Single Molecule Magnets Exploiting the 5f Electrons of Plutonium.

[NNadir]

The paper I'll discuss in this brief post is this one: Theoretical Investigation of Plutonium-Based Single-Molecule Magnets (Carlo Alberto Gaggioli and Laura Gagliardi,* Inorg. Chem., 2018, 57 (14), pp 8098–8105).

From a purely theoretical standpoint, plutonium is one of the most interesting elements in the periodic table. It's huge array of electrons and orbitals, traveling around a heavy nucleus and thus requiring the electrons to travel at relativistic speeds, a significant fraction of the speed of light, the shielding these electrons bring, the fact that it has a nearly half filled set of f orbitals and its myriad oxidation states and habit of disproportionation (oxidizing and reducing itself simultaneously), never mind its radiation effects all combine to produce a real sense of fascination.

A surprising paper, published this year, (the paper cited above) suggest that plutonium species are worthy of study because of a potential (but perhaps not practical) use in computer hardware. (Perhaps it can at least elucidate a path to other elements, in particular lanthanides, perhaps cerium.)

Or perhaps not, from the introductory text:

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...

...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.

However, after some very sophisticated computer modeling the authors note that such a mononuclear complex of plutonium has been synthesized. It is here:



The caption:

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].

It is known to be exhibit magnetic susceptibility, which the authors explore from a theoretical standpoint with a sophisticated computational analytical method:

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 (sextet 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 then performed a multistate CASPT2 calculation (MS-CASPT2)(66) using an IPEA shift of 0.25 and an imaginary shift of 0.2 atomic unit on a selected set of states (vide infra). 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 van-Vleck formalism (eq 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



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.



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.

It might be lots of jargon, but it gives a feel for the task...

The authors determine the energies of various electronic states, which is described in the following graphic:



The caption:

Figure 2. Scheme of CASSCF relative energies for compound 1. The red, blue, and orange rectangles represent the range of relative energies covered by the roots of the sextet, quartet, and doublet spin states, respectively. The first sextet root is the ground state, while the first quartet and doublet roots lie 16238 and 24627 cm–1 above the ground state, respectively. The green line represents the first root corresponding to a Pu 5f to 6d transition, which lies at 58283 cm–1. The black line represents the first root corresponding to a ligand to metal charge transfer, which lies at 105235 cm–1.

And the point of the calculation, the magnetic susceptibility:



The caption:

Figure 3. Magnetic susceptibility curves for PuTp3, system 1, and for system 2 using different methodologies. Experimental (black circles),(59) SO-CASSCF(5,7) set 1 for system 1 colored blue, SO-CASSCF(5,7) set 2 for system 1 colored red, SO-CASSCF(5,7) set 4 for system 1 colored green, and SO-CASSCF(5,7) set 1 for system 2 colored orange.

The success of a model really depends on how closely it matches experiment.

The authors comment:

We notice that the results depend on the number of states included in the calculation. For example, for set 1 and set 2, at low temperatures, the initial points are close to the experimental curve but the slope of the curve is different from the experimental one. On the other hand, by using set 4, the slope of the curve is more similar to the experimental one, even if the whole curve is shifted to lower χ values. The curves reported in Figure 3 do not show the same steep increase at low temperatures as that seen in the experimental curve. This is certainly due to the various approximations that we employ in the generation of the computed curves, such as the employed level of theory (here we used only SO-CASSCF calculations, because SO-MS-CASPT2 ones are prohibitively expensive), and probably intermolecular coupling and vibronic contributions (which are omitted and go beyond the scope of the work) that may have an effect on changing the shape of the curve. However, a closer inspection reveals that this increase in the magnetic susceptibility at low temperatures is quite small in absolute value.

But in their conclusion the authors note that they are on the path to success:

To explore the possible applications of actinides as SMMs, we performed a theoretical study of the electronic structure of a plutonium-based SMM, PuTp3, by means of multiconfigurational quantum chemical calculations, including spin–orbit coupling. The states arising from the Pu(III) 5f 5 electronic configuration occur in the energy range of 0–30000 cm–1, while the ligand to metal charge transfer and Pu 5f to 6d excitations occur at much higher energies (∼100000 and ∼60000 cm–1, respectively). We predicted the first Kramers doublet excited state to occur at 373 cm–1, in agreement with the experimentally measured first excited state (332 cm–1). Furthermore, the computed magnetic susceptibility curve is in qualitative agreement with the experimental one. To computationally predict more efficient SMMs, we investigated the electronic structure of a similar system with a modified ligand, namely a stronger σ-donor ligand (carbene).

It will be interesting to see if someone is able to synthesize the improved complex they predict will be superior.

It is difficult to imagine that plutonium based computer hardware will ever be practical of course; the reason for doing this work, besides testing theory that might be useful in other areas with other elements, is that it is extends pure knowledge, it causes to stretch our scientific intellectual muscles to inspire wonder.

Of, course, in the abstract, one notes that plutonium has at least two isotopes with very long half-lives, and thus lower radioactivity, that one might imagine might be sufficiently stable to build such a device, Pu-242 and Pu-244. The latter isotope has a half-life of 80 million years. However Pu-244 is very difficult to access. Other than atom-by-atom synthesis in an accelerator, the generation of this isotope is extremely complex, particularly if one is seeking high isotopic purity. It would involve the long term irradiation of pure americium, with the goal of displacing as much as the lower readily available isotope, Am-241, with the higher isotope, Am-243. This would require periods of irradiation punctuated by separations to remove resultant Pu-238 (from the decay of Cm-242) and Pu-242 (also from the branched decay of Cm-242), until reasonably pure Am-243 resulted for a final irradiation. Pu-244 arises from one branch (the minor branch, about 1%) of the decay of Am-244. The separation would need to take place fairly early, since the other isotope produced from the decay of Am-244, Cm-244, decays with an 18 year half life to a contaminating isotope (and neutron emitter) Pu-240.

...Not worth it I think.

Nevertheless, the paper itself was worth a read, because it's fun, and interesting, and it expands one's mind.

I hope your New Year's plans are proceeding nicely. Have fun and be safe.

[TexasTowelie]

1. The horrors of advanced inorganic chemistry have returned.

The professor that I had never deviated from the textbook so the only thing I had to do was bring a highlighter to class.

I understood about 80% of that discussion.

[Victor_c3]

2. Thanks for posting this

.... and the other articles that you’ve provided.

As the guy above mentioned, I only get about 80% of it, but I appreciate the mental workout and a the bit of understanding that I did gain.

Since my retirement nearly four years ago, I’ve missed working in the field of chemistry. I’m only 38 so I guess it’s possible that I could go back to work, but I’m doubtful. In the meantime, I certainly enjoy the articles you post.