Halogen Bonding with Phosphine: Evidence for Mulliken Inner Complexes and the Importance of Relaxation Energy

Types of noncovalent bonds within complexes of thiazole with CF4 and SiF4

The five-membered heteroaromatic thiazole molecule contains a number of electron-rich regions that could attract an electrophile, namely the N and S lone pairs that lie in the molecular plane, and π-system areas above the plane. The possibility of each of these sites engaging in a tetrel bond (TB) with CF4 and SiF4, as well as geometries that encompass a CH⋯F H-bond, was explored via DFT calculations. There are a number of minima that occur in the pairing of thiazole with CF4 that are very close in energy, but these complexes are weakly bound by less than 2 kcal mol-1 and the presence of a true TB is questionable. The inclusion of zero-point vibrational energies alters the energetic ordering, which is further modified when entropic effects are added. The preferred geometry would thus be sensitive to the temperature of an experiment. Replacement of CF4 by SiF4 leaves intact most of the configurations, and their tight energetic clustering, the ordering of which is again altered as the temperature rises. But there is one exception in that by far the most tightly bound complex involves a strong Si⋯N TB between SiF4 and the lone pair of the thiazole N, with an interaction energy of 30 kcal mol-1. Even accounting for its high deformation energy and entropic considerations, this structure remains as clearly the most stable at any temperature.

Quasi-atomic orbital analysis of halogen bonding interactions

A quasi-atomic orbital analysis of the halogen bonded NH3⋯XF complexes (X = F, Cl, Br, and I) is performed to gain insight into the electronic properties associated with these σ-hole interactions. It is shown that significant sharing of electrons between the nitrogen lone pair of the ammonia molecule and the XF molecule occurs, resulting in a weakening of the X-F bond. In addition, the N-X bond shows increasing covalent character as the size of the halogen atom X increases. While the Mulliken outer complex NH3⋯XF appears to be overall the main species, the strength of the covalent interaction of the N-X bond becomes increasingly similar to that of the N-X bond in the [NH3X]+ cation as the size of X increases.

Radial Potential Energy Functions of Linear Halogen-Bonded Complexes YX···ClF (YX = FB, OC, SC, N2) and the Effects of Substituting X by Second-Row Analogues: Mulliken Inner and Outer Complexes

Energies of linear, halogen-bonded complexes in the isoelectronic series YX···ClF (YX = FB, OC, or N₂) are calculated at several levels of theory as a function of the intermolecular distance r(X···Cl) to yield radial potential energy functions. When YX = OC, a secondary minimum is observed corresponding to lengthened and shortened distances r(ClF) and r(CCl), respectively, relative to the primary minimum, suggesting a significant contribution from the Mulliken inner complex structure [O=C–Cl]⁺···F^–. A conventional weak, halogen-bond complex OC···ClF occurs at the primary minimum. For YX = FB, the primary minimum corresponds to the inner complex [F=B–Cl]⁺···F^–, while the outer complex FB···ClF is at the secondary minimum. The effects on the potential energy function of systematic substitution of Y and X by second-row congeners and of reversing the order of X and Y are also investigated. Symmetry-adapted perturbation theory and natural population analyses are applied to further understand the nature of the various halogen-bond interactions.

A reduced electrophilicity for simple Lewis acids A involved in non-covalent interactions with Lewis bases B

Dissociation energies De for B⋯A = B +A can be written De = c′NBEA, where NB and EA are the nucleophilicities and electrophilicities of the Lewis base B and the Lewis acid A, respectively.

An Assessment of Radial Potential Functions for the Halogen Bond: Pseudo-Diatomic Models for Axially Symmetric Complexes B⋅⋅⋅ClF (B=N2 , CO, PH3 , HCN, and NH3 )

The radial potential energy is calculated ab initio at the explicitly correlated level of theory CCSD(T)(F12c)/cc-pVTZ-F12 for the five axially symmetric, halogen-bonded complexes B⋅⋅⋅ClF (B=N₂ , CO, PH₃ , HCN, and NH₃ ) as a function of the intermolecular distance r. The PE curves are fitted by the Hulburt-Hirschfelder analytical function under the assumption of a pseudo-diatomic model. The spectroscopic constants ω σ and ω σ x σ , and α σ of the intermolecular stretching mode υ σ are calculated by two closely related approaches. The first involves derivatives of a polynomial fitted to the ab initio calculated points near to r_e and evaluated at r=r_e . The second uses the constants of the fitted H-H function. Both procedures are tested on ³⁵ ClF by fitting (a) its RKR-type function and (b) the CCSD(T)(F12c)/cc-pVTZ-F12 version. The complexes OC⋅⋅⋅ClF and H₃ P⋅⋅⋅ClF behave differently from the other three. A point of inflection/secondary minimum with a shortened r(C⋅⋅⋅Cl) and an increased r(Cl-F) detected for B=CO, suggests a second isomer with a significant contribution from the valence-bond structure OC⁺ Cl⋅⋅⋅F^- . The shape of the ab initio calculated function for H₃ P⋅⋅⋅ClF is different from those involving B=N₂ , HCN, or NH₃ , a difference attributed to H₃ PCl⁺ ⋅⋅⋅F^- character. The ab initio generated curve for H₃ P⋅⋅⋅ClF is, nevertheless, satisfactorily fitted by the three-parameter H-H function.

The Electrophilicities of XCF3 and XCl (X=H, Cl, Br, I) and the Propensity of These Molecules To Form Hydrogen and Halogen Bonds with Lewis Bases: An Ab Initio Study

Equilibrium dissociation energies, De , of four series of halogen- and hydrogen-bonded complexes B⋅⋅⋅XCF3 (X=H, Cl, Br and I) are calculated ab initio at the CCSD(T)(F12c)/cc-pVDZ-F12 level. The Lewis bases B involved are N2 , CO, PH3 , C2 H2 , C2 H4 , H2 S, HCN, H2 O and NH3 . Plots of De versus NB , where the NB are the nucleophilicities assigned to the Lewis bases previously, are good straight lines through the origin, as are those for the corresponding set of complexes B⋅⋅⋅XCl. The gradients of the De versus NB plots define the electrophilicities EXCF3 and EXCl of the various Lewis acids. The determined values are: EXCF3 =2.58(22), 1.40(9), 2.15(2) and 3.04(9) for X=H, Cl, Br and I, respectively, and EXCl =4.48(22), 2.31(9), 4.37(27) and 6.06(37) for the same order of X. Thus, it is found that, for a given X, the ratio EXCl / EXCF3 is 2 within the assessed errors, and therefore appears to be independent of the atom X and of the type of non-covalent interaction (hydrogen bond or different varieties of halogen bond) in which it is involved. Consideration of the molecular electrostatic surface potentials shows that De and the maximum positive electrostatic potential σmax (the most electrophilic region of XCF3 and XCl, which lies on the symmetry axes of these molecules, near to the atom X) are strongly correlated.

Polycentric binding in complexes of trimethylamine-N-oxide with dihalogens

Dihalogens readily interact with trimethylamine-N-oxide under ambient conditions. Accordingly, herein, stable 1 : 1 adducts were obtained in the case of iodine chloride and iodine bromide. The crystal and molecular structure of the trimethylamine-N-oxide-iodine chloride adduct was solved. Furthermore, the geometry and electronic structure of the trimethylamine-N-oxide-dihalogen complexes were studied computationally. Only molecular ensembles were found in the global minimum for the 1 : 1 stoichiometry. The O⋯X-Y halogen bond is the main factor for the thermodynamic stability of these complexes. Arguments for electrostatic interactions as the driving force for this noncovalent interaction were discussed. Also, the equilibrium structures are additionally stabilised by weak C-H⋯X hydrogen bonds. Consequently, formally monodentate ligands are bound in a polycentric manner.

Hydrogen vs. Halogen Bonds in 1-Halo-Closo-Carboranes

A theoretical study of the hydrogen bond (HB) and halogen bond (XB) complexes between 1-halo-closo-carboranes and hydrogen cyanide (NCH) as HB and XB probe has been carried out at the MP2 computational level. The energy results show that the HB complexes are more stable than the XBs for the same system, with the exception of the isoenergetic iodine derivatives. The analysis of the electron density with the quantum theory of atoms in molecules (QTAIM) shows the presence of a unique intermolecular bond critical point with the typical features of weak noncovalent interactions (small values of the electron density and positive Laplacian and total energy density). The natural energy decomposition analysis (NEDA) of the complexes shows that the HB and XB complexes are dominated by the charge-transfer and polarization terms, respectively. The work has been complemented with a search in the CSD database of analogous complexes and the comparison of the results, with those of the 1-halobenzene:NCH complexes showing smaller binding energies and larger intermolecular distances as compared to the 1-halo-closo-carboranes:NCH complexes.

Relativistic Effects on NMR Parameters of Halogen-Bonded Complexes

Relativistic effects are found to be important for the estimation of NMR parameters in halogen-bonded complexes, mainly when they involve the heavier elements, iodine and astatine. A detailed study of 60 binary complexes formed between dihalogen molecules (XY with X, Y = F, Cl, Br, I and At) and four Lewis bases (NH₃, H₂O, PH₃ and SH₂) was carried out at the MP2/aug-cc-pVTZ/aug-cc-pVTZ-PP computational level to show the extent of these effects. The NMR parameters (shielding and nuclear quadrupolar coupling constants) were computed using the relativistic Hamiltonian ZORA and compared to the values obtained with a non-relativistic Hamiltonian. The results show a mixture of the importance of the relativistic corrections as both the size of the halogen atom and the proximity of this atom to the basic site of the Lewis base increase.

A Linear-Scaling Method for Noncovalent Interactions: An Efficient Combination of Absolutely Localized Molecular Orbitals and a Local Random Phase Approximation Approach

A novel method for the accurate and efficient calculation of interaction energies in weakly bound complexes composed of a large number of molecules is presented. The new ALMO+RPAd method circumvents the prohibitive scaling of coupled cluster singles and doubles while still providing similar accuracy across a diverse range of weakly bound chemical systems. Linear-scaling procedures for the Fock build are given utilizing absolutely localized molecular orbitals (ALMOs), resulting in the a priori exclusion of basis set superposition errors. A bespoke data structure and algorithm using density fitting are described, leading to linear scaling for the storage and computation of the two-electron integrals. Electron correlation is included through a new, linear-scaling pairwise local random phase approximation approach, including exchange interactions, and decomposed into purely dispersive excitations (RPAxd). Collectively, these allow meaningful decomposition of the interaction energy into physically distinct contributions: electrostatic, polarization, charge transfer, and dispersion. Comparison with symmetry-adapted perturbation theory shows good qualitative agreement. Tests on various dimers and the S66 benchmark set demonstrate results within 0.5 kcal mol^-1 of coupled cluster singles and doubles results. On a large cluster of water molecules, we achieve calculations involving over 3500 orbital and 12,000 auxiliary basis functions in under 10 min on a single CPU core.

Systematic behaviour of electron redistribution on formation of halogen-bonded complexes BXY, as determined via XY halogen nuclear quadrupole coupling constants

Equilibrium nuclear quadrupole coupling constants associated with the di-halogen molecule XY in each of 60 complexes BXY (where B is one of the Lewis bases N₂, CO, HCN, H₂O, H₂S, HCCH, C₂H₄, PH₃, NH₃ or (CH₃)₃N and XY is one of the di-halogens Cl₂, BrCl, Br₂, ICl, IBr or I₂) have been calculated ab initio. The Townes-Dailey model for interpreting the changes in the coupling constants when XY enters the complex was used to describe the electron redistribution in the di-halogen molecule in terms of the fraction δ_i of an electron transferred from the Lewis base B to atom X and the fraction δ_p of an electron transferred simultaneously from atom X to atom Y. Systematic relationships between the δ_i values for the six series are established. It is shown that, in reasonable approximation, δ_i decays exponentially as the first ionisation energy I_B of the Lewis base B increases, that is δ_i = A exp(-bI_B). It is concluded from the results for the series BBrCl, BBr₂, BICl, BIBr and BI₂ that the coefficients A and b in regression fits to the corresponding logarithmic version ln(δ_i) = ln(A) -b(I_B) of the equation are not strongly dependent on either the halogen atom X directly involved in the halogen bond in BXY or, for a given X, on the nature of Y. The behaviour of PH₃ as a Lewis base appears to be anomalous. Values of δ_i and δ_p calculated by the quantum theory of atoms-in-molecules and natural bond orbital methodologies are very close to those from application of the Townes-Dailey approach described.

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

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

A Simple Model for Halogen Bond Interaction Energies

Halogen bonds are prevalent in many areas of chemistry, physics, and biology. We present a statistical model for the interaction energies of halogen-bonded systems at equilibrium based on high-accuracy ab initio benchmark calculations for a range of complexes. Remarkably, the resulting model requires only two fitted parameters, X and B—one for each molecule—and optionally the equilibrium separation, R e , between them, taking the simple form E = X B / R e n . For n = 4 , it gives negligible root-mean-squared deviations of 0.14 and 0.28 kcal mol - 1 over separate fitting and validation data sets of 60 and 74 systems, respectively. The simple model is shown to outperform some of the best density functionals for non-covalent interactions, once parameters are available, at essentially zero computational cost. Additionally, we demonstrate how it can be transferred to completely new, much larger complexes and still achieve accuracy within 0.5 kcal mol - 1 . Using a principal component analysis and symmetry-adapted perturbation theory, we further show how the model can be used to predict the physical nature of a halogen bond, providing an efficient way to gain insight into the behavior of halogen-bonded systems. This means that the model can be used to highlight cases where induction or dispersion significantly affect the underlying nature of the interaction.

A theoretical investigation on Cu/Ag/Au bonding in XH2P⋯MY(X = H, CH3, F, CN, NO2; M = Cu, Ag, Au; Y = F, Cl, Br, I) complexes

Intermolecular interaction of XH₂P···MY (X = H, CH₃, F, CN, NO₂; M = Cu, Ag, Au; Y = F, Cl, Br, I) complexes was investigated by means of an ab initio method. The molecular interaction energies are in the order Ag < Cu < Au and increased with the decrease of R_P···M. Interaction energies are strengthened when electron-donating substituents X connected to XH₂P, while electron-withdrawing substituents produce the opposite effect. The strongest P···M bond was found in CH₃H₂P···AuF with -70.95 kcal/mol, while the weakest one was found in NO₂H₂P···AgI with -20.45 kcal/mol. The three-center/four-electron (3c/4e) resonance-type of P:-M-:Y hyperbond was recognized by the natural resonance theory and the natural bond orbital analysis. The competition of P:M-Y ↔ P-M:Y resonance structures mainly arises from hyperconjugation interactions; the bond order of b_P-M and b_M-Y is in line with the conservation of the idealized relationship b_P-M + b_M-Y ≈ 1. In all MF-containing complexes, P-M:F resonance accounted for a larger proportion which leads to the covalent characters for partial ionicity of MF. The interaction energies of these Cu/Ag/Au complexes are basically above the characteristic values of the halogen-bond complexes and close to the observed strong hydrogen bonds in ionic hydrogen-bonded species.

A Computational Study of Chalcogen-containing H2 X…YF and (CH3 )2 X…YF (X=O, S, Se; Y=F, Cl, H) and Pnicogen-containing H3 X'…YF and (CH3 )3 X'…YF (X'=N, P, As) Complexes

A computational study was undertaken for the model complexes H₂ X…YF and (CH₃ )₂ X…YF (X=O, S, Se; Y=F, Cl, H), and H₃ X'…YF and (CH₃ )₃ X'…YF (X'=N, P, As), at the MP2/6-311++G(d,p) level of theory. For H₂ X…YF and H₃ X'…YF, noncovalent interactions dominate the binding in order of increasing YF dipole moment, except for H₃ As…F₂ , and possibly H₃ As…ClF. However, for the methyl-substituted complexes (CH₃ )₂ X…YF and (CH₃ )₃ X'…YF the binding is especially strong for the complexes containing F₂ , implying significant chemical bonding between the interacting molecules. The relative stability of these complexes can be rationalized by the difference in the electronegativity of the X or X' and Y atoms.

Nucleophilicities of Lewis Bases B and Electrophilicities of Lewis Acids A Determined from the Dissociation Energies of Complexes B⋯A Involving Hydrogen Bonds, Tetrel Bonds, Pnictogen Bonds, Chalcogen Bonds and Halogen Bonds

It is shown that the dissociation energy D e for the process B⋯A = B + A for 250 complexes B⋯A composed of 11 Lewis bases B (N₂, CO, HC≡CH, CH₂=CH₂, C₃H₆, PH₃, H₂S, HCN, H₂O, H₂CO and NH₃) and 23 Lewis acids (HF, HCl, HBr, HC≡CH, HCN, H₂O, F₂, Cl₂, Br₂, ClF, BrCl, H₃SiF, H₃GeF, F₂CO, CO₂, N₂O, NO₂F, PH₂F, AsH₂F, SO₂, SeO₂, SF₂, and SeF₂) can be represented to good approximation by means of the equation D e = c ' N B E A , in which N B is a numerical nucleophilicity assigned to B, E A is a numerical electrophilicity assigned to A, and c ' is a constant, conveniently chosen to have the value 1.00 kJ mol-1 here. The 250 complexes were chosen to cover a wide range of non-covalent interaction types, namely: (1) the hydrogen bond; (2) the halogen bond; (3) the tetrel bond; (4) the pnictogen bond; and (5) the chalcogen bond. Since there is no evidence that one group of non-covalent interaction was fitted any better than the others, it appears the equation is equally valid for all the interactions considered and that the values of N B and E A so determined define properties of the individual molecules. The values of N B and E A can be used to predict the dissociation energies of a wide range of binary complexes B⋯A with reasonable accuracy.