 (R=OH), 5 (R=F), and 6 (R=CN), respectively, with the B3LYP method. Our findings for complexes 1 and 2 are in good agreement with the experimental observations. The calculated LS-HS difference of 17.9 kcal/mol for complex 7 (R=t-Bu) clearly demonstrates that the steric effect causes the Fe-N bonds to stretch and favors the high spin state. Comparison of the B3LYP and B3PW91 results with experiments and ab initio MP2 and CCSD(T) as well as pure DFT results shows that hybrid DFT methods provide a qualitatively correct description of the relative energies of low-lying electronic states of a model of the [(BPMEN)Fe(NCCH3)2](2+) complex, while pure DFT methods underestimate the stability of the HS state.

Theoretical study of the Fe(phen)(2)(NCS)(2) spin-crossover complex with reparametrized density functionals

The theoretical study of spin-crossover compounds is very challenging as those parts of the experimental findings that concern the electronic structure of these compounds can currently hardly be reproduced because of either technical limitations of highly accurate ab initio methods or because of inaccuracies of density functional methods in the prediction of low-spin/high-spin energy splitting. However, calculations with reparametrized density functionals on molecules of the thermal spin-crossover type can give improved results when compared with experiment for close-lying states of different spin and are therefore important for, e.g., transition metal catalysis. A classification of transition metal compounds within hybrid density functional theory is given to distinguish standard, critical, and complicated cases. From the class of complicated cases we choose the prominent spin-crossover compound Fe(phen)(2)(NCS)(2) and show in a first step how the electronic contribution to the energy splitting can be calculated. In a second step, the vibrational effects on the spin flip are investigated within the harmonic force-field approximation of the isolated-molecule approach. A main result of the study is the necessity of exact-exchange reduction in hybrid density functionals to arrive at reasonable electronic energy splittings. The study resolves problems that originated from the use of standard density functionals, which are not able to reproduce the electronic contribution to the low-spin/high-spin splitting correctly, and demonstrates to which extent reparametrized density functionals can be used for the prediction of the spin-crossover effect.

The spin distribution in low-spin iron porphyrins

In many low-spin (S = 1/2) iron porphyrin derivatives, electron spin resonance (ESR) spectra indicate that one of the d(pi) orbitals of iron, either a d(xz) or d(yz), depending on the axial ligands of the porphyrin complex as well as their orientation, is essentially singly occupied; the unpaired electron is almost completely located at the metal. In contrast, nuclear magnetic resonance (NMR) and electron nuclear double resonance (ENDOR) spectroscopy convincingly show that a significant share of the unpaired electron is delocalized. This apparent contradiction is explained by the present density-functional-theory (DFT) calculations performed on a heme a model as well as on bis-imidazole-ligated iron porphyrin without substituents. The calculations show that the integrated spin density at the iron atom is nearly one, in agreement with the ESR measurements. However, significant areas with opposite (beta) spin are found along the Fe-N bond axes, thus evoking a need for additional alpha-spin density to be present in the porphyrin ring, ring substituents, and the axial ligands to keep the net amount of unpaired spin exactly one. The gross spin density, that is, the sum of unpaired alpha and beta spins, amounts to about 1.3 electrons. It seems that the degree to which alpha and beta spin dominate in different regions of the heme structure, as evidenced in these calculations, has not been previously observed.