Obtaining Enhanced Circular Dichroism in [4]Heterohelicenium

Aug 2, 2012 - Stine T. Olsen , Jonas Elm , Freja Eilsø Storm , Aske Nørskov Gejl , Anne S. Hansen , Mia Harring Hansen , Jens Rix Nikolajsen , Mogen...
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Obtaining Enhanced Circular Dichroism in [4]Heterohelicenium Analogues Jonas Elm,*,† Jacob Lykkebo,† Thomas J. Sørensen,†,‡ Bo W. Laursen,†,‡ and Kurt V. Mikkelsen† †

Department of Chemistry and ‡Nano Science Center, H. C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark ABSTRACT: Electronic circular dichroism in the three helicenium analogues dimethoxyquinacridinium (DMQA+), dimethoxychromenoacridinium (DMCA+), and dimethoxychromenoxanthenium (DMCX+) were investigated in vacuum with time-dependent density functional theory methods using the CAM-B3LYP functional with the basis set 6-311++G**. The systems were thoroughly studied by designing derivatives with several different electron-donating and -withdrawing substituents while at the same time keeping the net charge of the molecule either positive, neutral, or negative. Fifty-six derivatives were examined, and we identify a superior substitution pattern that is found to be independent of the bridging atoms and gives a rotational strength close to 90 × 10−40 esu2 cm2 for DMQA, DMCA, and DMCX. The optimal system shows promising applications as a chromophore because it has a highly allowed primary electronic transition with an angle between the electronic and magnetic transition dipole moments close to 50° and its chiroptical response is thereby limited only by the magnetic transition.

1. INTRODUCTION Helicenes are ortho-condensed polycyclic aromatics and constitute a group of compounds in which several aromatic rings are linked to yield a helical shape.1 Since M. S. Newman and D. Lednicer first synthesized hexahelicene. The helicenes have received much attention due to their fascinating helical structure and their interaction with circularly polarized light while lacking a steriogenic carbon atom.2 This inherent chirality originates from the steric repulsion of the aromatic rings, which makes the isomeres nonsuperimposable. Several [n]-helicenes (n = 4 ... 14), aza-, and thia- heterohelicenes have been synthesized.3−9 Recently, there has been growing interest in structural heterohelicene chemistry because these structures show potential as circular polarized luminescence (CPL) emitters.10 CPL is the differential emission of left- and right-circularly polarized light and has previously been used to obtain information on excited states, since it allows for electronically forbidden but magnetically allowed excited states to be investigated. This method has been used extensively to study the forbidden electronic transition in ketones,11−17 and CPL shows promising applications within several fields, such as display devices;18−20 optical storage devices;21 in asymmetric photochemical synthesis;22 and as a sensor in several biological systems, such as transferrins,23 amino acid absolute configuration determination,24 and as a CPL probe in calcium binding proteins.25 Previous studies have been limited almost exclusively to chiral lanthanide complexes, in which the CPL is extremely sensitive to the structure of the lanthanide complexes, the metal ligand binding, and the solvent−complex interactions.26−37 The issue of connecting CPL with a chromophore system to create a circular polarized luminescence emitter has been addressed to only a limited extent. This type of emitter would show great applications in molecular imaging because it would © 2012 American Chemical Society

allow an alternative type of output compound to the conventional dyes. This could be very useful when using several different chromophores simultaneously because it would, for instance, be possible to view two different outputs at the same wavelength. The group of D. Venkataraman has successfully constructed a CPL emitter using a triarylamine motif.38 In this type of compound, the electronic transition is allowed while the magnetic transition is forbidden, which gives a very low degree of polarization (0.1%). The triangulenium derivative dimethoxyquinacridinium (DMQA+) shows structural similarity to the triarylamines and [4]-helicene and could be a promising model compound as a CPL emitter. DMQA+ has been shown to exhibit extraordinary conformational stability while still being a decent chromophore and can easily be isolated into pure enantiomeres.39,40 In Figure 1, the structural resemblance of DMQA+, [4]-helicene and triarylamine dyes can be seen. The DMQA+ system is prepared by consecutive ortho SNAr reactions of amines with the tris(2,6-dimethoxyphenyl)carbenium ion and can be isolated in good yields.41 The

Figure 1. The structural similarity of (left) [4]-helicene, (middle) triarylamine dyes, and (right) the helicenium dye DMQA+. Received: May 23, 2012 Revised: July 30, 2012 Published: August 2, 2012 8744

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twisted helical structure of DMQA+ arise from the steric repulsion of the methoxy groups in the 1- and 13-positions, preventing the system from adopting a planar ring structure. The DMQA+ system can be regarded as a stable [4]heterohelicenium analog. Recently, the oxygen-bridged analog DMCX+ and a sulfur/nitrogen-bridged [4]heterohelicene analog has been reported42,43 as well as the photophysical properties of DMQA+ with three different side chains.44 We recently published on the racemization mechanism and electronic circular dichroism of seven [4]-heterohelicenium derivatives.45 It was found that all the derivatives were highly configurationally stable and the electronic circular dichroism is highly dependent on both the molecular structure and heteroatoms of the compound. Hence, a screening of different systems is required to identify the key structures with maximized rotational strength. The work presented here is an investigation of the helicenium system as potential CPL emitters in an attempt to get a better understanding of the connection between molecular structure and the interaction with circular polarized light. We have screened 56 helicenium systems with different bridging atoms and electron-donating and -withdrawing substituents to find the superior design for new CPL-emitters.

3. COMPUTATIONAL METHODOLOGY All geometry optimizations were performed using the Gaussian 03 program package49 with the B88 three-parameter exchange functional50 with the Lee, Yang, and Parr correlation functional LYP51 combined into the well-known hybrid functional B3LYP52,53 utilizing the basis set 6-31+G*.54−56 All the rotational strengths were calculated with the quantum chemistry package Dalton 2.057 in vacuum using the longrange corrected CAM-B3LYP functional,58 which has been shown to provide a good representation of rotational strengths.59,60 DFT is known to consistently overestimate the calculated excitation energies compared with experiments. From recent investigations, the calculated excitation energies using CAM-B3LYP/6-311++G** have reliably been found to yield a constant offset of ∼−0.66 eV compared with experimental data of DMQA+, DMCX+, and ATOTA.45,61 All rotational strengths were calculated with London atomic orbitals62 (6-311++G** basis set) and are listed in 10−40 esu2 cm2. The electronic and magnetic transition dipole moments have been evaluated from the center of mass. All calculations have been performed with the (M)-helicenium conformation. 4. RATIONAL DESIGN OF THE HELICENIUM DYES In our previous investigation, we addressed that the enantiomers of the helicenium dyes DMQA+, DMCA+, and DMCX+ are stable, and it was established that the circular dichroism output is extremely sensitive to the overall molecular structure and is highly dependent on the collective contributions of the properties |μ|, |m|, and θ(μ, m), and therefore, a computational screening is necessary.45 To enhance the rotational strength, we have undertaken a systematic approach in investigating several different effects by screening of various structures. Therefore, a template helicenium system was created, as shown in Figure 2.

2. THEORETICAL BACKGROUND The absorption mechanism that gives rise to CPL is the circular dicroism (CD), which is the differential absorption of left and right circularly polarized light (Δε). The chiroptical response at the molecular level is expressed by the rotational strength, R. The rotational strength from the ground state, Ψ0, to the nth excited state, Ψn, is described as46 R = Im{ Ψ0 μα̂ Ψn Ψn m̂ β Ψ0 }

(1)

Here, μ̂ α and m̂ β are the electric and magnetic transition dipole moment operators, respectively, with the components α and β. The rotational strength is related to the circular dichroism spectra by being the integral of the absorbing band and thereby indicates the relative intensity of the transition.47 From Kasha’s rule, it is known that because of the fast process of vibrational relaxation, it can be assumed that all deactivating processes occur from the lowest excited state of a given multiplicity. Thereby, the rotational strength should yield an indication of the relative intensity of the circularly polarized emission as long as nonradiative deactivation processes are nonessential. The degree of circular polarization is estimated by the dissymmetry factor gabs, which determines the degree of polarization in the absorption:48 gabs

4|m||μ| Δε cos(θ) = = ε |m|2 + |μ |2

Figure 2. The used template of the [4]heterohelicenium system. The X and Y are either oxygen or nitrogen to simulate the core compounds DMQA+, DMCA+, and DMCX+. The R1, R2, and R3 positions are open for substitution with different electron-donating and -withdrawing substituents.

(2)

where |μ| and |m| are the electronic and magnetic transition dipole moments, respectively, and θ is the angle between them. This implies that the dissymmetry factor can obtain values in the interval [−2, 2] in the case that |μ| and |m| are of equal length and either parallel or antiparallel. The rotational strength is proportional to the transition dipole moments |μ|, |m|, and the angle between them, R ∝ |μ||m| cos(θ)

The versatile synthesis of the [4]heterohelicenium and triangulenium analogues allows for the addition of substituents in the R1, R2, and R3 positions,43,63−67 whereas X and Y can be either oxygen or nitrogen which gives the core compounds DMQA+ (X, Y = N), DMCA+(X = O, Y = N) and DMCX+ (X, Y = O). By adding substituents either symmetrically (C2 symmetry) or asymmetrically (C1 symmetry), it is possible to conduct an investigation of how important it is to confine the electron density at the front, back, or the sides of a helicenium dye. By using negatively charged electron-donating and

(3)

therefore it is of great interest to obtain as large electronic and magnetic moments as possible while keeping the angle as far away from 90° as possible to archive a high rotational strength. 8745

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Table 1. The Vacuum Chiroptical Properties of the DMQA Analoguesa Cationic compd H1 H1D,D,D H1W,D,D H1D,W,W H1W,W,W H1D,W,D H1W,D,W

freq eV (nm) 2.67 3.01 2.79 2.67 2.46 2.77 2.70

(617) (528) (582) (617) (689) (588) (608)

f

R

|μ|

|m|

θ (μ, m)

0.18 0.51 0.44 0.39 0.18 0.57 0.15

−13.13 31.74 37.92 25.84 −10.45 18.42 −11.33

1.64 2.64 2.53 2.43 1.74 2.90 1.49

0.08 0.05 0.05 0.03 0.10 0.13 0.11

101.87 58.24 49.13 44.12 97.72 84.01 98.16

g factor −3.0 2.8 3.7 2.7 −2.1 1.4 −3.2

× × × × × × ×

10−4 10−4 10−4 10−4 10−4 10−4 10−4

Neutral compd H1W̅ ,D,D H1D,W̅ ,D H1D̅ ,D,D H1D,D̅ ,D H1W̅ ,W,W H1W,W̅ ,W H1D̅ ,W,W H1W,D̅ ,W

freq eV (nm) 3.00 2.75 2.88 2.98 2.27 2.27 2.53 2.71

(530) (593) (559) (534) (770) (770) (663) (605)

f

R

|μ|

|m|

θ (μ, m)

0.35 0.28 0.41 0.38 0.00 0.12 0.24 0.09

40.36 9.80 35.99 −25.32 −0.77 −5.40 51.40 −2.30

2.17 2.00 2.43 2.28 0.16 1.47 1.97 1.15

0.08 0.14 0.05 0.02 0.03 0.22 0.12 0.18

59.44 85.90 46.26 180.09 109.26 87.89 58.17 91.38

g factor 5.3 1.5 3.8 −3.0 −1.9 −1.5 8.2 −1.1

× × × × × × × ×

10−4 10−4 10−4 10−4 10−5 10−4 10−4 10−4

Anionic compound

freq eV (nm)

f

R

|μ|

|m|

θ (μ, m)

H1D,W̅ ,W̅ H1W̅ ,D,W̅ H1D,D̅ ,D̅ H1D̅ ,D,D̅ H1W,W̅ ,W̅ H1W̅ ,W,W̅ H1W,D̅ ,D̅ H1D̅ ,W,D̅

2.70 (608) 2.92 (549) 2.73 (599) 2.84 (569) 2.39 (717) 2.54 (660) 1.86 (1033) 2.08 (873)

0.25 0.22 0.41 0.51 0.14 0.17 0.08 0.13

17.94 −5.76 −5.36 96.83 0.83 −14.43 2.28 1.98

1.94 1.76 2.46 2.70 1.55 1.63 1.33 1.60

0.13 0.07 0.11 0.13 0.22 0.10 0.05 0.07

81.41 95.54 92.54 53.60 89.75 100.42 85.75 88.02

g factor 3.0 −1.2 −5.5 8.3 2.1 −3.4 8.0 4.8

× × × × × × × ×

10−4 10−4 10−5 10−4 10−5 10−4 10−5 10−5

a

The lowest energy transition of the helicenium dyes are shown with the excitation frequency in eV and nm; the oscillator strength, f; rotational strength, R, in 10−40 esu2 cm2; the magnitude of the electronic transition moment, μ (au) and the magnitude of the magnetic transition moment, m (au) (both evaluated from the center of mass); the angle between the transition moments, θ(μ, m); and the dissymmetry factor, g. The electronic excitation energies listed in nanometers have all been shifted −0.66 eV to match the experimental values of H1 and H2.

because these will be implied in the name of the compound. The n indicates which core compound it is, such that 1 = DMQA+, 2 = DMCX+, and 3 = DMCA+. Using this notation, the compound H1W,D̅ ,D̅ would, for instance, refer to a DMQA+ analog with an NO2 group at R1 and O− at R2 and R3, thereby carrying an overall negative charge.

-withdrawing substituents, it is possible to change the net charge of the molecule and thereby investigate whether it is more favorable to have a positive, neutral, or negative overall charge. To simulate the most extreme cases, we have chosen the following substituents: Cationic Strongly donating (D): −N-Me2 Strongly withdrawing (W): −NO2 Neutral and anionic Strongly donating (D̅ ): −O− Strongly withdrawing (W̅ ): −SO−3 To obtain a complete analysis of the systems, all the possible substitution patterns were screened. This implies 22 individual calculations for the helicenium dyes DMQA+ and DMCX+. Since DMCA+ is not C2 symmetrical, it implies that all the asymmetrical substitution patterns should be done with R1 and R3 interchanged. To lower the number of structures in the following analysis, the asymmetrical substitutions of this compound will not be presented. To keep track of the different compounds in the analysis, the compounds will be denoted: HnR1,R2,R3, with the R groups denoted with a D if it is an electron-donating group and a W if it is an electronwithdrawing group. When the withdrawing/donating group is negatively charged the W/D will have a bar above it (W̅ /D̅ ). Thereby, it should be easier to discuss the different structures without continuously referring to figures of the structures

5. RESULTS AND DISCUSSION 5.1. DMQA Analogues. By employing the above substitution patterns and including all possible combinations, the unsubstituted DMQA+, six cationic, eight neutral, and eight anionic compounds are obtained. These compounds indicate which effects dominantly influence the rotational strength. In Table 1, there is an overview of the investigated DMQA+ helicenium analogues in vacuum. It is observed that the substitutions highly influence the rotational strength, with R ranging from 1 to 97 × 10−40 esu2 cm2 in helicenium H1W,W̅ ,W̅ and H1D̅ ,D,D̅ , respectively. The excitation energies are found to be within 2.27−3.00 eV, with the only exception being H1W,D̅ ,D̅ , which has a value of 1.86 eV. The electronic transition dipole moments are found to be of large magnitudes, ranging by a factor of around 2 only, from 1.15 to 2.70 au. The only exception is compound H1W̅ ,W,W, in which the electronic transition is forbidden with magnitude of the electronic transition dipole moment of 0.16 au. This compound contains three electron-withdrawing groups and is 8746

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Figure 3. Electronic transition dipole moments in the DMQA analogues. W represents −NO2; D, −N−Me2; W̅ , −SO3−; and D̅ represents an O− group. The magnitudes are arbitrarily represented at the same scale.

By sketching the electronic transition dipole moments, it gives an indication of how the different substitution patterns influence them. The orientations are intuitively governed by the charge distribution of the compound, which is affected by the substituent donor-strength, as indicated in Figure 3. In cases with three electron-withdrawing substituents (H1W,W,W, H1W̅ ,W,W, H1W,W̅ ,W, H1W,W̅ ,W̅ , H1W̅ ,W,W̅ ), the electronic transition dipole moment is found to have approximately the same orientation as the unsubstituted model compound DMQA+, regardless of the net charge of the molecule. Similar behavior is observed when a single electron-withdrawing group is placed at the rear of the molecule in the R2 position (H1D,W,D, H1D,W̅ ,D, H1D̅ ,W,D̅ ) or when two electron-withdrawing substituents are placed at the front in the R1 and R3 positions (H1W,D,W, H1W,D̅ ,W, H1W̅ ,D,W̅ ). The magnetic transition dipole moments in the cases with either one, two, or three symmetrical electron withdrawing substituents (H1W,W,W, H1W̅ ,W,W, H1W,W̅ ,W, H1W,W̅ ,W̅ , H1W̅ ,W,W̅ H1D,W,D, H1D,W̅ ,D, H1D̅ ,W,D̅ , H1W,D,W, H1W,D̅ ,W, H1W̅ ,D,W̅ ) are also found to have the same orientation as the unsubstituted DMQA+ compound. Since both the electronic and magnetic moments are oriented similarly in these compounds, the variation in angle is very limited. The angle varies only from 88 to 102°, which explains why all the rotational strengths are in a similar range (0-18 × 10−40 esu2 cm2). This deviation in angle could originate from small differences in the molecular framework. In the asymmetrical compounds with either two electronwithdrawing/-donating groups at the flanks of the molecule, the electronic transition dipole moment is dependent on the donor strength. When a single electron-withdrawing group is placed in the R1 position (H1W,D,D, H1W̅ ,D,D, H1W,D̅ ,D̅ ), the dipole moment is, as observed in Figure 3, pushed more toward the flank, where the electron-donating alkoxy groups are present. The difference between the compounds H1W̅ ,D,D and H1W,D,D is reflected in that −SO3− is a weaker electronwithdrawing group such that the transition dipole moment is less aligned with the flank than when a −NO2 group is present.

neutral. By investigation of the molecular orbitals, it is found that the highest occupied molecular orbital is located exclusively on the −SO3− group, which indicates an n → π* transition. Because of the character of the transition, the H1W̅ ,W,W compound will be omitted in the analysis of the transition moments below. Generally, it is seen that compounds with several electrondonating substituents have the highest magnitude of electronic transition moment. Especially, the amino substituent is found to increase the electronic transition dipole moment considerably. The opposite effect is seen when there are several electron-withdrawing groups, which then leads to low electronic transition moments, unless the compounds also contain at least one or two amino groups. The magnetic transition dipole moments are, in contrast, found to deviate considerably more. They range by a factor of around 10 from 0.024 to 0.22 au in the compounds H1D,D̅ ,D and H1W,W̅ ,W̅ , respectively. It is observed that the magnitude of the magnetic moment is highly dependent on the relative position of the substituents and easily deviates by a factor of 2−7 when varied from asymmetrical to symmetrical (or vice versa) substituent patterns. It appears that the magnetic moment is highest when there are several electron-withdrawing substituents and they are placed in a symmetrical pattern. The angle between the transition moments is also seen to be highly dependent on the relative positions of the substituents, and it is difficult to make any predictions as to what effect the substituents have on the angle. Most importantly, it is seen that the angle has the largest impact on the rotational strength. Since the angular variation is a cosine function, the rotational strength is crucially dependent on the angle being as far away from 90° as possible. In the investigation above, it is seen that the angles range from 89.75° to 180° in helicenium H1W,W̅ ,W̅ and H1D,D̅ ,D, respectively. This corresponds to a factor of ∼229 in the rotational strength due to the cosine dependence. This indicates that the angle between the transition dipole moments is the limiting factor in many of the DMQA+ helicenium analogues. 8747

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Table 2. The Vacuum Chiroptical Properties of the DMCX Analoguesa Cationic compound H2 H2D,D,D H2W,D,D H2D,W,W H2W,W,W H2D,W,D H2W,D,W

freq eV (nm) 2.74 3.00 2.71 2.79 2.54 2.76 2.85

(596) (530) (605) (582) (660) (590) (566)

f

R

|μ|

|m|

θ (μ, m)

0.02 0.55 0.57 0.40 0.02 0.67 0.57

−41.80 11.05 3.16 −6.03 −47.32 39.99 46.75

0.57 2.75 2.94 2.43 0.54 3.15 2.85

0.36 0.01 0.06 0.21 0.35 0.16 0.03

116.02 10.97 87.66 91.49 121.79 80.40 0.00

g factor −5.8 9.1 2.3 −6.3 −7.0 2.5 3.6

× × × × × × ×

10−3 10−5 10−5 10−5 10−3 10−4 10−4

Neutral compound

freq eV (nm)

f

R

|μ|

|m|

θ (μ, m)

H2W̅ ,D,D H2D,W̅ ,D H2D̅ ,D,D H2D,D̅ ,D H2W̅ ,W,W H2W,W̅ ,W H2D̅ ,W,W H2W,D̅ ,W

2.70 (608) 2.68 (614) 2.96 (539) 2.88 (559) 1.88 (1016) 1.79 (1097) 2.79 (282) 2.81 (577)

0.00 0.00 0.54 0.49 0.00 0.00 0.33 0.39

−0.18 0.11 16.11 −23.28 −0.05 −0.01 22.86 −38.13

0.12 0.10 2.72 2.64 0.10 0.09 2.19 2.37

0.03 0.05 0.05 0.02 0.06 0.08 0.05 0.03

95.94 87.28 75.20 180.02 90.92 90.11 63.64 179.94

compound

freq (eV)

f

R

|μ|

|m|

θ(μ, m)

H2D,W̅ ,W̅ H2W̅ ,D,W̅ H2D,D̅ ,D̅ H2D̅ ,D,D̅ H2W,W̅ ,W̅ H2W̅ ,W,W̅ H2W,D̅ ,D̅ H2D̅ ,W,D̅

2.82 (574) 2.85 (566) 2.66 (620) 2.85 (566) 2.46 (689) 2.52 (667) 1.90 (1000) 2.20 (805)

0.09 0.05 0.47 0.61 0.00 0.01 0.12 0.17

15.44 −65.73 −21.80 89.50 −1.38 −4.50 −8.12 21.62

1.11 0.87 2.69 2.96 0.27 0.35 1.58 1.78

0.28 0.43 0.13 0.10 0.10 0.11 0.03 0.03

83.90 111.71 97.50 50.69 95.98 104.89 113.55 40.03

g factor −7.7 5.4 1.4 −2.1 −2.9 −3.7 3.0 −4.2

× × × × × × × ×

10−4 10−4 10−4 10−4 10−4 10−5 10−4 10−4

Anionic g factor 7.3 −4.3 −1.9 6.3 −1.0 −2.1 −2.0 4.3

× × × × × × × ×

10−4 10−3 10−4 10−4 10−3 10−3 10−4 10−4

a

The lowest energy transition of the helicenium dyes are shown with the excitation frequency in eV and nm; the oscillator strength, f; rotational strength, R, in 10−40 esu2 cm2; the magnitude of the electronic transition moment, μ (au) and the magnitude of the magnetic transition moment, m (au) (both evaluated from the center of mass); the angle between the transition moments θ(μ, m); and the dissymmetry factor, g. The electronic excitation energies listed in nanometers have all been shifted −0.66 eV to match the experimental values of H1 and H2.

10−40 esu2 cm2. This is a collective contribution of the highly allowed electronic transition, a moderately allowed magnetic transition, and an angle between the moments that is far away from 90°. 5.2. DMCX Analogues. It is now possible to take a look at the DMCX+ analogues to see if some general trends can be deduced in a comparison with the DMQA+ data. The same substituent patterns as above were studied, the data are shown in Table 2. The excitation energies of the compounds span a range of 1.79−3.00 eV and are very similar to those of the DMQA+ compounds. As with the DMQA+ analogues, several of the DMCX+ compounds that include an −SO3 group have a forbidden electronic transition, and thus, all compounds with an electronic transition moment below 0.4 au are omitted in the following analysis. The magnitude of the electronic transition moment ranges from 0.54 to 3.15 au in H2W,W,W and H2D,W,D, respectively, corresponding to a factor of ∼6, which is a bit higher than in the DMQA+ compounds. The low-magnitude electronic transition moment is found in only three compounds (H2, H2W,W,W and H2D,W̅ ,W̅ ); the rest vary by a factor of approximately 2 or 3. As observed for the DMQA+ compounds, the magnitude of the electronic transition dipole moment is highly dependent on the electron-donating substituents, and the amino substituents are very important in obtaining a large magnitude. The magnetic moments are found to vary

The same effect of donor strength is seen in the case when there is a single electron donating group in the R1 position. In these asymmetrical compounds, the magnetic moments were difficult to interpret. The orientation of the magnetic moment varies from pointing slightly toward the amino groups in H1W,D,D to pointing away from the alkoxy groups in H1D,W̅ ,W̅ , and in H1W̅ ,D,D, it lies in the plane of the molecule pointing toward the flank with the −SO3− group. The last case is when there are three electron-donating substituents in the compound (H1D,D,D, H1D̅ ,D,D, H1D,D̅ ,D, H1D,D̅ ,D̅ , H1D̅ ,D,D̅ ). Again, the orientation is highly dependent on the position of the strongly activating alkoxy group, and as seen in Figure 3, the moment can be shifted from being across the molecule (H1D̅ ,D,D̅ , H1D,D,D) to being along the C2 axis of the molecule in H1D,D̅ ,D. The moments of the two compounds H1D̅ ,D,D and H1D,D̅ ,D̅ obtain an intermediate orientation, depending on the existence of either one or two alkoxide substituents. In the symmetrical compounds with three donating substituents, the magnetic moments are found to be very difficult to interpret. There is no clear pattern in these compounds; it appears that the position, type of substituent, and overall charge have an effect on both magnitude and orientation. In Table 1, it is observed that a single substitution pattern is vastly superior (H1D̅ ,D,D̅ ), yielding a rotational strength of 97 × 8748

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Figure 4. Electronic transition dipole moments in the DMCX+ helicenium analogues. W represents −NO2; D, −N−Me2; W̅ , −SO3−; and D̅ represents an O− group. The magnitudes are arbitrarily represented at the same scale.

leads to low rotational strengths of approximately −25 × 10−40 esu2 cm2. The compounds H1D,D̅ ,D̅ and H2D,D̅ ,D̅ have very similar orientation of the electronic and magnetic transition moments and slightly different magnitudes. The angle between the transition moments differs by 5°, but since it is close to 90°, this manifests as a difference in rotational strength of a factor of 4. Compounds H1D̅ ,D,D̅ and H2D̅ ,D,D̅ are found to be very similar: both have a very high rotational strength of ∼90. When a single electron-withdrawing group is placed at the R2 position (H2D,W,D, H2D̅ ,W,D̅ ) or when two electron withdrawing substituents are placed at the front in the R1 and R3 positions (H1W,D,W, H2W̅ ,D,W̅ ), the electonic transition moments in DMCX+ are found to be similar to the DMQA+ analogues. The molecules H1D,W,D and H2D,W,D have very similar orientations and only a little variation in the magnitude of the moments, but these small variations give a factor of 2 difference in the rotational strengths. In H1D̅ ,W,D̅ and H2D̅ ,W,D̅ , the orientation of the electronic transition moments is identical, but due to changes in magnetic moments, these two compounds exhibit very different rotational strengths, a difference dominated by variation of the angle between the moments. The compounds H1W,D,W and H2W,D,W have very different properties. Both the orientation and magnitude of the electronic and magnetic transition moments vary with the position of the two electron-withdrawing groups. The electronic moment in H1W,D,W is across the molecule as a result of the electron-donating nitrogen bridges, where it changes to be along the C2 axis in H2W,D,W. The magnetic moments also deviate, resulting in an angle between the moments of 0° to 98°. The molecules H1W̅ ,D,W̅ and H2W̅ ,D,W̅ are also very different: both moments have different orientation, and very different rotational strengths are found. In the asymmetrical compounds with two electron-withdrawing groups at the flank of the molecule, the electronic

considerably more than the electronic moments from 0.01 to 0.43 au in H2D,D,D and H2W̅ ,D,W̅ , respectively. By dividing the compounds into groups, as done for DMQA, it is possible to investigate the orientations of the transition moments. In Figure 4, the electronic transition dipole moments can be seen sketched for the compounds with similar substitution patterns. For the DMCX+ analogues, we observe that the orientation of the electronic transition moments can be predicted from the choice of substituents. As above, the compound that contains three electron-withdrawing substituents (H2, H2W,W,W) have properties very similar to those of the unsubstituted compound; that is, close to identical orientation and magnitude of the electronic and magnetic transition moments, which gives similar chiroptical properties. In the cases with three electron-donating substituents (H2D,D,D, H2D̅ ,D,D, H2D,D̅ ,D, H2D,D̅ ,D̅ , and H2D̅ ,D,D̅ ), the electronic transition moments adopt varying orientations, similarly to the DMQA+ analogues. The orientations of the transition moments are seen to differ significantly when changing the bridging atom from nitrogen to oxygen, as seen by comparing H2D,D,D and H1D,D,D. The electronic transition moment changes from being along the C2 axis in H2D,D,D to being across the molecule in H1D,D,D, and the magnetic moment also differs considerably both in magnitude and direction. In other cases, there is great similarity between the DMCX+ and DMQA+ analogues. By comparing H1D̅ ,D,D and H2D̅ ,D,D, it is seen that the electronic transition moments have the same orientation, but the magnetic moments differ, which gives a different angle and results in a factor of 2 in the resulting rotational strength of the compounds. H1D,D̅ ,D and H2D,D̅ ,D have identical orientations of the electronic and magnetic transition moments with slightly different magnitudes. Interestingly, both compounds have the optimum angle of 180°, but unfortunately, the magnetic transitions are very weak, which 8749

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Table 3. The Vacuum Chiroptical Properties of the C2 Symmetric DMCA Analoguesa Cationic compound H3 H3D,D,D H3W,W,W H3D,W,D H3W,D,W

freq eV (nm) 2.73 3.00 2.54 2.79 2.54

(599) (530) (660) (582) (660)

f

R

|μ|

|m|

θ (μ, m)

0.13 0.59 0.13 0.10 0.13

7.94 58.60 5.86 −16.27 5.86

1.38 2.83 1.45 3.07 1.19

0.21 0.07 0.22 0.12 0.19

86.75 49.77 73.43 98.99 87.82

f

R

|μ|

|m|

θ (μ, m)

0.29 0.42 0.00 0.19

38.28 −26.89 0.11 −43.71

2.05 2.41 0.11 1.71

0.19 0.05 0.06 0.15

77.70 115.83 87.86 111.97

g factor 2.5 4.6 3.3 −7.0 1.7

× × × × ×

10−4 10−4 10−4 10−4 10−4

Neutral compound H3D,W̅ ,D H3D,D̅ ,D H3W,W̅ ,W H3W,D̅ ,W

freq eV (nm) 2.85 2.93 2.08 2.67

(566) (546) (873) (617)

g factor 5.6 −2.9 4.5 −9.2

× × × ×

10−4 10−4 10−4 10−4

Anionic compound H3W̅ ,D,W̅ H3D̅ ,D,D̅ H3W̅ ,W,W̅ H3D̅ ,W,D̅

freq eV (nm) 2.91 2.83 2.58 2.14

(551) (571) (645) (838)

f

R

|μ|

|m|

θ (μ, m)

0.15 0.55 0.07 0.15

25.30 93.51 0.58 12.80

1.44 2.83 1.08 1.69

0.23 0.12 0.16 0.05

80.71 54.34 89.64 70.31

g factor 7.4 7.3 3.0 2.8

× × × ×

10−4 10−4 10−5 10−4

a

The lowest energy transition of the helicenium dyes are shown with the excitation frequency in eV and nm; the oscillator strength, f; rotational strength, R, in 10−40 esu2 cm2; the magnitude of the electronic transition moment μ (au) and the magnitude of the magnetic transition moment m (au) (both evaluated from the center of mass); the angle between the transition moments θ(μ, m); and the dissymmetry factor, g. The electronic excitation energies listed in nanometers have all been shifted −0.66 eV to match the experimental values of H1 and H2.

transition dipole moment is similar to the DMQA+ analog. The same is the case with the magnetic moments in H1D,W,W and H2D,W,W. The situation is different when there are asymmetrical electron-donating substituents at the flank. In this case, both the electronic and magnetic moments are very different. From the analysis of the DMQA+ and DMCX+ analogues, we can conclude that the electronic transition moments in several cases can be controlled by the choice of substitution pattern. From the above analysis of the DMQA+ and DMCX + analogues, it appears that the compounds with the clearest patterns in the electronic transition dipole moments have a C2 symmetry axis. Unfortunately, the orientation and magnitude of the magnetic transition dipole moments are still very unpredictable, and the same applies to the angle between the moments, which has a crucial role in the rotational strength. Nevertheless, in both the DMQA+ and DMCX+ analogues, a single substitution pattern (H1D̅ ,D,D̅ , H2D̅ ,D,D̅ ) is found to be vastly superior to the others, and the pattern is independent of whether the bridging atoms are nitrogen or oxygen. 5.3. DMCA Analogues. To get an extensive analysis, the DMCA+ analogues were also investigated. Since this compound inherently does not have C2 symmetry, only the symmetrical substitution patterns were included to see if these compounds have some of the general trends observed in the DMQA+ and DMCX+ analogues. The data are shown in Table 3. They do not provide additional information to the analysis. The cationic H3D,D,D is seen to have a high rotational strength due to the low angle and highly allowed electric transition. The compound that had the highest rotational strength in the DMQA+ and DMCX+ analogues also works well in the DMCA+ case. This is important because this indicates that this substitution pattern is superior in providing the highest rotational strength and a decent dissymmetry factor in all the helicenium dyes.

6. CONCLUSION The helicenium systems DMQA+, DMCX+, and DMCA+ have been investigated with a variety of substitution patterns. Generally, it is observed that the rotational strength is a difficult quantity to predict from the molecular structure because it depends on the collective contribution of three parameters: the electronic transition dipole moment, |μ|; the magnetic transition dipole moment, |m|; and the angle between the electronic and magnetic transition moments, θ(μ, m). In several cases, the electronic transition dipole moment is intuitively governed by the charge distribution in the system, and the magnitude of the magnetic transition dipole moment is given by the electronic current related to the transition. Unfortunately, we have not found a simple correlation for the orientation of the magnetic transition dipole moments. By changing the substitution pattern, the involved electronic states will evidently change, and accordingly, this will be reflected in the rotational strength. It is not possible to give a good estimate of the rotational strength before the actual calculation is performed, and to find an optimal substitution pattern in other systems, a computational screening analysis will have to be applied. It is observed for the helicenium systems studied here that electron-donating substituents increase the magnitude of the electronic transition dipole moment and symmetrical withdrawing substituents generally leads to a higher magnitude of the magnetic moments. In these systems, a high rotational strength is a matter of compromise between the two moments. A superior substitution pattern is found, which gives the highest rotational strength in all three helicenium systems (H1D̅ ,D,D̅ , H2D̅ ,D,D̅ , and H3D̅ ,D,D̅ ). These compounds have a highly allowed electronic transition and a favorable angle between the electronic and magnetic moments. Hence, it is the magnitude of the magnetic transition moments that limits the rotational strength in these compounds. 8750

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Danish Center for Scientific Computing, and J.E. thanks the Villum Kann Rasmussen Foundation for financial support. K.V.M. thanks the Danish Natural Science Research Council/The Danish Councils for Independent Research, and the Villum Kann Rasmussen Foundation for financial support. B.W.L. and T.J.S. thank the Danish “National Research Foundation under the Danish-Chinese Centre for Self-Assembled Molecular Electronic Nanosystems” for financial support. T.J.S. thanks the Danish Council for Independent Research, Technology and Production Sciences for a Grant (no. 10-093546).

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