Modeling expression ranks for noise-tolerant differential expression analysis of scRNA-seq data.

Systematic delineation of complex biological systems is an ever-challenging and resource-intensive process. Single-cell transcriptomics allows us to study cell-to-cell variability in complex tissues at an unprecedented resolution. Accurate modeling of gene expression plays a critical role in the statistical determination of tissue-specific gene expression patterns. In the past few years, considerable efforts have been made to identify appropriate parametric models for single-cell expression data. The zero-inflated version of Poisson/negative binomial and log-normal distributions have emerged as the most popular alternatives owing to their ability to accommodate high dropout rates, as commonly observed in single-cell data. Although the majority of the parametric approaches directly model expression estimates, we explore the potential of modeling expression ranks, as robust surrogates for transcript abundance. Here we examined the performance of the discrete generalized beta distribution (DGBD) on real data and devised a Wald-type test for comparing gene expression across two phenotypically divergent groups of single cells. We performed a comprehensive assessment of the proposed method to understand its advantages compared with some of the existing best-practice approaches. We concluded that besides striking a reasonable balance between Type I and Type II errors, ROSeq, the proposed differential expression test, is exceptionally robust to expression noise and scales rapidly with increasing sample size. For wider dissemination and adoption of the method, we created an R package called ROSeq and made it available on the Bioconductor platform.

sc-REnF: An entropy guided robust feature selection for single-cell RNA-seq data.

Annotation of cells in single-cell clustering requires a homogeneous grouping of cell populations. Since single-cell data are susceptible to technical noise, the quality of genes selected prior to clustering is of crucial importance in the preliminary steps of downstream analysis. Therefore, interest in robust gene selection has gained considerable attention in recent years. We introduce sc-REnF [robust entropy based feature (gene) selection method], aiming to leverage the advantages of $R{\prime}{e}nyi$ and $Tsallis$ entropies in gene selection for single cell clustering. Experiments demonstrate that with tuned parameter ($q$), $R{\prime}{e}nyi$ and $Tsallis$ entropies select genes that improved the clustering results significantly, over the other competing methods. sc-REnF can capture relevancy and redundancy among the features of noisy data extremely well due to its robust objective function. Moreover, the selected features/genes can able to determine the unknown cells with a high accuracy. Finally, sc-REnF yields good clustering performance in small sample, large feature scRNA-seq data. Availability: The sc-REnF is available at https://github.com/Snehalikalall/sc-REnF.

Electronic Structure of Metallophlorins: Lessons from Iridium and Gold Phlorin Derivatives.

Phlorins have long remained underexplored relative to their fully conjugated counterparts, such as porphyrins, hydroporphyrins, and corroles. Herein, we have attempted to bridge that knowledge gap with a scalar-relativistic density functional theory (DFT) study of unsubstituted iridium and gold phlorin derivatives and a multitechnique experimental study of iridium-bispyridine and gold complexes of 5,5-dimethyl-10,15,20-tris(pentafluorophenyl)phlorin. Theory and experiments concur that the phlorin derivatives exhibit substantially smaller HOMO-LUMO gaps, as reflected in a variety of observable properties. Thus, the experimentally studied Ir and Au complexes absorb strongly in the near-infrared (NIR), with absorption maxima at 806 and 770 nm, respectively. The two complexes are also weakly phosphorescent with emission maxima at 950 and 967 nm, respectively. They were also found to photosensitize singlet oxygen formation, with quantum yields of 40 and 28%, respectively. The near-infrared (NIR) absorption and emission are consonants with smaller electrochemical HOMO-LUMO gaps of ∼1.6 V, compared to values of ∼2.1 V, for electronically innocent porphyrins and corroles. Interestingly, both the first oxidation and reduction potentials of the Ir complex are some 600 mV shifted to more negative potentials relative to those of the Au complex, indicating an exceptionally electron-rich macrocycle in the case of the Ir complex.

Inverse Hypercorroles.

Ground-state and time-dependent density functional theory (TDDFT) calculations with the long-range-corrected, Coulomb-attenuating CAMY-B3LYP exchange-correlation functional and large, all-electron STO-TZ2P basis sets have been used to examine the potential "inverse hypercorrole" character of meso-p-nitrophenyl-appended dicyanidocobalt(III) corrole dianions. The effect is most dramatic for 5,15-bis(p-nitrophenyl) derivatives, where it manifests itself in intense NIR absorptions. The 10-aryl groups in these complexes play a modulatory role, as evinced by experimental UV-visible spectroscopic and electrochemical data for a series of 5,15-bis(p-nitrophenyl) dicyanidocobalt(III) corroles. TDDFT (CAMY-B3LYP) calculations ascribe these features clearly to a transition from the corrole's a2u-like HOMO (retaining the D4h irrep used for metalloporphyrins) to a nitrophenyl-based LUMO. The outward nature of this transition contrasts with the usual phenyl-to-macrocycle direction of charge transfer transitions in many hyperporphyrins and hypercorroles; thus, the complexes studied are aptly described as inverse hypercorroles.

Free-Base Corrole Anion.

Free-base corroles have long been known to be acidic, readily undergoing deprotonation by mild bases and in polar solvents. The conjugate base, however, has not been structurally characterized until now. Presented here is a first crystal structure of a free-base corrole anion, derived from tris(p-cyanophenyl)corrole, as the tetrabuylammonium salt. The low-temperature (100 K) structure reveals localized hydrogens on a pair of opposite pyrrole nitrogens. DFT calculations identify such a structure as the global minimum but also point to two cis tautomers only 4-7 kcal/mol above the ground state. In terms of free energy, however, the cis tautomers are above or essentially flush with the trans-to-cis barrier so the cis tautomers are unlikely to exist or be observed as true intermediates. Thus, the hydrogen bond within each dipyrrin unit on either side of the molecular pseudo-C2 axis through C10 (i.e., between pyrrole rings A and B or between C and D) qualifies as or closely approaches a low-barrier hydrogen bond. Proton migration across the pseudo-C2 axis entails much higher activation energies >20 kcal/mol, reflecting the relative rigidity of the molecule along the C1-C19 pyrrole-pyrrole linkage.

Is it possible to estimate sex from signatures and handwriting? A review of literature, observations, and future perspectives.

Estimation of sex holds great significance in the field of Forensic Science since it helps establish the identity of an individual during a crime scene investigation. Sex differences in human behaviour are the result of natural selection. Sexually dimorphic stimuli of cognitive and behavioural activities may influence the phenotypic expression of our motor skills. Human traits such as signatures and handwriting are phenotypic manifestation of these skills. These phenotypic biological and behavioural traits have inherent sexual dimorphism and may help to identify sex in different circumstances. For instance, to establish the sex of an individual or deceased, forensic samples of the human body such as voice samples, features of fingerprints and footprints, the skeleton, or its remains are helpful. Similarly, the sex of an individual may also be identified from their corresponding handwriting and signature. Handwriting experts can extract peculiar features from handwriting and signatures which could help establish whether the signatures belong to a male or a female. A female writer may have attractive, rounded, upright, tidy, skilled, well-formed strokes, artistic design, better penmanship, and greater length of the signature compared to the signature of a male. Here, we review the studies related to the identification of sex from signatures and handwriting and present inferences about vital features and methods of sex identification through handwriting. These mainly suggest that the accuracy of sex prediction from signature and handwriting ranges from 45 to 80%. We also present writing examples to show sex-based differences in the signature and handwriting of males and females. The female's handwriting is more decorative, arranged, aligned, neat, and clean as compared to that of the male. Based on the writing samples and the review of literature, we suggest that forensic handwriting experts may eliminate suspects based on the sex of the writer, which can simplify the identification process of disputed or questionable signatures and handwriting.

Local Oxidation States in {FeNO}6-8 Porphyrins: Insights from DMRG/CASSCF-CASPT2 Calculations.

A first DMRG/CASSCF-CASPT2 study of a series of paradigmatic {FeNO}6, {FeNO}7, and {FeNO}8 heme-nitrosyl complexes has led to substantial new insight as well as uncovered key shortcomings of the DFT approach. By virtue of its balanced treatment of static and dynamic correlation, the calculations have provided some of the most authoritative information available to date on the energetics of low- versus high-spin states of different classes of heme-nitrosyl complexes. Thus, the calculations indicate low doublet-quartet gaps of 1-4 kcal/mol for {FeNO}7 complexes and high singlet-triplet gaps of ≳20 kcal/mol for both {FeNO}6 and {FeNO}8 complexes. In contrast, DFT calculations yield widely divergent spin state gaps as a function of the exchange-correlation functional. DMRG-CASSCF calculations also help calibrate DFT spin densities for {FeNO}7 complexes, pointing to those obtained from classic pure functionals as the most accurate. The general picture appears to be that nearly all the spin density of Fe[P](NO) is localized on the Fe, while the axial ligand imidazole (ImH) in Fe[P](NO)(ImH) pushes a part of the spin density onto the NO moiety. An analysis of the DMRG-CASSCF wave function in terms of localized orbitals and of the resulting configuration state functions in terms of resonance forms with varying NO(π*) occupancies has allowed us to address the longstanding question of local oxidation states in heme-nitrosyl complexes. The analysis indicates NO(neutral) resonance forms [i.e., Fe(II)-NO0 and Fe(III)-NO0] as the major contributors to both {FeNO}6 and {FeNO}7 complexes. This finding is at variance with the common formulation of {FeNO}6 hemes as Fe(II)-NO+ species but is consonant with an Fe L-edge XAS analysis by Solomon and co-workers. For the {FeNO}8 complex {Fe[P](NO)}-, our analysis suggests a resonance hybrid description: Fe(I)-NO0 ↔ Fe(II)-NO-, in agreement with earlier DFT studies. Vibrational analyses of the compounds studied indicate an imperfect but fair correlation between the NO stretching frequency and NO(π*) occupancy, highlighting the usefulness of vibrational data as a preliminary indicator of the NO oxidation state.

Rhenium Biscorrole Sandwich Compounds: XAS Evidence for a New Coordination Motif.

The interaction of three free-base meso-tris(p-X-phenyl)corroles H3[TpXPC] (X = H, CH3, OCH3) with Re2(CO)10 at 235 °C in the presence of K2CO3 in o-dichlorobenzene has led to putative rhenium biscorrole sandwich compounds with the formula ReH[TpXPC]2. Density functional theory calculations and Re L3-edge extended X-ray absorption fine structure measurements suggest a seven-coordinate metal center, with the "extra" hydrogen located on one of the corrole nitrogens. The complexes can be deprotonated by a base such as 1,8-diazabicyclo[5.4.0]undec-7-ene, resulting in a substantial sharpening of the UV-vis spectra and split Soret bands, consistent with the generation of C2-symmetric anions. Both the seven-coordinate neutral and eight-coordinate anionic forms of the complexes represent a new coordination motif in the field of rhenium-porphyrinoid interactions.

Transition-Metal Isocorroles as Singlet Oxygen Sensitizers.

Building on a highly efficient synthesis of pyrrole-appended isocorroles, we have worked out conditions for manganese, palladium, and platinum insertion into free-base 5/10-(2-pyrrolyl)-5,10,15-tris(4-methylphenyl)isocorrole, H2[5/10-(2-py)TpMePiC]. Platinum insertion proved exceedingly challenging but was finally accomplished with cis-Pt(PhCN)2Cl2. All the complexes proved weakly phosphorescent in the near-infrared under ambient conditions, with a maximum phosphorescence quantum yield of 0.1% observed for Pd[5-(2-py)TpMePiC]. The emission maximum was found to exhibit a strong metal ion dependence for the 5-regioisomeric complexes but not for the 10-regioisomers. Despite the low phosphorescence quantum yields, all the complexes were found to sensitize singlet oxygen formation with moderate to good efficiency, with singlet oxygen quantum yields ranging over 21-52%. With significant absorption in the near-infrared and good singlet oxygen-sensitizing ability, metalloisocorroles deserve examination as photosensitizers in the photodynamic therapy of cancer and other diseases.

Robust Minimum Divergence Estimation for the Multinomial Circular Logistic Regression Model.

Circular data are extremely important in many different contexts of natural and social science, from forestry to sociology, among many others. Since the usual inference procedures based on the maximum likelihood principle are known to be extremely non-robust in the presence of possible data contamination, in this paper, we develop robust estimators for the general class of multinomial circular logistic regression models involving multiple circular covariates. Particularly, we extend the popular density-power-divergence-based estimation approach for this particular set-up and study the asymptotic properties of the resulting estimators. The robustness of the proposed estimators is illustrated through extensive simulation studies and few important real data examples from forest science and meteorology.

The Story of 5d Metallocorroles: From Metal-Ligand Misfits to New Building Blocks for Cancer Phototherapeutics.

Porphyrin chemistry is Shakespearean: over a century of study has not withered the field's apparently infinite variety. Heme proteins continually astonish us with novel molecular mechanisms, while new porphyrin analogues bowl us over with unprecedented optical, electronic, and metal-binding properties. Within the latter domain, corroles occupy a special place, exhibiting a unique and rich coordination chemistry. The 5d metallocorroles are arguably the icing on that cake.New Zealand chemist Penny Brothers has used the word "misfit" to describe the interactions of boron, a small atom with a predilection for tetrahedral coordination, and porphyrins, classic square-planar ligands. Steve Jobs lionized misfits as those who see things differently and push humanity forward. Both perspectives have inspired us. The 5d metallocorroles are misfits in that they encapsulate a large 5d transition metal ion within the tight cavity of a contracted porphyrin ligand.Given the steric mismatch inherent in their structures, the syntheses of some 5d metallocorroles are understandably capricious, proceeding under highly specific conditions and affording poor yields. Three broad approaches may be distinguished.(a) In the metal-alkyl approach, a free-base corrole is exposed to an alkyllithium and the resulting lithio-corrole is treated with an early transition metal chloride; a variant of the method eschews alkyllithium and deploys a transition metal-alkyl instead, resulting in elimination of the alkyl group as an alkane and insertion of the metal into the corrole. This approach is useful for inserting transition metals from groups 4, 5, and, to some extent, 6, as well as lanthanides and actinides.(b) In our laboratory, we have often deployed a low-valent organometallic approach for the middle transition elements (groups 6, 7, 8, and 9). The reagents are low-valent metal-carbonyl or -olefin complexes, which lose one or more carbon ligands at high temperature, affording coordinatively unsaturated, sticky metal fragments that are trapped by the corrole nitrogens.(c) Finally, a metal acetate approach provides the method of choice for gold and platinum insertion (groups 10 and 11).This Account provides a first-hand perspective of the three approaches, focusing on the last two, which were largely developed in our laboratory. In general, the products were characterized with X-ray crystallography, electrochemistry, and a variety of spectroscopic methods. The physicochemical data, supplemented by relativistic DFT calculations, have provided fascinating insights into periodic trends and relativistic effects.An unexpected feature of many 5d metallocorroles, given their misfit character, is their remarkable stability under thermal, chemical, and photochemical stimulation. Many of them also exhibit long triplet lifetimes on the order of 100 µs and effectively sensitize singlet oxygen formation. Many exhibit phosphorescence in the near-infrared under ambient conditions. Furthermore, water-soluble ReO and Au corroles exhibit impressive photocytotoxicity against multiple cancer cell lines, promising potential applications as cancer phototherapeutics. We thus envision a bright future for the compounds as rugged building blocks for new generations of therapeutic and diagnostic (theranostic) agents.

Metallaaromaticity - a protean world.

The nature of magnetically induced current densities (MICD) of metallabenzenes and related compounds has been examined with relativistic DFT calculations to assess the magnetic aromaticity of the molecules. The origin of the total MICD has been analyzed in terms of individual molecular orbital (MO) contributions. Our study reveals that the σ-framework of the molecules always makes a diamagnetic contribution to the MICD. On the other hand, π-MOs and Craig-Möbius type π-MOs, i.e., MOs in which the dxy/dxz orbitals of the metal centers change the phase of the wave function akin to a Möbius twist, may not make a diatropic contribution. We have identified metallabenzenes with multiple magnetic aromaticities. In the case of iridabenzenes, σ-MICD has been found to decrease dramatically from Ir(III) to Ir(V) systems. Furthermore, a brief examination of some recently synthesized metallapolycycles has shown that the metal center in a given ring can strongly modulate the aromaticity of neighboring rings. Finally, the finding that relatively minor perturbations in the ligand environment of the metal can substantially influence the aromaticity of metallabenzenes and related molecules underscores the protean character of metallaaromaticity and the need for even wider-ranging investigations. Considering the conflicts between magnetic response and ground-state aromaticity criteria (energetic, structural, and electronic criteria), we propose that the term aromatic be used for labeling a molecule if and only if all criteria confirm aromaticity. In other words, neither magnetic nor ground-state criteria are necessary and sufficient conditions for labeling a molecule aromatic.

Robust Wald-type tests under random censoring.

Randomly censored survival data are frequently encountered in biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to get conclusive inference but the existing likelihood-based tests, under a fully parametric model, are extremely nonrobust against outliers in the data. Although there exists a few robust estimators given randomly censored data, there is hardly any robust testing procedure available in the literature in this context. One of the major difficulties here is the construction of a suitable consistent estimator of the asymptotic variance of robust estimators, since the latter is a function of the unknown censoring distribution. In this article, we take the first step in this direction by proposing a consistent estimator of asymptotic variance of the M-estimators based on randomly censored data without any assumption on the censoring scheme. We then describe and study a class of robust Wald-type tests for parametric statistical hypothesis, both simple as well as composite, under such a set-up. Robust tests for comparing two independent randomly censored samples and robust tests against one sided alternatives are also discussed. Their advantages and usefulness are demonstrated for the tests based on the minimum density power divergence estimators and illustrated with clinical trials and other medical data.

Rhenium Corrole Dimers: Electrochemical Insights into the Nature of the Metal-Metal Quadruple Bond.

The interaction of free-base triarylcorroles with Re2(CO)10 in 1,2-dichlorobenzene in the presence of 2,6-lutidine at 180 °C under strict anerobic conditions afforded approximately 10% yields of rhenium corrole dimers. The compounds exhibited diamagnetic 1H NMR spectra consistent with a metal-metal quadruple bond with a σ2π4δ2 orbital occupancy. One of the compounds proved amenable to single-crystal X-ray structure determination, yielding a metal-metal distance of ∼2.24 Å, essentially identical to that in triple-bonded osmium corrole dimers. On the other hand, the electrochemical properties of Re and Os corrole dimers proved to be radically different. Thus, the reduction potentials of the Re corrole dimers are some 800 mV upshifted relative to those of their Os counterparts. Stated differently, the Re corrole dimers are dramatically easier to reduce, reflecting electron addition to δ* versus π* molecular orbitals for Re and Os corrole dimers, respectively. The data also imply electrochemical HOMO-LUMO gaps of only 1.0-1.1 V for rhenium corrole dimers, compared with values of 1.85-1.90 V for their Os counterparts. These HOMO-LUMO gaps rank among the first such values reported for quadruple-bonded transition-metal dimers for any type of supporting ligand, porphyrin-type or not.

Relativity as a Synthesis Design Principle: A Comparative Study of [3 + 2] Cycloaddition of Technetium(VII) and Rhenium(VII) Trioxo Complexes with Olefins.

The difference in [3 + 2] cycloaddition reactivity between fac-[MO3(tacn)]+ (M = Re, 99Tc; tacn = 1,4,7-triazacyclononane) complexes has been reexamined with a selection of unsaturated substrates including sodium 4-vinylbenzenesulfonate, norbornene, 2-butyne, and 2-methyl-3-butyn-2-ol (2MByOH). None of the substrates was found to react with the Re cation in water at room temperature, whereas the 99Tc reagent cleanly yielded the [3 + 2] cycloadducts. Interestingly, a bis-adduct was obtained as the sole product for 2MByOH, reflecting the high reactivity of a 99TcO-enediolato monoadduct. On the basis of scalar relativistic and nonrelativistic density functional theory calculations of the reaction pathways, the dramatic difference in reactivity between the two metals has now been substantially attributed to differences in relativistic effects, which are much larger for the 5d metal. Furthermore, scalar-relativistic ΔG values were found to decrease along the series propene > norbornene > 2-butyne > dimethylketene, indicating major variations in the thermodynamic driving force as a function of the unsaturated substrate. The suggestion is made that scalar-relativistic effects, consisting of greater destabilization of the valence electrons of the 5d elements compared with those of the 4d elements, be viewed as a new design principle for novel 99mTc/Re radiopharmaceuticals, as well as more generally in heavy-element coordination chemistry.

Ligand-Centered Triplet Diradical Supported by a Binuclear Palladium(II) Dipyrrindione.

Oligopyrroles form a versatile class of redox-active ligands and electron reservoirs. Although the stabilization of radicals within oligopyrrolic π systems is more common for macrocyclic ligands, bidentate dipyrrindiones are emerging as compact platforms for one-electron redox chemistry in transition-metal complexes. We report the synthesis of a bis(aqua) palladium(II) dipyrrindione complex and its deprotonation-driven dimerization to form a hydroxo-bridged binuclear complex in the presence of water or triethylamine. Electrochemical, spectroelectrochemical, and computational analyses of the binuclear complex indicate the accessibility of two quasi-reversible ligand-centered reduction processes. The product of a two-electron chemical reduction by cobaltocene was isolated and characterized. In the solid state, this cobaltocenium salt features a folded dianionic complex that maintains the hydroxo bridges between the divalent palladium centers. X-band and Q-band EPR spectroscopic experiments and DFT computational analysis allow assignment of the dianionic species as a diradical with spin density almost entirely located on the two dipyrrindione ligands. As established from the EPR temperature dependence, the associated exchange coupling is weak and antiferromagnetic (J ≈ -2.5 K), which results in a predominantly triplet state at the temperatures at which the measurements have been performed.

The Dog That Didn't Bark: A New Interpretation of Hypsoporphyrin Spectra and the Question of Hypsocorroles.

Nearly a half-century after Gouterman classified the UV-vis-NIR spectra of porphyrin derivatives as normal, hyper, or hypso, we propose a heretofore unsuspected "mechanism" underlying hypso spectra. Hypsoporphyrins, which exhibit blueshifted optical spectra relative to normal porphyrins (such as Zn porphyrins), typically involve dn transition metal ions, where n > 6. The spectral blueshifts have been traditionally ascribed to elevated porphyrin eg LUMO (lowest unoccupied molecular orbital) energy levels as a result of antibonding interactions with metal dπ orbitals. Herein, we have found instead that the blueshifts reflect a lowering of the a2u HOMO (highest occupied molecular orbital) energy levels. Electronegative metals such as Pd and Pt transfer smaller quantities of electron density to the porphyrin nitrogens, compared to a more electropositive metal such as Zn. With large amplitudes at the porphyrin nitrogens, the a2u HOMOs of Pd(II) and Pt(II) porphyrins accordingly exhibit lower orbital energies than those of Zn(II) porphyrins, thus explaining the hypso effect. Hypso spectra are also observed for corroles: compared with six-coordinate Al(III) corroles, which may be thought of exhibiting normal spectra, Au(III) corroles, for instance, exhibit blueshifted or hypso spectra.

Understanding Hyperporphyrin Spectra: TDDFT Calculations on Diprotonated Tetrakis(p-aminophenyl)porphyrin.

A detailed TDDFT study (with all-electron STO-TZ2P basis sets and the COSMO solvation model) has been carried out on the effect of diprotonation on the UV-vis-NIR spectra of free-base tetraphenylporphyrin and tetrakis(p-aminophenyl)porphyrin. The diprotonated forms have been modeled as their bis-formate complexes, i.e., as so-called porphyrin diacids. The dramatic redshift of the Q-band of the TAPP diacid has been explained in terms of an elevated "a2u" HOMO and lowered LUMOs, both reflecting infusion of aminophenyl character into the otherwise classic Gouterman-type frontier MOs. The exercise has also yielded valuable information on the performance of different exchange-correlation functionals. Thus, the hybrid B3LYP functional was found to yield a substantially better description of key spectral features, especially the diprotonation-induced redshifts, than the pure OLYP functional. Use of the range-separated CAMY-B3LYP functional, on the other hand, did not result in improvements relative to B3LYP.

An Exemplary Gay Scientist and Mentor: Martin Gouterman (1931-2020).

Martin Gouterman (1931-2020) was one of the foundational figures of modern porphyrin science. After completing his Ph.D. at The University of Chicago in 1958, he joined Harvard, where he developed his eponymous four-orbital model. In 1966, he moved to the University of Washington Seattle (UW). Here he came out as gay and helped set up Seattle's first gay rights group, the Dorian Society. At UW, Gouterman accomplished an "optical taxonomy" of the major classes of porphyrin derivatives and pioneered pressure-sensitive paints based on phosphorescent platinum porphyrins to map the partial pressure of oxygen on airplane wings. Revered by his students and co-workers for his brilliant yet gentle advising, Gouterman remains a beacon for a more humane and inclusive scientific enterprise.

Seven Clues to Ligand Noninnocence: The Metallocorrole Paradigm.

Noninnocent ligands do not allow an unambiguous definition of the oxidation state of a coordinated atom. When coordinated, the ligands also cannot be adequately represented by a classic Lewis structure. A noninnocent system thus harbors oxidizing (holes) or reducing equivalents (electrons) that are delocalized over both the ligand and the coordinated atom. To a certain degree, that is true of all complexes, but the phenomenon is arguably most conspicuous in complexes involving ligands with extended π-systems. The electronic structures of such systems have often been mischaracterized, thereby muddying the chemical literature to the detriment of students and newcomers to the field. In recent years, we have investigated the electronic structures of several metallocorrole families, several of which have turned out to be noninnocent. Our goal here, however, is not to present a systematic account of the different classes of metallocorroles, but rather to focus on seven major tools (in a nod to A. G. Cairns-Smith's Seven Clues to the Origin of Life) that led us to recognize noninnocent behavior and subsequently to characterize the phenomenon in depth. (1) The optical probe: For a series of noninnocent meso-triarylcorrole derivatives with different para substituents X, the Soret maxima are typically exquisitely sensitive to the nature of X, red-shifting with increasing electron-donating character of the group. No such substituent sensitivity is observed for the Soret maxima of innocent triarylcorrole derivatives. (2) Quantum chemistry: Spin-unrestricted density functional theory calculations permit a simple and quick visualization of ligand noninnocence in terms of the spin density profile. Even for an S = 0 complex, the broken-symmetry method often affords a spin density profile that, its fictitious character notwithstanding, helps visualize the intramolecular spin couplings. (3) NMR and EPR spectroscopy: In principle, these two techniques afford experimental probes of the electronic spin density. (4) Structure/X-ray crystallography. Ligand noninnocence in metallocorroles is often reflected in small but distinct skeletal bond length alternations in and around the bipyrrole part of the macrocycle. In addition, for Cu and some Ag corroles, ligand noninnocence manifests itself via a strong saddling of the macrocycle. (5) Vibrational spectroscopy. Unsurprisingly, the aforementioned bond length alternations translate to structure-sensitive vibrational marker bands. (6) Electrochemistry. Noninnocent metallocorroles exhibit characteristically high reduction potentials, but caution should be exercised in turning the logic around. A high reduction potential does not necessarily signify a noninnocent metallocorrole; certain high-valent metal centers also undergo metal-centered reduction at quite high potentials. (7) X-ray absorption spectroscopy (XAS). By focusing on a given element, typically the central atom in a coordination complex, X-ray absorption near-edge spectroscopy (XANES) can provide uniquely detailed local information on oxidation and spin states, ligand field strength, and degree of centrosymmetry. For metallocorroles, some of the most clear-cut distinctions between innocent and noninnocent systems have come from the K-edge XANES of Mn and Fe corroles. For researchers faced with a new, potentially noninnocent system, the take-home message is to employ a good majority (i.e., at least four) of the above methods to arrive at a reliable conclusion vis-à-vis noninnocence.