Embedding Nonrigid Solutes in an Averaged Environment: A Case Study on Rhodopsins.

Many simulation methods concerning solvated molecules are based on the assumption that the solvated species and the solvent can be characterized by some representative structures of the solute and some embedding potential corresponding to this structure. While the averaging of the solvent configurations to obtain an embedding potential has been studied in great detail, this hinges on a single solute structure representation. This assumption is re-examined and generalized for conformationally flexible solutes and tested on 4 nonrigid systems. In this generalized approach, the solute is characterized by a set of representative structures and the corresponding embedding potentials. The representative structures are identified by means of subdividing the statistical ensemble, which in this work is generated by a constant-temperature molecular dynamics simulation. The embedding potential defined in the Frozen-Density Embedding Theory is used to characterize the average effect of the solvent in each subensemble. The numerical examples concern the vertical excitation energies of protonated retinal Schiff bases in protein environments. It is comprehensively shown that subensemble averaging leads to huge computational savings compared with explicit averaging of the excitation energies in the whole ensemble while introducing only minor errors in the case of the systems examined.

N-representability of the target density in Frozen-Density Embedding Theory based methods: Numerical significance and its relation to electronic polarization.

The accuracy of any observable derived from multi-scale simulations based on Frozen-Density Embedding Theory (FDET) is affected by two inseparable factors: (i) the approximation for the ExcT nad[ρA,ρB] component of the FDET energy functional and (ii) the choice of the density ρB(r) for which the FDET eigenvalue equation for the embedded wavefunction is solved. A procedure is proposed to estimate the relative significance of these two factors. Numerical examples are given for four weakly bound intermolecular complexes. It is shown that the violation of the non-negativity condition is the principal source of error in the FDET energy if ρB is the density of the isolated environment, i.e., it is generated without taking into account the interactions with the embedded species. Reduction of both the magnitude of the violation of the non-negativity condition and the error in the FDET energy can be pragmatically achieved by means of the explicit treatment of the electronic polarization of the environment.

Frontiers in Multiscale Modeling of Photoreceptor Proteins.

This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

Embedding-theory-based simulations using experimental electron densities for the environment.

The basic idea of frozen-density embedding theory (FDET) is the constrained minimization of the Hohenberg-Kohn density functional EHK[ρ] performed using the auxiliary functional E_{v_{AB}}^{\rm FDET}[\Psi _A, \rho _B], where ΨA is the embedded NA-electron wavefunction and ρB(r) is a non-negative function in real space integrating to a given number of electrons NB. This choice of independent variables in the total energy functional E_{v_{AB}}^{\rm FDET}[\Psi _A, \rho _B] makes it possible to treat the corresponding two components of the total density using different methods in multi-level simulations. The application of FDET using ρB(r) reconstructed from X-ray diffraction data for a molecular crystal is demonstrated for the first time. For eight hydrogen-bonded clusters involving a chromophore (represented as ΨA) and the glycylglycine molecule [represented as ρB(r)], FDET is used to derive excitation energies. It is shown that experimental densities are suitable for use as ρB(r) in FDET-based simulations.

The deconvolution analysis of ATR-FTIR spectra of diacetylene during UV exposure.

We performed a detailed deconvolution analysis of ATR-FTIR peaks of a common diacetylene, 10,12-tricosadiynoic acid (TRCDA) during the polymerization and the blue-to-red transition. Based on the analysis and the solvent dependence on the IR signals, we found that the triple peak from CC stretching mode that has been previously suspected as a consequence of Fermi resonance is rather associated with the macromolecular assembly of TRCDA. Besides these CC triple peaks, we found that the background in the region increased during the UV exposure due to the CC signals from polymers. In addition, the anisotropic compression during polymerization was also detected, which supports the proposed interpretation of X-ray data reported previously. These results are the benefits from the deconvolution analysis.

Explicit vs. implicit electronic polarisation of environment of an embedded chromophore in frozen-density embedding theory.

Frozen-Density Embedding Theory (FDET) provides a system-independent formal framework for multi-level computational methods. Despite apparent similarity, the interaction energy components commonly used in QM/MM methods do not have their corresponding counterparts in FDET. We show how the effect of the polarisation on the electron distribution in the environment can be (or is) accounted for either explicitly or implicitly within the FDET framework. Numerical examples are provided for vertical excitation energies in four representative cases of embedded chromophores.

Benchmark of Excitation Energy Shifts from Frozen-Density Embedding Theory: Introduction of a Density-Overlap-Based Applicability Threshold.

We present a thorough investigation of the errors in results obtained with the combination of frozen-density embedding theory and the algebraic diagrammatic construction scheme for the polarization propagator of second order (FDE-ADC(2)). The study was carried out on a set of 52 intermolecular complexes with varying interaction strength, each consisting of a chromophore of fundamental interest and a few small molecules in its environment. The errors emerging in frozen-density embedding theory-based methods originate from (a) the solver of the quantum many-body problem used to obtain the embedded wave function (ΨAemb), (b) the approximation for the explicit density functional for the embedding potential, and (c) the choice of the density representing the environment (ρB( r⃗)). The present work provides a comprehensive analysis of the errors in the excitation energies based on the last two factors. Furthermore, a density-overlap-based parameter is proposed to be used as an a priori criterion of applicability.