1 INTRODUCTION

Chirality is omnipresent in life and related processes. The fraction of products extracted from natural sources containing one or more stereogenic elements is above 80%.1 Pharmaceutically active compounds, either derived from natural products or synthesized ex novo, are chiral in over 60% cases.1 It is also very well known that different stereoisomers of chiral substances, including enantiomers, very often display different pharmacology, ADME (absorption, distribution, metabolism, excretion), and toxicology.2 As a consequence, a complete stereochemical elucidation, including the assignment of the absolute configuration (AC), is a necessary requirement in natural products isolation and drug discovery. By far, the most accurate method for assigning ACs is x-ray diffraction.3-5 This method is however restricted to crystalline materials of compounds containing “heavy” elements, that is, exhibiting strong enough anomalous dispersion.

Chiroptical methods are a family of spectroscopic techniques based on the interaction between chiral, non-racemic matter with circularly polarized light.6, 7 In the context of AC assignment of natural products, the most popular methods are optical rotation (OR), electronic circular dichroism (ECD or simply CD), vibrational CD (VCD), and Raman optical activity (ROA). Nowadays, all these quantities can be calculated by quantum-mechanical (QM) means with good accuracy and acceptable computational cost for medium-size molecule.8 Therefore, the comparison between experimental and calculated spectra has become the most popular approach for assigning the AC of natural products, either using a single technique or a combination thereof.9-13 This computational approach is apparently very immediate and easily available to nonexperts. However, caution must be put in the choice of the correct calculation method.14 Another critical point is the correspondence between the input geometries and the actual conformational ensemble. For that reason, an efficient and accurate conformational analysis is imperative, based also on experimental data.14, 15

Despite the advancement and increasing popularity of QM calculations, there are several means available for interpreting chiroptical spectra that are able to provide AC assignments without calculations; this is especially true for ECD.16 The most important of such approaches is represented by the exciton chirality method (ECM). The theoretical basis of ECM lies in the concepts of exciton coupling, coupled oscillators, and group polarizability, which were developed by Davydov, Kuhn, and Kirkwood.17-19 The first application of these concepts to organic stereochemistry was provided by Mason.20 However, only after the report of the dibenzoate chirality rule by Harada and Nakanishi for compounds containing a diol moiety convertible into a bis(benzoate),21 a general protocol was established for the assignment of ACs by the ECM. Then, the method was extended to compounds with different skeletons and functionalities22, 23 and eventually applied by Berova, Nakanishi, Harada, and several other authors to a huge amount of diverse natural compounds and other substrates,24-31 including metal coordination compounds.32, 33

In essence, ECM applies to a chiral molecule containing two or more separate (i.e., nonconjugated) chromophores undergoing electric-dipole allowed electronic transitions (Figure 1). If a compound lacks the necessary chromophore(s), one may select among a whole family of derivatizing agents to be covalently linked to the chiral skeleton; by a proper choice thereof, the detection limit of exciton-coupled ECD spectra may be lowered down to sub-μg, or even below if detected in emission by fluorescence-detected CD (FDCD).34, 35 If the chromophores, or—more accurately—the electric transition dipole moments (TDMs) are properly arranged with respect to each other, the molecule will display an ECD spectrum characterized by an exciton couplet, which arises from the through-space exciton coupling between the TDMs. The couplet consists of two bands of opposite sign and similar intensity. If the two coupling transitions are the same, occurring on two equal chromophores, exciton coupling is said to be degenerate (degenerate exciton coupling [DEC]) and the couplet crossover point (i.e., where it crosses the CD baseline) occurs in correspondence of the chromophore UV maxima. Otherwise, for energetically separated transitions, one will observe two separated ECD bands, each in correspondence with one UV maximum; in this case, nondegenerate exciton coupling (NDEC) occurs. The ECD couplet has a sign, defined as the same of the long-wavelength component (Figure 1). This sign correlates with the absolute angle of twist defined by the two TDMs in a way summarized by the so-called exciton chirality rule: A positive couplet signifies that the two TDMs define a positive chirality, that is, when viewed along the line connecting the dipoles, one would need a clockwise rotation to move from the dipole in the front onto that in the back (Figure 1). The chirality defined by the TDMs is therefore a consequence of both the molecule AC and the molecular conformation. If a good molecular model is available, which is not always an easy piece of information to obtain, looking at the ECD spectrum will provide an immediate AC assignment. Moreover, contrary to other methods for chiroptical analysis used in the past and now faded out, such as many sector rules,6 ECM is not empirical in nature as it is based on a well-established theoretical basis.4, 7, 22

(A) Schematic representation of two exciton-coupled chromophores undergoing electric dipole allowed transitions and their transition dipole moments (TDMs). (B) Definition of CD exciton couplet and its sign. (C) Formulation of the exciton chirality rule

The combination of the aforementioned qualities makes the ECM still often employed in the AC assignment of natural products and other compounds, despite today's prevalence of QM calculations. This is demonstrated by the already quoted reviews that extend up to 2017,25-31 and by several other papers appeared in the meanwhile.36-52 In the present review, we will deal in particular with compounds already containing two or more chromophores, or covalently derivatized therewith; however, it is worth mentioning that AC assignments based on ECM are also possible through supramolecular non-covalent approaches53 or by the use of various dynamic probes.54

The aim of the present contribution is not to cover exhaustively the recent literature about ECM, but to use selected examples to discuss in a critical and illustrative way the principles and prerequisites that need to be met for a correct application of the ECM. These latter include: the knowledge of the molecular conformation, that is, the spatial relationship between coupled chromophores and the presence or absence of any conformational ambiguity; the knowledge of transition moment direction within each chromophore; the confidence that the ECM dominates the ECD spectrum, that is, that other mechanisms of optical activity (intrinsic chirality due to chromophore distortion or conjugation between chromophores) can be excluded. We will use the same lettered list (a)–(c) several times in the following, that is, any time that these prerequisites will be involved in the discussion. ECM should not be applied unless all these pieces of information have been collected and all prerequisites met. If not, its application is not justified and may lead to the correct AC assignment just fortuitously or lead to incorrect AC assignments. In the last years, we have demonstrated that both situations occurred in many recent literature reports,36-38, 55 and several other cases will be discussed in this review. This is especially inconvenient nowadays because simple QM calculations, without resorting to full and costly ECD calculations, may easily provide the desired information. Using both “classic” and recent examples, we will emphasize which are, and how to meet, the necessary criteria for a safe and accurate application of the ECM, which might compete in reliability with QM ECD calculations. Additionally, we will discuss the geometrical dependence of the couplet sign on the reciprocal arrangement of TDMs in a quantitative way. Finally, we will present a molecular orbital (MO) description of the ECM phenomenon. 2 CRITERIA AND PREREQUISITES FOR A CORRECT APPLICATION OF THE ECM

In order to apply the ECM to assign the AC of any compound, this latter must contain two or more chromophores, giving rise to electric-dipole allowed electronic transitions. The chromophores must be (relatively) close in space but not conjugated with each other or involved in charge-transfer transitions. The ECD spectrum should contain a diagnostic ECD couplet (defined above; see Figure 1), or at least one of its components should be clearly recognized (normally its long-wavelength one). At first sight, one may expect that these facts can be simply assessed by looking at the molecular diagram and ECD spectrum. At this point, the three-dimensional (3D) molecular structure comes into play, because one must establish the chirality defined by the two transition dipole moments to correlate it with the ECD couplet sign.

Knowing the molecular structure requires the molecular conformation to be established by a combination of molecular modeling and experimental techniques. Only on some occasions can this step be skipped, for example, for conformationally restricted compounds where the reciprocal arrangement between chromophores is unambiguous. In general, however, the conformational ensemble needs to be investigated, and all the relevant conformers determined, that is, those bringing the largest contribution to the experimental ECD spectrum. This concept attains to requisite (a) of our lettered list.

Once the conformation(s) is (are) known, one must correctly “put” in place each transition dipole within the respective chromophore. This requires the direction of TDMs within each chromophore be known in advance; otherwise, it must be established before applying the ECM (requisite (b) of the list).

Finally, one must correlate the experimental ECD spectrum with the exciton coupling between the chromophores. This necessitates, first of all, a safe identification of the ECD couplet. Second, one must assume that the ECD spectrum is actually dominated by the exciton coupling mechanism, whereas other sources of ECD signals are negligible (requisite (c) of the list).

None of the steps above is trivial, and the importance of correctly assessing all of them is easily overlooked by nonexperts. Application of ECM is possibly immediate and straightforward, and for the very same reason prone to errors. In the following sections, we will analyze how the prerequisites (a)–(c) listed above were—or were not—accounted for in some classic cases and in recent examples of application of the ECM.

3 OVERVIEW OF SELECTED ECM APPLICATIONS

In this section, we will overview selected applications of the ECM to organic compounds. Our classification in Sections 3.1–3.3, 3.1–3.3 will be based on the nature of the main chromophore(s) responsible for exciton-coupled ECD spectra. The reason for this choice is because requisites (b) and (c) depend largely, if not exclusively, on the type of the chromophore(s). Conformational issues (requisite (a)) will be recalled several times in Sections 3.1–3.4, 3.1–3.4 and treated more in detail in Section 3.5.

3.1 Exciton coupling between aromatic chromophores

Aromatic chromophores such as benzene and naphthalene derivatives undergo π–π* transitions, which are often amenable to exciton chirality treatment in a straightforward way, because the orientation of TDMs is well known by previous studies and/or dictated by the chromophore symmetry. This is not necessarily true for any aromatic chromophore, though. We will discuss first two classic applications of ECM to bis(benzoates) and biaryls and then a recent example of apparently incorrect application of the ECM leading to a wrong AC assignment.

3.1.1 Bis(benzoates) The first historical and most classic example of application of the ECM is that of steroidal bis(benzoates) (1).21, 22 These compounds are ideal because all requisites mentioned above are fully met: The polycyclic steroidal skeleton assures a certain rigidity of the system, so the only possible degree of conformational freedom is around the ester linkage, which is well established (Figure 2)21, 22; The p-substituted benzoate chromophore is well characterized; the most important electronic π–π* transition occurs at 230–300 nm, and it is polarized along the long axis of the chromophore (Scheme 1),22 which has an effective C2v symmetry. A short-axis transition occurs too, but it is weaker than long-axis one, that is, its transition dipole is smaller. Moreover, because of the partially allowed rotation around the C–O bond, any transverse transition concurs less efficiently to the exciton coupling56; The CD spectrum of 1 is by far dominated by the exciton coupling between the two benzoates. In fact, steroidal mono-benzoates have much weaker CD spectra.22 Application of the ECM to cholest-5-ene-3β,4β-diol bis(p-dimethylaminobenzoate) (1). (A,B) Diagram and ECD spectrum (ethanol) showing a negative exciton couplet. Adapted with permission from ref.57 Copyright 1974 American Chemical Society. (C) Negative helicity defined by the two transition dipoles. (D) Preferential conformation around each ester bond

Privileged chromophores for ECM applications. Blue double arrows represent the possible orientation of transition dipole moment according to the related effective symmetry, whose “shape” is suggested by red frames; the main symmetry elements are indicated by dotted lines and curved arrows

Summarizing, with compounds like 1, (a) there is no conformational ambiguity; (b) the transition dipole direction is known without any doubt; (c) other possible sources of ECD signals do not interfere with the exciton coupling. Such advantages make the benzoate groups ideal chromophores in the so-called derivatization strategy, that is, when the compound lacks suitable chromophores for exciton coupling but these latter can be easily introduced by chemical derivatization. By choosing a proper substituent X at the para position of the p-X-C6H4-COO− moiety, the wavelength maximum of the main π–π* transition may be modulated from 229 nm (X = H) to 244 nm (X = Br) and 257 nm (X = OMe), up to 307 nm (X = NMe2, data in methanol).22, 24 In all such cases, the effective C2v symmetry is preserved. The possibility of tuning the chromophore transition wavelength allows one to select the most suitable region of the spectrum to observe the diagnostic couplet, which is especially useful to avoid interference from preexisting chromophores. In that respect, several derivatizing agents have been developed for hydroxy and amino groups aimed at the introduction of redshifted chromophores.29, 58, 59 One of them is based on tetraarylporphyrins (Section 3.1.4).

3.1.2 Biaryls: 1,1′-Binaphthyls

A second wide family of compounds for which the exciton coupling mechanism is known to work remarkably well is that of biaryls, of which 1,1′-binaphthyls (2) are a significant example.60 In these compounds, requisites (b) and (c) mentioned above are again fully met. The naphthalene chromophore has D2h symmetry and undergoes a long-axis π–π* transition around 220 nm, which gives rise to a strong ECD couplet in 1,1′-binaphthyls (Figure 3). The short-axis π–π* transition at 280 nm is weaker, and its coupling is negligible in 2 because two such transitions lie parallel to each other. From the viewpoint of exciton coupling, C2v- and D2h-symmetric chromophores behave similarly (Scheme 1). Concerning requisite (a), the only degree of conformation freedom is the rotation around the 1,1′-bond, which is rather free for dihedral angles between 60° and 110°. This axis of chirality is in fact the only stereogenic element in 1,1′-binaphthyls. The value assumed by the dihedral angle is the major factor influencing ECD spectra, and, conversely, ECD spectra are good reporters of the absolute geometry around that axis.61, 62

Application of the ECM to 1,1′-binaphthyls (2). (A,B) Diagram and ECD spectrum of (aR)-2,2′-bis(chloromethyl)-1,1′-binaphthalene (R = CH2Cl, acetonitrile) showing a negative exciton couplet in the region of the long-axis transition. (C) Chirality defined by the two transition dipoles: A negative chirality (and couplet) is found for (aR) axial chirality

Recent applications of ECM to biaryl compounds include bis(indole) alkaloids63 and BODIPY dimers,64, 65 though these latter are complicated by the fact that the major π–π* transition around 500 nm is also magnetically dipole allowed.

3.1.3 Benzene derivatives with different substitution patterns

In p-substituted benzoates and naphthalene derivatives, the orientation of the TDMs is dictated by the chromophore C2v or D2h symmetry. However, benzene derivatives with different substitution patterns may lack any axial symmetry element, so their π–π* transitions may assume any orientation in the ring. Before applying the ECM, it is thus compulsory to know or study the exact orientation of the TDM. The classic study by Collet and Gottarelli on C3-cyclotriveratrylenes (3, Figure 4) demonstrated the dependence of ECD spectra on the nature of ring substituents.66, 67 The sign of the exciton couplets observed in correspondence with 1La and 1Lb transitions of the benzene chromophores is dictated by the orientation of the TDMs, which ultimately depends on X and Y. As an example, with Y=OMe, the 1Lb couplet is positive for X = OH and negative for X = OAc. A similar phenomenon occurs for chiral resorcin[4]arenes.68

Chiral cyclotriveratrylenes studied by Collet and coworkers. A tilt of 1Lb TDM in the direction of red arrow produces a negative couplet, and in the direction blue arrow a positive couplet in the 1Lb region, respectively

A more recent example will help us in demonstrating the importance of a correct assessment of TDM directions, that is, requisite (b) in our lettered list, in compounds containing complex benzene chromophores. The ferulic acid derivative ligusticumaldehyde A (4, Scheme 2) contains two aromatic rings that can be described as a 1,2-dimethoxybenzene and a 3,4-dimethoxybenzaldehyde (substituted dihydrobenzofuran ring).69

Diagram of the original structure of ligusticumaldehyde A (4*), its revised structure (4), and the truncated model used in our analysis (4a)

The ECD spectrum of 4 (Figure 5) shows various bands above 200 nm, two of which (at 232 and 297 nm) were interpreted as a positive exciton couplet arising from the NDEC between the two benzene chromophores. NDEC has been employed in several instances for AC assignments;22, 25, 29 however, it needs extra caution because it is intrinsically weaker than DEC (see Section 3.2.2). In the case of compound 4, the ECD spectrum is indeed weak (|Δε| < 0.5 M−1 cm−1), which should itself warn against a simple exciton interpretation. To rationalize the hypothetical positive couplet in the ECD of 4, the authors used the molecular model shown in Figure 5B where the two straight arrows indicate the directions of the relevant TDMs.69 However, the correct orientation of the 300-nm transition of the 2,3-dihydrobenzofuran-5-carbaldehyde moiety is not along the C-2/C-8′ direction, as depicted in Figure 5B, but rather along the C-1/C-4 direction, as depicted in Figure 5C (see Supporting Information, which contains the details about all calculations run purposely for the present review). This fact turns the positive chirality into a negative chirality, which is at odds with the observed couplet (if any). We must conclude that the absolute stereochemistry at C-7′ and C-8′ of ligusticumaldehyde A (4*)69 is incorrect and it must be revised as 4 in Scheme 2. To confirm our structural revision, we run ECD calculations with time-dependent density functional theory (TD-DFT) on the truncated model 4a (Scheme 2), showing a good agreement with the experimental spectrum for the revised (7'S,8'S) configuration and featuring a positive exciton chirality between the relevant TDMs (Figure 5A,D). It must be stressed that in the case of compound 4, the issue related to TDM directions (requisite (b) in lettered list) is particularly critical because the relevant TDMs are almost coplanar in the significant conformation, meaning that a small rotation in TDM directions may reverse the exciton chirality. In similar situations, assignments based on simple drawings like in Figure 5B are very prone to errors; a numerical evaluation of the geometrical factor allied with exciton chirality is especially desirable in these cases (see Section 4.1). More in general, any aromatic chromophore devoid of symmetry axes should be subdued to QM calculations to ascertain the actual direction(s) of TDMs, before application of the ECM.40, 70, 71

Application of the ECM and ECD calculations to ligusticumaldehyde A (4). (A) Experimental UV (top) and ECD (bottom) spectra (methanol) compared with the TD-DFT calculated spectra for model (7'S,8'S)-4a (this work). (B) Supposed positive helicity defined by the two transition dipoles for 4*. (C) Negative helicity defined by the two transition dipoles shown on the lowest energy conformer of (7'R,8'R)-4a. The direction of the TDM on the right was established by TD-DFT calculations on 7-methoxy-3-methyl-2,3-dihydrobenzofuran-5-carbaldehyde. (D) Correct positive exciton chirality for the revised configuration (7'S,8'S)-4a. Experimental spectra and panel (b) adapted from ref. 69 Copyright 2018, with permission from Elsevier. See Supporting Information for calculation details 3.1.4 Exciton coupling over large distances: Tetrarylporphyrins as “superbenzoates”

The use of tetraarylporphyrins as ECD reporter groups, which has been pioneered by Berova, Nakanishi, and coworkers, represents one of the most successful applications of the ECM in the last 25 years. The main advantage of using (tetraphenyl)porphyrin (TPP; Scheme 3) and its metal complexes (M-TPP) as ECD probes is the redshifted and very intense UV-Vis absorption, both in the Soret region (380–420 nm with ε = 400–450 000) and Q-band region (500–600 nm), also accompanied by fluorescence emission. The redshifted position avoids interference from preexisting chromophores (see Section 3.1.1), while the high ε values and fluorescence emission allow for a highly diagnostic detection at very low concentrations (μM and below).

Tetraarylporphyrins as “superbenzoates.” The Soret band can be described as a circular oscillator arising from the combination of two orthogonal TDMs. Due to the libration depicted by the purple arrow, the transverse component couples less effectively, and the exciton coupling is dominated by the longitudinal component that behaves as the effective TDM

In our classification of privileged chromophores for ECM applications, TPP and M-TPP may look anomalous. In fact, they belong (exactly or effectively) to D4h point group, meaning, for example, that the Soret transition, having Eu symmetry in the D4h point group, cannot be described in terms of a single TDM but rather as a circular oscillator, that is, the combination of two orthogonal TDMs oriented in the aromatic plane (Scheme 3).56 At first sight, this fact would tremendously complicate the exciton analysis of chiral bis-TPP derivatives, because one would need to consider four different exciton coupling terms. In fact, however, 5-(4′-carboxyphenyl)-TPP (TPP-COOH) or its metalated analogues can be used as an alternative to benzoate-like ECD reporter groups for ECM analysis of chiral systems, as they behave for almost all intents as “superbenzoates.”72 To understand the situation, one must consider the libration (wide-amplitude rotation) around the C5-phenyl bond in Scheme 3. Multiple evidence demonstrated that this dihedral angle may freely oscillate between 45° and 135°.56 As a consequence, the magnitude of the transverse component of the Soret circular oscillator is reduced, and the strength of the exciton coupling involving this component is also reduced. Then, the exciton coupling between two TPP chromophores attached to a chiral skeleton, for example a chiral diol, will be dominated by the longitudinal components, which behave like a single “effective” TDM oriented parallel to the two C–O bonds, as in standard benzoates (Scheme 3). The advantage of using TPP or M-TPP instead of benzoates or similar chromophores is obvious: The large ε values guarantee strong exciton couplet amplitudes, and the coupling may extend over large distances. This is spectacularly exemplified by the red-tide toxin brevetoxin B. Here, two TPP groups were attached at the two extrema of the polyoxygenated polycyclic skeleton, lying at a final distance of 40–50 Å, yet enough to produce a weak exciton couplet in the ECD spectrum of derivative 5 (Scheme 4).73 That such couplet is due to a real exciton coupling between the very distant TPP chromophores was proved later by TD-DFT calculations.74 Another noteworthy example is represented by gymnocin-B, a second toxic marine polycyclic polyether. In this case, the distance between the two TPP chromophores of derivative 6 (Scheme 4) amounted to approximately 30 Å.75 The synthesis of 6 called for the development of an efficient derivatization protocol for hindered secondary alcohols, also in light of the very low quantity of starting material. In the end, the ECD spectrum was collected using a sample of only 11 μg of 6.

Diagrams of brevetoxin B (5) and gymnocin-B (6) bis-TPP derivatives analyzed by means of ECM by Berova, Nakanishi, and coworkers. ECD data for 5 (nm [Δε], (CH3OH/H2O 4:1)): 419 (+11), 414 (−15); for 6 (CH2Cl2): 421 (−6), 408 (+1). The estimated distance between the TPP chromophores is 40–50 Å for 5 and 29 Å for 6.73, 75

At this point, it is useful to look at the application of TPP probes from the viewpoint of the ECM prerequisites epitomized by our lettered list. The nature of Soret transitions is well established, including the effective TDM approximation (requisite (b)). The prevalence of exciton coupling as leading ECD mechanism is assured by the redshifted Soret bands (requisite (c)). Concerning requisite (a), any bis-TPP derivative must of course be subject to a proper conformational investigation, as was indeed the case for both brevetoxin B and gymnocin-B derivatives, using molecular mechanics and nuclear magnetic resonance (NMR).

Although not covered by the present review, it must be recalled here that tetraarylporphyrin ECD probes are especially useful in the form of “tweezers”: In this supramolecular approach, an achiral bis-M-TPP compound forms a 1:1 complex with a chiral analyte or a multifunctional derivative thereof.76-79 The analyte chirality dictates the orientation assumed by the two TPP rings in the complex, which gives rise to an exciton couplet in the Soret region whose sign is correlated with the analyte AC.

3.2 Exciton coupling between polyenes, enones, and related systems

Enones and more extended conjugated systems (dienones, trienones, and so on) have been frequently considered in ECM applications.22 Interestingly enough, the exciton coupling between a polyenone-type chromophore (retinal) dominates the chiroptical signature of bacteriorhodopsin and related proteins.80-82 The main electronic transition on these systems is the π–π* transition, which occurs at 260 nm in simple enones, but it is progressively shifted to longer wavelengths upon increasing the conjugation. However, endocyclic enones may be distorted from planarity and become, as it is said, intrinsically chiral or belonging to first-sphere chirality.83 Such intrinsically chiral chromophores have their own CD spectra, and exciton coupling may not be anymore the leading source of ECD signals (see below). A long polyene chain, on the contrary, will preserve its planarity more efficiently because of extended conjugation; moreover, it may be thought to have an effective cylindrical symmetry where any practically relevant transition is polarized along the axis (Scheme 1). Therefore, prerequisites (b) and (c) above are often well satisfied, and the only uncertainty remains the molecular conformation (a), which needs to be properly investigated.

3.2.1 Quasi-degenerate coupling in polyenones

As an example of quasi-degenerate exciton coupling in polyenone derivatives, we consider saturnispol A (7) isolated from marine-derived Trichoderma saturnisporum.39 This compound contains two trienone moieties: one extending from C-1 to C-14 (Figure 6) and the other from C-8 to C-23. The ECD spectrum of 7 displays a clear-cut negative couplet around 360 nm, which can be safely attributed to the exciton coupling between the main π–π* transitions of the trienone chromophores. In fact, there are no other strong chromophores in the molecule. For the reasons explained above, there are no doubts about the direction of the relevant transition, which is long-axis polarized. The fused polycyclic skeleton and the network of intramolecular hydrogen bonds impart rigidity to the whole structure, fixing the two trienones in a specific position. The molecular conformation of saturnispol A (7) was studied by conformational searches with molecular mechanics and geometry optimizations with density functional theory (DFT). Moreover, although not explicitly stated in the original publication,39 it appears that measured nuclear Overhauser effect (NOE) correlations were rationalized looking at the energy-minimized molecular models. The lowest energy structure was seemingly employed to assign the chirality between trienoate transition dipoles (Figure 6), thus establishing the AC in a correct way. This latter was also checked by running TD-DFT calculations. Summing up, requisites (b) and (c) are fully satisfied for saturnispol A, and requisite (a) was also well complied with.

Application of the ECM to saturnispol A (7). (A,B) Diagram and ECD spectrum (in methanol; concentration and path length not reported) showing a negative exciton couplet. The black curve is the TD-DFT-calculated ECD (from the original paper). (C) Negative helicity defined by the two transition dipoles. Adapted from ref.39 3.2.2 NDEC between enones

Nondegenerate exciton coupling (NDEC) may occur between any two different chromophores with suitable electric-dipole allowed transition dipoles and properly arranged in space. However, there is a warning: NDEC is always weaker than the degenerate case7, 22 and may produce weak “couplets,” which can be easily overruled by other sources of ECD signals. This means that requisite (c) in our lettered list cannot be taken for granted. The larger the energy difference between the two chromophore transitions, the weaker will be their mutual exciton coupling.22 With “weak” chromophores such as simple enones, a small difference in the substitution pattern may be enough to remove the degeneracy between two chromophores and convert a moderately strong DEC into a much weaker NDEC. Nakanishi et al. reported the well-known case of quassin (8, Figure 7), a renowned insecticide, which contains two equivalent α-methoxyenones, giving rise to a clear-cut symmetrical positive exciton ECD couplet centered around 250 nm (Figure 7).84 More recently, the AC of a novel quassinoid, perforalactone C (9), was again established by the ECM.85 Here, however, the C-11/C-13 enone is not substituted at C-12, and the degeneracy with the C-1/C-3 enone is removed. This is enough to reduce the exciton coupling strength to ~5% of the previous degenerate case.38 In fact, the ECD spectrum of 9 shows only a faint couplet (Figure 7), which is actually due to other source of ECD signals (each enone chromophore in 9 is embedded in a chiral ring). This example emphasizes the importance of recognizing a diagnostic ECD couplet with no or little interference from other structural factors capable of generating CD signals of comparable strength, that is, point (c) in our list of prerequisites.

Diagram and ECD spectra (methanol) of quassin (8) and perforalactone (9) containing degenerate and nondegenerate enone systems, respectively. Adapted from ref.38 Copyright 2017, with permission from Wiley 3.3 Elusive NDEC in allylic benzoates

It may happen that one of the two transitions involved in NDEC occurs at too high energy (or short wavelengths, <200 nm) to be observed. This is the case of the alkene π–π* transition, which is polarized along the double bond direction and normally occurs at 195 nm. Nonetheless, this transition may be excitonically coupled to a second transition, for example, a benzoate π–π* transition. In this situation, only one component of the “couplet” will be observed, but this may be sufficient to assign the chirality defined by transition dipoles and hence the AC. In fact, the allylic benzoate method (Figure 8), also developed by Harada and Nakanishi, has been applied in several instances in the past.