Correlation between electron delocalization and structural planarization in small water rings

The discovery of the covalent‐like character of the hydrogen bonding (H‐bonding) system [Science 342 , 611(2013)] has promoted a renewal of our understanding of the electronic and geometric structures of water clusters. In this work, based on density functional theory calculations, we show that the preferential formation of a stable quasiplanar structure of (H₂O)_n(n = 3–6) is closely related to three kinds of delocalized molecular orbitals (MOs; denoted as MO‐I, II, and III) of water rings. These originate from the 2p lone pair electrons of oxygen (O), the 2p bond electrons of O and the 1s electrons of H and the 2s electrons of O and 1s electrons of H, respectively. To maximize the orbital overlaps of the three MOs, geometric planarization is needed. The contribution of the orbital interaction is more than 30% in all the water rings according to our energy decomposition analysis, highlighting the considerable covalent‐like characters of H‐bonds. © 2015 Wiley Periodicals, Inc.     

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.     

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals II. The Electronic Structure of N2 Molecules

Weinhold's natural hybrid orbitals can be chosen as the molecular adapted atomic orbitals to build the canonical molecular orbitals of N₂ molecules. The molecular Fock matrix expanded in the natural hybrid orbitals can reveal deeper insight of the electronic structure and reaction of the N₂ molecule. For example, the magnitude of F_ab can signify the bonding character of the paired electrons as well as the diradical character of the unpaired electrons for both σ‐ and π‐types. Discarding the concept of the overlap between non‐orthogonal atomic orbitals, the different orbitals for different spins in the unrestricted Hartree‐Fock wavefunction reveal that there are three pairs of opposite spin density flows between two atoms, which proceed until the bonding molecular orbitals form.     

Ab initio study of the transition-metal carbene cations

The geometries and bonding characteristics of the first-row transition-metal carbene cations MCH_2~ were investigated by ab initio molecular orbital theory (HF/LANL2DZ). All of MCH_2~ are coplanar. In the closed shell structures the C bonds to M with double bonds; while in the open shell structures the partial double bonds are formed, because one of the σ and π orbitals is singly occupied. It is mainly the π-type overlap between the 2p_x orbital of C and 4p_x, 3d_(xz), orbitals of M~ that forms the π orbitals. The dissociation energies of C—M bond appear in periodic trend from Sc to Cu. Most of the calculated bond dissociation energies are close to the experimental ones.     

Kinetic Study and NBO Analysis of the Dehydrogenation Mechanism of Five‐membered Ring Heterocyclic 2,5‐Dihydro‐[furan,thiophene, selenophene

The theoretical study of the dehydrogenation of 2,5‐dihydro‐[furan ( 1 ), thiophene ( 2 ), and selenophene ( 3 )] was carried out using ab initio molecular orbital (MO) and density functional theory (DFT) methods at the B3LYP/6‐311G**//B3LYP/6‐311G** and MP2/6‐311G**//B3LYP/6‐311G** levels of theory. Among the used methods in this study, the obtained results show that B3LYP/6‐311G** method is in good agreement with the available experimental values. Based on the optimized ground state geometries using B3LYP/6‐311G** method, the natural bond orbital (NBO) analysis of donor‐acceptor (bond‐antibond) interactions revealed that the stabilization energies associated with the electronic delocalization from non‐bonding lone‐pair orbitals [LP(e)_X3] to δ*_{C(1)  H(2)} antibonding orbital, decrease from compounds 1 to 3 . The LP(e)_X3→δ*_{C(1)  H(2)} resonance energies for compounds 1 – 3 are 23.37, 16.05 and 12.46 kJ/mol, respectively. Also, the LP(e)_X3→δ*_{C(1)  H(2)} delocalizations could fairly explain the decrease of occupancies of LP(e)_X3 non‐bonding orbitals in ring of compounds 1 – 3 ( 3 > 2 > 1 ). The electronic delocalization from LP(e)_X3 non‐bonding orbitals to δ*_{C(1)  H(2)} antibonding orbital increases the ground state structure stability, Therefore, the decrease of LP(e)_X3→δ*_{C(1)  H(2)} delocalizations could fairly explain the kinetic of the dehydrogenation reactions of compounds 1 – 3 (k ₁ >k ₂ >k ₃ ). Also, the donor‐acceptor interactions, as obtained from NBO analysis, revealed that the (_C(4)C(7)→δ*_{C(1)  H(2)} resonance energies decrease from compounds 1 to 3 . Further, the results showed that the energy gaps between (_C(4)C(7) bonding and δ*_{C(1)  H(2)} antibonding orbitals decrease from compounds 1 to 3 . The results suggest also that in compounds 1 – 3 , the hydrogen eliminations are controlled by LP(e)→δ* resonance energies. Analysis of bond order, natural bond orbital charges, bond indexes, synchronicity parameters, and IRC calculations indicate that these reactions are occurring through a concerted and synchronous six‐membered cyclic transition state type of mechanism.     

An orbital localization criterion based on the topological analysis of the electron localization function

This work proposes a new molecular orbital localization procedure. The approach is based on the decomposition of the overlap matrix in accordance with the partitioning of the three‐dimensional physical space into basins with clear chemical meaning arising from the topological analysis of the electron localization function. The procedure is computationally inexpensive, provides a straightforward interpretation of the resulting orbitals in terms of their localization indices and basin occupancies, and preserves the σ/π‐separability in planar N‐electron systems. The localization algorithm is tested on selected molecular systems. © 2012 Wiley Periodicals, Inc.     

Investigation of the change in the electronic properties of FeF3 by the introduction of oxygen using a molecular orbital method

FeF₃ has attracted interest as a conversion‐reaction‐based positive electrode material in applications to lithium ion batteries. However, slow reaction kinetics is a major drawback due to its poor electrical conductivity. The electronic features of FeF₃ were examined using the DV‐Xα molecular orbital method. This article reports the effects of oxygen doping on the bonding characteristics and electrical conductivity. An analysis of the bond overlap population and spatial distribution of electrons showed that the Fe? O bond has a more covalent nature than the Fe? F bond. New energy levels were generated in the original band gap region through an interaction between the Fe3d and O2p orbitals with the introduction of oxygen. The electrical conductivity of FeF₃ is expected to be increased by the partial substitution of oxygen for fluorine due to the higher covalent character and the formation of new energy levels. © 2013 Wiley Periodicals, Inc.     

Time‐Dependent Density Functional Theory Molecular Dynamics Simulations of Liquid Water Radiolysis

The early stages of the Coulomb explosion of a doubly ionized water molecule immersed in liquid water are investigated with time‐dependent density functional theory molecular dynamics (TD–DFT MD) simulations. Our aim is to verify that the double ionization of one target water molecule leads to the formation of atomic oxygen as a direct consequence of the Coulomb explosion of the molecule. To that end, we used TD–DFT MD simulations in which effective molecular orbitals are propagated in time. These molecular orbitals are constructed as a unitary transformation of maximally localized Wannier orbitals, and the ionization process was obtained by removing two electrons from the molecular orbitals with symmetry 1B₁, 3A₁, 1B₂ and 2A₁ in turn. We show that the doubly charged H₂O²⁺ molecule explodes into its three atomic fragments in less than 4 fs, which leads to the formation of one isolated oxygen atom whatever the ionized molecular orbital. This process is followed by the ultrafast transfer of an electron to the ionized molecule in the first femtosecond. A faster dissociation pattern can be observed when the electrons are removed from the molecular orbitals of the innermost shell. A Bader analysis of the charges carried by the molecules during the dissociation trajectories is also reported.     

Comparison of the Bonding of Benzene and C60 to a Metal Cluster: Ru3(CO)9(μ3-η2,η 2,η2-C6H6) and Ru3(CO)9(μ3-η2,η2,η2-C60)

The electron distributions and bonding in Ru₃(CO)₉( ³- ², ², ²-C₆H₆) and Ru₃(CO)₉( ³- ², ², ²-C₆₀) are examined via electronic structure calculations in order to compare the nature of ligation of benzene and buckminsterfullerene to the common Ru₃(CO)₉ inorganic cluster. A fragment orbital approach, which is aided by the relatively high symmetry that these molecules possess, reveals important features of the electronic structures of these two systems. Reported crystal structures show that both benzene and C₆₀ are geometrically distorted when bound to the metal cluster fragment, and our ab initio calculations indicate that the energies of these distortions are similar. The experimental Ru–C_fullerene bond lengths are shorter than the corresponding Ru–C_benzene distances and the Ru–Ru bond lengths are longer in the fullerene-bound cluster than for the benzene-ligated cluster. Also, the carbonyl stretching frequencies are slightly higher for Ru₃(CO)₉( ³- ², ², ²-C₆₀) than for Ru₃(CO)₉( ³- ², ², ²-C₆H₆). As a whole, these observations suggest that electron density is being pulled away from the metal centers and CO ligands to form stronger Ru–C_fullerene than Ru–C_benzene bonds. Fenske-Hall molecular orbital calculations show that an important interaction is donation of electron density in the metal–metal bonds to empty orbitals of C₆₀ and C₆H₆. Bonds to the metal cluster that result from this interaction are the second highest occupied orbitals of both systems. A larger amount of density is donated to C₆₀ than to C₆H₆, thus accounting for the longer metal–metal bonds in the fullerene-bound cluster. The principal metal–arene bonding modes are the same in both systems, but the more band-like electronic structure of the fullerene (i.e., the greater number density of donor and acceptor orbitals in a given energy region) as compared to C₆H₆ permits a greater degree of electron flow and stronger bonding between the Ru₃(CO)₉ and C₆₀ fragments. Of significance to the reduction chemistry of M₃(CO)₉( ³- ², ², ²-C₆₀) molecules, the HOMO is largely localized on the metal–carbonyl fragment and the LUMO is largely localized on the C₆₀ portion of the molecule. The localized C₆₀ character of the LUMO is consistent with the similarity of the first two reductions of this class of molecules to the first two reductions of free C₆₀. The set of orbitals above the LUMO shows partial delocalization (in an antibonding sense) to the metal fragment, thus accounting for the relative ease of the third reduction of this class of molecules compared to the third reduction of free C₆₀.     

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     

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.     

Theoretical Study on the Hydrogen Bonding Interactions in Complexes of 5‐Hydroxytryptamine with Water

The energies, geometries and harmonic vibrational frequencies of 1:1 5‐hydroxytryptamine‐water (5‐HT‐H₂O) complexes are studied at the MP2/6‐311++G(d,p) level. Natural bond orbital (NBO), quantum theory of atoms in molecules (QTAIM) analyses and the localized molecular orbital energy decomposition analysis (LMO‐EDA) were performed to explore the nature of the hydrogen‐bonding interactions in these complexes. Various types of hydrogen bonds (H‐bonds) are formed in these 5‐HT‐H₂O complexes. The intermolecular C4H5^5‐HT···O^w H‐bond in HTW3 is strengthened due to the cooperativity, whereas no such cooperativity is found in the other 5‐HT‐H₂O complexes. H‐bond in which nitrogen atom of amino in 5‐HT acted as proton donors was stronger than other H‐bonds. Our researches show that the hydrogen bonding interaction plays a vital role on the relative stabilities of 5‐HT‐H₂O complexes.     

Semiempirical study of electronic and bonding properties of iron silicide clusters

Summary Molecular orbital calculations of iron, silicon, and iron silicide clusters have been carried out using the UHF-MINDO/SR method. The nature of the bonding in these compounds has been investigated by analyzing the importance of bonding indexes and diatomic components of the total energy. It has been found that in iron silicide the strongest bond is formed between Fe-Si and that it arises mainly as the result ofsp-sp type orbital interactions. Althoughd orbitals show very little overlap withs-p orbitals, they do contribute significantly to bonding through electrostatic type diatomic interactions. By means of a detailed analysis ofsp, andd orbitals and total density of states (DOS) of Fe₇Si₇, Si₇Fe₇, Fe₁₅, and Si₁₇ clusters, the present calculations have permitted us to explain the origin of the iron silicide UPS experimental peaks.     

Density matrices for correlated Gaussians: Helium and dipositronium

Formulas are derived for the density matrices belonging to an n-particle wave function built on the basis of single-center explicitly correlated Gaussian basis functions. An explicit formula for the first-order density matrix, P(r₁, r′₁), is obtained for computing the probability distribution P(r₁, r₁). Other formulas are derived for matrix elements of the first-order density operator P on a basis of single-particle Gaussian orbitals so that natural orbitals (NOs) can be expressed in such a basis. The method is illustrated for the case of the ground state of the helium atom using the 16-term (geminal) wave function by Singer and Longstaff (E = −2.90233 au) and a set of even-tempered Gaussian orbitals. The resulting natural orbitals compare favorably with natural orbitals from Cl expansions. The method is also applied to our 20 term (trimal) wave function for the ground state of dipositronium (E = −0.51560 au). Analysis is made in this case for pair correlation functions of both the electron-electron and the positron-electron pairs; results include the radial distributions of these pairs and their relative angular momentum. © 1996 John Wiley & Sons, Inc.     

Electronegativity estimator built on QTAIM‐based domains of the bond electron density

The electron localization function, natural localized molecular orbitals, and the quantum theory of atoms in molecules have been used all together to analyze the bond electron density (BED) distribution of different hydrogen‐containing compounds through the definition of atomic contributions to the bonding regions. A function, g_AH, obtained from those contributions is analyzed along the second and third periods of the periodic table. It exhibits periodic trends typically assigned to the electronegativity (χ), and it is also sensitive to hybridization variations. This function also shows an interesting S shape with different χ‐scales, Allred–Rochow's being the one exhibiting the best monotonical increase with regard to the BED taken by each atom of the bond. Therefore, we think this χ can be actually related to the BED distribution. © 2014 Wiley Periodicals, Inc.     

[Cu6(NGuaS)6]2+ and its oxidized and reduced derivatives: Confining electrons on a torus

The hexanuclear thioguanidine mixed‐valent copper complex cation [Cu₆(NGuaS)₆]⁺² (NGuaS = o‐SC₆H₄NC(NMe₂)₂) and its oxidized/reduced states are theoretically analyzed by means of density functional theory (DFT) (TPSSh + D3BJ/def2‐TZV (p)). A detailed bonding analysis using overlap populations is performed. We find that a delocalized Cu‐based ring orbital serves as an acceptor for donated S p electrons. The formed fully delocalized orbitals give rise to a confined electron cloud within the Cu₆S₆ cage which becomes larger on reduction. The resulting strong electrostatic repulsion might prevent the fully reduced state. Experimental UV/Vis spectra are explained using time‐dependent density functional theory (TD‐DFT) and analyzed with a natural transition orbital analysis. The spectra are dominated by MLCTs within the Cu₆S₆ core over a wide range but LMCTs are also found. The experimental redshift of the reduced low energy absorption band can be explained by the clustering of the frontier orbitals. © 2017 Wiley Periodicals, Inc.     

Quantum Mechanical Study of Substituent Dependence on the Structure,Spectroscopic (13C, 1H NMR and UV), NBO,Hyperpolarizability and HOMO?LUMO Analysis of Ru(NHC)2Cl2(CH‐p‐C6H4X) Complexes

In this work, we have explored the structural, electronic properties, ¹³C and ¹H NMR parameters and first hyperpolarizability of Ru(NHC)₂Cl₂(CH‐p‐C₆H₄X) complexes (XH, F, Cl, Me, NH₂, OH, CN, NO₂, CHO, COOH) by mpw1pw91 quantum method. The X‐substituent effect on structural parameters, frontier orbital energies, spectroscopic (¹H and ¹³C NMR, UV) of complex was carried out. The results indicate that the substituent has played a significant role on the structures and properties of complex. ¹H and ¹³C NMR chemical shifts were calculated by using the gauge‐invariant atomic orbital (GIAO) method. Total and partial density of state (TDOS and PDOS) and also overlap population density of state (OPDOS) diagrams analysis were exhibited. In analyzing the bonding characteristics of this structure, Ru‐C_carbene and Ru‐C_NHC bonds were identified and characterized in details by Natural bond orbital (NBO) analysis.     

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.     

Localized orbital calculations of the bonding in SO,SO2F2, ClO3F and SOCL2

Localized valence molecular orbitals have been obtained for SO, SO₂F₂, ClO₃F and SOCl₂ by the method due to Boys and Foster. The bonding in these molecules, in which the second row atom is exhibiting an excess valency, is discussed in terms of the form of these localized orbitals. The bonding of the second row atom to an oxygen atom is described by three bent bond orbitals, whilst bonding to a halogen atom is described by a single bond orbital. The participation of 3d functions in the various bonding and nonbonding orbitals is analysed in this localized orbital framework.     

Model study of the impact of orbital choice on the accuracy of coupled-cluster energies. II. Valence-universal coupled-cluster method

The impact of the choice of molecular orbital sets on the results of the valence-universal coupled cluster method involving up to three-body amplitudes (VU-CCSDT) was studied for the H4 model. This model offers a straightforward way of representing all possible symmetry-adapted orbitals. Moreover, the degree of quasi-degeneracy of its lowest ¹A₁ states can be varied over a wide range by changing its geometry. Calculations were performed both for 13 sets of standard quantum chemical orbitals and for a vast variety of nonstandard orbital sets defined by nodes of a two-dimensional orbital grid. The performance of various standard orbital sets in VU-CCSDT calculations is compared. It is also documented that for every quasi-degeneracy region there exist nonstandard orbital sets which allow one to obtain more accurate VU-CCSDT energies than the standard orbital sets. In an attempt to provide a general interpretation for some of the alternative orbital sets, we defined a set of orbitals which maximize the proximity of the model and target spaces—maximum proximity orbitals (MPO). It is demonstrated that outside the strong quasi-degeneracy region the energies obtained for the VU-CCSDT approach based on the MPOs are more accurate than for the standard orbital sets. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 221–237, 1998