The Chemical Bond in C2

Quantum chemical calculations using the complete active space of the valence orbitals have been carried out for H_nCCH_n (n=0–3) and N₂. The quadratic force constants and the stretching potentials of H_nCCH_n have been calculated at the CASSCF/cc‐pVTZ level. The bond dissociation energies of the C?C bonds of C₂ and HC≡CH were computed using explicitly correlated CASPT2‐F12/cc‐pVTZ‐F12 wave functions. The bond dissociation energies and the force constants suggest that C₂ has a weaker C?C bond than acetylene. The analysis of the CASSCF wavefunctions in conjunction with the effective bond orders of the multiple bonds shows that there are four bonding components in C₂, while there are only three in acetylene and in N₂. The bonding components in C₂ consist of two weakly bonding σ bonds and two electron‐sharing π bonds. The bonding situation in C₂ can be described with the σ bonds in Be₂ that are enforced by two π bonds. There is no single Lewis structure that adequately depicts the bonding situation in C₂. The assignment of quadruple bonding in C₂ is misleading, because the bond is weaker than the triple bond in HC≡CH.     

Ab initio study of the π–π interactions between CO2 and benzene,pyridine, and pyrrole

The π–π interactions between CO₂ and three aromatic molecules, namely benzene (C₆H₆), pyridine (C₅H₅N), and pyrrole (C₄H₅N), which represent common functional groups in metal‐organic/zeoliticimidazolate framework materials, were characterized using high‐level ab initio methods. The coupled‐cluster with single and double excitations and perturbative treatment of triple excitations (CCSD(T)) method with a complete basis set (CBS) was used to calibrate Hartree–Fock, density functional theory, and second‐order M?ller–Plesset (MP2) with resolution of the identity approximation calculations. Results at the MP2/def2‐QZVPP level showed the smallest deviations (only about 1 kJ/mol) compared with those at the CCSD(T)/CBS level of theory. The strength of π–π binding energies (BEs) followed the order C₄H₅N > C₆H₆ ～ C₅H₅N and was roughly correlated with the aromaticity and the charge transfer between CO₂ and aromatic molecule in clusters. Compared with hydrogen‐bond or electron donor–acceptor interactions observed during BE calculations at the MP2/def2‐QZVPP level of theory, π–π interactions significantly contribute to the total interactions between CO₂ and aromatic molecules. © 2013 Wiley Periodicals, Inc.     

Understanding metal–ligand interactions in coordination polymers using Hirshfeld surface analysis

Properties related to the size and shape of Hirshfeld surfaces provide insight into the nature and strength of interactions among the building blocks of molecular crystals. In this work, we demonstrate that functions derived from the curvatures of the surface at a point, namely, shape index (S) and curvedness (C), as well as the distances from the surface to the nearest external (d_e) and internal (d_i) nuclei, can be used to help understand metal–ligand interactions in coordination polymers. The crystal structure of catena‐poly[[[(1,10‐phenanthroline‐κ²N,N′)copper(II)]‐μ‐4‐nitrophthalato‐κ²O¹:O²] trihydrate], {[Cu(C₈H₃NO₆)(C₁₂H₈N₂)]·3H₂O}_n, described here for the first time, was used as a prototypical system for our analysis. Decomposition of the coordination polymer into its metal centre and ligand molecules followed by joint analysis of the Hirshfeld surfaces generated for each part unveil qualitative and semi‐quantitative information that cannot be easily obtained either from conventional crystal packing analysis or from Hirshfeld surface analysis of the entire polymeric units. The shape index function S is particularly sensitive to the coordination details and its mapping on the surface of the metallic centre is highly dependent on the nature of the ligand and the coordination bond distance. Correlations are established between the shape of the Hirshfeld surface of the metal and the geometry of the metal–ligand contacts in the crystals. This could be applied not only to estimate limiting coordination distances in metal–organic compounds, but also to help establish structure–property relationships potentially useful for the crystal engineering of such materials.     

Cocrystals of 1,4‐diethynylbenzene with 1,3‐diacetylbenzene and benzene‐1,4‐dicarbaldehyde exhibiting strong nonconventional alkyne–carbonyl C—H…O hydrogen bonds between the components

Weak interactions between organic molecules are important in solid‐state structures where the sum of the weaker interactions support the overall three‐dimensional crystal structure. The sp‐C—H…N hydrogen‐bonding interaction is strong enough to promote the deliberate cocrystallization of a series of diynes with a series of dipyridines. It is also possible that a similar series of cocrystals could be formed between molecules containing a terminal alkyne and molecules which contain carbonyl O atoms as the potential hydrogen‐bond acceptor. I now report the crystal structure of two cocrystals that support this hypothesis. The 1:1 cocrystal of 1,4‐diethynylbenzene with 1,3‐diacetylbenzene, C₁₀H₆·C₁₀H₁₀O₂, (1), and the 1:1 cocrystal of 1,4‐diethynylbenzene with benzene‐1,4‐dicarbaldehyde, C₁₀H₆·C₈H₆O₂, (2), are presented. In both cocrystals, a strong nonconventional ethynyl–carbonyl sp‐C—H…O hydrogen bond is observed between the components. In cocrystal (1), the C—H…O hydrogen‐bond angle is 171.8 (16)° and the H…O and C…O hydrogen‐bond distances are 2.200 (19) and 3.139 (2) Å, respectively. In cocrystal (2), the C—H…O hydrogen‐bond angle is 172.5 (16)° and the H…O and C…O hydrogen‐bond distances are 2.25 (2) and 3.203 (2) Å, respectively.     

A theory of molecules in molecules

SCF wave functions have been calculated using a minimal atomic basis set of Gaussian lobe functions for the para-, meta-, and ortho-forms of the molecules C₆H₄XY, where X, Y can be either of CN, OH, or F. It is found that in all cases the total energies increase in the sequence meta-, para-, ortho-compound. For the molecules containing the CN group the energy differences are extremely small (0.1–1 kcal/mole) for the other molecules they are one to two orders of magnitude larger. The reliability of these results is discussed. The theory of molecules in molecules is applied to these cases. The wave function of C₆H₄XY is constructed from the fragments C₆H₅X and HY by transferring some of the localized orbitals of the wave functions of the fragments and recalculating the orbitals in the region of interaction. For the molecules containing the CN group the energy differences are too small so that they are not correctly reproduced except by the most exact calculations, which involve no approximations other than the transfer of localized orbitals. For the other molecules satisfactory results are obtained.     

Substituent Effect on the Electronic Properties and Nature of the W≡C Bond in trans‐Cl(OC)(H3P)3W(≡C‐para‐C6H4X) (X = H,F, SiH3, CN,NO2, SiMe3, CMe3, NH2, NMe2) Complexes: A Computational Quantum Chemistry Study

In this investigation, we describe substituent effect on the dipole moment, ionization potential, electron affinity, structure, frontier orbitals energy, in the trans‐Cl(OC)(H₃P)₃W(≡C‐para‐C₆H₄X) (X = H, F, SiH₃, CN, NO₂, SiMe₃, CMe₃, NH₂, NMe₂) complexes using MPW1PW91 quantum chemical calculations. The nature of chemical bond between the [Cl(OC)(H₃P)₃W]⁻ and [C‐para‐C₆H₄X]⁺ fragments was illustrated with energy decomposition analysis (EDA). Percentage composition in terms of the defined groups of frontier orbitals for these complexes was inspected to investigate the character in metal–ligand bonds. Quantum theory of atoms in molecules (QTAIM) was used for illustration of metal–ligand bonds in these complexes.     

Photoelectron spectra,penning ionization electron spectra,and character of canonical molecular orbitals

When canonical molecular orbitals are expanded in terms of a set of localized molecular orbital building blocks, called bond orbitals, the character of the canonical molecular orbitals can be characterized according to the component bond orbitals resembling the core, lone pair, and localized bond building blocks in an intuitive Lewis structure. Weinhold's natural bond orbital method can produce a unique Lewis structure with total occupancy of its occupied bond orbitals exceeding 99.9% of the total electron density for simple molecules. Two useful indices, Lewis bond order and weight of lone pair orbitals, can be defined according to the weights of the bonding and lone pair components of this unique Lewis structure. Calculation results for molecules N₂, CO, CS, NO, HCN, C₂H₂, H₂O, and H₂S show that the former index can account for the vibrational structures of photoelectron spectroscopy, whereas the latter index can account for the band intensity enhancement of Penning ionization electron spectroscopy. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 882–892, 1998     

Structure of molecular energy levels of homonuclear diatomic molecules

A new approach is given for the systematic prediction of the low‐lying electronic states of homonuclear diatomic molecules. The approach is based on the bond order and the energy levels of the separated atoms. The asymptotic wave functions are derived from two atomic wave functions by using new operators defined as linear combinations of certain ladder operators. We show that the low angular moment states tend to have a high bond order in the states derived from an asymptote. The observed low‐lying states of C₂, C, Sc₂, and Ti₂ molecules agree with the predictions. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 597–604, 1999     

Relation of the force constant of a bond to the electric field at a nucleus

The change in the electric field at a nucleus in a molecule due to bond stretch is related to the force constant of the stretched bond. The validity of this relationship using approximate wave functions at the SCF and MP2 levels of theory is tested for the diatomic molecules H₂, HF, CO, and N₂. The effect of basis set variation on H₂ is also investigated. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1664–1667, 1997     

Metal–metal bonding in biscycloheptatrienyl dimetal compounds of the second‐row transition metals

Density functional theory has been used to examine the dimetallocene‐like dicycloheptatrienyl dimetal compounds of the second‐row transition metals (C₇H₇)₂M₂ (M = Ru, Tc, Mo, Nb, Zr). The lowest energy (C₇H₇)₂Mo₂ structure is a coaxial structure with terminal η⁷? C₇H₇ rings, whereas the lowest energy (C₇H₇)₂M₂ structures (M = Ru, Tc, Nb, Zr) are perpendicular structures with bridging η⁴,η⁴? C₇H₇ rings except for the perpendicular (η⁴,η³? C₇H₇)₂Ru₂ structure. The metal–metal bond orders in the (C₇H₇)₂M₂ structures (M = Ru, Tc, Mo, Nb), as determined by analysis of their frontier molecular orbitals, suggest preferred 16‐ rather than 18‐electron configurations for the central metal atoms. Thus, in the coaxial (η⁷? C₇H₇)₂M₂ structures the formal bond orders are two for M = Tc and three for M = Mo. For the perpendicular structures both (η⁴,η³? C₇H₇)₂Ru₂ and (η⁴,η⁴? C₇H₇)₂Tc₂ have 16‐electron configurations with metal–metal single bonds owing to the different modes of bonding of the bridging C₇H₇ rings in the two structures. For the (C₇H₇)₂Zr₂ system the perpendicular structure has a formal Zr?Zr double bond and the coaxial structure has a very long (～3.5 Å) Zr? Zr bond indicating only 12‐ to 14‐electron configurations for the zirconium atoms.     

Binding energy of gas molecule with two pyrazine molecules as organic linker in metal�Corganic framework: its theoretical evaluation and understanding of determining factors

We explored the interactions of gas molecules such as H₂, CH₄, C₂H₄, C₂H₆, CO₂, and CS₂ sandwiched by two pyrazine (Pz) molecules, which were employed as a model of organic linker in the Hofmann-type metal?Corganic framework (MOF). The MP2.5/aug-cc-pVTZ method was employed here, because this method presents almost the same binding energy as that calculated by the CCSD(T)/aug-cc-pVDZ with MP2.5-evaluated basis set extension effects to aug-cc-pVTZ basis set. The binding energy of the gas molecule increases in the order H₂?<?CH₄?<?CO₂?<?C₂H₄????C₂H₆?<?CS₂. The energy decomposition analysis of the interaction energy indicates that the electrostatic term presents the largest contribution to the interaction energy at the Hartree?CFock level. However, the dispersion interaction provides dominant contribution to the total binding energy at correlated level. We newly found a linear correlation between the z-component of polarizability of gas molecules and dispersion energy, where the z-axis was taken to be perpendicular to two Pz rings. These results are useful for understanding and predicting the binding energy of the gas molecule with the organic linkers of MOF.     

Higher hydrogen uptake capacity of C2H4Ti+ than C2H4Ti: a quantum chemical study

Using density functionals theory, we show that gravimetric hydrogen uptake of C₂H₄Ti complex and its cation, C₂H₄Ti⁺, differ by about 2 wt%. Six and five hydrogen molecules are found to be adsorbed on C₂H₄Ti⁺ and C₂H₄Ti complexes thereby showing a hydrogen-uptake capacity of 13.74 and 11.72 wt%, respectively. All hydrogen molecules are adsorbed in molecular form on C₂H₄Ti⁺ ion with an increase in metal bond strength, whereas in some cases, the hydrogen molecules are found to be dissociated on C₂H₄Ti neutral complex. The uptake capacity of neutral C₂H₄Ti complex shown in this work is in excellent agreement with that reported experimentally, Phillips and Shivaram (Phys Rev Lett 100:105505, 2008). The H₂ adsorption energy and its dependence on exchange and correlation functions in density functionals method were illustrated. Even after the adsorption of maximum number of hydrogen molecules on C₂H₄Ti and C₂H₄Ti⁺ complexes, Ti and Ti⁺ remain strongly bound to C₂H₄ substrate.     

Poly[diaqua(μ‐4,4′‐bipyridine‐κ2N:N′)bis(μ‐cyanido‐κ2C:N)bis(cyanido‐κC)nickel(II)copper(II)]: a metal–organic cyanide‐bridged framework

The structure of the title compound, [NiCu(CN)₄(C₁₀H₈N₂)(H₂O)₂]_n or [{Cu(H₂O)₂}(μ‐C₁₀H₈N₂)(μ‐CN)₂{Ni(CN)₂}]_n, was shown to be a metal–organic cyanide‐bridged framework, composed essentially of –Cu–4,4′‐bpy–Cu–4,4′‐bpy–Cu– chains (4,4′‐bpy is 4,4′‐bipyridine) linked by [Ni(CN)₄]²⁻ anions. Both metal atoms sit on special positions; the Cu^II atom occupies an inversion center, while the Ni^II atom of the cyanometallate sits on a twofold axis. The 4,4′‐bpy ligand is also situated about a center of symmetry, located at the center of the bridging C—C bond. The scientific impact of this structure lies in the unique manner in which the framework is built up. The arrangement of the –Cu–4,4′‐bpy–Cu–4,4′‐bpy–Cu– chains, which are mutually perpendicular and non‐intersecting, creates large channels running parallel to the c axis. Within these channels, the [Ni(CN)₄]²⁻ anions coordinate to successive Cu^II atoms, forming zigzag –Cu—N[triple‐bond]C—Ni—C[triple‐bond]N—Cu– chains. In this manner, a three‐dimensional framework structure is constructed. To the authors' knowledge, this arrangement has not been observed in any of the many copper(II)–4,4′‐bipyridine framework complexes synthesized to date. The coordination environment of the Cu^II atom is completed by two water molecules. The framework is further strengthened by O—H...N hydrogen bonds involving the water molecules and the symmetry‐equivalent nonbridging cyanide N atoms.     

Zweidimensionale Polymere mit hydrophober Umhüllung: Kristallstrukturen der isostrukturellen Metallkomplexe [M{C6H4(SO2)2N}(H2O)] (M = K,Rb) und des strukturverwandten Ammoniumsalzes [(NH4){C6H4(SO2)2N}(H2O)]

Metal Salts of Benzene‐1,2‐di(sulfonyl)amine. 4. Hydrophobically Wrapped Two‐Dimensional Polymers: Crystal Structures of the Isostructural Metal Complexes [M{C₆H₄(SO₂)₂N}(H₂O)] (M = K, Rb) and of the Structurally Related Ammonium Salt [(NH₄){C₆H₄(SO₂)₂N}(H₂O)] The previously unreported compounds KZ · H₂O ( 1 ), RbZ · H₂O ( 2 ) and NH₄Z · H₂O ( 3 ), where Z^– is Ndeprotonated ortho‐benzenedisulfonimide, are examples of layered inorgano‐organic solids, in which the inorganic component is comprised of metal or ammonium cations, N(SO₂)₂ groups and water molecules and the outer regions are formed by the planar benzo rings of the anions. The metal complexes 1 and 2 were found to be strictly isostructural, whereas 3 is structurally related to them by a non‐crystallographic mirror plane ( 1 – 3 : monoclinic, space group P2₁/c, Z = 4; single crystal X‐ray diffraction at low temperatures). In each structure, the five‐membered 1,3,2‐dithiazolide heterocycle possesses an envelope conformation, the N atom lying about 40 pm outside the mean plane of the S–C–C–S moiety. The metal complexes feature two‐dimensional coordination networks interwoven with O–H…O hydrogen bonds originating from the water molecules. The metal centres adopt an irregular nonacoordination formed by five sulfonyl O atoms, two N atoms and two μ₂‐bridging water molecules; each M⁺ is connected to four different anions. When NH₄⁺ is substituted for M⁺, the metal–ligand bonds are replaced by N⁺–H…O hydrogen bonds, but the general topology of the lamella is not affected. In the three structures, the lipophilic benzo groups protrude obliquely from the surfaces of the polar lamellae and display marked interlocking between adjacent layers.     

On the optimal mixing of the exchange energy and the electron-electron interaction part of the exchange-correlation energy

The optimal mixing coefficient C of the exchange energy E_x and the electron-electron interaction part of the exchange-correlation energy W¹_xc in the formula for the total exchange-correlation energy E_xc was expressed through the ratio of the kinetic T_c and potential W_c contributions to the correlation energy E_c. This expression can be derived from a Heavyside step function model of the dependence of W^λ_xc on the coupling parameter of the electron interaction λ. Values of T_c and W_c obtained from ab initio wave functions were used to estimate C for a number of atoms and molecules. A strong dependence of T_c, W_c, and C on the bond distance was demonstrated for the case of the H₂ molecule. T_c and C approach zero in the bond-dissociation limit; so for an electron-pair bond, the admixing of exact exchange to obtain an accurate E_xc is strongly dependent on the bond length and has to disappear for weak interaction/large bond distances. The potential of the exchange-correlation hole constructed for H₂ from an ab initio second-order density matrix was compared with its generalized gradient approximation (GGA). © 1996 John Wiley & Sons, Inc.     

Structural diversity of homobinuclear transition metal complexes of the phenazine ligand: theoretical investigation

DFT/BP86 calculations have been carried out on a series of hypothetical binuclear compounds of general formula (L₃M)₂(C₁₂N₂H₈) (M?=?Sc–Ni, L₃?=?(CO)₃, (PH₃)₃ and Cp^?, and C₁₂N₂H₈?=?phenazine ligand-denoted Phn). The various structures with syn and anti configurations have been investigated, in order to determine the phenazine’s coordination to first-row transition metals of various spin states with syn and anti conformations. The lowest energy structures depend on the nature of the metal, the spin state, and the molecular symmetry. This study has shown that the electronic communication between the metal centers depends on their oxidation state and the attached ligands. The tricarbonyl and the triphosphine ligands gave rise to comparable results in terms of stability order of isomers, metal-metal bond distances, and the coordination modes. Metal-metal multiple bonding has been evidenced for Sc, Ti, and V complexes to compensate the electronic deficiency. The Cr, Mn, Fe, Co, and Ni-rich metals prefer the anti conformation due to the enhancement of the metal valence electron count. The spin density values calculated for the triplet and quintet spin structures point out that the unpaired electrons are localized generally on the metal centers. The Wiberg bond indices are used to evaluate the metal-metal bonding. Furthermore, calculations using the BP86-D functional which take into account the attractive part of the van der Waals type interaction potential between atoms and molecules that are not directly connected to each other gave comparable results to those obtained by BP86 functional in terms of coordination modes, HOMO-LUMO gaps, metal-metal bond orders, and the stability order between isomers, but with slight deviation of M–C, M–N, and M–M bond distances not exceeding 3%.     

Scorpionate‐Type Coordination in MFU‐4l Metal–Organic Frameworks: Small‐Molecule Binding and Activation upon the Thermally Activated Formation of Open Metal Sites

Postsynthetic metal and ligand exchange is a versatile approach towards functionalized MFU‐4l frameworks. Upon thermal treatment of MFU‐4l formates, coordinatively strongly unsaturated metal centers, such as zinc(II) hydride or copper(I) species, are generated selectively. Cu^I‐MFU‐4l prepared in this way was stable under ambient conditions and showed fully reversible chemisorption of small molecules, such as O₂, N₂, and H₂, with corresponding isosteric heats of adsorption of 53, 42, and 32 kJ mol^?1, respectively, as determined by gas‐sorption measurements and confirmed by DFT calculations. Moreover, Cu^I‐MFU‐4l formed stable complexes with C₂H₄ and CO. These complexes were characterized by FTIR spectroscopy. The demonstrated hydride transfer to electrophiles and strong binding of small gas molecules suggests these novel, yet robust, metal–organic frameworks with open metal sites as promising catalytic materials comprising earth‐abundant metal elements.     

A novel three‐dimensional coordination polymer constructed from pyrazine and copper(I): poly[[copper(I)‐di‐μ2‐pyrazine‐κ4N:N′] 3,5‐dicarboxybenzenesulfonate monohydrate]

In the title metal–organic framework complex, {[Cu(C₄H₄N₂)₂](C₈H₅O₇S)·H₂O}_n or {[Cu^I(pyz)₂](H₂SIP)·H₂O}_n (pyz is pyrazine and H₃SIP is 5‐sulfoisophthalic acid or 3,5‐dicarboxybenzenesulfonic acid), the asymmetric unit is composed of one copper(I) center, one whole pyrazine ligand, two half pyrazine ligands lying about inversion centres, one H₂SIP⁻ anion and one lattice water molecule, wherein each Cu^I atom is in a slightly distorted tetrahedral coordination environment completed by four pyrazine N atoms, with the Cu—N bond lengths in the range 2.017 (3)–2.061 (3) Å. The structure features a three‐dimensional diamondoid network with one‐dimensional channels occupied by H₂SIP⁻ anions and lattice water molecules. Interestingly, the guest–water hydrogen‐bonded network is also a diamondoid network, which interpenetrates the metal–pyrazine network.     

Two new two‐dimensional coordination polymers based on isophthalate and a flexible N‐donor ligand containing benzimidazole and pyridine rings: synthesis,crystal structures and a solid‐state UV–Vis study

In coordination chemistry and crystal engineering, many factors influence the construction of coordination polymers and the final frameworks depend greatly on the organic ligands used. N‐Donor ligands with diverse coordination modes and conformations have been employed to assemble metal–organic frameworks. Carboxylic acid ligands can deprotonate completely or partially when bonding to metal ions and can also act as donors or acceptors of hydrogen bonds and are thus good candidates for the construction of supramolecular architectures. Two new transition metal complexes, namely poly[diaqua(μ₄‐1,4‐bis{[1‐(pyridin‐3‐ylmethyl)‐1H‐benz[d]imidazol‐2‐yl]methoxy}benzene)bis(μ₂‐isophthalato)dicobalt(II)], [Co(C₈H₄O₄)(C₃₄H₂₈N₆O₂)_0.5(H₂O)]_n, (1), and poly[diaqua(μ₄‐1,4‐bis{[1‐(pyridin‐3‐ylmethyl)‐1H‐benz[d]imidazol‐2‐yl]methoxy}benzene)bis(μ₂‐isophthalato)dicadmium(II)], [Cd(C₈H₄O₄)(C₃₄H₂₈N₆O₂)_0.5(H₂O)]_n, have been constructed using a symmetric N‐donor ligand and a carboxylate ligand under hydrothermal conditions. X‐ray crystallographic studies reveal that complexes (1) and (2) are isostructural, both of them exhibiting three‐dimensional supramolecular architectures built by hydrogen bonds in which the coordinated water molecules serve as donors, while the O atoms of the carboxylate groups act as acceptors. Furthermore, (1) and (2) have been characterized by elemental, IR spectroscopic, powder X‐ray diffraction (PXRD) and thermogravimetric analyses. The UV–Vis absorption spectrum of complex (1) has also been investigated.     

Approximate theoretical determination of molecular static polarizabilities

Molecular polarizabilities are computed using ab initio SCF wave functions and second-order perturbation theory with special attention given to the use of a shifted denominator. Rather small basis sets are used, in order to obtain reasonable values at a reduced cost. Results are presented for H₂, CO, H₂O, C₂H₄, OCS, C₆H₆, Cl₂, Br₂, I₂.