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Delta-self-consistent field (ΔSCF) theory is a conceptually simple and computationally inexpensive method for finding excited states. Using the maximum overlap method to guide optimization of the excited state, ΔSCF has been shown to predict excitation energies with a level of accuracy that is competitive with, and sometimes better than, that of time-dependent density functional theory. Here, we benchmark ΔSCF on a larger set of molecules than has previously been considered, and, in particular, we examine the performance of ΔSCF in predicting transition dipole moments, the essential quantity for spectral intensities. A potential downfall for ΔSCF transition dipoles is origin dependence induced by the nonorthogonality of ΔSCF ground and excited states. We propose and test a simple correction for this problem, based on symmetric orthogonalization of the states, and demonstrate its use on bacteriochlorophyll structures sampled from the photosynthetic antenna in purple bacteria.

Dedicated to the memory of Yuriy Nikolayevich Kozlov Oxidation of bacteriochlorophyll (BChl) with potassium ferricyanide in membranes and LH2 complexes (carotenoid-less and control samples) from the purple bacteria Allochromatium minutissimum and Rhodobacter sphaeroides as well as BChl photobleaching in a model system have been studied. The oxidation of BChl depended on the type of bacteria. BChl850 was rapidly oxidized in samples from Alc. minutissimum, and BChl800 and BChl850 were slowly oxidized in samples from Rb. sphaeroides. The carotenoids were not involved in protecting BChl from chemical oxidation in the light-harvesting complexes. The appearance of BChl oxidation product was registered in the absorption spectra (absorption maximum about 700 nm) and by HPLC analysis. The oxidized BChl was identified as 3-acetyl-chlorophyll. It differed from BChl by the presence of a double bond in pyrrole ring II at the 7-8 position. The extinction coefficient of 3-acetyl-chlorophyll was about 10 times less than that of BChl850 in the LH2 complex from Alc. minutissimum. In the BChl → 3-acetyl-chlorophyll transition, the binding constant of the latter with LH2 complex as compared with that of BChl did not change dramatically, as indicated by: (i) preserved electrophoretic mobility of the complex; (ii) the presence of 3-acetyl-chlorophyll in the complex after separation; (iii) the presence of a 3-acetyl-chlorophyll CD signal that was proportional to its absorption spectrum.

The joint application of the precise X-ray data for isolated bacteriochlorophyll complexes of reaction centers and the fundamental formulae for the energy of interaction between two equal dipoles enabled us to suggest a new methodical approach for determination of the values of the index of dielectric permeability in the micro volume enclosing special pairs in Rhodobacter sphaeroides reaction centers. The most probable value for this parameter was thus determined within 1.66-1.76. This approach was generalized for the inner layer of the membranes of purple bacteria and yielded the index value about 1.70-1.85. It is argued that this range of dielectric permeability is adequate for bacterial and plant membranes as well. Low magnitude of this parameter contributes to higher efficiency of energy migration from vast light-harvesting chlorophyll "antenna" to the energy converting reaction centers and hence to higher efficiency of the whole photosynthesis.

The light harvesting 2 (LH2) antenna complex from purple photosynthetic bacteria is an efficient natural excitation energy carrier with well-known symmetric structure, but the molecular level design principle governing its structure-function relationship is unknown. Our all-atomistic simulations of nonnatural analogues of LH2 as well as those of a natural LH2 suggest that nonnatural sizes of LH2-like complexes could be built. However, stable and consistent hydrogen bonding (HB) between bacteriochlorophyll and the protein is shown to be possible only near naturally occurring sizes, leading to significantly smaller disorder than for nonnatural ones. Extensive quantum calculations of intercomplex exciton transfer dynamics, sampled for a large set of disorder, reveal that taming the negative effect of disorder through a reliable HB as well as quantum delocalization of the exciton is a critical mechanism that makes LH2 highly functional, which also explains why the natural sizes of LH2 are indeed optimal.

Unusual temperature behavior, observed in the initial electron transfer stages in the photosynthetic reaction centers of the purple bacteria, and a strong probing pulse wavelength dependence of transfer rates, determined in transient absorption spectroscopy, can easily be explained on assuming that the transfer takes place from dynamically unrelaxed states of protein environment. The transitions from the primary special pair (P) to a single bacteriochlorophyll (B) and next to a bacteriopheophytin (H) are controlled by diffusion down the energy value of underdamped vibrational modes of frequency 200 K, probably determining distances between the succeeding cofactors. The subsequent transition to the quinone A (Q) is controlled by diffusion in the position value of an overdamped conformational mode, probably corresponding to the local polarization. From the fit of available experimental data to simple theoretical formulas, the important physical conclusion arises that the very electronic transitions are fast as compared to the relaxation processes and, in the first approximation, only the latter contribute to the overall times of the initial electron transfer stages in photosynthesis.

We have proposed the mechanism of coherent modulations of the P* state in the transient absorption spectra of the reaction center isolated from purple bacteria. Two water molecules, located between special pair, Ba, Bb chlorophylls and histidine L173 and M202, are supposed to be ortho-H2O and para-H2O isomers with different magnetic properties. The distinctive modulation frequencies were labeling as rotational resonances of ortho-H2O. According to our assumption, the interaction of rotational modes of water isomers with the charge-transfer states is a reason of coherent modulations of kinetics. We have modified a Hamiltonian system in order to take into account the rotational modes of ortho-H2O. Evolution of the density matrix was calculated in Liouville space. The Redfield relaxation theory for molecular aggregates was used to model kinetics up to 3 ps.

Subsystem density-functional theory (DFT) is a powerful and efficient alternative to Kohn-Sham DFT for large systems composed of several weakly interacting subunits. Here, we provide a systematic investigation of the spin-density distributions obtained in subsystem DFT calculations for radicals in explicit environments. This includes a small radical in a solvent shell, a π-stacked guanine-thymine radical cation, and a benchmark application to a model for the special pair radical cation, which is a dimer of bacteriochlorophyll pigments, from the photosynthetic reaction center of purple bacteria. We investigate the differences in the spin densities resulting from subsystem DFT and Kohn-Sham DFT calculations. In these comparisons, we focus on the problem of overdelocalization of spin densities due to the self-interaction error in DFT. It is demonstrated that subsystem DFT can reduce this problem, while it still allows to describe spin-polarization effects crossing the boundaries of the subsystems. In practical calculations of spin densities for radicals in a given environment, it may thus be a pragmatic alternative to Kohn-Sham DFT calculations. In our calculation on the special pair radical cation, we show that the coordinating histidine residues reduce the spin-density asymmetry between the two halves of this system, while inclusion of a larger binding pocket model increases this asymmetry. The unidirectional energy transfer in photosynthetic reaction centers is related to the asymmetry introduced by the protein environment.

This work provides a detailed account of the application of our multichromophoric Förster resonance energy transfer (MC-FRET) theory (Phys. Rev. Lett. 2004, 92, 218301) for the calculation of the energy transfer rate from the B800 unit to the B850 unit in the light harvesting complex 2 (LH2) of purple bacteria. The model Hamiltonian consists of the B800 unit represented by a single bacteriochlorophyll (BChl), the B850 unit represented by its entire set of BChls, the electronic coupling between the two units, and the bath terms representing all environmental degrees of freedom. The model parameters are determined, independent of the rate calculation, from the literature data and by a fitting to an ensemble line shape. Comparing our theoretical rate and a low-temperature experimental rate, we estimate the magnitude of the BChl-Qy transition dipole to be in the range of 6.5-7.5 D, assuming that the optical dielectric constant of the medium is in the range of 1.5-2. We examine how the bias of the average excitation energy of the B800-BChl relative to that of the B850-BChl affects the energy transfer time by calculating the transfer rates based on both our MC-FRET theory and the original FRET theory, varying the value of the bias. Within our model, we find that the value of bias 260 cm-1, which we determine from the fitting to an ensemble line shape, is very close to the value at which the ratio between MC-FRET and FRET rates is a maximum. This provides evidence that the bacterial system utilizes the quantum mechanical coherence among the multiple chromophores within the B850 in a constructive way so as to achieve efficient energy transfer from B800 to B850.

In LH2 complexes of Rhodobacter sphaeroides the formation of a carotenoid radical cation has recently been observed upon photoexcitation of the carotenoid S2 state. To shed more light onto the yet unknown molecular mechanism leading to carotenoid radical formation in LH2, the interactions between carotenoid and bacteriochlorophyll in LH2 are investigated by means of quantum chemical calculations for three different carotenoids--neurosporene, spheroidene, and spheroidenone--using time-dependent density functional theory. Crossings of the calculated potential energy curve of the electron transfer state with the bacteriochlorophyll Qx state and the carotenoid S1 and S2 states occur along an intermolecular distance coordinate for neurosporene and spheroidene, but for spheroidenone no crossing of the electron transfer state with the carotenoid S1 state could be found. By comparison with recent experiments where no formation of a spheroidenone radical cation has been observed, a molecular mechanism for carotenoid radical cation formation is proposed in which it is formed via a vibrationally excited carotenoid S1 or S*state. Arguments are given why the formation of the carotenoid radical cation does not proceed via the Qx, S2, or higher excited electron transfer states.

This review describes the structures of the two major integral membrane pigment complexes, the RC-LH1 'core' and LH2 complexes, which together make up the light-harvesting system present in typical purple photosynthetic bacteria. The antenna complexes serve to absorb incident solar radiation and to transfer it to the reaction centres, where it is used to 'power' the photosynthetic redox reaction and ultimately leads to the synthesis of ATP. Our current understanding of the biosynthesis and assembly of the LH and RC complexes is described, with special emphasis on the roles of the newly described bacteriophytochromes. Using both the structural information and that obtained from a wide variety of biophysical techniques, the details of each of the different energy-transfer reactions that occur, between the absorption of a photon and the charge separation in the RC, are described. Special emphasis is given to show how the use of single-molecule spectroscopy has provided a more detailed understanding of the molecular mechanisms involved in the energy-transfer processes. We have tried, with the help of an Appendix, to make the details of the quantum mechanics that are required to appreciate these molecular mechanisms, accessible to mathematically illiterate biologists. The elegance of the purple bacterial light-harvesting system lies in the way in which it has cleverly exploited quantum mechanics.

In this work, we have examined, using Fourier-transform Raman (FT-R) spectroscopy, the bacteriochlorophyll a (BChl a) binding sites in light-harvesting (LH) antennae from different species of the Proteobacteria that exhibit unusal absorption properties. While the LH1 complexes from Erythromicrobium (E.) ramosum (RC-B871) and Rhodospirillum centenum (B875) present classic FT-R spectra in the carbonyl high-frequency region, we show that in the blue-shifted LH1 complex, absorbing at 856 nm, from Roseococcus thiosulfatophilus, as well as in the B798-832 LH2 from E. ramosum, or in the B830 complex from the obligate phototrophic bacterium Chromatium purpuratum, some H-bonds between the acetyl carbonyl of the BChl a and the surrounding protein are missing. The molecular mechanisms responsible for the unusual absorption of these complexes are thus similar to those responsible for tuning of the absorption of the LH2 complexes between 850 and 820 nm. Furthermore, our results suggest that the binding pocket of the monomeric BChl in the LH2 from E. ramosum is different from that of Rps. acidphila or Rb. sphaeroides. The FT-R spectra of Chromatium purpuratum indicate that, in contrast with every LH2 complex previously studied by FT-R spectroscopy, no free-from-interaction keto groupings exist in this complex.