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.

Is the non-additive kinetic potential always equal to the difference of effective potentials from inverting the Kohn-Sham equation?

The relation used frequently in the literature according to which the non-additive kinetic potential which is a functional depending on a pair of electron densities is equal (up to a constant) to the difference of two potentials obtained from inverting two Kohn-Sham equations, is examined. The relation is based on a silent assumption that the two densities can be obtained from two independent Kohn-Sham equations, i.e., are vs-representable. It is shown that this assumption does not hold for pairs of densities: ρtot being the Kohn-Sham density in some system and ρB obtained from such partitioning of ρtot that the difference ρtot - ρB vanishes on a Lebesgue measurable volume element. The inversion procedure is still applicable for ρtot - ρB but cannot be interpreted as the inversion of the Kohn-Sham equation. It is rather the inversion of a Kohn-Sham-like equation. The effective potential in the latter equation comprises a "contaminant" that might even not be unique. It is shown that the construction of the non-additive kinetic potential based on the examined relation is not applicable for such pairs.

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.

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.

Mechanism of nitrate reduction by Desulfovibrio desulfuricans nitrate reductase--a theoretical investigation.

The oxidative half-reaction of oxygen atom transfer from nitrate to an Mo(IV) complex has been investigated at various levels of theory. Two models have been used to simulate the enzyme active site. In the second, more advanced model, additional amino acid residues capable of significantly affecting the catalytic efficiency of the enzyme were included. B3LYP/6-31+G*, ONIOM, and orbital-free embedding approaches have been used to construct the potential energy profile and to qualitatively compare the results of a QM/MM study with those obtained by a full quantum mechanical strategy. The study has confirmed the utility of the orbital-free embedding method in the description of enzymatic processes.