Maarten T. P. Beerepoot

Intermolecular charge transfer enhances two-photon absorption in yellow fluorescent protein

We present a quantum chemical study of the two-photon absorption (TPA) properties of yellow fluorescent protein (YFP), a mutant of the extensively studied green fluorescent protein. The aromatic chromophore of YFP has a π-stacking interaction with the aromatic ring of a tyrosine residue (Tyr203) in a parallel-displaced structure with a distance of about 3.4 Å. We study the TPA spectrum of the π-stacking system of YFP using the well-established Coulomb-attenuated B3LYP density functional (CAM-B3LYP) and the second-order approximate coupled-cluster model CC2. This work presents both the first comprehensive study of the two-photon absorption spectrum of YFP and the largest-scale coupled-cluster calculation of two-photon absorption that has ever been performed. We analyze the intermolecular charge-transfer (ICT) transitions in this stacked system and show that the ICT transitions are an important mechanism for enhancing the TPA cross sections in YFP. We investigate the distance dependence of the ICT transitions and show that their TPA cross sections are strongly dependent on the separation of the aromatic moieties. This provides a means for tuning the TPA properties of YFP and other structurally related fluorescent proteins through molecular engineering.

Rotational averaging of multiphoton absorption cross sections

Rotational averaging of tensors is a crucial step in the calculation of molecular properties in isotropic media. We present a scheme for the rotational averaging of multiphoton absorption cross sections. We extend existing literature on rotational averaging to even-rank tensors of arbitrary order and derive equations that require only the number of photons as input. In particular, we derive the first explicit expressions for the rotational average of five-, six-, and seven-photon absorption cross sections. This work is one of the required steps in making the calculation of these higher-order absorption properties possible. The results can be applied to any even-rank tensor provided linearly polarized light is used.

Averaged Solvent Embedding Potential Parameters for Multiscale Modeling of Molecular Properties

We derive and validate averaged solvent parameters for embedding potentials to be used in polarizable embedding quantum mechanics/molecular mechanics (QM/MM) molecular property calculations of solutes in organic solvents. The parameters are solvent-specific atom-centered partial charges and isotropic polarizabilities averaged over a large number of geometries of solvent molecules. The use of averaged parameters reduces the computational cost to obtain the embedding potential, which can otherwise be a rate-limiting step in calculations involving large environments. The parameters are evaluated by analyzing the quality of the resulting molecular electrostatic potentials with respect to full QM potentials. We show that a combination of geometry-specific parameters for solvent molecules close to the QM region and averaged parameters for solvent molecules further away allows for efficient polarizable embedding multiscale modeling without compromising the accuracy. The results are promising for the development of general embedding parameters for biomolecules, where the reduction in computational cost can be considerable.

Molecular quantum mechanical gradients within the polarizable embedding approach—Application to the internal vibrational Stark shift of acetophenone

We present an implementation of analytical quantum mechanical molecular gradients within the polarizable embedding (PE) model to allow for efficient geometry optimizations and vibrational analysis of molecules embedded in large, geometrically frozen environments. We consider a variational ansatz for the quantum region, covering (multiconfigurational) self-consistent-field and Kohn-Sham density functional theory. As the first application of the implementation, we consider the internal vibrational Stark effect of the C=O group of acetophenone in different solvents and derive its vibrational linear Stark tuning rate using harmonic frequencies calculated from analytical gradients and computed local electric fields. Comparisons to PE calculations employing an enlarged quantum region as well as to a non-polarizable embedding scheme show that the inclusion of mutual polarization between acetophenone and water is essential in order to capture the structural modifications and the associated frequency shifts observed in water. For more apolar solvents, a proper description of dispersion and exchange-repulsion becomes increasingly important, and the quality of the optimized structures relies to a larger extent on the quality of the Lennard-Jones parameters.

Open-ended response theory with polarizable embedding: multiphoton absorption in biomolecular systems.

We present the theory and implementation of an open-ended framework for electric response properties at the level of Hartree-Fock and Kohn-Sham density functional theory that includes effects from the molecular environment modeled by the polarizable embedding (PE) model. With this new state-of-the-art multiscale functionality, electric response properties to any order can be calculated for molecules embedded in polarizable atomistic molecular environments ranging from solvents to complex heterogeneous macromolecules such as proteins. In addition, environmental effects on multiphoton absorption (MPA) properties can be studied by evaluating single residues of the response functions. The PE approach includes mutual polarization effects between the quantum and classical parts of the system through induced dipoles that are determined self-consistently with respect to the electronic density. The applicability of our approach is demonstrated by calculating MPA strengths up to four-photon absorption for the green fluorescent protein. We show how the size of the quantum region, as well as the treatment of the border between the quantum and classical regions, is crucial in order to obtain reliable MPA predictions.

Electronic circular dichroism of fluorescent proteins: a computational study.

The electronic circular dichroism (ECD) properties of the green fluorescent protein and other fluorescent proteins have been calculated with density functional theory. The influence of different embedding models on the ECD signal of the chromophore has been investigated by modeling the protein environment by the polarizable continuum model (QM/PCM), by the polarizable embedding model (PE-QM/MM), by treating the minimal environment quantum mechanically at the same footing as the chromophore (QM/QM), and by adding the remaining part of the protein by means of PCM (QM/QM/PCM). The rotatory strength is found to be more sensitive than the oscillatory strength to changes in the geometry of the chromophore and its surroundings and to the type of embedding model used. In general, explicit embedding of the surrounding protein (PE-QM/MM or QM/QM) induces an increase in the rotatory strength of the chromophore. Explicit inclusion of the whole protein through polarizable embedding is found to be an affordable embedding model that gives the correct sign of the rotatory strength for all fluorescent proteins. PCM is useful as a first approximation to protein environment effects, but as a rule seems to underestimate the rotatory strength.

Channel interference in multiphoton absorption

We extend the theory of channel interference to higher-order multiphoton absorption processes. We derive an explicit expression for channel interference in a three-photon absorption process and propose a general scheme for deriving such expressions for multiphoton absorption processes of any order. Based on this general scheme, we derive and analyze the simplest few-state models for multiphoton absorption in centrosymmetric molecules and discuss the criteria for maximizing the corresponding multiphoton absorption strengths.

Benchmarking the Performance of Exchange-Correlation Functionals for Predicting Two-Photon Absorption Strengths

The present work investigates the performance of exchange-correlation functionals in the prediction of two-photon absorption (2PA) strengths. For this purpose, we considered six common functionals used for studying 2PA processes and tested these on six organoboron chelates. The set consisted of two semilocal (PBE and BLYP), two hybrid (B3LYP and PBE0), and two range-separated (LC-BLYP and CAM-B3LYP) functionals. The RI-CC2 method was chosen as a reference level and was found to give results consistent with the experimental data that are available for three of the molecules considered. Of the six exchange-correlation functionals studied, only the range-separated functionals predict an ordering of the 2PA strengths that is consistent with experimental and RI-CC2 results. Even though the range-separated functionals predict correct relative trends, the absolute values for the 2PA strengths are underestimated by a factor of 2-6 for the molecules considered. An in-depth analysis, on the basis of the derived generalized few-state model expression for the 2PA strength for a coupled-cluster wave function, reveals that the problem with these functionals can be linked to underestimated excited-state dipole moments and, to a lesser extent, overestimated excitation energies. The semilocal and hybrid functionals exhibit less predictable errors and a variation in the 2PA strengths in disagreement with the reference results. The semilocal and hybrid functionals show smaller average errors than the range-separated functionals, but our analysis reveals that this is due to fortuitous error cancellation between excitation energies and the transition dipole moments. Our results constitute a warning against using currently available exchange-correlation functionals in the prediction of 2PA strengths and highlight the need for functionals that correctly describe the electron density of excited electronic states.