Role of Noncoplanar Conformation in Facilitating Ground State Hole

Article pubs.acs.org/JPCA

Role of Noncoplanar Conformation in Facilitating Ground State Hole Transfer in Oxidized Porphyrin Dyads Takashi Tsuchiya and Elena Jakubikova* Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695, United States ABSTRACT: We employ density functional theory to investigate ground state hole transfer in covalently linked oxidized zinc−zinc porphyrin ([ZnZn]+) and zinc−free-base porphyrin ([ZnFb]+) dyads in both coplanar and noncoplanar (tilted) conformations. We obtain reactant, product, and transition state (TS) for the hole transfer reaction in the [ZnZn]+ system. The hole is localized on a single porphyrin unit in the reactant and product states while delocalized in the TS, implying the dominance of superexchange mechanism in the hole transfer reaction. A metastable as well as stable states are located for the [ZnFb]+ system while no TS is found, indicating a barrierless hole transfer reaction. The hole lifetimes are calculated to be 15.80 and 0.034 ns for [ZnZn]+ in the coplanar and tilted conformation, respectively, and 14.45 and 0.313 ns for [ZnFb]+. The hole transfer rates are found to be several orders of magnitude faster in the tilted conformation than in the coplanar conformation for both dyads, showing the importance of noncoplanar conformation between the two porphyrin pigments in facilitating the hole transfer process. We also show that inclusion of solvent effects in calculations plays an important role in the proper ground state hole localization in oxidized dyads. These results provide an unconventional insight into the hole transfer mechanism in porphyrin arrays and are relevant to design of artificial photoharvesting materials.

1. INTRODUCTION Porphyrins and their derivatives play an essential role in artificial light-harvesting systems that mimic the highly efficient photosynthetic energy conversion that occurs in nature.1−3 Among them, covalently linked porphyrin arrays are increasingly interesting as simplified models of the natural photosynthetic antenna pigments and have been extensively studied both experimentally4−7 and theoretically.8−10 The photosynthesis is initiated by the absorption of solar light, followed by the excitation energy transfer to the reaction center. At the reaction center, an electron−hole pair is created and spatial charge separation takes place by means of the electron and hole migration.11 Charge (either electron or hole) migration process has been investigated in a variety of covalently linked arrays.12−15 Charge transfer can be divided into two large categories. First is the through space charge transfer,16−18 in which the charge transfers from one porphyrin to another by means of direct overlap of wave functions of the initial and final states. Second is the through bond charge transfer,19−25 in which the charge transfers from one pigment to another via the linker molecule connecting the two pigments. For the through bond charge transfer process, two different mechanisms have been further proposed: (1) the wirelike mechanism,19−22 in which a localized charge hops from one porphyrin to linker molecule and then to the next porphyrin; (2) the superexchange mechanism,23−25 in which linker orbitals mediate the superexchange between two adjacent porphyrins, and therefore charges are not found as discrete particles during the charge transfer process. © 2012 American Chemical Society

A number of experimental studies determining the rate of the ground state hole transfer between covalently linked equivalent and nonequivalent porphyrin sites have been performed.4,26−31 Seth et al. determined a lower limit of ∼(200 ns)−1 for the hole transfer rate between equivalent sites in the phenyl-linked zinc porphyrin dyad by static electron paramagnetic resonance (EPR) spectroscopy measurements.27 Thamyongkit et al. also employed EPR spectroscopy to determine the lower limit of ∼(50 ns)−1 for the hole transfer between equivalent zinc porphyrins.28 Recently, Song et al. measured ∼(20 ps)−1 ground state hole transfer rate in a covalently linked nonequivalent porphyrin dyad composed of free-base and zinc porphyrins by means of the transient optical spectroscopy.29 This serves as an upper limit to the rate of the ground state hole transfer between equivalent porphyrins, because the driving force is larger for the hole transfer between nonequivalent porphyrins than for the hole transfer between equivalent porphyrins. Song et al. also developed the means to measure the hole transfer rate between equivalent zinc porphyrin sites in porphyrin arrays. They utilized time-resolved optical spectroscopy and obtained the rate constant of (0.6 ns)−1 for the ground state hole transfer between equivalent zinc porphyrins connected by a phenyl linker. Song et al. also investigated the distance dependence of the rate constant in free-base−zinc porphyrin dyads connected by a Received: July 23, 2012 Revised: September 8, 2012 Published: September 10, 2012 10107

dx.doi.org/10.1021/jp307285z | J. Phys. Chem. A 2012, 116, 10107−10114

The Journal of Physical Chemistry A

Article

Figure 1. Structures of oxidized zinc−zinc ([ZnZn]+) and zinc−free-base ([ZnFb]+) porphyrin dyads.

Figure 2. Optimized structures of [ZnZn]+ in the coplanar (left) and tilted (right) conformations.

variety of linker molecules differing mainly in their length.30 They found only weak distance dependence in the rate of the ground state hole transfer. In the same study, they performed density functional theory (DFT) calculations on the linker molecules and compared the highest occupied molecular orbital (HOMO) energies between various linker molecules and porphyrins. They concluded that the energy barriers the hole needs to overcome to hop from a porphyrin to linker site are too large for the wirelike process to be likely. These results together imply that the superexchange mechanism should be exceedingly favored over the other. However, in their theoretical study, Felts et al. predicted an observation of the wirelike charge transfer under appropriate experimental conditions,32 and Goldsmith et al. pointed out the difficulty of distinguishing between the superexchange and hopping mechanisms, while claiming that the latter should be favored.33 There are a number of studies investigating the influence of linker molecule and the donor−acceptor distance on the charge transfer processes in porphyrin-related arrays.26,30,34,35 While the character of linker group and donor−acceptor distance are some of the key elements that influence the charge transfer rate, relative orientation of the porphyrin pigments is another fundamental factor that could impact the charge transfer mechanism. To our knowledge, studies investigating the effect of the relative orientation of porphyrin pigments on the charge transfer process are not readily available in the literature. Therefore, one of our research foci is placed on the porphyrin− porphyrin orientation dependence of the hole transfer activity. In the present study, we employ density functional theory (DFT) to investigate ground state hole transfer in equivalent and nonequivalent oxidized porphyrin dyads, zinc−zinc ([ZnZn]+) and zinc−free-base ([ZnFb]+), connected by a phenyl linker (Figure 1). We locate the transition state for [ZnZn]+ and the metastable state for [ZnFb]+ along their respective hole transfer reaction paths, elucidate the mechanism

of the hole transfer reactions, and examine the influence of the relative orientation of the two porphyrin pigments on the hole transfer rate constant. We also show the role of solvent molecules for the ground state hole localization and the importance of including the solvent effects in the computational studies of porphyrin systems. Results obtained provide us not only with an unconventional viewpoint of the charge transfer mechanism in porphyrin array systems but also with a guidepost on a pathway to design of artificial porphyrin-based architectures to achieve closer mimicry of natural light-harvesting systems.

2. COMPUTATIONAL METHOD The ground state geometries and energies were calculated at the density functional theory (DFT)36 level together with the B3LYP exchange-correlation functional37 using the Gaussian 0938 suite of programs. LANL0839 effective core potential (ECP) and the associated basis set were employed for zinc atoms, while the 6-31G* basis set40 was employed for all other atoms. All calculations were performed considering the solvent effect by means of the polarizable continuum model (PCM)41 using benzonitrile (PhCN) as the solvent, if not otherwise stated. All strcutures were optimized either in vacuum or in solution using the PCM. Figure 2 shows the optimized structures of [ZnZn]+ in both coplanar and tilted (noncoplanar) conformations. The coplanar and tilted conformations differ in relative orientation of the two porphyrin pigments. Note that relative orientations between each porphyrin pigment and phenyl group are almost identical in both conformations. Although only [ZnZn]+ structures are shown in Figure 2, similar optimized structures were obtained for [ZnFb]+. Table 1 shows the optimized tilt (dihedral) angles between both porphyrin−phenyl and porphyrin−porphyrin rings. Pophyrin−phenyl tilt angles are ∼60° in all dyads, while poprphyrin−porphyrin tilt angles are 0°∼6° in the coplanar 10108



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3.1. Solvent Effects. In this section, we investigate the influence of the solvent on the hole localization in the porphyrin dyads. As shown in Figure 4, the hole in the oxidized

Table 1. Porphyrin−Phenyl and Porphyrin−Porphyrin Tilt Angles (in deg) for the Oxidized Zinc−Zinc and Zinc−FreeBase Porphyrin Dyads in the Coplanar and Tilted Conformations coplanar a

+c

[ZnZn] [ZnZn]+‡d ZnFb+e Zn+Fbg

tilted b

P−Ph

P−P

56.46 55.81 64.15 58.97

6.04 0.03 1.19 4.20

a

P−Ph

P−Pb

56.07 57.00 (60.97)f 56.85

64.60 65.27 (62.26)f 62.93

a

Porphyrin−phenyl angle. bPorphyrin−porphyrin angle. cOxidized zinc−zinc porphyrin dyad. Equilibrium state. dOxidized zinc−zinc porphyrin dyad. Transition state. eOxidized zinc−free-base pophyrin dyad. Metastable state. fApproximate structure. See text in section 3.3.2. gOxidized zinc−free-base porphyrin dyad. Stable state.

dyads and ∼60° in the tilted dyads. Vibrational frequency analysis was performed for each optimized structure to ensure that they are either the minimum energy structures or the transition state (TS) structures. Connectivity of the TS to the reactant and product states was confirmed by the intrinsic reaction coordinate (IRC)42 calculations. Hole transfer reaction rates were calculated by means of the Marcus equation43 k = |V |2

Figure 4. Singly occupied natural orbitals (SONOs) of oxidized zinc− zinc ([ZnZn]+) and zinc−free-base ([ZnFb]+) porphyrin dyads at coplanar conformation in vacuum and in solution (acetonitrile). Solvent effects were incorporated through the polarizable continuum model (PCM).

⎧ (ΔE + E )2 ⎫ π λ ⎨− ⎬ exp 4EλkBT ⎭ ℏ2kBTEλ ⎩

coplanar zinc−zinc porphyrin dyad ([ZnZn]+) is delocalized over the entire molecule in vacuum, while localized on one of the zinc porphyrin units in solution (acetonitrile). In the same way, the hole in oxidized coplanar zinc−free-base porphyrin dyad ([ZnFb]+) is delocalized in vacuum, while localized on the zinc porphyrin unit in solution. The inclusion of solvent effects in calculations drastically changes the electronic structure of porphyrin dyads. Table 2 shows the ionization potentials (IPs) calculated for zinc porphyrin and free-base porphyrin monomers. The IPs are

where ℏ = h/2π, h is Planck's constant, kB is the Boltzmann constant, and T is the temperature. In the current work, T is set to be 300 K. The driving force (ΔE), reorganization energy (Eλ), and electronic coupling constant (V) are defined as shown in Figure 3. Time dependent DFT (TDDFT)44,45 was used to

Table 2. Calculated Ionization Potentials (in eV) of Zinc (Zn) and Free-Base (Fb) Porphyrin Monomersa Figure 3. Schematic representation of the adiabatic (broken line) and nonadiabatic (solid line) potentials and the driving force (ΔE), reorganization energy (Eλ), and electronic coupling constant (V) for the hole transfer reaction in the oxidized zinc−zinc ([ZnZn]+, left) and zinc−free-base ([ZnFb]+, right) porphyrin dyads.

Zn Fb

vacuum

1 PhCNb

2 PhCNb

PCM

5.931 5.896

5.491 5.779

5.290 5.578

4.895 5.023

a Ionization potentials are calculated as the total energy differences between neutral and cationic systems. bThe entire system was embedded in vacuum.

calculate the reorganization energies, Eλ. Eλ were obtained as the excitation energy to the excited state corresponding to the product electronic state at the reactant geometry with (for [ZnFb]+) or without (for [ZnZn]+) −ΔE added. Electronic coupling constants46 were calculated using either the molecular structure at TS (for [ZnZn]+) or metastable state (for [ZnFb]+) at the Hartree−Fock (HF) level of theory using the NWChem47 program.

almost identical for zinc and free-base porphyrins in vacuum (5.931 and 5.896 eV, respectively). However, the IP of zinc porphyrin becomes lower than the IP of free-base porphyrin in solution, and, therefore, zinc porphyrin is selectively oxidized in solution, which makes the hole localized on the zinc porphyrin unit. A large alteration of the IP of zinc porphyrin can be observed already when a single solvent molecule is added to the system; the IP decreases by 0.44 to 5.491 eV for zinc porphyrin, while the IP of the free-base porphyrin is lowered only by 0.12 to 5.779 eV. This is dominantly due to a stronger interaction between zinc porphyrin and a solvent molecule through zinc cation. Interestingly, when a second solvent molecule is added, IPs decrease by 0.2 eV for both zinc (to 5.290 eV) and free-base (to 5.578 eV) porphyrins. At the PCM limit, the difference in

3. RESULTS AND DISCUSSION Hereafter, we use the following notation to represent different electronic states of the oxidized porphyrin dyads: [ZnZn]+ and [ZnFb]+ denote the oxidized porphyrin dyads in general; Zn+Zn, ZnZn+, Zn+Fb, and ZnFb+ describe the hole localized states; [ZnZn]+‡ denotes the TS. 10109



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the ionization potential between zinc and free-base porphyrins is 0.128 eV, with zinc porphyrin being lower (4.896 eV for zinc porphyrin vs 5.023 eV for free-base porphyrin), which compares reasonably well with the experimental value of ∼0.2 eV.27 The role that solvent molecules play in changing the electronic structure of porphyrin dyads can be seen in Figure 5, which shows [ZnFb]+ with one and two explicit solvent

Figure 6. Singly occupied natural orbitals (SONOs) of oxidized zinc− zinc porphyrin dyad ([ZnZn]+) at the reactant (Zn+Zn, left), transition state ([ZnZn]+‡, middle), and product (ZnZn+, right) in the coplanar conformation.

Figure 5. Optimized structures and singly occupied natural orbitals (SONOs) of oxidized zinc−free-base porphyrin dyad ([ZnFb]+) with one solvent molecule (left) and two solvent molecules (right) attached to the zinc porphyrin unit.

molecules. The solvent molecule (acetonitrile) interacts attractively with the zinc cation via the cyanide group and at the same time draws the positively charged hole toward the zinc porphyrin site. Upon the attachment of the second solvent molecule, the hole almost completely localizes on the zinc porphyrin unit. Solvent molecules also influence the position of the zinc cation in the porphyrin ring. As can be seen in the structures shown in Figure 5, the first solvent molecule draws the zinc cation out of the porphyrin plane defined by four pyrrole units, while the second solvent molecule draws the zinc cation back into the plane.48 In the PCM treatment of the solvent effects, the zinc cation always remains in the plane. In [ZnZn]+, the first solvent molecule attached to either porphyrin decreases the ionization potential of that particular porphyrin which is then selectively oxidized, resulting in the hole localization on one of the porphyrin units. As was the case for zinc cation in [ZnFb]+, change in the position of the zinc cation in the porphyrin ring caused by the solvent molecules was observed. Due to the importance of the solvent effects for the hole localization in both [ZnZn]+ and [ZnFb]+ porphyrin dyads, all subsequent calculations are performed in acetonitrile, employing the PCM. 3.2. Hole Transfer in Zinc−Zinc Porphyrin Dyad. 3.2.1. Coplanar Conformation. Figure 6 depicts the hole transfer mechanism in [ZnZn]+. The two porphyrin units are coplanar with small tilt angles, 6.04° in the equilibrium and 0.03° in the TS structures (Table 1). Reactant and product lie at the same energy level, and the reaction barrier is calculated to be 0.250 kcal/mol. The hole is delocalized over the entire molecule in the transition state (TS). Vibrational frequency analysis has confirmed single imaginary frequency in the TS, 3888i cm−1. The vibrational mode corresponding to this imaginary frequency is shown in Figure 7. The imaginary vibrational mode can be described as the

Figure 7. Schematic representation of the imaginary vibrational mode (red arrows) at the transition state of oxidized zinc−zinc porphyrin dyad ([ZnZn]+‡).

“breathing” motion involving all eight pyrrole units in the dyad. Table 3 compares the carbon−carbon distances in the pyrrole units between Zn+Zn/ZnZn+ with the localized hole (reactant and product) and [ZnZn]+‡ with the delocalized hole (TS). In Zn+Zn/ZnZn+, the C−C distances in the oxidized porphyrin unit are shorter (2.206 Å on average) than those in [ZnZn]+‡ Table 3. Carbon−Carbon Distances (in Å) in the Pyrrole Units in Zinc−Zinc Porphyrin Dyad at the Reactant/Product (Zn+Zn/ZnZn+) and Transition State ([ZnZn]+‡) in the Coplanar and Tilted Conformations Zn+Zn/ZnZn+ coplanar tilted

[ZnZn]+‡

Zna

Zn+b

Zn1/2+a

Zn1/2+b

2.217 2.216

2.206 2.208

2.212 2.212

2.212 2.212

a

Average of the four distances represented by the red lines. bAverage of the four distances represented by the blue lines.

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(2.212 Å on average), while the C−C distances in the neutral unit of Zn+Zn/ZnZn+ are longer (2.217 Å on average). These differences are consistent with the imaginary vibrational mode (i.e., the breathing mode) found in the TS. These results suggest that the hole transfer occurs via the superexchange mechanism rather than the wirelike hopping. In fact, no hole state localized on the bridge was found. 3.2.2. Tilted Conformation. The same set of calculations was performed for [ZnZn]+ in the tilted conformation, in which the two porphyrin units are not coplanar (Figure 8). The geometry

Table 4. Driving Forces (ΔE), Reorientation Energies (Eλ), and Electronic Coupling Constants (V) for the Hole Transfer Reaction in Oxidized Zinc−Zinc ([ZnZn]+) and Zinc−Free-Base ([ZnFb]+) Porphyrin Dyads in the Coplanar and Tilted Conformationsa [ZnZn]+ energy

b

coplanar

tilted

coplanar

tilted

0.008 6.091 0.181

0.001 7.036 4.036

−3.693 8.416 0.205

−6.143 12.392 1.534

ΔE Eλ V a

[ZnFb]+

Values are in kcal/mol. bFor definition, see Figure 3.

introducing larger overlap between the reactant and product wave functions. This results in a significant difference in the rate constants between the two conformations. The calculated lifetimes (k−1) of the holes in [ZnZn]+ are 15.80 ns for the coplanar conformation and 0.034 ns for the tilted conformation as shown in Table 5. The hole transfer rate for tilted [ZnZn]+ is in fact 465 times faster than the rate for coplanar [ZnZn]+.

Figure 8. Singly occupied natural orbitals (SONOs) of oxidized zinc− zinc porphyrin dyad ([ZnZn]+) at the reactant (Zn+Zn, left), transition state ([ZnZn]+‡, middle), and product (ZnZn+, right) in the tilted conformation.

Table 5. Calculated Rate Constants (k) of the Hole Transfer Reaction in Oxidized Zinc−Zinc ([ZnZn]+) and Zinc−FreeBase ([ZnFb]+) Porphyrin Dyads in the Coplanar and Tilted Conformations Calculated at 300 K

optimization calculated the tilt angle to be 64.60° at the reactant structure and 65.27° at the TS structure (Table 1). The total energy of the reactant state of the tilted [ZnZn]+ was calculated to be lower by 0.559 kcal/mol than that of the coplanar [ZnZn]+. As Figure 8 shows, the hole is slightly more delocalized in the reactant and product states compared to their coplanar counterparts, in which the hole is almost completely localized (compare Figures 6 and 8). In the tilted dyad, 68% of the hole is localized on the porphyrin ring of the oxidized unit and 15% is on the neutral unit, while 78% and 6% of the hole are localized on the oxidized and neutral units, respectively, in the coplanar dyad. This indicates that the electronic interaction between the two porphyrins is stronger in the tilted [ZnZn]+ than in the coplanar [ZnZn]+. Next, we found the TS for the hole transfer reaction process in the tilted [ZnZn]+. At the TS, the hole is delocalized over the two porphyrin units as shown in Figure 8. The energy barrier, 0.054 kcal/mol, is five times smaller than that for the coplanar [ZnZn]+ (0.250 kcal/mol). Only one imaginary vibrational frequency, 982i cm−1, was calculated by the vibrational frequency analysis, which is approximately 4 times smaller than that of the coplanar [ZnZn]+ (3888i cm−1). The vibrational mode corresponds to the breathing motion of the pyrrole rings, just like in the case of the coplanar [ZnZn]+. The smaller value of the imaginary frequency indicates that the pyrrole units are more flexible and can change their shape more easily in the tilted conformation, which is consistent with the lower activation energy. These results again indicate that the hole transfer in [ZnZn]+ dyad occurs via the superexchange mechanism. 3.2.3. Hole Transfer Rates. The calculated driving forces (ΔE), reorganization energies (Eλ), and electronic coupling constants (V) for the hole transfer reaction are listed in Table 4. While the ΔE and Eλ are almost identical between the coplanar and tilted conformations, the coupling constant (V) is dramatically different. The V for the tilted [ZnZn]+ (4.036 kcal/mol) is 23 times larger than the V for the coplanar [ZnZn]+ (0.181 kcal/mol). This is consistent with the fact that the holes in the reactant and product states are less localized in the tilted [ZnZn]+ than the coplanar [ZnZn]+, therefore

lifetime (k−1) reaction Zn+Zn → ZnZn+

ZnFb+ → Zn+Fb

a

coplanar tilted weighted meanb coplanar tilted weighted meanb

calcd (ns)

exptla (ns)

15.80 0.034 4.5 14.45 0.313 0.34

0.6 ± 0.1 ns

0.017 ± 0.0017 ns

Reference 29. bSee text in Section 3.2.3.

An interesting fact is that the experimental value, 0.6 ns,29 is almost the average of these two calculated values. Assuming the Boltzmann distribution at 300 K, the conformation is 2.55 times more probable to be tilted than to be coplanar. Therefore, the weighted average of the hole lifetime is calculated to be 4.5 ns, which agrees reasonably well with the experimental value. This indicates that, under the experimental conditions, porphyrin units are changing their relative orientation almost freely and continually, and therefore the rate actually measured is the average of the rates for all the possible tilt angles. Note the very small energy difference between the coplanar and the tilted structures (0.559 kcal/ mol), and the small energy barrier (∼2 kcal/mol) for changing the relative orientation between the coplanar and tilted structures as shown in Figure 9. The barrier height shown in Figure 9 represents an upper limit since the [ZnZn]+ structure is not optimized in this estimate of the barrier height for the tilting motion. Also to note is the fact that the hole transfer rate is significantly faster in the tilted [ZnZn]+. These results suggest that, by fixing the relative orientation of the Zn units to be tilted, faster hole transfer rates can be achieved. In addition, the hole transfer rate can be controlled by altering the relative orientation of porphyrin pigments. 3.3. Hole Transfer in Zinc−Free-Base Porphyrin Dyad. 3.3.1. Coplanar Conformation. Figure 10 shows the hole transfer reaction mechanism in the coplanar [ZnFb]+ dyad. The 10111



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rings are shown in Table 6. Regardless of being a zinc porphyrin or a free-base porphyrin, the C−C distances in the Table 6. Carbon−Carbon Distances (in Å) in the Pyrrole Units in Zinc−Free-Base Porphyrin Dyad at the Metastable (ZnFb+) and Stable (Zn+Fb) States in the Coplanar and Tilted Conformations Zn+Fb Zn coplanar tilted

+a

2.206 2.206

ZnFb+ b

a

Fb

Zn

2.222 2.222

2.232 (2.232)c

Fb+b 2.204 (2.204)c

a

Average of the four distances represented by red lines. bAverage of the four distances represented by blue lines. cApproximate structure. See text in Section 3.3.2.

+

Figure 9. Energies of oxidized zinc−zinc porphyrin dyad ([ZnZn] ) relative to the minimum energy with respect to the tilt angle between two porphyrins. Only tilt angle is varied, and all other geometrical parameters are fixed to the values at the minimum structure with tilt angle of 64.60°.

oxidized unit (2.206 Å for Zn+ and 2.204 Å for Fb+) are shorter than their counterparts in the neutral unit (2.232 Å for Zn and 2.222 Å for Fb), which is equivalent with the results obtained for [ZnZn]+. 3.3.2. Tilted Conformation. Figure 11 shows the hole transfer mechanism in the tilted [ZnFb]+. The stable minimum (Zn+Fb) of the tilted conformation was calculated to be lower in energy than that of the coplanar conformation by 0.280 kcal/ mol. The porphyrin−porphyrin tilt angle in the stable state (Zn+Fb) was calculated to be 62.93°. The structure of the

Figure 10. Singly occupied natural orbitals (SONOs) of oxidized zinc−free-base porphyrin dyad ([ZnFb]+) at the reactant/metastable (ZnFb+, left) and product/stable (Zn+Fb, right) states in the coplanar conformation.

hole is localized on the free-base porphyrin unit in the metastable state (ZnFb+), while it is localized on the zinc porphyrin unit in the stable state (Zn+Fb). No TS was found for this system. Experimentally, the ZnFb+ state can be obtained upon excitation of Zn+Fb as a result of an excited state decay pathway.29 Although it is a minimum point of one potential energy surface, as the barrier to the hole transfer is almost zero due to the interaction with other closely lying potential surfaces, ZnFb+ is relatively short-lived and, therefore, metastable. Both stable and metastable states are the ground states at their respective molecular structures (refer to Figure 3). The porphyrin−porphyrin tilt angles are 4.20° in the stable state and 1.19° in the metastable state. The energy of the metastable state is higher by 3.693 kcal/mol than that of the stable state, and the reaction is predicted to be barrierless. Three imaginary frequencies (26i, 14i, and 0.8i cm−1) were found by the vibrational frequency analysis of the metastable state. However, each imaginary frequency corresponds to the rotation of one of methyl groups, which does not have any effect on the electronic structure of the state. Therefore, we took the structure as the optimized minimum. The average carbon−carbon distances in the pyrrole units in the porphyrin

Figure 11. Singly occupied natural orbitals (SONOs) of oxidized zinc−free-base porphyrin dyad ([ZnFb]+) at the reactant/metastable (ZnFb+, left) and product/stable (Zn+Fb, right) states in the tilted conformation. 10112



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metastable state (ZnFb+) in the tilted conformation could, however, not be obtained. Instead, we have calculated an approximate metastable state (ZnFb+) in the tilted conformation; we took the metastable (ZnFb+) structure in the coplanar conformation and tilted it by 61.07° with all the other geometrical parameters unchanged. The metastable state is 6.143 kcal/mol higher in energy than the stable state. The electronic structure of the metastable state (ZnFb+) in the tilted conformation is not a highly localized state anymore; 23% of the hole has populated the zinc porphyrin unit, while 61% of the hole remains on the free-base porphyrin unit, which is compared to 6% on the zinc porphyrin ring and 78% on the free-base porphyrin ring in the coplanar conformation. This indicates that the metastable state (ZnFb+) in the tilted conformation either does not exist or is considerably unstable and very short-lived. 3.3.3. Hole Transfer Rates. The calculated ΔE, Eλ, and V for the hole transfer reactions are listed in Table 4, and the hole transfer rates are shown in Table 5. The hole lifetimes in the [ZnFb]+ are calculated to be 14.45 ns for the coplanar conformation and 0.313 ns for the tilted conformation. The calculated lifetimes are longer than the experimental value of 0.017 ns29 by 1−3 orders of magnitude. The Boltzmannweighted mean of these lifetimes at 300 K is 0.34 ns, which again agrees reasonably well with experimental value. Note that we were unable to locate the transition state for this hole transfer reaction, and therefore the coupling constant, V, was calculated at the reactant, rather than transition state, structure. It is, however, quite likely that the TS exists even though the barrier height is negligibly small. The calculation of the coupling constant at the TS structure could possibly yield a larger value of V and shorter calculated lifetime in better agreement with the experimental value. It is also important to note that the calculated hole lifetimes for [ZnZn]+ and [ZnFb]+ systems are in both cases longer than the experimentally measured lifetimes (see Table 5, compare weighted mean with experimental values). While our calculations are not able to determine the hole lifetimes within the experimental error, they are reliable at reproducing the trends in the measured hole lifetimes among the systems. As is the case for the [ZnZn]+, the hole transfer rate in the [ZnFb]+ is faster in the tilted conformation than in the coplanar conformation; the rate constant for the tilted conformation is 46 times larger than that for the coplanar conformation. This is consistent with the larger value of V in the tilted conformation (1.534 kcal/mol for tilted conformation vs 0.205 kcal/mol for coplanar conformation) due to more delocalized nature of the electronic structure in the tilted conformation. These results again suggest that the control of the hole transfer rate can be achieved by changing the relative orientation of porphyrin units in the dimer. These ideas can be practically applicable to molecular design of artificial light-harvesting systems,1 as well as to the development of molecular photonic devices.49

The hole is localized on the single porphyrin unit in the equilibrium state while delocalized on both units in the TS. At the TS ([ZnZn]+‡), the imaginary vibrational mode corresponds to the breathing motion involving pyrrole subumits of the porphyrin rings. These results indicate that the hole transfer in [ZnZn]+ follows the superexchange mechanism. The hole has been found to be somewhat delocalized at the equilibrium structures in the tilted [ZnZn]+ while almost completely localized in the coplanar [ZnZn]+. The activation energy of the hole transfer reaction in the tilted [ZnZn]+ is found to be lower than that of the coplanar [ZnZn]+ (0.054 kcal/mol in tilted [ZnZn]+ versus 0.250 kcal/mol in coplanar [ZnZn]+). The electronic coupling constant of the tilted [ZnZn]+ is larger than that of the coplanar [ZnZn]+, indicating a larger overlap between the wave functions of the reactant (Zn+Zn) and product (ZnZn+) states in the tilted conformation. The hole transfer rate in [ZnZn]+ is calculated to be faster in the tilted conformation than in the coplanar conformation by the factor of 465. The hole transfer in [ZnFb]+ is predicted to be barrierless with no TS found along the reaction path. Although stable electronic structures (Zn+Fb) have been found for both coplanar and tilted conformations, the metastable electronic state (ZnFb+) is found for the coplanar conformation only. Due to the strong coupling between the stable (Zn+Fb) and metastable (ZnFb+) states in the tilted conformation, the metatable state (ZnFb+) can be considered to be very shortlived or nonexistent. Our results elucidate the ground state hole transfer mechanism occurring in natural and artificial systems, as well as introduce unconventional insights into practical aspects of the molecular design of artificial photoharvesting architectures. Among others, we elucidate the importance of noncoplanarity in mediating the hole transfer processes in porphyrin arrays and suggest the possibility of controlling the hole transfer rates by constraining the relative orientation of neighboring pigments.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the North Carolina State University (Department of Chemistry).

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4. CONCLUSIONS In this work, we investigated the ground state hole transfer mechanism in porphyrin arrays. The DFT calculations have been performed for the oxidized form of the equivalent and nonequivalent porphyrin dyads, [ZnZn]+ and [ZnFb]+. Calculations have shown that the explicit solvent molecules are involved in the localization process of the hole state, and the inclusion of the solvent effects, either implicitly or explicitly, is vital in the computational studies of porphyrin systems. 10113



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NOTE ADDED AFTER ASAP PUBLICATION This article posted ASAP on September 10, 2012. Tables 3 and 6 have been revised. The correct version posted on October 10, 2012.

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Role of Noncoplanar Conformation in Facilitating Ground State Hole

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