Coen de Graaf

Magnetic coupling in biradicals, binuclear complexes and wide-gap insulators: a survey of ab initio wave function and density functional theory approaches

Abstract. State-of-the-art computational approaches to magnetic coupling in biradicals, dinuclear complexes and wide-gap insulators are reviewed with the aim to provide a unified point of view. The most rigorous wave-function-based methods provide an accurate description of magnetic coupling in all these systems, whereas density-functional-based methods within the broken symmetry approach provide an alternative, yet efficient, computational tool. The use of mapping procedures permits the broken symmetry solution to be related to the appropriate spin state. Different arguments are given to show that the neglect of this procedure may lead to values in agreement with experiment, but at the cost of serious contradictions.

Magnetic interactions in molecules and highly correlated materials: physical content, analytical derivation, and rigorous extraction of magnetic Hamiltonians.

Physical Content, Analytical Derivation, and Rigorous Extraction of Magnetic Hamiltonians Jean Paul Malrieu,† Rosa Caballol,‡ Carmen J. Calzado, Coen de Graaf,‡,∥ and Nathalie Guiheŕy*,† †Laboratoire de Chimie et Physique Quantiques, Universite ́ de Toulouse 3, 118 route de Narbonne, 31062 Toulouse, France ‡Departament de Química Física i Inorgaǹica, Universitat Rovira i Virgili, Marcel·lí Domingo s/n, 43007 Tarragona, Spain Departamento de Química Física, Universidad de Sevilla, Profesor Garcia Gonzalez s/n, 41012 Sevilla, Spain Institucio ́ Catalana de Recerca i Estudis Avanca̧ts (ICREA), Passeig Lluis Companys 23, 08010 Barcelona, Spain

Universal Theoretical Approach to Extract Anisotropic Spin Hamiltonians

Monometallic Ni(II) and Co(II) complexes with large magnetic anisotropy are studied using correlated wave function based ab initio calculations. Based on the effective Hamiltonian theory, we propose a scheme to extract both the parameters of the zero-field splitting (ZFS) tensor and the magnetic anisotropy axes. Contrarily to the usual theoretical procedure of extraction, the method presented here determines the sign and the magnitude of the ZFS parameters in any circumstances. While the energy levels provide enough information to extract the ZFS parameters in Ni(II) complexes, additional information contained in the wave functions must be used to extract the ZFS parameters of Co(II) complexes. The effective Hamiltonian procedure also enables us to confirm the validity of the standard model Hamiltonian to produce the magnetic anisotropy of monometallic complexes. The calculated ZFS parameters are in good agreement with high-field, high-frequency electron paramagnetic resonance spectroscopy and frequency domain magnetic resonance spectroscopy data. A methodological analysis of the results shows that the ligand-to-metal charge transfer configurations must be introduced in the reference space to obtain quantitative agreement with the experimental estimates of the ZFS parameters.

Origin of the Magnetic Anisotropy in Heptacoordinate Ni-II and Co-II Complexes

The nature and magnitude of the magnetic anisotropy of heptacoordinate mononuclear Ni(II) and Co(II) complexes were investigated by a combination of experiment and ab initio calculations. The zero-field splitting (ZFS) parameters D of [Ni(H(2)DAPBH)(H(2)O)(2)](NO(3))(2)⋅2 H(2)O (1) and [Co(H(2)DAPBH)(H(2)O)(NO(3))](NO(3)) [2; H(2)DAPBH = 2,6-diacetylpyridine bis- (benzoyl hydrazone)] were determined by means of magnetization measurements and high-field high-frequency EPR spectroscopy. The negative D value, and hence an easy axis of magnetization, found for the Ni(II) complex indicates stabilization of the highest M(S) value of the S = 1 ground spin state, while a large and positive D value, and hence an easy plane of magnetization, found for Co(II) indicates stabilization of the M(S) = ±1/2 sublevels of the S = 3/2 spin state. Ab initio calculations were performed to rationalize the magnitude and the sign of D, by elucidating the chemical parameters that govern the magnitude of the anisotropy in these complexes. The negative D value for the Ni(II) complex is due largely to a first excited triplet state that is close in energy to the ground state. This relatively small energy gap between the ground and the first excited state is the result of a small energy difference between the d(xy) and d(x(2)-y(2)) orbitals owing to the pseudo-pentagonal-bipyramidal symmetry of the complex. For Co(II), all of the excited states contribute to a positive D value, which accounts for the large magnitude of the anisotropy for this complex.

Electronic Structure and Redox Properties of Metal Nitride Endohedral Fullerenes M3N@C2n (M=Sc, Y, La, and Gd; 2n=80, 84, 88, 92, 96)

An extensive study of the redox properties of metal nitride endohedral fullerenes (MNEFs) based on DFT computational calculations has been performed. The electronic structure of the singly oxidized and reduced MNEFs has been thoroughly analyzed and the first anodic and cathodic potentials, as well as the electrochemical gaps, have been predicted for a large number of M(3)N@C(2n) systems (M=Sc, Y, La, and Gd; 2n=80, 84, 88, 92, and 96). In particular, calculations that include thermal and entropic effects correctly predict the different anodic behavior of the two isomers (I(h) and D(5h)) of Sc(3)N@C(80), which is the basis for their electrochemical separation. Important differences were found in the electronic structure of reduced M(3)N@C(80) when M=Sc or when M is a more electropositive metal, such as Y or Gd. Moreover, the changes in the electrochemical gaps within the Gd(3)N@C(2n) series (2n=80, 84, and 88) have been rationalized and the use of Y-based computational models to study the Gd-based systems has been justified. The redox properties of the largest MNEFs characterized so far, La(3)N@C(2n) (2n=92 and 96), were also correctly predicted. Finally, the quality of these predictions and their usefulness in distinguishing the carbon cages for MNEFs with unknown structures is discussed.

On the applicability of multireference second-order perturbation theory to study weak magnetic coupling in molecular complexes.

The performance of multiconfigurational second‐order perturbation techniques is established for the calculation of small magnetic couplings in heterobinuclear complexes. Whereas CASPT2 gives satisfactory results for relatively strong magnetic couplings, the method shows important deviations from the expected Heisenberg spectrum for couplings smaller than 15–20 cm−1. The standard choice of the zeroth‐order CASPT2 Hamiltonian is compared to alternative definitions published in the literature and the stability of the results is tested against increasing level shifts. Furthermore, we compare CASPT2 with an alternative implementation of multiconfigurational perturbation theory, namely NEVPT2 and with variational calculations based on the difference dedicated CI technique.

Study of the Light-Induced Spin Crossover Process of the [FeII(bpy)3]2+ Complex

Ab initio calculations have been performed on [Fe(II)(bpy)3](2+) (bpy = bipyridine) to establish the variation of the energy of the electronic states relevant to light-induced excited-state spin trapping as a function of the Fe-ligand distance. Light-induced spin crossover takes place after excitation into the singlet metal-to-ligand charge-transfer (MLCT) band. We found that the corresponding electronic states have their energy minimum in the same region as the low-spin (LS) state and that the energy dependence of the triplet MLCT states are nearly identical to the (1) MLCT states. The high-spin (HS) state is found to cross the MLCT band near the equilibrium geometry of the MLCT states. These findings give additional support to the hypothesis of a fast singlet-triplet interconversion in the MLCT manifold, followed by a (3)MLCT-HS ((5)T2) conversion accompanied by an elongation of the Fe-N distance.

Light-induced excited-state spin trapping in tetrazole-based spin crossover systems.

Ab initio calculations have been performed on Fe (II) (tz) 6 (tz = 1- H-tetrazole) to establish the variation of the energy of the electronic states relevant to (reverse) light-induced excited-state spin trapping (LIESST) as function of the Fe-ligand distance. Equilibrium distances and absorption energies are correctly reproduced. The deactivation of the excited singlet is proposed to occur in the Franck-Condon region through overlap of vibrational states with an intermediate triplet state or an intersystem crossing along an asymmetric vibrational mode. This is followed by an intersystem crossing with the quintet state. Reverse LIESST involves a quintet-triplet and a triplet-singlet intersystem crossing around the equilibrium distance of the high-spin state. The influence of the transition metal is studied by changing Fe (II) for Co (II), Co (III), and Fe (III). The calculated curves for Fe (III) show remarkable similarity with Fe (II), indicating that the LIESST mechanism is based on the same electronic conversions in both systems.

Theoretical investigation of the electronic structure of Fe(II) complexes at spin-state transitions

The electronic structure relevant to low spin (LS)↔high spin (HS) transitions in Fe(II) coordination compounds with a FeN6 core are studied. The selected [Fe(tz)6]2+ (1) (tz = 1H-tetrazole), [Fe(bipy)3]2+ (2) (bipy = 2,2′-bipyridine), and [Fe(terpy)2]2+ (3) (terpy = 2,2′:6′,2″-terpyridine) complexes have been actively studied experimentally, and with their respective mono-, bi-, and tridentate ligands, they constitute a comprehensive set for theoretical case studies. The methods in this work include density functional theory (DFT), time-dependent DFT (TD-DFT), and multiconfigurational second order perturbation theory (CASPT2). We determine the structural parameters as well as the energy splitting of the LS–HS states (ΔEHL) applying the above methods and comparing their performance. We also determine the potential energy curves representing the ground and low-energy excited singlet, triplet, and quintet d6 states along the mode(s) that connect the LS and HS states. The results indicate that while DFT is well suited for the prediction of structural parameters, an accurate multiconfigurational approach is essential for the quantitative determination of ΔEHL. In addition, a good qualitative agreement is found between the TD-DFT and CASPT2 potential energy curves. Although the TD-DFT results might differ in some respect (in our case, we found a discrepancy at the triplet states), our results suggest that this approach, with due care, is very promising as an alternative for the very expensive CASPT2 method. Finally, the two-dimensional (2D) potential energy surfaces above the plane spanned by the two relevant configuration coordinates in [Fe(terpy)2]2+ were computed at both the DFT and CASPT2 levels. These 2D surfaces indicate that the singlet–triplet and triplet–quintet states are separated along different coordinates, i.e., different vibration modes. Our results confirm that in contrast to the case of complexes with mono- and bidentate ligands, the singlet–quintet transitions in [Fe(terpy)2]2+ cannot be described using a single configuration coordinate.

Energetics of [Fe(NCH)6]2+ via CASPT2 calculations: a spin-crossover perspective.

The importance of basis sets and active spaces in the determination of the potential energy curves and relevant energy differences in the Oh‐symmetry model system [Fe(NCH)6]2+ is analyzed using the Complete Active Space Self‐Consistent Field (CASSCF) method and subsequent second‐order perturbative treatment (CASPT2). By comparison of a series of atomic basis sets contraction, it is concluded that a balanced description of the Fe 7s6p5d3f2g1h and N 4s3p1d partners is needed to reach convergence upon the potential energy surface descriptions. Since the spin‐crossover phenomenon involves the simultaneous change in the spin nature and expansion of the coordination sphere of the metal ion (i.e., lengthening of the Fe‐N distances), the standard 10 electrons/12 orbitals complete active space is confronted to a chemically intuitive 18 electrons/15 orbitals picture. The role of a second d‐shell is finally examined using the extended RAS strategy. Using a valence‐bond type analysis, it is shown that the so‐called d′ orbitals allow for a significant charge redistribution (∼0.5 electron) along the transition. Our calculations are compared to reference coupled‐cluster estimations.