Theoretical studies on donor–acceptor based macrocycles for organic solar cell applications

We have designed a series of new conjugated donor–acceptor-based macrocyclic molecules using state-of-the-art computational methods. An alternating array of donors and acceptor moieties in these macrocycle molecules are considered to tune the electronic and optical properties. The geometrical, electronic, and optical properties of newly designed macrocyclic molecules are fully explored using various DFT methods. Five conjugated macrocycles of different sizes are designed considering various donor and acceptor units. The selected donor and acceptors, viz., thiophene (PT), benzodithiophene (BDT), dithienobenzodithiophene (DTBDT), diketopyrrolopyrrole (DPP), and benzothiazole (BT), are frequently found in high performing conjugated polymer for different organic electronic applications. To fully assess the potential of these designed macrocyclic derivatives, analyses of frontier molecular orbital energies, excited state energies, energy difference between singlet–triplet states, exciton binding energies, rate constants related to charge transfer at the donor–acceptor interfaces, and electron mobilities have been carried out. We found significant structural and electronic properties changes between cyclic compounds and their linear counterparts. Overall, the cyclic conjugated D–A macrocycles’ promising electronic and optical properties suggest that these molecules can be used to replace linear polymer molecules with cyclic conjugated oligomers.

shape, (ii) conjugated π-electronic delocalization, and (iii) low-energy unoccupied molecular orbital (LUMO), rendering these macrocycles as pseudo fullerenes 6 . The experimental studies of cyclo-phenylene-thienylenes (CPT) showed that the LUMO energy decreases with the increase of ring size. However, there was no substantial change in the HOMO energy 4 . At the same time, red-shift in absorption maxima and considerable blue shift in fluorescence maxima in CPT have been noticed. Similarly, Zhang et al. reported triphenylamine and benzothiadiazole-based donor-acceptor conjugated macrocycle 2 . Further, these authors have fabricated solar cells using C 60 derivatives as acceptor units. Both scanning tunneling microscopy (STM) and density functional theory (DFT) based calculations have been employed to understand the morphology and electronic structure. A host-guest architecture of fullerene acceptors encapsulated inside cycloparaphenylene (CPP) and its derivatives have also been reported. It is found that the solid-state packing directly impacts morphology and charge transfer. The predicted PCE using microscopic charge transport parameters and a time-domain drift-diffusion model is found to be 9% 24 .
In view of the significance of macrocyclic π-conjugated materials, we have designed and developed macrocyclic compounds employing electronic structure theory. Since thiophene-based molecules have received widespread attention from researchers in the development of materials for organic electronic materials, polythiophenes-based macrocyclic π-conjugated compounds have been considered. Furthermore, the thiophene unit has been systematically replaced with different donor and acceptor units to develop various new conjugated donor-acceptor macrocycles. Density functional theory methods are used to evaluate the electronic and optical properties, viz., energy levels, absorption spectra, and charge transport properties. Appropriate combinations of donor and acceptor units have been optimized by considering geometrical and electronic factors. In this context, we have taken into consideration of various critical parameters such as variation of molecule size, shape, length, orientation, and self-assembling nature, which in turn influence the nature of π-conjugation. In addition, corresponding linear counterparts have been studied to compare changes in the electronic and optical properties upon cyclization. Attempts have been made to compare experimental findings wherever possible. Overall, the findings from this study would pave the way for the development of a novel class of compounds for organic solar cell applications. The schematic representation of models considered in this study is shown in Fig. 1. As described earlier, in order to understand the impact of the size of the macrocycle on the electronic and optical properties, three different ring sizes are considered. Cyclic and linear oligothiophenes with 8, 10, and 12 repetitive thiophene units (C[PT] n and L[PT] n , where n = 8, 10, and 12, respectively) were considered 25

Results and discussion
Geometry analysis. Optimized 3  Strain energy. The energy associated with deforming a linear conjugated molecule when it is included in a conjugated macrocycle is defined as the macrocyclic strain energy (SE). SE in cyclic organic molecules arises due to the deviation in the structural parameters from their ideal angle to achieve maximum stability in a specific conformation. The SE arises due to the distortions of bond lengths and torsion angles from the typical values 32 . The energy associated with the formation of macrocyclic molecules from linear molecules is referred to as the macrocyclic strain energy 23,33 . The calculated strain energies for all the macrocyclic compounds using B3LYP-D/6-31G** are presented in Table 1. The calculated SE values of conjugated macrocycles are in the same range as the SE of previously reported macrocycles 16,[32][33][34][35] .
In cases of small and medium rings (C[PT] 8  Radial π-conjugation. We have evaluated the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies of C[TT-DPP] 4 and L[TT-DPP] 4 using three different functionals, viz., B3LYP, CAM-B3LYP, and mPW1PW91 functionals using the optimized geometries. The calculated results are compared with the previously reported experimental values (Table S1). We found that the mPW1PW91 functional can predict the HOMO and LUMO values comparable with the experimental values. www.nature.com/scientificreports/ Thus, we have considered the mPW1PW91 functional to evaluate the frontier energy values for both linear and cyclic molecules. HOMO, LUMO, and the difference between HOMO and LUMO energies (E g ) are the important factors that influence the optoelectronic properties and charge carrier transport properties of π-conjugated materials 20,36,37 . The pictorial representation of HOMO and LUMO wavefunctions obtained at the mPW1PW91/6-31G** level of theory for cyclic (C[PT] 12 4 ) molecules are depicted in Fig. 3. One can identify the difference in the π-electron distribution in cyclic and linear molecules. The radial π-conjugation can be observed in the cases of conjugated macrocycles, whereas the linear molecules show perpendicular π-conjugation. Also, except in the cases of C[DTBDT-DPP] 4 and C[DTBDT-BT] 4 , in all other cyclic molecules, HOMO and LUMO wavefunctions are delocalized entire ring. Such delocalization indicates the formation of infinite radial π-conjugation. The HOMO delocalized on the entire ring, whereas the LUMO predominantly localized on acceptor units of C[DTBDT-DPP] 4 and C[DTBDT-BT] 4 (Fig. 3). Overall, replacing thiophene units with the electron-rich and electron-poor units in the conjugated macrocycles leads to fascinating electronic properties. In the cases of linear molecules, HOMO and LUMO wavefunctions are localized on a few repeating units. This suggests that the conjugated macrocycles systems can offer unique electronic and optical properties due to infinite π-conjugation and shape-persistent cycle structure compared to the conventional linear π-conjugated oligomers.
The calculated energies of HOMO-LUMO gaps and the energy difference between LUMO and LUMO + 1 for the larger systems are depicted in Fig. 4. The same energy values for all molecules considered in this study are reported in Table S2. Out of five systems considered in this study, we observed different electronic properties in the cases of PT and TT-DPP systems. We noted that HOMO energy levels are stabilized, and LUMO energy levels are destabilized when linear L[PT] 12  Similarly, significant shrinkage in the HOMO-LUMO gaps is observed in the cases of C[PT] n , C[TT-DPP] n systems when the size of the ring is increased. However, marginal or no changes in the HOMO-LUMO gaps are noted in the other systems. This reveals the intriguing property of radial π-conjugation. As both PT and TT-DPP-based conjugated rings exhibit more radial π-conjugation character, the electronic properties of these molecules are different from other cases. Also, as expected, variation in the HOMO, LUMO, and HOMO-LUMO gaps values are observed depending on the electron-donating and the electron-accepting nature of donor and acceptor units. Overall, the choice of donor and acceptor units impacts the radial π-conjugation character along with the energy level alteration. Also, a good correlation between the energy gap between LUMO and LUMO + 1 (ΔE (LUMO+1)-LUMO ) of non-fullerene acceptors and power conversion efficiency (PCEs) is shown 37,38 . From Table S2, it is observed that in both linear and cyclic molecules designed, larger size compounds have the lower ΔE (LUMO+1)-LUMO when compared to smaller size compounds. Moreover, the ΔE (LUMO+1)-LUMO gap of larger cyclic compounds has similar values as linear compounds. Reorganization energies. As described in the previous sections, the conjugated macrocycles offer unique electronic properties compared to linear counterparts due to the orientation of π-orbitals. Recent studies highlighted that the radially π-conjugated materials based on conjugated macrocycles could offer a much larger conductance modulation range than linear oligomers 39 . Thus, it is important to explore the charge transport properties of conjugated macrocycles. The internal reorganization energy (λ) is one of the key determinants of charge transport in organic materials 37,[40][41][42] . The charge mobility exhibits an inverse relationship with reorganization energies, i.e., the lesser the λ value faster the charge mobility 20 . The calculated electron (λ − ) and hole (λ + ) reorganization energies for all the cyclic and linear compounds are listed in Table 2. The calculated hole and electron reorganization energy values for cyclic rings range from 0.09 to 0.26 eV and from 0.06 to 0.32 eV, respectively. The same values in linear oligomers range from 0.09 to 0.20 eV and from 0.06 to 0.19 eV, respectively. Slightly higher reorganization energies are observed in the cyclic structures than in the linear oligomers.
In the case of cyclic polythiophenes, λ + values are less than λ − values. This indicates that the energy required for hole transfer is lower than the electron transfer process. It is observed that λ − and λ + values for cyclic compounds are in good correlation with the size of the ring. Smaller λ + and λ − values are observed in the larger rings and longer oligomers ( Table 2) Open-circuit voltage. The open-circuit voltage (Voc) is an important factor in considering the device performance of any photovoltaic material and its operating mechanism. Voc can be explained as the entire quantity of current provided by the photovoltaic device without any external load for electricity generation 43,44 . The Voc is strongly related to fill factor and power conversion efficiency 45  (1)  The lower excitation transitions are forbidden for conjugated macrocyclic compounds, unlike linear oligomers. Thus, we have evaluated the lowest five excited states using the TD-DFT method (Table S4). From these Table 2. Calculated energies (in eV) of hole (λ + ) and electron (λ -) reorganization of cyclic and linear compounds (eV) calculated at B3LYP-D/6-31G** level of theory.  4 . We have calculated the NTOs for these excitations to understand the nature of the excited state (Fig. S9). From Fig. S9, the NTO analysis on the S 2 state of C[PT] 12 and C[DTBDT-DPP] 4 ; and the S 4 state in C[TT-DPP] 4 and C[BDT-DPP] 4 indicate that the hole and electron wavefunctions are localized throughout the Table 3. Calculated excited state energies (in eV) and oscillator strengths (au) of cyclic and linear molecules determined at mPW1PW91/6-31G** level of theory.  Exciton binding energy and singlet-triplet gap. The singlet-triplet energy gap (ΔE ST ), which is the energy difference between the lowest non-charge transfer singlet (S 1 ) and triplet (T 1 ) excited states, is an important parameter for OSC material. The exciton dissociation process occurs through singlet-CT states. Nongeminate or bimolecular recombination may occur during charge migration; this results in the creation of CT excitons, which can be of singlet or triplet character. Through back electron transfer triplet-CT, the state relaxes to the T 1 state, and recombination occurs. Due to the large difference between CT state energy and T 1 energy, the speed of T 1 to thermalize back into triplet-CT will be limited if the CT driving force is small (as required to maximize open-circuit voltage, V OC ). In order to reduce both voltage loss and nongeminate recombination, the ΔE ST needs to be minimized 51,52 . The calculated ΔE ST values for larger macrocyclic and linear compounds are included in Table 4. Indeed, from Table 4  www.nature.com/scientificreports/ Further, the exciton separation procedure leads to additional energy losses because of the high exciton binding energy E b . Large exciton binding energy must be overcome to dissociate exciton to charges successfully 44,46,53 . To overcome this, one of the key parameters is E b , which is directly related to the charge separation in OSCs. It can be calculated theoretically using following expression 44,52,54 . www.nature.com/scientificreports/ Where IP and EA are the ionization potential and electron affinity, respectively; and E opt is the optical band gap.
The E b of larger macrocyclic and linear compounds were calculated and given in Table 4. The table showed that macrocyclic compounds showed little more E b values of difference ~ 0.14 to 0. Electronic coupling. The charge transfer properties of organic molecules are primarily determined by lower reorganization energy and electronic coupling between molecules. The HOMO-HOMO coupling accelerates hole transport, whereas the LUMO-LUMO coupling enhances the electron transport. We evaluated the electronic couplings of dimer configurations of macrocyclic compounds in three packing arrangements. The first packing mode is the interaction of an acceptor unit of one macrocyclic ring with the acceptor unit of another ring (AA). The second packing mode corresponds to the acceptor unit of one ring interacting with the donor unit of another ring (AD). And the third packing mode is the donor unit of one ring with the donor unit of another ring (DD) (Fig. S10). The distance between the rings is fixed at 3.5 Å in all complexes. All transfer integral values are calculated using the B3LYP/6-31G(d,p) level of theory. All the findings of electronic coupling values are tabulated in Table 5. In the case of C[PT] 12 , we found similar HOMO-HOMO and LUMO-LUMO electronic coupling values. Also, we note lower reorganization energies (λ + and λ − ) are observed (Tables 2 and  5). Therefore C[PT] 12 Table 4. Calculated lowest singlet (S 1 ), triplet (T 1 ) excitation energies, Singlet-triplet gap ΔE ST and exciton binding energy E b of larger macrocyclic and linear compounds in eV obtained at mPW1PW91/6-31G** level of theory.   4 can act as electron acceptor materials based on strong LUMO-LUMO couplings and low electron reorganization energies. However, the molecular packing of macrocyclic molecules strongly influences the electronic coupling properties.
The hole/electron mobility. The intermolecular packing configurations of adjacent molecular segments have a considerable impact on the transfer integral. It has been widely reported that face-to-face parallel-stacking has greater orbital overlapping, resulting in a large-scale contribution to charge transfer in organic systems.
To estimate the charge transport rate constants (k h and k e ) and mobilities (μ h and μ e ), we have considered in three packing configurations (Fig. S10) as described above in electronic coupling calculations. Hole and electron transport rate constant calculated using Eq. (6) and hole and electron mobilities calculated using Eq. (7) for different configuration of packings of larger macrocyclic compounds are tabulated in Table 6. From this table one can observe that the mode of packing configuration impacted the hole and electron rate constants and mobilities. Increasing the conjugation length in macrocyclic compounds increases the rate of mobilities of hole and electron. Among the macrocyclic compounds C[DTBDT-BT] 4 showing the highest k e and μ e of 3.68 × 10 13 S −1 and 0.88 cm 2 V −1 S −1 due to highest LUMO-LUMO coupling and lower electron reorganization energy in AA configuration. As well in DA configuration it is showing hole transport rate of 8.42 × 10 12 S −1 and hole mobility 0.2 cm 2 V −1 S −1 . Among the macrocyclic compounds C[BDT-DPP] 4 consists of high hole transport rate 1.03 × 10 13 S −1 and hole mobility 0.25 cm 2 V −1 S −1 .  12 are considered as electron-acceptor and electron-donor materials, respectively. All the complexes were optimized at the B3LYP-D/6-31G(d,p) level of theory. Further, the excited state analysis was carried out on the ground-state optimized geometries. NTO analysis was also performed to understand the nature of excitation transition. One of the drawbacks of OSCs is that exciton lifetimes are typically very short due to the involvement of coulombically bound electron-hole pairs, resulting in short exciton diffusion lengths. Thus, an adequate driving force for charge separation is required for complete electron and hole separation. The spatial distance between the centroid of the hole and electron (Δr h-e ), which is the key factor in charge separation, is obtained by the Multiwfn code 55 . Pictorial representation of charge-transfer states of all complexes and CT state energies and Δr h-e values are shown in Fig. 9. Larger Δr h-e values are observed in the complexes where linear electron- Table 6. Calculated hole and electron charge transport rate constant k h /k e (S −1 ), hole and electron mobility μ h /μ e (cm 2 V −1 S −1 ) using coupling values obtained from three different packing configurations of macrocyclic compounds with charge transport distance r (Å) between two macrocycles, obtained with Eq. (6) and (7).  4 . In the case of linear electron-donor and linear electron-acceptor complexes, due to one-on-one packing, strong Coulomb interactions lead to a smaller Δr h-e of 5.5 Å.

Properties of electron-donor and electron-acceptor blends.
The calculated hole and electron charge transfer rates and rate of charge recombination (using Eq. (9)) of modeled interfaces are given in Table 7, along with free energy changes ΔG CT and ΔG CR . The negative ΔG CT and

Materials and methods
The geometries of neutral and charged macrocyclic molecules and corresponding linear counterparts were optimized using density functional theory (DFT) based B3LYP/6-31G(d) method with dispersion correction. Further, single-point calculations were carried out to calculate optical and electronic properties using various DFT methods such as CAM-B3LYP and mPW1PW91 using the optimized geometries. In order to understand the strain in macrocyclic molecules, strain energies were calculated using B3LYP-D functional with the 6-31G(d,p) basis set. Excited-state analyses were performed using optimized geometries at TD-B3LYP/6-31G(d,p), TD-CAM-B3LYP/6-31G(d,p), and TD-mPW1PW91/6-31G(d,p) level of theory. Natural Transition Orbital (NTO) analysis was carried out to understand the nature of excited states 56 . All calculations were performed using the Gaussian16 package 57 . The charge transport process in nonordered semiconductors can be explained using an incoherent hopping mechanism 40,46,58 . In the hopping mechanism, charge transfer occurs in sequential jumps between adjacent molecules 40,59,60 . Thus, the charge transfer rate can be described using Marcus theory. It is well known from the rate expression that the reorganization energy influences the rate of charge transfer 42,59,[61][62][63] . Therefore, both hole and electron reorganization energies (λ + and λ − ) were calculated by using the following Eqs. (3) and (4) 47 .
Where E 0 , E + , and E − represents energy of neutral, cationic, and anion respectively and M 0 , M + , and M − represents optimized geometries of neutral, cationic, and anion systems respectively.
At ambient temperature, the charge transport in organic solar cells is likely to occur through the thermally activated hopping model. In this model, the charge carriers localize on a single molecule and hop from one molecule to the adjacent molecule. The charge transfer rate constant (k) between equivalent neighbouring molecules can be defined by semiclassical Marcus theory. The charge transfer rate constant can be expressed as follows (the free energy difference (ΔG) for the self-exchange CT reaction process is neglected) 52,65,66 .
Where k is the rate of charge transfer for hole and electron (k h and k e respectively), V electronic coupling of the hole and electron transfer (V h and V e ) computed with the generalized Mulliken-Hush (GMH) method 44,67 . ħ is Planck's constant, k B is the Boltzmann constant, T is room temperature, and λ is the hole and electron reorganization energy (λ h and λ e ) of the charge transfer process calculated using Eqs. (3) and (4).
Further, to gain insights into impact of molecular modifications on the electron mobility (μ) in these newly designed NFAs, the Einstein-Smoluchowski equation is used estimate the drift mobility of hopping μ using given as follows 68,69 . where μ is the mobility of hole and electron (μ h and μ e ), e is the electron charge, k B is the Boltzmann constant, T is room temperature, and D is the diffusion coefficient which can be expressed in terms of the charge transfer rate constant k and r (the distance between two centroids of backbones of two molecules in one dimer) as follows: Charge transfer at the donor-acceptor interface is the process by which an electron/hole of the donor/acceptor injects into the acceptor/donor after local excitation. Charge transfer at the interface in the modeled D/A systems can be roughly interpreted as electron/hole transfer driven by the donor/acceptor local excitation states. The rate of charge transfer (k CT ) and charge recombination (k CR ) in D/A systems can be evaluated by the Marcus theory as follows 65 .
Where k is the rate constant for charge transfer (k CT ) and charge recombination (k CR ), V DA represents the CT integral between the donor and acceptor estimated using the GMH model, λ is the reorganization energy (internal and external), k B is the Boltzmann constant, T is temperature, and ΔG is the free energy change for electron transfer process. The ΔG during the CT process is denoted as ΔG CT , and for the charge recombination process represented as ΔG CR .
The reorganization energy comprises two parts, inner reorganization energy (λ i ) and external reorganization energy (λ s ) [70][71][72] . The λ i originates due to a change in the equilibrium geometry of the donor (D) and acceptor (A) sites of the complex system during charge transfer processes and it includes contribution of hole and electron which is formulated as follows: where E + (D 0 ) and E + (D + ) energies of radical cation donor at neutral geometry and optimal cation geometry. E 0 (A − ) and E 0 (A 0 ) are the energies of the neutral acceptor A at the anionic geometry and optimal ground state geometry, respectively. Calculating λ s quantitatively is difficult as it involves electronic and nuclear polarizations. So, the value of λ s is viewed as a constant equal to 0.3 eV.
The free energy change during charge recombination (ΔG CR ) can be calculated as given below Eq. [71][72][73] The IP(D) and EA(A) can be estimated as HOMO energy of donor and LUMO energy of acceptor, respectively. The free energy change at the CT process, ΔG CT , can be estimated using the Rehm-Weller equation as follows 73 .