Questions of Mirror Symmetry at the Photoexcited and Ground States of Non-Rigid Luminophores Raised by Circularly Polarized Luminescence and Circular Dichroism Spectroscopy. Part 2: Perylenes, BODIPYs, Molecular Scintillators, Coumarins, Rhodamine B, and DCM

Abstract

We investigated whether semi-rigid and non-rigid π-conjugated fluorophores in the photoexcited (S₁) and ground (S₀) states exhibited mirror symmetry by circularly polarized luminescence (CPL) and circular dichroism (CD) spectroscopy using a range of compounds dissolved in achiral liquids. The fluorophores tested were six perylenes, six scintillators, 11 coumarins, two pyrromethene difluoroborates (BODIPYs), rhodamine B (RhB), and 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM). All the fluorophores showed negative-sign CPL signals in the ultraviolet (UV)–visible region, suggesting energetically non-equivalent and non-mirror image structures in the S₁ state. The dissymmetry ratio of the CPL (g_lum) increased discontinuously from approximately −0.2 × 10⁻³ to −2.0 × 10⁻³, as the viscosity of the liquids increased. Among these liquids, C₂-symmetrical stilbene 420 showed g_lum ≈ −0.5 × 10⁻³ at 408 nm in H₂O and D₂O, while, in a viscous alkanediol, the signal was amplified to g_lum ≈ −2.0 × 10⁻³. Moreover, BODIPYs, RhB, and DCM in the S₀ states revealed weak (−)-sign CD signals with dissymmetry ratios (g_abs) ≈ −1.4 × 10⁻⁵ at λ_max/λ_ext. The origin of the (−)-sign CPL and the (−)-sign CD signals may arise from an electroweak charge at the polyatomic level. Our CPL and CD spectral analysis could be a possible answer to the molecular parity violation hypothesis based on a weak neutral current of Z⁰ boson origin that could connect to the origin of biomolecular handedness.

1. Introduction

Since the mid-19th century, one of the greatest puzzles for scientists has been why life on Earth selected L-amino acids and D-sugars, because the corresponding L/D enantiomers were considered to be energetically identical [1,2,3,4,5,6,7,8,9,10,11,12,13]. Regarding other life forms that existed in the past or may exist now on exoplanets, solar planets, satellites, and comets, it is a matter of great curiosity as to whether these stereogenic centers and/or stereogenic bonds would be identical to those upon which our life is now based [14,15,16]. Living organisms can exist only in a far-from-equilibrium system allowing open flows of solar/thermal energy and low-entropy food [17]. This mystery is intimately connected to the origins of life [2,3,4,5,6,7,8,9,10,11,12,13,14] and the accelerating expansion of the universe [18,19].

In 1831, Faraday discovered that an oscillating magnetic (M) field induces an electric (E) current [20]. In 1861, Maxwell formulated this phenomenon as the theory of electromagnetism (EM) [20]. In 1845, Faraday observed a magneto-optical phenomenon, now called the “Faraday effect”, in which a light–matter (LM) interaction causes linearly polarized (LP) light to be rotated clockwise (CW) and counterclockwise (CCW) (from the observer) by passing through achiral lead-containing glass and certain liquids under the influence of a static magnetic field. In 1860, Pasteur conjectured that molecular asymmetry is a consequence of dissymmetric forces of cosmological origin [1]. Possibly, the “Faraday effect” prompted Pasteur to attempt asymmetric crystallization under the influence of a magnetic field, but the quest failed [1]. In 1894, Curie considered that magnetic and electric fields need to align co-linearly or anti-colinearly to produce optically active substances [21].

Left (l)- or right (r)-handed circularly polarized (CP) light is a physical force carrying angular momentum (±ℏ) that is a pure chiral electromagnetic (EM) force, causing mirror-symmetric LM interactions [22]. Linearly polarized (LP) light is expressed as a superposition of r- and l-CP light. LeBel in 1874 and van’t Hoff in 1894 postulated that CP light could catalyze asymmetric chemical reactions to produce chiral substances [21,23]. In 1896, Cotton, who discovered the anomalous phenomenon of circular dichroism (CD) and optical rotation dispersion (ORD) of potassium chromium (III) tartrate [24], attempted to degrade an alkaline aqueous solution of racemic copper tartrate using CP light but failed [21]. The first successful CP light-driven asymmetric synthesis, in the destruction mode, was reported by Kuhn and coworkers in 1929 and 1930, in which r- and l-CP light at 280 nm predominantly decomposed one enantiomer in racemic mixtures of 1-bromopropionic ethyl ester and azidopropionic acid dimethylamide, yielding corresponding optically active substances with small % enantioexcess (ee) values [21].

In recent years, modern photochemical reactions using unpolarized (UP) light under the influence of an intense static magnetic field afforded preferential degradation of one of two enantiomers, in which the product chirality is controllable according to the collinear or anti-collinear conditions [25]. Alternatively, CW and CCW swirling of molecular/supramolecular/polymer systems was found to result in mirror symmetry breaking (MSB) [26,27,28]; the product chirality was determined by the direction of the mechanical rotations, while no MSB happened under static conditions. The macroscopic mechano-physical rotation is assumed to impart a preferred twist direction to rotatable C–C single bonds. However, a recent experimental result suggested the occurrence of MSB even under static conditions via a thermal gradient at specific temperatures [29].

In 1927, Wigner formulated the principle of parity (P) symmetry (corresponding to mirror symmetry in chemistry), in which all interactions in nature are invariant with respect to space inversion [30]. This idea led to the categorization of seven symmetries, i.e., charge (C), P, time (T), CP, PT, CT, and CPT [31,32]. Until 1956, the seven symmetries were thought to be invariant and conserved. However, these ideas had to be partly revised because of two groundbreaking experiments: P-violated β^±-decay in 1957–1959 [33,34,35,36,37,38], and CP-violated decay from a neutral K⁰ meson in 1964 [31,39] and neutral B⁰ meson in 2001 [40,41]. Without doubt, P and CP symmetries were broken at subatomic levels, although CPT symmetry was conserved. More recently, an astonishing experiment conducted by the Tokai-to-Kamioka (T2K) particle physics team investigated the possibility of CP-symmetry breaking between neutrino and antineutrino due to generation mixing between an electron-like lepton (first generation) and a muon-like lepton (second generation) [42]. The idea of generation mixing is like the mixing between S₁ and triplet (T₁) states of luminophores [43,44]: the S₁ state involves a small fraction of the T₁ state and, conversely, the T₁ state is contaminated by a small fraction of the S₁ state, thereby permitting the occurrence of intersystem crossing [45]. Additionally, the mixing in degenerate coupling of three anthracene dimers in a double-well (DW) was detected as quantum coherence beats from a radiation process in the S₁ state at room temperature [46].

Currently, physicists concur that all events in the cosmos and material world are governed by the strong, EM, weak, and gravitational forces, known as the four fundamental physical forces [9,47]. Their relative strengths at 10⁻¹⁵ m are ~1:10⁻²:10⁻¹³:10⁻³⁸, respectively [47]. However, among these fundamental physical forces, the only cosmologically dissymmetric force, causing MSB, is the weak force, which is responsible for nuclear fusion and fission reactions, while the other three forces conserve symmetry. Hence, a circularly polarized light source is a P-conserved physical source [47]. In the 1980s, physicists at Conseil Europeen pour la Recherche Nucleaire or European Organization for Nuclear Research (CERN) succeeded in the detection of charged W^± bosons (80.4 GeV) and the neutral Z⁰ boson (91.2 GeV) [48,49,50,51]. This experiment proved that the P-conserved EM and P-violated weak forces are unified as an electroweak (EW) force with massive W^± and Z⁰ bosons and the massless photon (γ) according to the Weinberg–Salam theory [48]. W^± and Z⁰ bosons gain their masses from the Higgs boson (125 GeV) [48] while γ remains massless. Although W^±, Z⁰, and γ are an equal family at high energies, Z⁰/γ and W^± bifurcate into neutral massive/massless and charged massive bosons, respectively.

Following 50 years of theoretical and experimental development, P- and CP-symmetry breaking in particle and atomic physics is now well established [51,52,53,54,55,56,57,58,59,60]. The EW force led to the further groundbreaking predictions theoretically [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88] and experimentally [89,90,91,92,93,94,95,96,97] that paired L/D molecules are no longer enantiomers and should behave as diastereomers. To date, several theories invoke the P-violating weak neutral current (PV-WNC) via handed electron–nucleus interactions mediated by the Z⁰ boson in the destabilization of one enantiomer by adding an extra energy bias (+E_PV) and, conversely, stabilizing the other by subtraction (−E_PV). This parity-odd energy bias is called a “parity violating energy difference” (PVED), ΔE_PV, called E_PV). The molecular parity violation (MPV) hypothesis definitively contradicts the accepted notion of enantiomers in the realm of modern stereochemistry and physical chemistry [98,99,100]. Molecular physicists have long argued whether P-symmetry of a molecular pair is exactly energetically equal and whether, if violated, E_PV is detectable [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88].

However, the MPV theories teach us that E_PV between mirror-image molecules is very small: around 10⁻⁸–10⁻¹⁴ kcal∙mol⁻¹ or 10⁻⁹–10⁻¹⁵ % ee [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88]. It is, thus, likely impossible that this radical hypothesis could be experimentally proven by ordinary UV–visible, infrared, microwave, or NMR spectrometers, or by enantioseparation column chromatography. If the potential barrier (E_b) between racemic molecules in a symmetrical DW is sufficiently small, the tunneling time between the two local minima is inversely proportional to the tunneling splitting energy, ΔE_± (hereafter called E_±), because of even- and odd-parity eigenstates [66,72,101,102,103].

In a previous paper [104] aiming to verify the MPV hypothesis experimentally, we used circularly polarized luminescence (CPL) and CD spectroscopy in an investigation of semi-rigid and non-rigid π-conjugated luminophores in symmetrical DW/multiple-well (MW) potentials with a smaller E_b in the lowest photoexcited (S₁) and ground (S_o) states. As we noted therein, a CPL spectropolarimeter may be regarded as a “low-energy spinning photon–molecule collider decelerator” to measure an inelastic scattering mode known as the Stokes’ shift [104], allowing for the detection of the subtle difference between l- and r-handed light speeds and the radiative lifetimes of enantiomers in the S₁ state. We chose a series of luminophoric racemates, including oligofluorenes, linear and cyclic oligo-p-arylenes, binaphthyls, and fused aromatics carrying rotatable side groups. To control the E_b value in DW/MW of the luminophores in the S₁ and S₀ states, we used achiral solvents, including linear and branched alkanes, linear and branched alcohols, alkyl halides, linear cyclic ethers, and water (light and heavy) [104]. The solvent viscosity (η, in cP) was tunable, ranging from 0.21 to 71.0 at 20–25 °C. We observed that all the non-rigid luminophores showed negative-sign CPL signals in the UV–visible region, suggesting generation of non-mirror image structures in the S₁ state. The Kuhn’s anisotropic parameter of CPL vs. photoluminescence (PL) signals (g_lum) of the non-rigid luminophores increased progressively but discontinuously in the range −0.2 × 10⁻³ to −2.0 × 10⁻³ as the solvent viscosity increased.

In this paper, to test the MPV hypothesis by further experiments, we investigated whether semi-rigid and non-rigid laser dyes, molecular scintillators, and other fluorophores in achiral liquids are mirror symmetrical by CPL and CD spectroscopy. Six perylenes, six scintillators, 11 coumarins, two 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene derivatives (BODIPYs), rhodamine B (RhB), and 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) were chosen. Negative-sign CPL signals were exhibited for all the fluorophores in the UV–visible region, suggesting the generation of non-mirror image structures in the S₁ state. Noticeably, BODIPY, RhB, and DCM in the S₀ states revealed clear (−)-sign CD signals with CD dissymmetry ratios (g_abs) of approximately −1.4 × 10⁻⁵ at λ_ext. The present comprehensive CPL/CD experimental datasets should support the long-argued MPV hypothesis regardless of PV-WNC scenarios [1].

2. Results

To validate the MPV hypothesis by CPL and CD spectroscopy, the crucial factors to choose are as follows: (i) semi-rigid and non-rigid racemic fluorophores carrying side chains allowing for rotatable freedom and/or flip-flop motional ability, (ii) fluorophores constituting only lighter atoms among the first three periods of the periodic table, and (iii) achiral liquids as solvents to continuously control the E_b value. Kasha’s rule predicts that fluorescence occurs spontaneously from the lowest S₁ electronic-and-vibration coupling states (vibronic modes) associated with a significant structural reorganization at the photoexcited states via non-radiative, ro-vibrational, and translational pathways even if the fluorophores are excited at the S₂ and higher S_n states [43,44].

Previously, Quack et al. [72,80,84], MacDermott and Hegstrom [83], and Bargueño [86] argued three representative cases, (i) E_PV >> E_±, (ii) E_PV << E_±, and (iii) E_PV ~ E_±, for several rigid, semi-rigid, and non-rigid cases of molecular chirality. Rigid enantiomers consisting of tetrahedral stereocenters cannot interfere with the E_± value due to the minuteness of the E_PV value. Quack et al. listed all the E_PV and E_± values of nearly 20 non-rigid rotamers [80,84]; the sign and magnitude of E_PV in non-rigid XY–YX rotamers (X = H, D, T, Cl, and Y = O, S, Se, Te) definitively depend on the dihedral angles. The E_PV and E_± values depend on the nature of the rotamers; the former changes by five orders of magnitude and the latter by considerably more (25 orders of magnitude). From this, an increase in the rotational barrier height of the rotamers may be inferred. Amongst the rotamers, only T₂S₂ can satisfy the E_PV~E_± criterion (ideally E_PV = E_±), although radioactive T is not feasible in ordinary chemistry laboratories [82,84].

The PV-WNC model allows CPL-silent/CD-silent racemic molecular mixtures to become CPL-active/CD-active in the S₀ state. This model is also applicable to racemates in the S₁ state. The E_PV value of luminophores can be amplified by heavier atoms (e.g., Si, Ge, Sn, Pb, Se, Te, Cl, Br, I) in periods 3–7 of the Periodic Table obeying the V_SO (∝ Z²) law [69,82,84]. However, luminophores containing such heavier atoms predominantly emit phosphorescence with a very low quantum yield (QY < 0.01). Herein, we focus on fluorophores without stereogenic centers, which are utilized as laser dyes and scintillators and have a high QY (typically, 0.1–0.9). Although these dyes and scintillators consist of only lighter C, N, O, F, and S atoms, their spin–orbit interactions (ζ) are non-zero and notably large with ζ = 0.1, 0.2, 0.4, 0.7, and 1.0 kcal∙mol⁻¹, respectively [44]. If a huge number of fluorophoric molecules (>10¹⁰–10¹⁶) in a cuvette are photoexcited simultaneously by focusing on them an incident laser beam, the faint 10⁻⁹–10⁻¹⁵ % ee or PVED of 10⁻⁸–10⁻¹⁴ kcal∙mol⁻¹ is expected to be resonantly boosted to a level that is detectable using an ordinary CPL spectrometer during spontaneous radiation in a synchronized fashion [104].

When non-rigid enantiomers drop into one well in preference to the other in a dissymmetrical DW at the S₁/S₀ states by ceasing to oscillate, we postulate that the diastereomeric characteristics may accord with one of the three following scenarios [104]: (i) the fluorophore does not reveal any CPL or CD signals; (ii) the fluorophore at the S₁ state does not reveal CPL signals but, at the S₀ state, shows CD signals; and (iii) the fluorophore reveals CPL signals at the S₁ state and CD signals at the S₀ state. Detectable signals, as (+)- or (−)-sign CPL or CD, are considered to arise due to handed rotational and/or flip-flop motions.

2.1. D_2h/D₂ Symmetrical Perylene and C₂/C₁ Symmetrical Derivatives

Firstly, to ascertain the achirality of unsubstituted rigid flat π-conjugated aromatics with D_2h symmetry such as the fluorophores naphthalene, anthracene, tetracene, and pyrene (see Chart 1), in the S₁ and S₀ states, we measured their CPL and CD spectra in the low-viscosity solvent methanol ([η] = 0.55 cP) and several other solvents, since it was pointed out that artefact-free precision measurements are serious concerns if CPL and CD spectrometers are operated using a single 50-kHz photoelastic modulator (PEM) [105,106]. We confirmed that no obvious CPL or CD signals in the corresponding PL and UV–visible spectral regions are detected by our CPL-200 [JASCO (Hachioji, Tokyo, Japan) model CPL-200]] and CD (JASCO model J-820) spectrometers [104].

Perylene has long been believed to adopt a D_2h symmetrical planar and achiral framework and is postulated as one of the polyaromatic hydrocarbons (PAHs) existing in molecular clouds of the interstellar universe [107]. In actuality, the interstellar PAHs emit infrared (IR) radiation in bright HII regions, and planetary and reflection nebulae. The interstellar IR spectral radiation upon excitation of vacuum–UV and UV–visible spectral lines (for example, Lyman and Balmer series) from ionized atomic hydrogen dominate most radiation sources of the galaxy and extragalaxies [108,109]. Our fundamental question, however, pertains to whether perylene truly remains achiral in the S₁ and S₀ states when all the hydrogen atoms attached to the framework are considered. To address this apparently naive query, we measured the CPL and CD spectra of unsubstituted perylene and five related derivatives carrying rotatable side groups, 5,8,11-tetra-tert-butylperylene (ttBuperylene), N′-bis(2,6-diisopropylphenyl)-1,6,7,12-tetraphenoxy-3,4,9,10-perylenetetracarboxylic diimide (iPrPhPhOperylene), N,N′-bis(2,5-di-tert-butylphenyl)-3,4,9,10-perylenedicarboximide (BTBPT-CDI), 16,17-bis(n-octyloxy)-anthrax[9,1,2-cde]-benzo[rst]-pentaphene-5,10-dione (Violanthrone 79), and N,N′-dioctyl-3,4,9,10-perylenedicarboxylic diimide (PTCDI-C8) (Chart 1).

It is possible to regard unsubstituted perylene as a fused dimer of l- and r-twistable biphenyl substructures; however, if there is a twist, then perylene should no longer exhibit D_2h symmetry but should exist as a mixture of D₂-symmetrical l- and r-twists and/or a C_S-symmetrical achiral folded framework. The structural hypothesis at the S₀ state is obvious for the five cases of (a) four bulky substituents in the 1-, 6-, 7- and 12-positions of iPrPh-PhO-perylene, (b) two bulky alkoxy substituents in the 16- and 17-positions in Violanthrone 79, (c) two bulky aromatic groups in the N,N′-positions of BTBPTCDI, (d) four bulky alkyl substituents in the 2-, 5-, 8- and 11-positions of ttBuperylene, and (e) two less-bulky alkyl groups in the N,N′-positions of PTCDI-C8. This query at the S₁ state is still unanswered.

Figure 1a–j display comparisons of the CPL/PL (photoluminescence) spectra of perylene and five derivatives in alcoholic solvents and chloroform at room temperature.

From Figure 1a,b, unsubstituted perylene in low-viscosity methanol (η, 0.55 cP) reveals a weak vibronic CPL signal at the corresponding PL emission at approximately 400–500 nm. The vibronic CPL band becomes more obvious, and g_lum reaches −0.45 × 10⁻³ at the first vibronic band when methanol is replaced with the more viscous 1,4-butanediol (η, 71.0 cP). The magnitude of the vibronic CPL band at the 0–0 and 0–1 peaks increases as solvent viscosity increases (Figure 1l and Figure S1a–f, Supplementary Materials). However, CD signals at the corresponding UV–visible bands cannot be distinguished due to π–π* transitions (Figure S1u, Supplementary Materials). These results imply that perylene in the S₁ state temporarily adopts a chiral twisted geometry. However, the observed chirality of perylene disappears in the S₀ state. Possibly, perylene in the S₀ state exists as a mixture of l- and r-twisted geometries, thereby resulting in a CD-silent pair of opposite chirality twisted conformers. Photoexcited perylene may be optically active.

Research on biaryl-sensitized terbium (III) complexes showed that fluorescence lifetime enhancement in these systems is due to solvent polarity and oxygen sensitivity rather than viscosity effects [110]. Nevertheless, oxygen solubilization does not significantly influence the fluorescence quantum yield of most organic luminophores including laser dyes, but does significantly suppress phosphorescence. Solvent viscosity is, therefore, considered to be a critical factor in the fluorescence lifetimes in our systems.

In ttBuperylene, when the four hydrogen atoms in the 2-, 5-, 8- and 11-positions of the perylene framework are replaced by four bulky three-fold symmetric tert-butyl groups as rotors, (−)-sign CPL signals for the 0–0 and 0–1 peaks at approximately 450–500 nm in methanol, 1,4-butanediol, and other solvents are more clearly evident (Figure 1c–d and Figure S1g–k, Supplementary Materials). Similarly, in iPrPh-PhO-perylene, when the four isopropyl groups in the 2-, 5-, 8-, and 11-positions of the perylene framework are replaced by four two-fold symmetric sterically hindered phenoxy groups as rotors, the (−)-sign CPL signals redshift to 530–570 nm and are without doubt more obvious in methanol, 1,4-butanediol, and other solvents (Figure 1e–f and Figure S1p–t, Supplementary Materials).

Similarly, BTBPTCDI, with two sterically hindered phenyl groups in the N,N′-positions of the perylene diimide framework unambiguously exhibits (−)-sign vibronic CPL signals at approximately 550–590 nm in methanol, 1,4-butanediol, and other solvents (Figure 1g–h and Figure S1l–n, Supplementary Materials). PTCDI-C8, bearing two less bulky n-octyl groups in the N,N′-positions of the perylene diimide framework, reveals obvious (−)-sign vibronic CPL signals at approximately 540–580 nm in 1,4-butanediol and n-dodecane (Figure 1i and Figure S1o, Supplementary Materials). CPL signals for Violanthrone 79 in chloroform were not detected (Figure 1j). A faint (−)-sign CD signal for iPrPh-PhO-perylene in methanol may be seen on the order of g_abs ≈ 10⁻⁶, but it is not obvious (Figure 1k). No detectable CD signals for perylene and ttBuperylene were observed (Figure S1f,g, Supplementary Materials).

Figure 1l summarizes the g_lum values of perylene, ttBuperylene, iPrPh-PhO-perylene, and BTBPTCDI as a function of solvent viscosity for the solvents methanol, ethanol (1.1 cP), n-propanol (2.0 cP), n-undecanol (17.0 cP), 1,3-propandiol (33.0 cP), and 1,4-butanediol (71.0 cP). We can thus conclude that the perylene and perylene diimide frameworks in the S1 state adopt a twisted geometry due to steric repulsion in the 2-, 5-, 8-, and 11-positions of the perylene framework. CPL signals of (−)-sign are apparent, and the g_lum value reaches a maximum of −2.0 × 10⁻³. Perylene, thus, does not adopt an achiral framework in the S₁ state, and the same is possibly true for the S₀ state.

To see the effect of twisted perylene in snapshot mode, we simulated the CD/UV–visible spectra with 0.20 eV full width at half maximum (fwhm) and electron density mapping at (c) the first first lowest unoccupied molecular orbital (1st LUMO) and (d) the first highest occupied molecular orbital (1st HOMO) for a hypothetical model of perylene twisted by 30° (Figure 2a–d). The twisted perylene clearly shows negative CD spectra at 443 nm and bisignate CD bands at approximately 300 nm. The value of g_abs at 443 nm is found to be 4 × 10⁻⁴. A closed-chiral-loop current (reddish zone) (Figure 2c) is obvious for the LUMO, while the same is not true for the HOMO (Figure 2d). The closed-loop current may interfere with the one-handed chiral WNC postulated.

2.2. Rigid Luminophores Bearing Multiple Three-Fold Symmetrical Alkyl Substituents

C_2v-symmetrical pyrromethene-difluoroborate (BODIPY) and its derivatives are established as excellent emitters with a high QY and a very small Stokes’ shift (350–500 cm⁻¹) [111,112]. Incorporation of alkyl groups into BODIPYs improves their solubility in common organic solvents. It is conceivable that certain BODIPYs carrying three-fold symmetrical alkyl groups may reveal optical activity due to handed gear motions between these alkyl groups. We, therefore, designed several C_2v BODIPYs as candidates to address the question of whether the handed gear motions occur with exactly equal energies and opposite senses [113]. If the gear-like motions in CW and CCW directions at the S₀ and S₁ states are equally operational, CD and CPL signals will not be detectable due to mutual cancellation of the opposite chiroptical signed bands, but they will have the same absolute magnitudes. However, if the gear-like motions in the S₀ and/or S₁ states are occurring unidirectionally due to unequal intramolecular gear energies, this should be detectable as CD and CPL signals. Unidirectional gear-like motions drive unidirectional molecular motors.

Firstly, we tested the gear-motion behaviors of pyrromethene 597 (BODIPY 597) and pyrromethene 546 (BODIPY 546) (Chart 2), which both have five three-fold symmetry methyl groups in the 1-, 3-, 5-, 7- and 8-positions of the BODIPY frameworks. Pyrromethene 597 has two additional three-fold symmetrical tert-butyl groups in the 4,4′-positions. The tert-butyl group itself consists of three methyl groups with three-fold symmetry. Both methyl and tert-butyl groups are assumed to act as gears.

Pyrromethene 597 (Chart 2) in methanol showed weakly vibronic CPL bands at 550–600 nm; however, in 1,4-butanediol, these were amplified significantly to g_lum = −1.0 × 10⁻³ at 562 nm (Figure 3a,d). Similarly, pyrromethene 546 (Chart 2) in methanol showed weakly vibronic CPL bands; however, in 1,4-butanediol, these bands were magnified to g_lum = −0.4 × 10⁻³ at 515 nm (Figure 3g,h). Pyrromethene 597 in n-undecanol, ethylene glycol, and other solvents showed similar vibronic CPL bands at 550–600 nm (Figure 3b,c). These (−)-sign CPL characteristics of pyrromethenes 597 and 546 depend on the nature of solvents (Figure S2a–h, Supplementary Materials).

More surprisingly, pyrromethene 597 in methanol revealed a clear (−)-sign CD band (Δε = 0.8 M⁻¹∙cm⁻¹ at 530 nm, g_abs = −1.5 × 10⁻⁵), whilst the λ_max of the visible band was 525 nm (Figure 3e). The Cotton CD band in viscous 1,4-butanediol showed a more intense (−)-sign CD band (Δε = 1.5 M⁻¹∙cm⁻¹, g_abs = −3.8 × 10⁻⁵ at 527 nm), with λ_max of the visible band at 525 nm (Figure 3f). Similarly, pyrromethene 546 in methanol revealed a clear (−)-sign CD band (Δε = 1.0 M⁻¹∙cm⁻¹ at 495 nm, g_abs = −1.5 × 10⁻⁵) with λ_max is 492 nm (Figure 3i). The Cotton CD band in viscous 1,4-butanediol revealed a (−)-sign CD band (Δε = 1.0 M⁻¹∙cm⁻¹, g_abs = −1.4 × 10⁻⁵ at 496 nm) (Figure 3j). These (−)-CD characteristics are unchanged and independent of the solvent (Figure S3a–h, Supplementary Materials). These (−)-sign g_abs values for the S₀ state are smaller by two orders of magnitude compared to those of the corresponding (−)-sign g_lum values for the S₁ state.

Pyrromethenes 597 and 546 (Chart 2) preferentially exhibit (−)-sign CD and CPL signals, indicating that they preferentially absorb and emit l-CP light over r-CP light. These unexpected chiroptical results imply the occurrence of handed gear-like motions between multiple alkyl rotors in the S₀ and S₁ states, causing a subtle distortion of the framework of the BODIPY ring. Gaussian09 simulations usng time dependent density functional theory (TD-DFT) and Becke, three-parameter, Lee-Yang-Parr exchange-correlation functional (B3LYP) with 6-31+G(d,p) basis set indicate that one of the subtly distorted pyrromethenes 597 has a negative Cotton CD band at 450 nm (Figure 3l). Its LUMO and HOMO orbitals correspond to symmetrical and anti-symmetrical electron density with respect to the C₂ molecular axis (Figure 3m,n). Green- and red-colored electron density maps merely indicate the phase of the electron wavefunctions. If one assumes that a handed closed loop WNC flows only in regions of the same phase (green regions) indicated by yellow arrows, pyrromethene 597 becomes a handed chiral π-electron system at the C₂ axis in the S₀ state. Although a handed current flow by the yellow arrows is not obvious for the S₁ state, the framework of photoexcited pyrromethene 597 may be more twisted and, thus, associated with more rapid gear motions of the seven three-fold symmetrical alkyl (methyl and tert-butyl) rotors, suggesting a potential application of UP-driven one-way alkyl rotors without chiral chemical entities detectable by CPL and CD spectroscopy.

2.3. Organic Scintillators

Spontaneous radiation produced by free electrons at the valence bands of molecules is responsible for the production of scintillation light in π-conjugated organic molecules in crystalline forms and molecularly disperse solutions [114]. Scintillation light is fluorescence from the S₁ state. This scenario should obey the Jablonski diagram [43,44]. Highly emissive fluorophores with a high QY are candidates for molecular scintillators.

In fact, the Kamioka Liquid Scintillator Antineutrino Detector (KamLAND) used a molecular scintillator to detect anti-neutrinos generated geologically from the β⁻-decay of ²³⁸U and ²³²Th in the Earth’s crust, but it cannot detect anti-neutrinos from ⁴⁰K due to the low energy [115,116]. Three radioactive nuclei (⁴⁰K, ²³⁸U, and ²³²Th) are responsible for geothermal power. These radioactive atoms are considered probes of supernova explosions that followed the nucleosynthesis of heavy elements and the birth of the Earth [117].

In KamLAND, 1000 tons of liquid scintillator was composed of n-dodecane (80 vol.%), 1,2,4-trimethylbenzene (20 vol.%), and 150 kg of diphenyloxazole (PPO, Chart 3) [115,116], although it is unclear to us why n-dodecane was considered the best solvent for the liquid scintillator. Anyway, fortuitous or otherwise, based on the g_lum–η relationship shown above and discussed in our previous paper [104], we assume that a viscous fluid medium such as n-dodecane is crucial to magnify the efficiency of scintillation light.

Non-rigid scintillators, 1,4-bis(2-methylstyryl)benzene (bis-MSB), 1,4-bis(5-phenyloxazol-2-yl)-benzene (POPOP), 1,4-bis(4-methyl-5-phenyloxazol-2-yl)benzene (DMPOPOP), 2,5-bis(5-t-butyl-2-benzoxalyl)thiophene (BBOT), 2,5-bis(4-biphenylyl)thiophene (BBT), are soluble in organic solvents, and 2,2″-([1,1′-biphenyl]-4.4′-diyldi-2,1-ethenediyl)bis-benzenesulfonic acid disodium salt (stilbene 420) is soluble in water and alcoholic solvents [118,119,120,121]. These molecular scintillators can adopt a polar C₂-symmetrical conformation in the S₁ and S₀ states due to their rotatable main axes. However, due to multiple C–C bonds with low rotational barrier (~1.5 kcal∙mol⁻¹) between the aromatic and trans-vinylene moieties, and due to the proximity effect of these C–H/H–C repulsions [122], those molecules cannot adopt planar structures. Thus, these molecules should exist as a mixture of many rotamers with an equal population of P- and M-twisted molecules in solution at ambient temperature.

Stilbene 420, as a trans-p-biphenylenevinylene-type oligomer, in H₂O (0.96 cP) and D₂O (0.96 cP) emitted (−)-sign CPL with g_lum = −0.5 × 10⁻³ at 430 nm (Figure 4a,b), possibly at the second vibronic 0–1’ band, indicating no marked isotope effect between H and D. The g_lum value increased to −2.0 × 10⁻³ at 410 nm at the first vibronic 0–0’ band when 1,4-butanediol was employed as a solvent. The g_lum–η relationships showed several transitions when η = 0.96–2.5 cP, 2.5-6 cP, and >22 cP (Figure 4e,f). This feature arises from 512° of rotational freedom of stilbene 420 with the five rotatable C–C bonds. From the (−)-sign in a vacuum in g_lum value extrapolated at η = 0.0 cP and the (−)-sign g_lum value in water and heavy water, water-soluble non-rigid PAHs in the interstellar universe could spontaneously favor a handed chiral and/or helical geometry that is radiating (−)-sign CP light.

CPL/PL spectra and g_lum–η characteristics of bis-MSB as a trans-p-phenylenevinylene-type oligomer are similar to those of stilbene 420 (Figure 5a–f). Moreover, bis-MSB in low-viscosity solvents (n-pentane, diethyl ether, and methanol) revealed several weak but clearly detectable vibronic CPL signals with (−)-sign at 400–450 nm (Figure 5a,c and Figure S5a–p, Supplementary Materials). The CPL signals were further amplified to −0.72 × 10⁻³ and −0.90 × 10⁻³ at 400 nm when the more viscous n-undecanol and squalane were employed, respectively (Figure 5b,d). The g_lum value progressively and discontinuously increased when carbon numbers increased in two series of n-alkanes and n-alkanols including ethanol (Figure 5e). The g_lum–η characteristics showed step-like transitions with at least three plateaus between η = 5–10 cP, 10–17 cP, and >30 cP, while the g_lum value changed linearly in response to the η value when η = 0.22–5 cP (Figure 5f). The g_lum value extrapolated to η = 0 cP is −0.5 × 10⁻³.

The scintillators bis-MSB, POPOP, DMPOP, BBOT, BBT, and stilbene 420 have rotational freedom along five, four, four, four, two, and five C–C bonds, respectively, producing huge numbers of rotamers. In actuality, these π-conjugated organic scintillators do not reveal noticeable CD bands at the corresponding π–π* transitions in UV–visible regions exemplified in Figure 6e,f and Figure 7c, and Figures S4k,l and S5q,r (Supplementary Materials). However, without exception, bis-MSB, POPOP, DMPOP, BBOT, BBT, and stilbene 420 revealed intense (−)-sign CPL signals at the corresponding PL bands in various solvents (Figure 4, Figure 5, Figure 6 and Figure 7 and Figures S4a–p and S5a–p, Supplementary Materials).

The (−)-sign CPL signals and PL spectra of POPOP in chloroform and n-hexadecane are very similar to those of DMPOPOP in chloroform and n-hexadecane (Figure 6a–d). The only difference is the luminescence wavelength; the λ_lum values of the CPL/PL bands at the 0-0’ band are 399 nm for POPOP and 407 nm for DMPOPOP (Figure 6a,b). Similarly, thiophene ring-containing scintillators BBOT and BBT in n-hexadecane showed (−)-sign CPL signals with g_lum = −0.6 × 10⁻³ at 428 nm (0–1’ band) and −1.0 × 10⁻³ at 409 nm (0–0’ band) (Figure 7a,b,d). No detectable CD signal of BBT in chloroform was confirmed (Figure 7c). This difference in g_lum value between BBOT and BBT should arise from the number of rotatable C–C bonds between the aromatic rings; BBOT has two, while BBT has four.

2.4. Luminophores Carrying Dialkylamino Group with Flip-Flop and/or Rotatable Motions

MacDermott and Hegstrom proposed that ammonia-type molecules (R₁R₂R₃N with a lone pair) able to undergo flip-flop motion are well suited to test the MPV hypothesis [83] experimentally. Coumarin derivatives, DCM, and RhB [118,119,120,121], which are C₁-symmetrical π-conjugated luminophores, are candidates because the frameworks of coumarin, rhodamine, 4-(dicyanomethylene)-6-styryl-4H-pyran possess dialkylamino groups, which are susceptible to flip-flop and/or rotatable motions in the S₁ and S₀ states. The temporal generation at the S₁ state and/or persistent generation at the S₀ state are detectable as CPL and/or CD signals if certain chiral geometries are indeed generated. Most researchers do not think that coumarins, DCM, and rhodamine B are optically inactive because of the lack of chiral stereocenters. Chemical structures of 11 coumarin derivatives, DCM, and rhodamine B, which all carry dialkylamino group(s) as side chains, are shown in Chart 4.

Firstly, we measured the CPL/PL spectra of coumarin 6 and coumarin 545 in several solvents (Figure 8a–f and Figure S6a–j, Supplementary Materials), and, for comparison, we measured the CD/UV–visible spectra in methanol (Figure 8g,h). Coumarin 6 and coumarin 545 showed very weak green-colored (−)-sign CPL signals on the order of g_lum = −0.1 × 10⁻³ at 505 nm and 520 nm, respectively (Figure 8a,b). When 1,4-butanediol was employed as the solvent, the weak (−)-sign CPL signals increased substantially to g_lum = −1.2 × 10⁻³ at 509 nm and g_lum = −1.3 × 10⁻³ at 526 nm, respectively (Figure 8e,f). The magnitude of the (−)-sign CPL signals in n-hexadecane (η = 3.47 cP) was between those in methanol and in 1,4-butanediol (Figure 8c,d). Coumarin 6 and coumarin 545 also showed very weak (−)-sign CD signals on the order of g_abs = −1.3 × 10⁻⁵ at 464 nm and g_abs = −1.3 × 10⁻⁵ at 479 nm, respectively.

These unexpected CD signals can be seen in ethanol and 1,4-butanediol. The major difference between coumarin 6 and coumarin 545 is that the former allows for free-rotation and flip-flop motions of the dialkylamino group, while, in the latter, free rotation is restricted, although the flip-flop motion is still permitted. We assume that certain flip-flop twists of the dialkylamino group commonly induce optically active conformations at the S₁/S₀ states of coumarin 6 and coumarin 545, giving rise to an optically active intramolecular charge transfer (ICT) state arising due to electron donation by the dialkylamino group to the electron-accepting benzothiazole ring.

Next, to clarify the effect of the benzothiazole ring, we measured the CPL/PL spectra of coumarin 466 and coumarin 6H in several solvents (Figure 9a–d and Figure S7a–f, Supplementary Materials), and, for comparison, the CD/UV–visible spectra in methanol (Figure 9e,f). Similarly, coumarin 466 and coumarin 6H showed very weak (−)-sign CPL signals on the order of g_lum = −0.1 × 10⁻³ at 457 nm and 481 nm (Figure 9a,b). In 1,4-butanediol, the (−)-sign CPL signals were enhanced to g_lum = −0.67 × 10⁻³ at 459 nm and g_lum = −0.53 × 10⁻³ at 482 nm, respectively (Figure 9c,d). These (−)- sign CPL magnitudes are half those of coumarin 6 and coumarin 545. Introduction of the benzothiazole ring appears, thus, to result in CPL signal amplification by a factor of two. Coumarin 466 and coumarin 6H also showed very weak bisignate-like CD signals although they are not obvious (Figure 9e,f). Similarly, the twisted flip-flop motion of the dialkylamino group may be crucial in inducing optically active conformations at the S₁ states of coumarin 466 and coumarin 6H.

To clarify the effect of the three-fold symmetrical but electron-accepting CF₃ group, we measured the CPL/PL spectra of coumarin 481/35 and coumarin 153 in several solvents (Figure 10a–f and Figure S8a–j, Supplementary Materials), and, for comparison, the CD/UV–visible spectra in methanol (Figure 10g,h). Coumarin 481/35 and coumarin 153 in methanol showed weak green-colored (−)-CPL signals at 507 nm and 527 nm, respectively (Figure 10a,b). Interestingly, these coumarins in squalane emitted blue-colored (−)-CPL signals with increased g_lum = −0.28 × 10⁻³ at 437 nm and g_lum = −0.39 × 10⁻³ at 455 nm, respectively (Figure 10c,d). In 1,4-butanediol, these (−)-CPL signals became enhanced to g_lum = −1.17 × 10⁻³ at 509 nm and g_lum = −0.59 × 10⁻³ at 527 nm, respectively (Figure 10e,f).

We tested the effect of the CH₃ group at the peripheral position of the coumarin framework in place of the CF₃ group. The CPL/PL spectra of coumarin 1/460 and coumarin 102 were recorded in several solvents (Figure 11a–d and Figure S9a–d, Supplementary Materials), and, for comparison, the CD/UV–visible spectra were recorded in methanol (Figure 11e,f). Coumarin 1/460 and coumarin 102 in methanol showed weak blue (−)-CPL signals at 450 nm and 480 nm (Figure 11a,b). In 1,4-butanediol, these increased to g_lum = −0.72 × 10⁻³ at 449 nm and −0.65 × 10⁻³ 465 nm, respectively. The CD signals of coumarin 1/460 and coumarin 102 in methanol are not obvious (Figure 11e,f).

To view the effect of the N-methyl group at benzimidazole, the CPL/PL spectra of coumarin 7 and coumarin 30 were recorded in several solvents (Figure 12a–d and Figure S10a–p, Supplementary Materials). Coumarin 7 and coumarin 30 in methanol showed weak blue-green vibronic (−)-CPL signals associated with g_lum = −0.16 × 10⁻³ at 465 nm and −0.22 × 10⁻³ at 482 nm, respectively (Figure 12a,b). In 1,4-butanediol, these (−)-CPL signals increased to g_lum = −1.21 × 10⁻³ at 497 nm and −1.20 × 10⁻³ at 452 nm, respectively (Figure 12c,d). Coumarin 7 and coumarin 30 in methanol may show similar bisignate features in their CD signals, but the spectral profile of coumarin 7 is the opposite of coumarin 30 (Figure 12e,f). Although the effect of the methyl group is minimal, the presence of the benzimidazole ring markedly affects the g_lum values in 1,4-butanediol, when compared to coumarins 466, 6H, 481/35, 153, 1/460, and 102. The presence of benzimidazole and benzothiazole groups in coumarins with dialkylamino groups may possibly be another crucial factor in photoinduced CPL signals.

As candidates of photoinduced red-light CPL emitters without stereocenters, we investigated whether 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) and rhodamine 6 in several solvents reveal CPL signals at the corresponding PL bands. DCM and rhodamine 6 are representative red-light emitters, and both bear flip-flop dialkylamino groups.

Surprisingly, DCM showed weak (−)-sign CD signals on the order of g_abs = −1.3 × 10⁻⁵ at 474 nm (Figure 13f). This weak CD signal was reproducible when measured on several different occasions and unchanged in ethanol, n-propanol, and 1,4-butanediol. Although DCM showed weak (−)-CPL signals in methanol on the order of g_lum = −0.18 × 10⁻³ at 615 nm (Figure 13a), the CPL signal increased to g_lum = −0.95 × 10⁻³ at 615 nm in ethylene glycol (Figure 13c), −1.44 × 10⁻³ at 617 nm in 1,4-butanediol (Figure 13d), and, more surprisingly, −1.17 × 10⁻³ at 549 nm in the low-viscosity solvent, 1,4-dioxane (η = 1.10 cP) (Figure 13b). The CPL/PL wavelengths of DCM in 1,4-dioxane greatly blue-shifted by ca. 70 nm and showed spectral narrowing compared to the alcoholic solvents. For reasons which are unclear, ethylene glycol and 1,4-dioxane are recommended for DCM when it is used as a laser dye.

More surprisingly, RhB had a clear (−)-sign CD signal on the order of g_abs = −2.0 × 10⁻⁵ at 550 nm (Figure 14f). This CD signal was reproducible when measured on several different occasions and was confirmed to be unchanged in ethanol, n-propanol, and 1,4-butanediol. Although RhB in methanol showed weak vibronic CPL signals at 572 nm (Figure 14a), it magnified abruptly to g_lum = −0.74 × 10⁻³ at 574 nm in n-C₁₁H₂₃OH (Figure 14c), g_lum = −0.72 × 10⁻³ at 581 nm in ethylene glycol (Figure 14d), g_lum = −0.83 × 10⁻³ at 596 nm in 1,4-dioxane (Figure 14b), and g_lum = −1.01 × 10⁻³ at 576 nm in 1,4-butanediol (Figure 14e). Similarly, ethylene glycol and 1,4-dioxane are recommended for RhB when it is used as a laser dye. Ethylene glycol and 1,4-dioxane are not the only solvents for RhB and are the key to magnified (−)-sign CPL signals in fluidic media with a higher viscosity.

Finally, we checked the CPL/PL and CD/UV–visible spectra of 3,3′-carbonylbis(7-diethylamino- coumarin) (bis-coumarin). As a result, bis-coumarin in 1,4-butanediol showed clear but broader (−)-sign CPL signals with g_lum = −0.65 × 10⁻³ at 531 nm (Figure 15a) and a clearly associated (−)-sign CD signal with g_abs = −1.0 × 10⁻⁵ at 463 nm (Figure 15b).

As exemplified in the cases of the fused aromatic rings with substituents, BINOL derivatives [104], BODIPY, and organic scintillators shown in the sections above, the magnitudes of the (−)-sign CPL signals in a series of coumarin dyes, DCM, and RhB are greatly amplified in response to the viscosity of the solvents. The g_lum–η relationships for ten sets of coumarin dyes, DCM, and RhB are summarized in Figure 16a–j and Figure 17a–b. The data show that, in most cases, the absolute g_lum values leveled off at specific values when η > 30 cP. The leveled-off g_lum values are highly dependent on the nature of the substituents such as, for example, the presence or absence of benzimidazole or benzothiazole as electron-accepting groups and the position of the alkyl substituents. Moreover, in all cases, the g_lum values extrapolated to η = 0.0 cP are non-zero values, −0.2 × 10⁻³, suggesting that these luminophores should emit (−)-CPL signals under solvent-free conditions, such as in a collision-free vacuum.

The non-zero g_lum values with (−)-sign extrapolated at η = 0.0 cP suggest that coumarins bearing dialkylamino group(s) with flip-flop capability adopt a handed chiral geometry preferentially by radiating (−)-sign CP light even in solvent-free, collision-free conditions. We conjecture that twisted flip-flop motions of the dialkylamino group in these luminophores may play a key role in the emergent photoinduced (−)-sign CPL signals at the S₁ state with inherent handedness dictated by the PV-WNC mediated by Z⁰ boson.

In Figure 18, we show the CD/UV–visible spectra and HOMO–LUMO electron density of coumarin 545 optimized by Gaussian09 (DFT, B3LYP/6-31G(d) level), followed by 20 singlet states by TD-DFT calculation at the B3LYP/6-31G(d) level. Optimized coumarin 545 adopts a chiral conformation such that the dihedral angle between the benzothiazole and coumarin rings is 27.7°, and the two dihedral angles between the nitrogen atom and the two nearest carbons are 4.1° and 7.8° (Figure 18a). In fact, the chiral coumarin 545 reveals CD signals at the corresponding UV–visible bands (fwhm = 0.20 eV). The g_abs value at the first Cotton band (397 nm) is calculated to be −8 × 10⁻⁵ M⁻¹∙cm⁻¹ (Figure 18b). From the estimated g_abs value, the experimental g_abs (= −1.3 × 10⁻⁵ at 479 nm) implies an enantiomeric excess (ee) of 16% in methanol. However, no CD signals are detected at the S₂ state (~300 nm). The weak (−)-CD with g_abs = −1.3 × 10⁻⁵ at the S₁ state (~480 nm) may be interpreted as the postulated PV-WNC under a zero magnetic field.

The mapping of electron densities in the first LUMO and first HOMO of the optimized coumarin 545 are displayed in Figure 18c,d, respectively. The nitrogen atom in the dialkylamino group retains high electron density at both HOMO and LUMO levels. However, the phases (from green to red or vice versa) differ between HOMO and LUMO. Coumarin 545 at the S₁ state may possibly adopt a more distorted geometry, simultaneously allowing a twisted flip-flop motion at the nitrogen atom.

3. Discussion

Weak interactions occur between all the six quarks and six leptons at the first., second, and third generations in the framework of elemental particle physics [47,81,123,124]. The weak interactions generate a “weak charge”, leading to a charged weak current and the weak neural current (WNC). Only left-handed particles and right-handed anti-particles carry the weak charge. The weak charge is analogous to Coulomb charges (+ and −) and Mulliken charges (δ+ and δ−) established in chemistry arising from the parity-conserving EM force. The weak charge is unique and is responsible for the basis of handedness at subatomic and atomic levels and, presumably, even at artificial molecular, oligomer, and polymer levels. The hierarchy in the handedness could be connected to the origin of biomolecular and biopolymer handedness, and beyond.

Charged left-particles and right-anti-particles can take part in the parity violating β⁻ decay process of neutrons in the n → p + e⁻ + anti-ν_e reaction. This event arises from a left-handed spinning electron (or right-handed electron from the observer) and right-handed spinning anti-neutrino (or left-handed anti-neutrino from the observer’s perspective).

According to Fermi’s theory, β⁻ decay is the result of current–current interactions, leading to the vector (V)–axial vector (A) components of the charged weak currents. The term V is a polar vector and A is carrying angular momentum. Although the charged currents may be considered analogously to the cationic or anionic charges in molecules, no suggestion of dynamically flowing current is applied to cationic or anionic static charges. The V–A terms can generate different electric charges between p → n and e⁻ → ν_e reactions, leading to the charged weak current.

Weinberg, Salam, and Glashow [47,123,124] formulated a unified theory of parity-conserving EM and parity-violating weak forces among the four fundamental physical forces based on gauge symmetry group SU(2) × U(1), while SU stands for special unitary (triplet states) and U unitary (singlet state) groups. The unified theory is popularly called the “Standard Model”, and formulates an electroweak (EW) force.

A spontaneous symmetry-breaking process with handedness is a result of three massive bosons (W⁺, W⁻, and Z₀) and the massless photon (γ) [47]. The WNC is coupled with the massive neutral Z⁰ boson, and the EM neutral current is coupled with γ. The unified theory connects the electric charge e to the effective weak coupling g_w, given by g_w = e/2√2 sinθ_w, where θ_w is the Winberg’s weak mixing angle. Experimental datasets are m_w (for W^± bosons) = 81.0 GeV, m_z (for Z⁰ boson) = 92.4 GeV, and sin²θ_w = 0. 223, because cosθ_w = m_w/m_z, while γ is kept massless.

Certainly, exchange of γ and Z⁰ occurs between electrons and the nucleus. The PV interaction in elemental particles can cause atomic parity violation (APV) effects as observable values in photon-induced absorption and radiation modes. Several APV theories invoked the idea that negatively charged electrons bonded to a positively charged nucleus by Coulomb force (γ) and the weak force (Z⁰), as illustrated in Figure 1.3 (Reference [47]) can involve three γ–γ–γ, Z⁰–γ–γ, and γ–γ–Z⁰ processes. PV potential is expressed as

$$V_{PV}=\frac{G_F}{4\sqrt{2}}\frac{Q_w}{m_{e}c}\left[\sigma \cdot \overleftarrow{p}{\delta }^3(r)+{\delta }^3(r)\sigma \cdot \overrightarrow{p}\right],$$

(1)

where G_F is Fermi’s weak coupling constant (1.16637 × 10⁻¹¹ eV or 2.68971 × 10⁻¹⁰ kcal∙mol⁻¹), r is the position of the electron, σ is the spin operator, m_e is the electron mass, c is the light speed, p = −iℏ∇ momentum operator, and δ is Dirac’s delta function. The admixing factor between the s_1/2 and p_1/2 states of the atom is on the order of 10⁻¹⁷ Z³K_r, whereby K_r is a relativistic correction factor (K_r ~ 3 for Cs and ~ 10 for Bi) [47]. The weak charge Q_w is expressed as

$$Q_w=2{\displaystyle \sum _{p,n}\left(C_{VP}+C_{Vn}\right)}=Z(1-4{\sin }^2{\theta }_w)-N\approx -N,$$

(2)

where C_Vp and C_Vn are the coupling constants of vectoral V of proton and neutron, and N and Z are the numbers of neutrons and protons. Because 1 − 4 sin²θ_W = 0.116 < 1, Q_w ≈ −N. In actuality, chiroptical rotation in visible and near infrared (NIR) regions due to APV effects for vapors of heavy atoms (Bi, Pb, Tl, and Cs) is always of (−)-sign, regardless of atomic mass, indicating the dominance of the −N term of Equation (2) [47].

A proton is constituted by two up quarks and one down quark, while a neutron is constituted by one up quark and two down quarks. All atoms are, thus, made of multiple up and down quarks and electrons. We radically postulate that the (−)-sign Q_w value of all molecules is linearly [61] and nonlinearly amplified by huge numbers of neutrons because molecules are polyatomic and polyneutron systems constituting parity-violating atoms: unsubstituted perylene contains 20 × 6 = 120 neutrons, while pyrromethene 597 and stilbene 420 have 169 neutrons and 248 neutrons, respectively. We conjecture that enantiomeric pairs are no longer equivalent energetically, and their characteristics behave diastereomerically, owing to hundreds of neutrons within the nuclei that leads to non-mirror-symmetric LM interactions as a consequence of the (−)-sign electroweak charge.

The consistent observation of (−)-sign CPL and (−)-sign CD signals may arise from the inherent (−)-sign of Q_w. If the negative-sign Q_w in Equation (2) can be applied to spontaneous radiation and non-radiative processes from photoexcited non-rigid fluorophores, the CPL (and CD) signals are postulated to be commonly the same (−)–sign regardless of their chemical structures. Because the CPL signals from the observer are defined as PL(left) − PL(right), the non-rigid fluorophores in the present results and previous study [104] are primarily radiating PL(right) over PL(left) during the non-radiating reorganization process at the S₁ state. Although the predicted signs in CPL and CD signals are inverted by dihedral angles of multiple C–C bonds in the non-rigid fluorophores [80], the weak (−)-charge Q_w may be efficiently coupled with dipolar (δ⁺ and δ^–) molecular structures that can adopt a significantly polar V-shape and syn-form (pseudo-C₂ symmetric rotamer), and a polar rod-like shape (C₁-symmetric rotamer) in the S₁ and S₀ states, as schematically illustrated in Chart 1, Chart 2, Chart 3 and Chart 4. The negative value Q_w is additive to δ⁻ (then, δ⁻ − |Q_w|) but is subtractive to δ⁺ (then, δ⁺ + |Q_w|), then |δ⁻ − |Q_w|| ≠ |δ⁺ + |Q_w|| for an enantiomeric pair of rotamers.

From the viewpoint of molecular dynamics, the PV-WNC force causes parity-odd rotational and/or flip-flop motions. The motions enforce (R)- and (S)-forms in the same direction (CW or CCW) that facilitates radiation with only (−)-sign CPL. However, the EM force, a parity-even, parity-conserved force, allows plural C–C bonds in the (R)-form to rotate and/or undergo flip-flop motions with CW motion and, conversely, those with the (S)-form to rotate and/or flip-flop CCW or vice versa. These motional dynamics should be mirror-symmetric. The handedness of motional dynamics by handed elemental particles can be recognized as chiral crystallization of achiral molecules: longitude polarized electrons and positrons that mirror image leptons oppositely affect an L/R preference in the crystallization of sodium chlorate and bromates in water solution [81].

In our previous paper [104], we grouped the apparent CPL and CD spectral characteristics with their signs, magnitudes, and wavelengths and associated barrier heights (E_b) in double-well and multi-well potentials into four categories as follows:

(i) Case 1. The value of E_b between rigid enantiomers is relatively high >30 kcal∙mol⁻¹ in the S₀ and S₁ states. Mirror-image CD and CPL spectra are evident for the enantiomers. The parity-conserved EM force is a determining factor. Racemization rate obeys the Arrhenius equation with activation energy (E_a).

(ii) Case 2. When 10 < E_b < 30 kcal∙mol⁻¹ at the S₀ and S₁ states, non-mirror-image CPL and CD spectra are often observed [15,27,90,95,120,122,125,126,127,128,129,130,131,132,133,134]. Although (+)- and (−)-signs in CPL and CD are primarily determined by atrope and point chirality, the absolute magnitudes and wavelengths at the CPL and CD bands differ considerably from each other.

(iii) Case 3. When 1 < E_b < 10 kcal∙mol⁻¹ at the S₁ and S₀ states, only (−)-sign CPL and (−)-sign CD spectra should be observed. The parity-violating weak force might be a determining factor in the S₁ and S₀ states [104].

(iv) Case 4. When 0 < E_b < 1 kcal∙mol⁻¹ in the S₁ and S₀ states, no detectable CD bands are observed, although (−)-sign CPL signals are obvious. Resonance quantum tunneling without E_a is responsible for dynamic racemization, oscillating chirality, and quantum beat [66,72,101]. The parity-violating weak force is a determining factor in the S₁ state, while the parity-conserved EM force is a determining factor in the S₀ state.

Moreover, regarding hidden molecular chirality, in 1970s, Mislow argued the cryptochirality of mirror-image molecules in which optical activity is non-detectable [135]. In 2006 and 2009, approaches to chemically decipher cryptochiral molecules and polymers were reported [136,137]. Additionally, with the help of CPL and CD spectroscopy, a photophysical deciphering approach was applied to the EM-originating cryptochirality of several CD-silent molecules [138,139,140,141,142].

The previous paper did not report Case 3, though we reported examples of Cases 1, 2, and 4 [104]. The present paper reports Case 3 for the first time, i.e., that pyrromethene 546, pyrromethene 597, DCM, RhB, and bis-coumarin all reveal (−)-sign CPL and (−)-sign CD spectra, even in low-viscosity solvents. EW-perturbed quantum chemistry [143], EW-perturbed photophysics and EW-perturbed photochemical reactions should be considered when open questions of unexpected L/R preference and their detectable L/R differences in non-rigid and semi-rigid artificial molecules, and supramolecules and biomolecules in the S₀ and S₁, S_n… states are raised.

Other plausible scenarios for the L/R preference are possible. The handedness of non-rigid molecules in an ultra-tiny % ee can be increased to ~100% ee upon photoexcitation of parity-conserved (PC) EM force-driven circularly polarized (CP) light carrying a single angular momentum (±nℏ, n = 1) in the broad range of γ-ray, X-ray, vacuum–UV, UV–visible–IR, far-IR far-THz, and cosmic microwave radiation according to certain nonlinear amplification scenarios [97,98,99,100,101,102,103,104,105,106,107,108,109], known as autocatalytic self-replication [144], sergeant-and-soldier and majority rules [145], and polymerization [146]. Parity-conserving EM force-originating macroscopic MSB was comprehensively reviewed for a large number of molecules, polymers, supramolecules, colloids, gels, and crystals [147,148,149,150]. These alternative modern scenarios provide other possible answers to the greatest mystery on the origin of homochirality on Earth.

Recently, lightning was found to be a natural particle accelerator, ubiquitously generating γ-rays. Lightning causes atmospheric photonuclear reactions. The γ-ray energy is captured by N₂ molecules, followed by producing, possibly, weak force-origin handed neutrons, right-handed positrons, and left-handed neutrinos [151]. Additionally, cosmological-origin right-handed anti-ν interacting with ¹⁴N in molecular clouds in star-forming regions of supernovae and neutron stars [87,152], gravitational origin parity violation [153,154], and hydrodynamic vortex flows with the opposite handedness in the north and south hemispheres on Earth [26,27,155] are of specific interest. In recent years, vortex light (alternatively called optical spanner, spiral light, twisted light, and helical light) [156,157,158,159,160,161,162,163,164,165,166,167,168,169] was recognized as a new sort of chiral light carrying multiple orbital angular momenta (OAM) with ± lℏ, l = 1, 2, 3, 4, 5, 10… up to 200. Vortex light with l = 0 is achiral. Vortex light can generate a torque enabling the rotation of molecular droplets, polymeric solids, and metallic particles in CW or CCW directions [158,161,164]. The helical wavefront for the Laguerre–Gaussian mode of vortex light allows for sculpturing spiral relief and motifs and for rotating small objects in CCW or CW directions [156,157,158,159,160,161,162,163,164,165,166,167,168,169,170]. Like CP light–matter interactions [171,172], vortex light can discriminate between enantiomers [164], and it is possible to predominantly generate handed chiral motifs from achiral polymers [162,163,169]. Astrophysical origin vortex light [156], CP light, and right-handed solar neutrinos may, thus, be connected to the L/R preference of biomolecular substances.

Recently, astonishing findings seeking source materials connecting with the handedness of biomolecules on Earth were reported. In 2009, a National Aeronautics and Space Administration (NASA) team characterized extraterrestrial-origin glycine-embedded samples returned from comet 81P/Wild2 using liquid chromatography and spectrometry [173]. In 2016, other researchers determined glycine, phosphorus and several organic substances involving O, S, and F in specimens collected from the coma of 67P/Churyumov–Gerasimenko using a double-focusing mass spectrometer [174]. Moreover, in 2016, radio astronomers found the first astronomical-origin chiral propylene oxide and achiral n-propanol in the Sagittarius B2 star-forming region of the Milky Way galaxy, although the existence of any L/R preference remains to be elucidated [175]. Comets and interstellar materials could deliver biomolecules or their precursors and water to Earth. Although it is possible to synthesize mirror-image DNA and proteins in laboratories [176,177], it is challenging to directly detect the L/R preference, possibly associated with (−)-sign circularly polarized radiation from the observation of interstellar PAHs at the S₁/S₀ states in the UV–visible region [175], and rigid and non-rigid non-π-conjugated organics at the near-IR/mid-IR/far-IR/microwave regions [108,109]. It remains a great challenge and a great curiosity to provide more realistic scenarios for biomolecular handedness.

4. Materials and Methods

Instrumentation details, lists of solvents and fluorophores and their vendors, preparation of sample solutions, and chiroptical analytical data [99,104] are described below.

4.1. Instrumentation

Using a JASCO (Tokyo, Japan) J-820 spectropolarimeter, UV–visible and CD spectra were simultaneously recorded at ambient temperature using a cylindrical quartz cuvette with a path length of 10 mm. The cylindrical cuvette assured a precise CD measurement compared to the rectangular cuvettes that are often used in routine experiments. Precise CD/UV–visible spectra were obtained by using a bandwidth of 2 nm, with one or two accumulations at scanning rates of 50 or 100 nm∙min⁻¹ with a response time of 2 s. The CD signals of the two BODIPYs and RhB were triply confirmed under the following conditions: bandwidth = 2 nm, response time = 8 s, scanning rate = 20 nm∙min⁻¹ with four accumulations. To minimize drifts in the light source and power supply, the instrument was aged for at least 2 h prior to measurements. CPL and PL spectra were likewise collected using a JASCO CPL-200 spectrofluoropolarimeter (Hachioji, Tokyo, Japan) employing cylindrical quartz cuvettes with path lengths of 10 mm at ambient temperature. The best experiment parameters were as follows: bandwidth = 10 nm for excitation and detection; response time of PMT = 8–16 s during measurements; two to eight accumulations with scanning rate = 20–50 nm∙min⁻¹.

4.2. Materials

4.2.1. Luminophores (vendor)

Section 1: Perylene (Tokyo Chemical Company (TCI), Tokyo, Japan), 5,8,11-tetra-tert- butylperylene (TCI), N,N′-bis(2,6-diisopropylphenyl)-1,6,7,12-tetraphenoxy-3,4,9,10-perylene-tetra-carboxylic diimide (TCI), N,N′-bis(2,5-di-tert-butylphenyl)-3,4,9,10-perylenedicarboximide (Sigma-Aldrich, St. Louis, MO, USA), 16,17-bis(n-octyloxy)-anthrax[9,1,2-cde]-benzo[rst]-pentaphene-5,10-dione (TCI), and N,N′-di-n-octyl-3,4,9,10-perylenetetracarboxylic diimide (Sigma-Aldrich) were obtained as indicated.

Section 2: Pyrromethene 546 (TCI) and pyrromethene 597 (TCI) were obtained as indicated.

Section 3: Stilbene 420 (Exciton, Tokyo Instruments Inc. (Tokyo, Japan)), bis-MSB (Exciton), POPOP (TCI), DMPOPOP (Dotite, Kumamoto, Japan), BBOT (Dotite), and BBT (TCI) were obtained as indicated.

Section 4: Coumarin 6 (TCI), coumarin 545 (TCI), coumarin 466 (TCI), coumarin 6H (Sigma- Aldrich), coumarin 481/35 (TCI), coumarin 153 (Sigma-Aldrich), coumarin 1/460 (Sigma-Aldrich), coumarin 102 (Sigma-Aldrich), coumarin 7 (Sigma-Aldrich), coumarin 30 (Sigma-Aldrich), biscoumarin) (TCI), DCM (Sigma-Aldrich), and RhB (TCI) were obtained as indicated.

4.2.2. Solvents

Vendor, viscosity in cP, and temperature in °C are provided in brackets [178,179,180,181,182,183]; in each series, entries are given in order of increasing viscosity as follows:

(1) n-Alkanes: n-pentane (FUJIFILM Wako, 0.21 (25)), n-hexane (FUJIFILM Wako, 0.30 (25)), n-heptane (Sigma-Aldrich, 0.39 (25)), n-octane (Sigma-Aldrich, 0.51 (25), n-nonane (Sigma-Aldrich, 0.71 (20)), n-decane (Sigma-Aldrich, 0.85 (25)), n-undecane (Sigma-Aldrich, 0.93 (20)), n-dodecane (Sigma-Aldrich, 1.36 (25), n-tridecane (Sigma-Aldrich, 1.88 (20)), n-tetradecane (Fluka, 2.08 (25), n-pentadecane (Sigma-Aldrich, 2.86 (20)), and n-hexadecane (Sigma-Aldrich, 3.71 (20)).

(2) Branched and cyclic alkanes: isooctane (Dotite, 0.50 (25)), cyclohexane (Dotite, 0.93 (22)), and squalane (2,6,10,15,19,23-hexamethyltetracosane) (Sigma-Aldrich, 29.50 (25)).

(3) Non-branched and n-alcohols: methanol (FUJIFILM Wako, 0.55 (25)), ethanol (FUJIFILM Wako, 1.09 (25)), n-propanol (Sigma-Aldrich, 1.96 (25)), n-butanol (FUJIFILM Wako, 2.59 (25)), n-pentanol (Sigma-Aldrich, 3.47 (25)), n-hexanol (Sigma-Aldrich, 4.59 (25)), n-heptanol (Wako, 5.97 (25)), n-octanol (Wako, 7.59 (25)), n-nonanol (Sigma-Aldrich, 9.51 (25)), n-decanol (Sigma-Aldrich, 11.50 (25)), ethylene glycol (FUJIFILM Wako, 16.1 (25), n-undecanol (Sigma-Aldrich, 16.95 (25)), 1,3-propandiol (FUJIFILM Wako, 33.0 (25)), and 1,4-butanediol (FUJIFILM Wako, 71.0 (25)).

(4) Branched alcohols: isopropanol (Dotite, 2.07 (25), isobutanol (Sigma-Aldrich, 3.38 (25)), and isopentanol (Sigma-Aldrich, 3.86 (25)).

(5) Chlorinated hydrocarbons: dichloromethane (Dotite, 0.41 (25)) and chloroform (Dotite, 0.55 (25)).

(6) Other solvents: diethyl ether (FUJIFILM Wako, 0.22 (25)), acetone (FUJIFILM Wako, 0.31 (25), acetonitrile (FUJIFILM Wako, 0.34 (25)), tetrahydrofuran (Dotite, 0.46 (25)), benzene (FUJIFILM Wako, 0.60 (25)), water (Wako, 1.00 (20)), 1,4-dioxane (Dotite, 1.10 (25)), anisole (TCI, 1.09 (25)), heavy water (Wako, 1.25 (20)), and sulfolane (TCI, 10.10 (25)).

4.3. Preparation of Sample Solutions

Firstly, a representative stock solution (10⁻³ M) of luminophore dissolved in spectroscopic grade CHCl₃ (Dotite, Kumamoto, Japan) was prepared. For RhB and stilbene 420, ethanol was used as the stock solution solvent. A small quantity of the stock solution was added to the desired liquid (1.9–2.1 mL) in the cylindrical quartz cuvette using a microsyringe. The CD/UV–visible and CPL/PL spectra were then recorded. Oxygen was not purged from the solvents or solutions in CPL and CD measurements since it does not significantly influence the fluorescence quantum yield of most organic luminophores.

4.4. Chiroptical Analysis

The dissymmetry factor of the circular polarization at the S₀ state (g_abs) was evaluated as g_abs = (ε_L − ε_R)/(1/2(ε_L+ε_R)), where ε_L and ε_R are the extinction coefficients for l- and r-CP light, respectively [99]. The dissymmetry factor of the circular polarization at the S₁ state (g_lum) was evaluated as g_lum = (I_L − I_R)/(1/2(I_L + I_R)), where I_L and I_R are the intensities of the signals for l- and r-CP light respectively, under the incident UP light [99]. The parameter g_abs was experimentally determined using the expression Δε/ε = (ellipticity (in mdeg)/32980)/absorbance at the CD extremum, similar to the parameter g_lum, calculated as ΔI/I = (ellipticity (in mdeg)/(32980/ln10))/total PL intensity (in volts) at the CPL extremum.

5. Conclusions

We tested whether or not semi-rigid and non-rigid π-conjugated fluorophores in the S₁ and S₀ states in a series of achiral liquids with η ranging from 0.22 cP to 71.0 cP are optically inactive and have mirror symmetry as measured by CPL and CD spectroscopy. The fluorophores included six perylenes with and without substituents, two BODIPYs, six scintillators, RhB, DCM, and 11 coumarins. Perylenes were models of interstellar small and large PAHs radiating IR spectra of bright HII regions, planetary nebulae, and reflection nebulae. Without exception, all the non-rigid fluorophoric enantiomers, and possibly also the highly twisted perylene derivatives, showed (−)-sign CPL signals radiating from the vibronic photoexcited state in support of the molecular parity-violating hypothesis based on the Z⁰ boson origin PV-weak neutral current mechanism. The fluorophore emission intensities increased progressively and discontinuously to approximately –0.2 × 10⁻³ and −2.0) × 10⁻³ as a function of the solvent viscosity. Of specific interest was the detection of weak but clear CD signals with g_abs values of −1.4 × 10⁻⁵ at λ_max/λ_ext for two pyrromethene derivatives, RhB, DCM, and bis-coumarin at the S₀ states. The results of the present CPL and CD spectral characteristics should provide a possible answer to the parity violation hypothesis at the molecular level based on a handed weak neutral current mediated by the Z⁰ boson. The present comprehensive and previous experimental datasets [104] led us to address the “Ozma problem” posed by Gardner [1]. The query was how we can correctly communicate the left-and-right issue to intellectually advanced alien lifeforms. Our answer is that, when an unpolarized UV light source is applied to excite semi-rigid and non-rigid π-conjugated luminophores, we define (−)-sign CPL signals from the observer as “right” without exception.