A stress tensor and QTAIM perspective on the substituent effects of biphenyl subjected to torsion

The Quantum Theory of Atoms in Molecules (QTAIM) defines quantities in 3D space that can be easily obtained from routine quantum chemical calculations. The present investigation shows that local properties can be related quantitatively to measures traditionally connected to experimental data, such as Hammett constants. We consider the specific case of substituted biphenyl to quantify the effects of a torsion φ, 0.0° ≤ φ ≤ 180.0°, of the C—C bond linking the two phenyl rings for C₁₂H₉‐x, where x = N(CH₃)₂, NH₂, CH₃, CHO, CN, NO_2, on the entire molecule. QTAIM interpreted Hammett constants, aΔH( r_b ) are introduced and constructed using the difference between the H( r_b ) value of C₁₂H₉‐x and the C₁₂H₉‐H, biphenyl which is the reference molecule, with a constant of proportionality a. This investigation unexpectedly yields very good or good agreement for the x groups with the Hammett para‐, meta‐, and ortho‐substituent constants and is checked against para‐substituted benzene. We then proceed to present the interpreted substituent constants of seven new biphenyl substituent groups, where tabulated Hammett substituent constant values are not available; y = SiH₃, ZnCl, COOCH₃, SO₂NH₂, SO₂OH, COCl, CB₃. Consistency is found for the QTAIM interpreted biphenyl substituent constants of the seven new groups y independently using the stress tensor polarizability P_σ. In addition, a selection of future applications is discussed that highlight the usefulness of this approach. © 2016 Wiley Periodicals, Inc.     

Hydrogen–hydrogen interaction in planar biphenyl: A theoretical study based on the interacting quantum atoms and Hirshfeld atomic energy partitioning methods

The nature of H‐H interaction between ortho‐hydrogen atoms in planar biphenyl is investigated by two different atomic energy partitioning methods, namely fractional occupation iterative Hirshfeld (FOHI) and interacting quantum atoms (IQA), and compared with the traditional virial‐based approach of quantum theory of atoms in molecules (QTAIM). In agreement with Bader's hypothesis of H? H bonding, partitioning the atomic energy into intra‐atomic and interatomic terms reveals that there is a net attractive interaction between the ortho‐hydrogens in the planar biphenyl. This falsifies the classical view of steric repulsion between the hydrogens. In addition, in contrast to the traditional QTAIM energy analysis, both FOHI and IQA show that the total atomic energy of the ortho‐hydrogens remains almost constant when they participate in the H‐H interaction. Although, the interatomic part of atomic energy of the hydrogens plays a stabilizing role during the formation of the H? H bond, it is almost compensated by the destabilizing effects of the intra‐atomic parts and consequently, the total energy of the hydrogens remains constant. The trends in the changes of intra‐atomic and interatomic energy terms of ortho‐hydrogens during H? H bond formation are very similar to those observed for the H₂ molecule. © 2014 Wiley Periodicals, Inc.     

Assessment of intermolecular interactions at three sites of the arylalkyne in phenylacetylene‐containing lithium‐bonded complexes: Ab initio and QTAIM studies

The intermolecular interactions existing at three different sites between phenylacetylene and LiX (X = OH, NH₂, F, Cl, Br, CN, NC) have been investigated by means of second‐order Møller?Plesset perturbation theory (MP2) calculations and quantum theory of “atoms in molecules” (QTAIM) studies. At each site, the lithium‐bonding interactions with electron‐withdrawing groups (? F, ? Cl, ? Br, ? CN, ? NC) were found to be stronger than those with electron‐donating groups (? OH and ? NH₂). Molecular graphs of C₆H₅C?CH···LiF and πC₆H₅C?CH···LiF show the same connectional positions, and the electron densities at the lithium bond critical points (BCPs) of the πC₆H₅C?CH···LiF complexes are distinctly higher than those of the σC₆H₅C?CH···LiF complexes, indicating that the intermolecular interactions in the C₆H₅C?CH···LiX complexes can be mainly attributed to the π‐type interaction. QTAIM studies have shown that these lithium‐bond interactions display the characteristics of “closed‐shell” noncovalent interactions, and the molecular formation density difference indicates that electron transfer plays an important role in the formation of the lithium bond. For each site, linear relationships have been found between the topological properties at the BCP (the electron density ρ_b, its Laplacian ?²ρ_b, and the eigenvalue λ₃ of the Hessian matrix) and the lithium bond length d(Li‐bond). The shorter the lithium bond length d(Li‐bond), the larger ρ_b, and the stronger the π···Li bond. The shorter d(Li‐bond), the larger ?²ρ_b, and the greater the electrostatic character of the π···Li bond. © 2012 Wiley Periodicals, Inc.     

Experimental and theoretical study of the intramolecular C–H···N and C–H···S hydrogen bonding effects in the 1H and 13C NMR spectra of the 2‐(alkylsulfanyl)‐5‐amino‐1‐vinylpyrroles: a particular state of amine nitrogen

In the ¹H NMR spectra of the 1‐vinylpyrroles with amino‐ and alkylsulfanyl groups in 5 and 2 positions, an extraordinarily large difference between resonance positions of the H_A and H_B terminal methylene protons of the vinyl group is discovered. Also, the one‐bond ¹J(C_β,H_B) coupling constant is surprisingly greater than the ¹J(C_β,H_A) coupling constant in pyrroles under investigation, while in all known cases, there was a reverse relationship between these coupling constants. These spectral anomalies are substantiated by quantum chemical calculations. The calculations show that the amine nitrogen lone pair is removed from the conjugation with the π‐system of the pyrrole ring so that it is directed toward the H_B hydrogen. These factors are favorable to the emergence of the intramolecular C–H_B???N hydrogen bonding in the s‐cis(N) conformation. On the other hand, the spatial proximity of the sulfur to the H_B hydrogen provides an opportunity of the intramolecular C–H_B???S hydrogen bonding in the s‐cis(S) conformation. Presence of the hydrogen bond critical points as well as ring critical point for corresponding chelate ring revealed by a quantum theory of atoms in molecules (QTAIM) approach confirms the existence of the weak intramolecular C–H???N and C–H???S hydrogen bonding. Therefore, an unusual high‐frequency shift of the H_B signal and the increase in the ¹J(C_β,H_B) coupling constant can be explained by the effects of hydrogen bonding. Copyright © 2013 John Wiley & Sons, Ltd.     

2,4‐Bis(α,α‐di­methyl­benzyl)­phenol

The structure of the title compound, 2,4‐bis(1‐methyl‐1‐phenylethyl)phenol, C₂₄H₂₆O, was found to have a torsion angle of 129.95 (13)° for the C—C bond that connects the benzyl carbon to the phenol ring ortho to the OH group. A value of ～50° was expected from molecular mechanics calculations. Intermolecular interactions, in particular O—H?O and edge–face π bonding, may contribute to this discrepancy. Intramolecular O—H?π bonding is also observed.     

4‐Fluoro‐2‐(phospho­no­methyl)­benzene­sulfonic acid monohydrate

The title compound, C₇H₈FO₆PS·H₂O, contains both phospho­nic and sulfonic acid functionalities. An extensive network of O—H?O hydrogen bonds is present in the crystal structure. The three acidic protons are associated with the phospho­nate group. Two protons experience typical hydrogen‐bond contacts with the sulfonate‐O atoms, while the third has a longer covalent bond of 1.05 (3) Å to the phospho­nate‐O atom and a short hydrogen‐bond contact of 1.38 (3) Å to the water O atom (all O—H?O angles are in the range 162–175°). The sulfonate group is positioned so that one S—O bond is nearly coplanar with the phenyl ring [torsion angle O—S—C—C ?8.6 (2)°]. The phospho­nate group is oriented approximately perpendicular to the ring [torsion angle P—C—C—C 99.2 (2)°] with one P—O bond anti to the benzyl C—C bond. The mol­ecules pack in layers in the b–c plane with the water mol­ecules in between adjacent pairs of inverted layers.     

Glycosidic linkage,N‐acetyl side‐chain,and other structural properties of methyl 2‐acetamido‐2‐deoxy‐β‐d‐glucopyranosyl‐(1→4)‐β‐d‐mannopyranoside monohydrate and related compounds

The crystal structure of methyl 2‐acetamido‐2‐deoxy‐β‐d ‐glycopyranosyl‐(1→4)‐β‐d ‐mannopyranoside monohydrate, C₁₅H₂₇NO₁₁·H₂O, was determined and its structural properties compared to those in a set of mono‐ and disaccharides bearing N‐acetyl side‐chains in βGlcNAc aldohexopyranosyl rings. Valence bond angles and torsion angles in these side chains are relatively uniform, but C—N (amide) and C—O (carbonyl) bond lengths depend on the state of hydrogen bonding to the carbonyl O atom and N—H hydrogen. Relative to N‐acetyl side chains devoid of hydrogen bonding, those in which the carbonyl O atom serves as a hydrogen‐bond acceptor display elongated C—O and shortened C—N bonds. This behavior is reproduced by density functional theory (DFT) calculations, indicating that the relative contributions of amide resonance forms to experimental C—N and C—O bond lengths depend on the solvation state, leading to expectations that activation barriers to amide cis–trans isomerization will depend on the polarity of the environment. DFT calculations also revealed useful predictive information on the dependencies of inter‐residue hydrogen bonding and some bond angles in or proximal to β‐(1→4) O‐glycosidic linkages on linkage torsion angles ? and ψ. Hypersurfaces correlating ? and ψ with the linkage C—O—C bond angle and total energy are sufficiently similar to render the former a proxy of the latter.     

The effect of hydrogen bonding on the conformations of 2‐(1H‐indol‐3‐yl)‐2‐oxoacetamide and 2‐(1H‐indol‐3‐yl)‐N,N‐dimethyl‐2‐oxoacetamide

In the title compounds, C₁₀H₈N₂O₂, (I), and C₁₂H₁₂N₂O₂, (II), the two carbonyl groups are oriented with torsion angles of −149.3 (3) and −88.55 (15)°, respectively. The single‐bond distances linking the two carbonyl groups are 1.528 (4) and 1.5298 (17) Å, respectively. In (I), the molecules are linked by an elaborate system of N—H...O hydrogen bonds, which form adjacent R²₂(8) and R⁴₂(8) ring motifs to generate a ladder‐like construct. Adjacent ladders are further linked by N—H...O hydrogen bonds to build a three‐dimensional network. The hydrogen bonding in (II) is far simpler, consisting of helical chains of N—H...O‐linked molecules that follow the 2₁ screw of the b axis. It is the presence of an elaborate hydrogen‐bonding system in the crystal structure of (I) that leads to the different torsion angle for the orientation of the two adjacent carbonyl groups from that in (II).     

Helical supramolecular assembly of N2,N2′‐bis[3‐(morpholin‐4‐yl)propyl]‐N1,N1′‐(1,2‐phenylene)dioxalamide dimethyl sulfoxide monosolvate

In the title compound, C₂₄H₃₆N₆O₆·C₂H₆OS, the carbonyl groups are in an antiperiplanar conformation, with O=C—C=O torsion angles of 178.59 (15) and −172.08 (16)°. An intramolecular hydrogen‐bonding pattern is depicted by four N—H...O interactions, which form two adjacent S(5)S(5) motifs, and an N—H...N interaction, which forms an S(6) ring motif. Intermolecular N—H...O hydrogen bonding and C—H...O soft interactions allow the formation of a meso‐helix. The title compound is the first example of a helical 1,2‐phenylenedioxalamide. The oxalamide traps one molecule of dimethyl sulfoxide through N—H...O hydrogen bonding. C—H...O soft interactions give rise to the two‐dimensional structure.     

Crystallographic characterization of the first reported crystalline form of the potent hallucinogen (R)‐2‐amino‐1‐(8‐bromobenzo[1,2‐b;5,4‐b′]difuran‐4‐yl)propane or `bromodragonfly': the 1:1 anhydrous proton‐transfer compound with 3,5‐dinitrosalicylic acid

The 1:1 proton‐transfer compound of the potent substituted amphetamine hallucinogen (R)‐2‐amino‐1‐(8‐bromobenzo[1,2‐b;5,4‐b′]difuran‐4‐yl)propane (common trivial name `bromodragonfly') with 3,5‐dinitrosalicylic acid, namely 1‐(8‐bromobenzo[1,2‐b;5,4‐b′]difuran‐4‐yl)propan‐2‐aminium 2‐carboxy‐4,6‐dinitrophenolate, C₁₃H₁₃BrNO₂⁺·C₇H₃N₂O₇⁻, forms hydrogen‐bonded cation–anion chain substructures comprising undulating head‐to‐tail anion chains formed through C(8) carboxyl–nitro O—H...O associations and incorporating the aminium groups of the cations. The intrachain cation–anion hydrogen‐bonding associations feature proximal cyclic R₃³(8) interactions involving both an N⁺—H...O_phenolate and the carboxyl–nitro O—H...O associations and aromatic π–π ring interactions [minimum ring centroid separation = 3.566 (2) Å]. A lateral hydrogen‐bonding interaction between the third aminium H atom and a carboxyl O‐atom acceptor links the chain substructures, giving a two‐dimensional sheet structure. This determination represents the first of any form of this compound and is in the (R) absolute configuration. The atypical crystal stability is attributed both to the hydrogen‐bonded chain substructures provided by the anions, which accommodate the aminium proton‐donor groups of the cations and give crosslinking, and to the presence of the cation–anion aromatic ring π–π interactions.     

Perturbed structures generated using coordinates derived from compliance constants in internal vibrations for QTAIM dual functional analysis: Intrinsic dynamic nature of interactions

Perturbed structures for QTAIM dual functional analysis (QTAIM‐DFA) are proposed to generate using the coordinates corresponding to the compliance force constants in internal vibrations (CIV). In QTAIM‐DFA, total electron energy densities H_b( r _c) are plotted versus H_b( r _c) – V_b( r _c)/2 at bond critical points (BCPs) of interactions in question, where V_b( r _c) are potential energy densities at BCPs. Each plot of an interaction based on the data from both perturbed structures and fully optimized one takes the form (θ_p, κ_p), where θ_p corresponds to the tangent line of the plot and κ_p is the curvature. The θ_p values evaluated with CIV are equal to those obtained by partial optimizations with the interaction distance in question being fixed suitably, within the calculation errors. Very high applicability of CIV is demonstrated to generate the perturbed structures for QTAIM‐DFA. Dynamic nature of interactions based on (θ_p, κ_p) with CIV is called “intrinsic dynamic nature of interactions.”     

Structures,vibrational frequencies,topologies, and energies of hydrogen bonds in cysteine‐formaldehyde complexes

The hydrogen bonding interactions between cysteine (Cys) and formaldehyde (FA) were studied with density functional theory regarding their geometries, energies, vibrational frequencies, and topological features of the electron density. The quantum theory of atoms in molecules and natural bond orbital analyses were employed to elucidate the interaction characteristics in the Cys‐FA complexes. The intramolecular hydrogen bonds (H‐bonds) formed between the hydroxyl and the N atom of cysteine moiety in some Cys‐FA complexes were strengthened because of the cooperativity. Most of intermolecular H‐bonds involve the O atom of cysteine/FA moiety as proton acceptors, while the strongest H‐bond involves the O atom of FA moiety as proton acceptor, which indicates that FA would rather accept proton than providing one. The H‐bonds formed between the CH group of FA and the S atom of cysteine in some complexes are so weak that no hydrogen bonding interactions exist among them. In most of complexes, the orbital interaction of H‐bond is predominant during the formation of complex. The electron density (ρ_b) and its Laplace (?²ρ_b) at the bond critical point significantly correlate with the H‐bond parameter δR, while a linearly relationship between the second‐perturbation energy E(2) and ρ_b has been found as well. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A comparison of the structure,flexibility and mesogenic properties of 4-methoxy-4′-cyanobiphenyl and the α,α,α-trifluorinated derivative

Abstract

The compound 4-cyano-4′-(α,α,α-trifluoromethoxy)biphenyl (1OCBF₃) has been synthesized. Unlike the fully protonated analogue, 4-cyano-4′-methoxybiphenyl (1OCB), it does not show a liquid crystalline phase on cooling from the melting point (51°C) to room temperature. The transition temperature to a monotropic nematic phase was obtained as approximately 0°C by determining the transition temperatures of mixtures with 1OCB. The structures, conformational properties and orientational ordering of both 1OCB and 1OCBF₃ as solutes in a nematic solvent ZLI 1132 have been investigated via the 17 dipolar couplings obtained by analysing the proton and fluorine NMR spectra of these solutions. It is concluded that the major difference between the two molecules lies in the potential, V(φ₂), governing rotation about the ring–oxygen bonds. In 1OCB the potential has the same form as in anisole, with a minimum when the C–O bond is in the plane of the attached ring (φ₂ = 0°), and a maximum of about 15 kJ mol^?1 when φ₂ is 90°. In 1OCBF₃ the barrier to rotation about the ring–O bond decreases substantially to being near zero.     

A one‐dimensional zinc(II) coordination polymer incorporating [1,1′‐biphenyl]‐4,4′‐dicarboxylate and N,N′‐bis(pyridin‐3‐ylmethyl)‐[1,1′‐biphenyl]‐4,4′‐dicarboxamide ligands

In the title compound, catena‐poly[[[N,N′‐bis(pyridin‐3‐ylmethyl)‐[1,1′‐biphenyl]‐4,4′‐dicarboxamide]chloridozinc(II)]‐μ‐[1,1′‐biphenyl]‐4,4′‐dicarboxylato‐[[N,N′‐bis(pyridin‐3‐ylmethyl)‐[1,1′‐biphenyl]‐4,4′‐dicarboxamide]chloridozinc(II)]‐μ‐[N,N′‐bis(pyridin‐3‐ylmethyl)‐[1,1′‐biphenyl]‐4,4′‐dicarboxamide]], [Zn₂(C₁₄H₈O₄)Cl₂(C₂₆H₂₂N₄O₂)₃]_n, the Zn^II centre is four‐coordinate and approximately tetrahedral, bonding to one carboxylate O atom from a bidentate bridging dianionic [1,1′‐biphenyl]‐4,4′‐dicarboxylate ligand, to two pyridine N atoms from two N,N′‐bis(pyridin‐3‐ylmethyl)‐[1,1′‐biphenyl]‐4,4′‐dicarboxamide ligands and to one chloride ligand. The pyridyl ligands exhibit bidentate bridging and monodentate terminal coordination modes. The bidentate bridging pyridyl ligand and the bridging [1,1′‐biphenyl]‐4,4′‐dicarboxylate ligand both lie on special positions, with inversion centres at the mid‐points of their central C—C bonds. These bridging groups link the Zn^II centres into a one‐dimensional tape structure that propagates along the crystallographic b direction. The tapes are interlinked into a two‐dimensional layer in the ab plane through N—H...O hydrogen bonds between the monodentate ligands. In addition, the thermal stability and solid‐state photoluminescence properties of the title compound are reported.     

2,2′‐Bi(9,9‐di­hexyl­fluorene)

The central part of the title mol­ecule, C₅₀H₆₆, is planar, all the rings being in the same plane; the lateral chains are also planar (excluding H atoms), almost perpendicular to the ring plane and grafted on the same side of the mol­ecule. The mol­ecule has nearly a mirror plane, perpendicular to the central C—C bond, instead of the centre of symmetry expected. The orientation of the plane of the rings is approximately 45° from the unit‐cell b axis, so that neighbouring mol­ecules are essentially perpendicular.     

Three structures containing (E)‐1,2‐bis­(benzimidazol‐2‐yl)ethene groups

Two of the title compounds, namely (E)‐1,2‐bis­(1‐methyl­benzimidazol‐2‐yl)ethene, C₁₈H₁₆N₄, (Ib), and (E)‐1,2‐bis­(1‐ethyl­benzimidazol‐2‐yl)ethene, C₂₀H₂₀N₄, (Ic), consist of centrosymmetric trans‐bis­(1‐alkyl­benzimidazol‐2‐yl)ethene mol­ecules, while 3‐eth­yl‐2‐[(E)‐2‐(1‐ethyl­benzimidazol‐2‐yl)­ethen­yl]benzimidazol‐1‐ium perchlorate, C₂₀H₂₁N₄⁺·ClO₄⁻, (II), contains the monoprotonated analogue of compound (Ic). In the three structures, the benzimidazole and benzimidazolium moieties are essentially planar; the geometric parameters for the ethene linkages and their bonds to the aromatic groups are consistent with double and single bonds, respectively, implying little, if any, conjugation of the central C=C bonds with the nitro­gen‐containing rings. The C—N bond lengths in the N=C—N part of the benzimidazole groups differ and are consistent with localized imine C=N and amine C—N linkages in (Ib) and (Ic); in contrast, the corresponding distances in the benzimidazolium cation are equal in (II), consistent with electron delocalization resulting from protonation of the amine N atom. Crystals of (Ib) and (Ic) contain columns of parallel mol­ecules, which are linked by edge‐over‐edge C—H⋯π overlap. The columns are linked to one another by C—H⋯π inter­actions and, in the case of (Ib), C—H⋯N hydrogen bonds. Crystals of (II) contain layers of monocations linked by π–π inter­actions and separated by both perchlorate anions and the protruding eth­yl groups; the cations and anions are linked by N—H⋯O hydrogen bonds.     

Density functional theory and topological analysis on the hydrogen bonding interactions in cysteine‐thymine complexes

Hydrogen bonding interactions between amino acids and nucleic acid bases constitute the most important interactions responsible for the specificity of protein binding. In this study, complexes formed by hydrogen bonding interactions between cysteine and thymine have been studied by density functional theory. The relevant geometries, energies, and IR characteristics of hydrogen bonds (H‐bonds) have been systematically investigated. The quantum theory of atoms in molecule and natural bond orbital analysis have also been applied to understand the nature of the hydrogen bonding interactions in complexes. More than 10 kinds of H‐bonds including intra‐ and intermolecular H‐bonds have been found in complexes. Most of intermolecular H‐bonds involve O (or N) atom as H‐acceptor, whereas the H‐bonds involving C or S atom usually are weaker than other ones. Both the strength of H‐bonds and the structural deformation are responsible for the stability of complexes. Because of the serious deformation, the complex involving the strongest H‐bond is not the most stable structures. Relationships between H‐bond length (ΔR_X‐H), frequency shifts (Δv), and the electron density (ρ_b) and its Laplace (?²ρ_b) at bond critical points have also been investigated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

1,7‐Dideaza‐2′‐deoxy‐6‐nitronebularine: a pyrrolo[2,3‐b]pyridine nucleoside with an intramolecular hydrogen bond stabilizing the syn conformation

The title compound [systematic name: 1‐(2‐deoxy‐β‐D‐erythro‐pentofuranosyl)‐4‐nitro‐1H‐pyrrolo[2,3‐b]pyridine], C₁₂H₁₃N₃O₅, forms an intramolecular hydrogen bond between the pyridine N atom as acceptor and the 5′‐hydroxy group of the sugar residue as donor. Consequently, the N‐glycosylic bond exhibits a syn conformation, with a χ torsion angle of 61.6 (2)°, and the pentofuranosyl residue adopts a C2′‐endo envelope conformation (²E, S‐type), with P = 162.1 (1)° and τ_m = 36.2 (1)°. The orientation of the exocyclic C4′—C5′ bond is +sc (gauche, gauche), with a torsion angle γ = 49.1 (2)°. The title nucleoside forms an ordered and stacked three‐dimensional network. The pyrrole ring of one layer faces the pyridine ring of an adjacent layer. Additionally, intermolecular O—H...O and C—H...O hydrogen bonds stabilize the crystal structure.