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About

Biosketch

I completed my Ph.D. in inorganic chemistry under Jonas C. Peters at Caltech. My dissertation research focused on nitrogen fixation via transition metal complexes, with a particular focus on the chemistry of iron. As an undergraduate at the University of Chicago, I obtained dual B.Sc. degrees in chemistry and mathematics, studying under the late Gregory L. Hillhouse.

Following the completion of my doctoral studies in 2018, I moved to Cambridge, MA to pursue postdoctoral training under Daniel L. M. Suess, another trainee of Jonas’s who had recently started his own laboratory at MIT. In Cambridge, we revitalized the program of Dick Holm to interrogate the physiochemical properties of iron–sulfur clusters, via novel synthetic approaches pioneered by Dan and his first cohort of students.

Delving into the complex electronic structures of metalloclusters forced my thinking beyond the molecular (few-Å) scale. Indeed, many interesting and unresolved questions emerge from the study of magnetic clusters with respect to their nano- and mesoscale properties. Moreover, the lability of, in particular, iron–sulfur clusters demands us to understand not only intramolecular structure, but also interactions beyond the primary coordination sphere of the metal ions. With this in mind, in 2021 I joined the Solar Energy Conversion Group at Argonne National Laboratory as a postdoctoral appointee under the supervision of David M. Tiede and Karen L. Mulfort.

At Argonne, I am interested in developing methodologies to study the local atomic structure of complex systems via total X-ray scattering. This work synthesizes atomistic simulation with experimental scattering studies, the latter conducted principally at the Advanced Photon Source (and occasionally at PETRA III). My initial interest in total scattering methodologies was due to the remarkable ability of this technique to elucidate solvation structure directly (in situ), and with exquisite resolution (sub-Å). While this remains a focus of my research activity at Argonne, experience with synchrotron X-ray scattering (diffraction) has also widened my interests into materials science, in particular, characterization of the atomic structures of complex, hierarchical materials, such as dye-sensitized metal-oxide thin films, relevant for artifical photosynthesis applications.

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Research interests

My research praxis is: Ask, precise, philisophico-scientific questions, develop the appropriate ansatz to interrogate those questions, and verify (or dispell) that ansatz through an attempted reconcilliation between experiment and theory.

In modern industrial society, it is all-too-easy to subsume Science into Technology, which means: All Science serves an end, an end which operationalizes knowledge. This is a profoundly non-classical position, and, if philosophy of science teaches us anything, an unnecessary one. I prefer the historical category of Natural Philosophy to ‘science’, so understood. This means: Phenomonology, on the one hand, and Philosophy, on the other. A dialectical tension, whose resolution we suppose is called knowledge.

As a pragmatism, one must take some things on faith (i.e., a priori): things (das Ding) happen. The consequences of which happening are measurable (i.e., the objects of observation). This does not mean one measures the things in-themselves. That we can reason about these things, not measurable in-themselves, is the essence (Wesen) of philosophy. Science, in its essentially proper understanding, occurs at the nexus of these axiomatic priors. One reasons the causes (the things) that produce (through an act of faith) the (measurable) phenomena. Rendered in comtemporary dogma, we might say that the many-particle wavefunctions exist, only insofar as we can measure certain projections of their eigenstates—living in (the ineffable) infinite-dimensional Hilbert space—in so-called reality.

[It remains that there may be im-measurable causes (c.f. the Banach-Tarski decomposition of the sphere). Here we move, inexorably, towards mathematics and theology.]

As such, the truth of Science lies precisely in that all true scientific theories are also, therefore, necessarly false. In chemistry, we have bonds, orbitals, atoms-in-molecules, etc. Each one of these concepts is endlessly argued about precisely because they are philosophical, and not natural. Nevertheless, such philosophical hallucinations evidently allow us to reconcile much, if not all, chemical phenomena.

Bioinorganic chemistry

Metals, particularly 3d metals, accomplish the most essential and most challenging chemical transformations that sustain ‘life’. According to H. B. Gray, these are: (i) water oxidation; (ii) carbon fixation, (iii) nitrogen fixation; and, for (iv), one can pick one’s favorite (proton reduction, for example). The study of the metal centers that catalyze these reactions lies at the heart of bioinorganic research.

My practice in bioinorganic chemistry spans the formal (‘model’ chemistry) to the actual (metallocofactors in natural proteins)—although, admittedly, my perspective remains metal-centric. Model chemistry, so-called, is often a purely conceptual exercise, where the species under consideration only abstractly resembles actual metals in biology. Nevertheless, such abstraction does not blunt the power of model chemistries; on the contrary, with the benefit of modern chemical synthesis, one can ask and interrogate bioinorganic questions far more precisely than if one were restricted to the ‘natural’ metallocofactors, bioengineering notwithstanding.

That said, there are certain, privileged classes of cofactors which can be prepared de novo, from their elements, via purely synthetic methods—most notably, perhaps, the iron–sulfur clusters. It is indeed at the level of (weak-field) metalloclusters where evolutionary biology still exceeds the synthetic chemist, and the future, here, lies, no doubt, in mimicking the mesoscale chemical engineering of the cell to template the synthesis of ever-more-complex clusters in vitro. The final dream of an ‘inorganic total sythesis’ is, surely, that of the M-cluster of nitrogenase.

Spectroscopy

Spectroscopy, broadly interpreted, encompasses all light–matter interactions. For the chemist, this means different things at different frequencies.

At very low frequencies, $\mathcal{O}(1\text{ MHz})$, and in reasonable magnetic field strengths, one can probe the nuclear Zeeman interaction (NMR spectroscopy). At slightly higher frequencies, $\mathcal{O}(1\text{ GHz})$, but similar field strengths, one instead probes the electronic Zeeman interaction (EPR spectroscopy). At still higher frequencies, $\mathcal{O}(1\text{ THz})$, one probes the vibrational (vibronic; if you like, phononic) modes typical of molecular materials (IR spectroscopy). Higher, still, $\mathcal{O}(1\text{ PHz})\sim\mathcal{O}(1\text{ eV})$, transitions between electronic states (UV-vis spectroscopy). In the low-energy gamma regime, 14.412 keV, one finds the first nuclear excited state of ⁵⁷Fe (Mößbauer spectroscopy). In a similar regime, $\mathcal{O}(1\text{ keV})$, one finds the 3d metal K-edges (a typical X-ray absorption spectroscopy energy).

All of which is to say, there are a plethora of spectroscopies, sensitive to distinct aspects of the generic ‘chemical system’. Typically, multiple distinct spectroscopic modalities are necessary to even approach what could be called ‘understanding’ of any such system.

Of course, the boundaries above are not strict, and many interesting phenomena occur when there is significant spectral overlap between distinct modalities of light–matter interaction.

X-ray Scattering

At very high photon energies, in the X-ray regime, and especially in the so-called ‘hard’ X-ray regime (say, $\mathcal{O}[0.1\text{ MeV}]$), the light–matter interaction is intrinsically weak. So weak, indeed, that the probability that photons impinging on a nucleus simply scatter, elastically, off of the core electron density (the K-shell), becomes significant.¹ If a coherent source of X-rays is used to illuminate a collection of atoms, then the elastic scattering of these coherent photons records, through their mutual interference, two-body information² pertaining to the collection of atoms.³

Hence, we have ‘diffraction’, as such, from the point-like⁴ Bragg scattering of (ideally) infinite lattices (at 0 K) to the diffuse halos of ‘amorphous’⁵ systems. Some, no doubt, would object to the classification of X-ray scattering as a category of spectroscopy; but, if photons admit a continuous spectrum, why not spectroscopy, if one understands it as light–matter interaction?

Quantum chemistry

Under the Born-Oppenheimer approximation, chemistry, as such, occurs at the level of electron dynamics. Hence, reified in contemporary (organic) synthesis, we have the `arrow-pushing diagram’. At the most elementary, leaving dynamics aside, one is concerned with solutions ($\psi$) to the time-independent eigenproblem,

\[(i{\not{\partial}} - m)\psi(\mathbf{x}) = \mathbf{0}\]

Here, $\mathbf{x}$ lives in the four-dimensional space-time⁶, and $\mathbf{0}$ is the zero functional living in spacetime, considered as a Hilbert space. Hence, we reason at the level of functional analysis.

Despite the apparent simplicity of this eigenproblem, difficulties arise from the added complexity incurred by passing from this simple 1-particle system to the generic $N$-body problem. Dirac summarizes,

The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.

Hence, contemporary electronic structure theories all represent different approaches to simplifying the complexity of these equations. We have an ‘exact’ theory, but must rely on developing practicable ansätze to approximate solutions.

Density Functional Theory

For transition metal complexes, and indeed, for all of chemistry and materials science, density functional theory (DFT) is the most popular single-reference ansatz to the time-independent, non-relativistic electronic structure problem. Its popularity is due to the favorable complexity scaling of the $N$-body DFT problem, which is polynomial ($\mathcal{O}[N^3]$), meaning that systems containing hundreds to thousands of atoms are tractable. DFT achieves this by reformulating the electronic structure problem from one of obtaining the correct $N$-body wavefunction, to obtaining the correct electron density that is (uniquely) associated with that wavefunction.

The central difficulty of DFT lies in the following: Although it is a provably-exact theory, we simply do not know the correct formulation of the DFT equations. If, as claimed by Dirac, the time-independent, non-relativistic Schrödinger wave-equation is an exact theory we can only solve approximately, then, in practice, DFT is an approximate theory we can solve exactly. Approximate, in that one must make some a priori choice for parameterizing the DFT equations, leading to the abundance of DFT formulations present in the literature. Beyond the risk of choice overload this induces, DFT presents other difficulties as well, such as the lack of proper spin-symmetry.

Nevertheless, with experience, DFT can provide detailed insights into electronic structure. One can even glean important qualitative details for systems where the lack of proper spin-symmetry might appear to make DFT an altogether inappropriate ansatz, as demonstrated by the relative success of so-called ‘broken-symmetry’ calculations.

Approximate approaches to Full Configuration Interaction

Under construction…

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Niklas B. Thompson ©