Exploring the Light-Capturing Properties of Photosynthetic Chlorophyll Clusters Using Large-Scale Correlated Calculations.

Chlorophylls are light-capturing units found in photosynthetic proteins. We study here the ground and excited state properties of monomeric, dimeric, and tetrameric models of the special chlorophyll/bacteriochlorophyll (Chl/BChl) pigment (P) centers P700 and P680/P870 of type I and type II photosystems, respectively. In the excited state calculations, we study the performance of the algebraic diagrammatic construction through second-order (ADC(2)) method in combination with the reduced virtual space (RVS) approach and the recently developed Laplace-transformed scaled-opposite-spin (LT-SOS) algorithm, which allows us, for the first time, to address multimeric effects at correlated ab initio levels using large basis sets. At the LT-SOS-RVS-ADC(2)/def2-TZVP level, we obtain vertical excitation energies (VEEs) of 2.00-2.07 and 1.52-1.62 eV for the P680/P700 and the P870 pigment models, respectively, which agree well with the experimental absorption maxima of 1.82, 1.77, and 1.43 eV for P680, P700, and P870, respectively. In the P680/P870 models, we find that the photoexcitation leads to a π → π* transition in which the exciton is delocalized between the adjacent Chl/BChl molecules of the central pair, whereas the exciton is localized to a single chlorophyll molecule in the P700 model. Consistent with experiments, the calculated excitonic splittings between the central pairs of P680, P700, and P870 models are 80, 200, and 400 cm(-1), respectively. The calculations show that the electron affinity of the radical cation of the P680 model is 0.4 V larger than for the P870 model and 0.2 V larger than for P700. The chromophore stacking interaction is found to strongly influence the electron localization properties of the light-absorbing pigments, which may help to elucidate mechanistic details of the charge separation process in type I and type II photosystems.

Excited state polarizabilities for CC2 using the resolution-of-the-identity approximation.

We report an implementation of static and frequency-dependent excited state polarizabilities for the approximate coupled cluster single and doubles model CC2 as analytic second derivatives of an excited state quasienergy Lagrangian. By including appropriate conditions for the normalization and the phase of the eigenvectors, divergent secular terms are avoided. This leads to response equations in a subspace orthogonal to the unperturbed eigenvectors. It is shown how these projected equations can be solved without storage of the double excitation part of the eigenvectors. By exploiting the resolution-of-the-identity approximation and a numerical Laplace transformation, the quadratic scaling of the main memory demands of RI-CC2 with the system size could be preserved. This enables calculations of excited state polarizabilities for large molecules, e.g., linear polyacenes up to decacene with almost 2500 basis functions on a single compute node within a few days. For a test set of molecules where measurements are available as reference data, we compare the orbital-relaxed and unrelaxed CC2 approaches with experiment to validate its accuracy. The approach can be easily extended to other response methods, in particular CIS(D∞). The latter gives results which, in the orbital-relaxed case, are within a few percent of the CC2 values, while coupled cluster singles results deviate typically by about 20% from orbital-relaxed CC2 and experimental reference data.

Benchmarks for 0-0 transitions of aromatic organic molecules: DFT/B3LYP, ADC(2), CC2, SOS-CC2 and SCS-CC2 compared to high-resolution gas-phase data.

In the present study a benchmark set of medium-sized and large aromatic organic molecules with 10-78 atoms is presented. For this test set 0-0 transition energies measured in supersonic jets are compared to those calculated with DFT and the B3LYP functional, ADC(2), CC2 and the spin-scaled CC2 variants SOS-CC2 and SCS-CC2. Geometries of the ground and excited states have been optimized with these methods in polarized triple zeta basis sets. Zero-point vibrational corrections have been calculated with the same methods and basis sets. In addition the energies have been corrected by single point calculations with a triple zeta basis augmented with diffuse functions, aug-cc-pVTZ. The deviations of the theoretical results from experimental electronic origins, which have all been measured in the gas phase with high-resolution techniques, were evaluated. The accuracy of SOS-CC2 is comparable to that of unscaled CC2, whereas ADC(2) has slightly larger errors. The lowest errors were found for SCS-CC2. All correlated wave function methods provide significantly better results than DFT with the B3LYP functional. The effects of the energy corrections from the augmented basis set and the method-consistent calculation of the zero-point vibrational corrections are small. With this benchmark set reliable reference data for 0-0 transition energies for larger organic chromophores are available that can be used to benchmark the accuracy of other quantum chemical methods such as new DFT functionals or semi-empirical methods for excitation energies and structures and thereby augments available benchmark sets augments present benchmark sets which include mainly smaller molecules.

Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolution-of-the-identity approximation.

We present an implementation of static and frequency-dependent polarizabilities for the approximate coupled cluster singles and doubles model CC2 and static polarizabilities for second-order Mo̸ller-Plesset perturbation theory. Both are combined with the resolution-of-the-identity approximation for electron repulsion integrals to achieve unprecedented low operation counts, input-output, and disc space demands. To avoid the storage of double excitation amplitudes during the calculation of derivatives of density matrices, we employ in addition a numerical Laplace transformation for orbital energy denominators. It is shown that the error introduced by this approximation is negligible already with a small number of sampling points. Thereby an implementation of second-order one-particle properties is realized, which avoids completely the storage of quantities scaling with the fourth power of the system size. The implementation is tested on a set of organic molecules including large fused aromatic ring systems and the C(60) fullerene. It is demonstrated that exploiting symmetry and shared memory parallelization, second-order properties for such systems can be evaluated at the CC2 and MP2 level within a few hours of calculation time. As large scale applications, we present results for the 7-, 9-, and 11-ring helicenes.

Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs.

An implementation of scaled opposite-spin CC2 (SOS-CC2) for ground and excited state energies is presented that requires only fourth order scaling computational costs. The SOS-CC2 method yields results with an accuracy comparable to the unscaled method. Furthermore the time-determining fifth order scaling steps in the algorithm can be replaced by only fourth order scaling computational costs using a "resolution of the identity" approximation for the electron repulsion integrals and a Laplace transformation of the orbital energy denominators. This leads to a significant reduction of computational costs especially for large systems. Timings for ground and excited state calculations are shown and the error of the Laplace transformation is investigated. An application to a chlorophyll molecule with 134 atoms results in a speed-up by a factor of five and demonstrates how the new implementation extends the applicability of the method. A SOS variant of the algebraic diagrammatic construction through second order ADC(2), which arises from a simplification of the SOS-CC2 model, is also presented. The SOS-ADC(2) model is a cost-efficient alternative in particular for future extensions to spectral intensities and excited state structure optimizations.