Biphenyl: A stress tensor and vector‐based perspective explored within the quantum theory of atoms in molecules

We use quantum theory of atoms in molecules (QTAIM) and the stress tensor topological approaches to explain the effects of the torsion φ of the C‐C bond linking the two phenyl rings of the biphenyl molecule on a bond‐by‐bond basis using both a scalar and vector‐based analysis. Using the total local energy density H( r _b), we show the favorable conditions for the formation of the controversial H–H bonding interactions for a planar biphenyl geometry. This bond‐by‐bond QTAIM analysis is found to be agreement with an earlier alternative QTAIM atom‐by‐atom approach that indicated that the H–H bonding interaction provided a locally stabilizing effect that is overwhelmed by the destabilizing role of the C‐C bond. This leads to a global destabilization of the planar biphenyl conformation compared with the twisted global minimum. In addition, the H( r _b) analysis showed that only the central torsional C‐C bond indicated a minimum for a torsion φ value coinciding with that of the conventional global energy minimum. The H–H bonding interactions are found to be topologically unstable for any torsion of the central C‐C bond away from the planar biphenyl geometry. Conversely, we demonstrate that for 0.0° < φ < 39.95° there is a resultant increase in the topological stability of the C nuclei comprising the central torsional C‐C bond. Evidence is found of the effect of the H–H bonding interactions on the torsion φ of the central C‐C bond of the biphenyl molecule in the form of the QTAIM response β of the total electronic charge density ρ( r _b). Using a vector‐based treatment of QTAIM we confirm the presence of the sharing of chemical character between adjacent bonds. In addition, we present a QTAIM interpretation of hyperconjugation and conjugation effects, the former was quantified as larger in agreement with molecular orbital (MO) theory. The stress tensor and the QTAIM H atomic basin path set areas are independently found to be new tools relevant for the incommensurate gas to solid phase transition occurring in biphenyl for a value of the torsion reaction coordinate φ ≈ 5°. © 2015 Wiley Periodicals, Inc.     

Forced Bonding and QTAIM Deficiencies: A Case Study of the Nature of Interactions in He@Adamantane and the Origin of the High Metastability

Calculations within the framework of the interacting quantum atoms (IQA) approach have shown that the interactions of the helium atom with both tertiary, tC, and secondary, sC, carbon atoms in the metastable He@adamantane (He@adam) endohedral complex are bonding in nature, whereas the earlier study performed within the framework of Bader’s quantum theory of atoms in molecules (QTAIM) revealed that only He???tC interactions are bonding. The He???tC and He???sC bonding interactions are shown to be forced by the high pressure that the helium and carbon atoms exert upon each other in He@adam. The occurrence of a bonding interaction between the helium and sC atoms, which are not linked by a bond path, clearly shows that the lack of a bond path between two atoms does not necessarily indicate the lack of a bonding interaction, as is asserted by QTAIM. IQA calculations showed that not only the destabilization of the adamantane cage, but also a huge internal destabilization of the helium atom, contribute to the metastability of He@adam, these contributions being roughly equal. This result disproves previous opinions based on QTAIM analysis that only the destabilization of the adamantane cage accounts for the endothermicity of He@adam. Also, it was found that there is no homeomorphism of the ρ( r ) and ‐v( r ) fields of He@adam. Comparison of the IQA and QTAIM results on the interactions in He@adam exposes other deficiencies of the QTAIM approach. The reasons for the deficiencies in the QTAIM approach are analyzed.     

Toward a Consistent Interpretation of the QTAIM: Tortuous Link between Chemical Bonds,Interactions, and Bond/Line Paths

Currently, bonding analysis of molecules based on the Quantum Theory of Atoms in Molecules (QTAIM) is popular; however, “misinterpretations” of the QTAIM analysis are also very frequent. In this contribution the chemical relevance of the bond path as one of the key topological entities emerging from the QTAIM’s topological analysis of the one‐electron density is reconsidered. The role of nuclear vibrations on the topological analysis is investigated demonstrating that the bond paths are not indicators of chemical bonds. Also, it is argued that the detection of the bond paths is not necessary for the “interaction” to be present between two atoms in a molecule. The conceptual disentanglement of chemical bonds/interactions from the bonds paths, which are alternatively termed “line paths” in this contribution, dismisses many superficial inconsistencies. Such inconsistencies emerge from the presence/absence of the line paths in places of a molecule in which chemical intuition or alternative bonding analysis does not support the presence/absence of a chemical bond. Moreover, computational QTAIM studies have been performed on some “problematic” molecules, which were considered previously by other authors, and the role of nuclear vibrations on presence/absence of the line paths is studied demonstrating that a bonding pattern consistent with other theoretical schemes appears after a careful QTAIM analysis and a new “interpretation” of data is performed.     

Quantum topology phase diagrams for the cis‐ and trans‐isomers of the cyclic contryphan‐Sm peptide

Within the quantum theory of atoms in molecules (QTAIM) framework we present a quantum topology phase diagram (QTPD) using the Poincaré–Hopf relation of a total of 17 all new QTAIM topologies of the cis‐ and trans‐isomers of the cyclic contryphan‐Sm peptide. The resultant QTPD consists of separate regions for the cis‐ and trans‐isomers that only overlap for topologies associated with the lowest energy minima of the cis‐ and trans‐isomers. We determine the QTAIM topologies of 29 “missing” isomers. A new, contracted formulation of the QTPD is presented, this contracted formulation includes the interamino acid bond critical points (BCPs) that link together the amino acid units, the disulphide bridge “pivot” BCP and side chain bonding interactions. The seven interamino acid BCPs linking the amino acid units coincide with the so‐called peptide backbone, the conventional qualitative approach to reduce the complexity of the peptide. We expand the interpretation of ellipticity to include the associated eigenvectors and find that higher values of the ellipticity ? are associated with a greater preference to conserve folding states. We quantify previous qualitative findings that suggested the disulfide bond is central to the folding behavior of the cyclic contryphan‐Sm peptide and why the cis‐isomer is the major form of the cyclic contryphan‐Sm peptide. © 2014 Wiley Periodicals, Inc.     

Accurate prediction of enthalpies of formation for a large set of organic compounds

This article describes a multiparameter calibration model, which improves the accuracy of density functional theory (DFT) for the prediction of standard enthalpies of formation for a large set of organic compounds. The model applies atom based, bond based, electronic, and radical environmental correction terms to calibrate the calculated enthalpies of formation at B3LYP/6‐31G(d,p) level by a least‐square method. A diverse data set of 771 closed‐shell compounds and radicals is used to train the model. The leave‐one‐out cross validation squared correlation coefficient q² of 0.84 and squared correlation coefficient r² of 0.86 for the final model are obtained. The meanabsolute error in enthalpies of formation for the dataset is reduced from 4.9 kcal/mol before calibration to 2.1 kcal/mol after calibration. Five‐fold cross validation is also used to estimate the performance of the calibration model and similar results are obtained. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

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.”     

Reinvestigation of intramolecular hydrogen bond in malonaldehyde derivatives: An ab initio,AIM and NBO study

The RAHB systems in malonaldehyde and its derivatives at MP2/ 6‐311++G(d,p) level of theory were studied and their intramolecular hydrogen bond energies by using the related rotamers method was obtained. The topological properties of electron density distribution in O? H···O intramolecular hydrogen bond have been analyzed in term of quantum theory of atoms in molecules (QTAIM). Correlations between the H‐bond strength and topological parameters are probed. The results of QTAIM clearly showed that the linear correlation between the electron density distribution at HB critical point and RAHB ring critical point with the corresponding hydrogen bond energies was obtained. Moreover, it was found a linear correlation between the electronic potential energy density, V(r_cp), and hydrogen bond energy which can be used as a simple equation for evaluation of HB energy in complex RAHB systems. Finally, the similar linear treatment between the geometrical parameters, such as O···O or O? H distance, and Lp(O)→σ*_OH charge transfer energy with the intramolecular hydrogen bond energy is observed. © 2010 Wiley Periodicals, Inc., Int J Quantum Chem, 2011     

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.     

A QTAIM and stress tensor perspective of large‐amplitude motions of the tetrasulfur tetranitride S4N4 molecular graph

The nature of the bonding interactions including the intramolecular S? S interactions in tetrasulfur tetranitride, S₄N₄ are probed by performing very large amplitude vibrations of all of the 18 normal modes of vibration. The QTAIM and stress tensor point properties are ‐then investigated and found to be highly dependent on the mode of vibration. A considerable degree of metallicity ξ( r _b) is found for the S? S and S? N bonding interactions. A unique bonding feature is found for a small amplitude vibration of the most anharmonic mode of this investigation, mode 2, where the S? S bond critical point (BCP) transforms from a closed‐shell S? S BCP to a shared‐shell S? S BCP. We find 17 new unique QTAIM topologies for the molecular graphs corresponding to the 18 modes of vibration along with seven “missing” topologies that are mapped onto a spanning 2‐D Quantum topology Phase Diagram (QTPD). In addition, eleven unique topologies existing on 3‐D QTPDs are found due to the presence of non‐nuclear attractors (NNAs). We use the stress tensor eigenvalues to explain the invariance of the numbers and types of QTAIM critical points. The applicability of both the stiffness S and stress tensor stiffness S_σ are also explored. Two new bond measures are introduced, a polarizability P and the stress tensor polarizability P_σ which are derived from the stiffness S and stress tensor stiffness S_σ, respectively. © 2016 Wiley Periodicals, Inc.     

Molecular insight into the interaction mechanisms of amino‐2H‐imidazole derivatives with BACE1 protease: A QM/MM and QTAIM study

In this study, we described quantitatively the interactions between two new amino‐2H‐imidazole inhibitors ((R)‐1t and (S)‐1m) and BACE1 using a hybrid quantum mechanics‐molecular mechanical (QM/MM) method together with a quantum theory of atoms In Molecules (QTAIM) analysis. Our computational calculations revealed that the binding affinity of these compounds is mostly related to the amino‐2H‐imidazole core, which interact tightly with the aspartate dyad of the active site. The interactions were stronger when the inhibitors presented a bulky substituent with a hydrogen bond acceptor motif pointing toward Trp76, such as the 3,5‐dimethyl‐4‐methoxyphenyl group of compound (S)‐1m. Furthermore, the QTAIM analysis revealed that many hydrophobic interactions complement cooperatively the hydrogen bond which is not present when compound (R)‐1t is bound to the enzyme. The combined QM/MM‐QTAIM analysis allows identifying the interactions that account for the activity difference between compounds, even at a nanomolar range.     

Next-generation QTAIM for scoring molecular wires in E-fields for molecular electronic devices

The effect of a varying, directional E _x , E _y, and E _z electric field on the ethene molecule was investigated using next-generation quantum theory of atoms in molecules (QTAIM). Despite using low E -field strengths that are within the realm of experiment and do not measurably alter the molecular geometry, significant changes to the QTAIM properties were observed. Using conventional QTAIM, the shifting of the C─C and C─H bond critical points (BCPs) demonstrates polarization through an interchange in the size of the atoms involved in a bond, since a BCP is located on the boundary between a pair of bonded atoms. Next-generation QTAIM, however, demonstrates the polarization effect more directly with a change in morphology of the 3-D envelope around the BCP. Modest increases of ≈ 2% in the ellipticity ε of the BCP were uncovered when the C─C bond was aligned parallel or anti-parallel to the applied E _x -field. Significant asymmetries were found in the response of the next-generation QTAIM 3-D paths of the C─H bonds to the applied E -field. When the E -field coincided with the C─C bond, the BCP moved in response and was accompanied by the envelope constructed from 3-D next-generation paths. The response displayed a polarization effect that increased with increasing magnitude of the E _x -field parallel and anti-parallel to the C─C bond. Our analysis demonstrates that next-generation QTAIM is a useful tool for understanding the response of molecules to E -fields, for example, for the screening of molecular wires for the design of molecular electronic devices. © 2019 Wiley Periodicals, Inc.     

Docking Study and Three‐Dimensional Quantitative Structure‐Activity Relationship (3D‐QSAR) Analyses and Novel Molecular Design of a Series of 4‐Aminoquinazolines as Inhibitors of Aurora B Kinase

The Aurora proteins are critical regulators of major mitotic events and attractive targets for anticancer therapy. 3D‐QSAR studies based on molecular docking were performed on a dataset of 40 4‐aminoquinazolines compounds. The CoMSIA model produced significantly better results than CoMFA model, with q²=0.652 and r²=0.991. The contours analysis provides useful information about the structural requirements for 4‐aminoquinazolines for inhibiting Aurora B. Scaffold hopping method was used to generate new structures based on the maximum common substructure of the training and test set compounds. The ADMET property, binding affinity and inhibitory activity of the new designed compounds were predicted, respectively. Finally 16 compounds were identified as the novel inhibitors for Aurora B kinase.     

Thermal dissociation of 1,2-dioxethane. II. Quantum topology of the charge distributions

The topological properties of the charge distribution of 1,2-dioxethane along the dissociation path (to formaldehyde products) and in different Hartree–Fock solutions are presented. At the equilibrium geometry of 1,2-dioxethane, all bond paths do not coincide with the corresponding internuclear axes. The outward curvature of the O? O bond path elaborates upon the concept of strain in the dioxethane ring. This weak binding of the ring is further confirmed by the considerably low ρ(r) value at the ring (3, +1) saddle point. An extension of the theory to the dynamic case has been discussed in terms of the topological changes in ρ(r) along the reaction path. The catastrophe of the chemical change, i.e., rupture of the dioxethane ring, takes the form of gradual merging and annhilation of the O? O (3, ?1) and the ring (3, +1) critical points. The values of ρ(r) at the positions of the critical points along the reaction path provide a topological characterization and definition of “partial valence.” The difference between the topological behavior of ρ(r), as obtained by different HF solutions, along the reaction path is analyzed and discussed.     

Density functional computations of the cyclopropanation of ethene catalyzed by iron (II) carbene complexes Cp(CO)(L)FeCHR,L = CO,PMe3, R = Me,OMe, ph,CO2Me

Density functional theory has been used to study the Fe‐catalyzed cyclopropanation of Fe‐carbene complexes with ethene. All the intermediates and transition states were optimized completely at the B3LYP/6‐31+G(d,p) level. Calculation results confirm that the cyclopropanation of Fe‐carbene complexes with ethene involves the two reaction paths I and II . In the reaction path I , the double bond of ethene attacks directly on the carbene carbon of Fe‐carbene complexes to generate the cyclopropane. In the reaction path II , ethene substitution for PMe₃ or CO in the Fe‐carbene complexes leads to the complexes M2 ; and the attack of one carbon of ethene on the carbene carbon results in the complexes M3 with a Fe? C? C? C four‐membered ring, and then generates the cyclopropane via the elimination reaction. For Fe‐carbene complexes A , C , D , E , and H , the main reaction mode is the reaction path I ; for Fe‐carbene complexes B , F , and G , the main reaction mode is the reaction path II . © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Charge‐Scaling Effect in Ionic Liquids from the Charge‐Density Analysis of N,N′‐Dimethylimidazolium Methylsulfate

The charge scaling effect in ionic liquids was explored on the basis of experimental and theoretical charge‐density analyses of [C₁MIM][C₁SO₄] employing the quantum theory of atoms in molecules (QTAIM) approach. Integrated QTAIM charges of the experimental (calculated) charge density of the cation and anion resulted in non‐integer values of ±0.90 (±0.87) e. Efficient charge transfer along the bond paths of the hydrogen bonds between the imidazolium ring and the anion was considered as the origin of these reduced charges. In addition, a detailed QTAIM analysis of the bonding situation in the [C₁SO₄]^? anion revealed the presence of negative π_O→σ*_S‐O hyperconjugation.     

Evaluation of N—H…S and N—H…π interactions in O,O′‐diethyl N‐(2,4,6‐trimethylphenyl)thiophosphate: a combination of X‐ray crystallographic and theoretical studies

In the crystal structure of O,O′‐diethyl N‐(2,4,6‐trimethylphenyl)thiophosphate, C₁₃H₂₂NO₂PS, two symmetrically independent thiophosphoramide molecules are linked through N—H…S and N—H…π hydrogen bonds to form a noncentrosymmetric dimer, with Z′ = 2. The strengths of the hydrogen bonds were evaluated using density functional theory (DFT) at the M06‐2X level within the 6‐311++G(d,p) basis set, and by considering the quantum theory of atoms in molecules (QTAIM). It was found that the N—H…S hydrogen bond is slightly stronger than the N—H…π hydrogen bond. This is reflected in differences between the calculated N—H stretching frequencies of the isolated molecules and the frequencies of the same N—H units involved in the different hydrogen bonds of the hydrogen‐bonded dimer. For these hydrogen bonds, the corresponding charge transfers, i.e. lp (or π)→σ*, were studied, according to the second‐order perturbation theory in natural bond orbital (NBO) methodology. Hirshfeld surface analysis was applied for a detailed investigation of all the contacts participating in the crystal packing.     

Molecular dynamics and pharmacophore modelling studies of different subtype (ALK and EGFR (T790M)) inhibitors in NSCLC

Extensively validated 3D pharmacophore models for ALK (anaplastic lymphoma kinase) and EGFR (T790M) (epithelial growth factor receptor with acquired secondary mutation) were developed. The pharmacophore model for ALK (r² = 0.96, q² = 0.692) suggested that two hydrogen bond acceptors and three hydrophobic groups arranged in 3-D space are essential for the binding affinity of ALK inhibitors. Similarly, the pharmacophore model for EGFR (T790M) (r² = 0.92, q² = 0.72) suggested that the presence of a hydrogen bond acceptor, two hydrogen bond donors and a hydrophobic group plays vital role in binding of an inhibitor of EGFR (T790M). These pharmacophore models allowed searches for novel ALK and EGFR (T790M) dual inhibitors from multiconformer 3D databases (Asinex, Chembridge and Maybridge). Finally, the eight best hits were selected for molecular dynamics simulation, to study the stability of their complexes with both proteins and final binding orientations of these molecules. After molecular dynamics simulations, one hit has been predicted to possess good binding affinity for both ALK and EGFR (T790M), which can be further investigated for its experimental in-vitro/in-vivo activities.     

Next-generation quantum theory of atoms in molecules for the photochemical ring-opening reactions of oxirane

The conical intersections corresponding to the C─O and C─C ring opening were optimized and the reaction paths traversing these intersections were obtained. Investigation of the C─O ring opening revealed that when traversing the lowest energy conical intersection, the reaction path returns to the closed ring geometry. The C─O path traversing the intersection featuring torsion of terminal CH₂ group however, led to a ring-opened geometry, an H-shift and the formation of acetaldehyde that can undergo further dissociation. The observation of different reaction paths was explained by the 3-D paths from quantum theory of atoms in molecules (QTAIM) that defined the most preferred direction of electronic motion that precisely tracked the mechanisms of bond breaking and formation throughout the photo-reactions. The size, orientation, and location of these most preferred 3-D paths indicated the extent and direction of motion of atoms, bonds, and the degree of torsion or planarity of a bond indicating a predictive ability.