Physicochemical, antioxidant properties of carotenoids and its optoelectronic and interaction studies with chlorophyll pigments

The physicochemical and antioxidant properties of seven carotenoids: antheraxanthin, β-carotene, neoxanthin, peridinin, violaxanthin, xanthrophyll and zeaxanthin were studied by theoretical means. Then the Optoelectronic properties and interaction of chlorophyll-carotenoid complexes are analysed by TDDFT and IGMPLOT. Global reactivity descriptors for carotenoids and chlorophyll (Chla, Chlb) are calculated via conceptual density functional theory (CDFT). The higher HOMO–LUMO (HL) gap indicated structural stability of carotenoid, chlorophyll and chlorophyll-carotenoid complexes. The chemical hardness for carotenoids and Chlorophyll is found to be lower in the solvent medium than in the gas phase. Results showed that carotenoids can be used as good reactive nucleophile due to lower µ and ω. As proton affinities (PAs) are much lower than the bond dissociation enthalpies (BDEs), it is anticipated that direct antioxidant activity in these carotenoids is mainly due to the sequential proton loss electron transfer (SPLET) mechanism with dominant solvent effects. Also lower PAs of carotenoid suggest that antioxidant activity by the SPLET mechanism should be a result of a balance between proclivities to transfer protons. Reaction rate constant with Transition-State Theory (TST) were estimated for carotenoid-Chlorophyll complexes in gas phase. Time dependent Density Functional Theory (TDDFT) showed that all the chlorophyll (Chla, Chlb)–carotenoid complexes show absorption wavelength in the visible region. The lower S1–T1 adiabatic energy gap indicated ISC transition from S1 to T1 state.

www.nature.com/scientificreports/ usually contain ring structures at each end, and most carotenoids contain oxygen atoms, usually as part of hydroxyl or epoxide groups. The absorption maxima is affected by the length of chromophore, the position of the end double bond in the chain or ring and the taking out of conjugation of one double bond in the ring or eliminating it through epoxidation. Carotenoids generally have three-peaked absorption spectrum with well-defined maxima and minima though they show different optical characteristics in various solvents which depend on the polarizability of the solvent 13,14 . The introduction of a carbonyl group in conjugation with the polyene system produces a bathochromic shift and the loss of fine structure 15 , while β-carotene, cryptoxanthin and zeaxanthin all produces identical absorption spectrums as the influence of other substituents group are negligible. The biosynthesis and accumulation of carotenoids in dark-grown etiolated seedling are essential for the assembly of membrane structure and benefits the development of chloroplast when seedlings emerge into the light 16 . For photosynthetic systems, carotenoid is the associated pigment which collects light energy in the spectral region and transfers this energy to chl pigment 17,18 as chl does not absorb this energy. Also in photoprotection, the role of carotenoid is to quench the triplet state of chl before it reacts with oxygen to form singlet oxygen species (ROS) 19,20 . Carotenoid regulates energy transfer in the light-harvesting antenna through xanthophyll cycle, to avoid over-excitation of the photosynthetic system by safely dissipating excess energy 21,22 . So understanding the relationship between structure and photophysical properties of these pigments can provide insights into a better study of how photosynthesis works at the molecular level in chloroplast.

Theoretical methods
First, a conformational analysis was performed by random rotations of the freely rotating bonds in the carotenoid complexes and chlorophylls in the range of 0 • to 360 • , generating 50 random structures for each system in this manner. Then the carotenoids are optimized by three different methods CAM-B3LYP 23 /6-31G**, wB97xD 24 /6-31G** and M062x 25 /6-31G** by G16 software programme 26 in gas phase. As Magnesium is present in Chlorophyll, Chla and Chlb are optimized with CAM-B3LYP/Lanl2dz 27 :6-31G**, wB97xD/Lanl2dz:6-31G** and M062x/Lanl2dz:6-31G** methods with G16 software programme in gas phase. Finally the lowest minima structure by wB97xD/Lanl2dz:6-31G** method was selected to study the physicochemical studies of carotenoid and chlorophyll in gas and solvent (water) medium by integral equation formalism-polarized continuum model (IEF-PCM) 28 according to the SMD solvation model. The pictorial visualization of Electrostatic potential (ESP) of carotenoids by Gaussview 29 is given in Supplementary Fig. 1. The optimized structures of carotenoid and chlorophyll are given in Fig. 1.
The energy values by three different basis sets are given in Supplementary Table 1. Vibrational frequency analysis has been carried out for all complexes and no negative frequency is found. Now with these lowest minima structures of carotenoid and chlorophyll, various sites have been created and all structures are optimized with wB97xD/Lanl2dz:6-31G** method in gas and water. Again the lowest minima structures have been selected for estimation of reaction rate (gas phase) and TDDFT (water phase) calculations. Vibrational frequency analysis has been carried out to check the stability of complexes and no negative frequency has been found. See Fig. 2a and b for Chla-carotenoid and chlb-carotenoid complexes respectively. These optimized structures and IGMPLOT figures are visualized by GaussView programme. The same optimized geometries have been used to generate the intermolecular and intramolecular interactions with IGMPLOT 30 .
Proton transfer reactions are of great importance in biomolecular processes of living organisms. In a gas phase environment, proton affinity (PA), is used which is defined as the negative of the enthalpy change at standard condition [i.e. temperature (298 K) and pressure]. Computational ab initio approaches can provide reliable values for proton affinities, which is important since it is difficult to determine experimentally. Chemical reactivity parameters have been used to predict the quantitative reactivity of the molecular system. The formulas used to calculate the proton affinities and global energy descriptors are given in Supplementary Information.
Antioxidants play very important role in the inhibition of the oxidative damage of the biomolecules. So quantitative analysis of the antioxidant activity of carotenoids has been obtained by the structure determination, energetics and global reactivity descriptors of carotenoid in gaseous and solvent (water) medium by DFT.
Transitivity code 31 has been used to calculate the reaction rate constant with Transition-State Theory (TST) for reactions in gaseous phase. The graph Log K versus 1000/K were plotted for the fourteen carotenoid-chlorophyll complexes for the default temperature range 273.15 K to 4000.00 K. In this window, it is possible to estimate reaction rate constant with TST and several one-dimensional tunneling corrections, thermodynamic (∆E, ∆H and ∆G) and kinetic (Eo, d, ν ‡, and α from ST model) properties of the reaction. β = 1⁄kBT, where kB is the Boltzmann's constant. The transition state calculations for carotenoid, chlorophyll and carotenoid-chlorophyll complexes have been carried out by G09 29 programme.
IGM (independent gradient model) represents a non-interacting system and the true ED gradient ( ∇ ρ ). It can be seen as a measure of electron sharing brought by ED contragradience. This model provides an automatic workflow that extracts the signature of interactions between selected groups of atoms. Also noncovalent Scientific Reports | (2021) 11:18365 | https://doi.org/10.1038/s41598-021-97747-w www.nature.com/scientificreports/ interaction (NCI) approach provides a visual understanding of the interactions present in chemical systems with both intermolecular and intramolecular interactions and to see the bond-by-bond picture that can be obtained from a wave function. In this way the specific interactions along reaction paths can easily monitor and the signature of inter and intra molecular interactions can be extracted. IGMPLOT is used to assess the role of non-covalent intramolecular interactions (intramolecular π-π stacking or hydrogen-bonding between two part of a single molecule along a reaction path). TDDFT calculations for the complexes have been carried out on the ground state stable geometies with wB97xD/Lanl2dz:6-31G** in solvent (water). The absorption wavelength, oscillatory strength and transitions for carotenoids, chlorophyll and chlorophyll-carotenoid interactions are given in Table 3 and Table 4 respectively. Transitions (%) are calculated by GaussSum 32 software.

Results
The reactivity of seven carotenoids is studied by DFT-based global reactivity descriptors using Chemical reactivity theory (CRT). C-DFT 33-37 used global reactivity parameters to predict structural and electronic properties of reactants and products which occur due to the chemical transformations during the reactions. It also gives a better microscopic insight to the whole interaction insight processes. To characterize the antioxidant property of carotenoids, it is important to analyse the global reactivity descriptors in detail. Chemical hardness measure the resistance to charge transfer, while the electronegativity measure the tendency to attract electrons in a chemical bond. The maximum electron flow between a donor and an acceptor is governed by the decomposition of binding energy between the atoms and it is determined by the factor electrophilicity index. Carotenoids act as  Table 1. An study conducted on Carotenoids of Marine origin displayed higher electrophilicity scale for astaxanthin and lower for zeaxanthin using different functional and solvents 38 . Both carotenoids and Chlorophyll have higher HL gap which indicated structural stability. Chemical hardness of carotenoids is higher in gas state. It was also observed that the HL gap for carotenoids and chlorophyll in solvent is more than the HL gap of these complexes in gaseous state. Our Global chemical reactivity parameters (IP and EA), energy levels and energy gap (HOMO-LUMO) results are consistent with the previously calculated results for β-Carotene, Neoxanthin, Violaxanthin and Zeaxanthin in the gaseous phase, and methanol (solvent) using B3LYP/6-31+G(d,p) method. The results show narrow HL energy gap which benefits energy transfer process for the carotenoid. The experimental value of the band gap is in the range of (1.87-1.92) eV for Chla and (1.90-1.92) eV for Chlb [39][40][41] . The HL gap for Chlaz is 1.883 in gas phase 42 , while the HL gap for Chlaz is 4.14 eV in aqueous medium. (See Fig. 2a). For Chla and Chlb, the ionization potentials are determined to be 4.19 eV and 4.45 eV in the PBE/DPZ level; however, it is obtained 4.96 and 5.22 by using the Octopus code, as well as 4.79 and 5.17 by applying the B3LYP/6-31G* hybrid functionals, The dipole moment of Chla (4.79 D) is larger than that of Chlb (1.36 D) 43 . Carotenoids are well-known antioxidants and they have the ability to quench singlet oxygen and scavenge toxic free radicals preventing or reducing damage to living cells. In our studies, the complexes have lower µ and ω which predicted that these carotenoids are good reactive nucleophile, also indicating their antioxidant behaviour. So we calculated proton affinities (PAs) and bond dissociation enthalpies (BDEs) for the studied carotenoids. BDE (numerical parameter) is related to Hydrogen atom transfer (HAT) mechanism and characterizes the stability of the corresponding hydroxyl group. The lower BDE value indicates that the stability of the corresponding O-H bond is lower and the corresponding O-H bond can be easily broken [44][45][46][47][48][49] . Hence, higher is the antioxidant capacity of the compound. In our studied complexes, proton affinities (PAs) are much lower than the bond dissociation enthalpies (BDEs), which indicate that direct antioxidant activity in these complexes is mainly due to the sequential proton loss electron transfer (SPLET) mechanism 50 . Lower PA of all the complexes indicated that antioxidant activity by the SPLET mechanism is a result of a balance between proclivity to transfer protons and the reaction kinetics of the conjugated base in the sequential electron transfer mechanism 46,47 . See Table 2. The electron transfer between the antioxidant and the radical can be determined from the IP and EA. A lower IP means a higher probability of losing an electron. It is clear from the trends observed in IP values that all these carotenoid molecules are capable of electronic charge transfer to the neutral ROS. This trend is compared to another theoretical studies 51 carried out for neutral ROS, i.e. · OH and · OOH, the average decrease in the vertical IP in the aqueous medium is 3.334 and 3.330, respectively. The EA also has crucial influence on the electron transfer between the antioxidant and the radical: a higher EA means a higher probability of gaining an electron. EAs obtained for the studied complexes are found to be lower than those for the neutral ROS · OH and · OOH in Table 1. Calculated IP, EA, Global reactivity descriptors-electronegativity (χ), global hardness (ƞ), global softness (S) and electrophilicity index (ω) in (eV) for studied carotenoid and Chlorophyll complexes with wB97xD/6-31G** and wB97xD/Lanl2dz6-31G** method respectively by DFT. *OH and *OOH parameters are taken from Ref. 41 . www.nature.com/scientificreports/ water medium. The IPs of our studied complexes are lower than those of the neutral ROS and the higher EAs of the neutral ROS compared to those of these molecules support the antioxidant behavior of the carotenoids. We also find that the presence of solvent significantly influences the EA. The η values of the ROS · OH and · OOH are 3.792 and 2.887 eV in the aqueous medium. Hence, the presence of the solvent increases the reactivities of these carotenoids molecules as well as the ROS. Consequently, the higher electrophilicity index predicts greater propensity of the ROS to attract electrons from a generic donor molecule. In our studied complexes the electrophilicity index is lower than the electrophilicity index of ROS · OH and · OOH, which indicates the high propensity of the ROS to attract electrons from these carotenoid molecules. The calculated redox potential is for the carotenoids are higher than the experimental values. The electron donating ability of carotenoid is related with the HOMO energies also. The molecules with higher HOMO orbital energy have stronger electron donating abilities, which is strongly correlated to the IP values also. Thus, the thermodynamically preferred reaction pathway involved in the free radical scavenging process can be determined by the BDEs and PAs. By comparison, it is found that in the gas phase, the calculated PAs of carotenoids are significantly lower than the BDEs, and hence thermodynamically, SPLETT represents the most favorable process in the gas phase. Strong intermolecular and intramolecular interaction has been observed among these complexes, with blue color isosurface plots between carotenoids and chlorophylls by IGMPLOT. The covalent chemical bond is intimately linked to the electron sharing between atoms. See Fig. 3a and b.

IP EA Electronegativity (χ) Hardness (ƞ) Softness (S) Electrophilicity Index ( ω)
Transitivity code has been applied to estimate the reaction rate constant with Transition-State Theory (TST) for reactions in gaseous phase. Good correlation has been observed for all fourteen complexes in gas phase. See Fig. 4a and b. The biological activities and the spectral properties are influenced by the variation in the structures of the complexes. The biological activity in plants includes the energy transfer, photoprotection and quenching of damaging singlet oxygen and bioactivities in humans and other organisms 51 . A wide variety of computational investigations have been used for computing excitation energies and absorption profiles, ranging from timedependent density functional theory (TD-DFT) [52][53][54][55][56] and DFT/multireference configuration interaction (MRCI) to various wave function methods such as SAC-CI 57 , CC2 58 , and ADC(2) 59 . The calculated position of the first peak is about 1.85 (1.91) eV for Chl a (Chl b) 39 , which agrees well with existing experimental data 40 . In another study the absorption energies of the Qy bands of Chla and chlb in acetone, diethyl ether, or ethanol were in the range (500-700) nm with CAM-B3LYP/e6-31G* basis sets 60 , while experimental results show (672 nm) and (652 nm) for Chla and Chlb in ethanol 61 . DLPNO−STEOM-CCSD calculations predict two excited states in the Q region, at 1.75 and 2.24 eV for chla in gas phase 62 . while the absorption peaks of chla were observed in (600-700) nm range 63 . Our TDDFT calculations show that the absorption wavelengths of the carotenoids are in visible region (432-452) nm, while chla and chlb has (356, 380) nm wavelength (water) respectively. See Table 3. The oscillatory strength of carotenoids are > 2, which is justified by the other theoretical results 64 . The wavelengths for β-Carotene, Neoxanthin, Violaxanthin and Zeaxanthin in the gaseous phase and methanol (solvent) using TDDFT with the CAM-B3LYP/6-31+G(d,p) are (293-303) nm 42,65 , which is slightly lower than our TDDFT results (430-452) nm measured in aqueous solvent. In one of the studies, the calculated TDDFT Excited States Energies (eV) were (2.20-3.65) eV using SVWN, B3LYP, and CAM-B3LYP Functionals for peridinin using Quantum Monte Carlo and Many Body Green's Function Theory 66 .
The first excited triplet state transitions were calculated with wB97xD/6-31G** basis sets for Chl(a,b) and carotenoids and wB97xD/Lanl2dz:6-31G** basis sets were used for the Chlorophyll-carotenoid interactions. The triplet wavelength for chlorophyll and carotenoid lies in (588-750) nm range (See Table 3) whiles the first triplet wavelength for chl-car complexes lies in (432-555) nm range. See Table 5. The results are consistent with the previous experimental results for ppLHCSR1-Vio (488 nm) and ppLHCSR1-Zea (491 nm) at pH 7. When pH is lowered to 5, the carotenoid bands slightly red-shifts to 489 nm (ppLHCSR1-Vio) and 492 nm (ppLHCSR1-Zea) 67 . Table 2. Calculated HOMO-LUMO Gap (eV) (gas, water), Proton affinity (PA), bond dissociation energies (BDE) and redox potential (meV) for studied carotenoid complexes and chlorophyll with wB97xD/6-31G**, wB97xD/Lanl2dz:6-31G** method respectively.  In another studies on Chl (a, b), the triplet energy is 0.8 eV lower than that of the S1 state 68 . The S 1 -T 1 adiabatic energy gap is lower for the studied complexes which is an implication on the ISC transition from S 1 to T 1 state. According to the energy gap law 69,70 , for electronic states with similar geometries, the smaller the energy gap, the larger is the ISC rate. So there will have a faster ISC rate for triplet formation in chl-car complexes. Certainly, carotenoids play major role in the photosynthetic apparatus for quenching of the Chl triplet state ( 3 Chl) through the triplet-triplet energy transfer (TTET) mechanism [71][72][73] . The direct population of the carotenoid triplet state ( 3 Car) by intersystem crossing (ISC) is a low probability event, due to a very short lifetime of the excited state of these molecules, that is dominated by internal conversion. Energy transfer from the 3 Chl, which is populated with a yield of ~ 0.6 in the absence of other quenching mechanisms 74,75 , is efficient in photosynthetic systems 70,76 because of the short average inter-pigment distances and because the 3 Car lays at an energy level which is below that of 3 Chl. Also it is well known that 3 Chl is an efficient sensitiser of singlet oxygen ( 1 O 2 ), which is an highly reactive species and plays major role in photo-oxidative stress 71,72,77 .

Conclusions
The chemical reactivity, antioxidant properties of carotenoids and chlorophyll has been studied by DFT. Results indicated high stability and lower reactivity for carotenoids and chlorophyll complexes. Lower proton affinities (PAs) than the bond dissociation enthalpies (BDEs) indicate that the direct antioxidant activity in these carotenoids is due to the SPLET mechanism with dominant solvent effects. Higher HL gap was observed for carotenoid