Computing chiroptical properties with first-principles theoretical methods: Background and illustrative examples

Structural variety and pharmacological potential of naphthylisoquinoline alkaloids

Naphthylisoquinoline alkaloids are a fascinating class of natural biaryl compounds. They show characteristic mono- and dimeric scaffolds, with chiral axes and stereogenic centers. Since the appearance of the last comprehensive overview on these secondary plant metabolites in this series in 1995, the number of discovered representatives has tremendously increased to more than 280 examples known today. Many novel-type compounds have meanwhile been discovered, among them naphthylisoquinoline-related follow-up products like e.g., the first seco-type (i.e., ring-opened) and ring-contracted analogues. As highlighted in this review, the knowledge on the broad structural chemodiversity of naphthylisoquinoline alkaloids has been decisively driven forward by extensive phytochemical studies on the metabolite pattern of Ancistrocladus abbreviatus from Coastal West Africa, which is a particularly "creative" plant. These investigations furnished a considerable number of more than 80-mostly new-natural products from this single species, with promising antiplasmodial activities and with pronounced cytotoxic effects against human leukemia, pancreatic, cervical, and breast cancer cells. Another unique feature of naphthylisoquinoline alkaloids is their unprecedented biosynthetic origin from polyketidic precursors and not, as usual for isoquinoline alkaloids, from aromatic amino acids-a striking example of biosynthetic convergence in nature. Furthermore, remarkable botanical results are presented on the natural producers of naphthylisoquinoline alkaloids, the paleotropical Dioncophyllaceae and Ancistrocladaceae lianas, including first investigations on the chemoecological role of these plant metabolites and their storage and accumulation in particular plant organs.

Significance of Vibronic Coupling that Shapes Circularly Polarized Luminescence of Double Helicenes

The circularly polarized luminescence (CPL) spectra of S- and X-shaped double helicenes exhibit distinct vibrational structures and overall shape variations. In this study, we conducted an in-depth investigation into the vibronic effects influencing the CPL spectra of two double helicenes, namely DPC and DNH. Employing state-of-the-art computations utilizing the FC-HT1|VH model at the CAM-B3LYP/def2-TZVP level, we unveiled the paramount impact of Franck-Condon (FC), Herzberg-Teller (HT), and Duschinsky effects on their chiroptical responses. Our research underscores the pivotal role of structural deformations associated with the S1-to-S0 electronic transition in molding CPL spectra and wavelength-dependent dissymmetry (g) factor values, as well as the significance of HT effects in shaping and enhancing CPL responses. This extensive investigation not only advances our comprehension of the vibronic characteristics in configurationally distinct double helicenes but also offers valuable insights for the design of chiral molecules featuring controllable or finely-tunable CPL responses.

Computed Gyration Tensors of Knotted Chiral and Achiral Topological Stereoisomers of C60 Cyclocarbons

The electronic origins of the computed optical rotations of the simplest chiral and achiral chemical knots with comparatively simple compositions and large, anticipated magnetoelectric polarizabilities are provided. Linear response theory (LRT) is used to calculate the gyration at 1064 nm of two knotted polyyne chains, topological stereoisomers of cyclo[60]carbon. One isomer is analogous to the trefoil knot with approximate D3 symmetry and the other to the figure eight knot with approximate S4 symmetry. The response in each case can be attributed largely to the magnetic dipole term that arises in a near degenerate E-like excited state. An oriented achiral figure eight knot is as optically active in some directions as the chiral knot in any direction, and its absolute eigenvalues are larger.

Palladium Complexes of N-Methylcorroles

Alkylation of one of the inner-core nitrogen atoms is one possible approach to obtain dianionic corrole ligands, suitable for the coordination of divalent metal ions, such as PdII . Inner-core N-methylation can be obtained by treating the corrole with CH3 I, but the reaction conditions should be optimized to limit the formation of the dimethylated derivative. Two regioisomers, the N-21 and the N-22 methyl derivatives are obtained from the reaction, with the first product achieved in a higher amount. Structural characterization of the reaction products evidenced the distortion induced by the introduction of the methyl groups; the N-methylcorroles are chiral compounds, and the enantiomers were separated by chromatography, with their absolute configuration assigned by ECD computation. Palladium insertion was achieved in the case of monosubstituted corroles, but not with the dimethylated macrocycle; X-ray characterization of the complexes showed the distortion of the macrocycles. The Pd complexes do not show luminescence emission, but are able to produce singlet oxygen upon irradiation. The PdII complexes were also inserted in human serum albumin (HSA) and dispersed in water; in this case, the protein protects the corroles from photobleaching, and a switch from the type II to the type I mechanism in reactive oxygen species (ROS) production is observed.

Comparative rotatory power of bent and twisted polyynes

Linear polyynes of the formula C18 H2 (symmetry D∞h ) were bent in silico by progressively introducing CCC angles less than 180°. The bent structures (symmetry C2v ) were then twisted by introducing torsion angles across the CCCC segments by as much as 60°. The gyration tensors of these 19 structures (linear, bent, and twisted) were computed by linear response methods. Bending is massively generative of optical activity in oriented structures, even achiral structures, whereas twisting in conjunction with bending, serves to linearize the molecules and diminish maximally observable optical activity. This computational exercise is intended to unbind the infelicitous linkage of optical activity and chirality, which is only meaningful in isotropic media. Although bent structures are not optically active in solution-the spatial average of the optical activity is necessarily zero-solution measurements that deliver the spatial averages are a special class of measurements, albeit the overwhelmingly most common chiroptical measurements, that prejudice our common understanding of how π-conjugated structures generate gyration. Bending is far more effective than twisting at generating optical activity along some directions for oriented structures. The respective contributions from the transition electric dipole-magnetic dipole polarizability and the transition electric dipole-electric quadrupole polarizability are compared.

2,4,5,7-Tetranitrofluorenone Oximate for the Naked-Eye Detection of H-Bond Donors and the Chiroptical Sensing of Enantiopure Reagents

Hydrogen bonding greatly influences rates and equilibrium positions of chemical reactions, conformations, and sometimes even stereochemistry. This study reports on tetranitrofluorenone oximate, a novel dye capable of naked-eye detection of hydrogen-bond donating species (HBDs) and of rapid determination of H-bond donation strength by hypsochromic shift monitoring. In addition, the molecule possesses atropisomeric conformations, of M and P configuration, as evidenced in solid and solution state studies by X-ray diffraction and electronic circular dichroism (ECD), respectively. In the latter case, enantiopure bis-thioureas were the most effective HBDs to promote a chiral induction (diastereoselective recognition, Pfeiffer effect); the ECD results being rationalized by time-dependent density functional theory (TDDFT) calculations. Based on these experiments, bis-thioureas were used as chiral reagents in asymmetric 1,3-dipolar cycloadditions of structurally-related nitrones; the ECD sensing of the stereoinduction between bis-thioureas and the oximate serving as an indirect method of selection of the most effective HBD for asymmetric synthesis.

Directing Intrinsic Chirality in Gold Nanoclusters: Preferential Formation of Stable Enantiopure Clusters in High Yield and Experimentally Unveiling the "Super" Chirality of Au144

Chiral gold nanoclusters offer significant potential for exploring chirality at a fundamental level and for exploiting their applications in sensing and catalysis. However, their widespread use is impeded by low yields in synthesis, tedious separation procedures of their enantiomeric forms, and limited thermal stability. In this study, we investigated the direct synthesis of enantiopure chiral nanoclusters using the chiral ligand 2-MeBuSH in the fabrication of Au25, Au38, and Au144 nanoclusters. Notably, this approach leads to the unexpected formation of intrinsically chiral clusters with high yields for chiral Au38 and Au144 nanoclusters. Experimental evaluation of chiral activity by circular dichroism (CD) spectroscopy corroborates previous theoretical calculations, highlighting the stronger CD signal exhibited by Au144 compared to Au38 or Au25. Furthermore, the formation of a single enantiomeric form is experimentally confirmed by comparing it with intrinsically chiral Au38(2-PET)24 (2-PET: 2-phenylethanethiol) and is supported theoretically for both Au38 and Au144. Moreover, the prepared chiral clusters show stability against diastereoisomerization, up to temperatures of 80 °C. Thus, our findings not only demonstrate the selective preparation of enantiopure, intrinsically chiral, and highly stable thiolate-protected Au nanoclusters through careful ligand design but also support the predicted "super" chirality in the Au144 cluster, encompassing hierarchical chirality in ligands, staple configuration, and core structure.

On the choice of coordinate origin in length gauge optical rotation calculations

In this work, we explore the issue of origin dependence in optical rotation (OR) calculations in the length dipole gauge (LG) using standard approximate methods belonging to density functional theory (DFT) and coupled cluster (CC) theory. We use the origin-invariant LG approach, LG(OI), that we recently proposed as reference for the calculations, and we study whether a proper choice of coordinate origin and molecular orientation can be made such that diagonal elements of the LG-OR tensor match those of the LG(OI) tensor. Using a numerical search algorithm, we show that multiple spatial orientations can be found where the LG and LG(OI) results match. However, a simple analytical procedure provides a spatial orientation where the origin of the coordinate system is close to the center of mass of the molecule. At the same time, we also show that putting the origin at the center of mass is not an ideal choice for every molecule (relative errors in the OR up to 70% can be obtained in out test set). Finally, we show that the choice of coordinate origin based on the analytical procedure is transferable across different methods and it is superior to putting the origin in the center of mass or center of nuclear charge. This is important because the LG(OI) approach is trivial to implement for DFT, but not necessarily for nonvariational methods in the CC family. Therefore, one can determine an optimal coordinate origin at DFT level and use it for standard LG-CC response calculations.

X-ray and Optical Circular Dichroism as Local and Global Ultrafast Chiral Probes of [12]Helicene Racemization

Chirality is a fundamental molecular property that plays a crucial role in biophysics and drug design. Optical circular dichroism (OCD) is a well-established chiral spectroscopic probe in the UV-visible regime. Chirality is most commonly associated with a localized chiral center. However, some compounds such as helicenes (Figure 1) are chiral due to their screwlike global structure. In these highly conjugated systems, some electric and magnetic allowed transitions are distributed across the entire molecule, and OCD thus probes the global molecular chirality. Recent advances in X-ray sources, in particular the control of their polarization and spatial profiles, have enabled X-ray circular dichroism (XCD), which, in contrast to OCD, can exploit the localized and element-specific nature of X-ray electronic transitions. XCD therefore is more sensitive to local structures, and the chirality probed with it can be referred to as local. During the racemization of helicene, between opposite helical structures, the screw handedness can flip locally, making the molecule globally achiral while retaining a local handedness. Here, we use the racemization mechanism of [12]helicene as a model to demonstrate the capabilities of OCD and XCD as time-dependent probes for global and local chiralities, respectively. Our simulations demonstrate that XCD provides an excellent spectroscopic probe for the time-dependent local chirality of molecules.

Electronic current densities and origin-independent property densities induced by optical fields

The interaction of a molecule with optical fields is customarily interpreted by means of induced time-dependent electric polarizabilities, magnetizabilities and mixed electric-magnetic polarizabilities. In general, these properties can be rationalized by integrals of density functions formulated in terms of induced charge and current densities. In this perspective, we focus on what has been done so far at the theoretical level, and on what can be expected to be unveiled from the topological study of suitable density functions, endowed with the fundamental requirement of origin invariance. Densities characterized by such a property can be integrated all over the configuration space to obtain electric dipole polarizability and optical rotatory power. Corresponding maps visualize domains mainly involved in the molecular response. The diagonal components of origin-independent density tensor functions that, on integration, yield corresponding electric dipole polarizability tensor of benzene, naphthalene, phenanthrene and ovalene, have been computed, confirming the ubiquitous presence of counter-polarization regions in the proximity of the atomic nuclei. They are associated with toroidal electron currents, induced by time derivative of the electric field of impinging radiation. Electron (de)localization in these systems is readily observed and estimated. The optical rotation density of the carbonyl chromophore is studied in detail. Its essential feature is the separation in quadrants of alternating sign of density about the CO bond. The presence of an extrachromophoric perturbation determines asymmetry in the extension of the quadrant distribution, thus causing optical rotation.

Enantiopure cycloplatinated pentahelicenic N-heterocyclic carbenic complexes that display long-lived circularly polarized phosphorescence

The preparation of the first enantiopure cycloplatinated complexes bearing a bidentate, helicenic N-heterocyclic carbene and a diketonate ancillary ligand is presented, along with their structural and spectroscopic characterization based on both experimental and computational studies. The systems exhibit long-lived circularly polarized phosphorescence in solution and in doped films at room temperature, and also in a frozen glass at 77 K, with dissymmetry factor g_lum values ≥10^-3 in the former and around 10^-2 in the latter.

Synthesis, structural characterization, and chiroptical properties of planarly and axially chiral boranils

2-Amino[2.2]paracyclophane reacts with salicylaldehyde or 2-hydroxyacetophenone to yield imines that then give access to a new series of boranils (8b-d) upon complexation with BF₂ . These novel boron-containing compounds display both planar and axial chiralities and were examined experimentally and computationally. In particular, their photophysical and chiroptical properties were studied and compared to newly prepared, simpler boranils (9a-d) exhibiting axial chirality only. Less sophisticated chiral architectures were shown to demonstrate overall stronger circularly polarized luminescence (CPL) activity.

Helicenic N-heterocyclic carbene copper(I) complex displaying circularly polarized blue fluorescence

Enantiopure copper(I) chloride complexes bearing a monodentate N-(carbo[6]helicenyl)-NHC ligand have been prepared and characterized experimentally and computationally. Their high stability enables the stereochemistry to be probed by X-ray crystallography and NMR spectroscopy. The resolved enantiomeric complexes emit circularly polarized blue fluorescence with g_lum ∼1.3 × 10^-3 in solution. The photophysical and chiroptical properties of these systems, with their helicene-centred origin, are similar to those of the organic helicene-benzimidazole precursor proligand, although the reverse axial chirality configuration is preferentially observed for the complex compared to the ligand.

Comparison of Length, Velocity, and Symmetric Gauges for the Calculation of Absorption and Electric Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory

A velocity and symmetric gauge implementation for real-time time-dependent density functional theory (RT-TDDFT) in the CP2K package using a Gaussian and plane wave approach is presented, including the explicit gauge-transformed contributions due to the nonlocal part of pseudopotentials. Absorption spectra of gas-phase α-pinene are calculated in length and velocity gauges in the long-wavelength approximation for the application of a δ pulse in linear and full order. The velocity gauge implementation is also applied to a solvated uracil molecule to showcase its use within periodic boundary conditions (PBC). For the calculation of the expectation value of the electric dipole moment in PBC, both the velocity representation and the modern theory of polarization give equivalent absorption spectra if a distributed reference point is used for the nonlocal term of the velocity operator. The discussion of linear response theory takes place in a unified framework in terms of linear response functions in propagator notation, distinguishing the parts of the linear response functions associated with perturbation and response. To further investigate gauge dependence, electric circular dichroism (ECD) spectra of α-pinene were calculated either as magnetic response to an electric field perturbation, in length or velocity gauge, or as electric response to a magnetic field perturbation in the symmetric gauge. Both approaches, electric and magnetic perturbations, have been found to yield equivalent ECD spectra.

Nontrivial spectral band progressions in electronic circular dichroism spectra of carbohelicenes revealed by linear response calculations

We demonstrate that contemporary computational resources allow for accurate theoretical studies of systems matching recent advances in experimental helicene chemistry. Concerned with first-principles calculations of carbohelicenes, our work surpasses CH[12] as the largest system investigated to date and unravels trends in the electronic structure of the low-lying states of the homologous series. Utilizing a highly efficient implementation of linear response algorithms, we present electronic circular dichroism (CD) spectra of carbohelicenes ranging from CH[5] to CH[30] at the level of Kohn-Sham density-functional theory. Our results for a systematic increase in system size show the emergence of new CD bands that subsequently rise to intensities dominating the spectrum. The spectral band progressions exhibit a periodicity directly linked to the number of overlapping layers of conjugation. While our findings rectify the current understanding of the electronic structure of carbohelicenes, they also serve as a general call for caution regarding the extrapolation of trends from small system ranges.

A Computational Protocol for Vibrational Circular Dichroism Spectra of Cyclic Oligopeptides

Cyclic peptides are a promising class of compounds for next-generation antibiotics as they may provide new ways of limiting antibiotic resistance development. Although their cyclic structure will introduce some rigidity, their conformational space is large and they usually have multiple chiral centers that give rise to a wide range of possible stereoisomers. Chiroptical spectroscopies such as vibrational circular dichroism (VCD) are used to assign stereochemistry and discriminate enantiomers of chiral molecules, often in combination with electronic structure methods. The reliable determination of the absolute configuration of cyclic peptides will require robust computational methods than can identify all significant conformers and their relative population and reliably assign their stereochemistry from their chiroptical spectra by comparison with ab initio calculated spectra. We here present a computational protocol for the accurate calculation of the VCD spectra of a series of flexible cyclic oligopeptides. The protocol builds on the Conformer-Rotamer Ensemble Sampling Tool (CREST) developed by Grimme and co-workers ( Phys. Chem. Chem. Phys. 2020, 22, 7169-7192 and J. Chem. Theory. Comput. 2019, 15, 2847-2862) in combination with postoptimizations using B3LYP and moderately sized basis sets. Our recommended computational protocol for the computation of VCD spectra of cyclic oligopeptides consists of three steps: (1) conformational sampling with CREST and tight-binding density functional theory (xTB); (2) energy ranking based on single-point energy calculations as well as geometry optimization and VCD calculations of conformers that are within 2.5 kcal/mol of the most stable conformer using B3LYP/6-31+G*/CPCM; and (3) VCD spectra generation based on Boltzmann weighting with Gibbs free energies. Our protocol provides a feasible basis for generating VCD spectra also for larger cyclic peptides of biological/pharmaceutical interest and can thus be used to investigate promising compounds for next-generation antibiotics.

Comparative Study of Vibrational Raman Optical Activity with Different Time-Dependent Density Functional Approximations: The VROA36 Database

A new database, VROA36, is introduced to investigate the performance of computational approaches for vibrational Raman optical activity (VROA) calculations. The database is composed of 36 molecules with known experimental VROA spectra. It includes 93 conformers. Normal modes calculated with B3LYP-D3(BJ)/def2-TZVP are used to compute the VROA spectra with four functionals, B3LYP-D3(BJ), ωB97X-D, M11, and optimally tuned LC-PBE, as well as several basis sets. SimROA indices and frequency scaling factors are used to compare calculated spectra with each other and with experimental data. The four functionals perform equally well independently of the basis set and usually achieve good agreement with the experimental data. For molecules in near- or at-resonance conditions, the inclusion of a complex (damped) linear response approach is important to obtain physically meaningful VROA intensities. The use of any of the tested functional approximations with the def2-SVPD Gaussian-type basis set, or a basis of similar flexibility, can be recommended for efficient and reliable theoretical VROA studies.

Origin invariant electronic circular dichroism in the length dipole gauge without London atomic orbitals

We present a method for obtaining origin-independent electronic circular dichroism (ECD) in the length-gauge representation LG(OI) without the usage of London atomic orbitals. This approach builds upon the work by Caricato [J. Chem. Phys. 153, 151101 (2020)] and is applied to rotatory strengths and ECD spectra from damped response theory. Numerical results are presented for time-dependent Hartree-Fock and density-functional theory, the second-order algebraic diagrammatic construction method, and linear-response coupled-cluster theory with singles and approximate doubles. We can support the finding that the common choice of placing the gauge origin in the center of mass of a molecule in conventional length-gauge calculations involving chiroptical properties might not be optimal and show that LG(OI) is a valuable alternative for the origin-independent calculation of ECD spectra. We show that, for a limited test set, the convergence of the rotatory strengths calculated with the LG(OI) approach toward the basis-set limit tends to be faster than for the established velocity gauge representation. Relationships between the sum-over-states expression of the optical rotation in the LG(OI) framework and its representation in terms of response functions are analyzed.

Basis Set Dependence of Optical Rotation Calculations with Different Choices of Gauge

In this work, the basis set dependence of optical rotation (OR) calculations is examined for various choices of gauge/level of theory. The OR is calculated for a set of 50 molecules using B3LYP and CAM-B3LYP and 17 molecules using coupled cluster with single and double excitations (CCSD). The calculations employ the correlation-consistent basis sets, aug-cc-pVζZ with ζ = D, T, Q. An inverse-power extrapolation formula is then utilized to obtain OR values at the complete basis set (CBS) limit. We investigate the basis set convergence for these methods and three choices of gauge: length gauge (with gauge-including atomic orbitals, LG(GIAOs), for DFT), the origin-invariant length gauge [LG(OI)], and the modified velocity gauge (MVG). The results show that all methods converge smoothly to the CBS limit and that the LG(OI) approach has a slightly faster convergence rate than the other choices of gauge. While the DFT methods reach gauge invariance at the CBS limit, CCSD does not. The significant difference between the MVG and LG(OI) results at the CBS limit, 26%, indicates that CCSD is not quite at convergence in the description of electron correlation for this property. On the other hand, gauge invariance at the CBS limit for DFT does not lead to the same OR values for the two density functionals, which is also due to electron correlation incompleteness. A limited comparison to gas-phase experimental OR values for the DFT methods shows that CAM-B3LYP seems more accurate than B3LYP. Overall, this study shows that the LG(OI) approach with the aug-cc-pVTZ basis set for DFT, and with the CBS(DT) extrapolation for CCSD, provides a good cost/accuracy balance.

The Assignment of the Absolute Configuration of Non-Cyclic Sesquiterpenes by Vibrational and Electronic Circular Dichroism: The Example of Chiliadenus lopadusanus Metabolites

9-Hydroxynerolidol, 9-oxonerolidol, and chiliadenol B are three farnesane-type sesquiterpenoids isolated from Chiliadenus lopadusanus that have shown an interesting activity against human pathogens as Gram+ and Gram- bacteria resistant to antibiotics. However, the absolute configuration (AC) of these interesting sesquiterpenes has not been assigned so far. Vibrational and electronic circular dichroism spectra have been recorded and correlations are pointed out for the three compounds. Density functional theory (DFT) calculations are used in conjunction with Mosher's method of investigation to assign AC. Statistical analysis is considered to quantitatively define the choice of AC from VCD spectra.

Automated Quantum Chemistry-Based Calculation of Optical Rotation for Large Flexible Molecules

The calculation of optical rotation (OR, [α]_D) for nonrigid molecules was limited to small systems due to the challenging problem of generating reliable conformer ensembles, calculating accurate Boltzmann populations and the extreme sensitivity of the OR to the molecules' three-dimensional structure. Herein, we describe and release the crenso workflow for the automated computation of conformer ensembles in solution and corresponding [α]_D values for flexible molecules. A comprehensive set of 28 organic drug molecules (28-144 atoms) with experimentally determined values is used in our assessment. In all cases, the correct OR sign is obtained with an overall mean relative deviation of 72% (mean absolute deviation of 82 °[dm(g/cm³)]^-1 for experimental values in the range -160 to 287 °[dm(g/cm³)]^-1). We show that routine [α]_D computations for very flexible, biologically active molecules are both feasible and reproducible in about a day of computation time on a standard workstation computer. Furthermore, we observed that the effect of energetically higher-lying structures in the ensemble on the OR is often averaged out and that in 23 out of 28 cases, the correct OR sign is obtained by just considering only the lowest free energy conformer. In four example cases, we show that the approach can also describe the OR of pairs of flexible diastereomers properly. In summary, even very sensitive, multifactorial physicochemical properties appear reliably predictable with minimal user input from efficiently automated quantum chemical methods.

Chiroptical anisotropy of crystals and molecules

Optical activity, a foundational part of chemistry, is not restricted to chiral molecules although generations have been instructed otherwise. A more inclusive view of optical activity is valuable because it clarifies structure-property relationships however, this view only comes into focus in measurements of oriented molecules, commonly found in crystals. Unfortunately, measurements of optical rotatory dispersion or circular dichroism in anisotropic single crystals have challenged scientists for more than two centuries. New polarimetric methods for unpacking the optical activity of crystals in general directions are still needed. Such methods are reviewed as well as some of the 'nourishment' they provide, thereby inviting to new researchers. Methods for fitting intensity measurements in terms of the constitutive tensor that manifests as the differential refraction and absorption of circularly polarized light, are described, and examples are illustrated. Single oriented molecules, as opposed to single oriented crystals, can be treated computationally. Structure-property correlations for such achiral molecules with comparatively simple electronic structures are considered as a heuristic foundation for the response of crystals that may be subject to measurement.

Origin invariant full optical rotation tensor in the length dipole gauge without London atomic orbitals

We present an origin-invariant approach to compute the full optical rotation tensor (Buckingham/Dunn tensor) in the length dipole gauge without recourse to London atomic orbitals, called LG(OI). The LG(OI) approach is simpler and less computationally demanding than the more common length gauge (LG)-London and modified velocity gauge (MVG) approaches, and it can be used with any approximate wave function or density functional method. We report an implementation at the coupled cluster with single and double excitations level (CCSD), for which we present the first simulations of the origin-invariant Buckingham/Dunn tensor in the LG. We compare LG(OI) and MVG results on a series of 22 organic molecules, showing good linear correlation between the approaches, although for small tensor elements, they provide values of opposite sign. We also attempt to decouple the effects of electron correlation and basis set incompleteness on the choice of gauge for specific rotation calculations on simple test systems. The simulations show a smooth convergence of the LG(OI) and MVG results with the basis set size toward the complete basis set limit. However, these preliminary results indicate that CCSD may not be close to a complete description of the electron correlation effects on this property even for small molecules and that basis set incompleteness may be a less important cause of discrepancy between choices of gauge than electron correlation incompleteness.

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes

The self-consistent coupled-perturbed (SC-CP) method in the CRYSTAL program has been adapted to obtain electromagnetic optical rotation properties of chiral periodic systems based on the calculation of the magnetic moment induced by the electric field. Toward that end, an expression for the magnetic transition moment is developed, which involves an appropriate electronic angular momentum operator. This operator is forced to be hermitian so that the chiroptical properties are real. In our formulation, the trace of the optical rotatory power matrix is gauge-origin-invariant as long as the electric dipole transition matrix elements are obtained using the velocity (rather than position) operator. On the other hand, the component along the optic axis is invariant in general for uniaxial and biaxial crystals. Under the same conditions, these properties also do not depend on the so-called missing integers that occur in the treatment of the electric dipole moment of quasi-one-dimensional periodic systems or the analogue of missing integers for the case of higher dimensionality. Tests on a model H₂O₂ polymer confirm the formalism and, as desired, show that the calculated properties are independent of the size and definition of the unit cell. In addition, an empirical relation to a finite oligomer gauge-including atomic orbital (GIAO) calculation is found. Applications, with comparison to experiment, are carried for α-quartz, tartaric acid crystal, and carbon nanotubes. Future developments of this initial approach to chiroptical properties in the solid state are noted.

Circularly Polarized Fluorescent Helicene-Boranils: Synthesis, Photophysical and Chiroptical Properties

Mono- and di-boranil-substituted helicenes were prepared by BF₂ -borylation of the corresponding anils, readily synthesized by condensation of 2-amino- and 2,15-diamino-helicenes with 4-(diethylamino)salicylaldehyde. After enantiomeric resolution using HPLC, their chiroptical properties including circularly polarized fluorescence in solution and in PMMA films were investigated and rationalized with the help of NMR, X-ray and quantum-chemical calculations.

Chiral Triphenylacetic Acid Esters: Residual Stereoisomerism and Solid-State Variability of Molecular Architectures

We have proven the usability and versatility of chiral triphenylacetic acid esters, compounds of high structural diversity, as chirality-sensing stereodynamic probes and as molecular tectons in crystal engineering. The low energy barrier to stereoisomer interconversion has been exploited to sense the chirality of an alkyl substituent in the esters. The structural information are cascaded from the permanently chiral alcohol (inducer) to the stereodynamic chromophoric probe through cooperative interactions. The ECD spectra of triphenylacetic acid esters are highly sensitive to very small structural differences in the inducer core. The tendencies to maximize the C-H···O hydrogen bonds, van der Waals interactions, and London dispersion forces determine the way of packing molecules in the crystal lattice. The phenyl embraces of trityl groups allowed, to some extent, the control of molecular organization in the crystal. However, the spectrum of possible molecular arrangements is very broad and depends on the type of substituent, the optical purity of the sample, and the presence of a second trityl group in the proximity. Racemates crystallize as the solid solution of enantiomers, where the trityl group acts as a protecting group for the stereogenic center. Therefore, the absolute configuration of the inducer is irrelevant to the packing mode of molecules in the crystal.

A Density Functional Theory Study of Optical Rotation in Some Aziridine and Oxirane Derivatives

We present time-dependent density functional theory (TDDFT) calculations of the electronic optical rotation (ORP) for seven oxirane and two aziridine derivatives in the gas phase and in solution and compare the results with the available experimental values. For seven of the studied molecules it is the first time that their optical rotation was studied theoretically and we have therefore investigated the influence of several settings in the TDDFT calculations on the results. This includes the choice of the one-electron basis set, the exchange-correlation functional or the particular polarizable continuum model (PCM). We can confirm that polarized quadruple zeta basis sets augmented with diffuse functions are necessary for converged results and find that the aug-pc-3 basis set is a viable alternative to the frequently employed aug-cc-pVQZ basis set. Based on our study, we cannot recommend the generalized gradient functional KT3 for calculations of the ORP in these compounds, whereas the hybrid functional PBE0 gives results quite similar to the long-range correct CAM-B3LYP functional. Finally, we observe large differences in the solvent effects predicted by the integral equation formalism of PCM and the SMD variant of PCM. For the majority of solute/solvent combinations in this study, we find that the SMD model in combination with the PBE0 functional and the aug-pc-3 basis set gives the best agreement with the experimental values.

Full optical rotation tensor at coupled cluster with single and double excitations level in the modified velocity gauge

This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10%-20% with CAM-B3LYP and 20%-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(-)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistent with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials.

Vibronic Spectra of π-Conjugated Systems with a Multitude of Coupled States: A Protocol Based on Linear Vibronic Coupling Models and Quantum Dynamics Tested on Hexahelicene

Hexahelicene is a prototype of an extended π-conjugated system with axial chirality. Its absorption (ABS) and electronic circular dichroism (ECD) spectra show vibronic features and strong nonadiabatic effects, challenging currently available computational methods. Here, we compute the nonadiabatic ABS and ECD vibronic spectra of hexahelicene in the full energy range, covering ∼2 eV and 14-18 coupled electronic states, including all of the relevant nuclear coordinates. To this end, we exploit a recently proposed protocol that uses time-dependent density functional theory to parameterize linear vibronic coupling models comprising several electronic states. Spectra are computed through quantum dynamical propagations with multiconfigurational time-dependent Hartree methods. Our results nicely reproduce the experimental spectra providing an assignment of the main observed bands. On the contrary, we document that the application of the Herzberg-Teller intensity-borrowing theory leads to large artifacts. The proposed approach is of general applicability for rigid systems and represents a viable tool for studying the photophysical properties of π-conjugated systems characterized by a dense manifold of interacting electronic states.

Dynamic Induction of Optical Activity in Triarylmethanols and Their Carbocations

A series of artificial triarylmethanols has been synthesized and studied toward the possibility of exhibiting an induced optical activity. The observed chiroptical response of these compounds resulted from the chiral conformation of a triarylmethyl core. The chirality induction from a permanent chirality element to the liable triarylmethyl core proceeds as a cooperative and cascade process. The OH···O(R) and/or (H)O···H_orthoC hydrogen bond formation along with the C–H···π interactions seem to be the most important factors that control efficiency of the chirality induction. The position of chiral and methoxy electron-donating groups within a trityl skeleton affects the amplitude of observed Cotton effects and stability of the trityl carbocations. In the neutral environment, the most intense Cotton effects are observed for ortho-substituted derivatives, which undergo a rapid decomposition associated with the complete decay of ECD signals upon acidification. From all of the in situ generated stable carbocations, only two exhibit intense Cotton effects in the low energy region at around 450 nm. The formation of carbocations is reversible; after alkalization, the ions return to the original neutral forms. Unlike most triarylmethyl derivatives known so far, in the crystal, the triarylmethanol, para-substituted with the chiral moiety, shows a propensity for a solid-state sorting phenomenon.

Triskelion-shaped iridium-helicene NHC complex

Triskelion-shaped cycloiridiated complexes with three N-[6]helicenyl-NHC ligands were prepared with uncommon diastereoselectivities and their configurations were assigned using NMR analyses. They show strong ECD and OR, and yellow CP phosphorescence.

Origin invariant optical rotation in the length dipole gauge without London atomic orbitals

We present an approach to perform origin invariant optical rotation calculations in the length dipole gauge without recourse to London atomic orbitals, called origin invariant length gauge [LG(OI)]. The LG(OI) approach works with any approximate wave function or density functional method, but here we focus on the implementation with the coupled cluster (CC) with single and double excitations method because of the lack of production-level alternatives. Preliminary numerical tests show the efficacy of the LG(OI) procedure and indicate that putting the origin in the center of mass of a molecule may not be an optimal choice for conventional CC-LG calculations.

Dinuclear Rhenium Complexes with a Bridging Helicene-bis-bipyridine Ligand: Synthesis, Structure, and Photophysical and Chiroptical Properties

By attaching pyridine groups to a diaza[6]helicene, a helical, bis-ditopic, bis-N N-coordinating ligand can be accessed. Dinuclear rhenium complexes featuring this bridging ligand, of the form [{Re(CO)₃ Cl}₂ (N N-N N)], have been prepared and resolved to give enantiopure complexes. These complexes are phosphorescent in solution at room temperature under one- and two-photon excitation. Their experimental chiroptical properties (optical rotation, electronic circular dichroism and circularly polarized emission) have been measured. They show, for instance, emission dissymmetry factors of c.a. ±3x10^-3 . Quantum-chemical calculations indicate the importance of stereochemistry on the optical activity, pointing towards further design improvements in such types of complexes.

Synthesis, Absolute Configuration, Antibacterial, and Antifungal Activities of Novel Benzofuryl β-Amino Alcohols

A series of new benzofuryl α-azole ketones was synthesized and reduced by asymmetric transfer hydrogenation (ATH). Novel benzofuryl β-amino alcohols bearing an imidazolyl and triazolyl substituents were obtained with excellent enantioselectivity (96-99%). The absolute configuration (R) of the products was confirmed by means of electronic circular dichroism (ECD) spectroscopy supported by theoretical calculations. Selected benzofuryl α-azole ketones were also successfully asymmetrically bioreduced by fungi of Saccharomyces cerevisiae and Aureobasidium pullulans species. Racemic and chiral β-amino alcohols, as well as benzofuryl α-amino and α-bromo ketones were evaluated for their antibacterial and antifungal activities. From among the synthesized β-amino alcohols, the highest antimicrobial activity was found for (R)-1-(3,5-dimethylbenzofuran-2-yl)-2-(1H-imidazol-1-yl)ethan-1-ol against S. aureus ATCC 25923 (MIC = 64, MBC = 96 μg mL-1) and (R)-1-(3,5-dimethylbenzofuran-2-yl)-2-(1H-1,2,4-triazol-1-yl)ethan-1-ol against yeasts of M. furfur DSM 6170 (MIC = MBC = 64 μg mL-1). In turn, from among the tested ketones, 1-(benzofuran-2-yl)-2-bromoethanones (1-4) were found to be the most active against M. furfur DSM 6170 (MIC = MBC = 1.5 μg mL-1) (MIC-minimal inhibitory concentration, MBC-minimal biocidal concentration).

Point-to-Axial Chirality Transmission: A Highly Sensitive Triaryl Chirality Probe for Stereochemical Assignments of Amines

A readily available stereodynamic and the electronic circular dichroism (ECD)-silent 2,5-di(1-naphthyl)-terephthalaldehyde-based probe has been applied for chirality sensing of primary amines. The chiral amine (the inductor) forces a change in the structure of the chromophore system through the point-to-axial chirality transmission mechanism. As a result, efficient induction of optical activity in the chromophoric system is observed. The butterflylike structure of the probe, with the terminal aryl groups acting as changeable "wings", allowed for the generation of exciton Cotton effects in the region of 1Bb electronic transition in the naphthalene chromophores. The sign of the exciton couplets observed for inductor-reporter systems might be correlated with an absolute configuration of the inductor, whereas the linear relationship between amplitudes of the specific Cotton effect and enantiomeric excess of the parent amine gives potentiality for quantitative chirality sensing. Despite the structural simplicity, the probe turned out to be unprecedentedly highly sensitive to even subtle differences in the inductor structure (i.e., O vs CH2).

Computation of Electromagnetic Properties of Molecular Ensembles

We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. The methodology is based on the link that we establish between quantum‐chemical simulations and the transfer matrix (T‐matrix) approach, a common tool in physics and engineering. We exemplify and analyze the accuracy of the methodology by using the time‐dependent Hartree‐Fock theory simulation data of a single chiral molecule to compute the T‐matrix of a cross‐like arrangement of four copies of the molecule, and then computing the circular dichroism of the cross. The results are in very good agreement with full quantum‐mechanical calculations on the cross. Importantly, the choice of computing circular dichroism is arbitrary: Any kind of electromagnetic response of an object can be computed from its T‐matrix. We also show, by means of another example, how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions. This is possible because, once the T‐matrices of the individual components of an ensemble are known, the electromagnetic response of the ensemble can be efficiently computed. This holds for arbitrary arrangements of a large number of molecules, as well as for periodic or aperiodic molecular arrays. We identify areas of research for further improving the accuracy of the method, as well as new fundamental and technological research avenues based on the use of the T‐matrices of molecules and molecular ensembles for quantifying their degrees of symmetry breaking. We provide T‐matrix‐based formulas for computing traditional chiro‐optical properties like (oriented) circular dichroism, and also for quantifying electromagnetic duality and electromagnetic chirality. The formulas are valid for light‐matter interactions of arbitrarily‐high multipolar orders.

The ONIOM/PMM Model for Effective Yet Accurate Simulation of Optical and Chiroptical Spectra in Solution: Camphorquinone in Methanol as a Case Study

This paper deals with the development and first validation of a composite approach for the simulation of chiroptical spectra in solution aimed to strongly reduce the number of full QM computations without any significant accuracy loss. The approach starts from the quantum mechanical computation of reference spectra including vibrational averaging effects and taking average solvent effects into account by means of the polarizable continuum model. Next, the snapshots of classical molecular dynamics computations are clusterized and one reference configuration from each cluster is used to compute a reference spectrum. Local fluctuation effects within each cluster are then taken into account by means of the perturbed matrix model. The performance of the proposed approach is tested on the challenging case of the optical and chiroptical spectra of camphorquinone in methanol solution. Although further validations are surely needed, the results of this first study are quite promising also taking into account that agreement with experimental data is reached by just a couple of full quantum mechanical geometry optimizations and frequency computations.

Amplification of the chiroptical response of UV-transparent amines and alcohols by N-phthalimide derivatization enabling absolute configuration determination through ECD computational analysis

The stereoselective transformation of chiral UV-transparent amines and alcohols to phthalimides has proved to be a simple and efficient method to enhance the chiroptical response of these substrates allowing their reliable absolute configuration determination by computational analysis of ECD spectra. Such a transformation also leads to a significant reduction in the molecular conformational flexibility thus simplifying the conformational analysis required by the computational treatment. The method described herein thus allows the absolute configuration assignment to these challenging substrates to be much easier and reliable.

Chiroptical Sensing: A Conceptual Introduction

Chiroptical responses have been an essential tool over the last decades for chemical structural elucidation due to their exceptional sensitivity to geometry and intermolecular interactions. In recent times, there has been an increasing interest in the search for more efficient sensing by the rational design of tailored chiroptical systems. In this review article, advances made in chiroptical systems towards their implementation in sensing applications are summarized. Strategies to generate chiroptical responses are illustrated. Theoretical approaches to assist in the design of these systems are discussed. The development of efficient chiroptical reporters in different states of matter, essential for the implementation in sensing devises, is reviewed. In the last part, remarkable examples of chiroptical sensing applications are highlighted.

Modulation of circularly polarized luminescence through excited-state symmetry breaking and interbranched exciton coupling in helical push-pull organic systems

π-Helical push-pull dyes were prepared and their (chir)optical properties were investigated both experimentally and computationally. Specific fluorescent behaviour of bis-substituted system was observed with unprecedented solvent effect on the intensity of circularly polarized luminescence (CPL, dissymmetry factor decreasing from 10-2 to 10-3 with an increase in solvent polarity) that was linked to a change in symmetry of chiral excited state and suppression of interbranched exciton coupling. The results highlight the potential of CPL spectroscopy to study and provide a deeper understanding of electronic photophysical processes in chiral π-conjugated molecules.

α-Costic acid, a plant sesquiterpene with acaricidal activity against Varroa destructor parasitizing the honey bee

The organic extract of the aerial parts of Dittrichia viscosa, a perennial native plant of the Mediterranean basin, showed a significant acaricidal activity against Varroa destructor, the parasite mite of Apis mellifera, commonly called honey bee. Among the metabolites isolated from the organic extract of this Asteraceae, α-costic acid showed to be one of the compounds responsible for the toxic activity exhibited by the crude plant extract on this parasite mite species. In addition to the toxic effect a clear acaricidal response has been recorded when the parasitic mite was exposed to 1 mg/mL concentration of α-costic acid while no effects have been showed on honey bees using the same compound at the same concentration. This finding suggests a potential use of α-costic acid to control Varroa mites. The possibility to reliably achieve absolute configuration of α-costic acid by DFT computational analysis of chiroptical spectra has been also demonstrated.^†.

Ab Initio Study of Circular Dichroism and Circularly Polarized Luminescence of Spin-Allowed and Spin-Forbidden Transitions: From Organic Ketones to Lanthanide Complexes

Complete and restricted active space self-consistent field (CAS-/RAS-SCF) wave function methods are applied for the calculation of circular dichroism (CD) and circularly polarized luminescence (CPL) of a series of molecules comprising four organic ketones, the chiral cobalt(III) complex [Co(en)₃]³⁺, and the europium(III) complex [Eu(DPA)₃]^3-. The ab initio results are in good agreement with the experimental data and previous results obtained with Kohn-Sham density functional theory in the case of the spin-allowed transitions. CD and CPL properties are calculated ab initio for the spin-forbidden transitions of both a transition metal and a lanthanide complex.