The generalized block-localized wavefunction method: a case study on the conformational preference and C-O rotational barrier of formic acid

A Lewis structure corresponding to the most stable electron-localized state is often used as a reference for the measure of electron delocalization effect in the valence bond (VB) theory. As the simplest variant of ab initio VB theory, the generalized block-localized wavefunction (BLW) method defines the wavefunction for an electron-localized state with block-localized orbitals without the orthogonalization constraint on different blocks. The validity of the method can be critically examined with experimental evidences. Here the BLW method has been applied to the investigation of the roles of both the π conjugation and σ hyperconjugation effects in the conformational preference of formic acid for the trans (Z) conformer over the cis (E) conformer. On one hand, our computations showed that the deactivation of the π conjugation or σ hyperconjugation has little impact on the Z-E energy gap, thus neither is decisive and instead the local dipole-dipole electrostatic interaction between the carbonyl and hydroxyl groups is the key factor determining the Z-E energy gap. On the other hand, the present study supported the conventional view that π conjugation is largely responsible for the C-O rotation barrier in formic acid, though the existence of hyperconjugative interactions in the perpendicular structure lowers the barrier considerably.     

Electron Density Analysis of Hyperconjugation

Hyperconjugation is analyzed through the electron density of orbitals responsible for hyperconjugative interactions, which cannot be detected by means of conventional electron‐density‐based calculations. This interaction is detected through the π electron density topology, by excluding σ electron density from the total. As the presence of the hyperconjugation phenomenon in carbocation systems is well understood, several carbocations are benchmarked, and the results show that the positive carbon atom establishes a hyperconjugative critical point with the adjacent methyl group(s). Also, π localization and delocalization indices are employed to support the conclusions made by the topological analysis.     

Source of Cooperativity in Halogen‐Bonded Haloamine Tetramers

Inspired by the isostructural motif in α‐bromoacetophenone oxime crystals, we investigated halogen–halogen bonding in haloamine quartets. Our Kohn–Sham molecular orbital and energy decomposition analysis reveal a synergy that can be traced to a charge‐transfer interaction in the halogen‐bonded tetramers. The halogen lone‐pair orbital on one monomer donates electrons into the unoccupied σ*_N?X orbital on the perpendicular N?X bond of the neighboring monomer. This interaction has local σ symmetry. Interestingly, we discovered a second, somewhat weaker donor–acceptor interaction of local π symmetry, which partially counteracts the aforementioned regular σ‐symmetric halogen‐bonding orbital interaction. The halogen–halogen interaction in haloamines is the first known example of a halogen bond in which back donation takes place. We also find that this cooperativity in halogen bonds results from the reduction of the donor–acceptor orbital‐energy gap that occurs every time a monomer is added to the aggregate.     

Isolation of Elusive Phosphinidene-Chlorotetrylenes: The Heavier Cyanogen Chloride Analogues

The elusive phosphinidene-chlorotetrylenes, [PGeCl] and [PSiCl] have been stabilized by the hetero-bileptic cyclic alkyl(amino) carbene (cAAC), N-heterocyclic carbene (NHC) ligands, and isolated in the solid state at room temperature as the first neutral monomeric species of this class with the general formulae (L)P-ECl(L′) (E=Ge, 3 a – 3 c ; E=Si, 6 ; L=cAAC; L′=NHC). Compounds 3 a – 3 c have been synthesized by the reaction of cAAC-supported potassium phosphinidenides [cAAC=PK(THF)_x]_n ( 1 a – 1 c ) with the adduct NHC:→GeCl₂ ( 2 ). Similarly, compound 6 has been synthesized via reaction of 1 a with NHC:→SiCl₂ adduct ( 4 ). Compounds 3 a – 3 c , and 6 have been structurally characterized by single-crystal X-ray diffraction, NMR spectroscopy and mass spectrometric analysis. DFT calculations revealed that the heteroatom P in 3 bears two lone pairs; the non-bonding pair with 67.8 % of s- and 32 % of p character, whereas the other lone pair is involved in π backdonation to the C_cAAC-N π* of cAAC. The Ge atom in 3 contains a lone pair with 80 % of s character, and slightly involved in the π backdonation to C_NHC. EDA-NOCV analyses showed that two charged doublet fragments {(cAAC)(NHC)}⁺, and {PGeCl}⁻ prefer to form one covalent electron-sharing σ bond, one dative σ bond, one dative π bond, and a charge polarized weak π bond. The covalent electron-sharing σ bond contributes to the major stabilization energy to the total orbital interaction energy of 3 , enabling the first successful isolations of this class of compounds ( 3 , 6 ) in the laboratory.     

Stereoelectronic Effects on the Nucleophilic Addition of Phosphite to the Carbonyl Double Bond: Ab Initio Molecular Orbital Calculations on Reaction Surfaces and the α-Effect

Ah initio molecular orbital calculations have been carried out on adducts of trihydroxy phosphine, P(OH)₃, and formaldehyde, H₂C=0. Stationary points were located and a reaction surface calculated. One stationary point exists as a stable pentacovalent phosphorane, and the other as a 1,3-dipolar transition state. Calculations differing in the conformation about the P-OH bonds of the phosphite reveal that an antiperiplanar (app) lone pair on oxygen to the phosphorus lone pair (acyclic analogue) raises the energy of the molecule by 1.7 kcal/mol relative to a phosphite conformation with no app lone pairs to the phosphorus lone pair (bicyclic analogue). In the transition state, the relative energy between the two conformations reverses with the acyclic analogue transition state 5 kcal/mol lower energy than the bicyclic analogue transition states. The lower energy for the acyclic analogue in the transition state is attributed to the mixing of the app lone pairs on the oxygens of the phosphite mixing with the σ orbital of the newly formed bond between phosphorus and carbon. This kinetic Stereoelectronic effect can explain why acyclic phosphites react much faster in nucleophilic reactions than bicyclic phosphites. This phenomenon suggests that the origin of the α-effect, the enhanced nucleophilicity of a base possessing a heteroatom with an adjacent unshared electron pair arises from the stereoelectronic effect.     

The mutual effect of a carbonyl polar bond and an endocyclic oxygen on the 1JC‐F coupling constant of fluorinated six‐membered rings

The ¹J_C‐F coupling constant can be useful to probe the conformational landscape of organofluorine compounds and the intramolecular interactions governing the stereochemistry of these compounds. Neighboring oxygen electron lone pairs and a carbonyl group relative to a C─F bond affect this coupling constant in an opposite way, and therefore, analysis of the interactions involving these entities simultaneously indicates which effect dominates ¹J_C‐F. Spin–spin coupling constant calculations for a series of fluorinated tetrahydropyrans, cyclohexanones, and dihydropyran‐3‐ones indicated that an electrostatic/dipolar interaction between the C─F and C═O bonds is more important than the steric interaction between the C─F bond and the oxygen electron lone pairs. An intuitive consequence of such outcome is that this interaction not only drives the coupling constant but can also be taken into account when aiming at the stereochemical control of functionalized organofluorine compounds.     

2‐(N,N‐Diphenylamino)benzoic acid

Shaped like a distorted propeller, mol­ecules of the title compound, C₁₉H₁₅NO₂, form centrosymmetric dimers in the crystalline phase in which the carboxy groups are linked through two hydrogen bonds. These dimers are arranged in columns held together via dispersive interactions between the phenyl moieties. The N atom and the three surrounding C atoms lie almost in the same plane, which implies that the lone electron pair of the N atom is involved in conjugation with the π systems of the phenyl fragments.     

Bonding Analysis of N‐Heterocyclic Carbene Tautomers and Phosphine Ligands in Transition‐Metal Complexes: A Theoretical Study

DFT calculations at the BP86/TZ2P level were carried out to analyze quantitatively the metal–ligand bonding in transition‐metal complexes that contain imidazole (IMID), imidazol‐2‐ylidene (nNHC), or imidazol‐4‐ylidene (aNHC). The calculated complexes are [Cl₄TM(L)] (TM=Ti, Zr, Hf), [(CO)₅TM(L)] (TM=Cr, Mo, W), [(CO)₄TM(L)] (TM=Fe, Ru, Os), and [ClTM(L)] (TM=Cu, Ag, Au). The relative energies of the free ligands increase in the order IMID<nNHC<aNHC. The energy levels of the carbon σ lone‐pair orbitals suggest the trend aNHC>nNHC>IMID for the donor strength, which is in agreement with the progression of the metal–ligand bond‐dissociation energy (BDE) for the three ligands for all metals of Groups 4, 6, 8, and 10. The electrostatic attraction can also be decisive in determining trends in ligand–metal bond strength. The comparison of the results of energy decomposition analysis for the Group 6 complexes [(CO)₅TM(L)] (L=nNHC, aNHC, IMID) with phosphine complexes (L=PMe₃ and PCl₃) shows that the phosphine ligands are weaker σ donors and better π acceptors than the NHC tautomers nNHC, aNHC, and IMID.     

A theoretical exploration of unexpected amine···π interactions

Counterintuitive amine lone pair···π interactions are computationally revealed by MP2 and CCSD(T) methods, attractive lone pair···π interactions are observed when the lone pair of nitrogen points toward the π system. Symmetry adapted perturbation theory (SAPT) calculations and atoms in molecules (AIM) analyses were performed and the origin of the calculated attractive interaction between nitrogen lone pairs and π rings is discussed. Dispersion effects were revealed to play a crucial role in the attractive lone pair···π interaction.     

π-Orbital electron–energy contributions to chemical reaction heats,I. Reactions involving only linear molecules containing up to three first–row atoms

Ab initio calculations of various expectation energies have been made for the reactant and product species in six reactions that involve only small linear molecules. The reactions include fission by hydrogen, addition of hydrogen, exchange of triply bonded atoms, fluorination, and oxygen atom transfer. The change in total electronic energy is not invariably the result of changes in inner shell energy and outer shell σ- and π-electron energies simply augmenting each other, but in several cases there is a complex interplay of opposing effects. This approach gives a different insight into the energetic aspects of changes in bonding from that derived from the concept of shared electron pairs in σ and π bonds together with lone pairs in valence shells. Changes in π-electron energy are shown to be important in a reaction in which neither reactant nor product molecules contain π bonds in the usual chemical sense. While in a reaction in which there is a complete change in the nature of the triple bonds, and hence the π bonding, the change in π-electron energy makes a smaller contribution than either the change in inner shell or the outer shell σ-electron energies.     

A unique transition metal-stabilized silicon cation

Trivalent silicon cations are exceptionally strong electron pair acceptors that react, either desired or undesired, with almost any σ and π basic molecule. One way of intramolecular attenuation of the Lewis acidity of these superelectrophiles is by installation of a ferrocene unit at the electron-deficient silicon atom. While well-understood for isoelectronic α-ferrocenyl-substituted carbenium ions and also boranes, the stabilizing interactions between the ferrocene backbone and a positively charged silicon atom are not clear due to the challenge of crystallizing such cations. The structural characterization of our ferrocene-stabilized silicon cation now reveals an unprecedented bonding motif different from its analogues. An extreme dip angle of the silicon atom toward the iron atom is explained by two three-center-two-electron (3c2e) bonds through participation of both the upper and the lower aromatic rings of the ferrocene sandwich structure. The positive charge is still localized at the silicon atom that also retains a quasi-planar configuration.     

Theoretical study on two types of weak interactions between methylenecyclopropane and XY (X,Y = H,F, Cl,and Br)

We present theoretical evidence that the two types of interactions exist in the complexes formed between methylenecyclopropane (MECP) and XY (X, Y = H, F, Cl, and Br). Two seats of XY interacted with MECP are located: (a) is via the pseudo‐π bonding electron pair associated with a C? C bond of the cyclopropane ring and (b) is via the typical‐π bonding of electron pair of the C?C bond of MECP. These two types of weak interactions are compared based on the calculated geometries, interaction energies, frequency changes, and topological properties of electron density. The integration of electron density over the interatomic surface is found to be a good measure for the strength of weak interaction. Furthermore, the total electron density and separated σ and π electron densities are also computed and discussed in this article. The separated electron density shows σ electron density determined the strength and π electron density influenced the direction of the hydrogen/halogen bond. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Hydrogen‐Bonding Interactions and Properties of Energetic Nitroamino[1,3,5]triazine‐Based Guanidinium Salts: DFT‐D and QTAIM Studies

The intramolecular hydrogen‐bonding interactions and properties of a series of nitroamino[1,3,5]triazine‐based guanidinium salts were studied by using the dispersion‐corrected density functional theory method (DFT‐D). Results show that there are evident LP(N or O; LP=lone pair)→σ*(N? H) orbital interactions related to O???H? N or N???H? N hydrogen bonds. Quantum theory of atoms in molecules (QTAIM) was applied to characterize the intramolecular hydrogen bonds. For the guanidinium salts studied, the intramolecular hydrogen bonds are associated with a seven‐ or eight‐membered pseudo‐ring. The guanylurea cation is more helpful for improving the thermal stabilities of the ionic salts than other guanidinium cations. The contributions of different substituents on the triazine ring to the thermal stability increase in the order of ? NO₂23 (? ONO₂)2. Energy decomposition analysis shows that the salts are stable owing to electrostatic and orbital interactions between the ions, whereas the dispersion energy has very small contributions. Moreover, the salts exhibit relatively high densities in the range of 1.62–1.89 g cm^?3. The detonation velocities and pressures lie in the range of 6.49–8.85 km s^?1 and 17.79–35.59 GPa, respectively, which makes most of them promising explosives.     

Moving toward Ylide‐Stabilized Carbenes

The effect of ylide substitution at the α position to the carbene carbon (C_c) atom on the stability and σ‐donating ability of a number of cyclic carbenes has been studied theoretically. The stabilities of all of the carbenes were investigated from an evaluation of their singlet–triplet energy gaps and stabilization energies. All carbenes were found to have a stable singlet state. The energy of the σ‐symmetric lone‐pair orbital at the C_c atom increases as a result of the introduction of ylide centers near to the C_c atom. This indicates an enhanced σ‐donating ability of the ylide‐containing carbenes. The calculated carbonyl‐stretching frequencies of the corresponding rhodium complexes, proton affinities, and nucleophilicity index values correlate well with the σ basicity of the carbenes.     

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.     

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.     

Transition‐Metal Complexes of Tetrylones [(CO)5W‐E(PPh3)2] and Tetrylenes [(CO)5W‐NHE] (E=C–Pb): A Theoretical Study

Quantum chemical calculations at the BP86/TZVPP//BP86/SVP level are performed for the tetrylone complexes [W(CO)₅‐E(PPh₃)₂] ( W‐1 E ) and the tetrylene complexes [W(CO)₅‐NHE] ( W‐2 E ) with E=C–Pb. The bonding is analyzed using charge and energy decomposition methods. The carbone ligand C(PPh₃) is bonded head‐on to the metal in W‐1 C , but the tetrylone ligands E(PPh₃)₂ are bonded side‐on in the heavier homologues W‐1 Si to W‐1 Pb . The W? E bond dissociation energies (BDEs) increase from the lighter to the heavier homologues ( W‐1 C : D_e=25.1 kcal mol^?1; W‐1 Pb : D_e=44.6 kcal mol^?1). The W(CO)₅←C(PPh₃)₂ donation in W‐1 C comes from the σ lone‐pair orbital of C(PPh₃)₂, whereas the W(CO)₅←E(PPh₃)₂ donation in the side‐on bonded complexes with E=Si–Pb arises from the π lone‐pair orbital of E(PPh₃)₂ (the HOMO of the free ligand). The π‐HOMO energy level rises continuously for the heavier homologues, and the hybridization has greater p character, making the heavier tetrylones stronger donors than the lighter systems, because tetrylones have two lone‐pair orbitals available for donation. Energy decomposition analysis (EDA) in conjunction with natural orbital for chemical valence (NOCV) suggests that the W? E BDE trend in W‐1 E comes from the increase in W(CO)₅←E(PPh₃)₂ donation and from stronger electrostatic attraction, and that the E(PPh₃)₂ ligands are strong σ‐donors and weak π‐donors. The NHE ligands in the W‐2 E complexes are bonded end‐on for E=C, Si, and Ge, but side‐on for E=Sn and Pb. The W? E BDE trend is opposite to that of the W‐1 E complexes. The NHE ligands are strong σ‐donors and weak π‐acceptors. The observed trend arises because the hybridization of the donor orbital at atom E in W‐2 E has much greater s character than that in W‐1 E , and even increases for heavier atoms, because the tetrylenes have only one lone‐pair orbital available for donation. In addition, the W? E bonds of the heavier systems W‐2 E are strongly polarized toward atom E, so the electrostatic attraction with the tungsten atom is weak. The BDEs calculated for the W? E bonds in W‐1 E , W‐2 E and the less bulky tetrylone complexes [W(CO)₅‐E(PH₃)₂] ( W‐3 E ) show that the effect of bulky ligands may obscure the intrinsic W? E bond strength.     

A theoretical approach to substituent effects. Structural consequences of electrostatic and orbital interactions in model mono- and disubstituted methanes

Ab initio molecular orbital theory is used to examine the effect of substituents on bond lengths in mono- and disubstituted methanes. The relative importance of electrostatic and orbital interaction terms are assessed. The results suggest that for substituents (X) which show powerful σ effects and weak π interactions (e.g., F), the changes in bond length are due primarily to the electrostatic component except in some disubstituted methanes in which case the change in the hyperconjugative ability of the C—X bond is also important. On the other hand, substituents X which show weak σ effects but powerful π interactions (e.g., NH₂) affect bond lengths primarily through hyperconjugative interaction of a filled or vacant π-type orbital on X with the adjacent bonds.     

Is Aerogen–π Interaction Capable of Initiating the Noncovalent Chemistry of Group 18?

The interactions between atoms of noble gases and π systems are generally considered as van der Waals interaction, which have not attracted attention yet. Herein, we present high‐level ab initio calculations to show the unexpected noncovalent interaction between a covalently bonded noble gas atom and a delocalized aromatic π electron using XeO₃?benzene as the prototype. The CCSD(T)/CBS reference data show its strength amounting to ?10.2 kcal mol^?1, comparable to a typical H‐bond or an anion–π interaction. The energy decomposition analysis reveals that the aerogen–π interaction is favored by the electrostatic interaction (27.7 %), the induction (13.4 %), and the dispersion (21.6 %). This interaction may prompt us to consider the noncovalent chemistry of aerogen derivatives in the near future.     

Reconciling Electrostatic and n→π* Orbital Contributions in Carbonyl Interactions

Interactions between carbonyl groups are prevalent in protein structures. Earlier investigations identified dominant electrostatic dipolar interactions, while others implicated lone pair n→π* orbital delocalisation. Here these observations are reconciled. A combined experimental and computational approach confirmed the dominance of electrostatic interactions in a new series of synthetic molecular balances, while also highlighting the distance‐dependent observation of inductive polarisation manifested by n→π* orbital delocalisation. Computational fiSAPT energy decomposition and natural bonding orbital analyses correlated with experimental data to reveal the contexts in which short‐range inductive polarisation augment electrostatic dipolar interactions. Thus, we provide a framework for reconciling the context dependency of the dominance of electrostatic interactions and the occurrence of n→π* orbital delocalisation in C=O???C=O interactions.