Transition metal bonding functions and their applications in catalytic adsorptions and reactions: Part II. Micromechanism of CO chemisorption and a new concept of σ-π coordination

A micromechanism of CO adsorption and a new concept of σ-π coordination on transition metal are proposed in this article. Based on experimental facts, we assume CO 5σ- and/ or CO 1 π interacts with the representative M.O.s of the metal valence band, ψ(Mi, Vs) and ψ(Mi, Vd), to form the bonding M.O. group and antibonding M.O. group. The bonding group is located below the Fermi level (E_f), in which some M.O.s are much more characteristic of metal orbitais (denoted as M-CO σ-bondings) while some M.O.s exhibit slight metal orbital characteristics, which belong to the excited valence M.O.s of adsorbed CO, conventionally assigned as adsorbed CO 5σ, CO 1 π and CO 4σ. The calculated data indicate that the peak positions of adsorbed CO 5σ, CO 1 π and CO 4σ are significantly higher than their corresponding M.O.s in the gaseous CO molecule, i.e. adsorbed CO is in an excited (or activated) state. The total energy generated (ΔE) from adsorbed CO 5σ, CO 1 π and CO 4σ can be used as a qualitative parameter for characterizing the ability for CO dissociation. On the other hand, the antibonding empty M.O. group of M-CO is located above the E_f, which exhibits some characteristics of metal d orbitais. The hybridization of CO 2π with dπ- orbitais in the Vs, Vd bands and dπ orbitais of the antibonding M.O. group of M-CO bondings results in the formation of unoccupied M.O.s with CO 2π-M dπ character. These M.O.s plus those unoccupied M.O.s without CO 2π-M dπ character contribute the adsorbate-derived resonances, located 3-5 eV above E_F and observed by Inverse Photo-Emission (IPE) difference spectra. We have used orbital overlap integrals of S(CO 5σ, dσ, Vd) and S(CO 2π, dπ, Vd) to characterize the relative competitive abilities for hybridization of CO 5σ and CO 2π with d orbitais. The calculated results show that CO 5σ possesses a stronger ability to hybridize d orbitals in the Vd band than does CO 2π-, thus the peaks of adsorbate-induced empty levels are shifted farther from the d band when the competitive hybridizing factor [CHF=S(CO 5σ, dσ, Vd)/S(CO 2π, dπ, Vd)] is increased. The calculated data demonstrate that the peak positions of CO adsorbate-derived resonances of Cu, Ni, Pd and Pt metals, observed by IPE difference spectra, are in good parallel with their CHF values. Moreover, the values of CHE also demonstrate that CO σ-bonding stimulates d electrons to transfer upward from the d band to the Vs band, where much more CO 2π-M dπ character exists. We propose here a new concept of d back-donation, i.e. d electrons transfer from the occupied d band to the unoccupied M.O.s exhibiting CO 2π-M dπ character in the Vs and Vd bands, which weakens the π bond of C-O and simultaneously strengthens the M-C bond; these phenomena have been confirmed by IR spectroscopy and EELS. The d back-donation is represented by the B bonding function. The calculations of A, B and AB bonding functions indicate that the AB bonding function of CO adsorption on Cu is significantly smaller than that on Ni, Pd and Pt, so that CO adsorbtion is weak on Cu and is strong on Ni, Pd and Pt. Our micromechanism and our new concept of σ-π coordination provide a unified interpretation of various CO adsorption electronic spectra from below to above the E_F, i.e. from occupied orbitals to empty orbitals; and a unified interpretation of the adsorbate vibration spectra measured by EELS and IR spectroscopy. The advantages of our new concept have been discussed and compared with the conventional concepts of Blyholder and CO 2π-derived resonances.     

Barium as Honorary Transition Metal in Action: Experimental and Theoretical Study of Ba(CO)+ and Ba(CO)−

Ba(CO)⁺ and Ba(CO)^? have been produced and isolated in a low‐temperature neon matrix. The observed C?O stretching wavenumber for Ba(CO)⁺ of 1911.2 cm^?1 is the most red‐shifted value measured for any metal carbonyl cations, indicating strong π backdonation of electron density from Ba⁺ to CO. Quantum chemical calculations indicate that Ba(CO)⁺ has a ²Π reference state, which correlates with the ²D(5d¹) excited state of Ba⁺ that comprises significant Ba⁺(5d_π¹)→CO(π* LUMO) backbonding, letting the Ba(CO)⁺ complex behave like a conventional transition‐metal carbonyl. A bonding analysis shows that the π backdonation in Ba(CO)⁺ is much stronger than the Ba⁺(5d_σ/6s)←CO(HOMO) σ donation. The Ba⁺ cation in the ²D(5d¹) excited state is a donor rather than an acceptor. Covalent bonding in the radical anion Ba(CO)^? takes place mainly through Ba(5d_π)←CO^?(π* SOMO) π donation and Ba(5d_σ/6s)←CO^?(HOMO) σ donation. The most important valence functions at barium in Ba(CO)⁺ cation and Ba(CO)^? anion are the 5d orbitals.     

Transition metal bonding functions and their applications in catalytic adsorptions and reactions: Part III. Effect of metal valence band and periodic trend of CO σ-π bonding functions on transition metals

Our model of metal valence band and our new concept of σ-π coordination are further discussed and confirmed in this paper.The infrared stretching frequencies of C-O decrease in the order 2056, 1886 and 1786 cm⁻¹ in Ni(CO)₄, Co(CO)₄⁻¹ and Fe(CO)₄⁻², which parallels the increase in d electron back-donation functions (B metal bonding functions) from 1.539, 2.121 to 2.895 on Ni, Co and Fe metals, respectively. On the other hand, the M-C bond orders increase from 1.33, 1.89 to 2.16 for Ni(CO)₄, Co(CO)₄⁻¹ and Fe(CO)₄⁻², which parallel the increase in A(CO5σ-Mσ)-B(CO2π-Mπ) metal bonding functions from 24.61, 30.01 to 33.19, respectively. They are in agreement with our new concept of σ-π coordination proposed in the previous paper. This new concept has also been used to analyze the mechanism of the formation of Ni(CO)₄, Co(CO)₄⁻¹ and Fe(CO)₄⁻², and to explain why they can automotively hybridize each other despite the energy differences between 3d and 4s, 4p, which are very large.The effects of metal valence bands have been accounted for on all transition metals (d¹ to d⁸), and it is demonstrated that d orbitals increase from the Vd band upward to the Vs band, and s orbitals from the Vs band downward to the Vd band, which is equivalent to a change in orbital potential, and would modify their orbital overlap integrals with the adsorbate M.O.s and the A, B metal bonding functions significantly. The effective potentials and the percentage s, d functions of Vs, Vd and d_occ bands are the most important factors for determining the effect of the metal valence band. The effects of promoter and support are also altered by changes in the above factors. For Group VIII metals, the valence band provides various s and d orbitals at various potentials, in which a certain number of s and d orbitals can match better with CO adsorbate M.O.s, which explains why CO adsorbed species on Group VIII metals are all stable and adsorption rates are all relatively rapid.The periodic trends of metal A, B, AB and D_c bonding functions depend on the structures of the metal valence band, i.e. the potential levels and s, d percentage functions of Vs, Vd and d_occ bands. For 4d and 5d metals, the potential levels of the Vs band are high, which cannot form a strong CO 5σ-M σ bond, but the potential levels of Vd band are higher and the width of the d band is wider than those of 3d metal, so their B bonding functions are larger, and they can be used to activate saturated and unsaturated hydrocarbons. In contrast, for 3d metals, the potentials of the Vs band are lower, which favour formation of strong CO 5σ-M σ and M-C bonds, i.e. their A and D_c bonding functions are larger, which can promote coke formation. While ABD_cD_o can be used to characterize CO dissociation, B/A can be used to characterize C-C formation.The characteristics of various metal bonding functions on each transition metal are useful for designing catalyst composition. A typical example has been illustrated, using the possibility to select non-noble metals instead of noble metals in hydrocarbon reactions.     

氮苄叉基苯胺分子的平面扭曲驱动力的DFT研究

为了探索DFT方法中氮苄叉基苯胺分子的扭曲驱动力, 通过把非平面氮苄叉基苯胺(NBA)分子的DFT能量分成π和σ的方法, 分析了垂直离域能ΔE^V(θ)及σ-π轨道作用能ΔE^σπ(θ)的失稳定性, 并讨论了在扭曲过程中它们所起的作用. 在B3LYP/6-31G*, 6-311G*, 6-31G(2d), 6-311G(2d)水平下的计算结果显示: 与经典观点不同, π电子的离域是失稳定的, 且平面时失稳定性最强, 是分子扭曲的动力; 但σ-π轨道作用也是失稳定的, 随着扭角的增大其失稳定性增强, 是分子扭曲的阻力. NBA分子的大扭角构象, 是包含π-π, σ-π轨道作用在内的各种电子相互作用共同作用的结果.     

Alkoxide Clusters of Molybdenum and Tungsten as Templates for Organometallic Chemistry: Comparison with Carbonyl Clusters of the Later Transition Elements

Alkoxide and carbonyl ligands complement each other because they both behave as “π buffers” to transition metals. Alkoxides, which are π donors, stabilize early transition metals in high oxidation states by donating electrons into vacant d_π orbitals, whereas carbonyls, which are π acceptors, stabilize later transition elements in their lower oxidation states by accepting electrons from filled d_π orbitals. Both ligands readily form bridges that span M? M bonds. In solution fluxional processes that involve bridge–terminal ligand exchange are common to both alkoxide and carbonyl ligands. The fragments [W(OR)₃], [CpW(CO)₂], [Co(CO)₃], and CH are related by the isolobal analogy. Thus the compounds [(RO)₃W ? W(OR)₃], [Cp(CO)₂W?W(CO)₂Cp], hypothetical [(CO)₃Co?Co(CO)₃], and HC?CH are isolobal. Alkoxide and carbonyl cluster compounds often exhibit striking similarities with respect to substrate binding—e.g., [W₃(μ₃-CR)(OR′)₉] versus [Co₃(μ₃-CR)(CO)₉] and [W₄(C)(NMe)(OiPr)₁₂] versus [Fe₄(C)(CO)₁₃]—but differ with respect to M? M bonding. The carbonyl clusters use e_g-type orbitals for M? M bonding whereas the alkoxide clusters employ t_2g-type orbitals. Another point of difference involves electronic saturation. In general, each metal atom in a metal carbonyl cluster has an 18-electron count; thus, activation of the cluster often requires thermal or photochemical CO expulsion or M? M bond homolysis. Alkoxide clusters, on the other hand, behave as electronically unsaturated species because the π electrons are ligand-centered and the LUMO metal-centered. Also, access to the metal centers may be sterically controlled in metal alkoxide clusters by choice of alkoxide groups whereas ancillary ligands such as tertiary phosphanes or cyclopentadienes must be introduced if steric factors are to be modified in carbonyl clusters. A comparison of the reactivity of alkynes and ethylene with dinuclear alkoxide and carbonyl compounds is presented. For the carbonyl compounds CO ligand loss is a prerequisite for substrate uptake and subsequent activation. For [M₂(OR)₆] compounds (M = Mo and W) the nature of substrate uptake and activation is dependent upon the choice of M and R, leading to a more diverse chemistry.     

A “double-zeta” type wavefunction for an organometallic: Bis-(π-allyl)nickel

A wavefunction which is of double-zeta quality at the level of the valence orbitals [based on a (11, 7, 5/8, 4/4) gaussian basis set contracted to (4, 3, 2/3, 2/2)] is reported for thebis-(π-allyl)nickel molecule. Independant SCF calculations for two ionized states substantiate the conclusion reached previously for a number of organometallics with a minimal basis set that Koopmans' theorem is not valid for these molecules, namely that the highest occupied orbital from the ground state calculation for the neutral molecule is mostly a ligand π orbital whereas the lowest ionization potential corresponds to the removal of an electron from a molecular orbital which is mostly a metal 3d orbital. The nature of the bonding inbis-(π-allyl)nickel is discussed on the basis of the possible interactions between the metal orbitals and the π orbitals of the allyl group. The interaction between the filled nonbonding π orbital of the allyl group and the empty 3d _xz orbital of the Ni atom appears responsible for most of the bonding, together with some backbonding through an interaction between the 3d x ²?y ²and 3d xyorbitals and the σ and π orbitals of the ligands. The computed value for the rotation barrier about the C-C allyl bond, 90 kcal/mole, rules out this rotation as one of the possible mechanisms which account for the equivalence of the terminal hydrogens in the proton magnetic resonance spectra of π-allyl complexes.     

The two-dimensional band structure of (polyphthalocyaninato)Ni(II)

The two-dimensional (2D) band structure of (polyphthalocyaninato)Ni(II), Ni(ppc), has been analyzed by a self-consistent field (SCF ) Hartree–Fock (HF ) crystal orbital (CO ) formalism based on an INDO (intermediate neglect of differential overlap) type Hamiltonian. The calculated HF band gap of Ni(ppc) amounts to 0.24 eV. The highest filled band is a ringlike a_1u combination (D_4h symmetry label) localized at the carbon sites of the organic fragment. Remarkable hybridization in the valence band leads to the considerable band width Δ?_v of 2.92 eV. This value is close to the Δ?_v numbers which are conventionally encountered in one-dimensional metallomacrocycles. The effective width of the states in Ni(ppc) is 13.8 eV. In graphite a net π interval of 13.0 eV is predicted by the present CO formalism; i.e., the energetic distribution of the π electrons is roughly comparable in both 2D solids. The Ni 3d states in Ni(ppc) are far below the Fermi level which is calculated at ?4.9 eV; they are predicted between ?12.2 and ?16.4 eV in the mean-field approximation. Quasi-particle corrections lead to a significant shift of these strongly metal-centered states. Important electronic structure properties of Ni(ppc) are compared with those of 1D metallomacrocycles with similar molecular stoichiometry. The total density of states distribution of Ni(ppc) has been fragmented into projected (ligand π and σ, Ni 3d) contributions in order to allow for a transparent interpretation of the 2D band structure.     

All-Metallic Zn=Zn Double-π Bonded Octahedral Zn2M4 (M=Li,Na) Clusters with Negative Oxidation State of Zinc

Zn=Zn double bonded-especially double-π bonded-systems are scarce due to strong Coulomb repulsion caused by the Zn atom's internally crowded d electrons and very high energy of the virtual π orbitals in Zn₂ fragments. It is also rare for Zn atoms to exhibit negative oxidation states within reported Zn−Zn bonded complexes. Herein, we report Zn=Zn double-π bonded octahedral clusters Zn₂M₄ (M=Li, Na) bridged by four alkali metal ligands, in which the central Zn atom is in a negative oxidation state. Especially in D_4h−Zn₂Na₄, the natural population analysis shows that the charge of the Zn atom reaches up to −0.89 |e| (−1.11 |e| for AIM charge). Although this cooperation inevitably increases the repulsion between two Zn atoms, the introduction of the s¹-type ligands results in occupation of degenerated π orbitals and the electrons being delocalized over the whole octahedral framework as well, in turn stabilizing the octahedral molecular structure. This study demonstrates that maintaining the degeneracy of the π orbitals and introducing electrons from equatorial plane are effective means to construct double-π bonds between transitional metals.     

SCF-α Scattered wave model cluster calculations for the adsorption systems CO/Ni and N2/Ni

SCF-α-SW calculations have been performed on model clusters which can be taken as representations of chemisorbed CO and N₂ on Ni(100). As a check of the influence of the cluster size, NiCO/NiN₂ and Ni₉N₂ clusters have been studied as well as the isolated molecules CO and N₂ . In order to recognize and eliminate errors due to the differing muffintin geometries, other reference molecular clusters (CO/N₂ in an enlarge outer sphere, and on 9 empty spheres corresponding in size to Ni₉) have also been calculated. The discussion of results is based on (Xα ground state and transition state) energy shifts and on charge distributions. The main conclusions reached about the surface bond in the two cases (dative 5 σ bond and π backbond for CO; for N₂ main dative bond through 4σ with a smaller 5σ contribution, and a weaker π backbond than for CO) agree with those reached by other methods. Additional information (e.g σ backbond contribution for the large clusters; a strong localization of the adsorbate bond for N₂, but noticeable delocalization for CO) is derived.     

Rücktitelbild: The Mo?Mo Quintuple Bond as a Ligand to Stabilize Transition‐Metal Complexes (Angew. Chem. 31/2015)

Herein, we report the employment of the Mo Mo quintuple bonded amidinate complex to stabilize Group 10 metal fragments {(Et₃P)₂M} (M=Pd, Pt) and give rise to the isolation of the unprecedented δ complexes. X‐ray analysis unambiguously revealed short contacts between Pd or Pt and two Mo atoms and a slight elongation of the Mo Mo quintuple bond in these two compounds. Computational studies show donation of the Mo Mo quintuple‐bond δ electrons to an empty σ orbital on Pd or Pt, and back‐donation from a filled Pd or Pt d_π orbital into the Mo Mo δ* level (LUMO), consistent with the Dewar–Chatt–Duncanson model.     

The MoMo Quintuple Bond as a Ligand to Stabilize Transition‐Metal Complexes

Herein, we report the employment of the Mo? Mo quintuple bonded amidinate complex to stabilize Group 10 metal fragments {(Et₃P)₂M} (M=Pd, Pt) and give rise to the isolation of the unprecedented δ complexes. X‐ray analysis unambiguously revealed short contacts between Pd or Pt and two Mo atoms and a slight elongation of the Mo? Mo quintuple bond in these two compounds. Computational studies show donation of the Mo? Mo quintuple‐bond δ electrons to an empty σ orbital on Pd or Pt, and back‐donation from a filled Pd or Pt d_π orbital into the Mo? Mo δ* level (LUMO), consistent with the Dewar–Chatt–Duncanson model.     

Electronic states and nature of bonding of the molecule NiSi by all electron ab initio HF-CI and CASSCF calculations

All electron ab initio Hartree-Fock (HF), configuration interaction (CI) and multiconfiguration self-consistent field (CASSCF) calculations have been applied to investigate the low-lying electronic states of the NiSi molecule. The ground state of the NiSi molecule is predicted to be¹Σ⁺. The chemical bond in the¹Σ⁺ ground state is a double bond composed of one σ and one π bond. The σ bond is due to a delocalized molecular orbital formed by combining the Ni 4s and the Si 3pσ orbitals. The π bond is a partly delocalized valence bond, originating from the coupling of the 3dπ hole on Ni with the 3pπ electron on Si. Withing the energy range 1 eV 18 electronic states have been identified. The lowest lying electronic states have been characterized as having a hole in either the 3dπ or the 3dδ orbital of Ni, and the respective final states are formed when either of these holes are coupled to the 3pπ valence electron of Si.     

Anion-(π)n-π Catalytic Micelles

Anion-π catalysis operates by stabilizing anionic transition states on π-acidic aromatic surfaces. In anion-(π)_n-π catalysis, π stacks add polarizability to strengthen interactions. In search of synthetic methods to extend π stacks beyond the limits of foldamers, the self-assembly of micelles from amphiphilic naphthalenediimides (NDIs) is introduced. To interface substrates and catalysts, charge-transfer complexes with dialkoxynaphthalenes (DANs), a classic in supramolecular chemistry, are installed. In π-stacked micelles, the rates of bioinspired ether cyclizations exceed rates on monomers in organic solvents by far. This is particularly impressive considering that anion-π catalysis in water has been elusive so far. Increasing rates with increasing π acidity of the micelles evince operational anion-(π)_n-π catalysis. At maximal π acidity, autocatalytic behavior emerges. Dependence on position and order in confined micellar space promises access to emergent properties. Anion-(π)_n-π catalytic micelles in water thus expand supramolecular systems catalysis accessible with anion-π interactions with an inspiring topic of general interest and great perspectives.     

Octacarbonyl Anion Complexes of the Late Lanthanides Ln(CO)8− (Ln=Tm,Yb, Lu) and the 32-Electron Rule

The lanthanide octacarbonyl anion complexes Ln(CO)₈⁻ (Ln=Tm, Yb, Lu) were produced in the gas phase and detected by mass-selected infrared photodissociation spectroscopy in the carbonyl stretching-frequency region. By comparison of the experimental CO-stretching frequencies with calculated data, which are strongly red-shifted with respect to free CO, the Yb(CO)₈⁻ and Lu(CO)₈⁻ complexes were determined to possess octahedral (O_h) symmetry and a doublet X²A_2u (Yb) and singlet X¹A_1g (Lu) electronic ground state, whereas Tm(CO)₈⁻ exhibits a D_4h equilibrium geometry and a triplet X³B_1g ground state. The analysis of the electronic structures revealed that the metal-CO attractive forces come mainly from covalent orbital interactions, which are dominated by [Ln(d)]→(CO)₈ π backdonation and [Ln(d)]←(CO)₈ σ donation (contributes ≈77 and 16 % to covalent bonding, respectively). The metal f orbitals play a very minor role in the bonding. The electronic structure of all three lanthanide complexes obeys the 32-electron rule if only those electrons that occupy the valence orbitals of the metal are considered.     

Why are the Homoleptic Diyl Complexes M(InR)4 with M = Ni and Pt Stable Compounds while only Ni(CO)4 but not Pt(CO)4 can become Isolated? A Theoretical Study of M(EMe)44 and M(CO)4 (M = Ni,Pd, Pt; E = B,Al, Ga,In, Tl)

The equilibrium geometries and first bond dissociation energies of the homoleptic complexes M(EMe)₄ and M(CO)₄ with M = Ni, Pd, Pt and E = B, Al, Ga, In, Tl have been calculated at the gradient corrected DFT level using the BP86 functionals. The electronic structure of the metal‐ligand bonds has been examined with the topologial analysis of the electron density distribution. The nature of the bonding is revealed by partitioning the metal‐ligand interaction energies into contributions by electrostatic attraction, covalent bonding and Pauli repulsion. The calculated data show that the M‐CO and M‐EMe bonding is very similar. However, the M‐EMe bonds of the lighter elements E are much stronger than the M‐CO bonds. The bond energies of the latter are as low or even lower than the M‐TlMe bonds. The main reason why Pd(CO)₄ and Pt(CO)₄ are unstable at room temperature in a condensed phase can be traced back to the already rather weak bond energy of the Ni‐CO bond. The Pd‐L bond energies of the complexes with L = CO and L = EMe are always 10 — 20 kcal/mol lower than the Ni‐L bond energies. The calculated bond energy of Ni(CO)₄ is only D_o = 27 kcal/mol. Thus, the bond energy of Pd(CO)₄ is only D_o = 12 kcal/mol. The first bond dissociation energy of Pt(CO)₄ is low because the relaxation energy of the Pt(CO)₃ fragment is rather high. The low bond energies of the M‐CO bonds are mainly caused by the relatively weak electrostatic attraction and by the comparatively large Pauli repulsion. The σ and π contributions to the covalent M‐CO interactions have about the same strength. The π bonding in the M‐EMe bonds is less than in the M‐CO bonds but it remains an important part of the bond energy. The trends of the electrostatic and covalent contributions to the bond energies and the σ and π bonding in the metal‐ligand bonds are discussed.     

Generation and Identification of the Linear OCBNO and OBNCO Molecules with 24 Valence Electrons

Two structural isomers containing five second-row element atoms with 24 valence electrons were generated and identified by matrix-isolation IR spectroscopy and quantum chemical calculations. The OCBNO complex, which is produced by the reaction of boron atoms with mixtures of carbon monoxide and nitric oxide in solid neon, rearranges to the more stable OBNCO isomer on UV excitation. Bonding analysis indicates that the OCBNO complex is best described by the bonding interactions between a triplet-state boron cation with an electron configuration of (2s)⁰(2p_σ)⁰(2p_π)² and the CO/NO⁻ ligands in the triplet state forming two degenerate electron-sharing π bonds and two ligand-to-boron dative σ bonds.     

The effect of pressure on electronic excitations in Mn2(CO)10 and Re2(CO)10

The shift with pressure has been measured for the σ → σ* excitations for crystalline Mn₂(CO)₁₀ and Re₂(CO)₁₀ to 120 kbar. The results are interpreted in terms of the relative importance of the effect of compression on stabilization of the bonding vis-a-vis the antibonding orbitals, and the importance of the van der Waals interaction with the surroundings. The π → σ* excitation in Mn₂(CO)₁₀ and the σ → π* excitation in Re₂(CO)₁₀ are briefly discussed.     

Electronic states and nature of the chemical bond in the molecule CrC by all-electron ab initio calculations

All-electron ab initio Hartree–Fock (HF ), valence configuration interaction (CI ), and multiconfiguration self-consistent-field (CASSCF ) calculations have been applied to investigate the electronic states of the CrC molecule. The molecule is predicted as having four low-lying electronic states, ³∑^?, ⁵∑^?, ⁷∑^?, and ⁹∑^?, separated by an energy gap of 0.55 eV from the next higher-lying state, ¹∑^?, which is followed by the states ⁵Π and ⁷Π. The four lowest-lying electronic states are due to the coupling of the angular momenta of the ⁶S_g Cr⁺ ion with those of the ⁴S_u C^? anion. The chemical bond in the ³∑^? ground state can be viewed as a quadruple bond composed of two σ and two π bonds. One σ bond is due to the formation of a molecular orbital that is doubly occupied. The remaining bonds, i.e., one σ and two π bonds, arise from valence-bond couplings. The π bonds originate from the valence-bond couplings of the electrons in the C 2pπ orbitals with those in the Cr 3dπ orbitals. The σ bond originates from the valence-bond coupling of the C 2pσ electron with an electron in the Cr 4s, 4p hybrid that is polarized away from the C atom.