Faraday Effect in Stacks of Aromatic Molecules - The Journal of

Subscriber access provided by TUFTS UNIV

Article

Faraday Effect in Stacks of Aromatic Molecules Orian Louant, Vincent Liégeois, Thierry Verbiest, Andre Persoons, and Benoît Champagne J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04177 • Publication Date (Web): 20 Jun 2017 Downloaded from http://pubs.acs.org on June 23, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Faraday Effect in Stacks of Aromatic Molecules Orian Louant,a Vincent Liégeois,a Thierry Verbiest,b André Persoonsb and Benoît Champagnea*, a.

Laboratory of Theoretical Chemistry, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, Rue de Bruxelles 61, 5000 Namur, Belgium.

b. Laboratory of Molecular Imaging and Photonics, University of Leuven, Celestijnlaan, 200F – Box 2404, 3001 Leuven, Belgium. (*) Corresponding author: [email protected]

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT: The effects of stacking aromatic units

on the Verdet constant are analyzed by employing quantum chemistry calculations and are compared to the effects of oligomerization. Building stacked oligomers leads to enhanced Verdet constants, but still smaller than in the corresponding linear oligomers. Further enhancements appear when going from simple to fused-ring polyaromatic compounds.

I. Introduction The Faraday effect,1 a magneto-optical effect present in all materials, is the rotation (θ) of the plane of polarization of a linearly polarized light when passing through a medium placed in a uniform magnetic field with non-zero component in the direction of light propagation. Faraday rotation is involved in many devices, encompassing displacement sensors2 and detection of biomagnetic fields.3 The amplitude of Faraday rotation is proportional to the Verdet constant, V(ω), =

where B is the amplitude of magnetic field parallel to the propagation of light and L is the length of propagation through the magnetic field. V(ω) is frequency-dependent and vanishes in the zero frequency limit. Using the response formalism it reads:

organic liquids5,7-8 as well as by carrying out computational investigations.9-20 Among these, V(ω) increases with the donor strength of the substituent in mono-substituted benzene derivatives.17-18 Still, the effect of packing aromatic units on the Verdet constant has not yet been investigated while intriguing results were obtained in mesogenic organic molecules and attributed to resonances with low-lying singlet and triplet excited states.6 Therefore, in this paper, quantum chemistry methods are employed to analyze the effects of stacking aromatic units on the Verdet constant. Besides the simple benzene (Figure 1a) and thiophene (Figure 1b) rings, 2,5,8-trimethylbenzo[1,2b;3,4-b’;5,6-b”]trithiophene, (BTT) (Figure 1c), and 2,3,6,7,10,11-hexamethoxytriphenylene (HMT) (Figure 1d) are considered. Recently, it has been shown that discotic mesogenic molecules can exhibit giant Faraday rotation.6 Both HMT and BTT are indeed disc-like and, when properly substituted, can exhibit liquid-crystalline behaviour.21 Therefore, we expect both of them to be potential candidates to show strong Faraday rotation. These stacking effects are compared to the effects of oligomerization for (a) and (b) and further investigations on the effect of planarity (i.e. of the dihedral torsion angle) are performed.

= ≪ ; , ≫,

Here is the Levi-Civita tensor, the circular frequency of the incident light, and ≪ ; , ≫, is the quadratic response function, with µ and L the electric dipolemoment and angular momentum operators, respectively. C is a proportionality constant given by $%& )

= # (# ( !" '% $*)

with + the speed of light, , and -. the charge and mass of the electron, the vacuum permittivity, and / the number density. At 273.15K and P = 1 atm, N = 3.9813 10-6 m-3 so that C amounts to 1.52118 10-8 a.u., which corresponds to gas phase The Verdet constant depends on the nature of the material, organic versus inorganic, metallic versus semi-conductor and insulator. Currently, owing to their processability, low sensitivity to temperature changes, and high saturation magnetic field, there is an interest in designing organic materials with large Faraday rotation4-6 and therefore in deducing structure-V(ω) relationships. This has been tackled by measuring the Verdet constant of

Figure 1: Molecular structures. a) benzene, b) thiophene, c) 2,5,8-trimethylbenzo[1,2-b;3,4b’;5,6b”]trithiophene (BTT), and d) 2,3,6,7,10,11hexamethoxytriphenylene (HMT).

II. Theoretical and computational aspects Geometry optimizations were carried out at the MP2/6-31G(d) level of theory using the Gaussian 09 computational chemistry package.22 Using the MP2 method allows London dispersion forces to be taken into account in the geometry optimizations which is the key point for aromatic stacking interactions. The calculations of the ≪ ; , ≫, response tensor23 were performed with Dalton 201524 at the B3LYP/aug-ccpVDZ level of approximation. This level was shown


Page 2 of 12

Page 3 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry to be adequate to closely reproduce experimental data as well as to match data obtained with methods including high-level electron correlation effects.16-17 The use of an augmented basis set is important since finite basis set calculations are not gauge-origin invariant. In all calculations, the center of mass is used as gauge-origin. As a complement to our earlier investigation,16 the gauge-origin dependence was assessed by carrying out calculations on the thiophene syn dimers (stacked and linear). When moving the gauge origin simultaneously along the x, y, and z axes by 3.78 Å (stacked) and 4.08 Å (oligomer) (which corresponds to the inter-ring distances), V(ω) evaluated at 500 nm changes by 2.3% and 3.0%, respectively. Smaller displacements along the stacking and oligomer axes are associated to even smaller variations of V(ω), substantiating the choice of basis set. Note that for centrosymmetric compounds, by symmetry, the Verdet constant is not gaugeorigin dependent. London dispersion forces were not taken into account in the V(ω) calculations because these forces mostly impact the geometry. Still, this assumption has been confirmed by performing a B3LYP-D3 calculation25 on the syn stacked thiophene dimer. It gave a V(ω) value that differs by less than 0.1% with respect to the B3LYP result obtained with the same aug-cc-pVDZ basis set, 500 nm wavelength, and geometry.

The V(ω) frequency dispersion curves for the isolated molecules in gas phase (Figure 3) show that V(ω) increases in the order: thiophene < benzene < BTT < HMT. Note that V(ω) is plotted as a function of ω2 (or of the square of the photon energy) instead of ω, since in regions far from absorption the variations of V(ω) are known to be proportional to ω2.5,11 The largest V(ω) values are observed for the fused-ring compounds, that present smaller excitation energies than the one-ring compounds. Indeed, the excitation energies corresponding to the lowestenergy transitions, as determined at the TDDFT/B3LYP/aug-cc-pVDZ level, amount to 5.36 eV, 5.63 eV, 3.70 eV, and 3.87 eV, for benzene, thiophene, HMT, and BTT, respectively.

The optimized geometry of the dimers of benzene and thiophene are presented in Figure 2a-f.

Figure 3: Frequency-dispersion of the Verdet constant of benzene, thiophene, BTT, and HMT.

V(ω) of benzene dimers

Figure 2: Optimized geometries of the stacked and linear dimers of benzene (a, b) and thiophene (c, d, e, f). For thiophene two configurations are considered: syn when the two sulfur atoms point in the same directions and anti when they point in opposite directions.

III. Results and discussion Frequency dispersion of V(ω)

Varying the distance (d) between a pair of stacked benzene molecules moderately impacts the Verdet constant as far as the distance is not much smaller than the sum of their van der Waals radii (Table 1). Still, the evolution of V(ω) as a function of d around the equilibrium distance (d = 3.76 Å) is not monotonic since it presents a minimum around d = 3.0 Å. In the case of biphenyl, a small impact of the inter-ring dihedral angle (θ) on V(ω) is evidenced (Table 1), with a maximum value close to the equilibrium geometry (θ = 44.6°). The minima in V(ω) correspond to the planar and perpendicular structures. The planar conformer (θ = 0°) presents a value 5-7% smaller than the maximum over the 500-1550 nm wavelength range whereas the smallest value is achieved for the perpendicular



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

conformer (θ = 90°) with V(ω) smaller by 1216% than the maximum. Table 1 Verdet constant (deg T−1 m−1) as a function of (left) the stacking distance (d) in the benzene dimer and of (right) the dihedral angle (θ) in biphenyl at 500, 980, and 1549 nm. Values in bold correspond to the equilibrium geometry. The vdW radius of carbon amounts to 1.70 Å. Stacked d (Å)

500 nm

980 nm

1.50

87.84

2.00

Linear θ (°)

500 nm

980 nm

1549 nm

3.45

154 9 nm 1.06

0.0

5.30

1.15

0.44

5.63

0.50

0.20

15.0

5.45

1.18

0.45

2.50

4.00

0.88

0.34

30.0

5.67

1.21

0.47

3.00

3.52

0.80

0.31

44.6

5.67

1.21

0.47

3.50

3.70

0.85

0.33

45.0

5.66

1.21

0.47

3.76

3.83

0.88

0.34

60.0

5.35

1.16

0.45

4.00

3.97

0.91

0.35

75.0

4.97

1.10

0.42

90.0

4.79

1.07

0.41

Page 4 of 12

the decrease due to stacking to the reduction of the xyz and yxz components, i.e. those components where the magnetic interaction is along the z axis, the stacking axis. In analogy, the increase of V(ω) of the linear oligomers results also mainly from an increase of the xyz and yxz tensor components with z defining the out-ofplane direction. Table 2 Verdet constant (deg T−1 m−1) as a function of the number (n) of units in (left) stacks of benzene molecules and in (right) oligomers of poly-pphenylene in comparison to benzene. Numbers in parentheses are the differences with respect to n times the value of the isolated benzene. Isolated n 1

3 4

Verdet constants for stacks of 2 to 4 benzene molecules are listed in Table 2. The optimized d values for n = 3 and 4 are slightly smaller (3.75 Å) than for n = 2 (3.76 Å). At 500 nm, going from benzene to its stacked dimer, V(ω) increases from 2.29 to 3.83 deg T−1 m−1, which corresponds to a decrease with respect to a pair of isolated benzene molecules. In other words, the contribution of the second benzene molecule to V(ω) attains 1.54 deg T−1 m−1 and similar V(ω) increments are observed when going from 2 to 3 as well as from 3 to 4 benzene molecules. Qualitatively, analogous variations on V(ω) are obtained at the other wavelengths. This evolution of V(ω) as a function of the number of stacked molecules is however opposite to the behavior found for linear oligomers of poly-p-phenylene where the addition of successive units enhances the Verdet constant. For instance, considering again λ = 500 nm, the successive V(ω) increments when going from n = 1 to 2, 2 to 3, and 3 to 4 amount to 3.38, 4.23, and 5.51 deg T−1 m−1, respectively. Note that frequency dispersion of V(ω) is similar in the oligomers and isolated molecule. Decomposing the Verdet constant into its tensor elements has enabled to trace

980 nm 0.52

Stacked

2

V(ω) of stacks of benzene and thiophene in comparison to their linear oligomers

500 nm 2.29 500 nm 3.83 (-0.75) 5.37 (-1.50) 6.90 (-2.26)

980 nm 0.88 (-0.16) 1.24 (-0.32) 1.59 (-0.49)

1549 nm 0.20 Linear

1549 nm 0.34 (-0.06) 0.48 (-0.12) 0.62 (-0.18)

500 nm

980 nm

1549 nm

5.67 (+1.09) 9.90 (+3.03) 15.41 (+6.25)

1.21 (+0.16) 2.01 (+0.45) 2.97 (+0.89)

0.47 (+0.07) 0.77 (+0.17) 1.13 (+0.33)

Then, replacing benzene by thiophene rings, the results are presented in Table 3. Both syn and anti structures are considered (Figure 2). d amounts to 3.9 Å for the syn structures while 3.5 Å for the anti ones. Moreover, these optimized structures are not planar and are characterized by dihedral torsion angles of about 43° (36°) in the syn (anti) conformations. Like for the stacked benzenes, the formation of a thiophene dimer is associated with a reduction of the V(ω) per ring, though smaller. On the other hand, there is a substantial enhancement between the dimer and the trimer, highlighting the role of the nature of the ring on the stacking effect on V(ω). Then, like in linear oligomers of poly-p-phenylene, the Verdet constant is enhanced in larger oligothiophenes and is larger than in the corresponding stacked structure. To a good extent, the variations of the Verdet constant originate also from differences of excitation energies, as also unraveled for the individual molecules. For instance, i) the first excitation energy for the benzene stacked dimer amounts to 5.87 eV in comparison to 4.91 eV for the linear dimer, which is consistent with the observed decrease of the V(ω) value per ring in the case of the stacked dimer; ii) similarly, for the syn (anti) thiophene stacked dimer, it amounts to 5.47 eV (5.03 eV) in


Page 5 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry comparison to 4.16 eV (4.08 eV) for the linear ones. Finally, another global trend emerges: for the stacked oligomers V(ω) is larger for the anti structures whereas the syn structures present larger V(ω) in the linear oligomers. The variation of V(ω) in the stacked and linear oligomers is also dominated by the xyz and yxz tensor components with z defining an effective out-of-plane direction.

Table 3 Verdet constant (deg T−1 m−1) as a function of the number (n) of units in (left) stacks of thiophene molecules and in (right) oligomers of polythiophene in comparison to thiophene. Numbers in parentheses are the differences with respect to n times the value of the isolated thiophene. See Fig. 2 for the meaning of syn and anti.

tion of ω (Figure 4). This is consistent with the results on the benzene dimer. The optimized geometry of the HMT dimer is characterized by a similar distance between centroids as BTT with a value of 3.24 Å as well as a rotation of 30° around the pseudo C3 axis. These results on the BTT and HMT dimers contrast with recent experimental data on mesogenic molecules,6 where the Verdet constant is strongly enhanced. Thus, when compared to our calculations, measurements of Ref. 6 seem to originate from a supramolecular organizational effect, which is beyond the scope of the present contribution owing to the much larger system sizes that should be considered to assess these.

Isolated

n 1

500 nm 1.60

980 nm 0.38

1549 nm 0.15

Stacked (syn)

n 2 3

500 nm 2.91 (-0.29) 4.98 (+0.18)

980 nm 0.70 (-0.06) 1.16 (+0.02)

1549 nm 0.27 (-0.03) 0.48 (+0.01)

Stacked (anti)

n 2 3

500 nm 3.15 (-0.05) 5.18 (+0.38)

980 nm 0.74 (-0.02) 1.20 (+0.06)

1549 nm 0.29 (-0.01) 0.47 (+0.02)

Linear (syn)

500 nm 3.29 (+0.09) 6.39 (+1.59)

980 nm 0.79 (+0.03) 1.34 (+0.20)

1549 nm 0.31 (+0.01) 0.52 (+0.07)

Linear (anti)

500 nm 3.12 (-0.08) 5.74 (+0.94)

980 nm 0.76 (0.00) 1.28 (+0.14)

1549 nm 0.29 (-0.01) 0.50 (+0.05)

Fused-ring systems: trimethylbenzotrithiophene and hexamethoxytriphenylene stacked dimers The Verdet constant of the dimers of the fused-ring compounds as well as its frequency dispersion is then investigated by considering the ratio between the dimer and monomer values, R(ω) = V(ω, dimer)/V(ω, monomer). This ratio should be exactly 2 for non-interacting monomers. V(ω) of the BTT dimer amounts to slightly less than twice the value of its monomer, in agreement with the results on the thiophene dimer (Figure 4). Still, owing to smaller excitation energies, at larger frequencies, an increased is observed. The optimized geometry of the BTT dimer is characterized by a distance of 3.32 Å between the centroids and a rotation of 30° around the pseudo C3 axis. Then, V(ω) of the HMT dimer presents the smallest ratio among the four compounds and it decreases as a func-

Figure 4: Frequency-dispersion of ratio between the Verdet constants of the dimer and monomer, R(ω) = V(ω, dimer)/V(ω, monomer).

IV. Conclusions First principles calculations have revealed that forming stacked oligomers of aromatic units enhances the Verdet constant but not as much as in linear oligomers. Moreover, calculations predict large Faraday rotation in polyaromatic compounds like BTT and mostly HMT, demonstrating the interest for studying larger stacks of polyaromatic compounds as well as the effect of chiral stacking.

Acknowledgements This work was supported by funds from the Belgian Government (IUAP No P7/5 “Functional Supramolecular Systems”) (O.L., V.L., and B.C.), the FWO



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

under convention G.0C02.13 (T.V.), the KU Leuven (IDO) (T.V.), and AOARD (T.V. and A.P.). V.L. thanks the Fund for Scientific Research (FRS.-FNRS) for his Research Associate position. The calculations were performed on the computing facilities of the Consortium des Équipements de Calcul Intensif (CÉCI, http://www.ceci-hpc.be ), particularly those of the Technological Platform of High Performance Computing, for which we gratefully acknowledge the financial support of the FNRS- FNRC (Conventions 2.4.617.07.F and 2.5020.11) and of the University of Namur.

References (1) Faraday M. Experimental Researches in Electricity; R. Taylor & W. Francis: London, 1839−1855; Vol. III. (2) Budker, D.; Kimball, D. F.; Rochester, S. M.; Yashchuk, V.; Zolotorev, M. Sensitive Magnetometry Based on Nonlinear Magneto-Optical Rotation. Phys. Rev. A, 2000, 62, 043403. (3) Bullmore, E.; Sporns, O. Retrograde Modulation of Presynaptic Release Probability Through Signaling Mediated by PSD-95–Neuroligin. Nat. Rev. Neurosci., 2009, 10, 186−198. (4) Koeckelberghs, G.; Vangheluwe, M.; Van Doorsselaere, K.; Robijns, E.; Persoons, A.; Verbiest, T. Regioregularity in poly(3-alkoxythiophene)s: Effects on the Faraday Rotation and Polymerization Mechanism. Macromol. Rapid Commun. 2006, 27, 1920-1925. (5) Vandendriessche, S.; Valev, V. K.; Verbiest, T. Faraday Rotation and its Dispersion in the Visible Region for Saturated Organic Liquids. Phys. Chem. Chem. Phys. 2012, 14, 1860-1864. (6) Vandendriessche, S.; Van Cleuvenbergen, S.; Willot, P.; Hennrich, G.; Srebro, M.; Valev, V. K.; Koeckelberghs, G.; Clays, K.; Autschbach, J.; Verbiest, T. Giant Faraday Rotation in Mesogenic Organic Molecules. Chem. Mater. 2013, 25, 1139-1143. (7) Isai, K.; Suwa, M.; Watarai, H. Pulsed Magnetic Field Faraday Imaging of Diamagnetic Liquid. Anal. Sci., 2009, 25, 1–3. (8) Egami, S.; Watarai, H. Microscopic Faraday Rotation Measurement System Using Pulsed Magnetic Fields. Rev. Sci. Instrum., 2009, 80, 093705. (9) Jørgensen, P; Oddershede, J.; Beebe, N. H. F. Polarization Propagator Calculations of Frequency‐dependent Polarizabilities, Verdet Constants, and Energy Weighted Sum Rules. J. Chem. Phys., 1978, 68, 2527-2532. (10) Bishop, D. M.; Cybulski, S. M. Magnetic optical rotation in H2 and D2. J. Chem. Phys., 1990, 93, 590-599. (11) Parkinson, W. A.; Sauer, S. P. A.; Oddershede, J.; Bishop D. M. Calculation of the Verdet Constants for H2, N2, CO, and FH. J. Chem. Phys., 1993, 98, 487-495. (12) Jaszunski, M.; Jørgensen, P.; Rizzo, A.; Ruud, K.; Helgaker, T. MCSCF Calculations of Verdet Constants. Chem. Phys. Lett., 1994, 222, 263-266. (13) Coriani, S.; Hättig, C.; Jørgensen, P.; Halkier, A.; Rizzo, A., Coupled Cluster Calculations of Verdet Constants. Chem. Phys. Lett., 1997, 281, 445-451. (14) Coriani, S.; Jørgensen, P.; Christiansen, O.; Gauss J. Triple Excitation Effects in Coupled Cluster Calculations of Verdet Constants. Chem. Phys. Lett., 2000, 330, 463-470. (15) Krykunov, M.; Banerjee, A.; Ziegler, T.; Autschbach, J. Calculation of Verdet Constants with Time-Dependent Density Functional Theory: Implementation and Results for Small Molecules. J. Chem. Phys., 2005, 122, 074105. (16) Botek, E.; Champagne, B.; Verbiest, T.; Gangopadhyay, P.; Persoons, A. A Joint Theoretical–Experimental Investigation of the Faraday Effect in Benzene, Toluene, and pXylene. ChemPhysChem, 2006, 7, 1654-1656.

(17) Botek, E.; Champagne, B.; Gangopadhyay, P.; Persoons, A.; Verbiest, T. Theoretical Evaluation of the Faraday Effect in Organic Compounds. Comput. Lett., 2007, 3, 193200. (18) Kjærgaard, T.; Jørgensen, P.; Thorvaldsen, A. J.; Paweł P.; Coriani S. Gauge-Origin Independent Formulation and Implementation of Magneto-Optical Activity within AtomicOrbital-Density Based Hartree-Fock and Kohn−Sham Response Theories. J. Chem. Theory Comput., 2009, 5, 19972020. (19) Savukov, I. M.; Particle-hole Configuration-Interaction Polarizabilities and Verdet Constants of Noble-Gas Atoms. Phys. Rev. A, 2012, 85, 052512. (20) Caputo, M. C.; Coriani, S.; Pelloni, S.; Lazzeretti, P.; On the Origin Independence of the Verdet Tensor. Mol. Phys., 2013, 111, 1405-1413. (21) Wöhrle T.; Wurzbach I.; Kirres J.; Kostidou A.; Kapernaum N.; Litterscheidt J.; Haenle J. C.; Staffeld P.; Baro A.; Gisselmann F.; Laschat S. Discotic Liquid Crystals. Chem. Rev., 2016, 116, 1139-1241. (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision D.01, 2009. (23) Olsen, J.; Jørgensen, P. Linear and Nonlinear Response Functions for an Exact State and for an MCSCF State, J. Chem. Phys. 1985, 82, 3235–3264 (24) Aidas, K.; Angeli, C.; Bak, K. L, Bakken, V.; Bast, R.; Boman, L.; Christiansen, O.; Cimiraglia, R.; Coriani, S.; Dahle, P.; et al. The Dalton Quantum Chemistry Program System. WIREs Comput. Mol. Sci., 2014, 4, 269-284. (25) S. Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys., 2010, 132, 154104.


Page 6 of 12

Page 7 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC graphic


7

The Journal of Physical O Chemistry

O

a)1 2 3 4 5 6 7 8 9 10 11 b)12 13 14 15 16 17

Page 8 of 12

O c) S

S

S d)

O S O ACS Paragon Plus Environment

O

Page 9 of 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34


Page 10 of 12

Page 11 The of Journal 12 of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


The Journal of Physical Chemistry Page 12 of 12

1 2 3 4 5 6 7


Faraday Effect in Stacks of Aromatic Molecules - The Journal of

Recommend Documents