Orbital overlap and chemical bonding

The chemical bonds in the diatomic molecules Li(2)-F(2) and Na(2)-Cl(2) at different bond lengths have been analyzed by the energy decomposition analysis (EDA) method using DFT calculations at the BP86/TZ2P level. The interatomic interactions are discussed in terms of quasiclassical electrostatic interactions DeltaE(elstat), Pauli repulsion DeltaE(Pauli) and attractive orbital interactions DeltaE(orb). The energy terms are compared with the orbital overlaps at different interatomic distances. The quasiclassical electrostatic interactions between two electrons occupying 1s, 2s, 2p(sigma), and 2p(pi) orbitals have been calculated and the results are analyzed and discussed. It is shown that the equilibrium distances of the covalent bonds are not determined by the maximum overlap of the sigma valence orbitals, which nearly always has its largest value at clearly shorter distances than the equilibrium bond length. The crucial interaction that prevents shorter bonds is not the loss of attractive interactions, but a sharp increase in the Pauli repulsion between electrons in valence orbitals. The attractive interactions of DeltaE(orb) and the repulsive interactions of DeltaE(Pauli) are both determined by the orbital overlap. The net effect of the two terms depends on the occupation of the valence orbitals, but the onset of attractive orbital interactions occurs at longer distances than Pauli repulsion, because overlap of occupied orbitals with vacant orbitals starts earlier than overlap between occupied orbitals. The contribution of DeltaE(elstat) in most nonpolar covalent bonds is strongly attractive. This comes from the deviation of quasiclassical electron-electron repulsion and nuclear-electron attraction from Coulomb's law for point charges. The actual strength of DeltaE(elstat) depends on the size and shape of the occupied valence orbitals. The attractive electrostatic contributions in the diatomic molecules Li(2)-F(2) come from the s and p(sigma) electrons, while the p(pi) electrons do not compensate for nuclear-nuclear repulsion. It is the interplay of the three terms DeltaE(orb), DeltaE(Pauli), and DeltaE(elstat) that determines the bond energies and equilibrium distances of covalently bonded molecules. Molecules like N(2) and O(2), which are usually considered as covalently bonded, would not be bonded without the quasiclassical attraction DeltaE(elstat).     

Spectroscopy and bonding in side-on and end-on Cu2(S2) cores: comparison to peroxide analogues

Spectroscopic methods combined with density functional calculations were used to study the disulfide-Cu(II) bonding interactions in the side-on micro -eta(2):eta(2)-bridged Cu(2)(S(2)) complex, [[Cu(II)[HB(3,5-Pr(i)(2)pz)(3)]](2)(S(2))], and the end-on trans- micro -1,2-bridged Cu(2)(S(2)) complex, [[Cu(II)(TMPA)](2)(S(2))](2+), in correlation to their peroxide structural analogues. Resonance Raman shows weaker S-S bonds and stronger Cu-S bonds in the disulfide complexes relative to the O-O and Cu-O bonds in the peroxide analogues. The weaker S-S bonds come from the more limited interaction between the S 3p orbitals relative to that of the O 2s/p hybrid orbitals. The stronger Cu-S bonds result from the more covalent Cu-disulfide interactions relative to the Cu-peroxide interactions. This is consistent with the higher energy of the disulfide valence level relative to that of the peroxide. The ground states of the side-on Cu(2)(S(2))/Cu(2)(O(2)) complexes are more covalent than those of the end-on Cu(2)(S(2))/Cu(2)(O(2)) complexes. This derives from the larger sigma-donor interactions in the side-on micro -eta(2):eta(2) structure, which has four Cu-disulfide/peroxide bonds, relative to the end-on trans- micro -1,2 structure, which forms two bonds to the Cu. The larger disulfide/peroxide sigma-donor interactions in the side-on complexes are reflected in their more intense higher energy disulfide/peroxide to Cu charge transfer transitions in the absorption spectra. The large ground-state covalencies of the side-on complexes result in significant nuclear distortions in the ligand-to-metal charge transfer excited states, which give rise to the strong resonance Raman enhancements of the metal-ligand and intraligand vibrations. Particularly, the large covalency of the Cu-disulfide interaction in the side-on Cu(2)(S(2)) complex leads to a different rR enhancement profile, relative to the peroxide analogues, reflecting a S-S bond distortion in the opposite directions in the disulfide/peroxide pi(sigma) to Cu charge transfer excited states. A ligand sigma back-bonding interaction exists only in the side-on complexes, and there is more sigma mixing in the side-on Cu(2)(S(2)) complex than in the side-on Cu(2)(O(2)) complex. This sigma back-bonding is shown to significantly weaken the S-S/O-O bond relative to that of the analogous end-on complex, leading to the low nu(S)(-)(S)/nu(O)(-)(O) vibrational frequencies observed in the resonance Raman spectra of the side-on complexes.     

Quantum chemical investigations and bonding analysis of iron complexes with mixed cyano and carbonyl ligands

The equilibrium structures and vibrational frequencies of the iron complexes [Fe(CN)(x)(CO)(y)](q) (x = 0-6 and y = 0-5) have been calculated at the BP86 level of theory. The nature of the Fe-CN and Fe-CO has been analyzed with an energy partitioning method. The calculated Fe-CO bond lengths are in good agreement with the results of X-ray structure analysis whereas the Fe-CN bonds are calculated somewhat longer than the experimental values. The theoretically predicted vibrational frequencies of the C-O stretching mode are always lower and the calculated CN(-) frequencies are higher than the observed fundamental modes. The results of the bonding analysis suggest that the Fe-CO binding interactions have approximately 55% electrostatic character and approximately 45% covalent character. There is a significant contribution of the pi orbital interaction to the Fe-CO covalent bonding which increases when the complexes become negatively charged. The strength of deltaE(pi) may even be larger than deltaE(sigma). The Fe-CN(-) bonds have much less pi character. The calculated binding energy of the Fe-CO pi-interactions correlates very well with the C-O stretching frequencies.     

Sigma bond activation by cooperative interaction with s2 atoms: B+ + nCH4, n = 1, 2

Ab initio investigations at the MP2 and CCSD(T) level with augmented double and triple zeta basis sets have identified various stationary points on the B+/nCH4, n = 1, 2 hypersurfaces. The electrostatic complexes show a strong variation in the sequential binding energy with De for the loss of one CH4 molecule calculated to be 16.5 and 6.8 kcal mol-1 for the n = 1 and n = 2 complexes, respectively. The covalent molecular ion, CH3BH+, is found to have the expected C3 nu geometry and to be strongly bound by 84.0 kcal mol-1 with respect to B+ + CH4. The interaction of CH4 with CH3BH+ is qualitatively very similar to the interaction of CH4 with HBH+, however, the binding is only about 50% as strong due to the electron donating characteristic of the methyl group. Of particular interest are the insertion transition states which adopt geometries allowing the B+ ion to interact with multiple sigma bonds. In the n = 1 case, the interaction with two CH bonds lowers the insertion activation energy by about 25 kcal mol-1 from that expected for a mechanism involving only one sigma bond. For n = 2, B+ interacts with two CH sigma bonds from one CH4 and one CH sigma bond from the other CH4 leading to an additional activation energy decrease of about 15.7 kcal mol-1 relative to B+ + nCH4.     

Spectroscopic and DFT investigation of [M{HB(3,5-iPr2pz)3}(SC6F5)] (M = Mn, Fe, Co, Ni, Cu, and Zn) model complexes: periodic trends in metal-thiolate bonding

A series of metal-varied [ML(SC6F5)] model complexes (where L = hydrotris(3,5-diisopropyl-1-pyrazolyl)borate and M = Mn, Fe, Co, Ni, Cu, and Zn) related to blue copper proteins has been studied by a combination of absorption, MCD, resonance Raman, and S K-edge X-ray absorption spectroscopies. Density functional calculations have been used to characterize these complexes and calculate their spectra. The observed variations in geometry, spectra, and bond energies are interpreted in terms of changes in the nature of metal-ligand bonding interactions. The metal 3d-ligand orbital interaction, which contributes to covalent bonding in these complexes, becomes stronger going from Mn(II) to Co(II) (the sigma contribution) and to Cu(II) (the pi contribution). This change in the covalency results from the increased effective nuclear charge of the metal atom in going from Mn(II) to Zn(II) and the change in the 3d orbital populations (d5-->d10). Ionic bonding also plays an important role in determining the overall strength of the ML(+)-SC6F5(-) interaction. However, there is a compensating effect: as the covalent contribution to the metal-ligand bonding increases, the ionic contribution decreases. These results provide insight into the Irving-Williams series, where it is found that the bonding of the ligand being replaced by the thiolate makes a major contribution to the observed order of the stability constants over the series of metal ions.     

An explanation of the unusual strength of the hydrogen bond in small water clusters

We seek to explain why the hydrogen bond possesses unusual strength in small water clusters that account for many of the complex behaviors of water. We have investigated and visualized the donation of covalent character from covalent (sigma) to hydrogen bonds by calculating the eigenvector coupling properties of quantum theory of atoms in molecules (QTAIM), stress tensor σ ( r ), and Ehrenfest Force F ( r ) on the F ( r ) molecular graph. The next-generation three-dimensional (3-D) bond-path framework sets are presented, and only the F ( r ) bond-path framework sets reproduce the earlier finding on the coupling between covalent (sigma) and hydrogen bonds that possess a degree of covalent character. Exploration of the bond-path between the covalent (sigma) and hydrogen bond's critical points provides an explanation for the previously obtained coupling results. The directional character of the covalent (sigma) and hydrogen bonds' 3-D bond-path framework sets for the F ( r ) explains differences found in the earlier results from QTAIM and the stress tensor σ ( r ).     

Characterizing the properties of the N7,N9-dimethylguaninium chloride ion pairs: prospecting for the design of a novel ionic liquid

The structures, infrared spectra, and electronic properties of the N7,N9-dimethylguaninium chloride have been studied. The interaction of one cation with one to four Cl anions and one Cl anion with two cations were investigated. Fifteen stable conformers are obtained. It is found that there are four acidic regions in the vicinity of the guaninium cations. In these regions, the cation could H-bond with one to three Cl anions but no more than three nearest anions. One Cl anion could H-bond with two cations. Additionally, evidence of a Cl...pi interaction between the anion and cation is observed. Among these structures, one cation interaction with two anions and two cations interaction with one anion have the larger interaction energies than the other series. Natural bond orbital analyses and molecular orbitals reveal that the charge transfer from anion(s) to the cation(s) occurs mainly through either the Cllp --> sigma C-H, Cllp --> sigma N-H, or Cllp --> pi C8-N7 interactions. The interaction between Cl and sigma (C/N-H) or pi C-N produces a small bond order. This indicates that the Cl...H (Cl...pi) interaction exhibits a weak covalent character and suggests a strong ionic H-bond (Cl...pi bond). What's more, formation of Cl...H/Cl...pi bond decreases the bond order of the associated C/N-H bond or C8-N7 bond. In addition, examination of vibrational spectrum of each conformer explains the origin of H-bonding character.     

Energy analysis of metal-ligand bonding in transition metal complexes with terminal group-13 diyl ligands (CO)(4)Fe-ER, Fe(EMe)(5) and Ni(EMe)(4) (E = B-Tl; R = Cp, N(SiH(3))(2), Ph, Me) reveals significant pi bonding in homoleptical molecules.

The metal-ligand bonds of the title compounds have been investigated with the help of an energy partitioning analysis at the DFT level. It was found that the attractive orbital interactions between Fe and ER in (CO)(4)Fe-ER arise mainly from Fe <-- ER sigma donation. Only the boron diyl complexes (CO)(4)Fe-BR have significant contributions by Fe --> ER pi back-donation, but the Fe <-- BR sigma-donation remains the dominant orbital interaction term. The relative contributions of Fe-ER sigma donation and pi back-donation are only slightly altered when R changes from a good pi donor to a poor pi donor. Electrostatic forces between the metal fragment and the diyl ligand are always attractive, and they are very strong. They arise from the attraction between the local negative charge concentration at the overall positively charged donor atom E of the Lewis base ER and the positive charge of the iron nucleus. Electrostatic interactions and covalent interactions in (CO)(4)Fe-ER complexes have a similar strength when E is Al--Tl and when R is a good pi donor substituent. The Fe-BR bonds of the boron carbonyldiyl complexes have a significantly higher ionic character than the heavier group-13 analogues. Weak pi donor substituents R enhance the ionic character of the (CO)(4)Fe-ER bond. The metal-ligand bonds in the homoleptic complexes Fe(EMe)(5) and Ni(EMe)(4) have a higher ionic character than in (CO)(4)Fe-ER. The contribution of the TM --> ER pi back-donation to the Delta E(orb) term becomes clearly higher and contributes significantly to the total orbital interactions in the homoleptic complexes where no other pi acceptor ligands are present. The ligand BMe is nearly as strong a pi acceptor in Fe(BMe)(5) as CO is in Fe(CO)(5).     

Intermolecular covalent pi-pi bonding interaction indicated by bond distances, energy bands, and magnetism in biphenalenyl biradicaloid molecular crystal

Density-functional theory (DFT) calculations were performed for energy band structure and geometry optimizations on the stepped pi-chain, the isolated molecule and (di)cations of the chain, and various related molecules of a neutral biphenalenyl biradicaloid (BPBR) organic semiconductor 2. The dependence of the geometries on crystal packing provides indirect evidence for the intermolecular covalent pi-pi bonding interaction through space between neighboring pi-stacked phenalenyl units along the chain. The two phenalenyl electrons on each molecule, occupying the singly occupied molecular orbitals (SOMOs), are participating in the intermolecular covalent pi-pi bonding making them partially localized on the phenalenyl units and less available for intramolecular delocalization. The band structure shows a relatively large bandwidth and small band gap indicative of good pi-pi overlap and delocalization between neighboring pi-stacked phenalenyl units. A new interpretation is presented for the magnetism of the stepped pi-chain of 2 using an alternating Heisenberg chain model, which is consistent with DFT total energy calculations for 2 and prevails against the previous interpretation using a Bleaney-Bowers dimer model. The obtained transfer integrals and the magnetic exchange parameters fit well into the framework of a Hubbard model. All presented analyses on molecular geometries, energy bands, and magnetism provide a coherent picture for 2 pointing toward an alternating chain with significant intermolecular through-space covalent pi-pi bonding interactions in the molecular crystal. Surprisingly, both the intermolecular transfer integrals and exchange parameters are larger than the intramolecular through-bond values indicating the effectiveness of the intermolecular overlap of the phenalenyl SOMO electrons.     

Carbonyl analogues? Analysis of Fe-E (E=B, Al, Ga) bonding in cationic terminal diyl complexes by density functional theory

A series of DFT calculations has been carried out with the aim of characterizing the metal-group 13 element interaction in the novel cationic borylene complex [(eta5-C2Me5)Fe(CO)2(BMes)]+ (1) and related species of the type [eta5-C5R5)M(L)2(EX)]n+. In addition, comparisons have been made with charge neutral borylene complexes and with related group 14 based ligand systems (e.g. cationic metal carbonyls, carbenes and vinylidenes) for which models of bonding have previously been established. In this regard particular attention has been focused on the interpretation of (i) molecular orbital composition; (ii) bond dissociation energies (BDEs) and the ratio of ionic to covalent contributions (DeltaEelstat/DeltaEorb); and (iii) sigma and pi symmetry covalent contributions. The molecular orbital compositions for the prototype borylene complex 1 and for related cationic and neutral systems [e.g.[(eta5-C5H5)Fe(PMe3)2(BMes)]+ and (eta5-C5H5)Mn(CO2(BMes)]] are consistent with the presence of bonding interactions between metal and borylene fragments of both sigma and pi symmetry. Furthermore, on the basis of BDEs, DeltaEorb values and sigma/pi covalent ratios, the bonding in cationic terminal borylene complexes such as 1 appears to have as much right to be termed a M=E double bond as does that in archetypal Fischer carbene and related complexes such as [(eta5-C5R5)Fe(CO)2(CCMe2)]+ and [(eta5-C5R5)Fe(CO)2(CH2)]+.     

Solution phase measurement of both weak sigma and C-H...X- hydrogen bonding interactions in synthetic anion receptors

A series of tripodal receptors preorganize electron-deficient aromatic rings to bind halides in organic solvents using weak sigma anion-to-arene interactions or C-H...X- hydrogen bonds. 1H NMR spectroscopy proves to be a powerful technique for quantifying binding in solution and determining the interaction motifs, even in cases of weak binding.     

Radical hydrogen bonding: origin of stability of radical-molecule complexes

Natural bond orbital analysis is used to investigate the nature of hydrogen bonding in a series of binary open-shell complexes involving hydroperoxy radical HO(2)...X and analogous closed-shell H(2)O(2)...X complexes (where X = H(2)O, H(2)O(2), HONO, HONO(2), CH(3)OH, HCOOH, CH(3)COOH, and H(2)SO(4)) in order to elucidate and identify the electronic factors responsible for the strength of radical hydrogen bonds. Results from this study suggest that the radical species strongly alters the strength of the characteristic n --> sigma(*) donor-acceptor interaction in the hydrogen bonding. This interaction is found to contribute to the unusually strong binding in radical-molecule complexes. These findings have important new ramifications for our fundamental understanding of radical hydrogen bonds.     

Hydrogen bonding in methanol clusters probed by inner-shell photoabsorption spectroscopy in the carbon and oxygen K-edge regions

Hydrogen bonding in methanol clusters has been investigated by using inner-shell photoabsorption spectroscopy and density functional theory (DFT) calculations in the carbon and oxygen K-edge regions. The partial-ion-yield (PIY) curves of H(CH(3)OH)(n)(+) were measured as the soft x-ray absorption spectra of methanol clusters. The first resonance peak in the PIY curves, which is assigned to the sigma*(O-H) resonance transition, exhibits a 1.20 eV blueshift relative to the total-ion-yield (TIY) curves of molecular methanol in the oxygen K-edge region, while it exhibits a shift of only 0.25 eV in the carbon K-edge region. Decreased intensities of the transitions to higher Rydberg orbitals were observed in the PIY curves of the clusters. The drastic change in the sigma*(O-H) resonance transition is interpreted by the change in the character of the sigma*(O-H) molecular orbital at the H-donating OH site due to the hydrogen-bonding interaction.     

Chemical bonding in view of electron charge density and kinetic energy density descriptors

Stalke's dilemma, stating that different chemical interpretations are obtained when one and the same density is interpreted either by means of natural bond orbital (NBO) and subsequent natural resonance theory (NRT) application or by the quantum theory of atoms in molecules (QTAIM), is reinvestigated. It is shown that within the framework of QTAIM, the question as to whether for a given molecule two atoms are bonded or not is only meaningful in the context of a well‐defined reference geometry. The localized‐orbital‐locator (LOL) is applied to map out patterns in covalent bonding interaction, and produces results that are consistent for a variety of reference geometries. Furthermore, LOL interpretations are in accord with NBO/NRT, and assist in an interpretation in terms of covalent bonding. © 2008 Wiley Periodicals, Inc.J Comput Chem, 2009.     

Crystal packing of TCNQ anion pi-radicals governed by intermolecular covalent pi-pi bonding: DFT calculations and statistical analysis of crystal structures

On the basis of a thorough Cambridge Structural Database survey, we present a statistical analysis of the packing of TCNQ anion pi-radicals in TCNQ charge transfer salts, which reveals three packing motifs between neighboring TCNQs: one with a zero longitudinal offset and an approximate 1 A transversal offset, another with an approximate 2 A longitudinal offset and zero transversal offset, and the third with a relatively long sigma-bond in the length of r = 1.6-1.7 A connecting two TCNQ fragments. Along with the statistical analysis of the crystal structures, we also present density functional theory calculations of the total energy, covalent pi-pi bonding interaction energy, and Coulombic repulsion energy for the [TCNQ](2)(2-)pi-dimers with various packing geometries. We find that the interactions between TCNQ anion pi-radicals include contributions from intermolecular covalent pi-pi bonding interaction and local dipole repulsions, in addition to Coulombic repulsion, van der Waals and the attractive electrostatic forces between counter-cations and TCNQ anions pointed out recently by other groups for TCNE anion radicals. We describe an approximate formula for intermolecular interaction energy, E(int) = E(coul) + E(bond) + E(vdW), for systems in vacuum, while in the solid state E(coul) is compensated by the attractive electrostatic forces between counter-cations and TCNQ anions. We conclude that the crystal packing of TCNQ molecules in their charge transfer salts is predominantly determined by the intermolecular covalent pi-pi bonding term, E(bond).     

Chemical bonding in refractory transition metal compounds with 8, 9, and 10 valence electrons

The chemical bonding in the refractory transition metal compounds TiC, TiN, and VN is investigated by experimental and theoretical techniques. High-precision X-ray diffraction is used to determine the electron densities in these three compounds experimentally. The X-ray structure factors and the respective valence electron densities are used twice, once to understand the chemical bonding and once to relate the experimental charge densities to those obtained from band structure calculations. These calculations, which in general are in very good agreement with experimental data, utilize the linearized augmented plane wave (LAPW) method. Theory and experiment lead to a detailed analysis of the chemical bonding in these compounds with 8, 9, and 10 valence electrons. By decomposition of the theoretical charge density into contributions from different states (energy regions), it was possible to show the strong covalent nonmetal p-metal d interaction, which is otherwise apparent only in TiC, but not in TiN or VN. In the latter two compounds the additional electrons occupy mainly metal d states with t_2g symmetry, so that in the total valence charge densities the most important bonding feature is covered. In addition to covalent interactions all compounds have a metallic bonding contribution as well as a considerable charge transfer from the metal to the nonmetal site. This mixture in chemical bonding accounts for the unusual combination of properties such as ultrahardness, high melting points, and good conductivity.     

Pentacoordinate 1H-phosphirenes: reactivity, bonding properties, and substituent effects on their structures and thermal stability

The synthesis, reactivity, and bonding properties of several pentacoordinate P-phenyl-substituted 1H-phosphirenes are discussed. X-ray crystallographic analysis of one of them reveals a highly distorted square pyramidal (SP) arrangement around the phosphorus. NMR studies confirm that they retain the SP structure in solution and demonstrate that the endocyclic P-C bonds in the three-membered ring have a very high degree of p character, which results from their being both basal bonds in the SP structure and endocyclic bonds of the three-membered ring. Structural parameters of the three-membered ring of the pentacoordinate phosphirenes obtained by experiment and theoretical calculations are very close to those of a tetracoordinate phosphirenium cation. Thus, by analogy with tetracoordinate phosphirenium cations, it can be considered that a sigma-pi interaction between the sigma orbital of the apical bond and the pi orbital of the C=C bond in the three-membered ring is operative in pentacoordinate phosphirenes. The sigma-pi interaction is found to lower the reactivity of the C=C bond of the three-membered ring. The reactivities of the pentacoordinate phosphirenes are also affected by the substituent on the carbon atom in the three-membered ring.     

Distinguishing the early and late transition states and exploring the validity of sigma --> sigma*#, sigma# --> sigma*, and sigma --> pi*(C=O) concepts in diastereoselection from NBO analysis

Natural bond orbital (NBO) analysis of several early TSs does not support the sigma --> sigma*# hypothesis. The sigma --> pi*(C=O) interaction controls the carbonyl pyramidalization that, in turn, controls the pi-selectivity of a nucleophilic addition. In contrast, late TSs are devoid of sigma --> pi*(C=O) interactions, and they benefit from sigma --> sigma*# interactions that control pi-selectivity. The evidence in favor of Anh-Felkin's sigma# --> sigma* hypothesis is weak. The electron-withdrawing sigma(C-F) in the 2-fluoropropanal-LiCN TS did not align anti to the incipient bond even though there was complete conformational freedom. The initial guess for the TS in which sigma(C-F) was held anti to sigma# optimized to what had lost the said geometrical relationship. Furthermore, in the TS for axial addition of LiCN to 2-ax-F-cyclohexanone, the net sigma --> sigma*# interaction was considerably larger than the net sigma# --> sigma* interaction. The relative TS energies require that the equatorial addition of LiCN to 2-ax-F-cyclohexanone be favored over the axial addition in good compliance with the available experimental results.