Article pubs.acs.org/IC
Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Theoretical Investigation of Plutonium-Based Single-Molecule Magnets Carlo Alberto Gaggioli and Laura Gagliardi* Department of Chemistry, Chemical Theory Center and Supercomputing Institute, University of Minnesota, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455-0431, United States
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S Supporting Information *
ABSTRACT: The electronic structure of a plutonium-based singlemolecule magnet (SMM) was theoretically examined by means of multiconfigurational electronic structure theory calculations, including spin−orbit coupling effects. All Pu 5f to 5f transitions for all possible spin states were computed, as well as ligand to metal charge transfer and Pu 5f to 6d transitions. Spin−orbit coupling effects were included a posteriori to accurately describe the electronic transitions. The spin− orbit coupled energies and magnetic moments were then used to compute the magnetic susceptibility curves. The experimental electronic structure and magnetic susceptibility curve were reproduced well by our calculations. A compound with a modified electron-donating ligand (namely a carbene ligand) was also investigated in an attempt to tune the electronic properties of the plutonium SMM, revealing a higher ligand field splitting of the 5f orbitals of Pu, which could in turn enhance the barrier against magnetic relaxation.
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INTRODUCTION
ionic interaction with surrounding spin-magnetized molecules.12 The actinide elements instead, because of their large spin− orbit coupling and the radial extension of the 5f orbitals, are more promising for the design of both mononuclear and exchange coupled molecules. Indeed, new actinide SMMs have emerged and are already demonstrating encouraging properties.18−25 The actinides present a non-negligible covalency of the metal−ligand interaction,26,27 and while covalency offers an advantage for the generation of strong magnetic exchange, it also makes the rational design of mononuclear actinide complexes more challenging than in the lanthanide case. For example, one successful way to rationally design mononuclear lanthanide systems is to choose a suitable ligand field symmetry to split the ground magnetic state of the complex into ±MJ sublevels, and the levels with the higher |MJ| values are stabilized with respect to the levels with the lower |MJ| values.28−30 Since for lanthanides the covalent interactions are minimal, the ligand field acts as an electrostatic perturbation that splits the degenerate MJ states within the ground J manifold. For actinides, this approach may present more challenges because of the possible presence of strong covalency, and therefore, the ligand would no longer participate only through a purely electrostatic contribution. On the other hand, covalency may be helpful for obtaining larger overall crystal field splitting with respect to the isoelectronic lanthanide complexes.
Single-molecule magnets (SMMs) can reduce the length scale of magnetic materials that have potential applications in information storage, quantum information processing, and spin electronics.1−6 Commonly used magnetic materials work because of the spin interactions between neighboring units in the bulk, while SMMs exhibit slow relaxation of the magnetization of purely molecular origin, and are thus able to retain their magnetization for a long time. A first example was the polynuclear manganese cluster Mn12O12(CH3COO)16(H2O)4,7 together with other manganese-based compounds.8,9 One of the greatest challenges in the realization of an SMM-based magnetic device consists of achieving higher blocking temperatures against magnetic relaxation, which are too low for practical applications, especially in transition metal-based SMMs.10,11 SMMs present high-spin ground states in which the effect of spin−orbit coupling produces a zero field splitting of the (2S + 1)-fold degenerate ground multiplet. Transition metals, by having a low spin−orbit coupling effect, give rise to SMMs with low blocking temperatures. SMMs that contain single and multiple lanthanide ions, on the other hand, present a larger first-order spin−orbit coupling, generating sizable magnetic anisotropies,12−15 which are in turn responsible for high relaxation barriers and therefore slow magnetic relaxation.15−17 However, the 4f orbitals have a limited radial extent and are energetically incompatible with ligand orbitals. As a result, well-isolated spin ground states are difficult to form, and only weak magnetic superexchange coupling can be obtained, because of prevailing © XXXX American Chemical Society
Received: January 19, 2018
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DOI: 10.1021/acs.inorgchem.8b00170 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
successful way to include dynamic correlation is to use perturbation theory, such as the implementation of CASPT245,46 or NEVPT2.47 While these methods have been extensively applied for transition metal complexes, there have been fewer applications to lanthanide and actinide SMMs.48−54 In a previous work,53 the electronic structure of four different uranium-based SMMs (experimentally synthesized)55−58 was theoretically analyzed, by means of multiconfigurational methodologies, to understand the effect of the ligand on the magnetic properties of these SMMs. We computed ligand to metal charge transfer transitions, and U 5f to 5f and U 5f to U 6d transitions, including spin−orbit coupling, which is related to the magnetization barrier. Furthermore, the magnetic susceptibility curve as a function of temperature was calculated. Recently, a Pu-based SMM [PuTp3, where Tp− = hydrotris(pyrazolyl)borate] (Figure 1, system 1) was synthesized and
Furthermore, the nature of the magnetization relaxation is still not completely understood, which makes it even more difficult the design of novel and more efficient SMMs.31,32 For example, in f systems, the relaxation often occurs via only one or two steps, which encompass direct, Van Vleck Raman, Orbach, second-order Raman, and quantum tunneling relaxation processes.31 The first four processes arise from the interaction of the magnetic ion and the lattice. In direct relaxation, the molecule makes a direct transition from a crystal field microstate to another, in which the energy gained is released by the lattice as a phonon. In the Raman process, a superposition of two lattice waves with an energy difference that exactly matches the relaxation energy absorbs the latter. In the first-order Raman process, a two-phonon process via a virtual intermediate state of the lattice is followed. If not only the lattice but also the magnetic ion undergoes a transition via a virtual intermediate state, the relaxation process is called a second-order Raman process. The Orbach process occurs instead when the magnetic ion possesses low-lying excited states, and an absorption of one phonon excites the spin system, which then relaxes to the ground state, with the concerted emission of a phonon. The quantum tunneling process instead does not require the interaction of the magnetic ion with the lattice (see ref 1 for further theory insights). Moreover, spin-phonon coupling can also play an important role in the nature of magnetic relaxation, and only very recently have papers tackling this problem appeared in the literature.33,34 From the modeling point of view, actinides are quite challenging because they present a complex electronic structure with open-shell 5f electrons and strong relativistic effects, including high spin−orbit coupling, which cannot be neglected. Actinide-based SMMs are inherently multiconfigurational systems, namely systems whose electronic structure cannot be accurately represented by a single Slater determinant approach, such as density functional theory (DFT). Indeed, the accuracy of Kohn−Sham DFT strongly depends on the functional employed.35−37 Multiconfigurational quantum chemistry methodologies are therefore usually needed. Of particular relevance are the multiconfigurational self-consistent field (MCSCF) methods, which can treat accurately near degeneracy of different electronic configurations and therefore recover the static contribution of the correlation energy. One of the most successful MCSCF methods is the complete active space SCF (CASSCF),38 which allows the selection of only chemically relevant orbitals and electrons (the active space). The wave function is constructed as a linear combination of all electronic configurations that can be generated by distributing the active electrons in the active orbitals in all possible ways, with a given spatial and spin symmetry. The major drawback of this methodology is the exponential increase in the number of determinants and configuration state functions (and therefore computational resources) with the number of orbitals and electrons included in the active space, which limits the applicability of CASSCF. Other methodologies have been developed to broaden the applicability of active space-based methods, such as the restricted active space (RASSCF)39,40 and generalized active space (GASSCF)41 methods. As stated before, these methods take into account static correlation but do not generally recover dynamic correlation,42−44 which arises from the instantaneous interactions of the electrons with each other and is an additional fundamental contribution to the total electronic energy that cannot be neglected. One
Figure 1. Schematic representation of the complexes studied. Left: system 1, PuTp3.59 Right: system 2, Pu complex with a modified ligand (carbene ligand) [Tp− = hydrotris(pyrazolyl)borate].
showed a slow magnetization relaxation, with a measured effective anisotropy barrier ∼5 times larger than that of the isostructural uranium-based SMM.59 In this study, we analyze theoretically the electronic and magnetic properties of this SMM and a variant of it with a different ligand. To the best of our knowledge, this is the first theoretical analysis of transuranium-based SMMs. The paper is structured as follows. After describing the computational methods employed, we analyze the electronic structure of the experimentally synthesized Pu SMM, by means of CASSCF and CASPT2, including spin−orbit coupling, and relate the results of this analysis to the magnitude of the magnetic relaxation barrier. We then explore a second system (Figure 1, system 2) with a different ligand, namely an electron-rich carbene, that should have an electronic structure different from that of 1. We finally compute the magnetic susceptibility curves for these species and compare them with available experimental results for 1. B
DOI: 10.1021/acs.inorgchem.8b00170 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
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μ ̂ = μB (geS ̂ + L̂)
COMPUTATIONAL METHODS
DFT calculations were performed using the ADF2016 software package.60 The BP86 functional was employed,61 which gave reliable geometries for closely related uranium SMMs,53 together with a TZ2P basis set for plutonium and DZP for all the other atoms, and the zeroth-order regular approximation (ZORA) to account for scalar relativistic effects.62 Geometry optimizations were performed for the maximum spin multiplicity, which corresponds to an MS of 5 (sextet 2 spin state), because plutonium is in the +3 oxidation state (five unpaired 5f electrons). The differences in DFT-optimized geometry and experimental geometry are very small [∼0.02 Å (Table S1)], and we can thus safely make use of DFT-optimized geometries. The electronic structures were further characterized using multireference methods. The wave functions were optimized at the complete active space self-consistent field (CASSCF)38 level of theory. All-electron basis sets of atomic natural orbital type with relativistic core corrections (ANO-RCC) were used,63 employing a triple-ζ plus polarization basis set for Pu (VTZP) and double-ζ plus polarization basis set for the other atoms (VDZP). The resolution of identity Cholesky decomposition (RICD)64 was employed to reduce the time for the computation of the two-electron integrals. Scalar relativistic effects were included by means of the Douglas−Kroll− Hess Hamiltonian.65 The smallest active space employed in this work is a CASSCF(5,7) active space, meaning five electrons and seven orbitals, which takes into account all the configuration state functions (CSFs) arising from the distributions of the five electrons of Pu(III) in the seven 5f orbitals. This active space gives rise to 21 sextet, 224 quartet, and 490 doublet roots. We further examined an enlarged active space [CASSCF(5,12)], in which we included the five unoccupied 6d orbitals of plutonium, to account for possible low-energy 5f to 6d excitations. We also tried to compute a CASSCF(9,9) wave function by adding to the CASSCF(5,7) two Π doubly occupied orbitals localized on the ligand, to encompass metal-to-ligand charge transfers (MLCTs). Unfortunately, we were unable to obtain the desired orbitals in the active space; namely, the two Π doubly occupied orbitals localized on the ligand always rotate out of the active space and are replaced by two p-type orbital localized on plutonium. Nevertheless, we noticed that the first two highest doubly occupied orbitals (inactive) in the CASSCF(5,7) wave function are actually the Π orbitals localized on the ligand (vide inf ra). We thus estimated the energy of the MLCT transitions by performing a CASCI optimization on the CASSCF(5,7) wave function using an active space of (9,9) (including the two Π doubly occupied orbitals localized on the ligand). The CASCI procedure performs only the optimization of the CI coefficients, avoiding the orbital optimization (and therefore also their rotation), and by including more roots in the calculation, we were able to estimate the energy of these transitions. We then performed a multistate CASPT2 calculation (MSCASPT2)66 using an IPEA shift of 0.25 and an imaginary shift of 0.2 atomic unit on a selected set of states (vide inf ra). Spin−orbit (SO) coupling effects were estimated a posteriori by using the RAS state interaction (SO-RASSI) method.67 Finally, we computed the magnetic susceptibilities with the SINGLE-ANISO code,68−70 which requests as input energies (ε) and magnetic moments (μ) of the spin−orbit states obtained from the RASSI calculation and uses them in an equation based on the vanVleck formalism (eq 1). χ (T ) ∝
where ge (=2.0023) is the free spin g factor, μB is the Bohr magneton, and Ŝ and L̂ are the operators of the total spin momentum and the total orbital momentum, respectively. Ŝ =
i=1
L̂ =
∑ li ̂ i=1
The summations run over all electrons of the complex. For compound 1, the calculations described above were also performed at the experimental geometry to confirm that the two different geometries give similar results. All multireference calculations were performed with the MOLCAS 8.2 software package.72
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RESULTS AND DISCUSSION We first discuss the experimentally characterized PuTp3 system (Figure 1, system 1), in which the sextet spin state is the ground state, corresponding to the Pu(III) atomic term S = 5 , 2 6 H5/2,59 with five unpaired electrons in the 5f orbitals. In the first instance, we performed a CASSCF(5,7) calculation using the state average (SA) approach, including all possible roots that can be generated with this active space (21 sextets, 224 quartets, and 490 doublets) that we term set 1. The absolute and relative energies for the different spin states are reported in Tables S2 and S3. The lowest-energy roots are two sextets, almost degenerate within 28 cm−1. They are followed by sextet states 3−11, which are within 1128 cm−1 of the lowest sextet root. There is then an energy gap between sextet roots 11 and 12 and a second energy gap between roots 18 and 19. The highest sextet spin root is located at 22223 cm−1. The most stable quartet and doublet roots lie 16238 and 24627 cm−1, respectively, above the ground sextet state. With regard to the quartet spin states, there is a gap in energy between roots 128 and 129, with the highest quartet root at 67301 cm−1. With regard to the doublet spin states, the most stable root is located at 24627 cm−1, with an energy gap between roots 272 and 273. The highest doublet root is 112558 cm−1 higher than the ground state. As stated in Computational Methods, we calculated the energies of the MLCT transitions (in the sextet spin state) by performing a CASCI with an active space of nine electrons in nine orbitals on top of the SA-CASSCF(5,7) (set 1) orbitals. We followed this procedure because inspection of the orbitals of the SA-CASSCF(5,7) calculation shows that the two first inactive orbitals below the active space are exactly the orbitals we would like to include in an extended active space, namely the two Π-ligand orbitals. So we used this orbital space of (9,9) but did not reoptimize the orbitals because they are the desired orbitals. This is an established procedure in multireference calculations, in which one first obtains the orbitals of interest and then performs a CI calculation, without reoptimizing the orbitals. We performed the aforementioned CASCI calculation with 25 sextet states, instead of 21, to inspect if the next four sextet states are of LMCT type. In Table S4, we show that the first 21 transitions are of Pu 5f−5f type, while the last four are ligand π to Pu 5f transitions. We further performed a SACASSCF(5,12) calculation (see Computational Methods for active space details) including 21 sextet, 128 quartet, and 272 doublet roots (named set 2). We would like to state that we employed the (5,12) active space to compute 5f to 6d transitions, not to corroborate the CASSCF(5,7) results. We employed set 2 (and not set 1) to facilitate the calculation
∑i e−εi / kT ∑j μ(i , j)2 ∑i e−εi / kT
Nel
Nel
∑ sî
(1)
The magnetic susceptibility is a function of temperature and arises from the sum over the spin states (i,j) of the magnetic moments weighted by the Boltzmann population of each state. The magnetic moments are calculated by applying the magnetic moment operator in the basis of multiplet eigenstates.71 The magnetic moment operator reads C
DOI: 10.1021/acs.inorgchem.8b00170 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
between roots 11 and 12 (see Table S3)]. This calculation was too expensive, and only eight single CASPT2 states were computed (Tables S6 and S7). We can see that the relative CASPT2 energies are close to the SA-CASSCF(5,7) (with set 3, compare the second and third columns in Table S7). The differences between CASSCF and CASPT2 relative energies are ∼160 cm−1 for the third, fourth, and sixth roots and ≤100 cm−1 for the others. Furthermore, the second root becomes more stable (only 2.7 cm−1 more stable than root 1). In summary, the effect of PT2 on top of the CASSCF wave function does not seem to be large. Furthermore, we have not computed the spin−orbit coupling on top of CASPT2, which may mitigate the energy difference with respect to CASSCF. The different sets of states used in the various multireference calculations are summarized in Table 1.
convergence, including the states below a large gap in energy (for example, up to sextet root number 21, up to quartet root 128, and up to doublet root 272). We believe that the inclusion of higher excited states would not change the description. The 5f to 6d excitation energies (in the sextet spin state) have been computed from the optimized SA-CASSCF(5,12) wave function performing a CASCI with 25 roots. In this way, the roots after 21 (the first 21 correspond to 5f to 5f transitions) represent the desired transitions (relative energies are listed in Table S3; see Table S5 for their assignment). The CASSCF(5,7) energies for the sextet, quartet, and doublet roots, together with the CASSCF(5,12) sextet and the estimated four ligand-Π to 5f charge transfer energies, are reported in Table S3. The Pu 5f to 6d transitions occur at high energy (the first one is at 58283 cm−1), and the LMCT transitions occur at even higher energies (the first one is at 105235 cm−1). Because the first sextet LMCT and 5f to 6d transition lie more than 58000 and 100000 cm−1 higher than the ground state, the quartet and doublet LMTCs and 5f to 6d transitions will lie even higher in energy, and they will thus not significantly interact through spin−orbit coupling with the lower-energy states. We therefore excluded the computation of both transitions for the quartet and doublet spin states. In Figure 2, a scheme with the relevant energy states is reported. Based
Table 1. Different Sets of States Used for Multireference Calculations (S, sextet; Q, quartet; D, doublet) set 1 21 S, 224 Q, 490 D states
set 2 21 S, 128 Q, 272 D states
set 3
set 4
11 S states
21 S states
We then performed RASSI calculations to estimate spin− orbit coupling effects. In Table 2, we report the first six Kramers doublet relative energies obtained from four different calculations, namely, a SA-CASSCF(5,7) calculation with set 1, set 2, and set 4 and a SA-CASSCF(5,12) calculation using set 2 (the description of the states employed in the calculations is reported in Table 1). The corresponding absolute energies are reported in Table S8. Set 1 represents the calculation with all the roots included, so it is the most accurate one. The number of roots to be included approaches the computational limit, so we decided to analyze the SO-RASSI results by using also set 2 and set 4, which include fewer roots and therefore are computationally less demanding. This analysis may be helpful in the future for systems with large active spaces and a large number of roots to be included in SO-RASSI. In set 2, we included all the sextet roots (21 sextets) and 128 quartets and 272 doublets, because there is a clear gap between quartet roots 128 and 129 and between doublet roots 272 and 273. The energy differences are quite similar to those of all the methods of choice. The first excited Kramers doublet (for set 1) occurs at 373 cm−1, in close agreement with the experimentally measured first excited state (332 cm−1).59 This value could be qualitatively correlated to the magnetization decay (in the double-potential well picture),31,73 in the sense that the higher the energy of the first excited state, the slower the magnetization relaxation, because the excited state will be less populated (according to the Boltzmann population) and the system will remain in the ground state for a longer period of time. The computed first excited state for PuTp3 (373 cm−1) is higher than that for the analogous uranium complex (258 cm−1 for UTp3).53 This trend is in agreement with the higher relaxation barrier for the Pu compound. However, other decay processes can be followed by the system,31,32 and for PuTp3, tunneling effects that foster the magnetization relaxation may play a role59 but are not considered in this study. Another important effect that can foster magnetic relaxation is spin-phonon coupling,33,34 a very complex effect that is not investigated in this work. Using set 2, the first Kramers doublet is located at 391.6, with a difference of
