Uncovering the mechanism for selective control of the visible and near-IR absorption bands in bacteriochlorophylls a, b and g

Abstract

Bacteriochlorophylls (BChls) play an important role as light harvesters in photosynthetic bacteria. Interestingly, bacteriochlorophylls (BChls) a, b, and g selectively tune their visible (Q_x) and near IR (Q_y) absorption bands by the substituent changes. In this paper, we theoretically study the mechanism for the selective control of the absorption bands. Density functional theory (DFT) and time-dependent DFT (TD-DFT) and four-orbital model analyses reveal that the selective red-shift of the Q_y band with the substituent change from BChl a to b occurs with the lower-energy shift of the (HOMO, LUMO) excited state directly induced by the molecular-orbital energy changes. In contrast, the Q_x band hardly shifts by the cancellation between the higher- and lower-energy shifts of the (HOMO-1, LUMO) excited state directly induced by the molecular-orbital energy changes and configuration interaction, respectively. On the other hand, with the substituent changes from BChl a to g, the Q_x band selectively blue-shifts by the larger higher-energy shift of the (HOMO-1, LUMO) excited state directly induced by the molecular-orbital energy shifts than the lower-energy shift due to the configuration interaction. In contrast, the Q_y band hardly shifts by the cancellation between the higher- and lower-energy shifts of the (HOMO, LUMO) excited state directly induced by the molecular-orbital energy changes and configuration interaction, respectively. Our work provides the important knowledge for understanding how nature controls the light-absorption properties of the BChl dyes, which might be also useful for design of porphyrinoid chromophores.

Bacteriochlorin chromophores play a crucial role as light absorbers in photosynthetic bacteria.1,2 In addition, bacteriochlorin dyes have been used as photosensitizers for photodynamic therapy.3 So far, three kinds of naturally synthesized bacteriochlorin chromophores, called bacteriochlorophylls (BChl) a, b, and g have been discovered.1,2 These BChl chromophores have a bacteriochlorin ring fused with cyclopentanone on the pyrrole ring C having a magnesium central ion, as shown in Figure 1.1,2 The BChls contain different peripheral substituents on the rings A, B, and D, as shown in Figure 2.1,2 By the substituent changes, the BChls selectively tune their visible (Q_x) and near IR (Q_y) absorption bands, as shown in Figure 3. For instance, by the dehydrogenation at the 8 and 81 positions on the ring B, the Q_y band in BChl a remarkably red-shifts in BChl b with a slight red-shift of the Q_x band. In addition, by both the dehydrogenation on the ring B and the replacement of the acetyl group on the ring A with a vinyl group, the Q_x band in BChl a blue-shifts in BChl g with a slight blue-shift of the Q_y band.2,4,5 This result suggests that nature successfully tunes the Q_x and Q_y bands selectively by the substituent changes. In order to get an insight into the mechanism, theoretical investigations are required. So far, the light-absorption properties of the BChl a, b, and g have been studied with several quantum chemical calculations.4–8 Linnanto et al. reported the Q_x and Q_y excitation energies of BChls a, b and g calculated by semi-empirical quantum chemical calculations.5,6 Their calculations reproduced the selective red-shift of the Q_y band with the substituent change from BChl a to b.4 On the other hand, their calculations failed to reproduce the selective blue-shift of the Q_x band from BChl a to g.5,6 Furthermore, the mechanism of the selective tuning has not been clarified yet. In this paper, we theoretically study the mechanism with density functional theory (DFT) and time-dependent DFT (TD-DFT) and four-orbital model analyses.

Figure 1.

Fundamental skeleton of BChls a, b, and g.

Figure 2.

Molecular structures of BChls a, b and g and an L-histidine-residue analog (His) for the axial ligand (bottom right).

Figure 3.

Schematic picture of the selective shifts of Q_y and Q_x absorption bands. Experimental peak energies and relative intensities of BChls a, b and g in diethyl ether are reported in Ref. 2.

Computational Details

The molecular structures in the ground states were optimized using DFT calculations9 with the B3LYP functional10 and 6-31G(d) basis set. With the optimized structures, absorption spectra were computed with TD-DFT calculations11 at the B3LYP/6-31G(d) level of theory. In the calculations of the optimized structures and excited states, the conductor-like polarizable continuum model (CPCM)12,13 was used to take into account solvent effects of diethyl ether, which was used in the previous experiments2. All calculations were performed with Gaussian 09 software14. DFT and TD-DFT calculations with the similar functional and basis set were reported to be sufficiently appropriate to study the properties of excited states and molecular orbitals of the BChl dyes.7,8

Results and Discussion

Models of BChls

Since most of the BChl molecules in photosynthetic bacteria are coordinated with a histidine residue as a fifth ligand from surrounding proteins,15,16 we have studied BChls a, b and g coordinated with an L-histidine-residue analog (His) (Fig. 2). In addition, as pointed out by Oba et al. and Balaban, the axial ligand is coordinated to the central magnesium ion from the face (β-coordination) or back side (α-coordination) with respect to the BChl ring.15,16 Therefore, we examined the BChls a, b and g coordinated with His from the face or back side.

Optimized Structures

Figure 4 shows the optimized structures of BChls a, b and g coordinated with His from the face or back side. The bacteriochlorin rings are planar for all the BChls. The His ligand is coordinated with the central magnesium ion almost perpendicularly. The central magnesium ion is located slightly above or below the bacteriochlorin ring by the face- or backside ligation, respectively. The bond length between the magnesium ion and the coordinating nitrogen atom of His was estimated to be 2.17 Å for face- and back-His-BChl a, face- and back-His-BChl b, and face-His-BChl g and the one for back-His-BChl g to be 2.18 Å. From X-ray single crystal structure analyses, the bond length between the Mg ion and N atom of a histidine residue was reported to be 2.27 and 2.32 Å for B850 BChl a pairs.17 Our estimated bond lengths are comparable to the experimental data, indicating the validity of the optimized structures.

Figure 4.

Optimized structures of BChls a, b and g coordinated with His from the face or back side obtained by DFT calculations. Gray: carbon, white: hydrogen, blue: nitrogen, red; oxygen, yellow: magnesium atoms.

Molecular-Orbital Shifts

Figure 5 shows the electronic distributions and energies of the second highest occupied molecular orbital (HOMO-1), highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and second lowest unoccupied molecular orbital (LUMO+1) of BChls a, b and g coordinated with His from the face or back side. This figure shows that the certain molecular orbitals are selectively shifted by the substituent changes. From BChl a to b, the energy of HOMO increases by 0.05 (face and back) eV and LUMO+1 decreases by 0.21(face)/0.19(back) eV. In contrast, the HOMO-1 and LUMO hardly shift. On the other hand, as compared to BChl b, the HOMO, LUMO, and LUMO+1 levels in BChl g are elevated by 0.09(face)/0.10(back) eV, 0.19(face)/0.20(back) eV, and 0.13(face)/0.12(back) eV, respectively, and the HOMO-1 energy just slightly increases by 0.04 eV (face and back). These selective molecular-orbital shifts are associated to the changes in the electronic distributions by the substituent variations on the rings A and B. Since those molecular orbitals have no electronic distributions on the longer alkyl chains (phytyl and farnesyl) on the ring D, the difference in the alkyl chain has almost no effects on the molecular-orbital shifts. In addition, no remarkable dependence of the direction of the axial ligation is confirmed. As shown by red circles in Figure 5, the HOMO and LUMO+1 in BChls b and g are delocalized on the ethylidene substituent by the dehydrogenation on the ring B. On the other hand, as shown by blue circles in Figure 5, the replacement of the acetyl group to a vinyl group causes delocalization of the HOMO, LUMO, and LUMO+1 on the vinyl group in BChl g.

Figure 5.

Energy-level diagrams and electronic distributions (|isovalue|=0.02) of the HOMO−1, HOMO, LUMO, and LUMO+1 of BChls a, b and g coordinated with His from the face or back side. The energies for the face- and back-side ligations are denoted with red and blue letters, respectively. In this figure, the phytyl and farnesyl chains are not displayed for clarity.

The selective molecular-orbital shifts are explained by the electronic distributions in BChl a on the rings A and B. For the dehydrogenation from BChl a to b, the electronic distributions on the carbon atoms at the 8 and 81 positions are important. As shown in Figure 6a, the HOMO and LUMO+1 in BChl a have discernible electronic distributions at the 8 and 81 positions, which give rise to above mentioned remarkable delocalizations in BChls b and g. In contrast, the HOMO-1 and LUMO in BChl a have no electronic distributions on the moiety, providing their little response to the structural change. On the other hand, for the substitution change on the ring A, electronic distributions on the carbon atoms at the 3 and 31 positions and neighboring oxygen atom are crucial. As shown in Figure 6b, the HOMO, LUMO, and LUMO-1 in BChl a are remarkably distributed on the acetyl group in contrast to the HOMO-1. The distributions of the HOMO, LUMO, and LUMO+1 on the acetyl group are consistent with the selective shifts of those molecular orbitals in BChl g.

Figure 6.

Magnified pictures of molecular orbitals (|isovalue|=0.02) of BChl a coordinated with His from the face side on the (a) ring B and (b) ring A.

The molecular-orbital shifts occur with the following mechanisms. For the dehydrogenation, the HOMO and LUMO+1 in BChl a are considered to be shifted by interactions with an additional ethylene group. As shown by the left figure in Figure 7a, the HOMO and LUMO+1 levels in BChl a interact with the HOMO (π orbital) and LUMO level (π* orbital) of the hypothetical methyl ethylene group, respectively. In consequence, the HOMO and LUMO+1 levels in BChl b are elevated and lowered, respectively. In fact, the anti-bonding and bonding interactions for HOMO and LUMO+1 in BChl b, respectively, are displayed by red circles in the right side in Figure 7a. On the other hand, the selective molecular-orbital shifts with the substituent replacement from BChl b to g are attributed to the difference in the electronic property between acetyl and vinyl groups. As shown in Figure 7b, an acetyl group has an electron withdrawing property that stabilizes the molecular orbitals. On the other hand, a vinyl group has no electron withdrawing property. Therefore, the replacement of the acetyl group with the vinyl group destabilizes the HOMO, LUMO, and LUMO+1 having the electronic distributions on the acetyl group (Fig. 6b).

Figure 7.

Mechanism of molecular-orbital shifts. (a) Dehydrogenation on the ring B and (b) substituent change on the ring A.

Absorption Properties

Figure 8 shows the TD-DFT calculated electronic excitation spectra for BChls a, b and g coordinated with His from the face or back side. The wavelengths, oscillator strengths, and configurations of the Q_y and Q_x electronic excitations are tabulated in Table 1. The calculated Q_x wavelengths of the BChls are comparable to the experimental data (Fig. 3). However, the Q_y wavelengths are underestimated as compared to the experimental data (Fig. 3). This underestimation was also reported in other papers.7,8 Regarding the absorption shift from BChl a to b, the Q_y band is significantly red-shifted by 0.075(face)/0.074(back) eV, while the Q_x band is hardly shifted. On the other hand, from BChl a to g, the Q_x band is blue-shifted by 0.108(face)/0.113(back) eV, retaining the Q_y band position. Even though the calculated shifts are larger than the experimental ones (0.050 and 0.035 eV), the calculations qualitatively reproduce the experimentally reported selective absorption shifts (Fig. 3). In addition, our calculations indicate that the back-side coordination systematically shows the slightly red-shifted Q_y and Q_x bands as compared to the face-side one.

Figure 8.

Calculated excitation spectra of BChls a, b and g coordinated with His from the face (red lines) or back (blue lines) side.

Table 1.

Excitation wavelengths, oscillator strengths, and contributions of Q_y and Q_x excitations in BChls a, b and g coordinated with His from the face or back side in diethyl ether

	Wavelength (nm) (Oscillator strength)	Contributions
face-His-BChl a	690.02 (0.4877)	H→L (97%), H-1→L+1 (3%)
	587.40 (0.1615)	H-1→L (91%), H→L+1 (6%)
back-His-BChl a	692.64 (0.4911)	H→L (97%), H-1→L+1 (3%)
	591.16 (0.1571)	H-1→L (92%), H→L+1 (6%)
face-His-BChl b	720.25 (0.439)	H→L (97%), H-1→L+1 (3%)
	589.84 (0.1253)	H-1→L (89%), H→L+1 (9%)
back-His-BChl b	722.47 (0.4455)	H→L (97%), H-1→L+1 (3%)
	592.65 (0.1243)	H-1→L (89%), H→L+1 (8%)
face-His-BChl g	692.99 (0.4355)	H→L (96%), H-1→L+1 (4%)
	558.71 (0.0996)	H-1→L (84%), H→L+1 (13%)
back-His-BChl g	695.95 (0.4426)	H→L (96%), H-1→L+1 (4%)
	561.04 (0.0962)	H-1→L (85%), H→L+1 (13%)

H-1: HOMO-1, H: HOMO, L: LUMO, and L+1: LUMO+1.

Linnanto et al. reported the Q_y and Q_x excitation energies of BChls a, b and g calculated by semi-empirical quantum chemical calculations.5,6 Their calculations reproduced the selective red-shift of the Q_y band with the substituent change from BChl a to b.4 On the other hand, their calculations showed that with the substituent changes from BChl a to g the Q_y band more largely blue-shifts than the Q_x band inconsistent with the experimental result. They also calculated the Q_y and Q_x excitation energies of 1:1 complexes of the BChl dyes with a solvent molecule. The complexation with a solvent molecule failed to reproduce the selective absorption shifts of the Q_y and Q_x bands not only from BChl a to g, but also from BChl a to b.5 On the other hand, our TD-DFT calculations well reproduced the selective absorption shifts from BChl a to b and from BChl a to g, as shown in Figure 8.

Table 1 shows the configurations of the Q_y and Q_x absorption bands in BChls a, b and g. The Q_y excited states in BChls a, b and g are predominantly attributed to the lowest (HOMO, LUMO) exited state with a minor contribution of the forth lowest (HOMO-1, LUMO+1) excited state. On the other hand, the Q_x excited states are dominated by the second lowest (HOMO-1, LUMO) excited state partially mixed with the third lowest (HOMO, LUMO+1) excited state. The mixings between the excited states take place by the configuration interaction based on electron repulsion between the corresponding excited states. The assignments of the Q_y and Q_x transitions are consistent with those based on the Gouterman’s four-orbital model2,18, supporting the validity of our calculation results. The contribution of the HOMO-1→LUMO+1 transition in the Q_y transition very slightly increases from 3% (face, back) in BChls a and b to 4% (face, back) in BChl g. On the other hand, the contribution of the HOMO→LUMO+1 in the Q_x transition more strikingly increases from 6% (face and back) in BChl a to 9%(face)/8%(back) in BChl b, 13% (face, back) in BChl g, indicating the enhancement of the configuration interaction for the Q_x band from BChl a to b, g.

Four-Orbital Model Analysis

In order to analytically understand the selective absorption shifts, we examined the calculation results with the four-orbital model.2,18 The schematic energy-level diagrams of the four-orbital model are shown in Figures 9a and 9b. From Figure 9a, we can see that there exist four electronically excited states, that are (HOMO, LUMO), (HOMO−1, LUMO), (HOMO, LUMO+1), and (HOMO−1, LUMO+1). The (HOMO, LUMO) and (HOMO−1, LUMO+1) excited states have transition dipole moments along the y axis (Fig. 1). On the other hand, the (HOMO−1, LUMO) and (HOMO, LUMO+1) excited states have transition dipole moments along the x axis (Fig. 1). Because of the symmetry, the (HOMO, LUMO) and (HOMO-1, LUMO+1) excited states interact with each other by configuration interactions and the (HOMO−1, LUMO) and (HOMO, LUMO+1) excited states do so, as shown in Figure 9b. The Hamiltonian matrices, eigenfunctions of Q_y and Q_x excited states and mixing coefficients are expressed by the following equations.

$$|1>\equiv |\hspace{0.17em}\text{HOMO},\hspace{0.17em}\text{LUMO}>$$ (1)

$$|2>\equiv |\hspace{0.17em}\text{HOMO}-1,\hspace{0.17em}\text{LUMO}>$$ (2)

$$|3>\equiv |\hspace{0.17em}\text{HOMO},\hspace{0.17em}\text{LUMO}+1>$$ (3)

$$|4>\equiv |\hspace{0.17em}\text{HOMO}-1,\hspace{0.17em}\text{LUMO}+1>$$ (4)

$$H_{1,4}=\left[\begin{array}{rr}\hfill E_1& \hfill V_{14}\\ \hfill V_{14}& \hfill E_4\end{array}\right]$$ (5)

$$H_{2,3}=\left[\begin{array}{rr}\hfill E_2& \hfill V_{23}\\ \hfill V_{23}& \hfill E_3\end{array}\right]$$ (6)

$$|Q_y>=\text{cos}\theta |1>+\text{sin}\theta |4>$$ (7)

$$|Q_x>=\text{cos}\phi |2>+\text{sin}\phi |3>$$ (8)

$${\text{sin}}^2\theta =\frac{1}{2}\left[1-{\left\{1+4{\left(\frac{V_{14}}{E_1-E_4}\right)}^2\right\}}^{-\frac{1}{2}}\right]$$ (9)

$${\text{sin}}^2\phi =\frac{1}{2}\left[1-{\left\{1+4{\left(\frac{V_{23}}{E_2-E_3}\right)}^2\right\}}^{-\frac{1}{2}}\right],$$ (10)

in which E_i is the energy of the |i> state and V_ij is the off-diagonal element of the configuration interaction between |i> and |j> states, <i|H_CI|j>. Assuming that the E_i value is approximated to be the energy difference between the relevant molecular orbitals, the energy differences of E₄−E₁ and E₃−E₂ and the magnitude of V_ij for the Q_y and Q_x transitions were estimated from Figure 5 and by using the mixing coefficients in Table 1 and eqs 9 and 10, respectively. As shown in Figure 10a, from BChl a to b, g, the E₄−E₁ and E₃−E₂ values systematically decrease. In particular, the latter energy difference responsible to the Q_x band more drastically reduces as compared with the former one. The magnitude of the configuration interaction has no remarkable difference between the BChls, as shown in Figure 10b. Thus, the remarkable increase of the mixing coefficient for the Q_x excited state mainly results from the enhancement of the configuration interaction due to the reduction of the responsible E₃−E₂ energy gap in the denominator of eq 10. The energies of the Q_y and Q_x excited states are given by the following equations.

$$E_{Q_y}=E_1+\Delta E_{Q_y}$$ (11)

$$E_{Q_x}=E_2+\Delta E_{Q_x}$$ (12)

$$\Delta E_{Q_y}=-\left\{\frac{1}{2}\left(E_1-E_4\right)+\sqrt{\frac{1}{4}{\left(E_1-E_4\right)}^2+{V_{14}}^2}\right\}$$ (13)

$$\Delta E_{Q_x}=-\left\{\frac{1}{2}\left(E_2-E_3\right)+\sqrt{\frac{1}{4}{\left(E_2-E_3\right)}^2+{V_{23}}^2}\right\}$$ (14)

The first and second terms in eqs 11 and 12 are the energy shifts that are directly induced by the molecular-orbital shifts and configuration interactions, respectively. Eqs 11–14 for the energy eigenvalues are derived by diagonalization of the Hamiltonian matrices (Eqs 5 and 6). By using the above estimated values of the configuration interactions and energy gaps, the energies of the Q_y and Q_x excited states are obtained, as shown in Figure 11. We found that the selective shifts of the Q_y and Q_x absorption bands are qualitatively reproduced by the four-orbital model, indicating the sufficient validity of the above-mentioned assumption. The slightly large difference for the Q_x excitation energy between the TD-DFT and four-orbital model calculations is considered to result from the configuration interaction with higher-energy excited states, as implied in Table 1. Figure 12 shows the first (E₁ and E₂) and second (ΔE_Qy and ΔE_Qx) terms of eqs 11 and 12 in the BChls. As shown in Figure 12, the shift of the Q_y band from BChl a to b is mainly attributed to the reduction in the E₁ energy by the molecular-orbital shifts. The invariance of the Q_x energy is explained by the cancellation between the higher-energy shift of the (HOMO-1, LUMO) excited state by the molecular-orbital shifts and the lower-energy shift by the configuration interaction. Similarly, for the Q_y band in BChl g, the higher-energy shift of the (HOMO, LUMO) excited state by the molecular-orbital shifts is cancelled with the lower-energy shift by the configuration interaction, retaining the excitation energy. On the other hand, for the Q_x band in BChl g, similar cancellation also happens, but the higher-energy shift of the (HOMO-1, LUMO) excited state by the molecular-orbital shifts overcomes the lower-energy shift by the configuration interaction, leading to the blue shift. Therefore, based on the four-orbital model analysis, it is found that the selective tuning of the visible and near IR absorption bands is realized by the three mechanisms, as summarized in Table 2.

Figure 9.

(a) Orbital and (b) state representations of four-orbital model. x and y stand for optical polarizations for electronic transitions.

Figure 10.

(a) Energy differences of E₄−E₁ (red) and E₃−E₂ (blue) and (b) magnitudes (V_ij) of configuration interactions for Q_y (red) and Q_x (blue) transitions in BChls a, b and g coordinated with His from the face (open circles) or back (open squares) side.

Figure 11.

Comparison of Q_y and Q_x excitation energies between TD-DFT calculations (blue) and four-orbital model based calculations (red) for BChls a, b and g coordinated with His from the face (open circles) or back (open squares) side.

Figure 12.

E₁ (red), E₂ (red), ΔE_Qy (blue), and ΔE_Qx (blue) of BChls a, b and g coordinated with His from the face (open circles) or back (open squares) side.

Table 2.

Mechanism for selective tuning of the visible and near IR absorption bands in BChls

		E1 or E2		Configuration interaction	Shift
BChl a to b	Qy	–		0	Red
	Qx	+	Cancellation	–	None
BChl a to g	Qy	+	Cancellation	–	None
	Qx	Large +	Partial cancellation	–	Blue

+ and − stand for higher and lower energy shifts, respectively.

Conclusion

In summary, we have theoretically studied the selective absorption shifts of the Q_y and Q_x bands in BChls a, b and g coordinated with the His ligand by DFT and TD-DFT and four-orbital model analyses. TD-DFT analyses successfully reproduced the experimentally reported selective absorption shifts of the Q_y and Q_x bands with the substituent changes from BChl a to b and from BChl a to g. By the analysis based on the four-orbital model, we found that the selective red-shift of the Q_y band from BChl a to b is caused by the lower-energy shift of the (HOMO, LUMO) excited state directly induced by the molecular-orbital energy changes. The Q_x band hardly shifts with the substituent change as a result of the cancellation between the higher- and lower-energy shifts of the (HOMO-1, LUMO) excited state directly induced by the molecular-orbital energy changes and configuration interaction, respectively. On the other hand, the Q_x band selectively blue-shifts from BChl a to g by the larger higher-energy shift of the (HOMO-1, LUMO) excited state directly induced by the molecular-orbital energy changes than the lower-energy shift due to the configuration interaction. In contrast, the Q_y band hardly shifts by the cancellation between the higher- and lower-energy shifts of the (HOMO, LUMO) excited state directly induced by the molecular-orbital energy changes and configuration interaction, respectively. The molecular orbital shifts were qualitatively explained on the basis of the molecular-orbital theory. Our results manifest the high level control of the molecular-orbital energies and configuration interactions in nature for the selective light-absorption tailoring. This knowledge could be also useful for designing new porphyrinoid dyes.