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Excited States of Light-Harvesting Systems Based on Fullerene/Graphene Oxide and Porphyrin/Smaragdyrin Gloria Ines Cardenas-Jiron, Merlys Borges-Martinez, Ember Sikorski, and Tunna Baruah J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12452 • Publication Date (Web): 14 Feb 2017 Downloaded from http://pubs.acs.org on February 25, 2017

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The Journal of Physical Chemistry

Excited States of Light-Harvesting Systems Based on Fullerene/Graphene Oxide and Porphyrin/Smaragdyrin Gloria Cárdenas-Jirón1*, Merlys Borges-Martínez1, Ember Sikorski2, Tunna Baruah2* 1

Laboratorio de Química Teórica, Facultad de Química y Biología, Universidad de Santiago de Chile (USACH), Casilla 40, Correo 33, Santiago, CHILE 2

Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA

ACS Paragon Plus Environment

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Abstract

In this work we present a theoretical study at the density functional theory (DFT) level and timedependent DFT of the ground and singlet excited states of electron donor-acceptor complexes formed by porphyrin (TPP)/smaragdyrin (TPOS) (expanded porphyrin), as light-harvesting systems, and fullerene (C60)/graphene oxide (GO), as acceptor nanocarbon structure. We investigate

the

effect

of

the

nanocarbon

on

UV-Vis

electronic

absorption

of

porphyrin/smaragdyrin, using the functionals B3LYP, PBE, M06 and wB97XD. The results showed the lowest deviation of the Q band for the functional M06 (0.01-0.02 eV). Electronic absorption spectra calculated for the complexes with M06 predict that: (a) graphene oxide increases the intensity of the Soret band; (b) fullerene produces a red-shift of the Q bands (4 nm) with respect to graphene oxide and (c) smaragdyrin causes a red-shift of Q (27-48 nm) and Soret (37 nm) absorption bands compared to porphyrin. We also investigate the effect of the nanocarbon structure on the charge-transfer (CT) excited states. Using the perturbative delta-SCF method with the PBE functional, we found that the charge-transfer excitation energy increases as TPOS-C60 (2.53 eV) < TPP-GO (2.89 eV) < TPP-C60 (3.01 eV) < TPOS-GO (3.28 eV). The presence of a nanocarbon structure affects more strongly to smaragdyrin (∼0.8 eV) than porphyrin (∼0.1 eV). We show that the binding between smaragdyrin and fullerene C60 favors the charge separation states with a lower energy cost, which means that these systems present an advantage for its application in photovoltaic cells.


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1. Introduction

The design of functional materials at a molecular level has attracted great interest due to its potential applications in different fields of science such as optoelectronics, catalysis, energy storage and energy conversion.1 Graphene, an allotrope of carbon, is one of the functional materials that has been widely investigated since its first isolation in 2004.2-3 It consist of a two-dimensional thick sheet of graphite composed of a hexagonal network of sp2 carbon atoms. The attraction for studying graphene and graphene like materials is due to their large surface area, high thermal conductivity, sp2 hybridized orbitals. Graphene is an electron acceptor that is easy to functionalize with other molecules. 4-5 Because of that graphene presents a set of properties like mechanical6-8, optical9, thermal10-12 and electrical transport.13-15 The combination of the physical and chemical properties of graphene allows that it has a variety of applications such as energy storage16, energy conversion17, nanoelectronics, photovoltaics, catalysis, gas sorption, sensing, between others.18 On the other hand, fullerene C60, an excellent multi-electron acceptor with a favorable reduction potential (-0.169 V), has played an important role in the development of molecular building blocks with photovoltaic applications.19-22

High electron affinity combined with low

reorganization energy in charge transfer (CT) reactions makes the fullerenes ideal electron acceptors.23 A variety of supramolecular assemblies with porphyrin molecules have been proposed as functional models for light-harvesting and photo-induced electron transfer.24-26 Porphyrins and fullerenes are complementary compounds owing to their large aromatic


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structures and they can form molecular architectures having a strong π-π interactions between them.27-31 Porphyrin is one of the most studied macrocyclic systems because the excellent photochemical and photophysical properties. It has an 18 π-conjugated electronic network in a square-planar circuit giving account of the aromatic character that is responsible of its stabilization. Porphyrin is a chromophore that absorbs visible light and is a good candidate as component of photoelectronic materials such as photosensitized solar cells.32-35 On the other hand, three types of expanded porphyrin36 containing five pyrroles exist, depending on the number of bridging carbons and direct bonds between the pyrrole rings; pentaphyrin that was synthesized in 1983 by Rexhausen and Gossauer37, and both sapphyrin and smaragdyrin reported by Woodward et. al in 1966.38 The expanded porphyrin macrocycles have applications in photodynamic therapy, contrast agent in magnetic resonant imaging, and for non-linear optics. The chemistry of smaragdyrin was not well-established until recently due to the poor stability and synthetic difficulties.39 Smaragdyrin is an expanded porphyrin containing five pyrrole units with 22 π electrons and two pyrrole-pyrrole links, which results in a macrocycle with only three methine bridges that correspond to the meso positions. The name of smaragdyrin is due to its intense green color in the solid state like smaragdus (emerald) that is a precious green stone. It is a synthetic analogue of porphyrins and possess a unique characteristic that porphyrins do not; it has the ability for anion complexing in the core region. We have previously performed theoretical studies about sapphyrins, their molecular structures and the UV-Vis electronic absorption spectra.40-41. Several studies39

have reported the synthesis of a variety of

smaragdyrins; β- and meso-aryl- substituted,42-44 isomers,45 protonated and anion binding,44 dyads46 and triads47.


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The combination of porphyrins and fullerenes is one of the most extensively organic donoracceptor pairs studied48-66 as also the assemblies formed by porphyrins and graphene for lightharvesting and photo catalysis.67-69 However, to our best knowledge, complexes containing smaragdyrin and nanocarbon structures like graphene or fullerene have not been reported. The purpose of this work is to evaluate how the light-harvesting ability of porphyrin and smaragdyrin can be improved when they are bonded to a nanocarbon system like fullerene C60 or graphene oxide. In a first hand, we examine the UV-vis electronic absorption properties of the donor-acceptor complexes formed by porphyrin and smaragdyrin as donor species, and fullerenepyrrolidine and graphene-oxide as acceptor species, as in their isolated forms. Since the charge transfer (CT) from the donor to the acceptor is important from the point of view of lightharvesting properties, we have also examined the lowest few CT excited states in these complexes. The donor molecule is connected to the acceptor one through an amide moiety in all the complexes.

2. Computational Aspects

We have studied two kinds of porphyrin-based compounds; 5,10,15,20-tetraphenylporphyrin (TPP) and tri-meso-phenyl-oxasmaragdyrin (TPOS), and two kind of nanocarbon structures; fullerene-C60-pyrrolidine (C60-py) and graphene oxide (GO), which are displayed in Figure 1. Note that the pyrrolidine fragment has been previously used bonded to C60 or other similar structures70-72 and in this work is used to connect appropriately the porphyrin-based compound. The molecular structures of such fragments and the corresponding complexes formed from the binding between these compounds were fully optimized using density functional theory (DFT) at


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the all-electron level using the Perdew-Burke-Ernzerhof exchange correlation functional (PBE).73 All the calculations related to the optimization of the molecular geometry were performed using the NRLMOL (Naval Research Laboratory Molecular Orbital Library) suite of codes.74-75 It is important to mention that the basis set used in this code is specially optimized to be used with the PBE functional. It correctly satisfies the Z10/3 rule for Gaussian basis sets, where Z is the atomic number; so that the basis set superposition errors are minimized.76 The basis set details are presented in the Supplementary Information (Table S1). We will use the notation TPP-C60 and TPP-GO to name the complexes formed by porphyrinpyrrolidine-fullerene and porphyrin-graphene oxide, respectively, and the notation TPOS-C60 and TPOS-GO for the complexes containing smaragdyrin-pyrrolidine-fullerene and smaragdyringraphene oxide, respectively. The total charge of the four complexes and their corresponding fragments is zero and the spin multiplicity for each molecular system is a singlet state. As graphene oxide, we used a cluster model formed by 19 hexagonal cells containing 54 carbon atoms in a monolayer form with the edges passivated with 18 hydrogen atoms, and one oxygen atom bonded to two carbon atoms in an epoxide form (C54H18O). The same graphene model was used by us in previous studies.13-15 Furthermore, it is known that the functional groups in the basal plane in graphene oxide consists of hydroxyl and epoxide groups that produces different concentrations of sp2 and sp3 regions along the network. The tuning of sp2 domains by remotion of oxygen groups leads to an improvement of the electrical, optical and transport properties of graphene oxide.77 In the present work, we preferred to use a structural model for GO with more sp2 domains than sp3 ones, this is the reason of why we only use one oxygen moiety (epoxide). The validity of the model was supported by the band gap values of GO calculated in this work.


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The band gap calculated for GO at the B3LYP/6-31G(d,p) level of theory is ∼2.5 eV, which is in agreement with the values reported by Eda et al. of ∼3.0 eV (B3LYP/6-31G(d)) for graphene with 19 aromatic rings and of ∼2.0 eV for LDA.78 These authors show that the band gap is reduced from one benzene ring (∼7 eV) to 19 aromatic rings. Other authors have also studied models of graphene oxide containing 19 rings and different oxygen moieties (-O-, COOH, OH) obtaining values going from 0.42 to 1.96 eV.79 Using the previously optimized structures, UV-vis electronic absorption spectra for the isolated fragments (4) and their complexes (4) were calculated in the solution phase within the timedependent DFT methodology (TD-DFT) as implemented in the Gaussian 09 package.80 We calculated 50 excited states for each the fragments and the corresponding complexes with the different functionals as singlet-singlet vertical excitations, giving a total of 700 excited states. The methodology TD-DFT has been widely tested in the literature and the results are comparable with UV-vis measurements. Some examples of them are the benchmark applied to organic molecules reported by Jacquemin et al.81 and the study of porphyrin-like compounds with application to photodynamic therapy published by Lanzo et al.82 In relation to the functionals used in this work, all of them belong to the class of generalized gradient approximation (GGA) functionals for the exchange-correlation energy. B3LYP is a hybrid functional that combines the Becke’s three-parameter nonlocal hybrid exchange potential with the nonlocal correlation functional of Lee, Yang, and Parr. This functional includes a 20% of the exact Hartree Fock (HF) exchange energy.83-86 PBE is a pure functional that does not contain HF exchange and only DFT electron exchange and correlation.73, 87

M06 is a global

hybrid meta GGA with 27% of HF exact exchange, where this functional includes a correction in the kinetic energy.88 Finally, wB97XD is a hybrid density functional that includes empirical


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atomic-pairwise dispersion corrections following the Grimme's D2 dispersion scheme (D), and exchange corrections for short range (X) and long-range (w). The wB97XD functional includes 22% of short-range HF exchange and 100% of long-range HF exchange.89 According to the available experimental data of the fragment and complexes, UV-vis absorption spectra have been measured in different solvents. In order to use a unique solvent for all the structures, we choose dichloromethane (dielectric constant ε=8.9) for performing the theoretical calculations in the solution phase. The calculations including the solvent were performed with the self-consistent reaction field (SCRF) using the Conductor Polarizable Continuum Model (CPCM)90-93 and a molecular-shaped cavity built with the United Atom Topological Model94 applied on atomic radii of the Universal Force Field (UFF). We also analyzed the surfaces of the molecular orbitals (MO) involved in the electronic transitions and particularly those that determine the reactivity of the molecule, that is, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). All the calculations for the ground and excited states are performed with the Gaussian 09 package.80 The charge transfer excited states are calculated in the gas phase using the perturbative delta-SCF method with the PBE functional as implemented in the NRLMOL code.

95-96

It was shown earlier that the delta-SCF method

could yield reliable values for the CT states with GGA functional. In this method, we start with the geometry of the ground state. The orthogonality between the ground and excited state wavefunctions is enforced.


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(a) 2

3

N C8

N22H

NH

C6 N21 C1 4

C2

C7

C4 C5 C3

1

Figure 1. View of the molecular structure of the compounds studied in this work in its isolated form: (a) porphyrin; (b) fullerene-pyrrolidine; (c) smaragdyrin and (d) graphene oxide.


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3. RESULTS AND DISCUSSION

3.1 Molecular Structures The more relevant geometrical parameters of the optimized structures of complexes and the fragments are shown in Table S2. In order to check the accuracy of the theoretical level used, we compare our results with the X-ray diffraction experimental values available for porphyrin

97-99

and smaragdyrin.43 Two X-ray structures of meso-tetraphenylporphyrin have been reported in literature; one of them with the tetragonal space group that requires four molecular symmetry97-98; the other one is a triclinic crystal form with the space group P1.

99

The problem of the former is that not

distinguish between pyrrole rings having or not hydrogen atoms bonded to nitrogen atoms. Because of lower symmetry, the triclinic form distinguishes two types of pyrrole and the hydrogen atoms of the imino groups. More relevant bond distances of both structures that involves pyrrole rings are included in Table S2 and compared with the theoretical values of TPP in its isolated form and as complexes TPP-GO and TPP-C60. We found that the theoretical values show a good agreement with respect to the triclinic form with deviation no more than 0.025 Å. The porphyrin framework in the triclinic structure is found nonplanar; one pair of pyrroles is coplanar and the other pair carrying the hydrogen atoms is inclined by 6.6° to this plane. Our theoretical results for TPP are in an excellent agreement with the experimental ones; two pyrrole rings present a dihedral angle of 0° indicating that are coplanar, and the other two rings that include the imino hydrogen atoms show a dihedral angle of 8° showing a little deviation of the plane. Phenyl groups of theoretical TPP are rotated out of the plane by about 68° that are very close to the value found for the crystalline structure (60°).

The good agreement observed


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between both theoretical and experimental structures of TPP allows the validation of the level of theory used. The binding of TPP with graphene oxide and fullerene destroys the near symmetry that the macrocycle framework has and as a consequence the N(pyrrole)-C bond lengths such as N21-C4 and N22-C6 undergo a larger change than the C-C bond lengths. The enlargement of N21-C4 in the complexes suggests that a diminishing in the electronic density occurred that would be coherent with the ability of the porphyrin as an electron donor. In the complexes, the porphyrin framework is not completely planar, in the case of TPP-GO a near planarity is found between two neighbor pyrrole rings (1° and 3°). For TPP-C60, pyrrole rings located face-to-face present a deviation out of the plane in 5°. In this complex, phenyl groups are rotated out of the plane in 90100° for those rings located along the binding direction of fullerene, and in 59-63° for the other phenyl rings. In the case of TPP-GO, the phenyl rings are rotated in 68-70° with respect to the pyrrole rings. Finally, we found that graphene oxide is not coplanar with porphyrin; GO presents a slight curvature in the region of the peroxide moiety where both carbon atoms bonded to oxygen atom are deviated out of the plane in 10°. In the case of smaragdyrin (TPOS), the X-ray structure reveals a non-planarity of the framework, which is attributed to the tension produced by the addition of one pyrrole ring, the pyrrolepyrrole link and the electronic repulsion between the imino hydrogen atoms of the inner macrocycle. The unit cell is composed of two smaragdyrin molecules and three molecules of solvent methanol located between two macrocycles.43 To perform the comparison between the experimental and theoretical structures, as shown in Figure 2, we choose one smaragdyrin of the unit cell. Figure 2(a) shows a superposition between smaragdyrin obtained from X-ray (orange)


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and that calculated in this work (black). As it can be seen, both structures are very similar and the main differences are observed in the phenyl rings in meso positions.

(a)

(b)

Figure 2. Comparison of the theoretical (black) and experimental43 (orange) structures of smaragdyrin: (a) front view; (b) side view.

Nitrogen (blue) and oxygen (red) atoms are

highlighted as balls. In general, the phenyl rings are in a nearly perpendicular form with respect to the smaragdyrin framework in both experimental and theoretical structures.

However, the main difference

between them is in the meso-phenyl 2. X-ray structure predicts a torsional angle of meso-phenyl 2 with porphyrin skeleton of 131°, while theoretical structure predicts a value of 56°. The second structure of TPOS in the unit cell predicts a torsional angle similar to the latter value (45°). The bipyrrolic unit located between meso-phenyls 1 and 2 is nearly planar in the theoretical structure (0.5°) and deviated in the experimental one (8°). While the bipyrrolic unit located between meso-


12

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phenyls 2 and 3 presents a torsional angle of 9.7° and 13° for the theoretical and experimental structures, respectively. On the other hand, in theoretical TPOS there are strong hydrogen bonding between the protons of the imino groups and the heteroatoms, such as O…H(N1) 2.39 Å, N3…H(N2) 1.76 Å, N3…H(N4) 2.63 Å and O…H(N4) 2.61 Å. Although slightly lower, these results are in very agreement with that observed for experimental structure being 2.56, 1.81, 2.71 and 2.61 Å, respectively. The imino hydrogen atoms H(N1) and H(N4) in experimental TPOS are out of the plane in a down position with a deviation with respect to the closest meso-carbon atom of 5° and 13°, respectively, while the H(N2) is nearly in the plane (1°). The same trend occurs for the second molecule of smaragdyrin in the unit cell. The strong hydrogen bonding interaction that occurs between both TPOS and two methanol molecules trapped in the unit cell explains this behavior. The theoretical TPOS is more planar with angles of 6°, 3° and 0.5° for H(N1), H(N4) and H(N2) measured with respect to the closest meso-carbon atoms. The root mean square deviation (RMSD) calculated between the theoretical and experimental TPOS is 1.16 Å that allows for validating the level of theory used to get the more stable molecular structure for smaragdyrin. In relation to the computed bond lengths and intramolecular distances involved in the inner macrocycle differed from the experimental values by -0.148 Å to +0.090 Å (more details are shown in Table S2).

(a)

(b)


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(c)

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(d)

Figure 3. Optimized molecular structures: (a) TPP-C60, (b) TPP-GO, (c) TPOS-C60, (d) TPOSGO. The smaragdyrin fragment in complexes TPOS-C60 and TPOS-GO do not show significant changes, a maximum value of -0.011 Å for bond lengths and of -0.103 Å for intramolecular distances (Table S2). Smaragdyrin maintains its non-planarity in the complexes, as can be seen in Figure 3 but slightly more planar than the isolated smaragdyrin. For complex TPOS-GO, the torsional angles are 1° and 6° for the bipyrrolic units close to phenyls 1 and 2 and phenyls 2 and 3, respectively. For the same bipyrrolic units, we found 1.5° and 8°, respectively in the complex


14

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TPOS-C60. These results indicate that the binding with the nanocarbon structure (graphene oxide, fullerene) favors that the macrocycle acquires a slight major planarity. The hydrogen binding interaction follows the trend observed for smaragdyrin, O…H(N1) 2.49 Å, N3…H(N2) 1.77 Å, N3…H(N4) 2.70 Å and O…H(N4) 2.50 Å for TPOS-GO and O…H(N1) 2.51 Å, N3…H(N2) 1.75 Å, N3…H(N4) 2.73 Å and O…H(N4) 2.45 Å for TPOS-C60. However, the complexes show a shortening in the O…H(N4) distance that contributes to a more rigid macrocycle. Since the van der Waals interactions in such systems are important, we have performed a DFTD3 calculations using Grimme’s parameters100-101 on the PBE optimized structures. We found that the largest gradient due to dispersion effects is on the order of 0.002 a.u.. The dispersion energies are -0.28 Hartree in TPOS-graphene oxide, -0.29 in porphyrin-graphene oxide, -0.33 in TPOS-fullerene, and -0.34 Hartree in the porphyrin-fullerene systems. The small forces show that the PBE geometries are fairly optimized.

3.2 Electronic Absorption Spectra by TD-DFT

Choice of the Density Functional. We have previously shown

13, 40, 102-105

that the simulation of

the UV-vis electronic absorption spectra by TD-DFT calculations is a complex task and must be carefully carried out considering several density functionals. In this section, we are interested for studying the electronic absorption spectra of porphyrin and smaragdyrin when they are bonded to fullerene and graphene oxide. Taking the optimized geometry of TPP and TPOS fragments, first, we performed a calibration procedure that consist of TD-DFT calculations of the electronic absorption spectra for such fragments by using four types of density functionals, B3LYP, PBE, M06 and wB97XD. The lower deviation between the theoretical results and the experimental


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available data will allow the choice of the functional that we will use to analyze the electronic transitions of the complexes. Table 1 collects the characteristic absorption bands of porphyrin and smaragdyrin obtained with TD-DFT where we have included the theoretical excitation wavelength (nm) (energy (eV) in parenthesis), the oscillator strength and the assignment in terms of the Soret and Q bands. Note that in both compounds, we obtain only two Q absorption bands instead of four bands as for the experimental data. The reason is due to the near degeneration that the pairs HOMO/HOMO-1 and LUMO/LUMO+1 molecular orbitals present in the theoretical calculation. The deviation of the theoretical absorption bands with respect to the experimental data is also included in the table. In order to perform the analysis with a unique solvent, we chose dichloromethane (CH2Cl2) (ε=8.93) because the available UV-vis spectrum of smaragdyrin was measured in such solvent. Although the available spectrum for porphyrin is measured in tetrahydrofuran (ε=7.58), the dielectric constant is very similar to the solvent used in the calculation (CH2Cl2).

Table 1. Characteristic electronic absorption bands of porphyrin and smaragdyrin including the wavelength (λ), excitation energy (E), oscillator strength (f) and the corresponding assignment of the electronic excitation calculated at the condensed phase (solvent: CH2Cl2). Deviation from the experimental data are included in eV and in percentage (%) in square parenthesis.

Density Functional

λ/nm (E/eV) f

Assignment

Porphyrin B3LYP

576 (2.15) 0.041 [0.05, 2%]

Q

540 (2.30) 0.058 [0.03, 1%]


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PBE

399 (3.11) 1.741 [0.15, 5%]

Soret

610 (2.03) 0.056 [0.07, 3%]

Q

575 (2.16) 0.074 [0.11, 5%]

M06

427 (2.91) 1.011 [0.05, 2%]

Soret

588 (2.11) 0.030 [0.01, 0.5%]

Q

555 (2.23) 0.045 [0.04, 2%]

wB97XD

402 (3.09) 1.829 [0.13, 4%]

Soret

612 (2.03) 0.020 [0.07, 3%]

Q

554 (2.24) 0.038 [0.03, 1%]

Exp.

381 (3.25) 1.979 [0.29, 10%]

Soret

649a (1.91), 591 (2.10)

Q

546 (2.27), 513 (2.42) 419 (2.96)

Soret

623 (1.99) 0.135 [0.03, 2%]

Q

Smaragdyrin B3LYP

595 (2.08) 0.027 [0.02, 1%]

PBE

443 (2.80) 1.871 [0.00, 0%]

Soret

674 (1.84) 0.128 [0.12, 6%]

Q

634 (1.96) 0.025 [0.14, 7%]

M06

479 (2.59) 1.604 [0.21, 8%]

Soret

627 (1.98) 0.122 [0.02, 1%]

Q

611 (2.03) 0.028 [0.07, 3%]

wB97XD

441 (2.81) 1.962 [0.01, 0.4%]

Soret

601 (2.06) 0.010 [0.10, 5%]

Q

558 (2.22) 0.154 [0.12, 6%] 390 (3.18) 2.104 [0.38, 14%]

Soret


17


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Exp.

696b (1.78), 633 (1.96)

Page 18 of 43

Q

591 (2.10), 552 (2.25) 443 (2.80)

Soret

in THF106, b in CH2Cl2 43. The bolded numbers are used for the calculation of the deviation of the theoretical values with respect to the experimental ones. a

For porphyrin we found that hybrid functionals like B3LYP and M06 predict lower deviation of Q bands up to 0.05 eV (2%) whose values are underestimated with respect to the experimental values with a blue-shifting of the absorption bands. However, Soret band is better predicted with a pure functional as PBE with a deviation up to 0.05 eV (2%), and in this case the absorption value is overestimated with respect to the experimental one with a red-shifting of the band. The functional that includes dispersion and long-range corrections as wB97XD poorly predict the UV-vis spectrum of porphyrin, the maximum error achieves to 10% (0.29 eV) and correspond to the Soret band. In the case of smaragdyrin, we found that both Q and Soret bands are well predicted by B3LYP and M06 functionals with deviations up to 0.07 eV (3%). The functional PBE presents deviations up to 0.21 eV (8%) for Soret band indicating that a pure DFT functional is not enough to describe the UV-vis spectrum. In the case of the functional wB97XD, the maximum deviation also correspond to Soret band and is 0.38 eV (14%). These results suggest that the inclusion of dispersion and long-range corrections are not needed for a good description of the spectra of porphyrin and smaragdyrin. Based in the obtained results, and considering that both B3LYP and M06 predict reasonably well the electronic spectra of the porphyrinic fragments, we will choice the functional M06 for calculating the electronic absorption spectra of the complexes.


18

Page 19 of 43

Electronic Absorption Spectra for the Complexes. Once we obtain the functional that better represent the electronic absorption spectra of the fragments (porphyrin, smaragdyrin), we can apply the functional M06 for the modelling of the spectra for the complexes using the TD-DFT methodology. Figure 4 shows the spectra calculated at the M06/6-31G(d,p) level of theory for the complexes in the range of 200-800 nm. We have included in the same figure the respective fragments in order to facilitate the comparison with them.

Table 2 shows the electronic

transitions associated to the Q and Soret bands for the complexes, where we include the excitation wavelengths/energy, oscillator strength and the surfaces of the molecular orbitals participating in such transitions. All the excited states shown in this table are not pure states instead a set of transitions between the occupied and the unoccupied molecular orbitals are obtained. The transitions shown in Table 2 corresponds to those having the higher contribution to the excited state.

160000

160000

(a)

C60 porphyrin

120000

(b)

140000

porphyrin-C60

100000 80000 60000 40000

epsilon/Lmol-1cm-1

140000

epsilon/Lmol-1cm-1

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


C60 smaragdyrin

120000

smaragdyrin-C60

100000 80000 60000 40000 20000

20000

0

0 200

300

400

500

600

700

800

200

300

400

500

600

700

800

λ/nm

λ/nm


19


280000

280000

porphyrin

200000

porphyrin-graphene oxide

160000 120000 80000

epsilon/Lmol-1cm-1

graphene oxide

(c)

240000

epsilon/Lmol-1cm-1

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

120000 80000

0 500

600

700

800

smaragdyrin-graphene oxide

160000

0 400

smaragdyrin

200000

40000

300

graphene oxide

(d)

240000

40000

200

Page 20 of 43

200

300

400

500

600

700

800

λ/nm

λ/nm

Figure 4. Electronic absorption spectra obtained using TD-DFT at the M06/6-31G(d,p) level of theory.

We can see in Table 2 that all the complexes present the Q and Soret characteristic bands, where the electronic transitions of the type porphyrin→porphyrin and smaragdyrin→smaragdyrin are obtained. In all cases, we obtained two weak Q bands, as in the fragments, because the pairs HOMO/HOMO-1 and LUMO/LUMO+1 are nearly degenerated molecular orbitals. In the case of complexes containing fullerene (Figs. 4(a) and (b)), it can be seen that both present a strong absorption for the Soret band that is nearly similar to the porphyrinic fragment (porphyrin and smaragdyrin) in wavelength and intensity. These results indicate that fullerene has a slight effect on these fragments. The absorption of the fullerene fragment with M06 functional occurs at 338 nm with a very low oscillator strength (0.082), which could be the reason of the weak effect on the spectra of the complexes having C60-py. We noted that smaragdyrin-fullerene presents Q and Soret bands (626, 610 and 443 nm) that are red shifted with respect to the porphyrin-fullerene complex (599, 565 and 409 nm). The electronic transitions displayed in Table 2 show that in both complexes, the occupied and unoccupied


20

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molecular orbitals are located on the macrocycle but in the case of that containing smaragdyrin, one phenyl ring also contributes in LUMO+3. For the complexes containing graphene oxide (Figs. 4(c) and (d)), we found that in both cases the intensity of Q and Soret bands increases with respect to the isolated fragments. This fact can be explained because the graphene oxide presents a strong absorption (f=0.785) in the same region of the Soret band (412 nm calculated with M06) that contributes to a larger absorption in the complexes. The epsilon values for the complexes containing graphene oxide are near to 250.000 Lmol-1cm-1, which would be compared to 160.000 Lmol-1cm-1 for complexes with fullerene. It is clear that we obtain an improved effect in the absorbance of the complexes when graphene oxide is included because the intensity of the Soret band increases. As occurred for the fullerene-based complexes, the smaragdyrin-graphene oxide complex (623, 608 and 444 nm) shows red-shifted absorptions (Q and Soret) with respect to porphyrin- graphene oxide (595, 562 and 407 nm). We also found a contribution of one phenyl ring to LUMO+1. Unfortunately, UV-vis spectra measured for the complexes, at exception of porphyrin (TPP)graphene oxide, are not available. At the experimental level, the electronic absorption spectrum of porphyrin-graphene oxide measured in dimethylformamide shows a characteristic band at 420 nm (Soret band), which corresponds to the covalently grafted porphyrin unit on GO.

67

The Q

bands at 516, 557, 589 and 648 nm of porphyrin were flattened to the base line in the TPP-GO material.67 It is observed that the absorption of porphyrin in the TPP-GO material is broadened and bathochromically shifted in 2 nm with respect to free porphyrin, which confirm the electronic interactions between GO and TPP. These results are in agreement with studies of porphyrins covalently grafted to carbon nanotubes107 and nanohorns.

108

Soret band obtained in

the present work for porphyrin-graphene oxide at 407 nm (3.05 eV) presents a good agreement


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Page 22 of 43

with the experimental data at 420 nm (2.95 eV) with a deviation of 0.1 eV that is well reasonable for TD-DFT calculations.

67

Additionally, the deviation of 0.02 eV for the Q bands when the

theoretical values (595 and 562 nm) are compared to the experimental ones (589 and 557 nm) confirm that: (a) the functional M06 can reproduce well the electronic absorption spectrum of porphyrin-graphene oxide, and (b) the reduced model for graphene oxide containing only one oxygen atom is adequate.

Table 2. Characteristic electronic absorptions for the Soret and Q bands of the complexes calculated with TD-DFT at the M06/6-31G(d,p) level of theory where excitation wavelength (λ), energy (E),

oscillator strength (f) and molecular orbitals corresponding to the electronic

transitions are included. λ/nm (E/eV) f

Assignment

Electronic Transition

Smaragdyrin-Fullerene 626 (1.98) 0.100

Q

HOMO

LUMO+3

Q

HOMO

LUMO+4

Soret

HOMO-1

LUMO+3

52%

610 (2.03) 0.028 51%

443 (2.80) 1.982 43%


22

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Smaragdyrin-Graphene Oxide 623 (1.99) 0.113

Q

HOMO

LUMO+1

Q

HOMO

LUMO+3

Soret

HOMO-1

LUMO+1

Q

HOMO

LUMO+3

Q

HOMO

LUMO+4

65%

608 (2.04) 0.020 46%

444 (2.80) 2.510 32%

Porphyrin-Fullerene 599 (2.07) 0.041 89%

565 (2.19) 0.064 84%


23


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409 (3.03) 1.928

Soret

Page 24 of 43

HOMO-1

LUMO+4

Q

HOMO-1

LUMO+1

Q

HOMO-1

LUMO+2

Soret

HOMO-3

LUMO+1

33%

Porphyrin-Graphene Oxide 595 (2.08) 0.056 55%

562 (2.21) 0.081 60%

407 (3.05) 1.584 59%

In summary, the results presented in both Table 2 and Figure 4 allows to conclude for the complexes that: (a) graphene oxide increases the intensity of the Soret absorption band; (b)


24

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fullerene produces a red-shift of the Q absorption bands with respect to graphene oxide; (c) smaragdyrin causes a red-shift of Q and Soret absorption bands compared to porphyrin.

3.3 Charge Transfer Excited States

Porphyrin-based complexes. The properties that influence the CT energy are the ionization energy of the donor molecule and the electron affinity of the acceptor molecule.

In the

complexes under study the fullerene is functionalized with a pyrrolidine ligand at the [6,6] position, which is the junction between two hexagonal rings of C60. It is known that the cycloaddition reactions of C60 show preference for the [6,6] site over the [5,6] site.109-110 The cycloaddition to a double bond at the [6,6] site leads to breaking of the double bond but a closed hexagonal ring structure remains. On the other hand, such an addition at a [5,6] site leads to an open ring structure. The vertical electron affinities and ionization potentials of the four complexes studied here are presented in Table 3. The vertical electron affinity of the C60 in the complexes with porphyrin and smaragdyrin (2.70 and 2.73 eV) shows mild deviation from that of pure C60 electron affinity (2.69 eV). This result is in very good agreement with our earlier result on a dye-attached pyrrolidine-C60 complex.111 As described earlier, we have also used a graphene oxide (with one oxygen atom) as an electron acceptor whose calculated electron affinity is 1.87 eV. Increasing the content to two oxygens reduces it only by 0.05 eV. We have noted that the electronic properties of the complex of porphyrin and graphene oxide show significant deviation from their individual properties. The electron affinity of the complex is raised by 0.42 eV to 2.29 eV, compared to the calculated electron affinity of the graphene oxide only. The vertical ionization potential of the TPP (6.11 eV) in the porphyrin-fullerene complex


25


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Page 26 of 43

is close to that of the isolated porphyrin (6.22 eV). On the other hand, in the porphyrin-graphene oxide complex the ionization potential is much lower (5.74 eV). These energetic changes point to significant interaction between the porphyrin and graphene oxide moieties. We have plotted the difference in the density of the anionic and neutral porphyrin-graphene oxide that is showed in Figure 5. The density difference shows that the extra electron density is spread over both the moieties, which leads to an electron affinity value different from that of the isolated graphene oxide cutout.

Figure 5. The density difference between the anionic and neutral porphyrin-graphene oxide.

Table 3. The vertical ionization potentials (vIP), vertical electron affinities (vEA) and the quasiparticle (QP) gaps for the complexes and the donor and acceptor fragments studied here. All energies are in eV.

vIP

vEA

QP gap

Complex TPP-C60

6.11 2.73

3.38

TPP-GO

5.74 2.29

3.45


26

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5.73 2.70

3.03

TPOS-GO 5.72 1.98

3.74

TPOS-C60

Fragment TPP

6.22

TPOS

5.79

C60

2.69

GO

1.87

The molecular density of states for each of these complexes calculated with the PBE functional as implemented in the NRLMOL code is presented in Figure 6. The molecular density of states shows the distribution of the Kohn-Sham eigenvalues for the occupied and unoccupied orbitals. The separation between the occupied and unoccupied states is indicated by the position of the Fermi energy. In the porphyrin-fullerene complex, the HOMO and HOMO-1 are located on the porphyrin and the lowest three unoccupied orbitals originate from the fullerene (Figure 7). The degeneracy of the LUMO of the C60 is lifted due to functionalization and the complex formation. Similar behavior was noted in earlier calculations.95, 111-112 The molecular DOS plot shows that in the porphyrin-graphene oxide complex, the graphene oxide occupied states are only slightly lower (by 0.09 eV) compared to that of the porphyrin. Consequently, the HOMO and HOMO-3 orbitals of the complex are on the porphyrin but the HOMO-1 and HOMO-2 are located on the graphene oxide sheet (Figure 7). The lowest charge transfer excited state in porphyrin-fullerene complex has energy 3.02 eV that corresponds to a transition from the HOMO to LUMO, which


27


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Page 28 of 43

is higher than our earlier calculated energy of 2.63 eV for a non-bonded porphyrin-fullerene complex with an edge-on geometry.112 In the TPP-C60 complex, the edge-to-edge separation between the porphyrin and the C60 is nearly 8.9 Ao that corresponds to the smallest distance between a carbon atom on C60 and another carbon on the porphyrin macrocycle. The higher CT energy of the bonded porphyrin-fullerene complex compared to our earlier calculations on nonbonded porphyrin-fullerene complex may be attributed to the larger separation between the porphyrin and fullerene and due to the functionalization. In the TPP-GO complex, the graphene oxide sheet is attached to the porphyrin through an amide connector. The smallest C-C separation between the porphyrin macrocycle and graphene oxide is 8.1 Ao, which is smaller than the 8.9 Ao separation for the porphyrin-fullerene complex. The CT excited state in this complex, which corresponds to the electron transfer from HOMO on the porphyrin to LUMO on the graphene oxide, occurs at 3.01 eV (Table 4). In the complex with GO, the LUMO+1 and LUMO+2 spread over both the porphyrin and graphene oxide, and therefore the transitions from the HOMO to these orbitals are not fully charge transfer states. The HOMO-3 state of the TPP-GO is located on the porphyrin and corresponds to the HOMO-1 state of the isolated porphyrin. The transition from the porphyrin HOMO-1 to the LUMO of GO occurs at

2.89 eV. This result shows that reordering of the levels takes place in the TPP-GO

complex leading to a smaller CT energy from the porphyrin HOMO-1→LUMO of graphene oxide. Such reordering is not seen in the porphyrin-fullerene complex (Table 4). The dipole moment for the HOMO→LUMO charge separated states are 57.8 D in TPP-GO and 73.6 D in TPP-C60 complexes.


28

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Figure 6. The molecular density of states for: A) porphyrin-fullerene B) porphyrin-graphene oxide C) smaragdyrin-fullerene D) smaragdyrin-graphene oxide complexes.

The exciton binding energy can be estimated from the quasi-particle (QP) gap and the CT energy as EQP - ECT. The quasi particle gaps in the porphyrin-based complexes are 3.38 and 3.45 eV for the porphyrin-fullerene and porphyrin-graphene oxide complexes, respectively. For the lowest CT excitations, the exciton binding energies are 0.36 and 0.56 eV in these complexes. The exciton binding energy in the graphene oxide is higher due to larger interaction between the latter and the porphyrin.


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Page 30 of 43

Table 4. Charge transfer excited state energies resulting for the transition from frontier orbitals of the donor moieties to the lowest few unoccupied orbitals of the acceptor. The L+1 and L+2 states of TPP-GO are porphyrin virtual orbitals. All energies are in eV. Transitions TPP-C60 TPP-GO TPOS-C60 TPOS-GO HL

3.02

HL+1

2.53

3.28

3.08

2.60

2.52

HL+2

3.38

2.89

2.23

H-1 L

3.09

2.90

3.57

H-1L+1

3.46

2.96

2.92

H-1L+2

3.77

3.24

2.48

H-3L

3.01

2.89


30

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Figure 7. Charge transfer excited states: (a) TPP-C60 (b) TPP-GO (c) TPOS-C60 (d) TPOS-GO.

Smaragdyrin-based complexes. We have replaced the porphyrin in the donor-acceptor complexes by a smaragdyrin (TPOS) to examine its effect on the electronic structure of the donor-acceptor complexes studied here. The ionization potential of the isolated TPOS is 5.79 eV that is lower than that of a porphyrin. The smaragdyrins are extended macrocycles with a HOMO orbital delocalized over the whole molecule (Figure 7). The larger size of the smaragdyrin compared to porphyrin is also reflected in the lower ionization potential. We find that in both the smaragdyrin containing donor-acceptor complexes the ionization potential changes only slightly by 0.05 and 0.06 eV, respectively, for the fullerene and graphene oxide complexes. The molecular density of states plot of the smaragdyrin-fullerene shows that the fullerene HOMO is comparatively deeper than that of the smaragdyrin. Although the HOMO and HOMO-1 of the GO are close in energy


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Page 32 of 43

to those of the smaragdyrin they are slightly deeper than those of TPOS. The HOMO and LUMO are spatially separated with the HOMO on the donor and the LUMO on the acceptor moieties in the TPOS based complexes (Figure 7). The HOMO-LUMO gaps calculated with the PBE functional are lower for the smaragdyrin-based complexes compared to those of the porphyrin-based complexes. The gaps for smaragdyrin-fullerene and smaragdyrin-graphene oxide are 0.33 and 1.06 eV respectively, whereas the gaps for porphyrin-fullerene and porphyringraphene oxide are 0.75 and 1.44 eV. The large size of the smaragdyrin leads to a more spread out of HOMO levels with higher eigenvalues. The minimum smaragdyrin-fullerene lowest C-C separation is 8.9 Å whereas this separation in the complex with graphene oxide is 8.1 Å The lowest excitation state of charge transfer in the smaragdyrin-fullerene complex has the energy of 2.53 eV, which combined with the quasiparticle gap of 3.03 eV yields a binding energy of the exciton of 0.5 eV in the gas-phase. The lowest CT state in this complex has a dipole moment of 75.2 D due to the large separation between the two moieties. The HOMO to LUMO transition occurs at 3.28 eV in smaragdyringraphene oxide complex with a corresponding dipole of 80.2 D. The QP gap is largest in the smaragdyrin-graphene oxide complex at 3.74 eV and the exciton binding energy is 0.46 eV. The higher LUMO+1 and LUMO+2 in TPOS-GO are extended up to the linker molecules (amide group). The HOMO→LUMO and HOMO-1→LUMO excited states show vanishingly small singlet–triplet energy difference in the TPOS-GO complex. On the other hand, the HOMO→LUMO+1,LUMO+2 and HOMO-1→LUMO+1,LUMO+2 excited states show a singlet-triplet splitting of 0.19, 0.22 and 0.11 eV respectively in these two sets of excited states. The triplet states correspond to one electron in LUMO+1 and the other one in LUMO+2, and the


32

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hole in the HOMO and HOMO-1. Such energy differences indicate larger interaction between the particle and hole states.

4. CONCLUSIONS

In this work, we investigate the effect of the nanocarbon structures like graphene oxide and fullerene C60 on the ability of light-harvesting systems as porphyrin/smaragdyrin (expanded porphyrin) in covalently bonded complexes. Using the time-dependent DFT methodology, we calculate the UV-Vis electronic absorption spectra for the complexes and the isolated form. Firstly, a calibration procedure looking the best functional was carried out for the fragments porphyrin and smaragdyrin with functionals pure (PBE), hybrid (B3LYP, M06) and long-range corrections including the Grimme´s D2 dispersion (wB97XD). We found that the lowest deviation of the Q band (longer wavelength) occurs for the functionals M06 (0.01-0.02 eV) and B3LYP (0.05-0.03 eV), where the errors are much lower to that accepted for TD-DFT methodologies (0.2-0.3 eV). Electronic absorption spectra calculated for the complexes with M06 predict that: (a) graphene oxide increases the intensity of the Soret band; (b) fullerene produces a red-shift of the Q bands with respect to graphene oxide and (c) smaragdyrin causes a red-shift of Q (27-48 nm) and Soret (37 nm) absorption bands compared to porphyrin. We also calculated the charge-transfer excited states for the complexes using perturbative deltaSCF method with the PBE functional. For the complexes with smaragdyrin, the charge transfer energies calculated in the gas-phase range from 2.53 eV (TPOS-C60) to 3.28 eV (TPOS-GO). Replacing smaragdyrin by porphyrin led to an increase (3.01 eV) in the CT energy for the fullerene complex (TPP-C60) but decreases (2.89 eV) in the graphene oxide complex (TPP-GO).


33


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Page 34 of 43

The singlet-triplet splitting in the CT states is large in the GO based complexes due to larger interaction between the GO and the donor moieties. The ionic relaxation as well as solvation effect is not included which is likely to reduce the CT energies.

Corresponding Authors *Gloria Cárdenas-Jirón and *Tunna Baruah Email: [email protected] [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. *These authors contributed equally.

ACKNOWLEDGMENT Financial support from US department of Energy Basic Energy Sciences (DE-SC0002168) and National Science Foundation (DMR1205302) is gratefully acknowledged. TB thanks to the Texas Advanced Computing Center (TACC) from the National Science Foundation (NSF) (Grant no.TG-DMR090071) and NERSC for the computational time. GCJ thanks the financial support of CONICYT by Project FONDECYT 1131002 and USACH/DICYT for funding a visit to the Dr. Baruah´s group. It is also appreciated the visit of Prof. Tunna Baruah to Universidad


34

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de Santiago de Chile financed by FONDECYT 1131002 where part of this work was performed. MBM thanks to CONICYT by a Doctorate fellowship.

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