Investigating and Quantifying Molecular Complexity Using Assembly Theory and Spectroscopy.

Current approaches to evaluate molecular complexity use algorithmic complexity, rooted in computer science, and thus are not experimentally measurable. Directly evaluating molecular complexity could be used to study directed vs undirected processes in the creation of molecules, with potential applications in drug discovery, the origin of life, and artificial life. Assembly theory has been developed to quantify the complexity of a molecule by finding the shortest path to construct the molecule from building blocks, revealing its molecular assembly index (MA). In this study, we present an approach to rapidly infer the MA of molecules from spectroscopic measurements. We demonstrate that the MA can be experimentally measured by using three independent techniques: nuclear magnetic resonance (NMR), tandem mass spectrometry (MS/MS), and infrared spectroscopy (IR). By identifying and analyzing the number of absorbances in IR spectra, carbon resonances in NMR, or molecular fragments in tandem MS, the MA of an unknown molecule can be reliably estimated. This represents the first experimentally quantifiable approach to determining molecular assembly. This paves the way to use experimental techniques to explore the evolution of complex molecules as well as a unique marker of where an evolutionary process has been operating.

Disentangling global and local ring currents.

Magnetic field-induced ring currents in aromatic and antiaromatic molecules cause characteristic shielding and deshielding effects in the molecules' NMR spectra. However, it is difficult to analyze (anti)aromaticity directly from experimental NMR data if a molecule has multiple ring current pathways. Here we present a method for using the Biot-Savart law to deconvolute the contributions of different ring currents to the experimental NMR spectra of polycyclic compounds. This method accurately quantifies local and global ring current susceptibilities in porphyrin nanorings, as well as in a bicyclic dithienothiophene-bridged [34]octaphyrin. There is excellent agreement between ring current susceptibilities derived from both experimental and computationally-predicted chemical shifts, and with ring currents calculated by the GIMIC method. Our method can be applied to any polycyclic system, with any number of ring currents, provided that appropriate NMR data are available.

Population and coherence dynamics in large conjugated porphyrin nanorings.

In photosynthesis, nature exploits the distinctive electronic properties of chromophores arranged in supramolecular rings for efficient light harvesting. Among synthetic supramolecular cyclic structures, porphyrin nanorings have attracted considerable attention as they have a resemblance to naturally occurring light-harvesting structures but offer the ability to control ring size and the level of disorder. Here, broadband femtosecond transient absorption spectroscopy, with pump pulses in resonance with either the high or the low energy sides of the inhomogeneously broadened absorption spectrum, is used to study the population dynamics and ground and excited state vibrational coherence in large porphyrin nanorings. A series of fully conjugated, alkyne bridged, nanorings constituted of between ten and forty porphyrin units is studied. Pump-wavelength dependent fast spectral evolution is found. A fast rise or decay of the stimulated emission is found when large porphyrin nanorings are excited on, respectively, the high or low energy side of the absorption spectrum. Such dynamics are consistent with the hypothesis of a variation in transition dipole moment across the inhomogeneously broadened ground state ensemble. The observed dynamics indicate the interplay of nanoring conformation and oscillator strength. Oscillatory dynamics on the sub-ps time domain are observed in both pumping conditions. A combined analysis of the excitation wavelength-dependent transient spectra along with the amplitude and phase evolution of the oscillations allows assignment to vibrational wavepackets evolving on either ground or excited states electronic potential energy surfaces. Even though porphyrin nanorings support highly delocalized electronic wavefunctions, with coherence length spanning tens of chromophores, the measured vibrational coherences remain localised on the monomers. The main contributions to the beatings are assigned to two vibrational modes localised on the porphyrin cores: a Zn-N stretching mode and a skeletal methinic/pyrrolic C-C stretching and in-plane bending mode.

Correspondence on "How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring".

A recent Research Article in this journal by Matito and co-workers claimed that none of the oxidation states of a butadiyne-linked six-porphyrin nanoring exhibit global aromaticity or antiaromaticity. Here we show that this conclusion is incorrect. Experimental data from NMR spectroscopy for a whole family of nanorings provide strong evidence for global ring currents. The NMR data reveal these ring currents directly, without needing analysis by density functional theory (DFT). Furthermore, DFT calculations reproduce the experimental results when a suitable functional is used.

A Helquat-like Compound as a Potent Inhibitor of Flaviviral and Coronaviral Polymerases.

Positive-sense single-stranded RNA (+RNA) viruses have proven to be important pathogens that are able to threaten and deeply damage modern societies, as illustrated by the ongoing COVID-19 pandemic. Therefore, compounds active against most or many +RNA viruses are urgently needed. Here, we present PR673, a helquat-like compound that is able to inhibit the replication of SARS-CoV-2 and tick-borne encephalitis virus in cell culture. Using in vitro polymerase assays, we demonstrate that PR673 inhibits RNA synthesis by viral RNA-dependent RNA polymerases (RdRps). Our results illustrate that the development of broad-spectrum non-nucleoside inhibitors of RdRps is feasible.

A Peierls Transition in Long Polymethine Molecular Wires: Evolution of Molecular Geometry and Single-Molecule Conductance.

Molecules capable of mediating charge transport over several nanometers with minimal decay in conductance have fundamental and technological implications. Polymethine cyanine dyes are fascinating molecular wires because up to a critical length, they have no bond-length alternation (BLA) and their electronic structure resembles a one-dimensional free-electron gas. Beyond this threshold, they undergo a symmetry-breaking Peierls transition, which increases the HOMO-LUMO gap. We have investigated cationic cyanines with central polymethine chains of 5-13 carbon atoms (Cy3+-Cy11+). The absorption spectra and crystal structures show that symmetry breaking is sensitive to the polarity of the medium and the size of the counterion. X-ray crystallography reveals that Cy9·PF6 and Cy11·B(C6F5)4 are Peierls distorted, with high BLA at one end of the π-system, away from the partially delocalized positive charge. This pattern of BLA distribution resembles that of solitons in polyacetylene. The single-molecule conductance is essentially independent of molecular length for the polymethine salts of Cy3+-Cy11+ with the large B(C6F5)4- counterion, but with the PF6- counterion, the conductance decreases for the longer molecules, Cy7+-Cy11+, because this smaller anion polarizes the π-system, inducing a symmetry-breaking transition. At higher bias (0.9 V), the conductance of the shorter chains, Cy3+-Cy7+, increases with length (negative attenuation factor, ß = -1.6 nm-1), but the conductance still drops in Cy9+ and Cy11+ with the small polarizing PF6- counteranion.

From Macrocycles to Quantum Rings: Does Aromaticity Have a Size Limit?

ConspectusThe ring currents of aromatic and antiaromatic molecules are remarkable emergent phenomena. A ring current is a quantum-mechanical feature of the whole system, and its existence cannot be inferred from the properties of the individual components of the ring. Hückel's rule states that when an aromatic molecule with a circuit of [4n + 2] π electrons is placed in a magnetic field, the field induces a ring current that creates a magnetic field opposing the external field inside the ring. In contrast, antiaromatic rings with 4n π electrons exhibit ring currents in the opposite direction. This rule bears the name of Erich Hückel, and it grew from his molecular orbital theory, but modern formulations of Hückel's rule incorporate contributions from others, particularly William Doering and Ronald Breslow. It is often assumed that aromaticity is restricted to small molecular rings with up to about 22 π electrons. This Account outlines the discovery of global ring currents in large macrocycles with circuits of up to 162 π electrons. The largest aromatic rings yet investigated are cyclic porphyrin oligomers, which exhibit global ring currents after oxidation, reduction or optical excitation but not in the neutral ground state. The global aromaticity in these porphyrin nanorings leads to experimentally measurable aromatic stabilization energies in addition to magnetic effects that can be studied by NMR spectroscopy. Wheel-like templates can be bound inside these nanorings, providing excellent control over the molecular geometry and allowing the magnetic shielding to be probed inside the nanoring. The ring currents in these systems are well-reproduced by density functional theory (DFT), although the choice of DFT functional often turns out to be critical. Here we review recent contributions to this field and present a simple method for determining the ring current susceptibility (in nA/T) in any aromatic or antiaromatic ring from experimental NMR data by classical Biot-Savart calculations. We use this method to quantify the ring currents in a variety of aromatic rings. This survey confirms that Hückel's rule reliably predicts the direction of the ring current, and it reveals that the ring current susceptibility is surprisingly insensitive to the size of the ring. The investigation of aromaticity in even larger molecular rings is interesting because ring currents are also observed when mesoscopic metal rings are placed in a magnetic field at low temperatures. The striking similarity between the ring currents in molecules and mesoscopic metal rings arises because the effects have a common origin: a field-dependent phase shift in the electronic wave function. The main difference is that the magnetic flux through mesoscopic rings is much greater because of their larger areas, so their persistent currents are nonlinear and oscillatory with the applied field, whereas the flux through aromatic molecules is so small that their response is approximately linear in the applied field. We discuss how nonlinearity is expected to emerge in large molecular nanorings at high magnetic fields. The insights from this work are fundamentally important for understanding aromaticity and for bridging the gap between chemistry and mesoscopic physics, potentially leading to new functions in molecular electronics.

Experimental and Theoretical Evidence for Aromatic Stabilization Energy in Large Macrocycles.

Enhanced thermodynamic stability is a fundamental characteristic of aromatic molecules, yet most previous studies of aromatic stabilization energy (ASE) have been limited to small rings with up to 18 π-electrons. Here we demonstrate that ASE can be detected experimentally in π-conjugated porphyrin nanorings with Hückel circuits of 76-108 π-electrons. This conclusion is supported by analyzing redox potentials to calculate the energy change for isodesmic reactions that convert an aromatic ring to an antiaromatic ring or vice versa. It is also supported by analyzing the energy barriers to conformational equilibria that disrupt aromaticity in the transition state. Both types of experiment indicate that cationic porphyrin nanorings display ASEs of 1-5 kJ mol-1. Density functional theory calculations reproduce the results for both types of experiment and predict ASEs in the range of 1-16 kJ mol-1. The experimental ASEs in porphyrin nanorings are compared with an experimental ASE of [18]annulene of ∼11 kJ mol-1, deduced from analysis of the energy barriers to conformational equilibria in [16], [18], and [20]annulene. Calculated energies of isodesmic reactions give an ASE of ∼37 kJ mol-1 in [18]annulene. This work contributes to a fundamental understanding of aromaticity in large macrocycles.

Allosteric Cooperativity and Template-Directed Synthesis with Stacked Ligands in Porphyrin Nanorings.

The link between allosteric cooperativity and template-directed synthesis has been investigated by studying complexes in which two oligopyridine ligands bind inside a zinc porphyrin nanoring in a stacked arrangement. The binding of a 6-porphyrin nanoring to two tridentate ligands (with s-triazine or benzene cores) occurs with high negative allosteric cooperativity (α ≈ 10-3-10-4). Formation constants for 1:1 and 1:2 complexes were determined by UV-vis-NIR denaturation titration, using pyridine as a competing ligand, and cooperativity factors were confirmed by NMR spectroscopy. The rate constants for formation of the 1:1 and 1:2 complexes are approximately equal, and the negative cooperativity can be attributed to faster dissociation of the 1:2 complex. These tridentate ligands are not effective templates for directing the synthesis of the 6-porphyrin nanoring, in keeping with their negative cooperativity of binding. In contrast, the binding of a 12-porphyrin nanoring to two hexadentate ligands occurs with high positive allosteric cooperativity (α > 40), and the ligand is an effective Vernier template for directing the synthesis of the 12-porphyrin nanoring. This stacked Vernier template approach creates the product in an open circular conformation, which is advantageous for preparing macrocycles that do not easily adopt a figure-of-eight geometry.

Global aromaticity at the nanoscale.

Aromaticity can be defined by the ability of a molecule to sustain a ring current when placed in a magnetic field. Hückel's rule states that molecular rings with [4n + 2] π-electrons are aromatic, with an induced magnetization that opposes the external field inside the ring, whereas those with 4n π-electrons are antiaromatic, with the opposite magnetization. This rule reliably predicts the behaviour of small molecules, typically with fewer than 22 π-electrons (n = 5). It is not clear whether aromaticity has a size limit, or whether Hückel's rule extends to much larger macrocycles. Here, we present evidence for global aromaticity in porphyrin nanorings with circuits of up to 162 π-electrons (n = 40); aromaticity is controlled by changing the constitution, oxidation state and conformation. Whenever a ring current is observed, its direction is correctly predicted by Hückel's rule. The largest ring currents occur when the porphyrin units have fractional oxidation states.

Mechanisms of IR amplification in radical cation polarons.

Break down of the Born-Oppenheimer approximation is caused by mixing of electronic and vibrational transitions in the radical cations of some conjugated polymers, resulting in unusually intense vibrational bands known as infrared active vibrations (IRAVs). Here, we investigate the mechanism of this amplification, and show that it provides insights into intramolecular charge migration. Spectroelectrochemical time-resolved infrared (TRIR) and two-dimensional infrared (2D-IR) spectroscopies were used to investigate the radical cations of two butadiyne-linked conjugated porphyrin oligomers, a linear dimer and a cyclic hexamer. The 2D-IR spectra reveal strong coupling between all the IRAVs and the electronic π-π* polaron band. Intramolecular vibrational energy redistribution (IVR) and vibrational relaxation occur within ∼0.1-7 ps. TRIR spectra show that the transient ground state bleach (GSB) and excited state absorption (ESA) signals have anisotropies of 0.31 ± 0.07 and 0.08 ± 0.04 for the linear dimer and cyclic hexamer cations, respectively. The small TRIR anisotropy for the cyclic hexamer radical cation indicates that the vibrationally excited polaron migrates round the nanoring on a time scale faster than the measurement, i.e. within 0.5 ps, at 298 K. Density functional theory (DFT) calculations qualitatively reproduce the emergence of the IRAVs. The first singlet (S1) excited states of the neutral porphyrin oligomers exhibit similar IRAVs to the radical cations, implying that the excitons have similar electronic structures to polarons. Our results show that IRAVs originate from the strong coupling of charge redistribution to nuclear motion, and from the similar energies of electronic and vibrational transitions.

Global Aromaticity and Antiaromaticity in Porphyrin Nanoring Anions.

Doping, through oxidation or reduction, is often used to modify the properties of π-conjugated oligomers. In most cases, the resulting charge distribution is difficult to determine. If the oligomer is cyclic and doping establishes global aromaticity or antiaromaticity, then it is certain that the charge is fully delocalized over the entire perimeter of the ring. Herein we show that reduction of a six-porphyrin nanoring using decamethylcobaltocene results in global aromaticity (in the 6- state; [90 π]) and antiaromaticity (in the 4- state; [88 π]), consistent with the Hückel rules. Aromaticity is assigned by NMR spectroscopy and density-functional theory calculations.

Tuning the Circumference of Six-Porphyrin Nanorings.

Most macrocycles are made from a simple repeat unit, resulting in high symmetry. Breaking this symmetry allows fine-tuning of the circumference, providing better control of the host-guest behavior and electronic structure. Here, we present the template-directed synthesis of two unsymmetrical cyclic porphyrin hexamers with both ethyne (C2) and butadiyne (C4) links, and we compare these nanorings with the symmetrical analogues with six ethyne or six butadiyne links. Inserting two extra carbon atoms into the smaller nanoring causes a spectacular change in binding behavior: the template affinity increases by a factor of 3 × 109, to a value of ca. 1038 M-1, and the mean effective molarity is ca. 830 M. In contrast, removing two carbon atoms from the largest nanoring results in almost no change in its template-affinity. The strain in these nanorings is 90-130 kJ mol-1, as estimated both from DFT calculation of homodesmotic reactions and from comparing template affinities of linear and cyclic oligomers. Breaking the symmetry has little effect on the absorption and fluorescence behavior of the nanorings: the low radiative rates that are characteristic of a circular delocalized S1 excited state are preserved in the low-symmetry macrocycles.

Single-Acetylene Linked Porphyrin Nanorings.

The synthesis of ethyne-linked porphyrin nanorings has been achieved by template-directed Sonogashira coupling. The cyclic hexamer and octamer are predicted by density functional theory to adopt low symmetry conformations, due to dihedral twists between neighboring porphyrin units, but their symmetries are effectively D6h and D8h, respectively, in solution by 1H NMR. The fluorescence spectra indicate that the singlet excited states of these nanorings are highly delocalized.

Tunable Chiral Second-Order Nonlinear Optical Chromophores Based on Helquat Dications.

Fourteen new dipolar cations have been synthesized, containing methoxy or tertiary amino electron donor groups attached to helquat (Hq) acceptors. These Hq derivatives have been characterized as their TfO- salts by using various techniques including NMR and electronic absorption spectroscopies. UV-vis spectra show intense, relatively low energy absorptions with λmax ≈ 400-600 nm, attributable to intramolecular charge-transfer (ICT) excitations. Single-crystal X-ray structures have been solved for two of the chromophores, one as its PF6- salt, revealing centrosymmetric packing arrangements (space groups Pbca and P1̅). Molecular quadratic nonlinear optical (NLO) responses have been determined directly by using hyper-Rayleigh scattering (HRS) with a 800 nm laser, and indirectly via Stark (electroabsorption) spectroscopy for the low energy absorption bands. The obtained static first hyperpolarizabilities ß0 range from moderate to large: (9-140) × 10-30 esu from HRS in MeCN and (44-580) × 10-30 esu from the Stark data in PrCN. The magnitude of ß0 increases upon either extending the π-conjugation length or replacing a methoxy with a tertiary amino electron donor substituent. Density functional theory (DFT) and time-dependent DFT calculations on selected tertiary amino chromophores confirm that the low energy absorptions have ICT character. Relatively good agreement between the simulated and experimental UV-vis absorption spectra is achieved by using the CAM-B3LYP functional with the 6-311G(d) basis set. The ßtot values predicted by using DFT at the same level of theory are large ((472-1443) × 10-30 esu in MeCN). Both the theoretical and experimental results show that para-conjugation between Hq and electron donor fragments is optimal, and enlarging the Hq unit is inconsequential with respect to the molecular quadratic NLO response.

Ferrocenyl helquats: unusual chiral organometallic nonlinear optical chromophores.

Three new dipolar cations have been synthesised, containing ferrocenyl (Fc) electron donor groups attached to helquat (Hq) acceptors. These organometallic Hq derivatives have been characterised as their TfO- salts by using various techniques including NMR and electronic absorption spectroscopies and electrochemical measurements. UV-vis spectra show multiple intense low energy absorptions attributable to intramolecular charge-transfer (ICT) excitations. Each compound displays a reversible Fc+/0 redox process, together with two reversible one-electron reductions of the Hq fragment. Molecular quadratic nonlinear optical (NLO) responses have been determined by using hyper-Rayleigh scattering at 1064 nm, and Stark (electroabsorption) spectroscopic studies on the visible absorption bands. The obtained first hyperpolarizabilities ß are moderate, consistent with the relatively short π-conjugation lengths between the Fc and attached pyridinium group. A single-crystal X-ray structure has been solved for one of the complexes as its PF6- salt, revealing a centrosymmetric packing in the triclinic space group P1[combining macron]. Density functional theory (DFT) and time-dependent DFT calculations indicate that the lowest energy absorption bands have mainly metal-to-ligand charge-transfer character. The donor orbitals involved in the electronic transitions forming the next lowest energy ICT band also have substantial contributions from the Fe atom. Good agreement between the simulated and experimental UV-vis absorption spectra is achieved by using the PBE0 functional with the 6-311++G(d)/LANL2DZ mixed basis set, and the theoretical ß values are reasonably large. Oxidation of the Fc unit is predicted to cause the ßtot value to decrease by more than 80% in one of the complexes.

Enantiopure Alleno-Acetylenic Helicages Containing Multiple Binding Sites.

Enantiopure alleno-acetylenic ligands, containing two chiral allene moieties, assemble diastereoselectively with zinc(II) ions to form trinuclear triple-stranded helicates, featuring two internal cavity binding sites ("helicages"). The addition of cycloalkanes or heteroalicycles results in inclusion complex formation with two guest molecules bound in one helicate. While no positive allosteric effects were observed, the chiroptical responses increased strongly upon complexation, with guest-induced circular dichroism (ICD) signals reaching up to ΔΔϵ=205 m-1 cm-1 . The highest binding affinity was observed for six-membered 1,4-dichalcogens, with binding constants (K1 ) of up to 2400 m-1 for 1,4-oxathiane in CD3 OD. The X-ray co-crystal structure of 1,4-dioxane bound to a dinuclear triple-stranded helicate confirmed the previously predicted guest orientation inside the helicage, with the two oxygen atoms facing towards the electropositive zinc(II) metal centers.

Homochiral [2]Catenane and Bis[2]catenane from Alleno-Acetylenic Helicates - A Highly Selective Narcissistic Self-Sorting Process.

Homochiral strands of alternating alleno-acetylenes and phenanthroline ligands (P)-1 and (P2)-2, as well as their corresponding enantiomers, selectively assemble with the addition of silver(I) salt to yield dinuclear and trinuclear double helicates, respectively. Upon increasing the solvent polarity, the dinuclear and trinuclear helicates interlock to form a [2]catenane and bis[2]catenane, bearing 14 chirality elements, respectively. The solid-state structure of the [2]catenane reveals a nearly perfect fit of the interlocked strands, and the ECD spectra show a significant amplification of the chiroptical properties upon catenation, indicating stabilization of the helical secondary structure. Highly selective narcissistic self-sorting was demonstrated for a racemic mixture consisting of both short and long alleno-acetylenic strands, highlighting their potential for the preparation of linear catenanes of higher order.

Functional helquats: helical cationic dyes with marked, switchable chiroptical properties in the visible region.

Helquat dyes are the first helicene-like cationic styryl dyes obtained as separate enantiomers. Their remarkable chiroptical properties are due to the unique combination of a cationic hemicyanine chromophore and a helicene-like motif. The magnitude of the ECD response and the pH switching along with their positioning in the visible region are unprecedented among helicenoids.

Study of deoxyribonucleic acid-ligand interactions by partial filling affinity capillary electrophoresis.

In this work, a new partial filling affinity capillary electrophoresis (PF-ACE) method has been developed and applied to investigation of non-covalent molecular interactions between double stranded DNA oligonucleotide (Dickerson dodecamer) and classical DNA intercalator ligand-ethidiumbromide (EtBr) or oligophenylene derivatives-based potential new type of DNA ligands. Binding constants of DNA-ligand complexes were determined from the dependence of migration time changes of DNA oligomer (applied as analyte) on the length of ligand zones introduced beforehand as plugs of various lengths (0-75mm with 12.5mm step) in hydroxypropylcellulose coated fused silica capillary of 50/375µm I.D./O.D. and 400/300mm total/effective length. PF-ACE experiments were performed in two background electrolytes, Tris-borate, pH 8.0, ionic strength 14.3mM (BGE1), and sodium phosphate, pH 7.5, ionic strength 133mM (BGE2). Binding constants of DNA-EtBr complex (ca 15300L/mol in the BGE1 and 4200L/mol in the BGE2) were found to be significantly higher than those of DNA complexes with oligophenylene derivatives (ca 2200-3600L/mol in the BGE1 and 1600-2300L/mol in the BGE2).