Vibrational Optical Activity of BODIPY Dimers: The Role of Magnetic

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Vibrational Optical Activity of BODIPY Dimers: the Role of Magnetic-electric Coupling in Vibrational Excitons Sergio Abbate, Torsten Bruhn, Gennaro Pescitelli, and Giovanna Longhi J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b11327 • Publication Date (Web): 14 Dec 2016 Downloaded from http://pubs.acs.org on December 16, 2016

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The Journal of Physical Chemistry

Vibrational Optical Activity of BODIPY Dimers: the Role of Magnetic-Electric Coupling in Vibrational Excitons Sergio Abbate1, Torsten Bruhn2, Gennaro Pescitelli3*, Giovanna Longhi1* 1

Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia, Viale Europa 11,

25123 Brescia (Italy) 2

Institut für Organische Chemie, Universität Würzburg Am Hubland, 97074 Würzburg

(Germany) 2

Dipartimento di Chimica e Chimica Industriale, Via Moruzzi 13, 56124 Pisa (Italy)

Corresponding Authors * E-mail: [email protected] (G.P.); [email protected] (G. L.)

ACS Paragon Plus Environment

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ABSTRACT The Vibrational Exciton (VE) interpretation of intense bisignated couplets in Vibrational Circular Dichroism (VCD) spectra of a pair of atropisomeric BODIPY (boron dipyrrin) dimers is discussed. The role of intrinsic magnetic moments is crucial to reproduce the different behaviors of quasi-isomeric BODIPY dimers with different aryl junction.


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INTRODUCTION The Coupled Dipole or Coupled Oscillator approach has been one of the first theoretical models for Vibrational Circular Dichroism (VCD).1-2 Originally proposed by Holzwarth,3-4 it has served to interpret many VCD spectra, first in the OH and CH stretching region, using in particular dimethyl tartrate as a model.5-7 Afterwards, the same method was applied to the C=O stretching by Keiderling,8 who also tested the model against ab initio calculations for the first time.9 Even after the advent of DFT calculations the C=O stretching region has remained the main source of data and subject of calculations with this model.10-12 More recently, Taniguchi and Monde re-investigated this concept13 and found that, in a number of molecules containing two C=O groups, a Vibrational Exciton (VE) rule holds, which correlates the sign of the VCD couplet (i.e., the succession of two VCD bands close in frequency and with opposite sign) with the chirality defined by the two C=O groups (i.e., the absolute sense of twist between the two C=O bonds). This is analogous to the well-established case occurring in Electronic Circular Dichroism (ECD), the so-called ECD exciton chirality.14-15 In both cases it is assumed that the electric dipole-electric dipole interaction is the main source of the observed optical activity, either vibrational or electronic. Since VCD spectra are nowadays mainly interpreted by means of Density Functional Theory (DFT) calculations, a straightforward method like the VE rule roused a lot of interest. However, subsequent analyses highlighted the existence of a few criticalities16-17 especially in the case of non-degenerate couplings (i.e. when the two C=O groups are not equivalent by symmetry). Very recently, Nicu has further stressed the limitation of the VE rule but has also demonstrated the usefulness of the coupled oscillator treatment. For any normal mode, in fact, the DFT-calculated rotational strength can be decomposed in two contributions, namely the


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generalized coupled dipole mechanism and other non-coupled dipole terms.18-19 Going beyond the mere application of the VE rule, a fragmentation approach like the coupled-oscillator one remains the only practical way of treating complex systems like large (bio)macromolecules or supramolecular aggregates.20 In the context of small molecules, which in turn serve as models for larger systems, the occurrence of the VE behavior has been found in instances other than the C=O stretching, encompassing coupled delocalized vibrations of two equivalent or nearby equivalent aromatic moieties.21-23

Chart 1. Structures of quasi-isomeric BODIPY dimers M-1 and M-2, and of model fragment 3. Recently, some of us studied the chiroptical properties of a pair of quasi-isomeric BODIPY dimers 1 and 2 (Chart 1) which were synthesized by Bröring et al. and enantioseparated by Bringmann and coworkers.24-25 Boron dipyrrin derivatives (BODIPY, 4,4difluoro-4-bora-3a,4a-diaza-s-indacene) are widely studied chromophores and fluorophores because of the very favorable absorption and emitting properties in the visible spectral region.2627

Enantiopure 1 and 2 show exciton ECD couplets between 400 and 650 nm, allied with the first

π–π* transition of the BODIPY chromophore which is both strongly electric-dipole and magnetic-dipole allowed.24 Moreover, the low-lying exciton-coupled level is the emitting state and strong Circularly Polarized Luminescence (CPL) spectra were also recorded.28 The specific combination of electric (µ µ) and magnetic dipole transition moments (m) depends on the aryl junctions: the electric/electric (µ−µ µ−µ) µ−m) µ−µ and electric/magnetic (µ− µ− couplings have the same sign


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for the 3,3’-coupled compound 1 but opposite sign for the 1,1’-coupled compound 2. This results in strong ECD and CPL bands for 1, and in weak ECD and CPL bands for 2, together with an apparent exception to the ECD exciton chirality rule.24, 28 In the present work we discuss how compounds 1 and 2 behave differently also in the context of VCD spectroscopy.

EXPERIMENTAL AND COMPUTATIONAL METHODS The synthesis, enantioseparation and full characterization of compounds 1 and 2 has been reported previously.24-25 VCD measurements were run with a Jasco FVS-6000 spectrometer using default acquisition parameters (resolution: 4 cm−1) and 4000 accumulations (total scan time: ≈1 h), on samples of compounds M-1 and M-2 in CCl4 (20 mg/mL) using a 65 µm BaF2 cell. A spectrum of the solvent in the same cell was used as blank to measure the baseline. All calculations were run with the Gaussian09 package.29 The input geometries of compounds 1 and 2 for VCD calculations were obtained from previous studies24, 28 and were re-optimized at the B3LYP/6-311+G(d,p) level in vacuo. In both cases, a single conformation was considered. For compound 1, this is the only ground-state minimum found by DFT calculations. For compound 2, this is the global minimum with a transoid conformation, which represents >99% population at room temperature, according to free energies.24, 28 The ethyl chains in 2 were also kept in the lowest energy conformation. The monomeric model 3 (single conformation) was similarly optimized at B3LYP/6-311+G(d,p) level and the coordinate origin was put in the center of masses. Frequency (VCD) calculations were run at the same B3LYP/6-311+G(d,p) level in vacuo. VCD spectra were plotted by applying a Lorentzian band-shape with 4 cm–1 full width at half maximum (FWHM), and a frequency scale factor of 0.975.


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RESULTS AND DISCUSSION In Figure 1 we compare the experimental mid IR-VCD spectra of (aR)-1 (or M-1) and (aR)-2 (or M-2) recorded in CCl4 and the corresponding DFT calculated ones at the B3LYP/6311+G(d,p) level (details can be found in the Experimental and Computational Section). DFT calculations correctly reproduce most of the observed experimental features, in particular they correctly predict, in sign and intensity, the two couplets for each molecule at ~1650 and 1250 cm-1. We were surprised to notice that the two couplets have the same sign for M-1 (both negative), while they have opposite sign for M-2 (negative at 1650 but positive at 1250 cm-1). The pattern of the normal modes underneath the two couplets is similar for M-1 and M-2, as analyzed

through

DFT

calculations.

The

normal

modes

at

~1250

cm–1 are fairly localized and may be described as almost pure in-plane methine bendings; interestingly enough, this is the first example of such distinctive VE couplets found for a C–H bending. On the contrary, the couplets at ~1650 cm-1 are mostly due to conjugated CC stretching modes in the three units of each BODIPY, similar to a ring breathing. A representation of the anti-symmetric combination of the two types of normal modes for both molecules is given in Figure 2. We notice that the anti-symmetric normal modes (labeled as –) are calculated at lower frequencies than the symmetric ones (+) in all cases, which is relevant for the following analysis.16-17


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Figure 1. Experimental (CCl4 solutions) and DFT-calculated (B3LYP/6-311+G(d,p) level) VCD spectra of compounds M-1 and M-2. See Experimental and Computational sections for details.

Figure 2. Normal modes calculated for compounds M-1 and M-2 with DFT (B3LYP/6311+G(d,p) level). See Computational Section for details.


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The question that arises is whether the two aforementioned couplets of compounds 1 and 2 are amenable to the VE treatment. In fact, all the prerequisites for a correct application of the model appear to be met in the present case. In particular: (a) we have two symmetric systems allowing for degenerate exciton coupling, that is, the two “local” vibrations have equal frequencies (diagonal force constants); (b) the two interacting units do not perturb much each other in their electrical response, in fact, for the relevant normal modes, the total electric dipole transition moments are approximated by the sum of the moments of the two separate units (see Tables 1 and 2 and discussion below), i.e., the total dipole strength is conserved; (c) the relevant normal modes are associated with large electric dipole transition moments, i.e. the corresponding IR bands are strong; this is necessary for the two units to interact through a dipole-dipole term; (d) the relevant normal modes give rise to intense bisignate doublets, with small frequency separation and nearly conservative, i.e. with similar band integral. (e) because of the 1,1’ or 3,3’ coupling in compounds 1 and 2, the dipole transition moments of the two BODIPY units are far from a parallel/antiparallel orientation:28 this situation, encountered for instance in 2,2’-coupled BODIPY dimers,30 would lead to a vanishing exciton coupling contribution, so other terms would dominate the rotational strengths. Moreover, a little deviation from this condition may generate opposite results,16, 18, 30 such deviations are difficult to calculate with precision and can be accessible through thermal energy fluctuations. Thus, the two couplets observed at 1250 and 1650 cm-1 seem to fulfill all the requirements for the application of the VE treatment. However, when checked against the VE chirality rule enunciated by Taniguchi and Monde,13 only three out of four couplets are in accord with the rule,


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while the couplet at ~1250 cm-1 for M-2 is at odds with that rule. In fact, for the M configuration around the BODIPY axis, negative chirality is obtained and negative VE couplets are expected. To explain the source of the inconsistency observed for M-2, we first apply the equations for the standard VE approach reported in ref. 16. For the special case of C2-symmetric molecules, the angles of the two dipoles with respect to the connecting line are equal, namely α1=α2=α (a geometric model with the definition of angles is drawn in the Supporting Information). The frequencies ν±, rotational strengths R± and dipole strengths D± for the two exciton-coupled normal modes are:16 ν± = ν ± (R12-3)[µ1·µ µ2 – 3(n·µ µ1)(n·µ µ2)] =ν ± (hc)-1 µ2 d-3 [sin2α cos φ + 2 cos2α]

R± = m

πν ± 2

(1)

⋅ ( R 2 − R1 ) ⋅ µ1 × µ 2 = − (±πν±/2)dµ2 sin2α sinφ

(2)

D± = D ± µ1·µ µ2 = D ± D [sin2α cos φ - cos2α]

(3)

In the above equations R12 (or d ) is the distance of the two equivalent interacting oscillators, whose electric dipole transition moments µ1 and µ2 (each with square modulus equal to D) form a dihedral angle φ; α is the angle between µ1 (µ µ2) and R1–R2 (R2–R1), R1 and R2 being the position

vectors

of

the

two

units;

n

is

the

distance

unit

vector,

namely

(R12–1)[R2-R1]; h is Planck’s constant, c the speed of light and wavenumbers ν± are in cm-1, while overall units are electrostatic c.g.s.. As a “monomeric ” model fragment

we used

compound 3 (Chart 1 and Figure 3). This fragment was characterized by DFT calculations in order to obtain the structure, vibrational modes, frequencies, and dipole strengths. In order to apply the VE model, we assume the electric dipole to be located at the geometrical centre of the two units (origin of black arrows in Figure 3), which is approximately the centre of the group of


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atoms involved in each relevant vibrational mode. This permits one to define also the angles α and φ involved in eqs. (1)-(3) and presented in Table 2.

Figure 3. DFT-optimized geometries for compounds M-1 and M-2 and model fragment 3 (B3LYP/6-311+G(d,p) level), and direction of electric (black) and magnetic (red) dipole transition moments for the normal modes responsible for the VCD couplets at 1250 and 1650 cm–1. The numerical predictions made on the basis of eqs. (1)-(3) are reported in Table 2. For both molecules M-1 and for M-2, negative exciton couplets are predicted for both frequency regions around 1650 and 1250 cm–1, in accord with the VE rule. Therefore, there is an apparent discrepancy for the doublet at ∼1250 cm-1 for M-2. A wrong sign prediction of a VE couplet might in principle be due to an inversion of the order of the symmetric and anti-symmetric


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modes, but from DFT calculations we know that the four doublets are all symmetric/antisymmetric modes in order of decreasing wavenumber. This is also reproduced by the estimated dipole-dipole interaction term (∆ν in Table 2). As anticipated, and discussed in refs.

16-17

, it is

important to check that the calculated interaction term gives the correct sequence; from Table 2 it is clear that not only the sign (∆ν is positive in all cases) but also the absolute frequency difference values of symmetric and anti-symmetric modes are calculated similarly by full DFT and by the VE approach.

Table 1. Computed DFT data for model compound 3.(a) Monomer fragment 3 First Normal Mode Second Normal Mode (ca. 1250 cm–1) (ca. 1650 cm–1) ν (cm–1) µ (10–20 esucm) m (10–24 esucm)

(a)

1269

1644

40

49

110

35

Calculated frequencies (ν),electric and magnetic dipole transition moments (µ and m) for the

model fragment 3, for the two normal modes studied.


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Table 2. Computed DFT and VE data for compounds M-1 and M-2.(a) Compound M-1

Compound M-2 Geometrical parameters

130 –64 5.85

α (°) φ (°) d (Å)

v+ v– D+ D–

∆ν (v+)–(v–)

R+ (10–44 esu2cm2) R– (a)

132 –91 6.41

First Couplet (ca. 1250 cm–1) DFT VE 1272 1273 1257 1265 927 1344 2540 1859

Second Couplet (ca. 1650 cm–1) DFT VE 1652 1651 1637 1638 1567 2012 3769 2782

+15

+15

+8

+13

First Couplet (ca. 1250 cm–1) DFT VE 1267 1272 1259 1266 787 875 2021 2328 +8

+6

Second Couplet (ca. 1650 cm–1) DFT VE 1646 1648 1639 1640 1088 1310 4736 3484 +7

+8

DFT

µ-µ eq.(2)

Total eq.(4)

DFT

µ-µ eq.(2)

Total eq.(4)

DFT

µ-µ eq.(2)

Total eq.(4)

DFT

µ-µ eq.(2)

Total eq.(4)

3984

986

5263

2741

1914

3578

–2458

1138

–2724

901

2207

703

–6098

–979

–5256

–4195

–1898

–3563

2290

–1133

2729

–1045

–2196

–693

Legend. Top: values of the distance d, the angle α and the dihedral angle φ between the two

interacting monomers in compounds M-1 and M-2. Bottom: Comparison of calculated frequencies (ν±), dipole strengths (D±) and rotational strengths (R±) from full DFT calculations, from the standard VE model of eq.(2), and from the VE-corrected model (Total, eq.(4)) described in the text for the two relevant normal modes of M-1 and M-2.

The reason for the observed inconsistency for M-2 has to be sought in the fact that purely dipole-dipole (µ−µ µ−µ) µ−µ contributions are not sufficient to account for observed rotational strengths, and the intrinsic magnetic dipole transition moments mi must be considered. In fact, equation (2) above is valid upon the assumption that the two units are independent from one other and have negligible intrinsic mi1 and mi2.1 This is analogous to the case of electronic CD, where intrinsic magnetic dipole transition moments are commonly neglected in exciton treatments14-15 but may in fact give large contributions to the overall rotational strength.24, 31 As far as VCD is concerned, negligible intrinsic magnetic dipole transition moments are often associated to C=O stretchings,


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although even such assumption fails for example when the bonds connecting the two C=O partecipate in the electric and magnetic dipole transition moment response, i.e. when the two units are not electrically and magnetically “independent”.16, 18-19 In the current case, the magnetic dipole transition moments of the vibrations calculated for the monomer 3 are reported in Table 1 in the so-called “standard orientation” used by the Gaussian code.29 The magnetic dipole moment is origin dependent: we refer to the “local” origin of the monomer speaking of local or intrinsic mi. The monomer is achiral, which implies that each mi is orthogonal to the respective µ. For both relevant normal modes of 3, the mi are relatively large. In particular, the intrinsic magnetic dipole transition moment for the mode at ~1250 cm-1 is the largest one among all normal modes of the monomer. To appreciate how mi1 and mi2 will combine with µ1 and µ2, in Figure 3 we report the DFToptimized structures for M-1 and M-2, showing in black the direction of the calculated electric dipole transiton moments (µ µ1 and µ2) and in red the direction of the intrinsic local magnetic dipole transition moments (mi1 and mi2). Considering the “local” origin, the direction of mi1 and mi2 is the same for both the ~1250 cm-1 and 1650 cm-1 vibrations of the monomer, i.e perpendicular to the aromatic plane. From Figure 3, it emerges that µ1 can give a contributiton by combining with mi2, and µ2 with mi1. On a quantitative ground, we may apply a “corrected” coupled dipole formula that takes into account the intrinsic magnetic dipole transition moments mi1 and mi2: R ± = ± Im

1 2

r r r r r r r πν ± r ( µ 1 ⋅ m 2i + µ 2 ⋅ m 1i ) m ( R 2 − R1 ) ⋅ µ 2 × µ 1 2

Equation (4) is discussed in the Supporting Information and also in refs.

(4) 1

(eq. A13, there)

and 2 (eq. A4.46, there). Within the generalized coupled oscillator approach discussed by Nicu,19


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the contribution of the intrinsic magnetic dipole transition moments may be taken into account by a corrective electric/electric term obtained by translating one of the two local origins to the r r r r so-called coupled oscillator origin (COC), for which it holds that µ1 ⋅ m2i + µ2 ⋅ m1i ,COC = 0 (eq. 16

in ref

19

). Eq. 4 and the unique µ−µ term referred to Nicu’s COC origin (eq. 17 in ref.

19

) are

equivalent from a numerical viewpoint. In Table 2, we show the results of VE calculations with eq. (4), where the moments mi1 and mi2 have been estimated by DFT calculations on fragment 3. It is clear that only by introducing these intrinsic magnetic dipole transition moments it is possible to reconcile VE calculations with both DFT and experimental results. The addition of the mi contribution changes substantially the overall rotational strengths for all modes considered. In the case of the 1250 cm1

couplet of molecule M-2, in particular, the correction leads to the observed sign inversion, but

also for the other modes the absolute values of VE rotational strengths are in better agreement with full DFT calculations. Within the geometric model discussed above, we may quantify the correction to the calculated rotational strengths brought about by the intrinsic magnetic dipole transition moments with the following formula (derived in the Supporting Information): r r r r r r r r ∆R± = Im ( µ ± •m± ) = Im(1/ 2)( µ1 ± µ 2 ) • ( m1a + m1b ± ( m2 a + m2b )) = = ± {(1/ 2) µ ma [sin 2α (cos ϕ + 1)] + 2 µ mb sin α sin ϕ }

(5)

The formula is valid for any C2-symmetric system composed of achiral units, i.e. with internal m1 and m2 perpendicular to the corresponding local electric dipole transition moments µ1 and µ2, respectively. Each term m1 and m2 may be divided into two contributions, one in the plane (z, µ1,2), which we call ma (m1a,2a), and one perpendicular to such plane, which we call mb (m1b,2b). Relatively large ma and mb components are responsible for sizable contributions to rotational strengths, possibly leading to sign inversion, as it happens for the present BODIPY


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dimers. Once again, we would like to stress that an analogous phenomenon occurs in the context of ECD, where a couplet sign inversion is observed for compound 2 with respect to the expectations of exciton-coupling theory based solely on electric dipoles. In the case of ECD too, the sign inversion was reproduced by including the intrinsic magnetic dipole transition moments.24 Finally, we notice that in the present calculations we have considered the corrected coupled oscillator model allowing only for the dipole-dipole dynamical coupling term and have neglected other types of inter-fragment interactions such as attractive London dispersion forces, repulsiveexcluded volume forces, interactions mediated by other internal coordinates, etc. These interactions are responsible for non-excitonic terms which may contribute substantially the coupling of the two moieties (and thus to the appearance of a positive or negative couplet in VCD spectra),19 and make it necessary to use quantum-mechanical calculations like DFT. In the current case, the large electric dipole moments associated with the relevant normal modes render the dipole-dipole interaction dominant by far, as it is demonstrated by the consistency between VE and DFT results. We have also neglected that the two units influence each other in their electric and magnetic response to some extent. Furthermore, an address to the question of the relative robustness of the two VE components18,

32-34

may be found in the Supporting

Information.

CONCLUSIONS In conclusion, our vibrational exciton calculations prove that in case of BODIPY dimers 1 and 2, considering the intrinsic magnetic dipole transition moment (perpendicular to electric dipole transition moment) is beneficial to understand the DFT VCD calculations and crucial to


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reproduce experimental data. These molecules, belonging to the C2-symmetry group and presenting intense, isolated, and nearly conservative couplets in the VCD spectra associated with strong vibrations, appear as ideal candidates to apply the coupled dipole model in a case outside the typical C=O stretching. Apart from organic molecules with a limited number of atoms, that can be treated by DFT, the VE method is especially suitable to characterize unit-unit interactions in reduced systems used as models for more complex structures: polymers, polypeptides and proteins, solids, and so on. This is true not only in the context of VCD but also in that of 2D-IR spectroscopy.

ASSOCIATED CONTENT Supporting Information: geometric model used in calculations; derivation of eqs. (1)-(5); discussion on the robustness of vibrational excitonic bands.

ACKNOWLEDGEMENTS Prof. Martin Bröring and Dr. Johannes Ahrens are gratefully acknowledged for providing the samples of compounds 1 and 2. Financial support from the University of Brescia and from the University of Pisa is acknowledged.


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REFERENCES 1.

Nafie, L. Vibrational optical activity, principles and applications. John Wiley & Sons:

New York, 2011. 2.

Polavarapu, P. L. Chiroptical spectroscopy: Fundamentals and applications. CRC Press:

Boca Raton (FL), 2016. 3.

Chabay, I.; Hsu, E. C.; Holzwarth, G. Infrared circular-dichroism measurement between

2000 and 5000 cm-1 - pr-3+-tartrate complexes. Chem. Phys. Lett. 1972, 15, 211-214. 4.

Holzwarth, G.; Chabay, I. Optical activity of vibrational transitions: A coupled oscillator

model. J. Chem. Phys. 1972, 57, 1632-1635. 5.

Keiderling, T. A.; Stephens, P. J. Vibrational circular-dichroism of dimethyl tartrate -

coupled oscillator. J. Am. Chem. Soc. 1977, 99, 8061-8062. 6.

Marcott, C.; Blackburn, C. C.; Faulkner, T. R.; Moscowitz, A.; Overend, J. Infrared

circular-dichroism associated with OH-stretching vibration in methyl-ester of mandelic-acid. J. Am. Chem. Soc. 1978, 100, 5262-5264. 7.

Su, C. N.; Keiderling, T. A. Conformation of dimethyl tartrate in solution - vibrational

circular-dichroism results. J. Am. Chem. Soc. 1980, 102, 511-515. 8.

Narayanan, U.; Keiderling, T. A. Coupled oscillator interpretation of the vibrational

circular-dichroism of several dicarbonyl-containing steroids. J. Am. Chem. Soc. 1983, 105, 64066410. 9.

Bour, P.; Keiderling, T. A. Computational evaluation of the coupled oscillator model in

the vibrational circular dichroism of selected small molecules. J. Am. Chem. Soc. 1992, 114, 9100-9105. 10.

Polavarapu, P. L.; Ewig, C. S.; Chandramouly, T. Conformations of tartaric acid and its

esters. J. Am. Chem. Soc. 1987, 109, 7382-7386. 11.

Buffeteau, T.; Ducasse, L.; Brizard, A.; Huc, I.; Oda, R. Density functional theory

calculations of vibrational absorption and circular dichroism spectra of dimethyl-l-tartrate. J. Phys. Chem. A 2004, 108, 4080-4086. 12.

Abbate, S.; Castiglione, F.; Lebon, F.; Longhi, G.; Longo, A.; Mele, A.; Panzeri, W.;

Ruggirello, A.; Liveri, V. T. Spectroscopic and structural investigation of the confinement of d and l dimethyl tartrate in lecithin reverse micelles. J. Phys. Chem. B 2009, 113, 3024-33.


17


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

13.

Page 18 of 21

Taniguchi, T.; Monde, K. Exciton chirality method in vibrational circular dichroism. J.

Am. Chem. Soc. 2012, 134, 3695-3698. 14.

Harada, N.; Nakanishi, K. Exciton chirality method and its application to configurational

and conformational studies of natural-products. Acc. Chem. Res. 1972, 5, 257-263. 15.

Harada, N.; Nakanishi, K.; Berova, N. Electronic CD exciton chirality method: Principles

and applications. In Comprehensive chiroptical spectroscopy, Berova, N.; Polavarapu, P. L.; Nakanishi, K.; Woody, R. W., Eds. John Wiley & Sons, Inc.: Hoboken (NJ), 2012; pp 115-166. 16.

Abbate, S.; Mazzeo, G.; Meneghini, S.; Longhi, G.; Boiadjiev, S. E.; Lightner, D. A.

Bicamphor: A prototypic molecular system to investigate vibrational excitons. J. Phys. Chem. A 2015, 119, 4261-4267. 17.

Covington, C. L.; Nicu, V. P.; Polayarapu, P. L. Determination of the absolute

configurations using exciton chirality method for vibrational circular dichroism: Right answers for the wrong reasons? J. Phys. Chem. A 2015, 119, 10589-10601. 18.

Nicu, V. P. Revisiting an old concept: The coupled oscillator model for VCD. Part 2:

Implications of the generalised coupled oscillator mechanism for the VCD robustness concept. Phys. Chem. Chem. Phys. 2016, 18, 21213-21225. 19.

Nicu, V. P. Revisiting an old concept: The coupled oscillator model for VCD. Part 1: The

generalised coupled oscillator mechanism and its intrinsic connection to the strength of VCD signals. Phys. Chem. Chem. Phys. 2016, 18, 21202-21212. 20.

Taniguchi, T.; Hongen, T.; Monde, K. Studying the stereostructures of biomolecules and

their analogs by vibrational circular dichroism. Polym. J. 2016, 48, 925-931. 21.

Mazzeo, G.; Abbate, S.; Longhi, G.; Castiglioni, E.; Boiadjiev, S. E.; Lightner, D. A. Ph

dependent chiroptical properties of (1r,2r)- and (1s,2s)-trans-cyclohexane diesters and diamides from VCD, ecd, and cpl spectroscopy. J. Phys. Chem. B 2016, 120, 2380-2387. 22.

Mazzeo, G.; Fuse, M.; Longhi, G.; Rimoldi, I.; Cesarotti, E.; Crispini, A.; Abbate, S.

Vibrational circular dichroism and chiroptical properties of chiral ir(III) luminescent complexes. Dalton. Trans. 2016, 45, 992-999. 23.

Setnička, V.; Urbanová, M.; Bouř, P.; Král, V.; Volka, K. Vibrational circular dichroism

of 1,1‘-binaphthyl derivatives: Experimental and theoretical study. J. Phys. Chem. A. 2001, 105, 8931-8938.


18

Page 19 of 21

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


24.

Bruhn, T.; Pescitelli, G.; Jurinovich, S.; Schaumloffel, A.; Witterauf, F.; Ahrens, J.;

Broring, M.; Bringmann, G. Axially chiral BODIPY dyemers: An apparent exception to the exciton chirality rule. Angew. Chem. Int. Ed. 2014, 53, 14592-14595. 25.

Nepomnyashchii, A. B.; Bröring, M.; Ahrens, J.; Bard, A. J. Chemical and

electrochemical dimerization of BODIPY compounds: Electrogenerated chemiluminescent detection of dimer formation. J. Am. Chem. Soc. 2011, 133, 19498-19504. 26.

Loudet, A.; Burgess, K. BODIPY dyes and their derivatives: Syntheses and

spectroscopic properties. Chem. Rev. 2007, 107, 4891-4932. 27.

Ulrich, G.; Ziessel, R.; Harriman, A. The chemistry of fluorescent bodipy dyes:

Versatility unsurpassed. Angew. Chem. Int. Ed. 2008, 47, 1184-1201. 28.

Zinna, F.; Bruhn, T.; Guido, C. A.; Ahrens, J.; Bröring, M.; Di Bari, L.; Pescitelli, G.

Circularly polarized luminescence from axially chiral BODIPY dyemers: An experimental and computational study. Chem. Eur. J. 2016, 22, 16089-10698. 29.

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, Gaussian, Inc.: Wallingford CT, 2013. 30.

Bruhn, T.; Pescitelli, G.; Witterauf, F.; Ahrens, J.; Funk, M.; Wolfram, B.; Schneider, H.;

Radius, U.; Bröring, M. Cryptochirality in 2,2′-coupled BODIPY dyemers. Eur. J. Org. Chem. 2016, 2016, 4236-4243. 31.

Jurinovich, S.; Guido, C. A.; Bruhn, T.; Pescitelli, G.; Mennucci, B. The role of

magnetic-electric coupling in exciton-coupled ecd spectra: The case of bis-phenanthrenes. Chem. Commun. 2015, 51, 10498-10501. 32.

Longhi, G.; Tommasini, M.; Abbate, S.; Polavarapu, P. L. The connection between

robustness angles and dissymmetry factors in vibrational circular dichroism spectra. Chem. Phys. Lett. 2015, 639, 320-325. 33.

Longhi, G.; Tommasini, M.; Abbate, S.; Polavarapu, P. L. Corrigendum to "the

connection between robustness angles and dissymmetry factors in vibrational circular dichroism spectra". Chem. Phys. Lett. 2016, 648, 208. 34.

Nicu, V. P.; Baerends, E. J. Robust normal modes in vibrational circular dichroism

spectra. Phys. Chem. Chem. Phys. 2009, 11, 6107-6118.


19


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

35.

Page 20 of 21

Measey, T. J.; Schweitzer-Stenner, R. Vibrational circular dichroism as a probe of

fibrillogenesis: The origin of the anomalous intensity enhancement of amyloid-like fibrils. J. Am. Chem. Soc. 2011, 133, 1066-1076. 36.

Gorbunov, R. D.; Kosov, D. S.; Stock, G. Ab initio-based exciton model of amide i

vibrations in peptides: Definition, conformational dependence, and transferability. J. Chem. Phys. 2005, 122, 224904. 37.

Hanson-Heine, M. W. D.; Husseini, F. S.; Hirst, J. D.; Besley, N. A. Simulation of two-

dimensional infrared spectroscopy of peptides using localized normal modes. J. Chem. Theory Comput. 2016, 12, 1905-1918. 38.

Hongen, T.; Taniguchi, T.; Nomura, S.; Kadokawa, J.; Monde, K. In depth study on

solution-state structure of poly(lactic acid) by vibrational circular dichroism. Macromolecules 2014, 47, 5313-5319.


20

Page 21 of 21

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Vibrational Optical Activity of BODIPY Dimers: The Role of Magnetic

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