Natural resonance-theoretic conceptions of extreme electronic delocalization in soft materials.

In the broad context of Dalton's atomic hypothesis and subsequent classical vs. quantum understanding of macroscopic materials, we show how Pauling's resonance-type conceptions, as quantified in natural resonance theory (NRT) analysis of modern wavefunctions, can be modified to unify description of interatomic interactions from the Lewis-like limit of localized e-pair covalency in molecules to the extreme delocalized limit of supramolecular "soft matter" aggregation. Such "NRT-centric" integration of NRT bond orders for hard- and soft-matter interactions is illustrated with application to a long-predicted and recently synthesized organometallic sandwich-type complex ("diberyllocene") that exhibits bond orders ranging from the soft limit (bBeC ≈ 0.01) to the typical values (bCC ≈ 1.35) of molecular resonance-covalency in the organic domain, with intermediate value (bBeBe ≈ 0.86) for intermetallic Be⋯Be interaction.

"Noncovalent Interaction": A Chemical Misnomer That Inhibits Proper Understanding of Hydrogen Bonding, Rotation Barriers, and Other Topics.

We discuss the problematic terminology of "noncovalent interactions" as commonly applied to hydrogen bonds, rotation barriers, steric repulsions, and other stereoelectronic phenomena. Although categorization as "noncovalent" seems to justify classical-type pedagogical rationalizations, we show that these phenomena are irreducible corollaries of the same orbital-level conceptions of electronic covalency and resonance that govern all chemical bonding phenomena. Retention of such nomenclature is pedagogically misleading in supporting superficial dipole-dipole and related "simple, neat, and wrong" conceptions as well as perpetuating inappropriate bifurcation of the introductory chemistry curriculum into distinct "covalent" vs. "noncovalent" modules. If retained at all, the line of dichotomization between "covalent" and "noncovalent" interaction should be re-drawn beyond the range of quantal exchange effects (roughly, at the contact boundary of empirical van der Waals radii) to better unify the pedagogy of molecular and supramolecular bonding phenomena.

High-Density "Windowpane" Coordination Patterns of Water Clusters and Their NBO/NRT Characterization.

Cluster mixture models for liquid water at higher pressures suggest the need for water clusters of higher coordination and density than those commonly based on tetrahedral H-bonding motifs. We show here how proton-ordered water clusters of increased coordination and density can assemble from a starting cyclic tetramer or twisted bicyclic (Möbius-like) heptamer to form extended Aufbau sequences of stable two-, three-, and four-coordinate "windowpane" motifs. Such windowpane clusters exhibit sharply reduced (~90°) bond angles that differ appreciably from the tetrahedral angles of idealized crystalline ice Ih. Computed free energy and natural resonance theory (NRT) bond orders provide quantitative descriptors for the relative stabilities of clusters and strengths of individual coordinative linkages. The unity and consistency of NRT description is demonstrated to extend from familiar supra-integer bonds of the molecular regime to the near-zero bond orders of the weakest linkages in the present H-bond clusters. Our results serve to confirm that H-bonding exemplifies resonance-covalent (fractional) bonding in the sub-integer range and to further discount the dichotomous conceptions of "electrostatics" for intermolecular bonding vs. "covalency" for intramolecular bonding that still pervade much of freshman-level pedagogy and force-field methodology.

Can a Wanzlick-like equilibrium exist between dicoordinate borylenes and diborenes?

Boron chemistry has experienced tremendous progress in the last few decades, resulting in the isolation of a variety of compounds with remarkable electronic structures and properties. Some examples are the singly Lewis-base-stabilised borylenes, wherein boron has a formal oxidation state of +I, and their dimers featuring a boron-boron double bond, namely diborenes. However, no evidence of a Wanzlick-type equilibrium between borylenes and diborenes, which would open a valuable route to the latter compounds, has been found. In this work, we combine DFT, coupled-cluster, multireference methods, and natural bond orbital/natural resonance theory analyses to investigate the electronic, structural, and kinetic factors controlling the reactivity of the transient CAAC-stabilised cyanoborylene, which spontaneously cyclotetramerises into a butterfly-type, twelve-membered (BCN)4 ring, and the reasons why its dimerisation through the boron atoms is hampered. The computations are also extended to the NHC-stabilised borylene counterparts. We reveal that the borylene ground state multiplicity dictates the preference for self-stabilising cyclooligomerisation over boron-boron dimerisation. Our comparison between NHC- vs. CAAC-stabilised borylenes provides a convincing rationale for why the reduction of the former always gives diborenes while a range of other products is found for the latter. Our findings provide a theoretical background for the rational design of base-stabilised borylenes, which could pave the way for novel synthetic routes to diborenes or alternatively non-dimerising systems for small-molecule activation.

Chlorine dioxide: An exception that proves the rules of localized chemical bonding.

We employ natural bond orbital and natural resonance theory tools to analyze the enigmatic properties of the C2v-symmetric isomer of chlorine dioxide radical (ClO2), whose many challenges to Pauling-type localized bonding concepts were recognized by Linus Pauling himself. Although spin-contamination is minimal in this species, ClO2 exhibits an unusually strong form of "different Lewis structures for different spins" bonding pattern, intrinsically outside the framework of "maximal pairing" concepts. We show how the novel spin-unpaired donor-acceptor interactions lead to weakened bonding in the supramolecular domain of polyradical (ClO2)n homoclusters and aqueous ClO2(H2O)n heteroclusters. Despite feeble binding energies and large inter-radical separations, the polyradical clusters are found to maintain coherent spin patterns in each cluster component, attesting to the quantal donor-acceptor nature of their interactions and the cooperative and anticooperative couplings that govern intra- and intermolecular spin distributions in such spin-clusters.

Anti-Electrostatic Pi-Hole Bonding: How Covalency Conquers Coulombics.

Intermolecular bonding attraction at π-bonded centers is often described as "electrostatically driven" and given quasi-classical rationalization in terms of a "pi hole" depletion region in the electrostatic potential. However, we demonstrate here that such bonding attraction also occurs between closed-shell ions of like charge, thereby yielding locally stable complexes that sharply violate classical electrostatic expectations. Standard DFT and MP2 computational methods are employed to investigate complexation of simple pi-bonded diatomic anions (BO-, CN-) with simple atomic anions (H-, F-) or with one another. Such "anti-electrostatic" anion-anion attractions are shown to lead to robust metastable binding wells (ranging up to 20-30 kcal/mol at DFT level, or still deeper at dynamically correlated MP2 level) that are shielded by broad predissociation barriers (ranging up to 1.5 Å width) from long-range ionic dissociation. Like-charge attraction at pi-centers thereby provides additional evidence for the dominance of 3-center/4-electron (3c/4e) nD-π*AX interactions that are fully analogous to the nD-σ*AH interactions of H-bonding. Using standard keyword options of natural bond orbital (NBO) analysis, we demonstrate that both n-σ* (sigma hole) and n-π* (pi hole) interactions represent simple variants of the essential resonance-type donor-acceptor (Bürgi-Dunitz-type) attraction that apparently underlies all intermolecular association phenomena of chemical interest. We further demonstrate that "deletion" of such π*-based donor-acceptor interaction obliterates the characteristic Bürgi-Dunitz signatures of pi-hole interactions, thereby establishing the unique cause/effect relationship to short-range covalency ("charge transfer") rather than envisioned Coulombic properties of unperturbed monomers.

Pauling's Conceptions of Hybridization and Resonance in Modern Quantum Chemistry.

We employ the tools of natural bond orbital (NBO) and natural resonance theory (NRT) analysis to demonstrate the robustness, consistency, and accuracy with which Linus Pauling's qualitative conceptions of directional hybridization and resonance delocalization are manifested in all known variants of modern computational quantum chemistry methodology.

Comment on "Superposition of Waves or Densities: Which Is the Nature of Chemical Resonance?" [J. Comput. Chem. 2021, 42, 412-417].

We reply to specific criticisms and misrepresentations of natural resonance theory (NRT) in a recent article [Y. Wang, J. Comput. Chem. 2021, 42, 412-417] and argue that it presents a false dichotomy with respect to theoretical efforts to comprehend the nature of resonance-type phenomena.

Sulfur Tetrahydride and Allied Superhydride Clusters: When Resonance Takes Precedence.

Sulfur offers a variety of bonding surprises compared to the parent oxygen atom of the chalcogen family. In the present work, we employ standard quantum chemistry methods to characterize formation of previously unrecognized sulfur tetrahydride (C4v -symmetric SH4 ) from hydrogen sulfide (H2 S) and molecular hydrogen (H2 ) on the ground state potential energy surface. The unusual intramolecular interactions of SH4 defy Lewis-like bonding conceptions, exhibiting the dominance of resonance-type donor-acceptor delocalizations well beyond those of SF4 (C2v sawhorse geometry) and other known tetrahalides. The distressed character of SH4 bonding also leads to exotic intermolecular structural motifs in clusters of pure (SH4 )n and mixed (SH4 ⋅⋅⋅H2 S)n composition. We evaluate structural, spectroscopic, and electronic properties for various 2D/3D coordination patterns and discuss how (SH4 ⋅⋅⋅H2 S)n -type building blocks may relate to recent experimental studies of superconductivity in high-pressure materials of "SH3 " stoichiometry.

NBO/NRT Two-State Theory of Bond-Shift Spectral Excitation.

We show that natural bond orbital (NBO) and natural resonance theory (NRT) analysis methods provide both optimized Lewis-structural bonding descriptors for ground-state electronic properties as well as suitable building blocks for idealized "diabatic" two-state models of the associated spectroscopic excitations. Specifically, in the framework of single-determinant Hartree-Fock or density functional methods for a resonance-stabilized molecule or supramolecular complex, we employ NBO/NRT descriptors of the ground-state determinant to develop a qualitative picture of the associated charge-transfer excitation that dominates the valence region of the electronic spectrum. We illustrate the procedure for the elementary bond shifts of SN2-type halide exchange reaction as well as the more complex bond shifts in a series of conjugated cyanine dyes. In each case, we show how NBO-based descriptors of resonance-type 3-center, 4-electron (3c/4e) interactions provide simple estimates of spectroscopic excitation energy, bond orders, and other vibronic details of the excited-state PES that anticipate important features of the full multi-configuration description. The deep 3c/4e connections to measurable spectral properties also provide evidence for NBO-based estimates of ground-state donor-acceptor stabilization energies (sometimes criticized as "too large" compared to alternative analysis methods) that are also found to be of proper magnitude to provide useful estimates of excitation energies and structure-dependent spectral shifts.

Substituted Ortho-Benzynes: Properties of the Triple Bond.

Ortho-benzyne has been well studied by both experiment and theory. Its substituted variants, however, have been less carefully examined. Benchmark data are computed for unsubstituted ortho-benzyne using several density functional theory functionals and basis sets, up to cc-pVQZ. Optimized geometries for the substituted ortho-benzyne as well as harmonic vibrational frequencies and singlet-triplet splittings are computed using the benchmarked functionals. A proximal (syn)OH substitution causes a mean θ1 distortion of +8.1 ± 1.4° from ortho-benzyne. Substituting in the proximal position with F shifts the singlet-triplet splitting by +4.5 ± 0.4 kcal mol-1 from ortho-benzyne. Natural bond orbital analysis, including natural Coulomb electrostatics, elucidates the presence of three influences from the selected substituents: hyperconjugative, resonance, and electrostatic effects.

Comment on "Observation of alkaline earth complexes M(CO)8 (M = Ca, Sr, or Ba) that mimic transition metals".

Wu et al (Reports, 31 August 2018, p. 912) claim that recently characterized octacarbonyls of Ca, Sr, and Ba mimic the classical Dewar-Chatt-Duncanson bonding motif of transition metals. This claim, which contradicts known chemistry and computed electron density distributions, originates in the assumption of a flawed reference state for energy decomposition analyses.

What Is the Nature of Supramolecular Bonding? Comprehensive NBO/NRT Picture of Halogen and Pnicogen Bonding in RPH2···IF/FI Complexes (R = CH3, OH, CF3, CN, NO2).

We employ a variety of natural bond orbital (NBO) and natural resonance theory (NRT) tools to comprehensively investigate the nature of halogen and pnicogen bonding interactions in RPH2···IF/FI binary complexes (R = CH3, OH, CF3, CN, and NO2) and the tuning effects of R-substituents. Though such interactions are commonly attributed to "sigma-hole"-type electrostatic effects, we show that they exhibit profound similarities and analogies to the resonance-type 3-center, 4-electron (3c/4e) donor-acceptor interactions of hydrogen bonding, where classical-type "electrostatics" are known to play only a secondary modulating role. The general 3c/4e resonance perspective corresponds to a continuous range of interatomic A···B bond orders (bAB), spanning both the stronger "covalent" interactions of the molecular domain (say, bAB ≥ ½) and the weaker interactions (bAB ˂ ½, often misleadingly termed "noncovalent") that underlie supramolecular complexation phenomena. We show how a unified NBO/NRT-based description of hydrogen, halogen, pnicogen, and related bonding yields an improved predictive utility and intuitive understanding of empirical trends in binding energies, structural geometry, and other measurable properties that are expected to be manifested in all such supramolecular interaction phenomena.

Nine questions on energy decomposition analysis.

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

NBO 7.0: New vistas in localized and delocalized chemical bonding theory.

We briefly outline some leading features of the newest version, NBO 7.0, of the natural bond orbital (NBO) wavefunction analysis program. Major extensions include: (1) a new NPEPA module implementing Karafiloglou's "polyelectron population analysis" in the NBO framework; (2) new RDM2 program infrastructure for describing electron correlation effects based on full evaluation of the second-order reduced density matrix; (3) improved convex-solver implementation of natural resonance theory (NRT), allowing a greatly expanded range of applications and associated "resonance NBO" (RNBO) visualization of chemical reactivity; (4) a variety of other improvements in well-established NBO algorithms. We also provide brief introduction to the new NBOPro@Jmol utility program, a plugin to the Jmol chemical structure viewer that serves as a convenient tool to provide on-demand NBO descriptors or orbital visualizations for a broad variety of chemical inquiries in research or classroom applications. © 2019 Wiley Periodicals, Inc.

Efficient optimization of natural resonance theory weightings and bond orders by gram-based convex programming.

We describe the formal algorithm and numerical applications of a novel convex quadratic programming (QP) strategy for performing the variational minimization that underlies natural resonance theory (NRT). The QP algorithm vastly improves the numerical efficiency, thoroughness, and accuracy of variational NRT description, which now allows uniform treatment of all reference structures at the high level of detail previously reserved only for leading "reference" structures, with little or no user guidance. We illustrate overall QPNRT search strategy, program I/O, and numerical results for a specific application to adenine, and we summarize more extended results for a data set of 338 species from throughout the organic, bioorganic, and inorganic domain. The improved QP-based implementation of NRT is a principal feature of the newly released NBO 7.0 program version. © 2019 Wiley Periodicals, Inc.

To Be or Not to Be: Demystifying the 2nd-Quantized Picture of Complex Electronic Configuration Patterns in Chemistry with Natural Poly-Electron Population Analysis.

We provide a didactic introduction to 2nd-quantized representation of complex electron-hole (e/h) excitation patterns in general configuration interaction wave functions built from orthonormal local orbitals of natural atomic orbital or natural bond orbital (NBO) type. Such local excitation patterns of chemically oriented basis functions can be related to the resonance concepts of valence bond theory, and quantitative evaluation of the associated excitation probabilities then provides an alternative assessment of resonance "weighting" that may be compared with those of NBO-based natural resonance theory. We illustrate the usefulness of anticommutation relations in deriving Pauli-compliant expressions for allowed excitation patterns, showing how the exciton-like promotions φλ → φν (creating an e/h excitation with h in φλ and e in φν ) impose strict constraints on associated e/h-probabilities (requiring, e.g., that the e-probability for an electron "to be" or "not to be" in φν must be rigorously linked to the complementary h-probabilities in φλ ). Specific examples are presented of the quantum Boolean logic for four or six local spin-orbitals, with emphasis on Natural Poly-Electron Population Analysis (NPEPA) evaluation of VB-type covalent and ionic contributions in conventional 2-center bonding, resonance weightings in 3-center hydrogen bonding, and general characteristics of higher-order m-center bonding motifs for m > 3. Numerical results are presented for methylamine, acrolein, and water dimer to illustrate current NPEPA implementation in the NBO program. © 2019 Wiley Periodicals, Inc.

Resonance Theory Reboot.

What is now called "resonance theory" has a long and conflicted history. We first sketch the early roots of resonance theory, its heritage of diverse physics and chemistry conceptions, and its subsequent rise to reigning chemical bonding paradigm of the mid-20th century. We then outline the alternative "natural" pathway to localized Lewis- and resonance-structural conceptions that was initiated in the 1950s, given semi-empirical formulation in the 1970s, recast in ab initio form in the 1980s, and successfully generalized to multi-structural "natural resonance theory" (NRT) form in the 1990s. Although earlier numerical applications were often frustrated by the ineptness of then-available numerical solvers, the NRT variational problem was recently shown to be amenable to highly efficient convex programming methods that yield provably optimal resonance weightings at a small fraction of previous computational costs. Such convexity-based algorithms now allow a full "reboot" of NRT methodology for tackling a broad range of chemical applications, including the many familiar resonance phenomena of organic and biochemistry as well as the still broader range of resonance attraction effects in the inorganic domain. We illustrate these advances for prototype chemical applications, including (i) stable near-equilibrium species, where resonance mixing typically provides only small corrections to a dominant Lewis-structural picture, (ii) reactive transition-state species, where strong resonance mixing of reactant and product bonding patterns is inherent, (iii) coordinative and related supramolecular interactions of the inorganic domain, where sub-integer resonance bond orders are the essential origin of intermolecular attraction, and (iv) exotic long-bonding and metallic delocalization phenomena, where no single "parent" Lewis-structural pattern gains pre-eminent weighting in the overall resonance hybrid.

Quantitative Theoretical Predictions and Qualitative Bonding Analysis of the Divinylborinium System and Its Al, Ga, In, and Tl Congeners.

A substituted divinylborinium cation was synthesized recently and characterized crystallographically as a gauche structure with a 153° C1-C2-C3-C4 dihedral angle. A full theoretical geometrical optimization of the bis(2-mesityl-1,2-diphenylvinyl)-borane cation shows excellent agreement with the crystal structure. However, for the parent unsubstituted divinylborinium cation, we predict a nearly 90° C1-C2-C3-C4 dihedral angle using the CCSD(T)/cc-pVTZ coupled cluster method. The cis and trans planar geometries (0° and 180° for the C1-C2-C3-C4 dihedral angle) proved to be transition states with energy barriers of 2.8 and 2.3 kcal/mol, respectively, with respect to unimolecular conversion to the gauche equilibrium. The structures of the heavier boron group cations (Al, Ga, In, and Tl) have also been investigated here, finding even lower energy barriers (0.3-0.7 kcal/mol). After the ZPVE corrections, the barriers are further decreased. The torsional angles for the unknown Al, Ga, In, and Tl dimesityl substituted compounds should be somewhat less than 153°. Many of these findings may be understood in terms of qualitative electronic structure theory. The torsional folding of borane complex, including cationic divinylborinium and elementary vinylborane (C2H3BH2) or chlorovinylborane (C2H3BHCl) precursors, are investigated with natural bond orbital (NBO) analysis to unveil the electronic origins of the torsional properties. The NBO-based descriptors are employed to systematically deconstruct complex torsional dependence into a balanced portrayal of hyperconjugative and steric effects.

Natural Bond Orbital Theory of Pseudo-Jahn-Teller Effects.

We describe a unified picture of symmetry-breaking electronic interactions that are usually described as "pseudo-Jahn-Teller (PJT) effects" and attributed to vibronic coupling but can also be associated with hyperconjugative donor-acceptor interactions in the framework of natural bond orbital (NBO) and natural resonance theory (NRT) analysis. We show how NBO/NRT descriptors offer a simplified alternative to the vibronic coupling picture of PJT effects that yields both improved cause-effect specificity and chemically enriched understanding of symmetry-breaking phenomena but with no necessary input from ground-state vibrational or excited-state electronic properties. Comparative NBO/NRT vs vibronic coupling analyses of PJT effects are illustrated for two well-known cases: trans-bending in Si2H4 and higher Group-14 homologues of ethylene and chain-kinking in cyclopentadienylideneketene (C5H4CCO) and related cumulene ketones. The conceptual and practical advantages of the NBO-based hyperconjugative approach may be expected to extend to numerous PJT-type symmetry-breaking phenomena throughout the chemical sciences.