Vis Absorption and

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Theoretical Prediction and Analysis of the UV/Vis Absorption and Emission Spectra of Chiral Carbon Nanorings Rathawat Daengngern, Cristopher Camacho, Nawee Kungwan, and Stephan Irle J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b07270 • Publication Date (Web): 30 Aug 2018 Downloaded from http://pubs.acs.org on August 30, 2018

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The Journal of Physical Chemistry

Theoretical Prediction and Analysis of the UV/Vis Absorption and Emission Spectra of Chiral Carbon Nanorings Rathawat Daengngern,†,‡ Cristopher Camacho, ‡,§ Nawee Kungwan,*,¢,¡ Stephan Irle*,‡,¿

†

Department of Chemistry, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand ‡

Institute of Transformative Bio-Molecules (WPI-ITbM) & Department of Chemistry, Graduate School of Science, Nagoya University, Nagoya 464-8601, Japan §

¢

School of Chemistry, University of Costa Rica, San José, 11501-2060, Costa Rica

Department of Chemistry, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand ¡

Center of Excellence in Materials Science and Technology, Chiang Mai University, Chiang Mai 50200, Thailand

¿

Computational Sciences and Engineering Division & Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.A.

Corresponding authors: [email protected] (N. K.) Tel: +66-53-943341 ext. 101. Fax: +66-53-892277 [email protected] (S.I.) Tel: +1-865-574-7192. Fax: +1-865-576-4368

ACS Paragon Plus Environment

The Journal of Physical Chemistry 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 UV/Vis absorption and emission spectra of recently synthesized chiral carbon nanorings were simulated using first principles-based molecular dynamics and time-dependent density functional theory (TD-DFT). The chiral carbon nanorings are derivatives of the [n]cycloparaphenylene ([n]CPP) macrocycles, containing an acene unit such as naphthalene, ([n]CPPN), anthracene ([n]CPPA), and tetracene ([n]CPPT), in addition to n paraphenylene units. In order to study the effect of increasing molecular size on absorption and emission spectra, we investigated the cases where n = 6 and 8. Frontier molecular orbital analysis was carried out to give insight into the degree of excitation delocalization and its relationship to the predicted absorption spectra. The lowest excited singlet state S1 corresponds to a HOMOLUMO π-π* transition, which is allowed in all chiral carbon nanorings due to lack of molecular symmetry, in contrast to the forbidden HOMO-LUMO transition in the symmetric [n]CPP molecules. The S1 absorption peak exhibits a blue-shift with increasing number of paraphenylene units in particular for [n]CPPN and [n]CPPA and less so in the case of [n]CPPT. In the case of CPPN and CPPA, the transition density mainly localizes over a semicircle of the macrocycle with the acene unit in its center, but strongly localizes on the tetracene unit in the case of CPPT. Molecular dynamics simulations performed on the excited state potential energy surfaces reveal red-shifted emission of these chiral carbon nanorings when the size of the πconjugated acene units is increased, although the characteristic [n]CPP blue-shift with increasing paraphenylene unit number n remains apparent. The anomalous emission blue-shift is caused by the excited state bending and torsional motions that stabilize the π HOMO and destabilize the π* LUMO, resulting in an increasing HOMO-LUMO gap.


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1. Introduction The electronic properties of single-walled carbon nanotubes (SWCNTs) are determined by structural parameters such as tube diameter and chirality (armchair, chiral, or zigzag), and to this day the precise control of these parameters during synthesis remains a great challenge. To this end, in recent years, considerable effort has been devoted to create molecular nanotube fragments as nucleation “seeds”,1-3 often carbon nanorings (sometimes termed “hoops”), that may be used as templates for the controlled growth of specific SWCNTs.1, 4-5 Therefore, over the past decade, a tremendous amount of effort has been put forward to the synthesis of various nanorings.2,

6-12

Among these macrocyclic molecules, [n]cycloparaphenylenes ([n]CPP),

consisting solely of n para-linked phenylene units as depicted in Scheme 1, are attracting great attention from researchers around the world.7-9, 11-18 Since the chemical synthesis of [n]CPPs has become possible, several derivatives19-23 and related carbon nanorings8, 10, 15, 24-30 and nanobelts31 have also been synthesized, often revealing unexpected trends in electronic properties. Experimental and theoretical investigations7-8,

18, 32-43

on the electronic properties of [n]CPPs

have been carried out, particularly focusing on their anomalous optical spectra which do not obey regular quantum confinement trends but instead show a marked blue-shift in emission with increasing molecular size. Electronic structure calculations were first to suggest that the origin of the blue-shifted fluorescence is related to the larger vibrational amplitudes in smaller [n]CPPs, causing a greater Stokes shift, whereas more rigid of larger [n]CPPs exhibit a smaller Stokes shift.39 Static and dynamic electronic structure calculations suggested that the double peak observed in fluorescence spectra19, 39 of the larger [n]CPPs is likely originated from the doublydegenerate bright B1E excited state, exhibiting a first-order Jahn-Teller effect involving two degenerate states into two bright S2 and S3 states, as well as invisible two dark corresponding states.43 Moreover, the vibronic coupling of the formally dark S1 state with higher electronic



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states S2 and S3 was revealed to be responsible for the surprisingly strong emission from the S1 state, in particular from smaller-sized nanorings.40, 43

Scheme 1. Shortest sidewall segments of achiral and chiral carbon nanorings.

Chirality can be induced in derivatives of CPPs by inserting different acene units, denoted as X, into the [n]CPP structure, as shown in Scheme 1 and extensively discussed in ref.

10

. For

example, when inserting naphthalene, anthrylene-2,6-diyl, and tetracenylene-2,8-diyl units with 2,6-linkages,

the

resulting

cyclo[n]paraphenylene-2,6-naphthylene

([n]CPPN),

cyclo[n]paraphenylene-2,6-anthrylene ([n]CPPA), and cyclo[n]paraphenylene-2,6-tetracenylene ([n]CPPT) are created, respectively.41,44 However, until now, only [13]CPPN as the shortest segment of a (15,14) SWCNT has been synthesized by the Itami group.10 Experimental photophysical properties of [n]CPPN, [n]CPPA, and [n]CPPT have not been reported before, and only theoretical predictions of UV/Vis selected absorption spectra41 and the photoexcitation


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dynamics for compounds with n = 10 were reported44 in the literature. It was described that the acene units break molecular symmetry and that the S0-S1 transition, which is symmetryforbidden in [n]CPPs, becomes allowed in CPPX derivatives, and should play a major role in both UV/Vis absorption and emission spectra.41,44 In this study, we aim to simulate UV/Vis absorption and emission spectra with focus on the size effect of a) the size of the acene unit, and b) the number of paraphenylene units n in the macrocycles. To this end, we performed both static quantum chemical calculations and quantum chemical molecular dynamics simulations on the excited state potential surfaces, as employed before when investigating the origin of the sizedependent fluorescence blueshift in [n]CPP.39 As molecular model systems, we usually chose [n]CPPN, [n]CPPA, and [n]CPPT with n = 6 and 8 as prototypical examples.

2. Computational Details For the static density functional theory (DFT) calculations, i.e. geometry optimizations and excitation energy and transition dipole moment calculations, we selected the Coulombattenuated CAM-B3LYP exchange-correlation functional45 in conjunction with the double-ζquality polarized def-SV(P) basis set developed by Ahlrichs et al.46 This selection of functional and basis set is consistent with our previous study and based on an extensive set of calculations.39 The static calculations were carried out using the GAUSSIAN 09 quantum chemical package.47

Ground and excited state geometries were optimized using tight

convergence criteria (10-6 Ha/a0). For the simulation of the absorption spectra, the ground state molecular structures were optimized on a pruned (99,590) numerical density grid. At the optimized ground-state geometries, we performed linear response time-dependent DFT (TDDFT) calculations to obtain the lowest eight singlet vertical excitation energies and oscillator strengths. The simulated spectra are plotted using Gabedit‒a graphical software.48



For the direct dynamic calculations, molecular dynamics (MD) simulations on the ground state potential energy surfaces were carried out with the self-consistent-charge density-functional tight-binding (SCC-DFTB, further denoted DFTB for brevity) method. Time-dependent DFTB (TD-DFTB)49 was employed for the direct excited state MD simulations. Both ground and excited state trajectories were started at geometries re-optimized from the aforementioned CAMB3LYP/def-SV(P) geometries by DFTB and TD-DFTB for ground and excited states, respectively. The details of the DFTB-based quantum chemical molecular dynamics (MD) procedure was introduced in our previous investigation.39 Since we follow the previous methodology closely in this study, only a brief description is presented here. Equations of motion for every time step were integrated by means of the Verlet algorithm with a time step of 0.29 fs with a nuclear temperature of 298 K (room temperature). The ground state of all carbon nanorings was separately simulated using respective gradients during the MD simulations under isothermal conditions in the NVT canonical ensemble for 580 fs with a velocity scaling thermostat with a scaling probability of 10%. Ten independent trajectories, starting from Cartesian coordinates and velocities obtained from this initial MD simulation at time intervals of 300-500 fs, were further run in the microcannonical (NVE) ensemble with a total length of simulation time up to 2.90 ps. Twenty-four geometries for each state (S0 for UV-Vis absorption spectra and S1, S2 and S3 for fluorescence spectra) were then randomly selected to compute the single-point excitation energies and oscillator strengths for the eight lowest excited singlet states, using TD-CAM-B3LYP/def-SV(P).


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3. Results and Discussion 3.1 HOMO and LUMO Frontier Molecular Orbitals The [n]CPPN, [n]CPPA, and [n]CPPT frontier molecular orbitals (MOs) for odd numbers of n = 5, 7, 9, 11, and 13, along with their energy levels, obtained at the optimized ground state minimum geometries, are shown in Figure 1. Plotted in Figure 1a-1c are the energy levels of six frontier MOs of [n]CPPN, [n]CPPA, and [n]CPPT, from HOMO-2 to LUMO+2, and the pictorial representations of four orbital shapes (HOMO-1 through LUMO+1 of compounds with n = 8 from bottom to top). In contrast to the symmetric CPP, the shape of the HOMO and LUMO in all carbon nanorings are no longer completely delocalized around the entire ring; rather, in most cases, their densities are localized within a semicircle, around the location of the acene units (naphthalene, anthracene, and tetracene). This localization of transition densities on the semicircle was reported before in ref. 40 and is particularly pronounced in the case of CPPT, where the frontier orbitals are almost entirely dominated by those of the tetracenylene unit. The orbital delocalization over the phenylene backbone units is largest in CPPN, while CPPA represents an intermediate situation. For CPPN, as shown in Figure 1a, the HOMO-LUMO gap, ∆EHL = εLUMO − εHOMO increases with increasing [n], similarly to the situation in [n]CPPs. As discussed earlier,8-9, 13-15, 30 dependence of the frontier orbitals on the number of p-phenylene units is opposite to that of linear π−conjugated systems; normally, larger oligomers exhibit smaller HOMO-LUMO gaps than smaller ones. In case of CPPN, we note that the energy gaps between HOMO-1 and LUMO+1 MOs also increase slightly with increasing n, different from the situation in CPPs39 where these MOs follow the normally anticipated behavior. For CPPA, as seen in Figure 1b, ∆EHL values also increases with increasing n, similar as in CPPN and CPP, while the gaps between energy levels of lower HOMOs and higher LUMOs decrease with increasing n. For CPPT, the ∆EHL values do not significantly change as the number of phenyl rings increases,



which is quite different from those of CPP, CPPN, and CPPA macrocycles. Moreover, the gaps between HOMO and HOMO-1, and LUMO and LUMO+1 are larger as a function of [n] size, similar to those of CPPN however other HOMOs and LUMO follow the expected trends, similar to the case of linear p-phenylenes.


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Figure 1. Frontier molecular orbital energies of different (a) [n]CPPNs, (b) [n]CPPAs, and (c) [n]CPPTs, computed at the TD-CAM-B3LYP/def-SV(P) level.



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3.2 Simulation of Absorption Spectra After randomly selecting 24 geometries from DFTB/MD trajectories of [n]CPPN, [n]CPPA, and [n]CPPT systems with n = 6 and 8 on the S0 ground state potential energy surface, we performed vertical excitation energy and oscillator strength calculations using TD-CAMB3LYP/def-SV(P), and simulated spectra of these carbon nanorings using a Gaussian convolution, illustrated in Figure 2.

The simulation of the optical spectra in the gas phase is a

reasonable approach since typical solvents are non-polar or only slightly polar and should not affect the optical properties of the macrocycles. Indeed, as expected from the lack of symmetry as opposed to the CPP systems, for all chiral nanorings, the lowest-energy S1←S0 excitation is observed. These minor absorption peaks of each carbon nanorings occur around 350 nm for CPPN, 375 nm for CPPA, and 450 nm for CPPT, and analysis of the TD-CAM-B3LYP wavefunction indicates that nature of these excitations corresponds to HOMO→LUMO transitions. Bright excitations occur at wavelengths around 300 nm in all investigated systems. These

major

peaks

originate

from

the

combination

of

HOMO-1→LUMO

and

HOMO→LUMO+1 for CPPN, HOMO-3→LUMO and HOMO-1→LUMO+1 for CPPA, and mostly HOMO→LUMO+1 for CPPT. The major and minor peaks of all chiral carbon nanorings are π−π* transitions. In line with the trends for ∆EHL for CPPN and CPPA compounds, and the static energy differences as shown in Figure 3, we observe that, when n increases, the corresponding minor peak associated with the S1←S0 excitation is blueshifted. We predict that for CPPT, in line with their ∆EHL trends, the minor absorption peaks do not show a dependence on the number of p-phenylene units n, the reason being the stronger localization of frontier orbitals on the tetracenylene unit.


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Figure 2. Absorption spectra of [n]CPPN, [n]CPPA, and [n]CPPT where n are 6 and 8 computed at the TD-CAM-B3LYP/def-SV(P).



Figure 3. Static energy state diagrams underlying vertical excitation from optimized FranckCondon geometry (left) and emission from S1-optimized geometry (right) of [n]CPPN, [n]CPPA, and [n]CPPT with n = 6 and 8, computed at the TD-CAM-B3LYP/def-SV(P) level of theory.

3.3 Emission Simulation We performed MD simulations in the excited states in analogy to the simulation of absorption spectra. The simulated emission spectra of all chiral carbon nanorings are depicted in Figure 4 with transitions from different states (emission from S1 (green), S2 (blue), and S3 (red)). Although the transitions from S2 and S3 states have higher intensity compared to that of the S1 state, their emission peaks appearing at shorter wavelengths seem to be impossible since the normal emission peaks of S2 and S3 states of [n]CPP are around 400 to 500 nm.1, 8 Therefore, the lowest bright state attributing to the emission spectra for these systems should be only from S1. The discussions of emission spectra from now on will be focused on the S1 state.


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Figure 4. Fluorescence (from S1 (black), S2 (blue), and S3 (red)) spectra of [n]CPPN, [n]CPPA, and [n]CPPT where n = 6 and 8 calculated at the TD-CAM-B3LYP/def-SV(P) ← TDDFTB/MD.

3.3.1 S1→S0 Emission Spectra from Excited-State Dynamics Emission maxima of the simulated spectra from S1→S0 states of [n]CPPN and [n]CPPT are found to be slightly blueshift from 475 nm to 470 nm (for [n]CPPN) and from 550 nm to 538 nm (for [n]CPPT), as the number of p-phenylene rings increases (see Figure 5). However, a larger blueshift is observed for the emission from [n]CPPA. The origin of these nanohoops may be explained by their HOMO-LUMO energy levels between phenylene and different acene units as introduced by Wong et al.41 In addition, these nanorings are expected to have redshift emission and higher oscillator strengths (from S1→S0) with larger acene unit. The HOMOs and LUMOs of the acenes increase and decrease, respectively with the number of p-phenylene rings (Figure 1). This finding was also reported in molecular orbital energies for [n]CPP reported by Segawa et al.20, 35 and they have proposed three factors to describe the behavior changes in



molecular orbital energies. Therefore, three factors affecting the behavior of HOMO and LUMO of these three nanorings such as length effect, bending effect, and torsion effect are discussed in the following sections.

Figure 5. S1→S0 emission spectra from 24 sampling geometries.


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3.3.2 Excited State Molecular Structure From static calculations performed at CAM-B3LYP/def-SV(P), our ground-state optimized geometries of all nanorings in terms of average C-C bond lengths and torsion angles (see Table S1 of the supplementary information) are in agreement with the calculations at the more standard B3LYP/6-31G(d) level of theory by Omachi et al.10 and by Wong et al.41 To provide insight into structural information of nanorings with the computationally more economical DFTB method, we compare two parameters (bond lengths and torsion angles) of all carbon nanorings. The average C‒C bond lengths performed at DFTB and CAMB3LYP/def-SV(P) levels of S0 optimized structures is slightly different in which average bond lengths at DFTB are shorter than those computed at CAM-B3LYP/def-SV(P) by about 0.01-0.02 Å. The average absolute torsions computed in DFTB is smaller than those computed at CAMB3LYP by about 12° for smaller ring size and by about 10° for the larger ring. For S1 and S2 optimized structures performed at TD-DFTB, the average bond lengths are also shorter than those computed at TD-CAM-B3LYP about 0.01-0.02 Å.

The average absolute torsions

computed at the TD-DFTB level for CPPNs and CPPAs are lower than TD-CAM-B3LYP in the range of 13-17° and 14-18° for S1 and S2, respectively, but slightly different within 2-3° for CPPTs.

For S3 optimized structures of all nanorings, the average bond length deviations

between these two methods are roughly 0.01 Å. The average absolute torsions from two methods are slightly different in the range of 8-11° for CPPNs and CPPAs, and 6-7° for CPPTs. These small differences of C-C bond lengths and torsion angles between two methods indicate that structures computed at TD-DFTB are more slightly rigid than those computed at TD-CAMB3LYP. The geometrical differences are in line with the minimum basis set employed in the DFTB method, and are small enough to justify the use of DFTB and TD-DFTB to perform MD simulations and further snapshot sampling at the TD-CAM-B3LYP/def-SV(P) level of theory for predicting emission spectra.



In order to determine the behaviors of the occupied MO and unoccupied MO, the geometrical change (torsion, bending, and length) during the excited state simulations were analyzed: (i) the average bond length (R) between phenylene and a unit of naphthalene, anthracene, or tetracene, (ii) the average bending angle (α) of the acene units (planarity of acene) and (iii) the average absolute torsion angle (ϕ) between all rings in the nanorings for 24 geometries from snapshot sampling as defined and summarized in TABLE 1. For the ground state, average distances (length effect) are about 1.47-1.48 Å for all chiral nanorings. Average bending angles are less bent and average torsion angles (torsion effect) are more twisted when the number of benzene rings increases. For S1 excited state, average bond lengths are slightly shorter than those in the ground state by about 0.01-0.02 Å. The influence of length effect is suggested to be very small to HOMO and LUMO. Overall, average bending angles become less bent compared to their ground state. As the ring size increases, the bending angle becomes smaller, while the energy gap between HOMO and LUMO becomes larger. By increasing the size of acene unit, the bending angle, however, are found to be larger (see values of S1) which causes the energy gap between HOMO and LUMO to be smaller (see Figure 1). Moreover, average torsion angles of S1 are smaller and less twisted compared to their ground state structures and these values are larger as the ring size increases, resulting in stabilizing HOMO but destabilizing LUMO energy. With larger acene unit, the energy gap between HOMO and LUMO (Figure 1) decreases which follows the expected quantum confinement trends.


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TABLE 1. Average bond lengths (Rv), bending angles (αv) and dihedral angles (ϕv ) of [n]CPPN, [n]CPPA, and [n]CPPT (where n = 6 and 8) from 24 snapshot geometries.

S0

S1

Rv (Å) αv (°)

ϕv (°)

Rv (Å)

αv (°)

ϕv (°)

[6]CPPN

1.479

25.8

14.9

1.464

24.1

13.3

[8]CPPN

1.473

18.6

21.9

1.461

18.3

15.7

[6]CPPA

1.481

32.2

17.5

1.462

31.9

12.6

[8]CPPA

1.475

25.1

22.3

1.463

24.1

15.9

[6]CPPT

1.479

39.3

21.1

1.479

38.7

16.4

[8]CPPT

1.483

33.6

24.4

1.474

32.7

21.3



The structural deformation upon excitation to the singlet-excited state (S1) should be noted that torsion angles are larger and bending angles are smaller with greater n from 6 to 8. This structural deformation was also found in larger CPPs as they retain more of their aromatic character than smaller CPPs.35 Figure 6 shows the relative energy and transition energies of S0 and S1 as a function of average absolute values of the torsion angles (ϕ) for the 24 snapshot geometries. The distributed points represent range of structural change along horizontal axis. Torsion angle of all nanorings for S1 geometries are found to be more twisted with the number of benzene rings, indicating that smaller nanorings are more rigid than the larger ones. The bending effect of different acene units tends to be smaller because of rigidity of their units. From torsion and bending effects, therefore, the CPPNs and CPPAs and CPPTs are less deformed compared to their larger rings.


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Figure 6. Relative energy with respect to S1 optimized energy (left panel) and transition energy (right panel) as a function of the dihedral angle for 24-sampling geometries of [n]CPPN, [n]CPPA, and [n]CPPT with n = 6 and 8.



According to the analyses of three factors, the length effect insignificantly influences the behavior of HOMO and LUMO energies. While bending and torsion factors affect greatly to HOMO and LUMO energies. When increasing ring size (i.e., n = 6 to 8), bending angles are less bent and torsion angles are more twisted corresponding to increasing HOMO-LUMO gaps, resulting in the blueshift emission. In addition to increase acene unit, bending angles are more bent and torsion angles are slightly twisted (values of [n]CPPN and [n]CPPA are not significantly different) which result in redshifted emission. With increasing ring size and acene unit of carbon nanorings, the main contributor for the HOMO and LUMO energies is bending angles. While, torsion can be used as a good indicator as a main contributor of LUMO that can be influenced only by increasing the ring size of carbon nanorings but it is not a good indicator for describing the behavior LUMO energy when increasing acene unit of these systems. Thus, bending and torsion effects play a crucial role in stabilization of a π orbital (HOMO) and destabilization of a π* orbital (LUMO) resulting in HOMO-LUMO gap increase as increasing ring size but this energy gap decrease as enlarge the unit of naphthalene, anthracene, or tetracene (Scheme 1).


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4. Conclusions In summary, we simulated absorption and fluorescence spectra using the TD-CAMB3LYP/def-SV(P) sampling from TD-DFTB/MD simulations for [n]CPPN, [n]CPPA, and [n]CPPT, where n = 6 and 8. Comparison of the structural information between DFTB (TDDFTB) and CAM-B3LYP (TD-CAM-B3LYP) methods were performed and small deviations were observed between these two methods, therefore we have strong confidence in the accuracy of the snapshot sampling TD-CAM-B3LYP/def-SV(P) ← TD-DFTB/MD method for predicting both UV/Vis absorption and emission spectra for the first time. Static calculations of different chiral nanorings show that transition densities fully localize on the semicircle part near the acene units, particularly in the case of CPPT, where the frontier orbitals entirely localize on the tetracene unit. From the calculated results of simulated emission spectra, chiral nanorings with broken symmetry allow the lowest excited-state transition from S1→S0 to be observed. Moreover, the predicted the emission spectra of carbon narorings showed redshifted emission when increasing the pi-conjugation of the acene unit, yet a blueshift when increasing the ring size n. These blueshifted emission spectra are mainly attributed from the bending (reducing HOMO energy) and torsion effect (increasing LUMO energy) upon the excitation, consequently giving a larger HOMO-LUMO gap, similar as in the case of the [n]CPP parent compounds.



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Acknowledgements This work was supported by the Graduate School of Science, Nagoya University, Nagoya, Japan. S. I. acknowledges partial support from a CREST grant by JST and partial support from the Laboratory Directed Research and Development (LDRD) Program of Oak Ridge National Laboratory. ORNL is managed by UT-Battelle, LLC, for DOE under Contract DE-AC05-00OR22725. N. K. thanks Thailand Research Fund (RSA6180044) for financial support. R. D. thanks the Science Achievement Scholarship of Thailand (SAST), Faculty of Science, Chiang Mai University. C. C. acknowledges support from the OAICE and from the Vice-Rectory for Research (grant 115-B4-605) of the University of Costa Rica.

Notes and References Notice: This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally

sponsored

research

in

accordance

with

the

DOE

Public

Access

Plan

(http://energy.gov/downloads/doe-public-access-plan).

1.

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131x94mm (300 x 300 DPI)


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Vis Absorption and

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