Fluorescence of Half-Twisted 10-Acyl-1-methyltetrahydrobenzoquinolines

The steric interference of proximal dialkyl amino and acyl groups at the peri (1,8) positions of naphthalene affects the intramolecular charge transfer fluorescence. Previous studies indicate that acyl and freely rotating dimethyl amino groups twist toward coplanarity with the naphthalene ring in the excited state. The present study examines the effect of constraining the amino group in a ring. The photophysical properties of 2,2-dimethyl-1-(1-methyl-1,2,3,4-tetrahydrobenzo[h]quinolin-10-yl)propan-1-one (4), ethyl 1-methyl-1,2,3,4-tetrahydrobenzo[h]quinoline-10-carboxylate (5), and 1-methyl-1,2,3,4-tetrahydrobenzo[h]quinoline-10-carbaldehyde (6) are compared with the dimethyl amino derivatives 2 and 3. Crystal structures of 4–6 show that the amine ring adopts a chair conformation, where the N-methyl group is axial. Computational results suggest that the pyramidal amino group planarizes and twists together with the acyl toward coplanarity in the excited state. The ring structure does not thwart the formation of a planar intramolecular charge transfer (PICT) state.


Introduction
Amino-carbonyl disubstituted naphthalenes are often highly fluorescent.They emit from an intramolecular charge transfer (ICT) excited state, where electron density has shifted from the donor amino group toward the acceptor carbonyl group.The archetypal member of this class of compounds is 6-propionyl-2-(dimethyl-amino)naphthalene (1, 2,6-Prodan, Figure 1) [1].The arrangement of the donor and acceptor groups at the 2 and 6 positions gives them the maximum possible separation.The spatial separation of the charge in the excited state results in a dipole moment that is almost twice that of the ground state.Solvent molecules in the cybotactic region will reorient to stabilize the new charge distribution.Solvents with a higher polarity will stabilize the excited state better, leading to longer-wavelength emission (solvato-chromism) [2][3][4][5].Similar solvato-chromism is observed with the 1,5-and even the 1,8-disubstituted derivatives.In the simplest examples, the substituents can rotate about the bond to the naphthalene and modulate the degree of conjugation.
Molecules 2024, 29, 3016 2 of 13 Model compounds that prevent the rotation of the dialkyl-amino groups give the same ICT behavior as the unconstrained parent compounds.The 1,8-derivatives of Prodan reported by Kiefl have unusual structural features [18].If large enough, substituents at these positions will interact sterically with each other and will twist about the bond to the naphthalene to minimize the steric strain [19][20][21][22][23].Our previous paper showed that when the carbonyl and amino groups are constrained to be Because charge transfer is integral to the behavior of these systems, the preferred geometry of the groups is important.For a related compound, dimethyl-amino-benzonitrile (DMABN), intramolecular charge transfer occurs from the amino group to the para-cyano group.The fluorescence behavior of model compounds suggests that the amino group twists 90 • in the excited state, giving rise to a twisted intramolecular charge transfer (TICT) excited state [6][7][8][9][10].Electronic de-coupling of the pi-systems provides maximum charge separation.Several donor-acceptor-substituted fluorophores possessing a dialkylamino group as the donor are thought to form twisted intramolecular charge transfer (TICT) excited states [11][12][13].We have found that 2,6-, 1,5-, and 1,8-Prodan derivatives likely have planar intramolecular charge transfer (PICT) excited states [14][15][16][17].Model compounds that prevent the rotation of the dialkyl-amino groups give the same ICT behavior as the unconstrained parent compounds.
The 1,8-derivatives of Prodan reported by Kiefl have unusual structural features [18].If large enough, substituents at these positions will interact sterically with each other and will twist about the bond to the naphthalene to minimize the steric strain [19][20][21][22][23].Our previous paper showed that when the carbonyl and amino groups are constrained to be nearly coplanar, the ICT emission was similar to the freely rotating derivative 2. Given the importance of the geometry of the donor and acceptor groups, we wondered how the behavior of these systems would be affected if only the rotation of the amino portion was constrained.To this end, we prepared 4-6 (Figure 1) and compared their photophysical behavior to 2-3.

X-ray Structures
Compounds 4, 5, and 6 formed crystals upon slow evaporation of a hexane/ethyl acetate solution and gave resolved crystal structures (Figure 2).The three structures display some common features.The piperidine ring has a pseudo-chair shape, and the N-methyl group is in an axial orientation.The carbonyl oxygen points in the same direction as the N-methyl group.While the carbonyl groups in 4 and 5 are twisted nearly 90 • to the naphthalene ring, the carbonyl group of 6 is almost coplanar.Nevertheless, the carbonyl group and N-methyl group remain co-directional in 6.Unlike the dimethyl amino derivatives 1 and 2, the amino groups in 4-6 do not have two equivalent substituents.This inequivalence means that the carbonyl group can be 'syn' or 'anti' to the N-methyl group, or more specifically (R a ,R a ), (S a ,S a ) or (R a ,S a ), (S a ,R a ), since the conformations are axially chiral along both the C aryl -C=O and C aryl -N bonds.The crystal structures in Figure 2

NMR Studies
Proton NMR spectra corroborate the pseudo-chair conformations of the piperidine rings in 4-6 and 10 (Figure 3, showing only 4 and 6).The N and the other peri position must be substituted for the chair to be rigid.In compound 9, where H is attached to the N

NMR Studies
Proton NMR spectra corroborate the pseudo-chair conformations of the piperidine rings in 4-6 and 10 (Figure 3, showing only 4 and 6).The N and the other peri position must be substituted for the chair to be rigid.In compound 9, where H is attached to the N instead of a methyl group, conformational interconversion results in an apparent triplet (2 ′ ), quintet (3 ′ ), triplet (4 ′ ) pattern (A 2 M 2 X 2 ).With N-methyl substituents, the 2 ′ and 3 ′ methylenes display significant diastereotopicity (e.g., 4 and 6, Figure 3).The pseudo-axial hydrogens on C2 ′ and C3 ′ show two large coupling constants for the geminal and trans-diaxial interactions, whereas the pseudo-equatorial hydrogens show just the large geminal coupling.Proton and carbon NMR spectra of 4-6 are included in the Supplementary Information.

NMR Studies
Proton NMR spectra corroborate the pseudo-chair conformations of the piperidine rings in 4-6 and 10 (Figure 3, showing only 4 and 6).The N and the other peri position must be substituted for the chair to be rigid.In compound 9, where H is attached to the N instead of a methyl group, conformational interconversion results in an apparent triplet (2'), quintet (3'), triplet (4') pattern (A2M2X2).With N-methyl substituents, the 2' and 3' methylenes display significant diastereotopicity (e.g., 4 and 6, Figure 3).The pseudo-axial hydrogens on C2' and C3' show two large coupling constants for the geminal and transdiaxial interactions, whereas the pseudo-equatorial hydrogens show just the large geminal coupling.Proton and carbon NMR spectra of 4-6 are included in the Supplementary Information.The piperidine rings in 4-6 are rigid.Heating a solution of 4 in CD 3 CN to 68 • C does not give any hint of broadening, much less coalescence for the diastereotopic hydrogens.Heating a solution of 10 in CDCl 3 to 62 • C shows very slight broadening of the saturated ring hydrogens.While the piperidine ring remains fixed, the carbonyl groups still might be able to rotate about the C aryl -C=O bond.Kiefl characterized the rotation of the carbonyl groups in the analogous N,N-dimethyl derivatives 1 and 2 using dynamic NMR [18].The Computational results indicate the preference for the N-methyl group to be aligned with the carbonyl group.Of the three carbonyl groups, the carboethoxy group in 5 is calculated to have the lowest energy for the (R a ,S a ), (R a ,S a ) rotamer (vide infra).Heating a toluene-d 8 sample of 5 to 110 • C did not give any indication for this rotamer.The difference in energy between the rotamers is significant enough that dynamic NMR would be ineffective in revealing rotation.

Photophysical Studies 2.2.1. Absorption
The long-wavelength absorption maxima for 4-6 are at 312 ± 2, 324 ± 2, and 331 ± 2 nm, respectively, over a series of solvents ranging from apolar, aprotic to polar, protic (toluene, dichloromethane, acetone, and ethanol).For comparison, 2 and 3 show absorbance maxima at 304 and 303 nm [17].Absorption spectra are shown in Figures S1-S3.Thus, one effect of the ring structure is to shift the absorption maxima to slightly longer wavelengths.The explanation for these differences is discussed in the computational results section.

Fluorescence
The fluorescence spectra of 4-6 in various solvents are shown in Figure 4.All three show charge transfer emission.For Figures 4 and 5 the strongest fluorescence occurs in cyclohexane, the least polar solvent in the solvent series.The emission intensities decrease with increasing solvent polarity.This decrease has been attributed to enhanced non-radiative deactivation due to the smaller energy gap between the ground and excited states in these charge transfer systems [14].All show dual emission from a higher energy, possibly locally excited (LE), state.Emission from this state predominates in 6, and is strongest in DMSO for all three.
(toluene, dichloromethane, acetone, and ethanol).For comparison, 2 and 3 show absorbance maxima at 304 and 303 nm [17].Absorption spectra are shown in Figures S1-S3.Thus, one effect of the ring structure is to shift the absorption maxima to slightly longer wavelengths.The explanation for these differences is discussed in the computational results section.

Fluorescence
The fluorescence spectra of 4-6 in various solvents are shown in Figure 4.All three show charge transfer emission.For Figures 4 and 5 the strongest fluorescence occurs in cyclohexane, the least polar solvent in the solvent series.The emission intensities decrease with increasing solvent polarity.This decrease has been attributed to enhanced nonradiative deactivation due to the smaller energy gap between the ground and excited states in these charge transfer systems [14].All show dual emission from a higher energy, possibly locally excited (LE), state.Emission from this state predominates in 6, and is strongest in DMSO for all three.Relative quantum yields were determined in toluene using anthracene (Φ = 0.30) as a reference.This method gives values of 0.02 ± 0.01, 0.06 ± 0.01, and 0.02 ± 0.01, respectively, for 4-6.The quantum yields in Table 1 are based on the toluene value after adjusting for the differences in refractive indices (n 2 solvent/n 2 toluene) [24].These values are similar to those for 2 and 3, 0.08 and 0.03, respectively, in toluene.

Solvato-Chromism
Solvato-chromism in acyl naphthylamines results from charge transfer from the nitrogen donor to the carbonyl acceptor.Because more polar solvents can better stabilize a greater charge, the emission shifts to lower energy with increasing solvent polarity.The plot of the fluorescence maxima vs. the ET(30) solvent polarity parameter serves as a measure of the magnitude of the solvato-chromism (Figure 4) [25].A steep negative slope indicates strong solvent stabilization of the excited state.The slopes of the plots for 4 and 5 are similar in magnitude.The standard deviation of the slopes is 11%.By comparison, the slopes for 2 and 3 are −216 and −177, respectively, which are in line with 6.The ring structure reduces the size of the solvato-chromism.The Stokes shifts for 4-6 are 15,400, 14,500, and 14,700 cm −1 , respectively, in acetonitrile.The Stokes shifts for 2-3 in acetonitrile are 16,300 and 15,400 cm −1 .The two pivaloyl derivatives, 3 and 4, give identical Stokes shifts.While the absorption of 4 is at a longer wavelength than 3, its emission is also at a longer wavelength (599 vs. 567 nm).Relative quantum yields were determined in toluene using anthracene (Φ = 0.30) as a reference.This method gives values of 0.02 ± 0.01, 0.06 ± 0.01, and 0.02 ± 0.01, respectively, for 4-6.The quantum yields in Table 1 are based on the toluene value after adjusting for the differences in refractive indices (n 2 solvent /n 2 toluene ) [24].These values are similar to those for 2 and 3, 0.08 and 0.03, respectively, in toluene.

Solvato-Chromism
Solvato-chromism in acyl naphthylamines results from charge transfer from the nitrogen donor to the carbonyl acceptor.Because more polar solvents can better stabilize a greater charge, the emission shifts to lower energy with increasing solvent polarity.The plot of the fluorescence maxima vs. the E T (30) solvent polarity parameter serves as a measure of the magnitude of the solvato-chromism (Figure 4) [25].A steep negative slope indicates strong solvent stabilization of the excited state.The slopes of the plots for 4 and 5 are similar in magnitude.The standard deviation of the slopes is 11%.By comparison, the slopes for 2 and 3 are −216 and −177, respectively, which are in line with 6.The ring structure reduces the size of the solvato-chromism.The Stokes shifts for 4-6 are 15,400, 14,500, and 14,700 cm −1 , respectively, in acetonitrile.The Stokes shifts for 2-3 in acetonitrile are 16,300 and 15,400 cm −1 .The two pivaloyl derivatives, 3 and 4, give identical Stokes shifts.While the absorption of 4 is at a longer wavelength than 3, its emission is also at a longer wavelength (599 vs. 567 nm).

Computational Studies
The optimized electronic structures for the ground and excited states of 4-6 were calculated using Gaussian 16 [26].The frontier molecular orbitals of 4-6 for the gas phase ground state are shown in Figure 6.As with the dimethylamino derivatives 2 and 3, the HOMO is principally the nitrogen lone pair for all three.The carbonyl group is a component of the LUMO only in 6.This conjugation results in the longer wavelength absorption maximum for 6.In 4 and 5, the LUMO is largely the naphthalene B 2g LUMO.The lowest energy singlet excited state (S 1 ) results mostly from a simple HOMO→LUMO transition (Table S1).
The restricted acyl group rotation and slow piperidine chair interconversion in 4-6 result in chiral axes along the C aryl -C=O and C aryl -N bonds and four stereoisomers: (R a ,R a ), (S a ,S a ) or (R a ,S a ), (S a ,R a ).In the first pair of enantiomers, the carbonyl group points in the same direction as the N-methyl group.The stereoisomers shown in Figure 6 are all (S a ,S a ).Rotation about the C aryl -C=O gives the (R a ,S a ), (R a ,S a ) pair of enantiomers.Optimization of these structures results in local energy minima that are higher energy than the (R a ,R a ), (S a ,S a ) structures by 5.1, 3.8, and 4.2 kcal/mol, respectively.These energy differences explain why dynamic NMR gives no indication of rotation about the C aryl -C=O bond, even with 6, where steric hindrance is negligible.At 120 • C, ester 5, having the smallest energy difference between the conformations, would have an equilibrium population of only 1% for the (R a ,S a ), (S a ,R a ) enantiomers (vide supra).The restricted acyl group rotation and slow piperidine chair interconversion in 4-6 result in chiral axes along the Caryl-C=O and Caryl-N bonds and four stereoisomers: (Ra,Ra), (Sa,Sa) or (Ra,Sa), (Sa,Ra).In the first pair of enantiomers, the carbonyl group points in the same direction as the N-methyl group.The stereoisomers shown in Figure 6 are all (Sa,Sa).Rotation about the Caryl-C=O gives the (Ra,Sa), (Ra,Sa) pair of enantiomers.Optimization of these structures results in local energy minima that are higher energy than the (Ra,Ra), (Sa,Sa) structures by 5.1, 3.8, and 4.2 kcal/mol, respectively.These energy differences explain why dynamic NMR gives no indication of rotation about the Caryl-C=O bond, even with 6, where steric hindrance is negligible.At 120 °C, ester 5, having the smallest energy difference between the conformations, would have an equilibrium population of only 1% for the (Ra,Sa), (Sa,Ra) enantiomers (vide supra).
The calculated structures for the ground and excited states of 4-6 share several structural features.Most relevant are the dihedral angles about the Caryl-C=O (d1, d2), Caryl-N (d3, d4), and the central naphthalene C=C (d5, d6), shown in Table 2.If the paired dihedral angles are nearly the same, this indicates that the groups on either end of the common atoms of the dihedral angles are nearly planar.In this case, a twist angle can be calculated as the absolute value of the average of the paired dihedral angles (Table 2).The planar approximation does not hold for the Caryl-N bond in the ground-state structures.Here, the N atom is significantly pyramidal, and, as shown in the crystal structures, the methyl group is in an axial orientation.The difference between the paired dihedral angles is a measure of the degree of pyramidalization.
In the ground state, the carbonyl groups of 4 and 5 are twisted significantly (~75°), while in 6, the carbonyl is twisted only half as much.The central naphthalene C=C has almost no twist (~6°).In the excited states, the planar approximation for the end groups holds for all three dihedral angle pairs in all three structures.The carbonyl groups of 5 and 6 show little twisting (~5°) and therefore are nearly coplanar with the naphthalene ring.The carbonyl group of 4 still twists significantly in the excited state (40°), but this value is nearly half that of the ground state (76°).This result is due to the steric effect of the tert-butyl group.In the excited states, not only have the amino groups become planar, but they show a relatively small degree of twisting from the naphthalene (~22°).Finally, the naphthalene nucleus doubles its twist (13°) about the central bond in the excited state.The torque responsible for this deformation comes from the planarization of the amino group and the resulting steric hindrance with the carbonyl group.The calculated structures for the ground and excited states of 4-6 share several structural features.Most relevant are the dihedral angles about the C aryl -C=O (d1, d2), C aryl -N (d3, d4), and the central naphthalene C=C (d5, d6), shown in Table 2.If the paired dihedral angles are nearly the same, this indicates that the groups on either end of the common atoms of the dihedral angles are nearly planar.In this case, a twist angle can be calculated as the absolute value of the average of the paired dihedral angles (Table 2).The planar approximation does not hold for the C aryl -N bond in the ground-state structures.Here, the N atom is significantly pyramidal, and, as shown in the crystal structures, the methyl group is in an axial orientation.The difference between the paired dihedral angles is a measure of the degree of pyramidalization.The calculated absorption and emission values are shown in Table 3.Both the calculated absorption and emission values are predicted to be at shorter wavelengths than the experimental values.As with 2 and 3, the dipole moments of the ground and relaxed excited states are nearly the same, except for 5.The solvato-chromism shown in Figure 4 indicates that the solvent stabilizes the excited states.The 2,6 and 1,5-prodan regioisomers show similar solvato-chromism, but much larger changes in the dipole moments [14,15].In the 1,8-donor-acceptor fluorophores, 2-3 and 4-6, solvato-chromism likely results from an increase in charge more so than the separation of charge.
The calculated Stokes shifts in Table 3 compare favorably with the experimental ones in toluene (13,800, 13,100, and 12,300 cm −1 , respectively).The Stokes shifts are large because the structures of the excited and ground states differ greatly.In the ground state, the carbonyl groups of 4 and 5 are twisted significantly (~75 • ), while in 6, the carbonyl is twisted only half as much.The central naphthalene C=C has almost no twist (~6 • ).In the excited states, the planar approximation for the end groups holds for all three dihedral angle pairs in all three structures.The carbonyl groups of 5 and 6 show little twisting (~5 • ) and therefore are nearly coplanar with the naphthalene ring.The carbonyl group of 4 still twists significantly in the excited state (40 • ), but this value is nearly half that of the ground state (76 • ).This result is due to the steric effect of the tert-butyl group.In the excited states, not only have the amino groups become planar, but they show a relatively small degree of twisting from the naphthalene (~22 • ).Finally, the naphthalene nucleus doubles its twist ( 13• ) about the central bond in the excited state.The torque responsible for this deformation comes from the planarization of the amino group and the resulting steric hindrance with the carbonyl group.
The calculated absorption and emission values are shown in Table 3.Both the calculated absorption and emission values are predicted to be at shorter wavelengths than the experimental values.As with 2 and 3, the dipole moments of the ground and relaxed excited states are nearly the same, except for 5.The solvato-chromism shown in Figure 4 indicates that the solvent stabilizes the excited states.The 2,6 and 1,5-prodan regio-isomers show similar solvato-chromism, but much larger changes in the dipole moments [14,15].In the 1,8-donor-acceptor fluorophores, 2-3 and 4-6, solvato-chromism likely results from an increase in charge more so than the separation of charge.a Φ is the relative quantum yield and ε is the molar absorptivity (M −1 cm −1 ).b Radiative rate calculated as f osc ×∆E 2 /1.5, where f osc is the oscillator strength for the emission [27].
The calculated Stokes shifts in Table 3 compare favorably with the experimental ones in toluene (13,800, 13,100, and 12,300 cm −1 , respectively).The Stokes shifts are large because the structures of the excited and ground states differ greatly.

Materials and Methods
Reagents were obtained from Acros Organics or Sigma-Aldrich unless otherwise indicated.N-bromosuccinimide was recrystallized from water.Proton and carbon nuclear magnetic resonance spectra were obtained with an Agilent DD2-400 spectrometer.Xray measurements were made using graphite-monochromated Mo Kα radiation on a Bruker-AXS three-circle Apex DUO diffractometer equipped with a SMART Apex II CCD detector.All solvents used for absorption and fluorescence were spectrophotometric grade.Absorption and fluorescence data were collected using a fiber optic system with an Ocean Optics Maya CCD detector using a miniature deuterium/tungsten lamp and a 365 nm LED light source, respectively.Cuvettes were thermostated at 23 • C for fluorescence studies.Emission intensities were processed by subtracting the electronic noise, converting wavelengths to wavenumbers, multiplying by λ 2 /λ max 2 to account for the effect of the abscissa-scale transformation [24], and dividing by the spectral response of the Hamamatsu S10420 CCD.Relative quantum yields were determined using anthracene as the reference (Φ = 0.30).
Electronic structure calculations were carried out using Gaussian 16 [26].Ground-state geometries were optimized using the DFT CAM-B3YLP method with the 6-311G + (2d,p) basis set and the IEFPCM solvent model for toluene.Excited states were optimized using the TD-SCF DFT CAM-B3LYP method with the 6-311G + (2d,p) basis set and the IEFPCM solvent model for toluene.The optimization for 5 did not converge, and the lowest energy iteration is reported.
The syntheses of 4-6 are shown in Scheme 1. Bromination of 7 is directed to the peri-position by the palladium catalyst [25].Exhaustive reduction of the heteroaromatic ring with sodium cyanoborohydride followed by forcing methylation gives the common intermediate 10.Metal halogen exchange forms the lithiated aryl species 11 and gives 4-6 after reaction with pivaloyl chloride, ethyl chloroformate, and ethyl formate, respectively.Reaction of 10 with carbonyl electrophiles with α-hydrogens gives only hydrogen atom abstraction.
IEFPCM solvent model for toluene.The optimization for 5 did not converge, and the lowest energy iteration is reported.
The syntheses of 4-6 are shown in Scheme 1. Bromination of 7 is directed to the periposition by the palladium catalyst [25].Exhaustive reduction of the heteroaromatic ring with sodium cyanoborohydride followed by forcing methylation gives the common intermediate 10.Metal halogen exchange forms the lithiated aryl species 11 and gives 4-6 after reaction with pivaloyl chloride, ethyl chloroformate, and ethyl formate, respectively.Reaction of 10 with carbonyl electrophiles with α-hydrogens gives only hydrogen atom abstraction.
Crystals for X-ray diffraction were grown by dissolving the compounds in a minimum amount of ethyl acetate (~1 mL), diluting with hexanes (~10 mL), and allowing the solvents to evaporate slowly.

Discussion
The groups on the peri positions of naphthalene affect the behavior of donor-acceptorsubstituted fluorophores due to steric interference.For the three carbonyl groups studied here, the bulkier pivaloyl (4) and carboethoxy (5) groups twist nearly 90 • from the naphthalene ring in both the crystal and calculated structures.The small formyl group (6) still twists slightly but is sufficiently planar for the carbonyl group to be incorporated in the LUMO, resulting in a longer-wavelength absorption.In all cases, the piperidine ring adopts a pseudo-chair conformation, where the N-methyl group is in an axial orientation.While an equatorial orientation is typically lower energy, an equatorial methyl group would have a strong steric interaction with the adjacent carbonyl group, even the formyl group.The axial methyl group and chair structure result in a pyramidal nitrogen atom that is conjugated poorly with the naphthalene ring.Surprisingly, the geometries of the amino groups in 4-6 are very similar to the freely rotating dimethyl amino groups in 2 and 3 in the ground-state structures.In the excited state, the amino group flattens and twists along with the carbonyl group to near coplanarity with the naphthalene ring.For the piperidine ring, this means that it is no longer chair-like, and the N-methyl is neither axial nor equatorial nor pyramidal.Given the extra constraint of the piperidine ring, it is even more surprising that both the carbonyl groups and the amino groups have nearly the same geometries in 4-6 as in 2-3.The smaller solvato-chromism observed for 4-6 is likely a consequence of the extra alkyl group substitution and ring structure that affects the charge distribution and interaction with solvent molecules.Finally, the constraint imposed by the piperidine ring excludes the possibility of forming a TICT state.Chen and Fang have shown that such TICT states may be a source of non-radiative deactivation in these systems [12,13,29].The present study offers corroboration that these systems emit from a mostly PICT state.
b Shoulder.c ICT band.

Table 2 .
Dihedral and twist angles for the calculated ground and excited states of 4

Table 2 .
Dihedral and twist angles for the calculated ground and excited states of 4