Anchoring the Torsional Potential of Biphenyl at the ab Initio Level: The Role of Basis Set versus Correlation Effects

Linking solid-state phenomena via energy differences in `archetype crystal structures'

Categorization underlies understanding. Conceptualizing solid-state structures of organic molecules with `archetype crystal structures' bridges established categories of disorder, polymorphism and solid solutions and is herein extended to special position and high-Z' structures. The concept was developed in the context of disorder modelling [Dittrich, B. (2021). IUCrJ, 8, 305-318] and relies on adding quantum chemical energy differences between disorder components to other criteria as an explanation as to why disorder - and disappearing disorder - occurs in an average structure. Part of the concept is that disorder, as probed by diffraction, affects entire molecules, rather than just the parts of a molecule with differing conformations, and the finding that an R·T energy difference between disorder archetypes is usually not exceeded. An illustrative example combining disorder and special positions is the crystal structure of oestradiol hemihydrate analysed here, where its space-group/subgroup relationship is required to explain its disorder of hydrogen-bonded hydrogen atoms. In addition, we show how high-Z' structures can also be analysed energetically and understood via archetypes: high-Z' structures occur when an energy gain from combining different rather than overall alike conformations in a crystal significantly exceeds R·T, and this finding is discussed in the context of earlier explanations in the literature. Twinning is not related to archetype structures since it involves macroscopic domains of the same crystal structure. Archetype crystal structures are distinguished from crystal structure prediction trial structures in that an experimental reference structure is required for them. Categorization into archetype structures also has practical relevance, leading to a new practice of disorder modelling in experimental least-squares refinement alluded to in the above-mentioned publication.

Torsional Wave-Packet Dynamics in 2-Fluorobiphenyl Investigated by State-Selective Ionization-Detected Impulsive Stimulated Raman Spectroscopy

We report the creation and observation of vibrational wave packets pertinent to torsional motion in a biphenyl derivative in its electronic ground-state manifold. Adiabatically cooled molecular samples of 2-fluorobiphenyl were irradiated by intense nonresonant ultrashort laser pulses to drive impulsive stimulated Raman excitation of torsional motion. Spectral change due to the nonadiabatic vibrational excitation is probed in a state-selective manner using resonance-enhanced two-photon ionization through the S₁ ← S₀ electronic transition. The coherent nature of the excitation was exemplified by adopting irradiation with a pair of pump pulses: observed signals for excited torsional levels exhibit oscillatory variations against the mutual delay between the pump pulses due to wave-packet interference. By taking the Fourier transform of the time course of the signals, energy intervals among torsional levels with v = 0-3 were determined and utilized to calibrate a density functional theory (DFT)-calculated torsional potential-energy function. Time variation of populations in the excited torsional levels was assessed experimentally by measuring integrated intensities of the corresponding transitions while scanning the delay. Early time enhancement of the population (up to ∼2 ps) and gradual degradation of coherence (within ∼20 ps) appears. To explain the observed distinctive features, we developed a four-dimensional (4D) dynamical calculation in which one-dimensional (1D) quantum-mechanical propagation of the torsional motion was followed by solving the time-dependent Schrödinger equation, whereas three-dimensional (3D) molecular rotation was tracked by classical trajectory calculations. This hybrid approach enabled us to reproduce experimental results at a reasonable computational cost and provided a deeper insight into rotational effects on vibrational wave-packet dynamics.

Planar in Brooker's mode and twisted in Reichardt's mode: defying the steric forces in biphenyl types of zwitterionic systems through metameric resonance stabilizations

To be planar or to be twisted at the bridge junctions in biphenyls or biaryl types of molecular systems depends on two conflicting forces: (1) steric repulsions (destabilizations) and (2) conjugation assisted electron delocalizations (resonance stabilizations). This work reports an unfamiliar kind of behaviour shown by metamers of a zwitterionic biphenyl type of system, where the Reichardt's metamer was found to be in an usual twisted conformation (delicate balance of conflicting forces), but the Brooker's metamer was found to be in a fully planar conformation. Interestingly, at the ωB97xD/aug-cc-pVDZ level, energetically (ΔE) the planar Brooker's metamer was found to be 16.7 kcal mol^-1 lower (22.9 kcal mol^-1 lower in the CASSCF method) in energy (more stable) than the isoelectronic twisted Reichardt's metamer, and also thermodynamic ΔG values were found to be close to ΔE values for various methods (for example, 15.6 kcal mol^-1 in the above case using the ωB97xD method). When the steric repulsions are in their full potentials at the ring junction site, attainment of a conformational planarity by any biaryl type of system has not been reported previously. Without reducing the steric constraints or even without inducing any attractive forces, determining what other factors were responsible for defying the steric forces is the main focus of this investigation. Using the results of quantum mechanical computations of NBO, rotational barriers, and other saddle points (metastable conformations in singlet and triplet surfaces) in the potential energy surfaces, the dominant contribution of the resonance stabilized quinonoid form to the ground state was delineated as the possible reason for this unusual behaviour.

Steric clash in real space: biphenyl revisited

A textbook case of twisted structure due to hydrogen-hydrogen steric clash, the biphenyl molecule, has been studied in real space from a new perspective. Long-term discrepancies regarding the origin of the steric repulsion are now reconciled under the NCI (Non Covalent Interaction) method, which reflects in 3D the balance between attractive and repulsive interactions taking place in the region between the phenyl rings. The NCI method confirms that the steric repulsion does not merely come from the H-H interaction itself, but from the many-atom interactions arising from the Cortho-H region, therefore providing rigorous physical grounds for the steric clash. This method allows a continuous scan of all the subtle changes on the electron density on going from the planar to the perpendicular biphenyl structure. The NCI results agree with other topological approaches (IQA, ELF) and are in line with previous findings in the literature regarding controversial H-H interactions in steric clash situations: H-H interactions are attractive, but repulsion appears between (Cortho-H)(Cortho-H), raising the intraatomic energy of the ortho H. ELF is also used to support these conclusions. Indeed, deformations are observed in compressed basins that allow to visualize the intraatomic effect of steric repulsion. These results can be easily extrapolated to systems with similar topological features in which steric clash is claimed to be the reason for instability.

Enantiomerization of Axially Chiral Biphenyls: Polarizable MD Simulations in Water and Butylmethylether

In this study, we investigate the influence of chiral and achiral cations on the enantiomerization of biphenylic anions in n-butylmethylether and water. In addition to the impact of the cations and solvent molecules on the free energy profile of rotation, we also explore if chirality transfer between a chiral cation and the biphenylic anion is possible, i.e., if pairing with a chiral cation can energetically favour one conformer of the anion via diastereomeric complex formation. The quantum-mechanical calculations are accompanied by polarizable MD simulations using umbrella sampling to study the impact of solvents of different polarity in more detail. We also discuss how accurate polarizable force fields for biphenylic anions can be constructed from quantum-mechanical reference data.

Solving the COF trilemma: towards crystalline, stable and functional covalent organic frameworks

Strategies in covalent organic frameworks and adjacent fields are highlighted for designing stable, ordered and functional materials.

A relative energy gradient (REG) study of the planar and perpendicular torsional energy barriers in biphenyl

Biphenyl is a prototype molecule, the study of which is important for a proper understanding of stereo-electronic effects. In the gas phase it has an equilibrium central torsion angle of ~ 45° and shows both a planar (0°) and a perpendicular (90°) torsional energy barrier. The latter is analysed for the first time. We use the newly proposed REG method, which is an exhaustive procedure that automatically ranks atomic energy contributions according to their importance in explaining the energy profile of a total system. Here, the REG method operates on energy contributions computed by the interacting quantum atoms method. This method is minimal in architecture and provides a crisp picture of well-defined and well-separated electrostatic, steric and exchange (covalent) energies at atomistic level. It is shown that the bond critical point occurring between the ortho-hydrogens in the planar geometry has been wrongly interpreted as a sign of repulsive interaction. A convenient metaphor of analysing football matches is introduced to clarify the role of a REG analysis.

Rapid assessment of conformational preferences in biaryl and aryl carbonyl fragments

The ability to rapidly assess the preferred conformation of key fragments in a structure “by visual inspection” is a very useful starting point in the process of drug design. With the ability to do so, one could address questions like: “How could we avoid planarity in a molecule?”, “Will a molecule change its conformational preference if we make it more or less basic?” or “How does this electronic repulsion affect the conformational preference in the system?” in timely fashion. In this paper, we describe how the conformational energy profile (CEP, plot of energy as a function of dihedral bond angle) of a fragment can be interpreted through the understanding the interplay between resonance stabilization, steric effects and electrostatic interactions. Fifty-nine biaryl and aryl carbonyl fragments present in oral drugs or which are close derivatives thereof were selected. Calculation of their CEPs using ab initio methodology allowed us to conclude the relative importance of these factors in the conformational preference of these fragments as follows: “steric repulsion > lone pair—lone pair repulsion > lone pair—fluorine repulsion > resonance stabilization” and to formulate “rules of thumb” that the practicing medicinal/organic chemist can apply when analysing molecules that contain these fragments.

25th anniversary article: high-mobility hole and electron transport conjugated polymers: how structure defines function

The structural organization of three different families of semicrystalline π-conjugated polymers is reported (poly(3-hexylthiophene) (P3HT), poly[2,6-(4,4-bis-alkyl-4H-cyclopenta-[2,1-b;3,4-b0]-dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)](cyclopentadithiophene-benzothiadiazole) (CDT-BTZ) and poly(N,N"-bis-2-octyldodecylnaphtalene-1,4,5,8-bis-dicarboximide-2,6-diyl-alt-5,5-2,2-bithiophene (P(NDI2OD-T2))). These have triggered significant interest for their remarkable charge-transport properties. By performing molecular mechanics/dynamics simulations with carefully re-parameterized force fields, it is illustrated in particular how the supramolecular organization of these conjugated polymers is driven by an interplay between the length and nature of the conjugated monomer unit and the packing of their alkyl side chains, and to what extent it impacts the charge-carrier mobility, as monitored by quantum-chemical calculations of the intermolecular hopping transfer integrals. This Progress Report is concluded by providing generic guidelines for the design of materials with enhanced degrees of supramolecular organization.

Characterization of biaryl torsional energetics and its treatment in OPLS all-atom force fields

The frequency of biaryl substructures in a database of approved oral drugs has been analyzed. This led to designation of 20 prototypical biaryls plus 10 arylpyridinones for parametrization in the OPLS all-atom force fields. Bond stretching, angle-bending, and torsional parameters were developed to reproduce the MP2 geometries and torsional energy profiles. The transferability of the new parameters was tested through their application to three additional biaryls. The torsional energetics for the 33 biaryl molecules are analyzed and factors leading to preferences for planar and nonplanar geometries are identified. For liquid biphenyl, the computed density and heat of vaporization at the boiling point (255 °C) are also reported.

First-principles computational studies of the torsional potential energy surface of the sec-butyl radical

First-principles calculations were carried out to investigate the torsional potential energy surface (PES) of the sec-butyl radical. All the wave function methods employed predict a cis-like stable conformation with a dihedral angle of about 47° in addition to the trans-like global minimum conformation and a gauche conformation. However, most of the popular density functional approaches predict only the latter two local minima and lack the cis conformation that was experimentally observed. On the other hand, some density functional methods that incorporate the exact exchange and asymptotically corrected correlation functionals can locate the cis conformation successfully. The basis-set effect was also measured using popular B3LYP and MP2 Hamiltonians: only moderate shape changes were found for PES profiles upon basis-set variations. The stationary structures and their Hessians were obtained at both MP2 and B3LYP levels, with or without incorporating the zero-point energies. Opposite to the relative stability within the Born–Oppenheimer approximation, the cis conformation is more stable than the gauche conformation upon the zero-point correction, consistent with the experiment observations.

A general measure of conjugation in biphenyls and their radical cations

Changes in the amount of conjugation in the biphenyl system upon torsion have been investigated with quantum chemistry computations. For the unsubstituted biphenyl and its radical cation, the change in the energy for the first electronic transition as determined from time-dependent density functional theory, specifically TD-B3LYP, upon an imposed change in torsion angle appears to provide a good general measure of the delocalization of the π-electrons. Upon substitution, though, a relationship could not be established between the excitation energy and the twist across the C–C bond connecting the two phenyl rings. In contrast, the π-interaction energy, i.e., the π–π interaction across the central C–C bond, determined from a natural bond orbital analysis, provides a uniform description of conjugation in the electronically different systems, for an imposed twist as well as upon substitution. Substituent effects are found to be larger and more varied for the biphenyl radical cations. Of particular interest is the introduction of the oxidizable substituents OCH3 (methoxyl) and SCH3 (methylthio), as this leads to the smallest changes in torsion angle in the biphenyl unit upon removal of an electron from the molecule. The findings of this work could ultimately prove useful for the rational design of conductive polymer materials.

A comparative study of the binding of QSY 21 and Rhodamine 6G fluorescence probes to DNA: structure and dynamics

Molecular dynamics (MD) simulations and ab initio quantum chemical calculations were employed to investigate the structure, dynamics and interactions of the QSY 21 nonfluorescent quencher and the fluorescence dye Rhodamine 6G bound to a B-DNA decamer. For QSY 21, two binding motifs were observed. In the first motif, the central xanthene ring is stacked on one base of the adjacent cytosine-guanine DNA base pair, whereas one of the 2,3-dihydro-1-indolyl aromatic side rings is stacked on the other base. In the second motif, the QSY 21 stacking interaction with the DNA base pair is mediated only by one of the side rings. Several transitions between the motifs are observed during a MD simulation. The ab initio calculations show that none of these motifs is energetically preferred. Two binding motifs were found also for Rhodamine 6G, with the xanthene ring stacked predominantly either on the cytosine or on the guanine. These results suggest that the side rings of QSY 21 play a crucial role in its stacking on the DNA and indicate novel binding mode absent in the case of Rhodamine 6G, which lacks aromatic side rings.

Structures and thermodynamics of biphenyl dihydrodiol stereoisomers and their metabolites in the enzymatic degradation of arene xenobiotics

A key step in the metabolic degradation of biphenyl xenobiotics is catechol formation upon dehydrogenation of cis- and trans-dihydrodiols in prokaryotic and eukaryotic pathways, respectively. Structure and thermodynamics of stereoisomers of cis-, trans-2,3-biphenyl-dihydrodiols (I) and their dehydrogenation products (hydroxyketones, II), as well as final catechol (2,3-biphenyldiol, III) are studied by means of ab initio MP2/6-311++G(2df,2p)//MP2/6-311G(d,p) calculations. Formation of stereoisomers I and II is exothermic and endergonic, whereas III is enthalpically and entropically driven. Dehydrogenations are endothermic (DeltaHR0 approximately 1.5-4 kcal mol(-1)) and exergonic (DeltaGR0 approximately -5 to -7.5 kcal mol(-1)) without noticeable differences between cis and trans pathways, although the same keto stereoisomer II-(2S) is found to be the more favored product from both cis- and trans-I. The final II --> III tautomerization is thermodynamically enhanced (DeltaHR0 approximately -27, DeltaGR0 approximately -28 kcal mol(-1)) but the process is shown to have a large activation energy if it had to occur via unimolecular path. Although this tautomerization is generally assumed to be a nonenzymatic process as it involves rearomatization of an oxygenated ring, proton transfer with an anionic intermediate might be a more probable process.

Dependence of Optical Properties of Oligo-para-phenylenes on Torsional Modes and Chain Length

A systematic characterization of excited-state properties of para-phenylene oligomers constructed from two to eight aromatic rings is presented using density functional theory (DFT) and the coupled-cluster singles and doubles (CC2) method. Geometry optimizations have been performed for the ground state and for the electronically excited state. Vertical excitations and the fluorescence transitions have been calculated. Time-dependent DFT (TDDFT) method underestimates excitation and fluorescence energies systematically in comparison with experimental results. The computed TDDFT lifetime for the polymer limit (0.43 ns) is in agreement with the experimental value of 0.55 ns. The TDDFT torsional potential curves were investigated for biphenyl, terphenyl, and quarterphenyl oligomers in their electronic ground and excited states. Our calculations show an increase in the separation of the lowest excited state (S1) to the next higher one with increasing molecular size. No indication is found for state crossings of the S1 state with higher ones from planar structures up to torsional angles of 60 degrees to 70 degrees. Thus, an adiabatic description of the dynamics of the S1 state might significantly simplify any dynamics simulations of torsional broadenings.

Dual-basis second-order Møller-Plesset perturbation theory: A reduced-cost reference for correlation calculations

The resolution-of-the-identity (RI) approximation has placed the onus of the cost of a second-order Moller-Plesset (MP2) calculation on the underlying self-consistent field (SCF) calculation for many moderately sized molecules. A dual-basis approach to the SCF calculation, based on previous methods demonstrated for density functional theory, is combined with RI-MP2 calculations, and small basis subsets for cc-pVTZ, cc-pVQZ, and 6-311++G(3df,3pd) are presented. These subsets provide time savings of greater than 90%, with negligible errors in absolute and relative energies, compared to the associated full-basis counterpart. The method is tested with a series of rotational barriers, relative conformational energies of alanine tetrapeptides, as well as the full G3/99 molecular set. RI-MP2 calculations on alanine octapeptides (40 heavy atoms, 3460 basis functions), using cc-pVQZ, are presented. Results improve upon previous methods that diagonalize the virtual space separately.

Li−Biphenyl−1,2-Dimethoxyethane Solution: Calculation and Its Application

Metallic lithium reacts with biphenyl in 1,2-dimethoxyethane (DME) solvent at room temperature. This reaction has been studied using density functional theory (DFT) at the B3LYP level together with the 6-311++G (d,p) basis set. From the energy results of the corresponding optimized geometries for intermediate complexes, the reaction can be interpreted as a charge-transfer process between lithium and biphenyl followed by Li+ coordination with ether oxygens in DME. In addition, the experimentally observed vibrational bands can be unambiguously assigned and interpreted according to the normal modes calculated for the biphenyl-Li-DME complex. This organic complex solution has been demonstrated as a very effective chemical lithiation agent. V2O5 can be lithiated up to 1.45 lithium ions per formula. The lithiated V2O5 shows a high Li-extraction capacity of 173 mAh/g as cathode material for lithium ion batteries.

Assessing a new nonempirical density functional: Difficulties in treating π-conjugation effects

The reliability of the Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation functional for the description of conjugation effects in model pi-conjugated systems has been thoroughly assessed through the calculation of torsion energy profiles. The functional reproduces qualitatively the shape of torsional potentials but, interestingly, the mixing of TPSS and exact exchange governs the quantitative results: thus, well-defined hybrid extensions of the functional are consistently employed to improve the results. The hybrid approaches led to more accurate descriptions of conjugation effects but, however, the finest performance along the whole range of dihedral angles was obtained by a customized mixing of pure or hybrid TPSS functionals and wave function methods in a multicoefficient fashion. Despite the successful construction of this nonempirical functional, higher rungs of the ladder of methods in which TPSS is based are hoped to reduce the errors with respect to reference data for pi-conjugated systems.

Hydrogen–Hydrogen Bonding in Planar Biphenyl, Predicted by Atoms-In-Molecules Theory, Does Not Exist

Based on an Atoms-in-Molecules (AIM) analysis, Matta et al. recently claimed evidence for the existence of hydrogen-hydrogen bonding between ortho-hydrogen atoms, pointing towards each other from adjacent phenyl groups in planar biphenyl. This AIM result is opposed to the classical view that nonbonded steric repulsion between the ortho-hydrogen atoms is responsible for the higher energy of the planar as compared to the twisted geometry of biphenyl. In the present work, we address the question if hydrogen-hydrogen bonding in biphenyl exists, as suggested by AIM, or not. To this end, we have analyzed the potential energy surface for internal rotation of biphenyl in terms of two interacting phenyl radicals using density functional theory (DFT) at BP86/TZ2P. A detailed analysis of the bonding mechanism and a quantitative bond energy decomposition in the framework of Kohn-Sham DFT show that Pauli (or overlap) repulsion, mainly between C(ortho)--H(ortho) phenyl MOs, prevents biphenyl from being planar and forces it to adopt a twisted equilibrium geometry. Furthermore, a derivative of biphenyl in which all four ortho-hydrogen atoms have been removed does adopt a planar equilibrium geometry. Thus, our results confirm the classical view of steric repulsion between ortho-hydrogen atoms in biphenyl and they falsify the hypothesis of hydrogen-hydrogen bonding.