Art, fact and artifact: reflections on the cross-talk between theory and experiment.

With the increasing sophistication of each, theory and experiment have become highly specialized endeavors conducted by separate research groups. A result has been a weakening of the coupling between them and occasional hostility. Examples are given and suggestions are offered for strengthening the traditional synergy between theory and experiment.

Emergence of Linnett's "double quartets" from a model of "Lewis dots".

Chemists routinely explicate molecular structures and chemical reactions in terms of the propensities of semiclassical valence electrons (aka "Lewis dots"). Typically, the electrons are viewed as forming spin pairs and recent efforts to translate this concise and intuitive qualitative picture into an efficient and relatable quantitative model have made good progress. But electrons are not always paired and advanced quantum calculations have shown that this is so even in small diamagnetic species such as dicarbon and benzene. Here we show that the latest semiclassical model for paired electrons can clarify the limitations on pairing simply by dissecting the elements of the interparticle potentials. Although not trained to do so, these elements produce a Linnett-like benzene, with three valence electrons in each CC bond, when the electrons are free to move singly. At the same time, sustaining higher order bonds with independently mobile electrons requires adjustments in the details of the model potentials at short distances. This is addressed with new training data and new forms for the contributions from Coulomb integrals. Although trained on hydrogen and carbon species separately, the combination applied to ethyne predicts the pairing of spins in the CH bonds and the dispersion of spins in the CC bond that is found in ab initio calculations. This adjusted force field is named LINNETT, in appreciation of Linnett's insightful double quartet interpretation of the Lewis octet.

A Carbon Is a Carbon Is a Carbon: Orbital-Free Simulations of Hydrocarbon Chemistry without Resort to Atom Types.

Semiclassical electrons (aka Lewis dots) have been a mainstay of chemists' thinking about molecular structure, polarizability, and reactivity for over a century. This utility has motivated the development of a corresponding quantitative description. Here we devise pairwise potentials that describe the behavior of valence electron pairs in hydrocarbons, including those in single, double, bridge, and bent bonds of linear, branched, and cyclic compounds, including anionic and cationic states. Beyond predicting structures and energies, the new subatomistic force field, dubbed LEWIS-B, efficiently simulates carbocation addition to a double bond and cation migration to a neighboring carbon. A crucial feature of the semiclassical electrons is variable spread, a fourth degree of freedom in addition to three Cartesian coordinates. In spontaneously adapting to different environments, the spread provides a signature of electron stability, with more contracted clouds where the electron interactions are favorable and expanded clouds where electrons are less tightly held. In addition, the pair potentials provide insight into the subtle trade-offs that govern isomerizations and reactions.

Bending the Curve: Molecular Manifestations of Electron Antisymmetry.

As very light fermions, electrons are governed by antisymmetric wave functions that lead to exchange integrals in the evaluation of the energy. Here we use the localized representation of orbitals to decompose the electronic energy in a fashion that isolates the enigmatic exchange contributions and characterizes their distinctive control over electron distributions. The key to this completely general analysis is considering the electrons in groups of three, drawing attention to the curvatures of pair potentials, rather than just their amplitudes and slopes. We show that a positive curvature at short distances is essential for the mutual distancing of electrons and a negative curvature at longer distances is essential to account for the influence of lone pairs on bond torsion. Neither curvature is available in the absence of the exchange contributions. Thus, although exchange energies are much shorter range than Coulomb energies, their influence on molecular geometry is profound and readily understood.

Primary Transfer Step in the Light-Driven Ion Pump Bacteriorhodopsin: An Irreversible U-Turn Revealed by Dynamic Nuclear Polarization-Enhanced Magic Angle Spinning NMR.

Despite much attention, the path of the highly consequential primary proton transfer in the light-driven ion pump bacteriorhodopsin (bR) remains mysterious. Here we use DNP-enhanced magic angle spinning (MAS) NMR to study critical elements of the active site just before the Schiff base (SB) deprotonates (in the L intermediate), immediately after the SB has deprotonated and Asp85 has become protonated (in the Mo intermediate), and just after the SB has reprotonated and Asp96 has deprotonated (in the N intermediate). An essential feature that made these experiments possible is the 75-fold signal enhancement through DNP. 15N(SB)-1H correlations reveal that the newly deprotonated SB is accepting a hydrogen bond from an alcohol and 13C-13C correlations show that Asp85 draws close to Thr89 before the primary proton transfer. Concurrently, 15N-13C correlations between the SB and Asp85 show that helices C and G draw closer together just prior to the proton transfer and relax thereafter. Together, these results indicate that Thr89 serves to relay the SB proton to Asp85 and that creating this pathway involves rapprochement between the C and G helices as well as chromophore torsion.

Floating Orbitals Reconsidered: The Difference an Imaginary Part Can Make.

Floating orbitals for valence electrons have made cameo appearances at several stages in the history of quantum chemistry. Most often, they were considered as potentially useful basis functions and, more recently, also as muses for the development of subatomistic force fields. To facilitate computation, these orbitals are generally taken to be real spherical Gaussians. However, the computational advantages carry over to complex Gaussians. Here, we explore the potential utility of an imaginary part. Analytical equations for two mobile electrons show that an imaginary part shifts the balance between contributions to the exchange energy that favor parallel versus antiparallel electron spins. However, an imaginary part also carries a large kinetic energy penalty. The imaginary part is therefore negligible for two valence electrons, except in the case of strong core-valence exchange interactions. This consideration allows a self-consistent model for the nd2 triplet ground states of transition metal ions versus the ns2 singlet ground states of main group ions.

Chemistry with semi-classical electrons: reaction trajectories auto-generated by sub-atomistic force fields.

For a century now, "Lewis dots" have been a mainstay of chemical thinking, teaching and communication. However, chemists have assumed that this semi-classical picture of electrons needs to be abandoned for quantitative work, and the recourse in computational simulations has been to the extremes of first principles treatments of electrons on the one hand and force fields that avoid explicit electrons on the other hand. Given both the successes and limitations of these highly divergent approaches, it seems worth considering whether the Lewis dot picture might be made quantitative after all. Here we review progress to that end, including variations that have been implemented and examples of applications, specifically the acid-base behavior of water, several organic reactions, and electron dynamics in silicon fracture. In each case, the semi-classical approach is highly efficient and generates reasonable and readily interpreted reaction trajectories in turnkey fashion (i.e., without any input about products). Avenues for further progress are also discussed.

Peptide and Protein Dynamics and Low-Temperature/DNP Magic Angle Spinning NMR.

In DNP MAS NMR experiments at ∼80-110 K, the structurally important -13CH3 and -15NH3+ signals in MAS spectra of biological samples disappear due to the interference of the molecular motions with the 1H decoupling. Here we investigate the effect of these dynamic processes on the NMR line shapes and signal intensities in several typical systems: (1) microcrystalline APG, (2) membrane protein bR, (3) amyloid fibrils PI3-SH3, (4) monomeric alanine-CD3, and (5) the protonated and deuterated dipeptide N-Ac-VL over 78-300 K. In APG, the three-site hopping of the Ala-Cß peak disappears completely at 112 K, concomitant with the attenuation of CP signals from other 13C's and 15N's. Similarly, the 15N signal from Ala-NH3+ disappears at ∼173 K, concurrent with the attenuation in CP experiments of other 15N's as well as 13C's. In bR and PI3-SH3, the methyl groups are attenuated at ∼95 K, while all other 13C's remain unaffected. However, both systems exhibit substantial losses of intensity at ∼243 K. Finally, with spectra of Ala and N-Ac-VL, we show that it is possible to extract site specific dynamic data from the temperature dependence of the intensity losses. Furthermore, 2H labeling can assist with recovering the spectral intensity. Thus, our study provides insight into the dynamic behavior of biological systems over a wide range of temperatures, and serves as a guide to optimizing the sensitivity and resolution of structural data in low temperature DNP MAS NMR spectra.

Special Pairs Are Decisive in the Autoionization and Recombination of Water.

Although water's chemical properties are no less important than its exceptional physical properties, its acid-base behavior is relatively poorly understood. In fact, the Grotthus trajectories for ion recombination predicted by density functional theory do not comport well with the almost 100-fold slower diffusive trajectories observed in time-resolved spectroscopy. And, in the reverse reaction, the barrier to autoionization is not well characterized. Here we develop a self-consistent picture of both processes based on the occurrence and role of ultrashort hydrogen bonds. The predicted populations of these special pairs in bulk water are consistent with the high frequency electrodynamics of water and its pressure dependence. The rate-limiting role of the special pairs manifests in autoionization as a two-stage barrier, first to form a contact ion pair and then to separate it by one water molecule. From this configuration, similar frequencies are observed for further separation vs recombination. The requirement of ultrashort hydrogen bonds for proton transfer in autoionization is consistent with the rise in Kw with increasing pressure and points to a role for density fluctuations in autoionization events. In neutralization, the manifestation of the role of special pairs is the prolonged diffusional process observed in time-resolved spectroscopy experiments. The requirement of special pairs as transition states for proton transfer is less obvious for neutralization in isolated water chains than in the bulk liquid only because an unbroken sequence of ultrashort H-bonds is more easily formed in a 1D H-bonded chain than in a 3D H-bonded network.

Exchange potentials for semi-classical electrons.

Semi-classical electrons offer access to efficient and intuitive simulations of chemical reactions. As for any treatment of fermions, the greatest difficulty is in accounting for anti-symmetry effects. Semi-classical efforts to-date either reference Slater-determinants from ab initio treatments or adopt a heuristic approach inspired by density functional treatments. Here we revisit the problem with a combined approach. We conclude that semi-classical electrons need to reference a non-conventional wave function and find that (1) contrary to earlier suppositions, contributions from the electrostatic terms in the Hamiltonian are of similar magnitude to those from the kinetic terms and (2) the former point to a need to supplement pair potentials with 3-body potentials. The first result explains features of reported heuristic potentials, and the second provides a firm footing for extending the transferability of potentials across a wider range of elements and bonding scenarios.

Surface Propensities of the Self-Ions of Water.

The surface charge of water, which is important in a wide range of chemical, biological, material, and environmental contexts, has been a subject of lengthy and heated debate. Recently, it has been shown that the highly efficient LEWIS force field, in which semiclassical, independently mobile valence electron pairs capture the amphiproticity, polarizability and H-bonding of water, provides an excellent description of the solvation and dynamics of hydroxide and hydronium in bulk water. Here we turn our attention to slabs, cylinders, and droplets. In extended simulations with 1000 molecules, we find that hydroxide consistently prefers the surface, hydronium consistently avoids the surface, and the two together form an electrical double layer until neutralization occurs. The behavior of hydroxide can largely be accounted for by the observation that hydroxide moving to the surface loses fewer hydrogen bonds than are gained by the water molecule that it displaces from the surface. At the same time, since the orientation of the hydroxide increases the ratio of dangling hydrogens to dangling lone pairs, the proton activity of the exposed surface may be increased, rather than decreased. Hydroxide also moves more rapidly in the surface than in the bulk, likely because the proton donating propensity of neighboring water molecules is focused on the one hydrogen that is not dangling from the surface.

Magnetism and Bond Order in Diatomic Molecules Described by Semiclassical Electrons.

The past decade has seen the first attempts at quantifying a semiclassical description of electrons in molecules. The challenge in this endeavor is to find potentials for electron interactions that adequately capture quantum effects. As has been the case for density functionals, the challenge is particularly great for the effects that follow from the requirement for wave function antisymmetry. Here we extend our empirical inquiry into effective potentials, from prior work on the monatomic atoms and ions of nonmetals, to diatomic molecules and ions formed by these elements. Newly adjusted and trained for the longer distances relevant to diatomics, pairwise potentials are able to fit the bond orders and magnetic properties of homonuclear species. These potentials are then found to do an excellent job of predicting the magnetism of heteronuclear species. In these molecules the predicted distribution of electrons also correctly reflects increasing ionic character with increasing difference in the electronegativities of the participating atoms. The distinctive features of the current potential are discussed, along with issues calling for further improvements.

Transferable pseudoclassical electrons for aufbau of atomic ions.

Generalizing the LEWIS reactive force field from electron pairs to single electrons, we present LEWIS• in which explicit valence electrons interact with each other and with nuclear cores via pairwise interactions. The valence electrons are independently mobile particles, following classical equations of motion according to potentials modified from Coulombic as required to capture quantum characteristics. As proof of principle, the aufbau of atomic ions is described for diverse main group elements from the first three rows of the periodic table, using a single potential for interactions between electrons of like spin and another for electrons of unlike spin. The electrons of each spin are found to distribute themselves in a fashion akin to the major lobes of the hybrid atomic orbitals, suggesting a pointillist description of the electron density. The broader validity of the LEWIS• force field is illustrated by predicting the vibrational frequencies of diatomic and triatomic hydrogen species.

Gas vesicles across kingdoms: a comparative solid-state nuclear magnetic resonance study.

The buoyancy organelles of aquatic microorganisms have to meet stringent specifications: allowing gases to equilibrate freely across the proteinaceous shell, preventing the condensation of water vapor inside the hollow cavity and resisting collapse under hydrostatic pressures that vary with column depth. These properties are provided by the 7- to 8-kDa gas vesicle protein A (GvpA), repeats of which form all but small, specialized portions of the shell. Magic angle spinning nuclear magnetic resonance is uniquely capable of providing high-resolution information on the fold and assembly of GvpA. Here we compare results for the gas vesicles of the haloarchaea Halobacterium salinarum with those obtained previously for the cyanobacterium Anabaena flos-aquae. The data suggest that the two organisms follow similar strategies for avoiding water condensation. On the other hand, in its relatively shallow habitat, H. salinarum is able to avoid collapse with a less costly GvpA fold than is adopted by A. flos-aquae.

Selectively dispersed isotope labeling for protein structure determination by magic angle spinning NMR.

The power of nuclear magnetic resonance spectroscopy derives from its site-specific access to chemical, structural and dynamic information. However, the corresponding multiplicity of interactions can be difficult to tease apart. Complimentary approaches involve spectral editing on the one hand and selective isotope substitution on the other. Here we present a new "redox" approach to the latter: acetate is chosen as the sole carbon source for the extreme oxidation numbers of its two carbons. Consistent with conventional anabolic pathways for the amino acids, [1-(13)C] acetate does not label α carbons, labels other aliphatic carbons and the aromatic carbons very selectively, and labels the carboxyl carbons heavily. The benefits of this labeling scheme are exemplified by magic angle spinning spectra of microcrystalline immunoglobulin binding protein G (GB1): the elimination of most J-couplings and one- and two-bond dipolar couplings provides narrow signals and long-range, intra- and inter-residue, recoupling essential for distance constraints. Inverse redox labeling, from [2-(13)C] acetate, is also expected to be useful: although it retains one-bond couplings in the sidechains, the removal of CA-CO coupling in the backbone should improve the resolution of NCACX spectra.

Efficient, balanced, transmission line RF circuits by back propagation of common impedance nodes.

We present a new, efficient strategy for designing fully balanced transmission line RF circuits for solid state NMR probes based on back propagation of common impedance nodes (BPCIN). In this approach, the impedance node phenomenon is the sole means of achieving mutual RF isolation and balance in all RF channels. BPCIN is illustrated using a custom double resonance 3.2 mm MAS probe operating at 500 MHz ((1)H) and 125 MHz ((13)C). When fully optimized, the probe is capable of producing high homogeneity (810°/90° ratios of 86% and 89% for (1)H and (13)C, respectively) and high efficiency (γB1=100 kHz for (1)H and (13)C at 70 W and 180 W of RF input, respectively; up to 360 kHz for (1)H). The probe's performance is illustrated by 2D MAS correlation spectra of microcrystals of the tripeptide N-f-MLF-OH and hydrated amyloid fibrils of the protein PI3-SH3.

High frequency dynamic nuclear polarization.

During the three decades 1980-2010, magic angle spinning (MAS) NMR developed into the method of choice to examine many chemical, physical, and biological problems. In particular, a variety of dipolar recoupling methods to measure distances and torsion angles can now constrain molecular structures to high resolution. However, applications are often limited by the low sensitivity of the experiments, due in large part to the necessity of observing spectra of low-γ nuclei such as the I = 1/2 species (13)C or (15)N. The difficulty is still greater when quadrupolar nuclei, such as (17)O or (27)Al, are involved. This problem has stimulated efforts to increase the sensitivity of MAS experiments. A particularly powerful approach is dynamic nuclear polarization (DNP) which takes advantage of the higher equilibrium polarization of electrons (which conventionally manifests in the great sensitivity advantage of EPR over NMR). In DNP, the sample is doped with a stable paramagnetic polarizing agent and irradiated with microwaves to transfer the high polarization in the electron spin reservoir to the nuclei of interest. The idea was first explored by Overhauser and Slichter in 1953. However, these experiments were carried out on static samples, at magnetic fields that are low by current standards. To be implemented in contemporary MAS NMR experiments, DNP requires microwave sources operating in the subterahertz regime, roughly 150-660 GHz, and cryogenic MAS probes. In addition, improvements were required in the polarizing agents, because the high concentrations of conventional radicals that are required to produce significant enhancements compromise spectral resolution. In the last two decades, scientific and technical advances have addressed these problems and brought DNP to the point where it is achieving wide applicability. These advances include the development of high frequency gyrotron microwave sources operating in the subterahertz frequency range. In addition, low temperature MAS probes were developed that permit in situ microwave irradiation of the samples. And, finally, biradical polarizing agents were developed that increased the efficiency of DNP experiments by factors of ∼4 at considerably lower paramagnet concentrations. Collectively, these developments have made it possible to apply DNP on a routine basis to a number of different scientific endeavors, most prominently in the biological and material sciences. This Account reviews these developments, including the primary mechanisms used to transfer polarization in high frequency DNP, and the current choice of microwave sources and biradical polarizing agents. In addition, we illustrate the utility of the technique with a description of applications to membrane and amyloid proteins that emphasizes the unique structural information that is available in these two cases.

Continuously Tunable 250 GHz Gyrotron with a Double Disk Window for DNP-NMR Spectroscopy.

In this paper, we describe the design and experimental results from the rebuild of a 250 GHz gyrotron used for Dynamic Nuclear Polarization enhanced Nuclear Magnetic Resonance spectroscopy on a 380 MHz spectrometer. Tuning bandwidth of approximately 2 GHz is easily achieved at a fixed magnetic field of 9.24 T and a beam current of 95 mA producing an average output power of >10 W over the entire tuning band. This tube incorporates a double disk output sapphire window in order to maximize the transmission at 250.58 GHz. DNP Signal enhancement of >125 is achieved on a 13C-Urea sample using this gyrotron.

Efficient resonance assignment of proteins in MAS NMR by simultaneous intra- and inter-residue 3D correlation spectroscopy.

Resonance assignment is the first step in NMR structure determination. For magic angle spinning NMR, this is typically achieved with a set of heteronuclear correlation experiments (NCaCX, NCOCX, CONCa) that utilize SPECIFIC-CP (15)N-(13)C transfers. However, the SPECIFIC-CP transfer efficiency is often compromised by molecular dynamics and probe performance. Here we show that one-bond ZF-TEDOR (15)N-(13)C transfers provide simultaneous NCO and NCa correlations with at least as much sensitivity as SPECIFIC-CP for some non-crystalline samples. Furthermore, a 3D ZF-TEDOR-CC experiment provides heteronuclear sidechain correlations and robustness with respect to proton decoupling and radiofrequency power instabilities. We demonstrate transfer efficiencies and connectivities by application of 3D ZF-TEDOR-DARR to a model microcrystalline protein, GB1, and a less ideal system, GvpA in intact gas vesicles.