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     

The physical nature of the lone pair

Despite the large number of experimental and theoretical studies on the size, shape, and orientation of lone pairs and their resulting stereochemical character, lone pairs still remain poorly defined in terms of quantitative observable properties of a molecule. Using the conformation of saturated molecules and barriers to internal rotation, experimental chemists have arrived at conflicting sizes and orientations for lone pairs. Most theoretical attempts to define lone pair properties have centered on such non-observables as localized molecular orbitals or have been based on studies on isolated molecules.The use of observable properties to construct a consistent set of physical models to analyze the physical nature of lone pairs is discussed. Much as one probes an electric field with a test charge, probes such as H⁺, H^–, He and H could be used to probe regions of molecules such as NH₃ and H₂O where lone pairs are often postulated to exist.Ab initio quantum mechanical studies can be analyzed using electron density (and resulting changes during interaction), total pair density of electrons, the electrostatic potential about the molecule and bond energy analysis to study lone pair properties. A simple study of NH₃ using an H⁺ probe is presented to clarify the approach.     

Two‐Orbital Three‐Electron Stabilizing Interaction for Direct Co2+?As3+ Bonds involving Square‐Planar CoO4 in BaCoAs2O5

The quest for new oxides with cations containing active lone‐pair electrons (E) covers a broad field of targeted specificities owing to asymmetric electronic distribution and their particular band structure. Herein, we show that the novel compound BaCoAs₂O₅, with lone‐pair As³⁺ ions, is built from rare square‐planar Co²⁺O₄ involved in direct bonding between As³⁺E and Co²⁺ d_z2 orbitals (Co As=2.51 Å). By means of DFT and Hückel calculations, we show that this σ‐type overlapping is stabilized by a two‐orbital three‐electron interaction allowed by the high‐spin character of the Co²⁺ ions. The negligible experimental spin‐orbit coupling is expected from the resulting molecular orbital scheme in O₃AsE–CoO₄ clusters.     

Two‐Orbital Three‐Electron Stabilizing Interaction for Direct Co2+As3+ Bonds involving Square‐Planar CoO4 in BaCoAs2O5

The quest for new oxides with cations containing active lone‐pair electrons (E) covers a broad field of targeted specificities owing to asymmetric electronic distribution and their particular band structure. Herein, we show that the novel compound BaCoAs₂O₅, with lone‐pair As³⁺ ions, is built from rare square‐planar Co²⁺O₄ involved in direct bonding between As³⁺E and Co²⁺ d_z2 orbitals (Co? As=2.51 Å). By means of DFT and Hückel calculations, we show that this σ‐type overlapping is stabilized by a two‐orbital three‐electron interaction allowed by the high‐spin character of the Co²⁺ ions. The negligible experimental spin‐orbit coupling is expected from the resulting molecular orbital scheme in O₃AsE–CoO₄ clusters.     

New insight into the electronic structure of iron(IV)‐oxo porphyrin compound I. A quantum chemical topological analysis

The electronic structure of iron‐oxo porphyrin π‐cation radical complex Por^·+Fe^IV?O (S? H) has been studied for doublet and quartet electronic states by means of two methods of the quantum chemical topology analysis: electron localization function (ELF) η(r) and electron density ρ(r). The formation of this complex leads to essential perturbation of the topological structure of the carbon–carbon bonds in porphyrin moiety. The double C?C bonds in the pyrrole anion subunits, represented by pair of bonding disynaptic basins V_i=1,2(C,C) in isolated porphyrin, are replaced by single attractor V(C,C)_i=1–20 after complexation with the Fe cation. The iron–nitrogen bonds are covalent dative bonds, N→Fe, described by the disynaptic bonding basins V(Fe,N)_i=1–4, where electron density is almost formed by the lone pairs of the N atoms. The nature of the iron–oxygen bond predicted by the ELF topological analysis, shows a main contribution of the electrostatic interaction, Fe^δ+···O^δ?, as long as no attractors between the C(Fe) and C(O) core basins were found, although there are common surfaces between the iron and oxygen basines and coupling between iron and oxygen lone pairs, that could be interpreted as a charge‐shift bond. The Fe? S bond, characterized by the disynaptic bonding basin V(Fe,S), is partially a dative bond with the lone pair donated from sulfur atom. The change of electronic state from the doublet (M = 2) to quartet (M = 4) leads to reorganization of spin polarization, which is observed only for the porphyrin skeleton (?0.43e to 0.50e) and S? H bond (?0.55e to 0.52e). © 2012 Wiley Periodicals, Inc.     

Unconventional Metal–Framework Interaction in MgSi5

The silicon‐rich cage compound MgSi₅ was obtained by high‐pressure high‐temperature synthesis. Initial crystal structure determination by electron diffraction tomography provided the basis for phase analyses in the process of synthesis optimization, finally facilitating the growth of single crystals suitable for X‐ray diffraction experiments. The crystal structure of MgSi₅ (space group Cmme, Pearson notation oS24, a=4.4868(2) Å, b=10.1066(5) Å, and c=9.0753(4) Å) constitutes a new type of framework of four‐bonded silicon atoms forming Si₁₅ cages enclosing the Mg atoms. Two types of smaller Si₈ cages remain empty. The atomic interactions are characterized by two‐center two‐electron bonds within the silicon framework. In addition, there is evidence for multi‐center Mg?Si bonding in the large cavities of the framework and for lone‐pair‐like interactions in the smaller empty voids.     

Bonding/antibonding character of “lone pair” molecular orbitals from their energy derivatives; consequences for experimental data

The derivative of molecular orbitals (MO) energies with respect to a bond length (dynamic orbital force [DOF]) is used to estimate the bonding/antibonding character of valence MOs along this bond, with a focus on lone pair MOs, in a series of small molecules: AH (A = F, Cl, Br), AH₂ (A = O, S, Se), AX₃ (A = N, P, As; X = H, F), and H₂CO. The HOMO DOF agrees with the calculated variation of bond length and force constant in the corresponding ground state cation, and of bond length variation by protonation. These results also agree with available experimental data. It is worthy to note that the p‐type HOMOs in AH and AH₂ are found bonding. The lone pair MO is bonding in NH₃, while it is antibonding in PH₃, AsH₃, and AF₃.     

Substituent effects in second-row molecules: Basis set performance in calculations of normal valency phosphorus and sulfur compounds

Ab inito molecular orbital calculations of the phosphorus- and sulfur-containing series PH₂X, PH₃X⁺, SHX, and SH₂X⁺ (X = H, CH₃, NH₂, OH, F) have been carried out over a range of Gaussian basis sets and the results (optimized geometrical structures, relative energies, and electron distributions) critically compared. As in first-row molecules there are large discrepancies between substituent interaction energies at different basis set levels, particularly in electron-rich molecules; use of basis sets lower than the supplemented 6-31G basis incurs the risk of obtaining substituent stabilizations with large errors, including the wrong sign. Only a small part of the discrepancies is accounted for by structural differences between the optimized geometries. Supplementation of low level basis sets by d functions frequently leads to exaggerated stabilization energies for π-donor substituents. Poor performance also results from the use of split valence basis sets in which the valence shell electron density is too heavily concentrated in diffuse component of the valence shell functions, again likely to occur in electron-rich molecules. Isodesmic reaction energies are much less sensitive to basis set variation, but d function supplementation is necessary to achieve reliable results, suggesting a marginal valence role for d functions, not merely polarization of the bonding density. Optimized molecular geometries are relatively insensitive to basis set and electron population analysis data, for better-than-minimal bases, are uniform to an unexpected degree.     

Localized molecular orbital studies in momentum space. II. Correspondence between coordinate and momentum space properties of various electron pairs

The momentum space properties of the ten-electron systems Ne, HF, H₂O, NH₃ and CH₄ as well as those of CH₃CH₃, CH₃NH₂, CH₃OH and FCH₂OH were investigated using localized molecular orbitals (LMO) obtained from ab initio self-consistent-field (SCF) wavefunctions constructed from double zeta quality gaussain basis sets.Compton profiles of various LMO electron pairs (CC, CN, CO, CF; CH, NH, OH, FH bond pairs and C, N, O, F lone pairs) are tabulated. In order to understand the correspondence between the momentum and the coordinate space properties of those electron pairs, the concept of the size and the shape of an LMO electron pair charge distribution has been utilized. The use of the intermediate expectation values of pⁿ is introduced for the purpose of interpreting the momentum space properties.The dependence of molecular property partitioning on different localization schemes and on different basis sets is also studied by using the H₂O profile as an example.     

O?H stretching force constant in associated methanol species and the cooperativity effect

The effect of molecular interaction on the O? H stretching force constant of methanol (MeOH) is reported for its associated species. The various electron donors (D) and acceptors (A) considered include organic molecules such as methanol, dimethylether, acetone, acetonitrile, dimethyl formamide, pyridine, and ions such as F^?, Cl^?, Li⁺, and H⁺. The variation in the O? H stretching force constant of MeO? H…?D species on interaction with the electron acceptor such as in the species is explained on the basis of the cooperativity effect. (CE ). The effect is discussed in terms of the relationship CE = (ΔF/F) × 100, where ΔF is the reduction is force constant of the hydrogen-bonded O? H stretching mode of the associated methanol species MeOH…?D when the lone pair electrons on oxygen of the methanol molecule are involved in hydrogen bonding with A, and F is the hydrogen-bonded O? H stretching force constant of the species when the lone pair electrons are free. The cooperativity effect (CE ) is found to increase with increasing electron acceptor and electron donor capacities of A and D. The calculated force constants are compared with the experimental results.     

An ab initio evaluation of the role of p,π interaction: I. Ethylene derivatives

The RHF/6-311G(d) and MP2/6-311G(d) calculations with full geometry optimization were performed for XCH=CH₂ molecules (X = F, Cl, Br, CH₃, CH₂CH₃, CH₂F, CHO). The p _y electron density distribution in these molecules and the bonding molecular orbitals formed by the p _y orbitals of atoms of the planar fragment of these molecule (atomic orbitals whose symmetry axes are perpendicular to this plane) are not determined by the p,π conjugation between the lone electron pair of the heteroatom in substituent X and π electrons of the C=C bond. Changes in the population of the p _y orbitals of the halogen and carbon atoms in going from X = F to X = Cl and Br are not associated with changes in the extent of this p,π interaction. Taking into account the electon correlation in the MP2 method does not noticeably alter the features of the electron density distribution in these molecules estimated by restricted Hartree-Fock calculations.     

Study on Pair Correlation Energies of Isoelectronic Systems F^－, HF and H2F^＋

The intrapair and interpair correlation energies of F-, HF and H2F^ systems are calculated and analyzed using MP2-OPT2 method of MELD program with cc-PVSZ^* basis set. From the analysis of pair correlation energies of these isoelectronlc sysoterns, it is found that the 1sF^2 pair correlation energy is trans-ferable in these three isociectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H—F bonding electron pair in HF molecule with those in H2F^ system are compared. The results indicate that the bonding effect of a molecule is one of the im-portant factors to influence electron correlation energy of the system. The comparison of correlation energy contributions in-cluding triple and quadruple excitations with those only includ-ing singles and doubles calculated with 6-311 G(d) basis set shows that the higher.excitation correlation energy contribution gives more than 2 % of the total correlation energy for these sys-tems.     

Directionality of Pb2+ lone pair electrons dictated hemi-directed coordination mode of methyl- and ferrocenylcarboxylate complexes

The experimentally observed hemi-directed coordination mode in 1D polymeric Pb²⁺ ferrocenylcarboxylate system is examined computationally for gaining better insights on the structure of polymeric systems. By considering the different size of the ligands such as methylcarboxylate (model system) and ferrocenylcarboxylates (real system), the coordination mode is systematically explored in the complexes 1–6 . As expected due to the possibility of free rotation in the methylcarboxylate systems in solution, it may follow holo-directed geometrical arrangements but interestingly, it shows only hemi-directed geometry as observed in the experimental studies on ferrocenylcarboxylate system (N. Palanisami et al. Science of Advanced Materials, 2014, 6, 2364). The present computational studies predict that the lone pair electrons in Pb²⁺ play the dictating role for formation of hemi-directed coordination mode in methylcarboxylates as well as in ferrocenylcarboxylates. The directionality of the lone pair electrons makes the remarkable differences in the structural arrangements. Notable difference observed is that the methylcarboxylate shows the linear fashion of hemi-directed coordination whereas ferrocenylcarboxylate shows the zig-zag fashion of hemi-directed coordination. The quantitative and qualitative characteristics of lone pair electrons in reported systems are assessed through NBO analysis thus it shows the s-LP character occupancy in each case varies from 96% to 93% which is the strong evidence for the availability of lone pair electrons in Pb²⁺ carboxylate systems. Further, frontier molecular orbital analysis, vibrational modes and hydrogen bonding pattern are explored in the complexes 1–6 .     

STERIC AND ELECTRONIC BALANCE IN METAL-PHOSPHINE COORDINATION: THE PHOSPHINE TWIST

Abstract

The relationship between the bite angles of cis phosphines and the electron distribution and bonding to the metal is studied by gas phase valence photoelectron spectroscopy. The complexes selected for the electronic structure comparison are cis-Mo(CO)₄(PMe₃)₂, Mo(CO)₄DMPE (DMPE = 1,2-bis dimethylphosphinotethane), Mo(CO)₄DMPM (DMPM = bis(dimethylphosphino) methane), cis-W(CO)₄(PMe₃)₂, W(CO)₄DMPE, and cis-W(CO)₄DMPM. The Mo carbonyl complexes give simple photoelectron spectra with the valence ionizations originating from the phosphine lone pairs bonding to the metals and from the metal d ⁶ configurations. The W complexes give similar spectra, but have an additional electronic spin-orbit perturbation. The ionizations from the phosphine lone pairs that donate to the metals in σ bond formation show the effects of the different bite angles of the ligands. However, the total interaction and charge distribution of the phosphines with the metals look very similar in each case. The metal-based ionizations also show very similar bonding and charge distribution in each case. The similarity of the cis-(PMe₃)₂ and DMPE spectra is interesting in light of the ～15° difference in P-M-P angles. The metal-based ionizations of the DMPM complexes are slightly different from those of the other complexes, primarily because of through-space interactions with the methylene carbon in the phosphine backbone. The similarity in electronic interactions with the metal in these complexes is traced to a twist of the phosphine coordination to the metal which adjusts for the steric or bite angle constraints of the ligands with a minimum effect on the bonding to the metal. This results in slightly bent metal-phosphorus bonds.     

Density functional and molecular orbital study of physical process of inversion of nitrogen trifluoride (NF3) molecule

The physical process of the umbrella inversion of the nitrogen trifluoride molecule has been studied invoking the formalisms of the density functional theory, the frontier orbital theory, and the molecular orbital theory. An intuitive structure and dynamics of evolution of the transition state for the event of inversion is suggested. The physical process of dynamic evolution of the molecular conformations between the equilibrium (C_3v) shape and the planar (D_3h) transition state has been followed by a number of molecular orbital and density functional parameters like the total energy, the eigenvalues of the frontier orbitals, the highest occupied molecular orbital and lowest unoccupied molecular orbital, the (HOMO–LUMO) gap, the global hardness and softness, and the chemical potential. The molecular conformations are generated by deforming the ∠FNF angle through steps of 2° from its equilibrium value, and the cycle is continued till the planar transition state is reached, and the geometry of each conformation is optimized with respect to the length of the N? F bond. The geometry optimization demonstrates that the structural evolution entails an associated slow decrease in the length of the N? F bond. The dipole moment at the equilibrium form is small and that at the transition state is zero and shows a strange behavior with the evolution of conformations. As the molecular structure begins to distort from its equilibrium shape by opening of the ∠FNF angle, the dipole moment starts increasing very sharply, and the trend continues very near to the transition state but abruptly vanishes at the transition state. A rationale of the strange variation of dipole moment as a function of evolution of conformations could be obtained in terms of quantum mechanical hybridization of the lone pair on the N atom. The pattern of charge density reorganization as a function of geometry evolution is a continuous depletion of charge from the F center and piling up of charge on the N center. The continuous shortening of bond length and the pattern of variation of net charge densities on atomic sites with evolution of molecular conformations predicts that the bond moment would decrease continuously. The quantum mechanical hybridization of the lone pair of the central N atom shows that the percentage of s character of the lone‐pair hybrid on the N atom decreases at a very accelerated rate, and the lone pair at the transition state is accommodated in a pure p orbital. The result of the continued destruction of asymmetry of charge distribution in the lone pair on the central N atom due to the elimination of contribution of the s orbital with evolution of molecular conformations is the sharp decrease in lone‐pair moment. The decrease in bond moment is overcompensated by the sharp fall of its offsetting component, the lone‐pair moment, resulting in a net gain in dipole moment with the evolution of molecular geometry. Since the offsetting component decreases very sharply, the net effect is a sharp rise of dipole moment with the evolution of molecular conformations just before the transition state. The lone‐pair moment is zero by virtue of the symmetry of the pure p orbital, the lone pair of the central atom in the transition state, and the sum of the bond moments is zero by symmetry of the geometry. The barrier height is quite high at ～65.45 kcal/mol, which is close to values computed through more sophisticated methods. It is argued that an earlier suggestion regarding the development of high barrier value of NF₃ system seems to be misleading and confronting with the conclusions of the density functional theory. An analysis and a comparative study of the physical components of the one‐ and two‐center energy terms reveals that the pattern of the charge density reorganization has the principal role in deciding the origin and the magnitude of barrier of inversion of the molecule and the barrier originates not from a particular energetic effect localized in a particular region of the molecule, rather the barrier originates from a subtle interplay of one‐ and two‐center components of the total energy. The decomposed energy components show that the F?F nonbonded interaction and N? F bonded interaction favor the formation of transition state, while the one‐center energy terms prohibit the formation of the transition state. The barrier principally develops from the one‐center energy components. The profile of the HOMO is isomorphic and that of the LUMO is homomorphic with the potential energy curve for the physical process of the event of umbrella inversion of the molecule. The variation of the HOMO–LUMO gap, ?ε, the global hardness, η, and the softness, S, as a function of the reaction coordinates of angular deformation of NF₃ molecule are quite consistent with the predictions of the molecular orbital and the density functional theories in connection with the deformation of molecular geometry. The profiles of ?ε, η, and S, as a function of reaction coordinates, mimic the potential energy curve of the molecule. The eigenvalues of the frontier orbitals, and the ?ε, η, S parameters are found to be equally effective theoretical parameters, like the total energy, to monitor the physical process of the inversion of pyramidal molecules. The nature of the variation of the global hardness parameter between the equilibrium shape and the transition state form for the inversion is in accordance with the principle of maximum hardness (PMH). © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

Interproton coupling constant variations in 3-membered ring heterocycles. Separation of lone pair and inductive effects

In order to separate inductive and lone pair effects on geminal and vicinal coupling constants in a stereochemically well-defined system, the ¹H NMR spectra of phenylcyclopropane (1), N-methyl-2-phenylaziridine (2), styrene oxide (3) and 1,1-dimethyl-2-phenylaziridinium fluorosulfonate (4) were compared. In D₂O the heterocyclic ring protons of 4 were split into an ABX pattern which gave J(cis) = 8.5, J(trans) = 7.4 and J(gem) = ?4.8 Hz (signs consistent with INDOR results). From the small solvent effects on J(vic) determined from 4-d₁, it was concluded that J(gem) is ?5.0 ± 1.0 Hz in methylene chloride. The absolute values for the coupling constants for 1 and 4 provide a measure of the inductive effect of the ring hetero group on J. Values of J(gem) for 2 and 3 deviated from those predicted on the basis of the above inductive effect, suggesting lone pair contributions to J(gem) of c. +5.5 Hz per lone pair. With this estimate it was possible to predict accurately the J(gem) values for 2-t-butyloxaziridine and 1-t-butyldiaziridine. The values of J(cis) and J(trans) for 2 and 3 likewise suggested a contribution of ?2.5 Hz to J(cis) and ?2.7 Hz to J(trans) per lone pair. The present results suggest that the major factors causing positive J(gem) values in epoxides and aziridines are increased s character to the C? H bonds and lone pair effects, while the so-called electronegativity effect actually operates in the opposite direction to decrease J(gem). Also, the unusually low J(vic) values of epoxides relative to cyclopropanes are now seen to be due more to negative lone pair contributions than to the electron withdrawing ability of oxygen.     

Ab initio investigation of tautomeric stability,molecular structure,and internal rotation of methylphosphonic dicyanide,methoxydicyanophosphine, and their isocyano analogs

The equilibrium geometric parameters and structures of the transition states of internal rotation for MeP(O)(CN)₂, McOP(CN)₂, and their isocyano analogs, MeP(O)(NC)₂ and MeOP(NC)₂, have been calculated by theab initio SCF method and with inclusion of electron correlation effects according to the second-order Muuller-Plesset perturbation theory (MP2). At both levels the 6-31G* basis set has been used. The estimation of relative stability of these tautomeric forms depends largely on the calculation level. The total energies of the cyanides calculated by the MP2 method are 25–30 kcal mol^–1 lower than those of the corresponding isocyanides. The oxo-tautomeric forms containing four-coordinate phosphorus are 15–25 kcal mol^–1 more stable than the three-coordinate phosphorus aci-derivatives. The internal rotation potential curves of the aci-forms are characterized by a deep minimum for thetrans-arrangement of the methoxy group and phosphorus lone electron pair. Two additional less clearly pronounced minima are located symmetrically on both sides of the weak maximum, which corresponds to thecis-arrangement. The equilibrium oxo-form structures have a staggered configuration of the methyl group with respect to the phosphorus atom bonds.Translated from izvestiyaAkademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1104–1115, May, 1996.