Bonding with Parallel Spins: High-Spin Clusters of Monovalent Metal Atoms

Bonding is a glue of chemical matter and is also a useful concept for designing new molecules. Despite the fact that electron pairing remains the bonding mechanism in the great majority of molecules, in the past few decades scientists have had a growing interest in discovering novel bonding motifs. As this Account shows, monovalent metallic atoms having exclusively parallel spins, such as ¹¹Li₁₀, ¹¹Au₁₀, and ¹¹Cu₁₀, can nevertheless form strongly bound clusters, without having even one traditional bond due to electron pairing. These clusters, which also can be made chiral, have high magnetic moments. We refer to this type as no-pair ferromagnetic (NPFM) bonding, which characterizes the ^<i>n</i>+1M_<i>n</i> clusters, which were all predicted by theoretical computations. The small NPFM alkali clusters that have been “synthesized” to date, using cold-atom techniques, support the computational predictions.In this Account, we describe the origins of NPFM bonding using a valence bond (VB) analysis, which shows that this bonding motif arises from bound triplet electron pairs that spread over all the close neighbors of a given atom in the cluster. The bound triplet pair owes its stabilization to the resonance energy provided by the mixing of the local ionic configurations, [³M(↑↑)⁻]M⁺ and M⁺[³M(↑↑)⁻], and the various excited covalent configurations (involving p_<i>z</i> and d_<i>z</i>² atomic orbitals) into the repulsive covalent structure ³(M↑↑M) with the s¹s¹ electronic configuration. The NPFM bond of the bound triplet is described by a resonating wave function with “in–out” and “out–in” pointing hybrids. The VB model accounts for the tendency of NPFM clusters to assume polyhedral shapes with rather high symmetry. In addition, this model explains the very steep rise of the bonding energy per atom (<i>D</i>_e/<i>n</i>), which starts out small in the ³M₂ dimer (<1 kcal/mol) and reaches 12–19 kcal/mol for clusters with 10 atoms. The model further predicts that usage of heteroatomic clusters should increase the bonding energy of an NPFM cluster.These NPFM clusters are excited state species. We suggest here stabilizing these states and making them accessible, for example, by using magnetic fields, or a combination of magnetic and electric fields. The advent of NPFM clusters offers new horizons in chemistry and enriches the scope of chemical bonding. These prospects form a strong incentive to investigate the origins of the bound triplet pairs and further chart the territory of NPFM clusters, for example, in clusters of Be, Mg, or Zn, possibly in clusters of their monosubstituted species, and the group III metalloids, such as B, Al, as well as in transition metals such as Sc

Formation of Carbon–Carbon Triply Bonded Molecules from Two Free Carbyne Radicals via a Conical Intersection

The recent proposal (Bogoslavsky, B.; Levy, O.; Kotlyar, A.; Salem, M.; Gelman, F.; Bino, A. <i>Angew. Chem., Int. Ed.</i> <b>2012</b>, <i>51</i>, 90–94) that metallo–alkylidyne complexes decompose in aqueous solution and give rise to free carbynes, which couple to yield acetylenes, is examined here theoretically. On the basis of the known marker reactions of carbynes in the doublet and quartet state, it is concluded that most of the reactivity patterns observed in the Bino experiment arose from quartet carbynes. Indeed, theory shows that quartet carbynes can be funneled to acetylene via a conical intersection. Moreover, many of the minor products are also identified as markers of the quartet carbynes. Carbynes formation in their doublet state is a minor channel that branches from the conical intersection and leads to the formation of dienes and olefins in the Bino experiment. Thus, we show that conical intersections are important also in thermally initiated reactions. Coupled to the experimental approach, the study opens a window to studies of carbynes under mild conditions

On The Nature of the Halogen Bond

The wide-ranging applications of the halogen bond (X-bond), notably in self-assembling materials and medicinal chemistry, have placed this weak intermolecular interaction in a center of great deal of attention. There is a need to elucidate the physical nature of the halogen bond for better understanding of its similarity and differences vis-à-vis other weak intermolecular interactions, for example, hydrogen bond, as well as for developing improved force-fields to simulate nano- and biomaterials involving X-bonds. This understanding is the focus of the present study that combines the insights of a bottom-up approach based on ab initio valence bond (VB) theory and the block-localized wave function (BLW) theory that uses monomers to reconstruct the wave function of a complex. To this end and with an aim of unification, we studied the nature of X-bonds in 55 complexes using the combination of VB and BLW theories. Our conclusion is clear-cut; most of the X-bonds are held by charge transfer interactions (i.e., intermolecular hyperconjugation) as envisioned more than 60 years ago by Mulliken. This is consistent with the experimental and computational findings that X-bonds are more directional than H-bonds. Furthermore, the good linear correlation between charge transfer energies and total interaction energies partially accounts for the success of simple force fields in the simulation of large systems involving X-bonds

A Unified Theory for the Blue- and Red-Shifting Phenomena in Hydrogen and Halogen Bonds

Typical hydrogen and halogen bonds exhibit red-shifts of their vibrational frequencies upon the formation of hydrogen and halogen bonding complexes (denoted as D···Y–A, Y = H and X). The finding of blue-shifts in certain complexes is of significant interest, which has led to numerous studies of the origins of the phenomenon. Because charge transfer mixing (i.e., hyperconjugation in bonding systems) has been regarded as one of the key forces, it would be illuminating to compare the structures and vibrational frequencies in bonding complexes with the charge transfer effect “turned on” and “turned off”. Turning off the charge transfer mixing can be achieved by employing the block-localized wave function (BLW) method, which is an ab initio valence bond (VB) method. Further, with the BLW method, the overall stability gained in the formation of a complex can be analyzed in terms of a few physically meaningful terms. Thus, the BLW method provides a unified and physically lucid way to explore the nature of red- and blue-shifting phenomena in both hydrogen and halogen bonding complexes. In this study, a direct correlation between the total stability and the variation of the Y–A bond length is established based on our BLW computations, and the consistent roles of all energy components are clarified. The <i>n</i>(D) → σ*­(Y–A) electron transfer stretches the Y–A bond, while the polarization due to the approach of interacting moieties reduces the HOMO–LUMO gap and results in a stronger orbital mixing within the YA monomer. As a consequence, both the charge transfer and polarization stabilize bonding systems with the Y–A bond stretched and red-shift the vibrational frequency of the Y–A bond. Notably, the energy of the frozen wave function is the only energy component which prefers the shrinking of the Y–A bond and thus is responsible for the associated blue-shifting. The total variations of the Y–A bond length and the corresponding stretching vibrational frequency are thus determined by the competition between the frozen-energy term and the sum of polarization and charge transfer energy terms. Because the frozen energy is composed of electrostatic and Pauli exchange interactions and frequency shifting is a long-range phenomenon, we conclude that long-range electrostatic interaction is the driving force behind the frozen energy term

Catalysis of Methyl Transfer Reactions by Oriented External Electric Fields: Are Gold–Thiolate Linkers Innocent?

Oriented external electric fields (OEEFs) are potent effectors of chemical change and control. We show that the Menshutkin reaction, between substituted pyridines and methyl iodide, can be catalyzed/inhibited at will, by just flipping the orientation of the EEF (<i>F</i>_<i>Z</i>) along the “reaction axis” (<i>Z</i>), N---C---I. A theoretical analysis shows that catalysis/inhibition obey the Bell–Evans–Polanyi principle. Significant catalysis is predicted also for EEFs oriented off the reaction axis. Hence, the observation of catalysis can be scaled up and may not require orienting the reactants vis-à-vis the field. It is further predicted that EEFs can also catalyze the front-side nucleophilic displacement reaction, thus violating the Walden-inversion paradigm. Finally, we considered the impact of gold–thiolate linkers, used experimentally to deliver the EEF stimuli, on the Menshutkin reaction. A few linkers were tested and proved not to be innocent. In the presence of <i>F</i>_<i>Z</i>, the linkers participate in the electronic reorganization of the molecular system. In so doing, these linkers induce local electric fields, which map the effects of the EEF and induce catalysis/inhibition at will, as in the pristine reaction. However, as the EEF becomes more negative than −0.1 V/Å, an excited charge transfer state (CTS), which involves one-electron transfer from the 5p lone pair of iodine to an antibonding orbital of the gold cluster, crosses below the closed-shell state of the Menshutkin reaction and causes a mechanistic crossover. This CTS catalyzes nucleophilic displacement of iodine radical from the CH₃I^•+ radical cation. The above predictions and others discussed in the text are testable

Nature of the Three-Electron Bond

We analyze the properties of 15 3-electron bonds, which include σ-3-electron-bonds, such as dihalide radical anions and di-noble gas radical cations, π-3-electron-bonds as in hydrazine radical cations, and doubly-π-(3e)-bonded species such as O₂, FeO⁺, S₂, etc. The primary analytical tool is the breathing-orbital valence-bond (BOVB) method, which enables us to quantify the charge shift resonance energy (RE_CS) of the three electrons, and the bond dissociation energies (<i>D</i>_e). BOVB is tested reliable against MRCI calculations. Our findings show that in all 3-electron bonds, none of the VB structures have by themselves any bonding. In fact, in each VB structure, the three electrons maintain Pauli repulsion, while the entire bonding energy arises from resonance due to the charge shift between the two or more constituent VB structures. Hence, 3e-bonds are charge shift bonds (CSBs). The CSB character is probed by calculating the Laplacian (<i>L</i>) of the 3e-bond. Thus, much like the CSBs in electron-pair bonds, such as F₂ or the central bond in [1.1.1]­propellane, here too <i>L</i> is positive, thus showing the excess kinetic energy of the shared density due to the Pauli repulsion in the 3-electron VB structures. The RE_CS values for 3-electron bonds are invariably larger than the corresponding bond energies. For the doubly-π-(3e)-bonded species, RE_CS is very large, exceeding 100 kcal mol^–1. As such, it is fitting to conclude that σ- and π-3-electron-bonds find their natural place in the CSB family along with two-electron CSBs, with which they share identical energetic and topological characteristics. Experimental manifestations/tests of 3e-CSBs are proposed

Understanding the Nature of the CH···HC Interactions in Alkanes

To understand the dispersion stabilization of hydrocarbons in solids and of encumbered molecules, wherein CH···HC interactions act as sticky fingers, we developed here a valence bond (VB) model and applied it to analyze the H···H interactions in dimers of H₂ and alkanes. The VB analysis revealed two distinct mechanisms of “dispersion.” In the dimers of small molecules like H–H···H–H and H₃CH···HCH₃, the stabilization arises primarily due to the increased importance of the VB structures which possess charge alternation, e.g., C⁺H^–···H⁺C^– and C^–H⁺···H^–C⁺, and hence bring about electrostatic stabilization that holds the dimer. This is consistent with the classical mechanism of oscillating dipoles as the source of dispersion interactions. However, in larger alkanes, this mechanism is insufficient to glue the two molecules together. Here, the “dispersion” interaction comes about through perturbational mixing of VB structures, which reorganize the bonding electrons of the two interacting CH bonds via recoupling of these electrons to H···H, C···C, and C···H “bonds.” Finally, an attempt is made to create a bridge from VB to molecular orbital (MO) and local pair natural-orbital coupled electron pair approximation (LPNO-CEPA/1) analyses of the interactions, which bring about CH···HC binding

Spin–Orbit Coupling and Outer-Core Correlation Effects in Ir- and Pt-Catalyzed C–H Activation

The transition metal-dependent spin–orbit coupling (SOC) and outer-core (5s5p) correlation effects in Ir- and Pt-catalyzed C–H activation processes are studied here using high level ab initio computations. The catalysts involve complexes with oxidation states: Ir­(I), Ir­(III), Pt(0), and Pt­(II). It is demonstrated that for these heavy 5d transition metal-containing systems, the SOC effect and outer-core correlation effect on C–H activation are up to the order of ∼1 kcal/mol, and should be included if chemical accuracy is aimed. The interesting trends in our studied systems are: (1) the SOC effect consistently increases the C–H activation barriers and is apparently larger in higher oxidation states (Pt­(II) and Ir­(III)) than in low-oxidation states (Pt(0) and Ir­(I)); and (2) the magnitude of outer-core (5s5p) correlation effects is larger in less coordinate-saturated system. The effect of basis set on the outer-core correlation correction is significant; larger basis sets tend to increase the C–H activation barriers

Valence Bond Theory Reveals Hidden Delocalized Diradical Character of Polyenes

The nature of the electronic-structure of polyenes, their delocalization features, and potential diradicaloid characters constitute a fundamental problem in chemistry. To address this problem, we used valence bond self-consistent field (VBSCF) calculations and modeling of polyenes, C_2<i>n</i>H_2<i>n</i>+2 (<i>n</i> = 2–10). The theoretical treatment shows that starting with <i>n</i> = 5, the polyene’s wave function is mainly a shifting 1,4-diradicaloid, a character that increases as the chain length increases, while the contribution of the fundamental Lewis structure with alternating double and single bonds (<b>1</b>) decays quite fast and becomes minor relative to the diradicaloid pack. We show how, nevertheless, it is this wave function that predicts that polyenes will still exhibit alternating short/long CC bonds like the fundamental structure <b>1</b>. Furthermore, despite the decay of the VB contribution of <b>1</b>, it remains the single structure with the largest weight among all the individual structures. The mixing of all the 1,4-diradicaloid structures into <b>1</b> follows perturbation theory rules, with the result that the delocalization energy due to this mixing is additive and behaves as a linear function of the number of the double bonds, Δ<i>E</i>_del = −6.9 × <i>n</i> (kcal mol^–1). The VB modeling shows that while the conjugation stabilizes structure <b>1</b>, this stabilization energy is energetically overridden by the Pauli repulsion between two adjacent double bonds. Nevertheless, unsubstituted polyenes remain planar; this observation is addressed. Potential manifestations of the diradicaloid nature of polyenes are discussed, and it is concluded that the diradicaloid character is clearly not a well-defined physical property as in real diradicals. Thus, we went full circle to realize that our philosophical question may not be strictly resolved. The localized/delocalized properties of polyenes seem to define a “chemical duality principle”. This duality of molecular wave functions is a ubiquitous beguiling phenomenon

Charge-Shift Bonding Emerges as a Distinct Electron-Pair Bonding Family from Both Valence Bond and Molecular Orbital Theories

The charge-shift bonding (CSB) concept was originally discovered through valence bond (VB) calculations. Later, CSB was found to have signatures in atoms-in-molecules and electron-localization-function and in experimental electron density measurements. However, the CSB concept has never been derived from a molecular orbital (MO)-based theory. We now provide a proof of principle that an MO-based approach enables one to derive the CSB family alongside the distinctly different classical family of covalent bonds. In this bridging energy decomposition analysis, the covalent–ionic resonance energy, RE_CS, of a bond is extracted by cloning an MO-based purely covalent reference state, which is a constrained two-configuration wave function. The energy gap between this reference state and the variational TCSCF ground state yields numerical values for RE_CS, which correlate with the values obtained at the VBSCF level. This simple MO-based method, which only takes care of static electron correlation, is already sufficient for distinguishing the classical covalent or polar-covalent bonds from charge-shift bonds. The equivalence of the VB and MO-based methods is further demonstrated when both methods are augmented by dynamic correlation. Thus, it is shown from both MO and VB perspectives that the bonding in the CSB family does not arise from electron correlation. Considering that the existence of the CSB family is associated also with quite a few experimental observations that we already reviewed (Shaik, S.; Danovich, D.; Wu, W.; Hiberty, P. C. Nat. Chem., 2009, 1, 443−449), the new bonding concept has passed by now two stringent tests. This derivation, on the one hand, supports the new concept and on the other, it creates bridges between the two main theories of electronic structure