Probing the Electronic Structure of Bacteriochlorophyll Radical Ions—A Theoretical Study of the Effect of Substituents on Hyperfine Parameters^†

Introduction

Photosynthesis is the fundamental process of converting light into chemical energy; it is performed by plants, algae and different classes of bacteria 1. Phylogenetic relationships were found between all presently known photosystems 2. The first step of photosynthesis is light absorption in the antennas, followed by an exciton transfer to the photosynthetic reaction centers (RCs). The subsequent charge separation and further electron transfer processes in the RCs involve the creation of radical ions. Two classes of photosystems (PS) were defined with regard to their electron acceptors. While type I RCs contain iron–sulfur centers, quinones are found in type II RCs. Both types of photosystems are present in green plants, algae and cyanobacteria (PS I and PS II), whereas simple green or helio, and purple bacteria contain only one photosystem 3. The long-range electron transfer in the RCs involves a primary electron donor and a chain of acceptors including (bacterio)chlorophylls and (bacterio)pheophytins, before the electron is passed to quinones and/or iron–sulfur centers.

Electron paramagnetic resonance (EPR), electron-nuclear double resonance (ENDOR) and electron spin echo envelope modulation (ESEEM) spectroscopy 4-7 turned out to be very useful for the study of the involved radical ions. The obvious advantage of these techniques is that they are sensitive exclusively to the radical cofactors while the remaining part of the protein is EPR silent. Many studies were performed so far on intact type I and II RCs 4, 8, 9. In addition, in vitro investigations of the respective radical ions and related model systems were performed employing magnetic resonance spectroscopy 9-19.

Bacteriochlorophyll a (BChl a) is the most common bacteriochlorophyll pigment in photosynthetic purple bacteria, but the existence of other BChl pigments in the RCs was reported 20. Two such species are BChl b from purple bacteria like Rhodopseudomonas viridis 21-26 and BChl g from Heliobacterium chlorum 27-30. A comparison of the molecular structures of BChl a, BChl b and BChl g is given in Fig. 1. The pigments differ in the esterified alcohols at rings IV, and in the side chains at positions 2 and 4. It was proposed that BChl g might be the precursor for the biosynthesis of any other (bacterio)chlorophyll species since all known chlorophylls can be obtained by isomerization and reduction reactions of chlorophyll intermediates that carry an ethylidene group at ring II 31-34. This is further supported by the close phylogenetic relationship of helio and cyanobacteria 35. Likewise, it was possible to convert BChl b into chlorophyll species, closely related to BChl a 36. With this in mind, a careful investigation of the electronic structures of these minor pigments appears to be important.

While it is known that BChl a, BChl b and BChl g show only small differences in their visible absorption spectra 31, 37, 38, a deeper understanding of the electron transfer processes in the RCs would noticeably benefit from a knowledge of the spin density distributions in the respective radical ions. Isotropic hyperfine coupling constants (hfcs), as available from liquid-solution ENDOR studies, are an excellent probe for the spin density distribution in radical systems. However, experimental hfcs were only reported for BChl a^·+ 13-15, BChl 16, 17 and partly for BChl b radical ions 18, 19, 39. The investigation of BChl b and BChl g radical ions suffers from the instability of these species 18, 31. Especially BChl g is extremely sensitive to air and light. Therefore, theoretical calculations on these systems are an efficient alternative for obtaining information on these radical ions.

Theoretical investigations of tetrapyrroles using density functional methods 40 have become popular, providing insight into the magnetic resonance properties 41-50, and into electronic excitation characteristics 51-56. In addition, there have been attempts of modeling the electron transfer in photosynthetic RCs 57, 58. Furthermore, RHF-INDO/SP calculations of hfcs were performed for many (bacterio)chlorophyll species 59-62.

In this work, density functional theory is used to study (bacterio)chlorophyll radical ions. Isotropic hyperfine coupling constants of BChl b and BChl g radical cations and anions are calculated and discussed in comparison to the experimental data. Furthermore, a careful comparison of hyperfine parameters obtained for BChl a, b, g is given.

In addition, ¹⁴N nuclear quadrupole coupling constants (nqcs) were calculated for BChl a, b, g, and also for Chl a in the charge neutral, reduced and oxidized states. The nitrogen nqcs are important experimental quantities that probe the electric field gradient at the ¹⁴N nucleus and therefore deliver details of the electronic structure. The ¹⁴N nqcs can be extracted from ESEEM spectra as it was, for example, demonstrated in studies of the protein backbone hydrogen bonding to the quinones and in PSII 63-65, as well as on monomeric and dimeric (bacterio)chlorophyll species that occur in photosynthesis, including work on BChl , Chl , and the cation radicals of the primary donors in bacterial RCs () and in PS I, () 10, 66-69. The calculated nqcs from this work are compared to the experimental values that are available for BChl and Chl 66, 68, which makes an assignment of the experimental data possible.

To the best of our knowledge, such a comparative set of data for hyperfine and nuclear quadrupole data of bacteriochlorophyll species is given for the first time. This is particularly helpful for a better understanding of the influence of different tetrapyrrole substitution patterns on charge and spin density distributions, that is essential for a detailed picture of the electronic structure and for understanding the function of these pigments in vivo.

Materials and Methods

Complete geometry optimizations of the BChl b and BChl g radical cations, anions and charge neutral molecules were performed employing the model systems displayed in Fig. 1. Considering the side chain orientations (e.g. at positions 7 or 10), similar conformers were chosen as in our previous study on the BChl a radical ions 49. All geometry optimizations were performed employing the BLYP density functional 70, 71 in combination with the DGAUSS DZVP basis set 72, 73. In case of the radical anions, a diffuse p-function with an exponent equal to one-third of the smallest exponent in the respective shell was added for N, C, O and Mg, respectively. The geometry optimizations were performed with the DGAUSS density functional program 74.

Isotropic hyperfine coupling constants and ¹⁴N electric field gradients were obtained from subsequent single point calculations employing the Gaussian 98 software 75. In these calculations, the B3LYP 71, 76 hybrid density functional was used together with the EPR-II basis sets for H, N, C and O 77. For magnesium, not supported by the EPR-II basis set library, the TZVP DGAUSS basis set was employed 72, 73.

The isotropic hfcs A_iso are proportional to the spin density at the respective nucleus ρ_s 78:

(1)

Here, g_e and g_N refer to the electronic and nuclear g-factors, β_e and β_N are the electronic and nuclear magnetons, respectively. 〈S_z〉 is the expectation value of the z-component of the total electron spin S, which is one half for the investigated doublet systems. Spin contamination, that is, the contamination of the calculated ground state wave function by improper spin states caused by an artificial mixing of states was found to be small in all investigated radicals. Values between 0.77 and 0.78 were calculated for the expectation value of 〈S²〉, which has an ideal value of 0.75. This small deviation indicates that the calculated spin properties can be expected as reliable.

A nuclear quadrupole moment Q(¹⁴N) of 0.020 barn 79 was used for the calculation of ¹⁴N nqcs from the electric field gradients V_i in a coordinate system with |V_z| ≥ |V_y| ≥ |V_x| 80:

(2)

Here, e is the elementary charge and h is Planck's constant. The largest nuclear quadrupole coupling constant χ_z is usually denoted as e²qQ/h with eq = V_z.

The asymmetry parameter η of the nuclear quadrupole tensor was determined from

(3)

In this work, nuclear quadrupole coupling constants and asymmetry parameters were not only calculated for the BChl b and BChl g species, but also for the BChl a and Chl a radical ions and neutral molecules. The geometrical structures of these species were taken from our previous studies 49, 50.

Results and Discussion

Complete geometry optimizations of the BChl and BChl model systems yielded tetrapyrrole core structures very similar to that of BChl 49. Considering the magnesium–nitrogen bond distances, similar values within 0.01 Å were found for BChl , BChl and BChl . Also the spin density distributions appeared very similar at first glance and show an almost circular shape for all three species (see e.g. BChl in Fig. 1). As a consequence, the same qualitative hyperfine patterns were obtained for BChl , BChl and BChl (Table 1): (i) The largest hfcs were found for the β-¹H nuclei at positions 3, 7 and 8. (ii) The methyl groups 1a and 5a are characterized by hfcs of 4–5 MHz and 9–10 MHz, respectively, while very small hfcs were obtained for the methyl groups at positions 3a and 8a. (iii) Positive hfcs of moderate magnitudes were calculated for the methine hydrogens (2–4 MHz) in all three cases. (iv) Four negative ¹⁴N hyperfine coupling constants were computed with similar values for N_I/N_III and N_II/N_IV. Nevertheless, the calculations revealed also a few characteristic differences in the hyperfine data of the three radical cations: the ethylidene group at position 4 in BChl and BChl carries a large amount of spin density, leading to large hfcs for the hydrogen atoms bound to the carbon nuclei at position 4a (≈−12 MHz) and the methyl groups at positions 4b (≈ +15 MHz), see Table 1. On the other hand, the large and positive hfc of the β-¹H at position 4 from BChl vanishes in BChl and BChl . In conclusion, ENDOR spectra of BChl and BChl should show one additional, large ¹H hfc in comparison to BChl . This has indeed been observed for BChl 18. A distinction between BChl and BChl from ENDOR data can be achieved with the help of the additional hyperfine coupling constants from the vinyl group at position 2 in BChl . For these ¹H nuclei, hfcs with absolute values of ≈ +2 MHz can be expected, while the methyl group of the acetyl side chain in BChl and BChl shows a distinctly smaller hyperfine interaction.

Table 1. Calculated ¹H, ¹⁴N and ²⁵Mg isotropic hyperfine coupling constants (MHz) of bacteriochlorophyll radical ions and comparison with experimental results

		DFT calculations (B3LYP/EPR-II//BLYP/DZP)a						Experimental resultsb
Position		BChl	BChl	BChl	BChl	BChl	BChl	BChl	BChl	BChl	BChl
β-H	3	+12.25	+13.30	+13.49	−0.14	+1.14	+2.47	+13.47	+12.45	−0.50	–
	4	+14.84	–	–	−1.50	–	–	+16.35	–	−1.60	–
	7	+14.40	+12.21	+12.41	−1.57	−1.51	−1.79	+13.11	+11.60	−1.60	–
	8	+13.21	+12.10	+11.54	+0.43	+0.73	+1.87	+11.76	+10.55	+0.95	–
CH3	1a	+4.55	+4.97	+3.71	+7.48	+7.62	+6.07	+4.93	+4.70	+7.63	+8.7
	3a	−0.27	−0.37	−0.28	+0.62	+0.63	+0.67	−0.36	<0.4	≤0.50	–
	5a	+9.99	+9.19	+9.29	+9.14	+8.78	+8.35	+9.62	+8.95	+9.19	+8.7
	8a	−0.16	−0.14	−0.16	+0.66	+0.64	+0.71	−0.15	<0.4	≤0.50	–
	4b	+0.10	+14.63	+14.92	−0.06	−1.12	−1.44	–	+9.70	–	–
Methine	α	+4.11	+4.01	+3.81	−7.04	−7.63	−6.21	+2.35	+2.50	−9.65	−7.3
	β	+2.93	+2.24	+2.60	−7.17	−6.86	−6.82	+1.30	+1.20	−6.91	−6.7
	δ	+3.39	+2.87	+3.35	−5.41	−5.08	−4.31	+1.30	+1.20	−6.23	−5.3
Other	10	−5.14	−4.66	−5.06	+0.09	+0.17	+0.45	−1.64	−1.20	≤0.50	–
	4a	−0.17	−11.68	−12.03	+0.95	+1.15	+1.41	−0.36	−8.02	≤0.50	–
	7a	−0.82	−0.71	−0.73	+0.29	+0.29	+0.29	−0.53	−0.40	≤0.50	–
	2a	–	–	+1.83	–	–	+3.24	–	–	–	–
	2b	+0.19	0.00	2b1: −1.75 2b2: −1.96	+1.25	+1.25	2b1: −4.07 2b2: −4.22	−0.15	<0.4	≤0.50	–
14N	I	−2.52	−2.36	−2.27	−1.26	−1.23	−1.90	−2.25	−2.3	−1.18	–
	II	−3.58	−3.65	−3.57	+5.85	+6.18	+6.11	−3.14	−3.3	+6.52	+6.2
	III	−2.67	−2.43	−2.52	−0.63	−0.61	−0.50	−2.32	−2.3	−0.52	–
	IV	−3.74	−3.31	−3.40	+5.62	+5.50	+5.41	−2.91	−3.0	+5.86	+6.2
25Mg		−0.69	−0.68	−0.67	+1.16	+1.18	+1.11	−0.30	–	+0.85	–

• ^a DFT results for BChl , BChl , BChl and BChl from this work. Calculated data for BChl and BChl from a previous study employing the same methods and programs 49.
• ^b Experimental values from Lubitz et al. 14, 17 (BChl and BChl ), Lendzian et al. 18 (BChl ) and Davis et al. 19 (BChl ). For numbering of positions see Fig. 1.

The bacteriochlorophyll radical anions of BChl a, BChl b and BChl g showed likewise very similar geometrical parameters and spin densities, which led to the following common hyperfine characteristics (Table 1): (i) Rather small β-¹H isotropic hfcs were found (<2.5 MHz). (ii) Large values were calculated for the methyl groups at positions 1a (6–7 MHz) and 5a (8–9 MHz). (iii) The largest methine hfcs were calculated for the α and β hydrogen atoms (−6 up to −8 MHz). (iv) Positive hfcs were obtained for the nitrogen atoms in rings II and IV, negative values were computed for the ¹⁴N nuclei in rings I and III. In contrast to the radical cations, the ethyl group of BChl a, and the ethylidene group of BChl b and BChl g show only small spin densities in the radical anions (Fig. 1). Therefore, no characteristic hyperfine coupling constants are available from these groups that could be used for a clear distinction between these three species. Nevertheless, the acetyl groups of BChl , BChl and the vinyl group of BChl carry much more spin density than their positively charged counterparts. As a consequence, these data might be useful for a distinction between BChl /BChl and BChl : BChl showed two negative ¹H hfcs of ≈ −4 MHz at position 2b not present in BChl and BChl . However, the distinction between BChl and BChl is difficult only on the basis of ¹H and ¹⁴N hyperfine data.

Almost complete sets of experimental ¹H, ¹⁴N (and partly ²⁵Mg) isotropic hfcs are available for BChl 14, BChl 17 and BChl 18, 19. These data, obtained by ENDOR and TRIPLE resonance spectroscopy 7, 9 in solution, are displayed in Table 1 together with the few experimental hfcs of BChl , reported so far 19. In previous work, good agreement between theory and experiment was reported for BChl and BChl 49. In particular, the methyl groups at positions 1a, 3a, 5a and 8a were very well described by the theoretical approach. Considering BChl , similar good agreement between theory and experiment was found in this work. Again, the methyl groups are best described by the DFT calculations, while an accurate calculation of the methine hydrogen hyperfine data once more turned out to be more problematic. Furthermore, it is evident from Table 1 that the available experimental data for BChl and their assignments are in good agreement with our calculated data.

In our recent work, a comparison of calculated isotropic hfcs from DFT and RHF-INDO/SP was given for chlorophyll a and bacteriochlorophyll a radical ions 49, 50, 59, 61. It was concluded that the semi-empirical approach gives data of similar quality in comparison to the density functional calculations. BChl was also studied employing the RHF-INDO/SP approach, and especially the newer study gave results in good agreement with the experimental data 18, 59. Nevertheless, it should be pointed out that the DFT method offers several advantages in comparison to the semi-empirical approach: (i) DFT is applicable to a wider range of systems including transition metal complexes. (ii) No empirical Q factors that relate spin densities and isotropic hfcs must be introduced. (iii) A large number of spectroscopic parameters can be calculated consistently with DFT (e.g. anisotropic and isotropic hfcs including spin-orbit effects, g-tensors, nqcs, Mössbauer parameters) in combination with complete geometry optimizations.

¹⁴N nqcs χ and asymmetry parameters η of the Chl a, BChl a, BChl b and BChl g radical ions are given in Table 2. Comparing the bacteriochlorophyll species, very similar results were obtained for the three radical cations with χ ≈ 2.7 MHz (¹⁴N in rings I and III) and χ ≈ 2.9–3.1 MHz (rings II and IV). Especially the nqcs and asymmetry parameters η of N(III) and N(IV) remain very constant in all three species, which can be attributed to the fact that the rings III and IV carry the same side chains in BChl a, BChl b and BChl g. In all cationic bacteriochlorophyll radical ions, the largest nqcs were obtained for the ¹⁴N nuclei in ring II, which is the nitrogen nucleus that forms the weakest (longest) bond to the central magnesium ion. The bacteriochlorophyll radical anions are characterized by smaller nqcs that are similar for all four nitrogen atoms (2.6–2.7 MHz). A comparison of the nuclear quadrupole coupling constants of BChl and Chl revealed an interesting difference: While similar values were obtained for N(I), N(III) and N(IV), a noticeable deviation (0.41 MHz) was found in the calculated data for N(II). A similar effect was found for BChl and Chl (0.13 MHz). This can be interpreted as a result of the additional double bond in ring II of Chl a in comparison to BChl a and its contribution to the π-system.

Table 2. Calculated and experimental ¹⁴N nqcs χ = e²qQ/h (MHz) and asymmetry parameters η of (bacterio)chlorophyll radical ions

		DFT calculations (B3LYP/EPR-II//BLYP/DZP)								Exptl. Resultsa
		Chl	BChl	BChl	BChl	Chl	BChl	BChl	BChl	Chl	BChl
N(I)	χ	2.71	2.76	2.70	2.74	2.59	2.59	2.58	2.61	2.68	2.72
	η	0.56	0.44	0.50	0.43	0.70	0.65	0.65	0.60	0.6	0.67
N(II)	χ	2.68	3.09	3.06	3.07	2.81	2.68	2.66	2.65	2.68	2.92
	η	0.73	0.42	0.49	0.50	0.53	0.84	0.89	0.94	0.6	0.8
N(III)	χ	2.70	2.73	2.74	2.74	2.58	2.59	2.60	2.59	2.68	2.72
	η	0.68	0.60	0.60	0.60	0.79	0.73	0.74	0.74	0.6	0.67
N(IV)	χ	2.91	2.97	2.92	2.96	2.63	2.55	2.55	2.55	3.20	2.92
	η	0.60	0.49	0.48	0.49	0.86	0.97	0.96	0.94	0.5	0.8

• ^a ESEEM experiments on BChl ^· gave two groups of non-equivalent nitrogen atoms with nuclear quadrupole coupling constants of 2.92 MHz (η = 0.8) and 2.72 MHz (η = 0.67) 66. Experimental values of 3.23 MHz (η = 0.49) and 2.64 MHz (η = 0.60) are available for the cation radical of methyl-chlorophyllide a 68. Very similar sets of nuclear quadrupole parameters of 3.20 MHz (η = 0.5) and 2.68 MHz (η = 0.6) were measured for Chl 66. The experimental data were assigned in the table on the basis of our calculations.

For BChl and Chl , experimental nqcs are available 66, 68 and compare well with the calculated results: Considering BChl , the two groups of non-equivalent nitrogen atoms with experimental nqcs of 2.92 and 2.72 MHz 66 are well reproduced by the calculations (3.09/2.97 MHz for N(II)/N(IV) and 2.76/2.73 MHz for N(I)/N(III)). For Chl , experimental nqcs of 3.20 MHz and 2.68 MHz were published 66. Also here, the small value is very well reproduced in the calculations (2.68–2.71 MHz for N(I), N(II) and N(III)), while the large experimental nqc is underestimated by ~10% (2.91 MHz). In Table 2, the experimental data are assigned to the nitrogen nuclei on the basis of our calculations. Table 3 contains the ¹⁴N nuclear quadrupole data of the charge neutral Chl a, BChl a, BChl b and BChl g species. Similar nqcs and asymmetry parameters were calculated for the bacteriochlorophyll ¹⁴N nuclei N(III) and N(IV), while the N(I) nqc of BChl g (with an ethenyl group at ring I) is somewhat larger than the values found for N(I) in BChl a and BChl b (with acetyl groups at ring I). Also the different substitution patterns at ring II of BChl a in comparison to BChl b and BChl g are reflected in the calculated data.

Conclusion

EPR and ENDOR/TRIPLE methods have been established as important tools to study radicals that are involved in the long-range electron transfer processes in the photosynthetic reaction centers. The provided hyperfine coupling constants including signs are extremely useful to study the electronic structure of these species. In the present work, isotropic hyperfine parameters of the rather unstable BChl b and BChl g radical ions were calculated employing density functional theory. Whenever possible, the quality of the computed data was tested by a comparison of the calculated with the available experimental results 14, 17-19. In combination with our previous study on BChl a radical ions 49 a consistent data set of isotropic hfcs available for BChl a, BChl b and BChl g radical cations and anions is now provided. These data were used to test the possibility of a distinction between these species on the basis of magnetic resonance data. A comparison of the calculated EPR parameters has revealed that the substitution of the ethyl group in BChl with an ethylidene group in BChl and BChl leads to an additional large ¹H hyperfine coupling constant for both, BChl and BChl . A distinction between BChl and BChl appears to be possible by the additional ¹H hfc of the vinyl group in BChl in comparison to the acetyl group in BChl . All these effects are local in nature, the other hyperfine data of the BChl , BChl and BChl radical cations remain similar. A distinction between BChl and BChl by EPR/ENDOR data appears to be very difficult, while additional isotropic hyperfine coupling constants between −2 and −4 MHz are expected to occur for BChl , caused by the vinyl group at position 2. The calculated data from this study should be very valuable for an assignment of experimental hfcs obtained in future studies. This is especially true for studies on radical ions of BChl g, which is regarded as the ancestor of Chl a in oxygenic photosynthesis 31-34, 81.

The measurement of ¹⁴N nuclear quadrupole coupling constants continuously gains importance for the investigation of photosynthetic reaction centers, accurate data are available from ESEEM experiments 10, 18, 63, 64, 66-69. In this work, ¹⁴N nuclear quadrupole coupling constants and asymmetry parameters were calculated for Chl a, BChl a, BChl b and BChl g in their charge neutral, radical cation and radical anion states for the first time. A comparison with the experimental data available for Chl and BChl is given 66, 68, and the calculations were used for an assignment of the measured ¹⁴N data. Characteristic changes in the nqcs were traced back to structural changes in the (bacterio)chlorophyll systems.

The comparison of calculated magnetic and electric properties with experimental hfcs 14, 15, 17-19, 39 and nqcs 10, 66, 68 has further demonstrated the suitability of density functional methods for the calculation and interpretation of spectroscopic data of (bacterio)chlorophyll radicals. This is an important point, since the combination of theory and experiment helps to use the full information content of the spectra 82-84.