The excited-state properties and photoinduced charge-transfer (CT) kinetics in a series of symmetrical and asymmetrical Zn- and Au-ligated meso–meso-connected bacteriochlorin (BChl) complexes are studied computationally. BChl derivatives, which are excellent near-IR absorbing chromophores, are found to play a central role in bacterial photosynthetic reaction centers but are rarely used in artificial solar energy harvesting systems. The optical properties of chemically linked BChl complexes can be tuned by varying the linking group and involving different ligated metal ions. We investigate charge transfer in BChl dyads that are either directly linked or through a phenylene ring (1,4-phenylene) and which are ligating Zn or Au ions. The directly linked dyads with a nearly perpendicular arrangement of the BChl units bear markedly different properties than phenylene linked dyads. In addition, we find that the dielectric dependence of the intramolecular CT rate is very strong in neutral Zn-ligated dyads, whereas cationic Au-ligated dyads show negligible dielectric dependence of the CT rate. Rate constants of the photo induced CT process are calculated at the semiclassical Marcus level and are compared to fully quantum mechanical Fermi’s golden rule based values. The rates are calculated using a screened range separated hybrid functional that offers a consistent framework for addressing environment polarization. We study solvated systems in two solvents of a low and a high scalar dielectric constant.

Singly and doubly hydrogenated porphyrins, chlorins, and bacteriochlorins (BChls), respectively, are the core macrocycles of key pigments in photosystems (PSs).1–3 Their electronic, optical, and redox properties markedly differ from those of porphyrins. For example, hydroporphyrins exhibit a significantly enhanced absorption and emission in deep-red (chlorins) and near-IR (bacteriochlorins) spectral windows.2 Hydroporphyrins are easier to oxidize and harder to reduce compared to their porphyrin analogs4 and appear to be more prone for photoinduced charge transfer (CT).5,6

In photosystems, the light absorbing pigments are made of BChls and chlorin derived pigments, and, in particular, include the special pair, a dimer of BChls or chlorins, that functions as the primer for the cascade of energy and electron-transfer steps leading to the photosynthetic function.5,7 Excitonic states within the pair are the donor states of the electron-transfer photosynthesis process. CT from the photoexcited BChl special pair to the adjacent bacteriopheophytin is the initial step in the electron-transfer process in bacterial reaction center based photosynthesis.7–17 The actual mechanism by which the special pair is coupled to the CT process and the particular role of an intrapair CT state remain under debate.17–23 

Asymmetry in the special pair has been indicated to lead to a CT state that is coupled to excitonic special pair states.19,23–26 More specifically, orientation of functional groups is suggested to affect a symmetry broken charge density and, therefore, also the CT states in the semi-symmetric pair.27–29 Recently, we addressed the relationship of spatial asymmetry in the special pair with the intrapair CT23 and explained measured17 excitonic splitting as affected by the dielectric environment in the photosystem (PS).22 There remains the need to understand at the molecular level structure–function relationships affecting the photoinduced CT in the context of designing artificial solar energy molecular harvesting systems.30–32 

Arrays containing hydroporphyrins33 are studied as mimics of the units within PSs34 and for the design of effective artificial light harvesting systems.35 Chlorin and BChl arrays are formed by ethynyl or butadienyl linkers,36 where the strongly coupled hydroporphyrin optical properties are significantly altered compared to the monomers.36 For example, the positions at which the macrocycles are connected and the dihedral angle between the macrocycles are found to strongly affect the optical properties.37 

Photoinduced CT in symmetrical BChl arrays has been analyzed computationally, and intermolecular CT was observed for complexes of bacteriochlorophyll derivatives.38–40 Wasielewski and Tamiaki prepared and examined a series of covalently linked dyads, containing bacteriochlorophyll derivatives.41,42 Jakubikova examined the electronic properties of a series of strongly and weakly conjugated BChl arrays.43 Wahadoszamen et al. studied CT in synthesized BChl proteins.44 We studied the photoinduced CT in a series of BChl derived dimers exploring the dependence on the intrapair distance.40,45,46 In addition, dyads consisting of BChl complexes are found through computational studies to be associated with favorable CT kinetics over those of the porphyrin or chlorin based dyads.45 

Directly linked (i.e., without any intervening spacer) tetrapyrrolic arrays are of particular interest.47 In these systems, where the pigments are aligned perpendicularly, the coupling is not through the π-bonding conjugation. The short distance between macrocycles results in strong through space coupling that widely affects the optical properties, compared to those of the corresponding monomers.48,49 These trends are affected in spite the orthogonal orientation of the pigments enforced by the steric interactions.50 In this regard, the directly linked tetrapyrrolic arrays represent an intermediate case between strongly conjugated arrays51 and weakly conjugated arrays.37 

There still remains the need to explore arrays of hydroporphyrins to enhance our understanding of their optical and CT properties. In particular, effects of electronic asymmetry in a heterodimer special pair of mutated bacterial reaction centers on CT and subsequent photoinduced dynamics were studied.20,21,52 Furthermore, CT in bacteriochlorophyll arrays seems to play a crucial role in light harvesting photosynthetic antenna.44,53 It is, therefore, imperative to better understand the effect of redox properties of constituent pigments as well as electronic and redox asymmetry in electronically coupled pigments on the CT character of the derived dyads. Such knowledge should help us understand the photophysics of natural photosynthetic arrays and to develop improved artificial solar energy conversion systems. However, to the best of our knowledge, the synthesis and study of directly linked chlorin or BChl arrays and of asymmetric derived dyads is scarce.40,54

Below, we study molecular dimers and dyads consisting of BChl units that are either directly linked or bonded through a phenyl spacer and which are ligating a pair of a single Zn(II) or Au(III) ions. Zn(II) ligated BChls are known to be easier to oxidize and, therefore, are expected to present enhanced photoinduced CT.55 Au(III) ligated BChls, on the other hand, result in a charged complex and, therefore, present a weaker solvent-dependent CT process.56 We computationally investigate the dependence of photoinduced CT on the polarity of the solvent contrasting the cationic Au-ligated systems to the neutral Zn-ligated systems and compare the CT in directly linked and phenyl-linked BChl dimers or dyads. Photoinduced CT in the asymmetric and symmetric BChl systems, where either the Zn(II) or Au(III) centers are ligated by one or both of the rings, is addressed. We calculate CT rates using a well benchmarked protocol57 at the Fermi golden rule (FGR) level and, for comparison, the rates at the semiclassical Marcus theory level. We employ the state of the art electronic structure framework that addresses the environment polarization consistently combining a screened range-separated hybrid (SRSH) functional with a polarizable continuum model (PCM) (SRSH-PCM).58 

We study molecular dimers of BChl units that are either directly linked, noted as BC1, or phenyl-linked, noted as BC2. The complexes are ligated by a single Zn(II) or Au(III) ion or pairs of these ions. The symmetrically ligated complexes are noted as ZnBC or AuBC, and the singly ligated complexes are noted as aZnBC or aAuBC. The studied set of the symmetric and asymmetric Zn- and Au-ligated complexes is shown in Fig. 1. The type of the linker and total charge of the complex for the different considered systems are detailed in Table I.

FIG. 1.

Series of symmetric and asymmetric Zn- and Au-ligated BChl linked dimers. See listed properties of overall charge and linker length in Table I.

FIG. 1.

Series of symmetric and asymmetric Zn- and Au-ligated BChl linked dimers. See listed properties of overall charge and linker length in Table I.

Close modal
TABLE I.

Central ring ligated metal ions, number of phenyl rings in the linker (n), and total charge (q).

ComplexM1M2nq
ZnBC1 Zn Zn 
ZnBC2 Zn Zn 
aZnBC1 Zn H; H 
aZnBC2 Zn H; H 
AuBC1 Au Au 
AuBC2 Au Au 
aAuBC1 Au H; H 
aAuBC2 Au H; H 
ComplexM1M2nq
ZnBC1 Zn Zn 
ZnBC2 Zn Zn 
aZnBC1 Zn H; H 
aZnBC2 Zn H; H 
AuBC1 Au Au 
AuBC2 Au Au 
aAuBC1 Au H; H 
aAuBC2 Au H; H 

To clarify, in the equilibrium state, the rings that are Zn-ion ligated or non-ligated are of a neutral overall charge, whereas those ligated by the Au ion are of +1 charge. Therefore, in the charge-transfer states where the donor ring is Zn-ion ligated, it becomes of +1 charge, and where it is Au-ion ligated, it becomes of +2 charge. (Similarly, in the CT states where the acceptor ring is Zn-ion ligated, it becomes of −1 charge, and where it is Au-ion ligated, it becomes of neutral charge.) In the asymmetric cases of a single ion ligation, a Zn-ion ligated ring is the donor (the unligated ring is the acceptor) and an Au-ion ligated ring is the acceptor (the unligated ring is the donor).

Range-separated hybrid (RSH) functionals59–62 were shown to correct the notorious tendency of traditional density functional theory (DFT)63–69 to underestimate the fundamental orbital gap and, therefore, the CT state energies.70–76 Below, we employ a screened RSH version77–79 with a PCM80–83 (SRSH-PCM)58,84 in a time-dependent DFT (TDDFT) framework to obtain electronic excited states of solvated molecular systems.85,86 In the SRSH-PCM framework,58,84 the environment polarization of the electron density is addressed by screening the long-range (LR) Coulombic interactions by the scalar static dielectric constant ϵ consistently through both the SRSH functional parameters and the self-consistent reaction field iterations implementing the PCM.

More specifically, the SRSH functional setup follows the generalized exchange–correlation functional formulation, where the energy expression is

(1)

Here, the subscripts “X” and “C” denote exchange and correlation, the subscripts “F” and “DF” denote Fock exchange and a semilocal density functional of the exchange or correlation, and the superscripts “SR” and “LR” denote short-range and long-range. In this SRSH exchange–correlation expression, α determines the fraction of Fock exchange in the SR and α + β determines the fraction of Fock exchange in the LR. In this study, we use the ωPBE-h functional87 as employed in earlier studies.22,58,78,84,88 The range-separation parameter γ = 0.12 bohr−1 is obtained by optimal tuning in the gas phase based on the J2(γ) scheme,70 followed by resetting the β functional parameter such that α + β equals 1/ϵ with α preset to 0.2.58 

The single molecule calculations at the SRSH-PCM level describe well the electronic structure of the molecular system in the condensed phase, where the frontier orbital energies correspond well to the ionization potential and electron affinity. The SRSH-PCM was benchmarked successfully to reproduce transport properties of molecular crystals.58 Furthermore, the SRSH-PCM framework used within time-dependent DFT (TDDFT) can describe well electronic excitations85,86 and, in particular, charge-transfer (CT) states85 of solvated molecular pigment systems in a balanced quality to the absorbing states. The TD-SRSH-PCM was also used to study the spectra of photosystem pigments88 and to explain measured17 spectral trends due to pigment pairs within the core of the bacterial reaction center (BRC).22,23

CT rates are obtained by considering the transition between donor states, which are assumed to be of a high oscillator strength (OS) localized on one of the rings, and acceptor states that are of a charge-transfer character with the charges localized on the rings. The rates for the donor to acceptor transitions are calculated following the FGR picture that is fully quantum mechanically consistent at the weakly coupled regime.89 We follow a similar framework as implemented for several systems including related series of dyads.23,40,45,57,90–92 The FGR rate constants, kFGR, are compared below to rate constants, kM, obtained at the semiclassical limit following the Marcus picture of photo induced CT.

The fully quantum mechanical FGR rate constant expression is given by

(2)

Here, ΔE is the energy difference between the donor and acceptor states, and nα=exp{ωαkBT}11 are the normal modes’ thermal occupancies. Importantly, in the FGR framework, the electron-vibration coupling is addressed by the Huang Rhys factors (HRFs), denoted by {Sα}, obtained by projecting the geometry displacement due to the reaction on the normal modes, {ωα}, calculated at the equilibrium geometry. The inner-sphere reorganization energy can be calculated using the HRFs: Erin = ∑αℏωαSα. The overall reorganization energy is expressed as Er=Erex+Erin. The external intermolecular reorganization energy, Erex, accounts for outer-shell solvation, where Frex(t)=exp[kBTErext2/2]. The semiclassical limit corresponding to the Marcus theory rate constants is obtained by

(3)

The HRFs and the Er due to electron transfer are obtained by considering the individual rings upon change in their charge.93,94 Here, the role of the linker is assumed to play only a minor role in the reorganization of the relatively rigid molecular systems. For example, in ZnBC1, the displacement is obtained by combining contributions due to the ring changing from a neutral state to anionic and cationic rings. Under this approximation, ZnBC2 is associated with the same displacement as ZnBC1 since the role of the linking ring in the displacement is neglected. The HRFs are obtained by projection onto the normal mode coordinates of the equilibrium geometry of the single ring using the Dushin program.95,96 The ΔE is obtained as the difference between the absorbing state energy and the CT state obtained using the TD-SRSH-PCM at the equilibrium geometry and corrected by the Er,

(4)

Electronic coupling, Vel, between the TD-SRSH-PCM electronic excited states is obtained via the fragment-charge difference (FCD) method.97,98

Equilibrium geometry optimizations are performed using the dispersion-corrected RSH ωB97X-D functional99 with the 6-31G(d) basis set.100 All optimizations are performed within the PCM.101–104 We consider a relatively nonpolar solvent, toluene, of scalar and optical dielectric constants of 2.37 and 2.240, respectively, and a relatively polar solvent N,N-dimethylformamide (DMF) of scalar and optical dielectric constants of 37.22 and 2.046. Calculations are performed using the Q-Chem software.105 Excited electronic states are obtained using the TD-SRSH-PCM framework and 6-31G(d) basis set.

We start our analysis by considering the key frontier molecular orbitals that affect the low electronic excited states. The calculated energies of the key frontier (and near frontier) molecular orbitals (next OMO, HOMO, LUMO, and next UMO) at the SRSH-PCM level in DMF are listed in Fig. 2. The corresponding data calculated in toluene are provided in the SI, Fig. 1. The orbital shapes are also illustrated in Fig. 2. In the DMF solution, the orbital gap increases slightly with the addition of a linker for symmetric and asymmetric Zn-ligated dyads. In the asymmetric Au-ligated systems, the orbital gap decreases by ≈0.50 eV. In the toluene solution, we observe the same trend where the asymmetric dyads present smaller gaps than the symmetric systems, while overall, the gaps are significantly larger by ≈1 eV than in the case of the larger dielectric constant of DMF.

FIG. 2.

Energies of molecular orbitals of the complexes in DMF (the energies in toluene are listed in the supplementary material, Fig. 1). The asymmetric systems present localized molecular orbitals, and those in the symmetric systems are delocalized. The corresponding numerical values for DMF and toluene are listed in the supplementary material.

FIG. 2.

Energies of molecular orbitals of the complexes in DMF (the energies in toluene are listed in the supplementary material, Fig. 1). The asymmetric systems present localized molecular orbitals, and those in the symmetric systems are delocalized. The corresponding numerical values for DMF and toluene are listed in the supplementary material.

Close modal

The molecular orbitals in the symmetric dyads (ZnBC1, ZnBC2, AuBC1, and AuBC2) are delocalized and localized for the asymmetric dyads (aZnBC1, aZnBC2, aAuBC1, and aAuBC2). For the asymmetric Zn-ligated systems, the HOMO is localized on the ion-ligated ring, whereas in the Au ion-ligated system, it is the LUMO that is localized on the ion-ligated ring. The molecular orbital energies are more stabilized in toluene than in DMF solvated dyads except the L and L + 1 orbitals for the Zn-ligated systems (see supplementary material, Table S1).

We consider next the electronic excited states calculated at the ground state geometry. The S1 lowest excitation energies (ES1) are listed in Table III. Slightly blue-shifted absorption spectra are found for all the cases with an increase in the solvent polarity (excitation energies in toluene are provided in the parenthesis). In the case of the Zn-ligated systems, the shift is of 0.2 for the directly bonded systems (ZnBC1 and aZnBC1), where involving a linking ring (ZnBC2 and aZnBC2) reduces the shift to 0.05 eV. In the case of the cationic Au-ligated systems, the shift reduces to below 0.1 eV.

We next proceed to consider the CT state energies (ECT) that show stabilization by the solvent. The detachment and attachment densities illustrated in Fig. 3 are well separated indicating clearly the direction of charge transfer. (All the CT states are associated with close to complete electron transfer where the charge transferred, dQ, is larger than 0.96e.) The CT states are red-shifted with the increase in the scalar dielectric constant from toluene to DMF values, whereas in the cases of the Zn-ligated system, the shifts are in the range of [0.5–0.7] eV, and in the cases of the cationic Au complexes, the shift is significantly smaller with an exception of slight blue shifting for the AuBC1 dyad. Importantly, in all the Zn-ligated systems, even in the more polar solvent, the CT state energies are higher than the S1 state by ≈0.20 eV. On the other hand, the asymmetric Au-ligated cases (aAuBC1 and aAuBC2) present significantly lower CT state energies compared to S1 energies by ≈0.30 eV–0.40 eV. The lower CT state energies reflect the significantly reduced HOMO–LUMO gaps, where the HOMO in aAuBC1 is significantly destabilized compared to that in the AuBC1 case, while the LUMOs remain similar in energy (see supplementary material, Table and Fig. S1).

FIG. 3.

Isosurfaces of the detachment (blue/left) and attachment (red/right) densities.

FIG. 3.

Isosurfaces of the detachment (blue/left) and attachment (red/right) densities.

Close modal

The monomer based reorganization energies (Erin) are provided in Table II. The CT energy parameters, the overall Er, and the driving force (ΔE) are listed in Table III. (Following earlier estimates, Erex0.01 eV and 0.003 eV in DMF and toluene solutions, respectively,106 and, therefore, of a negligible effect on the FGR rates.) We find that the absolute values of the ΔE are strongly affected by the dielectric constant reflecting the significantly increased CT state stabilization by the larger dielectric constant of DMF compared to the toluene cases. The effect is more pronounced in the Zn-ligated systems, where in DMF, the energies are close to zero, while in toluene, all the processes are uphill with energies larger than 0.5 eV. In the Au-ligated systems, the asymmetric cases present ΔE that are well below −0.5 eV and for the symmetric cases are close to zero. The reorganization energy is less affected by the dielectric constant, where it appears to vary only slightly within 0.01 eV between the two considered dielectric constants.

TABLE II.

Single ring reorganization energies corresponding to the ring as the donor, Er+, and as the acceptor, Er. The three types of rings considered in this work include the unligated BChl, Zn(II) ion-ligated Zn-BChl, and the cationic Au(III) ligated ring, Au-BChl. Values correspond to DMF as the solvent, and those to toluene are provided in parenthesis (eV).

Single ringEr+Er
BChl-HH 0.15 (0.15) 0.10 (0.12) 
Zn-BChl 0.09 (0.08) 0.15 (0.15) 
Au-BChl 0.09 (0.09) 0.17 (0.16) 
Single ringEr+Er
BChl-HH 0.15 (0.15) 0.10 (0.12) 
Zn-BChl 0.09 (0.08) 0.15 (0.15) 
Au-BChl 0.09 (0.09) 0.17 (0.16) 
TABLE III.

TD-SRSH-PCM solvated excited states S1 and CT energies at equilibrium structure (ES1 and ECT respectively), reorganization energy (Er), CT stabilized energy ECT*, energy difference (ΔE), and electronic coupling (in meV), and transfer rate constants obtained using the FGR and Marcus levels (kFGR and kM). Values correspond to DMF as the solvent, and those to toluene are provided in parenthesis (energy unit: eV).

DyadES1ECTErECT*ΔEVel.kFGRkM
ZnBC1 2.05 (1.86) 2.23 (2.63) 0.24 (0.23) 1.99 (2.40) −0.06 (0.54) 10.50 (14.95) 1.49 × 1012 (3.30 × 10109.59 × 1011 (1.11 × 103
ZnBC2 2.01 (1.96) 2.28 (2.92)  2.04 (2.69) 0.03 (0.73) 0.26 (1.04) 4.29 × 108 (1.29 × 1081.24 × 108 (3.64 × 10−4
aZnBC1 2.02 (1.88) 2.19 (2.64) 0.19 (0.20) 2.00 (2.44) −0.02 (0.56) 8.27 (6.90) 1.81 × 1012 (3.71 × 1085.62 × 1011 (7.60 × 102
aZnBC2 2.02 (1.97) 2.22 (2.90)  2.03 (2.70) 0.01 (0.73) 0.69 (0.82) 6.84 × 109 (1.34 × 1062.25 × 109 (5.47 × 10−2
AuBC1 1.92 (1.82) 2.18 (1.92) 0.26 (0.25) 1.92 (1.67) 0.00 (-0.15) 2.60 (2.67) 1.15 × 1011 (1.31 × 10111.73 × 1010 (1.51 × 1011
AuBC2 1.93 (1.88) 2.15 (2.20)  1.89 (1.95) −0.04 (0.07) 1.49 (1.91) 4.32 × 1010 (4.27 × 1091.18 × 1010 (2.49 × 109
aAuBC1 1.92 (1.90) 1.59 (1.53) 0.32 (0.31) 1.26 (1.21) −0.66 (-0.69) 8.33 (10.12) 3.35 × 1011 (3.83 × 10117.00 × 1010 (3.87 × 1010
aAuBC2 1.93 (1.90) 1.54 (1.56)  1.21 (1.24) −0.72 (-0.66) 2.30 (1.78) 1.83 × 1010 (1.48 × 10101.44 × 109 (2.45 × 109
DyadES1ECTErECT*ΔEVel.kFGRkM
ZnBC1 2.05 (1.86) 2.23 (2.63) 0.24 (0.23) 1.99 (2.40) −0.06 (0.54) 10.50 (14.95) 1.49 × 1012 (3.30 × 10109.59 × 1011 (1.11 × 103
ZnBC2 2.01 (1.96) 2.28 (2.92)  2.04 (2.69) 0.03 (0.73) 0.26 (1.04) 4.29 × 108 (1.29 × 1081.24 × 108 (3.64 × 10−4
aZnBC1 2.02 (1.88) 2.19 (2.64) 0.19 (0.20) 2.00 (2.44) −0.02 (0.56) 8.27 (6.90) 1.81 × 1012 (3.71 × 1085.62 × 1011 (7.60 × 102
aZnBC2 2.02 (1.97) 2.22 (2.90)  2.03 (2.70) 0.01 (0.73) 0.69 (0.82) 6.84 × 109 (1.34 × 1062.25 × 109 (5.47 × 10−2
AuBC1 1.92 (1.82) 2.18 (1.92) 0.26 (0.25) 1.92 (1.67) 0.00 (-0.15) 2.60 (2.67) 1.15 × 1011 (1.31 × 10111.73 × 1010 (1.51 × 1011
AuBC2 1.93 (1.88) 2.15 (2.20)  1.89 (1.95) −0.04 (0.07) 1.49 (1.91) 4.32 × 1010 (4.27 × 1091.18 × 1010 (2.49 × 109
aAuBC1 1.92 (1.90) 1.59 (1.53) 0.32 (0.31) 1.26 (1.21) −0.66 (-0.69) 8.33 (10.12) 3.35 × 1011 (3.83 × 10117.00 × 1010 (3.87 × 1010
aAuBC2 1.93 (1.90) 1.54 (1.56)  1.21 (1.24) −0.72 (-0.66) 2.30 (1.78) 1.83 × 1010 (1.48 × 10101.44 × 109 (2.45 × 109

Following the trends of the electronic coupling, the directly linked systems of BC1 are of the higher rates than those of the corresponding BC2 systems. The aZnBC1 dyad of the considered set of systems is associated with the highest rate, a trend that results for the energy level alignment and the relatively high coupling energy. The effect of asymmetric ligation appears to affect the most by stabilizing the CT states in the Au-ligated system, while their overall effect on the rates, however, appears to overall only slightly enhance the transfer rates. The dielectric constant dependence is stronger for the neutral systems, whereas for the charged systems, we find that the energetic parameter including the coupling energy is only weakly affected by the dielectric constant.

Finally, we note that the semiclassical Marcus rate constants reproduce well the FGR values in the DMF solvent. In toluene with a smaller dielectric constant, the solvated CT states are destabilized. Consequently, the CT processes are associated with a relatively large uphill ΔE. In the Zn-ligated system solvated in toluene, the CT processes fall in the far-inverted regime, where |ΔE| ≫ Er. Here, the FGR becomes essential with the rate constants obtained as the semiclassical level rates are greatly underestimated.107 Indeed, at the far-inverted regime, quantum mechanical corrections become essential,89 where nuclear tunneling becomes dominant over thermal activation imposed by the semiclassical Marcus picture.108,109 Rates described at the FGR level were shown to achieve good agreement with measured CT rates in the far-inverted regime, whereas rates obtained at the semiclassical limit are effectively vanishing.107 The aAuBC1 and aAuBC2 present downhill processes of similar ΔE at around −0.7 eV with however larger Er therefore appear to not fall in the far-inverted regime and therefore present kM that reproduces well the FGR values.

CT processes in a series of chemically linked BChl pairs are investigated at the semiclassical Marcus picture and the more complete fully quantum mechanically consistent FGR level. The polarization consistent SRSH-PCM framework is used to calculate the energy parameters. Overall, we find that the Marcus rate constants reproduce well the FGR values with the exception of the Zn ligating toluene-solvated systems of an uphill CT process, where the ΔE is significantly larger than Er (in absolute values) placing the processes in the far-inverted regime. The FGR CT rates are strongly affected by the types of the linking and metal ion ligation. For the asymmetric charged Au complex, electron transfer results in a charge shift, while in the asymmetric Zn complex, electron transfer leads to charge separation. Therefore, stabilization by solvation plays a much more important role for the Zn complex than for the Au complex. We find that the CT in most of the neutral Zn-ligated systems depends strongly on solvent dielectrics, whereas the cationic Au-ligated systems are associated with only weak dependence on the dielectric constant. We also find that Zn ligation tends to enhance the CT rate compared to Au ligation in DMF. At the solvent of the lower scalar dielectric constant, the CT rates in Zn ligate systems drop significantly, where the Au-ligated systems present more robust CT. We also find that the directly linked complexes, the BC1 systems, are associated with higher CT rates than the corresponding BC2 systems, reflecting the stronger electronic coupling. Finally, CT rates are also enhanced by asymmetric ligation. Therefore, of all the systems, the aZnBC1 followed by ZnBC1 at DMF are of the highest CT rates, and in toluene, the aAuBC1 is of the highest rate and aZnBC2 and ZnBC2 are of the smallest rates.

See the supplementary material for frontier molecular orbital energies of dyads in DMF and toluene solutions and isosurfaces of molecular orbitals in toluene, and atomic coordinates of the different molecules.

The data that support the findings of this study are available within this article.

B.D.D. is grateful for support from the Department of Energy, Basic Energy Sciences (Grant No. DE-SC0016501). Computing facilities were provided by the Ohio Supercomputer Center110 (Project No. PAA-0213) and from the College of Arts and Sciences, Kent State University.

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