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

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 (glum) 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 glum ≈ −0.5 × 10−3 at 408 nm in H2O and D2O, while, in a viscous alkanediol, the signal was amplified to glum ≈ −2.0 × 10−3. Moreover, BODIPYs, RhB, and DCM in the S0 states revealed weak (−)-sign CD signals with dissymmetry ratios (gabs) ≈ −1.4 × 10−5 at λmax/λext. 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.

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 (±h) that is a pure chiral electromagnetic (EM) force, causing mirror-symmetric LM interactions [22].Linearly polarized (LP) light is expressed as a superposition of rand 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 rand 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 K 0 meson in 1964 [31,39] and neutral B 0 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 S 1 and triplet (T 1 ) states of luminophores [43,44]: the S 1 state involves a small fraction of the T 1 state and, conversely, the T 1 state is contaminated by a small fraction of the S 1 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 S 1 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 Z 0 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 Z 0 bosons and the massless photon (γ) according to the Weinberg-Salam theory [48].W ± and Z 0 bosons gain their masses from the Higgs boson (125 GeV) [48] while γ remains massless.Although W ± , Z 0 , and γ are an equal family at high energies, Z 0 /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  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 Z 0 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), ∆E 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 .
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 .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, ∆E ± (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 (S 1 ) 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 land r-handed light speeds and the radiative lifetimes of enantiomers in the S 1 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 S 1 and S 0 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 S 1 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 S 1 state.Noticeably, BODIPY, RhB, and DCM in the S 0 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].

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 S 1 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 S 2 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 T 2 S 2 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 S 0 state.This model is also applicable to racemates in the S 1 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 (∝ Z 2 ) 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 (>10 10 -10 16 ) 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].
It is possible to regard unsubstituted perylene as a fused dimer of land 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 D 2 -symmetrical land r-twists and/or a C S -symmetrical achiral folded framework.The structural hypothesis at the S 0 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 S 1 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.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 D2h symmetry but should exist as a mixture of D2-symmetrical l-and r-twists and/or a CS-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 and 1b, unsubstituted perylene in low-viscosity methanol (, 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 glum reaches −0.45 × 10 −3 at the first vibronic band when methanol is replaced with the more viscous 1,4-butanediol (, 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 Figures 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 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 S 1 state temporarily adopts a chiral twisted geometry.However, the observed chirality of perylene disappears in the S 0 state.Possibly, perylene in the S 0 state exists as a mixture of land 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 S 1 state, and the same is possibly true for the S 0 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.

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 S 0 and S 1 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 S 0 and/or S 1 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.

Rigid Luminophores Bearing Multiple Three-Fold Symmetrical Alkyl Substituents
C2v-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 C2v 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.
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 S 0 and S 1 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 C 2 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 C 2 axis in the S 0 state.Although a handed current flow by the yellow arrows is not obvious for the S 1 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.

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 S 1 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 238 U and 232 Th in the Earth's crust, but it cannot detect anti-neutrinos from 40 K due to the low energy [115,116].Three radioactive nuclei ( 40 K, 238 U, and 232 Th) 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.
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 glum- 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.
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.

Luminophores Carrying Dialkylamino Group with Flip-Flop and/or Rotatable Motions
MacDermott and Hegstrom proposed that ammonia-type molecules (R 1 R 2 R 3 N 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 C 1 -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 S 1 and S 0 states.The temporal generation at the S 1 state and/or persistent generation at the S 0 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 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 S 1 /S 0 states of coumarin 6 and coumarin 545, giving rise to Symmetry 2019, 11,363 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 S 1 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 Figures S8a-j, Supplementary Materials), and, for comparison, the CD/UV-visible spectra in methanol (Figure 10g,h   We tested the effect of the CH3 group at the peripheral position of the coumarin framework in place of the CF3 The CPL/PL spectra of coumarin 1/460 and coumarin 102 were recorded in several solvents (Figure 11a-d and Figures S9a-d, Supplementary Materials), and, for comparison, the CD/UV-visible spectra were recorded in methanol (Figure 11e,f).Coumarin 1/460 and coumarin We tested the effect of the CH 3 group at the peripheral position of the coumarin framework in place of the CF 3 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 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 glum = −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 glum = −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 glum 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.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 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 glum = −0.18× 10 −3 at 615 nm (Figure 13a), the CPL signal increased to glum = −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 ( = 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.
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 glum- relationships for ten sets of coumarin dyes, DCM, and RhB are summarized in Figures 16a-16j and Figures 17a-17b.The data show that, in most cases, the absolute glum values leveled off at specific values when  > 30 cP.The leveled-off glum 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 glum values extrapolated to  = 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.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-C 11 H 23 OH (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-diethylaminocoumarin) (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 Figures 16a-j and 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 S 1 state with inherent handedness dictated by the PV-WNC mediated by Z 0 boson.The non-zero glum 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 Z 0 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 gabs value at the first Cotton band (397 nm) is calculated to be −8 × 10 −5 M −1 •cm −1 (Figure 18b).From the estimated gabs value, the experimental gabs (= −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 gabs = −1.3× 10 −5 at the S1 state (~480 nm) may be interpreted as the postulated PV-WNC under a zero magnetic field.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 S 2 state (~300 nm).The weak (−)-CD with g abs = −1.3× 10 −5 at the S 1 state (~480 nm) may be interpreted as the postulated PV-WNC under a zero magnetic field.
(Figure 18a).In fact, the chiral coumarin 545 reveals CD signals at the corresponding UV-visible bands (fwhm = 0.20 eV).The gabs value at the first Cotton band (397 nm) is calculated to be −8 × 10 −5 M −1 •cm −1 (Figure 18b).From the estimated gabs value, the experimental gabs (= −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 gabs = −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 S 1 state may possibly adopt a more distorted geometry, simultaneously allowing a twisted flip-flop motion at the nitrogen atom.

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 Z 0 ) and the massless photon (γ) [47].The WNC is coupled with the massive neutral Z 0 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) = 81.0GeV, m z (for Z 0 boson) = 92.4GeV, and sin 2 θ w = 0. 223, because cosθ w = m w /m z , while γ is kept massless.
Certainly, exchange of γ and Z 0 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 (Z 0 ), as illustrated in Figure 1.3 (Reference [47]) can involve three γ-γ-γ, Z 0 -γ-γ, and γ-γ-Z 0 processes.PV potential is expressed as 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 = −ih∇ 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 Z 3 K 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 where 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 S 1 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-C 2 symmetric rotamer), and a polar rod-like shape (C 1 -symmetric rotamer) in the S 1 and S 0 states, as schematically illustrated in Charts 1-4.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 S 0 and S 1 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 ).
(iii) Case 3. When 1 < E b < 10 kcal•mol −1 at the S 1 and S 0 states, only (−)-sign CPL and (−)-sign CD spectra should be observed.The parity-violating weak force might be a determining factor in the S 1 and S 0 states [104].
(iv) Case 4. When 0 < E b < 1 kcal•mol −1 in the S 1 and S 0 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 S 1 state, while the parity-conserved EM force is a determining factor in the S 0 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 S 0 and S 1 , S n . . .states are raised.
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, 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 S 1 /S 0 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.

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.

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 .

Preparation of Sample Solutions
Firstly, a representative stock solution (10 −3 M) of luminophore dissolved in spectroscopic grade CHCl 3 (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.

Chiroptical Analysis
The dissymmetry factor of the circular polarization at the S 0 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 land r-CP light, respectively [99].The dissymmetry factor of the circular polarization at the S 1 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 land r-CP light respectively, under the incident UP light [99].The parameter g abs was experimentally determined using the expression ∆ε/ε = (ellipticity (in mdeg)/32980)/absorbance at the CD extremum, similar to the parameter g lum , calculated as ∆I/I = (ellipticity (in mdeg)/(32980/ln10))/total PL intensity (in volts) at the CPL extremum.

Conclusions
We tested whether or not semi-rigid and non-rigid π-conjugated fluorophores in the S 1 and S 0 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 Z 0 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 S 0 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 Z 0 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.
Author Contributions: M.F. and J.R.K. have long discussed searching for experimental verification of the MPV hypothesis over 20 years.M.F.designed the application of CPL/CD spectroscopy to test the MPV hypothesis of the π-conjugated luminophores.M.F. and S.A. measured and analyzed CPL and CD datasets.M.F. and J.R.K. cowrote the manuscript.Requests for all original and processed CPL/CD datasets (saved in several file formats JASCO ##.jws, their converted ##.txt, followed by processed data using KaleidaGraph (mac, ver 4.53) ##.qpc, and ##.qda) should be sent to M.F.(fujikim@ms.naist.jp).
: (i) the fluorophore does not reveal any CPL or CD signals; (ii) the fluorophore at the S 1 state does not reveal CPL signals but, at the S 0 state, shows CD signals; and (iii) the fluorophore reveals CPL signals at the S 1 state and CD signals at the S 0 state.Symmetry 2019, 11, 363 5 of 41 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 /D 2 Symmetrical Perylene and C 2 /C 1 Symmetrical Derivatives

Figure 2 .
Figure 2. (a) Hypothetical model of perylene twisted by 30 • ; (b) simulated CD/UV-visible spectra with 0.2 eV full width at half maximum (fwhm) and electron density mapping at (c) first lowest unoccupied molecular orbital (1st LUMO) and (d) first highest occupied molecular orbital (1st HOMO).For this time dependent density functional theory (TD-DFT) and Becke, three-parameter, Lee-Yang-Parr exchange-correlation functional (B3LYP) with 6-31G(d) basis set, Gaussian09 rev D.01 (GaussView5 package)-calculated structures, a closed-chiral-loop current (red) is obvious for the LUMO, although this is not the case for the HOMO.

Figure 2 .
Figure 2. (a) Hypothetical model of perylene twisted by 30°; (b) simulated CD/UV-visible spectra with 0.2 eV full width at half maximum (fwhm) and electron density mapping at (c) first lowest unoccupied molecular orbital (1 st LUMO) and (d) first highest occupied molecular orbital (1 st HOMO).For this time dependent density functional theory (TD-DFT) and Becke, three-parameter, Lee-Yang-Parr exchange-correlation functional (B3LYP) with 6-31G(d) basis set, Gaussian09 rev D.01 (GaussView5 package)-calculated structures, a closed-chiral-loop current (red) is obvious for the LUMO, although this is not the case for the HOMO.

Symmetry 2019, 11 , 363 19 of 41 (
Figure9e,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.

Figure 9 . 41 (
Figure 9.Comparison of CPL/PL spectra of coumarin 466 and coumarin 6H at room temperature (path length: 10 mm, cylindrical cuvette, concentration 2.5-10 × 10 −5 M. CPL/PL spectra of coumarin 466 excited at 370 nm in (a) methanol, and (c) 1,4-butanediol at room temperature.CPL/PL spectra of coumarin 6H excited at 400 nm in (b) methanol, and (d) n-hexadecane.CD/UV-visible spectra of (e) coumarin 466 and (f) coumarin 6H in methanol.To clarify the effect of the three-fold symmetrical but electron-accepting CF 3 group, we measured the CPL/PL spectra of coumarin 481/35 and coumarin 153 in several solvents (Figure10a-f and FigureS8a-j, Supplementary Materials), and, for comparison, the CD/UV-visible spectra in methanol

Symmetry 2019 ,
11, 363 23 of 41when it is used as a laser dye.Ethylene glycol and 1,4-dioxane are not the only for RhB and are the key to magnified (−)-sign CPL signals in fluidic media with a higher viscosity.

Figure 18 .Figure 18 .
Figure 18.(a) Chemical structure of coumarin 545 optimized by Gaussian09 (DFT, B3LYP/6-31G(d) level) (b) Simulated CD/UV spectra with fwhm 0.20 eV, (c) 1 st LUMO, and (d) 1 st HOMO of coumarin 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 sin 2 θ 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].