Specific optical rotation ([α]_D) is simply called “optical rotation” (OR) in this text. Different OR values measured at different wavelengths are termed “optical rotatory dispersion” (ORD). In the absence of an ORD spectrometer, OR at several wavelengths is used in ORD study—633, 589, 546, 436, and 365 nm. Quantum method theories are widely applied for AC study (Grauso et al., 2019). Some typical chiral molecules were used in the study (Egidi et al., 2019). As one of the simplest and cheapest tools in AC determination, calculating chiral molecular OR and then comparing it with the experimental value is a valid and effective method for OR values that are generally not less than 20 degrees (Raghavan and Polavarapu, 2017). OR and ORD have been widely used in the study of AC (Reinscheid and Reinscheid, 2016; Saito and Schreiner, 2020). For example, the chiral compounds 23–25 were assigned using OR methods; they are listed in Figure 5A (Li et al., 2011a; Li et al., 2011b; Ding et al., 2016).

Compound 27 was obtained because natural concentricolide (26) has an anti-HIV property; it was assigned as (R) configuration with a −59.2 of OR (Qin et al., 2006). Quantum methods were used in the AC study (Ren et al., 2009). Method 1: B3LYP/aug-cc-pVDZ//B3LYP/6-31+G(d), and Method 2: B3LYP/aug-cc-pVDZ//MP2/6-311+G(d) were used for OR computations of (S)-26. Both methods predicted −43.7 and −66.1. Thus, the configuration of 26 must be (S). The other compound 28 with OR value of −64.6 (Li and Si, 2012) provided other evidence to support this conclusion (Method 3: (B3LYP/6-31+G(d,p)/PCM//B3LYP/6-31+G(d,p) and Method 4 PCM/B3LYP/6-31++G(d,p)//B3LYP/6-1+G(d,p)) (Figure 5A). Other kinds of chiral compounds, such as sulfone (29) or Si-, Br-atom-containing compound (30) could be used in OR computations using current theoretical methods (Figure 5A) (Haghdani et al., 2016). The interesting chirality of >S=O in 29 and 30 have been well investigated. Like CAM-B3LYP functional and the second-order approximate coupled cluster singles and doubles (CC2) method. Currently, OR values for any chiral compounds that contain most elements of the periodic table could be computed using quantum methods.

Firstly, it should be clear that the assigned AC concluded from OR must be the same as the other quantum theories or experimental results. The bioactive metabolite phyllostin (31) was isolated from Phyllosticta cirsii fungus (Evidente et al., 2008); its relative configuration was established as (3R,4aS,8R,8aS) by NMR and X-ray analyses (Tuzi et al., 2010) while its AC remained unknown. Total synthesis (Muralidharam et al., 1990) and the ECD exciton chirality method (Isogai et al., 1985; Mu et al., 2021) permitted the determination of the AC of its C8 epimer. The ORD study gave the same conclusion: (-)-(3S,4aR,8S,8R)-31 (Figure 5B) (Mazzeo et al., 2013).

It is simple to assign one compound’s AC if one chiral compound is relatively rigid and its relative configuration is known. It is only necessary to compute its OR directly and then compare its OR value with the experimental results to assign its AC. Compound 32 was obtained with a known relative configuration via X-ray (Mo radiation) (Ding et al., 2010); its OR was +57.4 in MeOH. The computed OR for (R)-32 was +74.3 in the gas phase and +66.2 in methanol using the PCM model (Figure 5C). This means the (+)-32 must have the configuration as illustrated in Figure 5C. Indeed, ideal situations are rare.

In some cases, there are several diastereoisomers—for example, 33 (Figure 5C) (Figueroa et al., 2009). Its side-chain configurations with ethylene oxide moiety were not assigned. By comparing the Δ[α]_D values among the four diastereoisomers, isomer 33B with the smallest Δ[α]_D value was assigned as the most likely structure.

Many chiral compounds may have flexible structures and their AC assignment is not easy due to many conformations in solution. For example, with chiral compound halisphingosine A (34) (Molinski et al., 2013), a very flexible linear chiral compound with three stereogenic centers, it is hard to compute its OR to assign its AC. A simpler model is needed—to be discussed latter—or making its derivatives for ECD exciton chirality spectra. Compounds (7R,8R)-35 (Zhang et al., 2021a) and 36 (Zaman et al., 2021) are not as flexible as those of 34 (Figure 5D); they can be used directly in computations of OR or ECD.

It has been reported that the structurally similar compounds rubiginone A₂ (37) and benzopyrenomycin (38) have close OR values; 37 had an OR of +50 and 38 had +38 in CHCl₃ (Figure 6). However, the computed OR values were 14 to 87 for 37 and −12 to −50 for 38, using different quantum methods (Li et al., 2013). Therefore, 37 had the (2R,3S) configuration and 38 must have (2S,3R) configurations. Why is there such a big difference from the viewpoint of structural features? The key point is that these two molecules formed different helical chirality, as illustrated below (Figure 6). When both had (2R,3S) configuration, their conformation analyses were performed. The minor conformers S-37a had an OR value of −240.8 and major conformer M-37b had 211.6. After the Boltzmann statistics, the OR value depended on the major conformer M-37b′s OR sign. In contrast, the major conformer S-38a had −605 and the minor M-38b had 622.8. Finally, the simulated OR value and sign were decided by the major conformer S-38a. Thus, if both had (2R,3S) configuration, they should have a reversed OR sign. Consequently, when both had the same OR sign, they must have different ACs.

This example provided an important hint: when two structures are very similar, the real conformer structures must be carefully examined before identifying their AC using their OR values. Helical structures exist widely and, importantly, generally have large OR values. This example again indicates that conformational study is very important, as we have emphasized previously.

ORD provided more information in other wavelengths for various structures. Since different structures have different sensitivity at different wavelengths, different structures may have obvious and different ORD curves. The AC of C8 of jonquailine (39) was assigned as (R) (Vergura et al., 2018) based on the computations of ORD at the level of B3LYP/aug-cc-pVDZ//B3LYP/TZVP level in the gas phase. The (8S)-39 had a large difference in ORD from the (8R)-39 and the experimental ORD (Figure 7). The ORD values of 39 in methanol were larger than those in chloroform.

Because, for some chiral phenol compounds, the -OH is acidic, its ORD or other properties are dependent on the pH values of the solution. In this case, different solvents may have varying effects on the OR. For example, different ORD curves were recorded for the diesters of (1R,2R)- and (1S,2S)-cyclohexanediols and diamides of (1R,2R)- and (1S,2S)-diaminocyclohexane (40 and 41) with p-hydroxycinnamic acid (Figure 7) (Mazzeo et al., 2016). This is due to the equilibrium under different pH values (Eq. 1). The compounds also exhibited different chiroptical spectroscopies in solution. (1)

In addition, the ORD of any chiral compounds, such as the reaction atropisomer 45 from 42, could be also used in the AC assignment (Figure 8A) (Mirco et al., 2019). The enantiomers (+)-45 and (-)-45 exhibited a very good mirror image as expected. The (S)-45 was used in the ORD study.

Finally, an important phenomenon should be noted. Many linear chiral compounds have only very small OR values (Lu et al., 2020). In these cases, it is common to use quantum methods to compute OR values to assign AC unless there is a so-called known analogue’s OR (theoretical and experimental OR values used as reference). For more about this study, please see the simplified model section. The OR analysis of four additional chiral compounds (46–49) are summarized below (Figure 8B) (Taniguchi et al., 2009; Ding et al., 2012; Yang et al., 2013; Sun et al., 2021a).

A notable case is the computed OR value being generally larger than the experimental datum. In some cases, the computed OR is two or more times larger than the experimental OR values using current DFT methods. Therefore, it is better to refer to other methods in AC determinations for complex chiral compounds, particularly if any of the OR values are small, such as less than 20°.

OR has been widely used for a long time and it will continue to be, as has the ORD method. However, its application for AC study is not as frequent as OR or ECD.

Electronic circular dichroism (ECD) spectra have been used for AC determination since the 1960s. ECD was originally known more simply as CD, and, more recently, many reports use the term ECD for AC assignment (Guo et al., 2020; Zhang et al., 2021b; Kim et al., 2021; Nhoek et al., 2021; Quan et al., 2021). As mentioned above, a detailed conformational search should first be performed (Mazzeo et al., 2014). Many known chiral compounds have been used this way in chiroptical spectroscopic study (Molteni et al., 2015; Stepanek and Bour, 2015; Pescitelli and Bruhn, 2016; Rossi et al., 2016; Johnson et al., 2018) while new synthetic chiral compounds have also been studied (Paolino et al., 2021; Yajima et al., 2021). Chiral compounds require one or two UV-vis chromophores in order to use ECD in their configuration assignments.

The DFT theory has been widely used in ECD computations for various chiral organic compounds (Polavarapu and Covington, 2014; Jiang et al., 2021a; Ji et al., 2021; Niu et al., 2021), including metallic chiral compounds (Enamullah et al., 2016; Saha et al., 2017; Ravutsov et al., 2021). This method provides not only a good balance in treating different molecular systems but also gives relatively accurate computational results when applied to real molecules. For example, using the functional B3LYP at the 6-311+G(d) set level basis can obtain relatively good agreement between theoretical prediction and experimental results. An improved theory, such as cam-DFT (Yanai et al., 2004), is also used in ECD computation. Other methods, like simplified TD-DFT, may give fast and accurate assignment for some chiral compounds (Cerra et al., 2019; Martynov et al., 2019; Ianni et al., 2022). For some chiral molecules, this method can provide more accurate results, although this varies depending on different molecules. A general mixed quantum/classical method for the calculation of the vibronic ECD has been reported as valid tests (Cerezo et al., 2018). Compared to DFT calculations, its computational cost is relatively larger, but it is useful in cases where the ECD shape arises from a subtle balance between vibronic effects and conformational varieties. Indeed, as an active research area, many developed methods have been reported (Liu et al., 2016a; Hodecker et al., 2016; Hong et al., 2016; Nørby et al., 2017; Jimenez et al., 2019; Scott et al., 2021; Wibowo et al., 2021), including the efficient simplified time-dependent density functional theory (sTD-DFT) that has been used to compute large molecular systems with more than 100 atoms (María-Magdalena and Jorge, 2015) such as helicene (Bannwarth et al., 2016), which consists of 102 atom and 16 annulated benzene rings. Simulations of ECD for nucleic acids have also effectively used quantum theory (Zhu et al., 2014; Padula et al., 2016a; Zou et al., 2021).

DFT methods should first be used and, if the predicted ECD curves are greatly different from the experimental results after UV correction, cam-DFT, such as cam-B3LYP theory, can be used in computations to compare both measured and predicted ECD spectra.

DFT is an efficient tool used in AC determinations. Some typical compounds and their ECD spectra are summarized below, such as an unprecedented C9-spiro-fused 7,8-seco-ent-abietane, decandrinin (50) (Figure 9A) (Wang et al., 2014a). The ECD signals had almost no red or blue shifts. The ECD of organic salts, such as clavulanate potassium, can also be calculated using DFT method shift (Li et al., 2018). The structure of some chiral compounds, such as anacolosins A (51), contain some isolated C=C or C=O groups, and ECD signals mostly appear from 200–250 nm (Cai et al., 2019). The best evidence is its match of the predicted VCD with experimental results.

In ECD study generally, chiral molecules have one or more vis-UV chromophores in the UV wavelength range of 200–400 nm for organic compounds. The short wavelength range, such as 180–210 nm, can also provide valid information for aliphatic compounds, such as terpenoids, peptides, or proteins (Farkas et al., 2016; Banerjee and Sheet, 2017). However, signals of 180–210 nm are more difficult to measure without distortions. Most ECD study involves the range of 210–400 nm for organic compounds (Li et al., 2014; Nicu et al., 2014; Podlech et al., 2014; Yu, 2014; Han et al., 2021; Omar et al., 2021; Saetang et al., 2021). The ECD wavelength range for chiral metallic ion-containing organic compounds or poly-conjugated compounds may cover 500 nm or more (Wu et al., 2014; Saleh et al., 2015; Enamullah et al., 2016; Vesga and Hernandez, 2016).

One configurationally stable chiral dithia-bridged hetero (Marty et al., 2014) helicene radical cation (52) was studied (Figure 9B) (Gliemann et al., 2017) involving nitrogen N-chirality. This molecule had a bulky negative ion SbF₆, which is located close to the N atom to fix its conformation. This provides stability to the N chirality formation—natural compounds containing N-cation in natural products are not rare.

Some novel types of chiral compounds were recently obtained from natural sources. Anti-inflammatory cassane-type diterpenoids from the seed kernels of Caesalpinia sinensis have a novel framework formed with the new ring D. This rigid framework (+)-53 was confirmed by X-ray, and its analogues (+)-54 must have the same AC; this has been confirmed by comparing the computed ECD for (5S,6R,8R,9S,10R,14S)-54 with the experimental ECD of (+)-54 as (5S,6R,8R,9S,10R,14S) (Figure 9C) (Wang et al., 2021a) The ACs confirmed by X-ray structure and ECD spectra are the same.

The dimeric form of axial carboline compound 55 has been isolated and identified using ECD (CAM-B3LYP/6-31G(d)//B97D/TZVP) (Jin et al., 2021), which was obtained from the culture broth of a cold-seep derived actinomycete, Streptomyces olivaceus OUCLQ19-3 (Figure 9D). Its other axial diastereisomer was also obtained and the predicted ECD spectrum agreed well with the experimental result. The N-C single bond rotation was seriously restricted; if the rotation barrier was provided there, we could more clearly understand the atropisomer’s properties of NMR in solution.

Finally, we consider the standard deviation (σ) factor of the data. Among the various factors that affect the AC determinations, one problem that has been ignored in the teaching process is the data of σ. The wrong assignment of AC was caused by a wrong use of the sigma. Thus, this factor must be used carefully by beginners to this method.

The data of σ could be 0.2 to 0.5 ev, but 0.3 and/or 0.4 ev has mostly been used in ECD simulations. The general principle of using σ depends on the ECD signals recorded in experiments. Unless the experimental ECD resolution is very high, 0.3 or 0.4 ev can be used in most cases. Once the signal resolution is very high, where the signal’s half-height is small, 0.2 or 0.25 ev can be used to simulate the ECD. In contrast, 0.5 ev may be used in simulation of ECD spectra. Generally, the smaller the σ value, the sharper the signals of ECD will be and the resolution of the ECD will be high.

However, when the ECD signals are complex, it is not easy to select their σ values. For example, one wrong assignment of chiral compound 56 was reported (Ji et al., 2013). The conformational search for all geometries was performed correctly, and the excitation state numbers were covered from 200 nm to 400 nm in the calculations. Its ECD simulation was performed at the B3LYP/6-31G(d) level. The wrong σ value of 0.2 ev was used. After its analogues A–C were obtained, the ACs were assigned again. The original AC of 56 was corrected to 57 by using 0.35 ev (Figure 10A) (Li et al., 2016b). Obviously, the small σ value of 0.2 ev in the report led to the wrong assignment of the compound 56.

The default sigma value of 0.4 ev is used in ECD data treatment in GaussView software; there is much no-cost software can be used for ECD simulations. For more details, please refer to the corresponding websites and download the appropriate software. The corresponding website for ECD spectra is at https://github.com/jbloino/estampes. Readers who need to use it may contact the corresponding person there. Other software may exist on different websites.

As mentioned above, correct conformer structures are extremely important for ACs. This procedure must use quantum theory. Due to the computational limits from before 2000 or earlier, the use of a high basis set, such as 6–311+G(d) for a large chiral molecule, was then difficult. In 1997, two spiro compounds 58 and 59 with very similar skeletons exhibited almost identical ECD spectra (Figure 10B) (Ripa et al., 1997). Compound 59 just had one more CH₂ than 58; both had the same two chromophoric moieties. It was expected that both (S)-58 and (S)-59 would have the same ECD spectra since their spiro-center structure was identical. However, an early report argued that both would have mirror-image ECD spectra using Schellman matrix methods (Sandström, 2000a)—a popular approach in 1990s based on independent system approximation (ISA). For more details about ISA, refer the corresponding materials (Raabe et al., 2012; Sandström, 2000b).

The two structures were then carefully examined using DFT theory (Padula et al., 2016b). The new study “…demonstrates that the main source of the error in the original investigation lies in the fact that the aromatic and N-formyl enamine chromophores are not independent in the sense implied by the ISA; therefore, the ECD spectra of both compounds 58 and 59 cannot be correctly treated by the matrix method approach (Padula et al., 2016b).” Obviously, the early conclusion was not correct. After using all the new conformers in the ECD simulations, the correct results were obtained (Figure 10B). The key reason was that a TDDFT-based fragmentation approach (ISA) led to very different results from full TDDFT calculations. All theories of B3LYP, CAM-B3LYP, and M06-2X with the def2-TZVP basis sets predicted the same conclusion. With the development of computers, full chiral molecules are now used in computations unless the chiral molecules are extremely large.

In general, solvents may have some effect on ECD spectra. In a very unusual case, naproxen (60) had completely different ECD in different solvents (Figure 10C) (Ximenes et al., 2018). It had a (+)-Cotton signal at near 235 nm in acetonitrile and one (−)-Cotton signal at 210 nm. In contrast, it had a (−)-Cotton signal at 230 and 231 nm in ethanol and water and an unremarkable (+)-Cotton effect from 200 to 220 nm. However, the simulated ECD spectra in the three solvents gave very similar curves. All predicted ECD had a (+)-Cotton effect at a 240–245 nm range and a (−)-Cotton effect of 202–205 nm. This is an extremely unusual case, in that the predicted ECD did not match the experimental results in different solvents. Its importance may be that

This finding deserves great attention because polar protic and aprotic solvents are widely used for HPLC analysis in quality control of pharmaceutical drugs. If we consider the importance of discrimination between the active drug [(S)‐naproxen, anti‐ inflammatory] and the toxic one [(R)‐naproxen, hepatotoxic] using ECD detector coupled to HPLC, the findings reported here could represent an important source of error in these analyses (authors’ statement).

The reason was not analyzed until now. It is possible that there was a very strong solvation effect on the formation of different geometries with different energies.

The use of ECD to assign a chiral molecule’s AC requires the chiral center(s) to be close to the chromophore. If the stereogenic center is too far from the chromophores, it can be only used when this molecular relative configuration is reliable. An example is compound 62 (Yuan et al., 2010), which has very limited chromophores. If one had one to two different configurations from the current one (61) illustrated below, it is impossible to record the obvious ECD spectra difference from the 62s ECD. Only when its relative configuration is reliable, such as the X-ray information, then can its AC using ECD be significant and correct (62, Figure 10D) (Avula et al., 2016).

Once again, it must be emphasized that, although compound 61 has one more sugar moiety with five chiral centers, it has no chromophores and its stereogenic centers have very little effect on its ECD spectra. This raises another question: if a chiral molecule has polychiral centers but its relative configuration is not identified, then, if anyone wants to use ECD to identify its AC, it is impossible, since its ECD curves would hardly change, no matter which stereogenic center changes its configuration,.

When the chiral center is located on the side chain, then it is the favored relative to the neighboring ring structures. For example, sparticols A (63) has a chiral center at C8 connected to a hydroxyl group, and its computed ECD and experimental ECD spectrum matched well (Figure 10E) (Garcia et al., 2021). Due to the through space interaction of the -OH with the phenyl ring and the intramolecular H-bond, it has limited flexibility. In this case, its major contribution to the conformer generally played a key role in ECD spectra. Other examples, like asperglaucin A, have been reported (Lin et al., 2021).

Diols with a diol moiety often have biological activities, such as antibiotics (Fischbach and Walsh, 2009) and steroidal hormones (Norman et al., 2004; Niwa and Niwa, 2014). In organic chemistry, a diol fragment can be used as a chiral building block (Hartung and Grubbs, 2014) and promotor used in asymmetric synthesis (Huo et al., 2014). On the other hand, many diol-containing compounds are transparent in the UV-vis spectral range. Thus, they need to be converted into a derivative with a chromophoric group. Chiroptical methods can be used to identify the ACs of some diols (Jawiczuk et al., 2015). It is convenient to convert diols, which may be located on one ring moiety or on a linear carbon chain, into a new cyclic moiety to reduce the conformers in various sugar-derivatives or poly-alcohol-containing compounds in AC study (Pardo-Novoa et al., 2016).

The method of determining the AC of diols is to use dimolybdenum methodology with dimolybdenum tetracarboxylates which act as auxiliaries (Jawiczuk et al., 2014; Masuda et al., 2021). This consists of the in situ formation of chiral complexes (Mo₂-core). The measured ECD spectra of the chiral complexes minus the free-ligand spectrum afford a different spectrum. The determination is strictly associated with the dependence of the signs of the Cotton effect (Górecki et al., 2007). Identical signs occurred respectively at near 400 nm and 310 nm, which is consistent with the sign of the O-C-C-O torsion angle. Examples are introduced here using 64 and 65 (Popik et al., 2014). Hexose 65 negative signs of decisive ECD band at 310 nm and 380 nm conform to the negative sign of the O-C-C-O torsion angle. The second requirement—the antiperiplanar orientation of both hydroxyl groups versus 1,2-O-isopropylidene ring and acetyl group—is also met (Figure 11). On this basis, the assignment of 3S,4S AC in compound 65 was directly possible from the level of the ECD spectrum. However, it is difficult to assign the AC of 64 because it has two possible Newman projections with two states (+) and (-); when two hydroxy groups and two connected Mo atoms were located at the bottom, the large groups had two different positions in space. Thus, it is important to give the proper Newman projection for a given chiral molecule using this method.

A popular method of analysis is to calculate ECD and compare it with the experimental spectrum. Many examples have been studied and the predicted ECD curves agreed well with the experimental results (Junior et al., 2014; Wang et al., 2014b; Fleming et al., 2015; Pescitelli and Bruhn, 2016; Masnyk et al., 2016; Lee et al., 2018; Zhu et al., 2018; Liu et al., 2019a; Liu et al., 2019b; Guo et al., 2021a; Arreaga-González et al., 2021; Guo et al., 2021b; Wang et al., 2021b; Rao et al., 2021; Tan et al., 2021; Xie et al., 2021); this includes the compounds in which the ECD were compared with the compound’s configuration that was assigned using quantum theory methods (Socolsky et al., 2016). Some examples (66–84) are summarized in Figure 12 (Zhang et al., 2008; Pazderkova et al., 2014; Zhang et al., 2014; Bultinck et al., 2015; Sherer et al., 2015; Liu et al., 2016b; Xu et al., 2016b; Evidente et al., 2016; Nakashima et al., 2016; Yu et al., 2016; Endo et al., 2017; Maslovskaya et al., 2017; Xu et al., 2019; Zhou et al., 2019; He et al., 2021a; Sun et al., 2021b; Lu et al., 2021; Xue et al., 2021; Yang et al., 2021).

Another CD method is CD exciton chirality (Pescitelli, 2018). This method generally requires two chromophores to be present in the molecule (could be obtained by synthesis). It is different from the ECD calculations using Gaussian or another package via quantum equations, since the CD exciton method does not give a specific ECD curve or a series of excitation state energy for any chiral compounds. Instead, it uses the relative position of di-chromophores, such as the dibenzoates of acyclic 1,2-glycols in space to determine the ACs. This may entail uncertainties for some chiral compounds where it is not easy to correctly orientate the chromophores’ position. It is useful to determine the AC of the acyclic 1,2-glycols, acetylene alcohols (Naito et al., 2005), or similar chiral compounds. As emphasized above, a key step is to locate the relative positions of two chromophores for a specific chiral compound by conformational considerations.

The Mosher ester method is valid for the AC assignment of secondary alcohols or others (Dale and Mosher, 1973; Seco et al., 2004). This method provides very valid assistance in the study of ACs. In most cases, this method requires the substituents adjacent to the stereogenic center to be small. A previous example clearly stated this point. If there is a very bulky group, it may change the most and second-most stable conformers’ distribution and will finally lead to a wrong conclusion. This point must be clearly remembered.

Both methods are out of the scope of the present review; therefore, the two useful methods are just mentioned here rather than described in detail. Readers interested in the two methods can look for the corresponding reports (Gao et al., 2021), including other experimental methods (Fujii et al., 1998).

Generally, vibrational circular dichroism (VCD) spectroscopy can be used for the AC determinations of any chiral compounds. It differs from ECD in that ECD spectrometers were quickly commercialized in the 1970s and were widely applied to the study of AC. VCD was first applied to AC determinations in 1990s by using magnetic field perturbation equations (Nafie, 1983; Stephens, 1985; Nafie, 1992; Stephens et al., 1994), especially when quantum theory was developed and computational methods became available by use of the Gaussian package (commercially available from 1998, and then more widely for Gaussian 03 in 2003). Modern VCD instruments provide important assistance for AC study (Zhu et al., 2015; Keiderling and Lakhani, 2018; Ren et al., 2019) while computational methods (Polavarapu and Covington, 2014), including anharmonic VCD methods or other theoretical methods (Barone et al., 2012; Domingos et al., 2015; Fuse et al., 2019), make it possible for scientists to perform calculations and comparisons with a wide range of experimental results (Rossi et al., 2017; Taniguchi, 2017; Kohout et al., 2016; Góbi et al., 2015; Abbate et al., 2014; Frelek et al., 2014; Batista et al., 2015; Giovannini et al., 2016; Nieto et al., 2010; Böselt et al., 2019; Demarque et al., 2020; Ren and Zhu, 2009; Monde et al., 2003; Cichewicz et al., 2005; Batista et al., 2011a).

VCD spectroscopy is a valid method used in ACs determination for various chiral compounds (Polavarapu and Santoro, 2020). Since it uses IR light as the source for covering vibrational transitions in all parts of a molecule, it does not require any chromophores in the vis-UV region. It has been widely used in the past decade in the AC assignment of various natural products (Nafie, 2008; Batista et al., 2011b; Debie et al., 2011; Felippe et al., 2012; Lourenço et al., 2012; Cheng et al., 2020; Nafie, 2020).

Raman optical activity (ROA) spectroscopy is hampered by lower sensitivity than VCD for small molecules; however, there are some possibilities for enhancing its signal. Here, we note a recently developed mechanism wherein chirality is enhanced using the resonance that results from supramolecular aggregation. This mechanism is aggregation-induced resonance Raman optical activity (AIRROA). As an example, J-aggregates of astaxanthin (AXT) strongly absorb circularly polarized light in the range of ROA excitation at 532 nm. The implications of aggregation-induced signal enhancement for chiroptical spectroscopy are discussed by Nafie (1996), Vargek et al. (1998), and Zajac et al. (2016). Some ROA studies have been reported (Daugey et al., 2014), including the AC determination of ribifolin (Pinto et al., 2015), which is a kind of cyclopeptide with moderate effectiveness (IC₅₀ = 42 μM) against the Plasmodium falciparum strain 3D7. However, this method has not been widely used in AC study until now, and will not be further discussed in this review.

It has been theoretically shown using nuclear velocity perturbation theory that crystal packing induces the enhancement of VCD or other methods (He et al., 2001; Nafie, 2004; Domingos et al., 2014a; Jahnigen et al., 2018). A so-called “switchable amplification of VCD” for chiral structures was reported to amplify VCD signals (Domingos et al., 2014b). Another way is to use lanthanide tris(β-diketonates) as useful probes in the stereogenic center determination of biological amino alcohols near 1500 cm⁻¹ (β-diketonate IR absorption region) due to the formation of ternary complexation with racemic lanthanide tris(β-diketonates) (Miyake et al., 2014).

In some cases, flexible chiral compounds, such as β-peptides and foldamers, could be analyzed by careful conformational study (Farkas et al., 2019)—for example, compounds 85 (Santoro et al., 2019) to 98 (Mazzeo et al., 2017a; Taniguchi et al., 2017; Gimenesa et al., 2019). Typical structures are 86 (Gimenesa et al., 2019) and 87 (Taniguchi et al., 2017), boron-containing chiral compound 88 (Mazzeo et al., 2017a), chiral thiophene sulfonamide 89 (Rode et al., 2017), chiral Si-containing compound 90 (Xia et al., 2018), pseudoenantiomeric atropisomers anti-(S)-streptorubin B (91A) and syn-(S)-streptorubin (91B) (Andrade et al., 2015), axial chiral ligand 92 (Zhu et al., 2015), 93 (Qiu et al., 2013), bioactive compound 94 (Junior et al., 2015), axial N-BF₂ compound 95 (Abbate et al., 2017), Möbius-shaped cycloparaphenylenes 96 (Nishigaki et al., 2019), and axial 3,3′-bithiophene atropisomeric scaffold 97 (Gabrieli et al., 2016). The chirality of isotope of ¹²C and ¹³C-containing compound (98) can be assigned using VCD (Miura et al., 2019). These compounds nearly cover most important organic compound types (Figure 13). Many other natural products have been well investigated using VCD methods (Nafie, 2011; Ji et al., 2014; Kessler et al., 2014; Mazzeo et al., 2015; Taniguchi et al., 2015; Cheng et al., 2016; Covington et al., 2016; Zhang et al., 2016).

As a useful tool, VCD has been widely examined experimentally and theoretically by theoretical chemists (Ortega et al., 2015a; Nafie et al., 2018; Nafie and Laane, 2018). An interesting example is the N-chirality molecule, the analogue (99) of Tröger’s base. It can be obtained using HPLC with mixtures of CH₂Cl₂ and n-heptane as eluents (Runarsson et al., 2015). A frequency-scaling factor was not applied to the predicted spectra for correcting the calculated spectra appearing at a higher wave number (Figure 14A). In this case, the calculated VCD/IR spectra were calculated at the B3LYP/6–311++G(d,p) level of theory, and the calculation results matched the experimental results well.

As mentioned previously, it is hard to find all conformers for linear chiral compounds. It is also difficult to compute all found geometries in simulations of VCD. The conformer numbers increased quickly with the free rotated single bonds in linear chiral compounds. In one example, the conformers of citronellal (100, Figure 14B), a kind of flavor, were 162 in liquid (Koenis et al., 2019). The total geometries were used in VCD simulations with good agreement between the experimental and computed spectra. Similar examples included compound 101 (Górecki et al., 2017) and others (Zinna and Pescitelli, 2016).

In some cases, chiral molecules are quite large. As with ECD study, significant progress in the study of VCD using quantum mechanical theory for large molecules has been made in the past decade using fragment-based methods (Gordon et al., 2012). The molecules-in-molecules (MIM) fragment-based method is now suggested for handling large molecular VCD treatment (Mayhall and Raghavachari, 2011; Jose et al., 2015). It employs a multilayer method with multiple levels of theory using a generalized hybrid energy expression, or when considering many solvent molecules mixed with chiral molecules using QM/MM methods (Ghidinelli et al., 2018). This is similar to the ONIOM methods used in optimization for large molecules. For more details, readers can refer to the corresponding reports.

For 1,2-diol compounds, VCD can use the di-Mo-intermediates as used in ECD (Jawiczuk et al., 2015). On the other hand, converting the molecule into a five-ring structure is also helpful when the two hydroxyl groups are located on a linear carbon chain, such as pseurotin A₃ with an unusual hetero-spirocyclic system (Xu et al., 2016c).

To compute a VCD spectrum requires calculating both atomic polar and atomic axial tensors based on the force constant matrix, which is generally time-consuming. Density functional-based tight binding (DFTB) theory was recently developed by Visscher (Teodoro et al., 2018), making it possible to obtain accurate VCD spectra with a much lower computational demand than standard DFT methods.

As mentioned above, the ECD spectrum is sensitive to chromophores. In a series of chiral analogues, these molecules have very similar ECD spectra. However, the corresponding VCD spectra are quite different. Even though two chiral compounds have extremely similar structures, they may have totally different VCD spectra. For example, compounds 102 and 103 are two extremely similar analogues (Zhu and Zhao, 2015; Cao et al., 2017), but, while their ECD spectra are similar, their VCD spectra are extremely different (Figure 14C).

Therefore, it is impossible to compare the VCD spectra among a similar series of chiral compounds to assign their AC by comparing the unknown compound’s VCD with the known structure’s VCD. One must compute the VCD using the quantum methods and then compare this with the experimental result.

An advantage of VCD is that it can be used to treat the interaction of two molecules in space. One early report studied the structural arrangement of four molecules of 6,6′-dimethyl-[1,1′-biphenyl]-2,2′-dicarboxylic acid in space (Urbanová et al., 2005). It is now possible to study the self-assembly of supramolecular polymers of N-centered triarylamine trisamides (Koenis et al., 2020). In a catalytic reaction, solvent-induced conformational changes of the thiourea and the evidence for an unexpected binding topology were discussed between the thiourea and an acetate anion interaction in space (Kreienborg et al., 2016). In real systems, the interaction of water with chiral molecules such as dipeptides is quite strong. Careful investigation of the water-molecule interaction has been performed. For example, there are six water molecules around the alanine dipeptide using the VCD probe (Mirtic et al., 2014). Many similar cases, like conformational equilibrium in (-)-S-nicotine, have been reported (Ortega et al., 2015b).

The aim of using simplified models in chiroptical calculations is to reduce computational time without greatly reducing the accuracy of the calculation. This involves a new concept: a conformation pair (or conformer pair) (Zhao et al., 2019; Zhu, 2022b). For example, butane (S) has four conformers: a, b, c, and d (Figure 20A). Conformation c has no symmetric element, so its OR will not be 0, as with d. Since c and d are mirror-image symmetric, their relative energy and OR magnitudes will be same, but the OR signs will be reversed. Thus, the net OR value from c and d is 0. Therefore, the total OR for 143 will be 0.

In the next example, (R)-2-chlorobutane 144 (Figure 20A) has one pair of conformers (144c and 144d) that have symmetric Et substituent structures (Figure 20B); this pair has opposite OR signs. This is very similar to the case in 143c and 143d, which are complete mirror-images. The symmetric structures that appear in 144c and 144d exist within their Et substituents. Therefore, the sum of the OR contributions of conformations 144c and 144d have a very small magnitude of only 7.4 degrees, calculated from their individual OR values at the B3LYP/6-31G(d)//B3LYP/6-31G(d) level and based on their relative conformer populations derived from their relative energies. Thus, the calculated OR ([α]_D) contribution (7.4^o) of this 144c and 144d pair of conformers was only 15% of the OR value of –48.3 from conformation 144a.

Conformer pairs like 143c and 143d, or 144c and 144d, are expected in any chiral linear molecules existing in solution. The final contribution from a summation of all the enantiomeric conformer pairs and the closely symmetric pairs will only represent a small fraction of the total measured molecular [α]_D value. The major [α]_D contribution is from the most stable conformer, as illustrated by conformer 144a in (R)-2-chlorobutane.

As the number of a chain's carbons increase, the number of stable conformations increases by 3⁽ⁿ⁻²⁾ (here n is the number of single bond rotations and must be larger than 3). This formula is applicable to many chiral linear compounds like the above molecules. No matter how long the chain is, only a unique conformer with the lowest energy exists; it has the largest OR values. The conformer pairs must exist in double numbers, and their Boltzmann statistic fraction will not be larger than the most stable conformation’s OR values. Theoretically, the major OR contribution is from this OR: the most stable conformer’s OR sign closely represents the chiral molecular AC. Thus, the fundamental basis for using simplified models is the existence of conformer pairs for chiral compounds with a long chain.

When the carbon chain numbers are more than six, it is difficult to find all conformations. This may lead to computational errors since some conformer pairs, where there is not another conformer to form a pair to the conformer pair, are not found in the conformational search. At the same time, every theoretical method must have its accuracy level in energy and OR computations. This point again entails computation errors. Therefore, both sides entail such errors. Thus, when using a short carbon chain to representative a long chain, it is easier to simulate a large OR value than use a long carbon chain. To use an ethyl to representative a long chain with an even carbon number or a propyl to represent an odd carbon chain number may be a good choice. For example, the chiral compound 145 was assigned based on the following the OR values of three model molecules (models 146–148) (Figure 20C) (Wang et al., 2010). The computed OR of 147 with four carbons was almost 16 degrees smaller than the compound 146 with a three-carbon chain. If the side chain was simplified as an acetyl (148), its OR became 8 degrees less than 147. All of the models have over-estimated OR values compared to the OR of the actual molecule of +57.3^o. Some suggested simplified substituents to replace the corresponding large and complex substituents are summarized in Table 2.

Although the use of simplified models is determined above from the OR, it can also be used in related calculations for ECD and VCD. Many natural products are too complex or flexible to use their large number of low energy conformations in calculations of ECD, OR, or VCD spectra. Thus, model molecules must be selected that are representative of the original structure. The choice of satisfactory model structures is the focus of this section. For example, the compounds 149 and 150 can be simplified as the models 151 and 152 in the ECD study (Figure 21A) (Tanaka et al., 2017), including ¹³C NMR simulations.

The highlighted red is the core framework of cyclohelminthols in 149. It was thus separated as two parts: 151A and 151B and X (Figure 21A) for 149. The 152 part and X part were used for 150. Conformational searches were performed using semiempirical AM1 MMFF provided for only a limited number of candidate conformers for some models. The DFT theory of BHLYP/def2-TZVP was used for ECD calculations, and ωB97X-D17 was used at the 6-31G* basis set in the ¹³C NMR calculation.

The two parts were independently computed. Thus, different combinations were used for the calculations (Supplementary Table S3); good agreement between the theoretical results and the experimental data was achieved.

However, use of a wrong simplified group may result in the wrong assignment. For example, ourwacin and plumerichi are very similar natural products (Stephens et al., 2007a). Ourwacin’s (153) experimental OR is 193. (1R,5S,8S,9S,10S)-plumerichi (154) had a +198. It is easy to assign (+)-ourwacin as (1R,5S,8S,9S,10S). If the (1R,5S,8S,9S,10S)-ourwacin was used in OR calculations, –193 was obtained. However, if (1R,5S,8S,9S,10S)-plumerichi was used in the calculations, the +195 of OR value was recorded. This clearly shows that a phenyl ring cannot be simplified as a methyl group in calculations. As an opposite example, the compound 155 had –25.4 of OR values (Hajıcek and Trojanek, 1981; Laguna et al., 1984), and its structural similar compound 156 had [α]_D of +15.5 in CHCl₃) (Renner and Kernweisz, 1963). Its AC was assigned as the (2R,7S,20S,21S) using ECD, VCD, and ORD (Stephens et al., 2007b). It has no phenyl group. The same configuration had the same OR sign.

In this case, it is easy to see that simplifying a phenyl group as a non-aromatic substitute like methyl leads to a wrong conclusion. This can be observed again in another example: 157 (Figure 21C) (Zhao et al., 2016). The model molecule 158 was not the best in the simulations of ECD or OR.

In this model study, consider for computing OR that the -OMe on the phenyl ring may restrict some stable conformation formations. Thus, it is necessary to keep this OMe at its ortho-position instead of replacing it as a H atom since OR is more sensitive to geometries and spatial locations while ECD is more sensitive to the positions of double bond or phenyl ring chromophores.

The structure psammaplysin A (161) has a large side chain (Mandi et al., 2015). It was simplified as the model molecule 162 in ECD computations (Figure 21D). In this way, the chromophore is a long distance from the stereogenic centers. Its effect on ECD curves is not large enough to affect the assignment of AC.

A cyclic peptide (motobamide 163) was simplified as 164 below and used in ECD study (Figure 21E) (Takahashi et al., 2021). This simplification is quite bold, since the >C=O is also a chromophore, although it has a weak contribution to entire molecular ECD spectra. It should be noted that the model is a linear structure and the peptide is cyclic. Although conformer structures of the linear model are expected to be different from cyclic ones, it remains enigmatic whether this difference should yield a ECD difference or not.

As mentioned above, the effect of the carbon chain length on the OR has its limitation, which means that, even if the chain is very long, its OR value will not increase significantly. This clearly leads to the question of why the chain increase does not have an effect on its OR value.

Although this conclusion is obtained from OR calculations, it can be used in other calculations as mentioned above, such as VCD. For example, chiral compound 165 can be simplified as 166 in its VCD calculations (Figure 21F) (Batista et al., 2009; Mota et al., 2009; Batista et al., 2010).

Fluralaner (167), a racemic animal health product used to prevent fleas and ticks, was used in a VCD study that used the entire molecule and its simplified model (168) (Kong et al., 2017). Six conformers were found using the entire molecule and only two for the simplified model molecule. There is good agreement using the simplified model in simulations of its VCD spectra (Figure 22A).

If a chiral molecule has several stereogenic centers on its carbon chain, such as pitiamide A (169) (Nagle et al., 1997), one possible method is to cut the structure into several small molecules that have one or two stereogenic centers in OR calculations (Ribe et al., 2000).Another example hennoxazole A (170) had been treated similarly (Figure 22B) (Kondru et al., 1997; Kondru et al., 1998). These are only model molecules and it is not easy to cut similar molecules into small molecules in practice if one has had no experience in this study.

Consider a chiral molecule with a single stereogenic center: molecule 171 (Lu et al., 2010). If the entire molecule was used in ECD calculation, the number of conformers would be large. To reduce the computation time, it was simplified as the model 172 for ECD computations. In this case, the ortho-OH cannot be cut off since it restricts the rotation of the phenyl ring and thereby affects the geometry’s overall structure and energy distribution. Simplification is possible by using an ethyl to replace the isopentyl group. Considering that the chiral molecule has only three isolated phenyl rings, its ECD maximum of CD signal must appear at the 220–240 nm range. Here, the long chain may have a relatively large effect on the observed CD. Indeed, to use model B in the ECD simulation agrees well with the experimental results obtained (Figure 23A). This conclusion also agrees with the matrix method results.

The matrix may thus be another approach to this study. For example, molecule 171 yielded a very small OR value of 4.4^o. If the entire molecule is used in OR calculations, the large number of conformers needs to be investigated. On the other hand, use of the matrix model is relatively quick. For the current group order (S) configuration, its determinant was +9.75. Based on the positive k₀ value (0.45) for a tertiary-alcohol derivative, it is concluded that it has S configuration. This conclusion agrees with that from the ECD calculations using simplified model molecule 172.

Many other chiral compounds have been similarly reported. For example, the compound 173 is bioactive; its AC was assigned using Mosher and ECD analysis (Liu et al., 2015). If a simplified model can be used, it may be easily assigned since it can form a six-membered ring structure via an intramolecular H-bond if using the model 174 as illustrated below (Figure 24A).

A total of 46 conformers were found for 174 using the Gaussian package. The lowest energy conformer which had an intramolecular H-bond was about 7.4 kcal/mol lower than the lowest energy conformer without this bond (Figure 24B). It is surprising that the energy of the conformer with a side chain located on an axial-bond is lower by about 5.4 kcal/mol than the conformer that has its H-bond as an equatorial-bond. If the large group is on equatorial-bond, the intramolecular conformer is only about 2.0 kcal/mol lower than the one without H-bond and also has the large group located on equatorial-bond. To clearly state the conformer question, the conformational search was performed using a MMFF94S force field. All the conformers were then computed at HF/3-21G*. Both kinds of conformer with or without H-bonds with relative energy from 0–2.0 kcal/mol were then re-optimized at B3LYP/6-31G* level in the gas phase. These B3LYP/6-31G*-optimized conformers with relative energy from 0.0 to 2.0 kcal/mol were finally optimized at the B3LYP/6-311G* level. All optimizations were performed in the gas phase. Since the conformers with low energy are very limited, they could be used for ECD or other spectroscopic computations.