Estimating local bonding/antibonding character of canonical molecular orbitals from their energy derivatives. The case of coordinating lone pair orbitals

According to Koopmans theorem, the derivative of the energy of a canonical molecular orbital (MO) with respect to nuclear coordinates quantifies its bonding/antibonding character. This quantity allows predictions of bond length variation on ionisation in a panel of 19 diatomic species. In polyatomic molecules, the derivative of a MO energy with respect to a given bond length reveals the nature and the degree of the bonding/antibonding contribution of this MO with respect to this bond. Accordingly, the HOMO “lone pairs” of CO and CN^? and the HOMO‐2 of CH₃CN are found to be antibonding with respect to the C? X bond (X = N, O), whereas the HOMO of N₂ is found to be bonding. With the same approach, the variation of the bonding character in the MOs of CO and CH₃CN on interaction with an electron acceptor (modeled through the approach of a proton) or by applying an electric field was studied. © 2016 Wiley Periodicals, Inc.     

Theoretical study of the intermolecular hydrogen bond interaction for furan-HCl and furan-CHCl<Subscript>3</Subscript> complexes

The nature of the intermolecular hydrogen bond for the furan-HCl and furan-CHCI₃ complexes has been studied using ab initio calculations with MP2 level of theory. The new hydrogen bond type of C(CI)-H...O and π interactions are studied also. It is shown that, for the optimized geometries of furan-CHCI₃, C-H bond lengths contract and vibrational frequencies are blue-shifted, while for the furan-HCl complex, H-CI bond lengths elongate and vibrational frequencies are red-shifted. In addition, the NBO analysis indicates that, for the furan-CHCI₃ complex, the charge transfers from the lone pair of the proton acceptor to both σ *(CH) antibonding MO and lone pairs of CI atom.     

The “Inverted Bonds” Revisited: Analysis of “In Silico” Models and of [1.1.1]Propellane by Using Orbital Forces

This article dwells on the nature of “inverted bonds”, which refer to the σ interaction between two sp hybrids by their smaller lobes, and their presence in [1.1.1]propellane. Firstly, we study H₃C−C models of C−C bonds with frozen H-C-C angles reproducing the constraints of various degrees of “inversion”. Secondly, the molecular orbital (MO) properties of [1.1.1]propellane and [1.1.1]bicyclopentane are analyzed with the help of orbital forces as a criterion of bonding/antibonding character and as a basis to evaluate bond energies. Triplet and cationic states of [1.1.1]propellane species are also considered to confirm the bonding/antibonding character of MOs in the parent molecule. These approaches show an essentially non-bonding character of the σ central C−C interaction in propellane. Within the MO theory, this bonding is thus only due to π-type MOs (also called “banana” MOs or “bridge” MOs) and its total energy is evaluated to approximately 50 kcal mol⁻¹. In bicyclopentane, despite a strong σ-type repulsion, a weak bonding (15–20 kcal mol⁻¹) exists between both central C−C bonds, also due to π-type interactions, though no bond is present in the Lewis structure. Overall, the so-called “inverted” bond, as resulting from a σ overlap of the two sp hybrids by their smaller lobes, appears highly questionable.     

Quantum-chemical study of crystal formation of supramolecular silver compounds with trans-1,2-Bis(4-pyridyl)ethylene and their electronic absorption spectra

The energies of singlet-singlet transitions in different supramolecular compounds formed by interaction of trans-1,2-bis(4-pyridyl)ethylene (DPyEt) with AgNO₃ have been calculated by the TDDFT method. The calculations show that the absorption peaks at 305.7 and 318.3 nm can be assigned to a superposition of the spectra of small suprastructures, e.g., (Ag)(DPyEt)₂(NO₃), (Ag)₂(DPyEt)(NO₃)₂, and (Ag)(DPyEt)(NO₃). These transitions correspond to the excitation of an electron from the bonding orbital into the antibonding orbital with respect to the C=C bond. Strong absorption bands at 350–360 nm, typical of a solid phase, can be assigned to the transition from the MO of the lone pair of the nitrogen of DPyEt into the antibonding MO with respect to the C=C bond. Such bands are present in the calculated excitation spectra of the (Ag)₁(DPyEt)₃(NO₃)₁ and (Ag)₂(DPyEt)₄(NO₃)₂ suprastructures.     

Analysis of carbon-carbon bonding in small hydrocarbons and dicarbon using dynamic orbital forces: Bond energies and sigma/pi partition. Comparison with sila compounds

The CC bonding is analyzed using dynamic orbital forces (DOF) in the series cyclopropane-ethane- benzene-ethylene-acetylene. The sum Σ(DOF)_t of the DOF over occupied molecular orbitals (MOs) is found linearly correlated to bond energies and thus can be used as a tool for determination of CC bond strength. A partition of bonding into σ and π components indicates a weakening of the σ bonding along the series, mainly due to the decrease of the bonding character of the highest σ MO. For C₂ molecule, Σ(DOF) _t was computed taking into account the four dominant configurations. On the basis of the preceding correlation, the C₂ bond was found about 15 kcal/mol weaker than that of acetylene, with a 25% σ participation; the bond order of C₂ can be evaluated at about 2.8 if we assume bond orders of 3 for acetylene and 2 for ethylene. Some sila homologs of the preceding carbon compounds have been studied. They exhibit characteristics generally close to the carbon compounds. A quite good correlation between Σ(DOF)_t and bond energies is also observed.     

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.     

Interpreting geometric preferences in π‐stacking interactions through molecular orbital analysis

The preference of π‐stacking interactions for parallel‐displaced (PD) and twisted (TW) conformations over the fully eclipsed sandwich (S) in small π‐stacked dimers of benzene, pyridine, pyrimidine, 1,3,5‐trifluorobenzene, and hexafluorobenzene are examined in terms of enhancement of the inter‐ring density through mixing of the monomer orbitals (MOs). PD and/or TW conformations are consistent with a non‐zero “stack bond order” (SBO), defined in analogy to the bond order of conventional MO theory, as the difference in the occupation of bonding and antibonding π‐type dimer MOs. In the S conformation, the equal number of bonding and antibonding MOs cancel overall stack bonding character between the monomers for an SBO of zero and an overall repulsive interaction. PD from the S shifts the character of at least one antibonding combination of monomer π‐type MOs with nodes perpendicular to the coordinate for PD to bonding, leading to an attractive nonzero SBO. The inter‐ring density measured through the Wiberg bond index analysis shows an enhancement at the PD conformations consistent with greater interpenetration of the monomer densities. This intuitive bonding model for π‐stacking interactions is complementary to highly accurate calculations of π‐stacking energies and allows a predictive understanding of relative stability using cheaper quantum chemical methods.     

Molecular and electronic structure of B10H12L2 compounds,where L is a lewis base

The geometrical characteristics of the B₁₀H₁₂L₂ complexes of the borane nido-cluster |B₁₀H₁₂| with Lewis base molecules L=NH₃, CH₃CN, Me₂S, Py, which are typical electron pair donors, are analyzed. The complexes are calculated by the MNDO quantum chemical method. Chemical bonding between |B₁₀H₁₂| and L is characterized using, the fragment analysis of molecular orbitals (MOs). It is shown that both occupied and unoccupied MOs of the |B₁₀H₁₂| fragment make important contributions to the bonding. The higher MOs of the system as well as its lower MOs with orbital energies up to 20 eV and higher involve the unoccupied orbitals of the cluster. The electron density is transferred from one L orbital to two unoccupied MOs of |B₁₀H₁₂|, 9a₁ and 6b₂. There is a large group of HOMOs defined as lone electron pairs of |B₁₀H₁₂| (boron AOs), whose energies change almost symbatically due to bonding to L. The localization of the electron paris by an ab initio calculation in the STO-3G basis set revealed ten three-center bonds and one four-center bond, B(1)-B(2)-B(3)-B(4). The charge transferred from L to |B₁₀H₁₂| is localized mainly on the B(6) and B(9) atoms. The B-L bond is of σ type; a significant θ component is observed for L=CH₃CN and Py. It is shown that the simplest two-orbital model of a donor-acceptor bond is inapplicable in the case of the B₁₀H₁₂L₂ compounds. Deceased. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 4, pp. 652–663, July–August, 1996. Translated by I. Izvekova     

The importance of lone pair delocalizations: theoretical investigations on the stability of cis and trans isomers in 1,2-halodiazenes

The relative and thermodynamic stabilities of cis and trans isomers of 1,2-dihalodiazenes (XN=NX; X = F, Cl, or Br) were examined using high level ab initio and density functional theory (DFT) calculations. For 1,2-dihalodiazenes, it was found that the cis isomers were more stable than the corresponding trans isomers, despite the existence of several cis destabilizing mechanisms, such as steric exchange between halogen lone pairs and dipole-dipole electrostatic repulsions (Delta(trans-cis) = 3.15, 7.04, and 8.19 kcal mol(-1), respectively, at BP86/6-311++G(3df,3pd)//B3LYP /6-311++G(3df,3pd) level). Their origin of the cis-preferred difference in energy was investigated with natural bond orbital (NBO) analysis to show that the "cis effect" came mainly from antiperiplanar interactions (AP effect) between the nitrogen lone pair and the neighboring antibonding orbital of the N-X bond (n(N) --> sigma(N'X'*)). The delocalization of halogen lone-pair into the antibonding orbital of the N=N bonds (the LP effects) was also found to enhance the cis preference by 1.20 to 6.58 kcal mol(-1), depending on the substituted halogen atom. The total amount of the AP effect increased as the halogen atom became larger, and the increased AP effect promoted the triple-bond-like nature of the N=N bond (shorter N=N bond length and wider NNX angle). The greater AP effect also made the N'-X' bond easier to cleave (longer N-X bond length), and a higher energy level than that of the nitrogen lone pair was found in the N-Br bonding orbital in 1,2-dibromodiazenes, thus indicating the significant instability of this molecule. The degradability of the N-Cl bond in 1,2-dichlorodiazenes and the fair stability of the N-F bond in 1,2-fluorodiazenes were also confirmed theoretically, and were found to be consistent with the previous experimental and theoretical reports. These results clearly indicate the dominance of lone-pair-related hyperconjugations on the basic electronic structure and energetic natures of 1,2-dihalodiazene systems.     

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.     

Dependence of approximate ab initio molecular loge sizes on the quality of basis functions

Size and shape parameters for the core, bonding, and lone electron pairs of the ten-electron hydrides (CH₄, NH₃, H₂O, HF) were determined from ab initio MO wave functions using various Gaussian basis sets. The fundamental features of approximate electron pair loge representation are somewhat more sensitive to the quality of the basis functions than the molecular total energy. The total size of the molecular electron distribution is less affected by basis set variations than its components: the core, bonding, and lone pair sizes. There is an apparent tendency to “preserve” the total size of molecular distribution.     

Mindo/3 study of the addition of hydrogen to vinylidene

The addition of hydrogen to vinylidene is studied using the MINDO/3 method. The results obtained are then compared with those for the addition of hydrogen to methylene applying ab initio and other semi-empirical methods. As expected, the pathways of these two reactions are qualitatively similar. The insertion is a non-least-motion process in which two phases can be easily distinguished: (i) an electrophilic step in which the empty orbital of the carbene interacts with the bonding orbital of H₂, forming a three-center bond in the process, (ii) a nucleophilic step in which the lone pair orbital of the carbene interacts with the antibonding orbital of H₂. The quantitative differences between the two reactions are also discussed.     

Quantum-chemical investigation of nature of neutral intermolecular hydrogen bond in complex H3PO...HF

Results are presented from modeling the complex H₃PO...HF by the ab initio Hartree-Fock-Roothaan method. A generalized method is proposed for the quantitative fragmentary analysis of molecular orbitals (MOs). It is shown that when the complex is formed, the chemical bond between the phosphine oxide and the HF molecule is formed by means of a shift of the electron pair of the -bond of the HF to a 2p orbital of the O atom and the formation of a bonding three-center MO localized on the O, H, and F atoms, and also through a shift of an electron pair from the O atom to a 2p orbital of the F atom and the formation of a nonbonding MO localized on the O and F atoms.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 1, pp. 38–41, January–February, 1992.     

Peroxynitrite in the hemoglobin composition

Electronic characteristics of trHbN hemoglobin whose composition contains the (ONOO) group with the structure close to the structure of 1) peroxynitrite and 2) a nitrate anion in the gas phase are calculated. Electron correlation is considered by the multiconfigurational self-consistent field (MCSCF) method during the optimization of the geometry of the whole structure. Localized molecular orbitals (MOs) are used as starting ones. In the wave function of the MCSCF method two complete active subspaces (CASs) are set. These are the subspace of iron atom 3d orbitals and the subspace describing chemical bonds in peroxynitrite (bonding and antibonding MOs plus the orbital of one lone pair on the O₂ moiety. The composition of the system involves two water molecules. The peroxynitrite structure is considered in two different spin states that correspond to the singlet and triplet states of this anion in the gas phase where the vibrational spectrum is characterized by frequencies of about (70-30) cm^?1. The protective reaction of the active center of the tubercule bacillus is discussed.     

Using (FH)2 and (FH)3 to Bridge the σ‐Hole and the Lone Pair at P in Complexes with H2XP,for X=CH3, OH,H, CCH,F, Cl,NC, and CN

Ab initio MP2/aug′‐cc‐pVTZ calculations are used to investigate the binary complexes H₂XP:HF, the ternary complexes H₂XP:(FH)₂, and the quaternary complexes H₂XP:(FH)₃, for X=CH₃, OH, H, CCH, F, Cl, NC, and CN. Hydrogen‐bonded (HB) binary complexes are formed between all H₂XP molecules and FH, but only H₂FP, H₂ClP, and H₂(NC)P form pnicogen‐bonded (ZB) complexes with FH. Ternary complexes with (FH)₂ are stabilized by F?H???P and F?H???F hydrogen bonds and F???P pnicogen bonds, except for H₂(CH₃)P:(FH)₂ and H₃P:(FH)₂, which do not have pnicogen bonds. All quaternary complexes H₂XP:(FH)₃ are stabilized by both F?H???P and F?H???F hydrogen bonds and P???F pnicogen bonds. Thus, (FH)₂ with two exceptions, and (FH)₃ can bridge the σ‐hole and the lone pair at P in these complexes. The binding energies of H₂XP:(FH)₃ complexes are significantly greater than the binding energies of H₂XP:(FH)₂ complexes, and nonadditivities are synergistic in both series. Charge transfer occurs across all intermolecular bonds from the lone‐pair donor atom to an antibonding σ* orbital of the acceptor molecule, and stabilizes these complexes. Charge‐transfer energies across the pnicogen bond correlate with the intermolecular P?F distance, while charge‐transfer energies across F?H???P and F?H???F hydrogen bonds correlate with the distance between the lone‐pair donor atom and the hydrogen‐bonded H atom. In binary and quaternary complexes, charge transfer energies also correlate with the distance between the electron‐donor atom and the hydrogen‐bonded F atom. EOM‐CCSD spin‐spin coupling constants ^2hJ(F–P) across F?H???P hydrogen bonds, and ^1pJ(P–F) across pnicogen bonds in binary, ternary, and quaternary complexes exhibit strong correlations with the corresponding intermolecular distances. Hydrogen bonds are better transmitters of F–P coupling data than pnicogen bonds, despite the longer F???P distances in F?H???P hydrogen bonds compared to P???F pnicogen bonds. There is a correlation between the two bond coupling constants ^2hJ(F–F) in the quaternary complexes and the corresponding intermolecular distances, but not in the ternary complexes, a reflection of the distorted geometries of the bridging dimers in ternary complexes.     

Chemical Bonding in Silicon Carbonyl Complexes

Although silylene-carbonyl complexes are known for decades, only recently isolable examples have been accomplished. In this work, the bonding situation is re-evaluated to explain the origins of their remarkable stability within the Kohn-Sham molecular orbital theory framework. It is shown that the chemical bond can be understood as CO interaction with the silylene via a donor-acceptor interaction: a σ-donation from the σ_CO into the empty p-orbital of silicon, and a π-back donation from the sp² lone pair of silicon into the π*_CO antibonding orbitals. Notably, it was established that the driving force behind the surprisingly stable Si−CO compounds, however, is another π-back donation from a perpendicular bonding R−Si σ-orbital into the π*_CO antibonding orbitals. Consequently, the pyramidalization of the central silicon atom cannot be associated with the strength of the π-back donation, in sharp contrast to the established chemical bonding model. Considering this additional bonding interaction not only shed light on the bonding situation, but is also an indispensable key for broadening the scope of silylene-carbonyl chemistry.     

Electron-rich three-center bonding: role of s,p interactions across the p-block

This paper analyzes the importance of s,p mixing-a necessary addition to the simplest Rundle-Pimentel picture-and periodic and group trends in electron-rich three-center bonding. Our analysis proceeds through a detailed quantum chemical study of the stability of electron-rich three-center bonding in triatomic 22-valence electron anions. To provide interpretations, a perturbational molecular orbital (MO) analysis of s,p mixing is carried out. This analysis of the orbitals and the overlap populations is then tested by density functional calculations for a number of linear trihalides, trichalcogenides, and tripnictides. The most important effect of s,p mixing on the in-line bonding is in destabilization of the 3sigma(g) orbital and is determined by the overlap between the s orbital of the central atom and the p orbital of the terminal atom. Further destabilization arises from the repulsion of p(pi) lone pairs. Both of these antibonding effects increase with increasing negative charge of the system. The stability of isoelectronic X(3) systems thus decreases when moving from right to left in the periodic table. Interesting group trends are discerned; for instance, for the electron-rich tripnictides, the ability to accommodate a hypervalent electron count is the largest in the middle rather at the end of the group. Particularly strong s,p mixing can reverse the bonding/antibonding character of MOs: thus MO 2sigma(u) that is responsible for bonding for trihalides and trichalcogenides is actually antibonding in N(3)(7)(-).     

Tetrel bonds between PhSiF3/PhTH3 (T = Si,Ge, Sn) and H3ZO (Z = N,P, As): A pentacoordinate silicon (IV) complex

The nature of the complexes PhTH₃ H₃ZO and PhSiF₃ H₃ZO (T = Si, Ge, and Sn; Z = N, P, and As) has been investigated at the MP2/aug’‐cc‐pVTZ(PP) level. These complexes are primarily stabilized by one T···O tetrel bond. Interaction energies of these complexes vary from 11 to 220 kJ/mol, and T···O separations from 1.89 to 3.09 Å. Charge transfer from the O lone pair into the C T and T H σ* antibonding orbitals leads to the stabilization of these complexes. The T···O tetrel bond between PhTH₃/PhSiF₃ and H₃NO exhibits a significant degree of covalence, characterized by the large interaction energy, negative energy density, and large charge transfer. Furthermore, a pentacoordinate silicon (IV) complex is formed in PhSiF₃ H₃NO with the Si···O distance almost close to the length of Si O bond. This indicates that the oxygen atom in N‐oxides shows a strong affinity to the silicon atom in organosilicon compounds.     

Vacuum ultraviolet spectra of CClF2CH2Cl and CClF2CHCl2, and Rydberg assignment based on ab initio molecular orbital calculations

The absorption spectra of CClF₂CH₂Cl and CClF₂CHCl₂ are measured in the spectral range 115–200 nm. The bands observed are assigned on the basis of ab initio molecular orbital calculations. The strong absorption bands in the 115–150 nm range are assigned to the transitions from lone pair orbitals of chlorine atoms to the Rydberg states. The population of the electrons in each molecular orbital (MO) is calculated to clarify the MO character. The four highest MOs for CClF₂CH₂Cl and six for CClF₂CHCl₂, which contribute to the absorption spectra in the 115–150 nm range, are typical chlorine lone pair orbitals, and are responsible for the spectra in this range.