Equilibrium constants of HF,F-, HF-2 and H2F2 species in formic acid.

Equilibrium constants for the fluorinated species HF, F^-, HF^-₂ and H₂F₂ in formic acid and in a 1M potassium formate solution in formic acid have been studied by ¹⁹F NMR. The chemical shifts of these species have been determined from measurements of the shifts for various initial mixtures of differing concentrations of dissolved HF, F^- and HF^-₂. From these values, relative concentrations of HF, F^-, and HF^-₂ and H₂F₂ in each solution have been calculated through a numerical method. The following constants were obtained: K₁ = [H⁺][F^-]/[HF] = 1.1 x 10^-5M; K_D = [HF][F^-]/[HF^-₂] = 0.5 M; K′₁ = [H⁺][HF^-₂]/[H₂F₂]= 1.1 x 10^-5 M; K′_D = [HF]²/[H₂F₂]=0.5 M.     

Raman spectra and structural features of ClOF2 + cation in a solution of anhydrous HF

The Raman spectra of ClOF₂ ⁺ cation in solutions of anhydrous HF were studied. In the ClOF₂ ⁺HF₂ ⁻ and ClOF₂ ⁺BF₄ ⁻−HF systems, this cation exists as a pyramidal structure (C _s symmetry), while in the ClOF₂ ⁺AuF₆ ⁻−HF system, it exists as a planar structure (C _2v symmetry). Based on nonempirical calculations by the Hartree-Fock-Roothaan method, an explanation for the dependence of the structure of the ClOF₂ ⁺ cation on the nature of the anion was proposed. For the Cl−O bond vibrations, the correlation functions of vibrational and rotational relaxations were calculated, and the characteristic times of these processes were determined. The main contribution to the formation of the band contours corresponding to the above-mentioned modes is made by the vibrational dephasing. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 432–437, March, 1998.     

Structure and stability of the HFF and FHF radicals

The structure and stability of the HFF and FHF isomers in their two lowest electronic states is studied by means of ab initio SCF and CI calculations employing a double-zeta basis plus various polarization functions. Both complexes can be essentially described by an HF dipole (exhibiting a standard HF bond length) attracting a fluorine atom, with an FF distance of 5.14 bohr calculated for the HF··F ground state and an H··F bond of 4.3 bohr for the most stable FHF species. The HF₂ radical is found to prefer a bent structure in its ²Σ⁺ - ²A' ground state with an extremely flat potential curve, while the first very low-lying excited state of HF₂ as well as both components of the ground (in this case ²Π) state of the FH··F complex are calculated to be linear. The symmetric FHF structure exhibits optimal bond lengths at approximately 2.1 bohr but is considerably less stable than the asymmetrical arrangement of nuclei. With respect to dissociation into HF + F the HF₂ form is found to be stable in both (²Σ⁺ - A') and ²Π states while the conformer FH··F shows a minimum only for the ²Π ground state; the exothermicity of the H + F₂ → HF + F reaction is calculated to be 104.6 kcal mol^?1 in good agreement with the experimental quantity of 102.5 ± 2.8 kcal mol^?1. Comparison with the negative ions HF₂^?and FHF^? is made whenever appropriate.     

Hartree-Fock energy curves for XΠ and Σ states of HF

Hartree-Fock energy curves have been calculated for the X²Π and ²Σ⁺ states of HF⁺ and applied to an analysis of the photoelectron spectra of HF. The ²Σ⁺ energy curve is found to have a barrier about 0.07 eV high due primarily to a repulsive ion-quadrupole interaction, and a depth of 0.37 eV. This curve will support two bound states and one shape resonance with a half-width of 0.015 eV. The energy curves are probably accurate to 0.1 eV but the analysis shows that results accurate to within 0.03 eV are required to resolve the experimental questions on the dissociation energy for the ground state of HF. The most recent experimental photoelectron results of Berkowitz (following article) encouraged a model calculation of the vibrational states of the ²Σ⁺ state. Assuming a dissociation energy of 0.45 eV and retaining the barrier three bound and one shape resonance vibrational levels are calculated for HF⁺ in agreement with the results reported by Berkowitz.     

A comparison of perfect pairing and molecular orbital methods for the calculation of molecular properties of HF and HF+

The perfect pairing and molecular orbital methods are compared using minimum bases of Slater-type orbitals for the calculation of properties of HF and two states of HF^*. A discussion is given of the calculations of bond lengths and of valence and core ionization potentials.     

A valence bond study of the oxygen molecule

Ab initio valence bond calculations are performed for the three lowest states of the oxygen molecule (³Σ⁻_g, ¹Δ_g, and ¹Σ⁺_g). One objective of the present study was to make a contribution to previous valence bond discussions about the oxygen “double” bond. Further, we study the origin of a small barrier in the potential energy surface of the ground state. Two compact models are employed to maintain the clear picture that can be offered by the valence bond method. The first model has only the Rumer structures that are essential for bonding and a proper dissociation. The second model, in addition, has structures which represent excited atoms. These prove to be important for the dissociation energies. For both models, the orbitals are fully optimized. The spectroscopic data obtained are significantly better than are the (few) valence bond results on O₂ that have been published and have the quality of multiconfiguration self-consistent field calculations in which the same valence space is used. The “hump” in the potential energy surface of the ground state is shown to arise from a spin recoupling. The free atoms correspond to a spin coupling that is incapable of describing the formation of bonds. Only at short distances, an alternative spin coupling provides bonding and the repulsive curve is converted into an attractive one. Our results on this subject support a valence bond explanation previously given by McWeeny [R. McWeeny, Int. J. Quantum Chem. Symp. 24 , 733 (1990)]. © 1996 John Wiley & Sons, Inc.     

Study of chemical bonding in H2 and HF molecules: Wave function and density functional theory (DFT) parameters approach

Balint Kurti's Fourier grid Hamiltonian method is employed to obtain the molecular wave function and equilibrium bond length for H₂ and HF molecules. The density functional theory parameter, namely, the chemical hardness (η) value, was determined for some diatomic hydride molecules using this wave function and the results are found to be in good agreement with the values obtained from the ab initio HF–SCF method. A new formula for chemical hardness (η=1/2Dr, where D is the proportionality constant and r is the internuclear distance) is introduced in binding energy and change of hardness equations to determine the chemical hardness and chemical potential values for different bond lengths. The binding energy and change of hardness values are calculated for H₂, H, H, HF, HF⁺, and HF⁻ molecules and the bond stability is discussed. Finally, the concept of an atom in a molecule is examined in the context of DFT parameters and comparison is made between an atom in a molecule and the isolated atom. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 662–669, 2000     

The electronic structure of weakly bound systems. II. NeX+ and ArX+(X = H2O,HCl, and HF) bimolecular cations

The theoretical framework developed and tested in our previous study of weakly bound systems is applied to a sequence of bimolecular cations: (NeX)⁺ and (ArX)⁺, where X = HF, H₂O, and HCl. The equilibrium structure, binding energies, and vibrational frequencies for this sequence of bimolecular cations are computed using several post-Hartree-Fock methods and triple zeta basis sets. In all cases, the absolute minima in the potential energy surface involves a hydrogen bond. The existence and stability of the aforementioned systems are established with binding energies ranging from 0.1 eV to 1.0 eV. The stability for the systems is explained in terms of the possible dissociative channels and changes in the electron density of the constituent monomers. © 1995 by John Wiley & Sons, Inc.     

HF and MP2 calculations on CN−, N2, AlF,SiO, PN,SC, ClB,and P2 using correlated molecular wave functions

Contracted basis sets of double zeta valence quality plus polarization functions (DZP) and augmented DZP basis sets, which were recently constructed for the first‐ and second‐row atoms, are applied to study the electronic ground states of the diatomic molecules CN^?, N₂, AlF, SiO, PN, SC, ClB, and P₂. At the Hartree–Fock (HF) and/or Møller–Plesset second‐order (MP2) levels, total and molecular orbital energies, dissociation energies, bond lengths, harmonic vibrational frequencies, and dipole moments are calculated and compared with available experimental data and with the results obtained from correlation consistent polarized valence basis sets of Dunning's group. For N₂, calculations of polarizabilities at the HF and MP2 levels with the sets presented above are also done and compared with results reported in the literature. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Theoretical calculation of the potential curves of the states of HF below 14 eV

Potential energy curves obtained through extensive ab initio configuration interaction calculations are reported for the states of HF below 14 eV as well as that for the ground state of HF⁺. Agreement with ultraviolet absorption data is obtained to within 0.2 eV. The disagreement between the reported UV absorption and electron scattering data is examined.     

Hydrogen Bonding Properties of the Complexes of Formaldehyde and its Derivatives with HF and HCl

 The complexes of formaldehyde and some of its derivatives with HF and HCl were investigated at HF/6-311 + +G^** and MP2/6-311 + +G^** levels of theory. Interaction energies were corrected for the basis set superposition error (BSSE). The full optimizations of dimers and monomers were performed during calculations. The Bader theory of atoms-in-molecules (AIM) was also applied for the localization of bond critical points (BCP) and for the calculation the electron densities and their Laplacians at these points. The relationships between H-bond energy and parameters obtained from calculations were also studied.     

Hydrogen Bonding Properties of the Complexes of Formaldehyde and its Derivatives with HF and HCl

Summary.  The complexes of formaldehyde and some of its derivatives with HF and HCl were investigated at HF/6-311 + +G^** and MP2/6-311 + +G^** levels of theory. Interaction energies were corrected for the basis set superposition error (BSSE). The full optimizations of dimers and monomers were performed during calculations. The Bader theory of atoms-in-molecules (AIM) was also applied for the localization of bond critical points (BCP) and for the calculation the electron densities and their Laplacians at these points. The relationships between H-bond energy and parameters obtained from calculations were also studied. Received June 29, 2001. Accepted (revised) October 29, 2001     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

Molecular structure and vibrational assignment of melaminium phthalate by density functional theory (DFT) and ab initio Hartree-Fock (HF) calculations

The molecular geometry, the normal mode frequencies and corresponding vibrational assignment of melaminium phthalate (C₃H₇N₆⁺·C₈H₅O₄⁻) in the ground state were performed by HF and B3LYP levels of theory using the 6-31G(d) basis set. The optimized bond length numbers with bond angles are in good agreement with the X-ray data. The vibrational spectra of melaminium phthalate which is calculated by HF and B3LYP methods, reproduces vibrational wave numbers with an accuracy which allows reliable vibrational assignments. The title compound has been studied in the 4000–100 cm⁻¹ region where the theoretical evaluation and assignment of all observed bands were made.     

Penning ionization and photoionization electron spectrometry of hydrogen fluoride

An electron spectrometric study has been performed on HF using metastable helium and neon atoms as well as helium and neon resonance photons. High-resolution electron spectra were obtained for a pure He(2³ S) beam, a mixed He(2¹ S, 2³ S) beam, a mixed Ne(3s,³ P ₂,³ P ₀) beam, and for HeI and NeI VUV light. From the comparison of vibrational populations of HF⁺ (X ²£ _i ,v′) and HF⁺ (A ²Σ⁺,v′) produced by He(2³ S) metastables and HeI resonance photons, we conclude that there is only a slight perturbation of the HF (X ¹Σ⁺) potential in He(2³ S) Penning ionization; no perturbation is found for HF⁺ (X ²Π _i ,v′) formation from Ne(³ P _2,0) metastable ionization of HF. For He(2¹ S)+HF theX- andA-ionic state vibrational peak shapes are substantially broader than in the He(2³ S)+HF case pointing to an additional, charge exchanged interaction (He⁺+HF^?) in the entrance channel of the former system. The vibrational population found for NeI _α photoionization of HF for formation of HF⁺ (X ²Π _i ,v′) is found to differ considerably from that for NeI _β photoionization and from the Franck-Condon factors for unperturbed HF(X ¹Σ⁺) and HF⁺ (X ²Π _i ) potentials suggesting the presence of an autoionizing superexcited state of HF in the energy vicinity of the NeI _α resonance photons. The HF⁺ (X)²Π_3/2:²Π_1/2 fine-structure branching ratios vary significantly with the ionizing agent in a similar way as previously found in HCl and HBr.     

Cooperativity between the Halogen Bond and the Hydrogen Bond in H3N⋅⋅⋅XY⋅⋅⋅HF Complexes (X,Y=F,Cl, Br)

Ab initio calculations are used to provide information on H₃N???XY???HF triads (X, Y=F, Cl, Br) each having a halogen bond and a hydrogen bond. The investigated triads include H₃N???Br₂‐HF, H₃N???Cl₂???HF, H₃N???BrCI???HF, H₃N???BrF???HF, and H₃N???ClF???HF. To understand the properties of the systems better, the corresponding dyads are also investigated. Molecular geometries, binding energies, and infrared spectra of monomers, dyads, and triads are studied at the MP2 level of theory with the 6‐311++G(d,p) basis set. Because the primary aim of this study is to examine cooperative effects, particular attention is given to parameters such as cooperative energies, many‐body interaction energies, and cooperativity factors. The cooperative energy ranges from ?1.45 to ?4.64 kcal mol^?1, the three‐body interaction energy from ?2.17 to ?6.71 kcal mol^?1, and the cooperativity factor from 1.27 to 4.35. These results indicate significant cooperativity between the halogen and hydrogen bonds in these complexes. This cooperativity is much greater than that between hydrogen bonds. The effect of a halogen bond on a hydrogen bond is more pronounced than that of a hydrogen bond on a halogen bond.     

Blue-shifted hydrogen-bonded complexes. II. CH3F(HF)1 n 3 and CH2F2(HF)1 n 3

The equilibrium structures, binding energies, and vibrational spectra of the clusters CH₃F(HF)_{1 n 3} and CH₂F₂(HF)_{1 n 3} have been investigated with the aid of large-scale ab initio calculations performed at the Møller–Plesset second-order level. In all complexes, a strong C–FH–F halogen–hydrogen bond is formed. For the cases n = 2 and n = 3, blue-shifting C–HF–H hydrogen bonds are formed additionally. Blue shifts are, however, encountered for all C–H stretching vibrations of the fluoromethanes in all complexes, whether they take part in a hydrogen bond or not, in particular also for n = 1. For the case n = 3, blue shifts of the ν(C–H) stretching vibrational modes larger than 50 cm⁻¹ are predicted. As with the previously treated case of CHF₃(HF)_{1 n 3} complexes (A. Karpfen, E. S. Kryachko, J. Phys. Chem. A 107 (2003) 9724), the typical blue-shifting properties are to a large degree determined by the presence of a strong C–FH–F halogen–hydrogen bond. Therefore, the term blue-shifted appears more appropriate for this class of complexes. Stretching the C–F bond of a fluoromethane by forming a halogen–hydrogen bond causes a shortening of all C–H bonds. The shortening of the C–H bonds is proportional to the stretching of the C–F bond.     

Configuration-Interaction study of lower excited states of O2: Valence and rydberg characters of the two lowest 3Σu − states

Configuration-interaction calculations, with an extended basis, are carried out on the ground and lower excited states of O₂ and O₂⁺ at and near the equilibrium internuclear distance (R = 2.3 a.u.) of the ground state of O₂. Particular attention has been paid to the two lowest ³Σ_u^? states, and the mixing of the valence and Rydberg characters in these states are studied. The lowest ³Σ_u^? state is a Rydberg-type state for R < 2.3 a.u., but becomes valence-type for R ? 2.3 a.u. The second ³Σ_u^? state, which is 1.6 eV above the lowest ³Σ_u^? at R = 2.3 a.u., changes its character from Rydberg to valence, valence to Rydberg, and then to valence again when R increases from 1.9 to 3.1 a.u. Satisfactory agreement between the calculated and experimental vertical excitation energies is obtained.     

Electronic charge density and mean kinetic energy of lithium orbitals in LiH,LiH+, Li2, Li2+, LiH2+, and Li2H+

The electron density near the lithium nucleus in the species LiH, LiH⁺, Li₂, Li₂⁺, LiH₂⁺, and Li₂H⁺ was analyzed by transforming the SCF molecular orbitals into a sum of atomic contribnutions, for both core and valence orbitals. These “hybrid-atomic” orbitals were used to compare: electron densities, orbital polarizations, and orbital mean kinetic energies with the corresponding lithium atom quantities. Core-orbital electron densities at the lithium nucleus were observed to increase by up to 0.5% relative to the lithium atom 1s orbital. Lithium cores also exhibited polarization but, surprisingly, in the direction away from the internuclear region. Similar dramatic changes were seen in the electron densities of the valence orbitals of lithium: The electron density at the nucleus for these orbitals increased two-fold for homonuclear species and twenty-fold for heteronuclear triatomic species relative to the electron density at the nucleus in lithium atom. The polarization of the valence orbital electronic charge, in the vicinity of the lithium nucleus, was also away from the internuclear region. The mean “hybrid-atomic” orbital kinetic energies associated with the lithium atom in the molecules also showed changes relative to the free lithium atom. Such changes, accompanying bond formation, were relatively small for the lithium core orbitals (within 0.2% of the value for lithium atom). The orbital kinetic energies for the lithium valence electrons, however, increased considerably relative to the lithium atom: By a factor of about 2 in homonuclear diatomics, by a factor of 7 in heteronuclear diatomics, and by a factor of 11 in the triatomic species. In summary, the total electronic density (core plus valence) at the lithium nucleus remained remarkably constant for all of the species studied, regardless of the effective charge on lithium. Thus, the drastic changes noted in the individual lithium orbitals occurred in a cooperative fashion so as to preserve a constant total electron density in the vicinity of the lithium nucleus. In all cases, bond formation was accompanied by an increase in the orbital kinetic energy of the lithium valence orbital. We suggest that these two observations represent important and significant features of chemical bonding which have not previously been emphasized.     

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.