Electronic Energy Transfer in Polarizable Heterogeneous Environments:a Systematic Investigation of Different Quantum Chemical Approaches

Theoretical prediction of transport and optical properties of protein–pigment complexes is of significant importance when aiming at understanding the structure–function relationship in such systems. Electronic energy transfer (EET) couplings represent a key property in this respect since such couplings provide important insight into the strength of interaction between photoactive pigments in protein–pigment complexes. Recently, attention has been payed to how the environment modifies or even controls the electronic couplings. To enable such theoretical predictions, a fully polarizable embedding model has been suggested (Curutchet, C., et al. <i>J. Chem. Theory Comput.</i>, 2009, <i>5</i>, 1838–1848). In this work, we further develop this computational model by extending it with an ab initio derived polarizable force field including higher-order multipole moments. We use this extended model to systematically examine three different ways of obtaining EET couplings in a heterogeneous medium ranging from use of the exact transition density to a point-dipole approximation. Several interesting observations are made, for example, the explicit use of transition densities in the calculation of the electronic couplings, and also when including the explicit environment contribution, can be replaced by a much simpler transition point charge description without comprising the quality of the model predictions

A quantum-mechanical perspective on linear response theory within polarizable embedding

The derivation of linear response theory within polarizable embedding is carried out from a rigorous quantum-mechanical treatment of a composite system. Two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are presented, and the pole structures as well as residues of the individual terms are analyzed and discussed. This theoretical analysis clarifies which form of the response function to use in polarizable embedding, and we highlight complications in separating out subsystem contributions to molecular properties. For example, based on the nonsymmetric decomposition of the complex linear response function, we derive conservation laws for integrated absorption cross sections, providing a solid basis for proper calculations of the intersubsystem intensity borrowing inherent to coupled subsystems and how that can lead to negative subsystem intensities. We finally identify steps and approximations required to achieve the transition from a quantum-mechanical description of the composite system to polarizable embedding with a classical treatment of the environment, thus providing a thorough justification for the descriptions used in polarizable embedding models

Conformational Dependence of Isotropic Polarizabilities

We perform a statistical and energetic analysis of atomic polarizabilities obtained with the LoProp approach for all atoms in the avidin tetramer for 70 snapshots from molecular dynamics simulations with seven different biotin analogues, and from the crystal structure of the photosynthetic reaction center (in total 560 698 individual polarizabilities). Dynamic effects give a variation of the polarizabilities of 0.09 angstrom(3) on average. Atoms at different positions in the sequence show a variation of 0.14 angstrom(3) on average, caused by the conformational dependence of the polarizabilities. This variation gives errors of 2 and 1 kJ/mol for relative conformational and ligand-binding induction energies. Averaged elementwise or atom type polarizabilities give larger errors, e.g., 9 and 7 kJ/mol, respectively, for the relative conformational energies. Therefore, we recommend that polarizabilities should be assigned atomwise (i.e., individual polarizabilities for each atom in all residues), in the same way as for charges. We provide such a set of extensively averaged polarizabilities (xAvPol) for all atoms in avidin and the photosynthetic reaction center, applicable at the B3LYP/aug-cc-pVTZ level, which is converged with respect to the basis-set limit

Ligand affinities estimated by quantum chemical calculations

We present quantum chemical estimates of ligand-binding affinities performed, for the first time, at a level of theory for which there is a hope that dispersion and polarization effects are properly accounted for (MP2/cc-pVTZ) and at the same time effects of solvation, entropy, and sampling are included. We have studied the binding of seven biotin analogues to the avidin tetramer. The calculations have been performed by the recently developed PMISP approach (polarizable multipole interactions with supermolecular pairs), which treats electrostatic interactions by multipoles up to quadrupoles, induction by anisotropic polarizabilities, and nonclassical interactions (dispersion, exchange repulsion, etc.) by explicit quantum chemical calculations, using a fragmentation approach, except for long-range interactions that are treated by standard molecular-mechanics Lennard-Jones terms. In order to include effects of sampling, 10 snapshots from a molecular dynamics simulation are studied for each biotin analogue. Solvation energies are estimated by the polarized continuum model (PCM), coupled to the multipole-polarizability model. Entropy effects are estimated from vibrational frequencies, calculated at the molecular mechanics level. We encounter several problems, not previously discussed, illustrating that we are first to apply such a method. For example, the PCM model is, in the present implementation, questionable for large molecules, owing to the use of a surface definition that gives numerous small cavities in a protein

Combining Polarizable Embedding with the Frenkel exciton model:Applications to absorption spectra with overlapping solute-solvent bands

Modeling of spectral properties of extended chemical systems, such as the case of a solute in a solvent, is often performed based on so-called hybrid models in which only part of the complete system is given a quantum chemical description. The remaining part of the system is represented by an embedding potential treating the environment either by a discrete or continuum model. In order to successfully make use of minimally sized quantum chemical regions, theembedding potential should represent the environment as authentic as possible. Here, the importance of exactly such an accurate description of the embedding potential is investigated by comparing the performance of the Polarizable Embedding scheme against larger sized full quantum mechanical calculations. Our main conclusion is that as long as the solute and solvent do not overlap in their absorption spectra, the Polarizable Embedding approach shows results consistent with full quantum chemical calculations. For partly overlapping absorption spectra the Polarizable Embedding approach can furthermore successfully be expanded within a Frenkel exciton approach based on only economical monomeric quantum chemical calculations. Thus, by extending the Polarizable Embedding scheme to the exciton picture it is possible to cover computations of the whole absorption spectrum andstill reduce the computational cost compared to costly cluster calculations.<br

How Far Does a Receptor Influence Vibrational Properties of an Odorant?

The biophysical mechanism of the sense of smell, or olfaction, is still highly debated. The mainstream explanation argues for a shape-based recognition of odorant molecules by olfactory receptors, while recent investigations suggest the primary olfactory event to be triggered by a vibrationally-assisted electron transfer reaction. We consider this controversy by studying the influence of a receptor on the vibrational properties of an odorant in atomistic details as the coupling between electronic degrees of freedom of the receptor and the vibrations of the odorant is the key parameter of the vibrationally-assisted electron transfer. Through molecular dynamics simulations we elucidate the binding specificity of a receptor towards acetophenone odorant. The vibrational properties of acetophenone inside the receptor are then studied by the polarizable embedding density functional theory approach, allowing to quantify protein-odorant interactions. Finally, we judge whether the effects of the protein provide any indications towards the existing theories of olfaction

Theoretical Fe-57 Mossbauer spectroscopy: isomer shifts of [Fe]- hydrogenase intermediates

Mossbauer spectroscopy is an indispensable spectroscopic technique and analytical tool in iron coordination chemistry. The linear correlation between the electron density at the nucleus ("contact density'') and experimental isomer shifts has been used to link calculated contact densities to experimental isomer shifts. Here we have investigated relativistic methods of systematically increasing sophistication, including the eXact 2-Component (X2C) Hamiltonian and a finite-nucleus model, for the calculation of isomer shifts of iron compounds. While being of similar accuracy as the full four-component treatment, X2C calculations are far more efficient. We find that effects of spin-orbit coupling can safely be neglected, leading to further speedup. Linear correlation plots using effective densities rather than contact densities versus experimental isomer shift lead to a correlation constant a = -0.294 a(0)(-3) mm s(-1) (PBE functional) which is close to an experimentally derived value. Isomer shifts of similar quality can thus be obtained both with and without fitting, which is not the case if one pursues a priori a non-relativistic model approach. As an application for a biologically relevant system, we have studied three recently proposed [ Fe]-hydrogenase intermediates. The structures of these intermediates were extracted from QM/MM calculations using large QM regions surrounded by the full enzyme and a solvation shell of water molecules. We show that a comparison between calculated and experimentally observed isomer shifts can be used to discriminate between different intermediates, whereas calculated atomic charges do not necessarily correlate with Mossbauer isomer shifts. Detailed analysis reveals that the difference in isomer shifts between two intermediates is due to an overlap effect

Unraveling the similarity of the photoabsorption of deprotonated p-coumaric acid in the gas phase and within the photoactive yellow protein

Using advanced QM/MM methods, the surprisingly negligible shift of the lowest-lying bright electronic excitation of the deprotonated p-coumaric acid (pCA(-)) within the photoactive yellow protein (PYP) is shown to stem from a subtle balance between hypsochromic and bathochromic effects. More specifically, it is found that the change in the excitation energy as a consequence of the disruption of the planarity of pCA(-) inside PYP is nearly canceled out by the shift induced by the intermolecular interactions of the chromophore and the protein as a whole. These results provide important insights about the primary absorption and the tuning of the chromophore by the protein environment in PYP

Polarizable Density Embedding for Large Biomolecular Systems

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of Chemical Theory and Computation, Copyright © 2020 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acs.jctc.0c00763.We present an efficient and robust fragment-based quantum–classical embedding model capable of accurately capturing effects from complex environments such as proteins and nucleic acids. This is realized by combining the molecular fractionation with conjugate caps (MFCC) procedure with the polarizable density embedding (PDE) model at the level of Fock matrix construction. The PDE contributions to the Fock matrix of the core region are constructed using the local molecular basis of the individual fragments rather than the supermolecular basis of the entire system. Thereby, we avoid complications associated with the application of the MFCC procedure on environment quantities such as electronic densities and molecular-orbital energies. Moreover, the computational cost associated with solving self-consistent field (SCF) equations of the core region remains unchanged from that of purely classical polarized embedding models. We analyze the performance of the resulting model in terms of the reproduction of the electrostatic potential of an insulin monomer protein and further in the context of solving problems related to electron spill-out. Finally, we showcase the model for the calculation of one- and two-photon properties of the Nile red molecule in a protein environment. Based on our analyses, we find that the combination of the MFCC approach with the PDE model is an efficient, yet accurate approach for calculating molecular properties of molecules embedded in structured biomolecular environments