Carolin König

Quantum Chemical Description of Absorption Properties and Excited‐State Processes in Photosynthetic Systems

The theoretical description of the initial steps in photosynthesis has gained increasing importance over the past few years. This is caused by more and more structural data becoming available for light-harvesting complexes and reaction centers which form the basis for atomistic calculations and by the progress made in the development of first-principles methods for excited electronic states of large molecules. In this Review, we discuss the advantages and pitfalls of theoretical methods applicable to photosynthetic pigments. Besides methodological aspects of excited-state electronic-structure methods, studies on chlorophyll-type and carotenoid-like molecules are discussed. We also address the concepts of exciton coupling and excitation-energy transfer (EET) and compare the different theoretical methods for the calculation of EET coupling constants. Applications to photosynthetic light-harvesting complexes and reaction centers based on such models are also analyzed.

Sate-specific embedding potentials for excitation-energy calculations

Embedding potentials are frequently used to describe the effect of an environment on the electronic structure of molecules in larger systems, including their excited states. If such excitations are accompanied by significant rearrangements in the electron density of the embedded molecule, large differential polarization effects may take place, which in turn can require state-specific embedding potentials for an accurate theoretical description. We outline here how to extend wave function in density functional theory (WF/DFT) methods to compute the excitation energies of a molecule in a responsive environment through the use of state-specific density-based embedding potentials constructed within a modified subsystem DFT approach. We evaluate the general expression of the ground- and excited-state energy difference of the total system both with the use of state-independent and state-dependent embedding potentials and propose some practical recipes to construct the approximate excited-state DFT density of the active part used to polarize the environment. We illustrate these concepts with the state-independent and state-dependent WF/DFT computation of the excitation energies of p-nitroaniline, acrolein, methylenecyclopropene, and p-nitrophenolate in various solvents.

Protein Effects on the Optical Spectrum of the Fenna-Matthews-Olson Complex from Fully Quantum Chemical Calculations.

We present a fully quantum-chemical study on the optical spectra of the Fenna-Matthews-Olson (FMO) protein. We have investigated the structural and environmental effects on the site energies and excitonic couplings as well as on the UV/vis absorption spectra. Our largest model of the entire protein-pigment network contains more than 7000 atoms. Structures of all bacteriochlorophyll pigments have been optimized in their binding pockets, comprising more than 1000 atoms in some cases. We find that the site energies are quite sensitive to structural and environmental changes in the model setup, while excitonic couplings are more robust. It is shown that nonoptimized pigment structures lead to site energies closer to the ones for pigments optimized in their binding pocket than to those for conformations fully optimized in vacuum. The determination of reliable site energies is one of the key factors for an understanding of the excited-state properties of the FMO protein.

Direct determination of exciton couplings from subsystem time-dependent density-functional theory within the Tamm–Dancoff approximation

In subsystem time-dependent density functional theory (TDDFT) [J. Neugebauer, J. Chem. Phys. 126, 134116 (2007)] localized excitations are used to calculate delocalized excitations in large chromophore aggregates. We have extended this formalism to allow for the Tamm-Dancoff approximation (TDA). The resulting response equations have a form similar to a perturbative configuration interaction singles (CIS) approach. Thus, the inter-subsystem matrix elements in subsystem TDA can, in contrast to the full subsystem-TDDFT case, directly be interpreted as exciton coupling matrix elements. Here, we present the underlying theory of subsystem TDDFT within the TDA as well as first applications. Since for some classes of pigments, such as linear polyenes and carotenoids, TDA has been reported to perform better than full TDDFT, we also report applications of this formalism to exciton couplings in dimers of such pigments and in mixed bacteriochlorophyll-carotenoid systems. The improved description of the exciton couplings can be traced back to a more balanced description of the involved local excitations.

Wavefunction-in-density functional theory embedding for excited states: Which wavefunctions, which densities?

We present a detailed analysis of our recently proposed wavefunction in density functional theory method to include differential polarization effects through state-specific embedding potentials. We study methylenecyclopropene and acrolein in water by using several wavefunction approaches to validate the supermolecular reference and to assess their response to embedding. We find that quantum Monte Carlo, complete-active space second-order perturbation theory, and coupled cluster methods give very consistent solvatochromic shifts and a similar response to embedding. Our scheme corrects the excitation energies produced with a frozen environment, but the values are often overshot. To ameliorate the problem, one needs to use wavefunction densities to polarize the environment. The choice of the exchange-correlation functional in the construction of the potential has little effect on the excitation, whereas the approximate kinetic-energy functional appears to be the largest source of error.

Automatic determination of important mode–mode correlations in many-mode vibrational wave functions

We introduce new automatic procedures for parameterizing vibrational coupled cluster (VCC) and vibrational configuration interaction wave functions. Importance measures for individual mode combinations in the wave function are derived based on upper bounds to Hamiltonian matrix elements and/or the size of perturbative corrections derived in the framework of VCC. With a threshold, this enables an automatic, system-adapted way of choosing which mode-mode correlations are explicitly parameterized in the many-mode wave function. The effect of different importance measures and thresholds is investigated for zero-point energies and infrared spectra for formaldehyde and furan. Furthermore, the direct link between important mode-mode correlations and coordinates is illustrated employing water clusters as examples: Using optimized coordinates, a larger number of mode combinations can be neglected in the correlated many-mode vibrational wave function than with normal coordinates for the same accuracy. Moreover, the fraction of important mode-mode correlations compared to the total number of correlations decreases with system size. This underlines the potential gain in efficiency when using optimized coordinates in combination with a flexible scheme for choosing the mode-mode correlations included in the parameterization of the correlated many-mode vibrational wave function. All in all, it is found that the introduced schemes for parameterizing correlated many-mode vibrational wave functions lead to at least as systematic and accurate calculations as those using more standard and straightforward excitation level definitions. This new way of defining approximate calculations offers potential for future calculations on larger systems.

Hybrid Optimized and Localized Vibrational Coordinates.

We present a new type of vibrational coordinates denoted hybrid optimized and localized coordinates (HOLCs) aiming at a good set of rectilinear vibrational coordinates supporting fast convergence in vibrational stucture calculations. The HOLCs are obtained as a compromise between the recently promoted optimized coordinates (OCs) and localized coordinates (LCs). The three sets of coordinates are generally different from each other and differ from standard normal coordinates (NCs) as well. In determining the HOLCs, we optimize the vibrational self-consistent field (VSCF) energy with respect to orthogonal transformation of the coordinates, which is similar to determining OCs but for HOLCs we additionally introduce a penalty for delocalization, by using a measure of localization similar to that employed in determining LCs. The same theory and implementation covers OCs, LCs, and HOLCs. It is shown that varying one penalty parameter allows for connecting OCs and LCs. The HOLCs are compared to NCs, OCs, and LCs in their nature and performance as basis for vibrational coupled cluster (VCC) response calculations of vibrational anharmonic energies for a small set of simple systems comprising water, formaldehyde, and ethylene. It is found that surprisingly good results can be obtained with HOLCs by using potential energy surfaces as simple as quadratic Taylor expansions. Quite similar coordinates are found for the already established OCs but obtaining these OCs requires much more elaborate and expensive potential energy surfaces and localization is generally not guaranteed. The ability to compute HOLCs for somewhat larger systems is demonstrated for coumarin and the alanine quadramer. The good agreement between HOLCs and OCs, together with the much easier applicability of HOLCs for larger systems, suggests that HOLCs may be a pragmatically very interesting option for anharmonic calculations on medium to large molecular systems.

Exciton Coupling Mechanisms Analyzed with Subsystem TDDFT: Direct vs Pseudo Exchange Effects

The dominant effect in exciton coupling is usually the so-called Coulomb coupling contribution, that is the Coulomb interaction between transition densities of localized excitations. At short distances, Dexter-type exchange effects are discussed to play a role, which are not well described by (semi)local functionals in time-dependent density functional theory (TDDFT) calculations. Overall, a large effect of the percentage of exact exchange on the resulting exciton splittings is known. Subsystem TDDFT allows one to analyze the exciton coupling mechanism by distinguishing direct from indirect effects, that is, changes in the actual coupling mechanism from modifications in the underlying local excitations. Our analysis shows that the strong influence of exact exchange is not due to a direct Dexter-type (exchange) coupling, but rather to an increased Coulomb (or pseudo-exchange) coupling triggered by a change in transition densities. This is demonstrated in calculations for 2-pyridone and chlorophyll dimers. We finally propose a route to efficient calculations of excited states of large pigment aggregates with hybrid functionals, which so far has been out of reach for quantum chemical methods.

Linear-scaling generation of potential energy surfaces using a double incremental expansion

We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local coordinates in this context allows the generation of PESs in a very cost-efficient way. For this, we employ the recently introduced flexible adaptation of local coordinates of nuclei (FALCON) coordinates. By introducing an additional transformation step, concerning only a fraction of the vibrational degrees of freedom, we can achieve linear scaling of the accumulated cost of the single point calculations required in the PES generation. Numerical examples of these double incremental approaches for oligo-phenyl examples show fast convergence with respect to the maximum number of simultaneously treated fragments and only a modest error introduced by the additional transformation step. The approach, presented here, represents a major step towards the applicability of vibrational wave function methods to sizable, covalently bound systems.