Assessment of Approximations to the Embedding Potential in Frozen-Density Embedding Theory for the Calculation of Electric Field Gradients.

The approximations to the embedding potential in frozen-density embedding theory (FDET) have been assessed for the first time for the calculation of the electric field gradient (EFG) at a nucleus. FDET-based methods using a hierarchy of approximations are applied to evaluate the EFG at the nuclei of an HCl molecule in several noncovalently bound clusters chosen to represent potential liquid or molecular crystal systems. A detailed assessment of such approximations is made for the Hartree-Fock treatment of electron-electron correlation (both in FDET and in the reference calculations for the whole cluster). The emerging choice of the optimal set of approximations is reconfirmed in calculations in which electron-electron calculations are treated at the MP2 level. Our optimized protocol produces average errors in the complexation-induced EFG shift on the order of 25% relative to conventional quantum mechanical calculations for the whole cluster. This protocol is shown to be numerically robust and leads to enormous computational savings compared to a complete quantum mechanical treatment of the embedded species and its environment. For a cluster comprising a Na+ cation and up to 24 water molecules, the computation time is reduced by a factor of 30,000 at the expense of introducing an error in the environment-induced EFG shift of 22%.

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.

Impact of M Dwarfs Ultraviolet Radiation on Prebiotic Chemistry: The Case of Adenine.

To date, several exoplanets have been found to orbit within the habitable zone of main sequence M stars (M dwarfs). These stars exhibit different levels of chromospheric activity that produces ultraviolet (UV) radiation. UV may be harmful to life, but it can also trigger reactions of prebiotic importance on the surface of a potentially habitable planet (PHP). We created a code to obtain the adenine yield for a known adenine synthesis route from diaminomaleonitrile (DAMN). We used computational methods to calculate the reaction coefficient rates (photolysis rate J and rate constant K) for the intermediate molecules DAMN, diaminofumaronitrile (DAFN), and 4-aminoimidazole-5-carbonitrile (AICN) of the adenine synthesis route. We used stellar UV sources and a mercury lamp to compare the theoretical results with experiments performed with lamps. The surface UV flux of planets in the habitable zone of two active M dwarfs (Proxima Centauri and AD Leonis) and the prebiotic Earth was calculated using the photochemical model ATMOS, considering a CO2-N2-H2O atmosphere. We obtained UV absorption coefficients for DAMN and DAFN and thermodynamic parameters that are useful for prebiotic chemistry studies. According to our results, experiments using UV lamps may underestimate the photolysis production of molecules of prebiotic importance. Our results indicate that photolysis reactions are fast with a yield of 50% of AICN in 10 s for the young Sun and ∼1 h for Proxima Centauri b. Planets around active M dwarfs may provide the most favorable environment for UV-mediated production of compounds relevant to the origins of life. The kinetic reaction AICN + HCN  adenine is the bottleneck of the pathway with reaction rates <10-22 L/(mol·s).

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.

A non-decomposable approximation on the complete density function space for the non-additive kinetic potential.

A new non-decomposable approximation of the non-additive kinetic energy potential is constructed starting from the same exact property in the limit (ρA → 0 and ∫ρB = 2), as introduced in the work of Lastra et al. [J. Chem. Phys. 129, 074107 (2008)]. In order to cover the complete function space for exponentially decaying densities, the kernel of a differential operator Dγ[ρ] is introduced and analyzed in dependence of γ. The conclusive choice of γ = 1 assures that the solution functions span the complete space of molecular electron densities. As a result, the new approximant preserves the desired feature of the older approximation, which is the reciprocal singularity if the electron density decays exponentially, and eliminates artificial shallow wells (holes), which are responsible for an artificial "charge leak." Numerical considerations using the standard validation procedure introduced by Wesolowski and Weber [Chem. Phys. Lett. 248, 71-76 (1996)] demonstrate the numerical performance of the developed approximation, which increases the range of applicability of semilocal functionals.

Quantifying Fluctuations of Average Solvent Environments for Embedding Calculations.

The viability and effectiveness of replacing an ensemble of embedded solute calculations by a single calculation using an average description of the solvent environment are evaluated. This work explores the fluctuations of the average description of the system obtained in two ways: from calculations on an ensemble of geometries and from an average environment constructed from the same ensemble. To this end, classical molecular dynamics simulations of a rigid acetone solute in SPCE water are performed in order to generate an ensemble of solvent environments. From this ensemble of solvent configurations, a number of different approaches for constructing an average solvent environment are employed. We perform a thorough numerical analysis of the fluctuations of the electrostatic potential experienced by the solute, as well as the resulting fluctuations of the solute's electronic density, measured through its dipole moment and fitted atomic point charges. At the same time, we inspect the accuracy of the methods used to construct average environments. Finally, the proposed method for generating the embedding potential from an average environment density is applied to estimate the solvatochromic shift of the first excitation of acetone. In order to account for quantum confinement effects, which may be important in certain cases, the fluctuations in the shift due to the interaction with the solvent are evaluated using frozen-density-embedding theory. Our results demonstrate that, for normally distributed environments, the constructed average environment is a reasonably good representation of a fluctuating molecular solvent environment. We then provide guidance for future comparisons between these theoretical treatments of solute/solvent systems to experimental measurements.

Benchmark of the Extension of Frozen-Density Embedding Theory to Nonvariational Correlated Methods: The Embedded-MP2 Case.

The extension of the frozen-density embedding theory for nonvariational methods [J. Chem. Theory Comput. 2020, 16, 6880] was utilized to evaluate intermolecular interaction energies for complexes in the Zhao-Truhlar basis set. In the applied method (FDET-MP2-FAT-LDA), the same auxiliary system is used to evaluate the correlation energy by means of the second-order Møller-Plesset perturbation theory (MP2), as in our previous work [J. Chem. Phys. 2019, 150, 121101]. Local density approximation is used for ExcTnad[ρA,ρB] in both cases. Additionally, the contribution to the energy due to the neglected correlation potential was evaluated and analyzed. The domain of applicability of the local density approximation for ExcTnad[ρA,ρB] was determined based on deviations from the interaction energies from the conventional MP2 calculations. The local density approximation for ExcTnad[ρA,ρB] performs well for hydrogen- or dipole-bound complexes. The relative errors in the interaction energy lie within 3-30%. While for charge-transfer complexes, this approximation fails consistently, and for other types of complexes, the performance of this approximation is not systematic. The sources of error are discussed in detail.

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.

Electron correlation effects of the ThO and ThS molecules in the spinor basis. A relativistic coupled cluster study of ground and excited states properties.

We present a comprehensive relativistic coupled cluster study of the electronic structures of the ThO and ThS molecules in the spinor basis. Specifically, we use the single-reference coupled cluster and the multi-reference Fock Space Coupled Cluster (FSCC) methods to model their ground and electronically-excited states. Two variants of the FSCC method have been investigated: (a) one where the electronic spectrum is obtained from sector (1,1) of the Fock space, and (b) another where the excited states come from the doubly attached electronic states to the doubly charged systems (ThO2+ and ThS2+), that is, from sector (0,2) of the Fock space. Our study provides a reliable set of spectroscopic parameters such as bond lengths, excitation energies, and vibrational frequencies, as well as a detailed analysis of the electron correlation effects in the ThO and ThS molecules. Finally, we examine the first ionization potential and electron affinity of the above mentioned molecules.

Communication: Two types of flat-planes conditions in density functional theory.

Using results from atomic spectroscopy, we show that there are two types of flat-planes conditions. The first type of flat-planes condition occurs when the energy as a function of the number of electrons of each spin, Nα and Nß, has a derivative discontinuity on a line segment where the number of electrons, Nα + Nß, is an integer. The second type of flat-planes condition occurs when the energy has a derivative discontinuity on a line segment where the spin polarization, Nα - Nß, is an integer, but does not have a discontinuity associated with an integer number of electrons. Type 2 flat planes are rare-we observed just 15 type 2 flat-planes conditions out of the 4884 cases we tested-but their mere existence has implications for the design of exchange-correlation energy density functionals. To facilitate the development of functionals that have the correct behavior with respect to both fractional number of electrons and fractional spin polarization, we present a dataset for the chromium atom and its ions that can be used to test new functionals.