Quantifying Fluctuations of Average Environments for Embedding Calculations

In the context of employing embedding methods to study spectroscopic properties, the viability and effectiveness of replacing an ensemble of calculations by a single calculation using an average description of the system of study are evaluated. This work aims to provide a baseline of the expected fluctuations in the average description of the system obtained in the two cases: from calculations of an ensemble of geometries, and from an average environment constructed with the same ensemble. To this end, the classical molecular dynamics simulation of a very simple system was used: a rigid molecule of acetone in a solution of rigid water. We perform a careful numerical analysis of the fluctuations of the electrostatic potential felt by the solute, as well as the fluctuations in the effect on its electronic density, measure through the dipole moment and the atomic charges derived from the corresponding potential. At the same time, we inspect the accuracy of the methods used to construct average environments. Finally, the proposed approach to generate 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 that may be important in certain cases, the fluctuations on the shift due to the interaction with the solvent are evaluated using Frozen-Density Embedding Theory. Our results demonstrate that, for normally-behaved environments, the constructed average environment is a reasonably good representation of a discrete solvent environment.

Embedding non-rigid 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 structure of the solute and some embedding potential corresponding to this structure. This assumption is re-examined and generalized for conformationally flexible solutes. In the proposed and investigated generalization, 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 Frozen-Density Embedding Theory is used to characterize the average effect of the solvent in each subensemble. The numerical examples concern vertical excitation energies of protonated retinal Schiff bases in protein environments. It is comprehensively shown that subensemble averaging leads to huge computational savings compared to explicit averaging of the excitation energies in the whole ensemble while introducing only minor errors.

Flexible boundary layer using exchange for embedding theories. I. Theory and implementation

Embedding theory is a powerful computational chemistry approach to exploring the electronic structure and dynamics of complex systems, with QM/MM being the prime example. A challenge arises when trying to apply embedding methodology to systems with diffusible particles, e.g. solvents, if some of them must be included in the QM region, for example in the description of solvent-supported electronic states or reactions involving proton transfer or charge-transfer-to-solvent: without a special treatment, inter-diffusion of QM and MM particles will lead eventually to a loss of QM/MM separation. We have developed a new method called Flexible Boundary Layer using Exchange (FlexiBLE) that solves the problem by adding a biasing potential to the system that closely maintains QM/MM separation. The method rigorously preserves ensemble averages by leveraging their invariance to exchange of identical particles. With a careful choice of the biasing potential, and the use of a tree algorithm to include only important QM and MM exchanges, we find the method has an MM-forcefield-like computational cost and thus adds negligible overhead to a QM/MM simulation. Furthermore, we show that molecular dynamics with the FlexiBLE bias conserves total energy and remarkably, dynamical quantities in the QM region are unaffected by the applied bias. FlexiBLE thus widens the range of chemistry that can be studied with embedding theory.

Investigation of Faddeev variant of embedding theory

Faddeev variant of embedding theory is an example of using the embedding approach for the description of gravity. In the original form of the embedding approach, the gravity is described by an embedding function of a four-dimensional surface representing our spacetime. In Faddeev variant, the independent variable is a non-square vielbein, which is a derivative of embedding function in embedding theory. We study the possibility of the existence of extra solutions in Faddeev variant, which makes this theory non-equivalent to GR. To separate the degrees of freedom corresponding to extra matter, we propose a formulation of this theory as GR with an additional contribution to the action. We analyze the equations of motion for a specific class of solutions corresponding to a weak gravitational field. We construct a simple exact solution corresponding to arbitrary matter and nontrivial torsion, which is an extra solution in Faddeev variant in the absence of real matter.

Neuromorphous structures of the adaptive control for technological modules

The article develops a scientific direction, which is based on the organization of the functioning of a complex technological process according to the rules of a simple, well-studied TP based on the methods of the theory of investment. The main thesis of embedding theory: comparison of complexly organized multiply connected physical systems with relatively simple, well-studied systems. TP in this case is a multi-agent system consisting of a set of parallel TMs - single-layer neural networks with a given topology of connections between agents.

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

Flexible boundary layer using exchange for embedding theories. I. Theory and implementation

Embedding theory is a powerful computational chemistry approach to exploring the electronic structure and dynamics of complex systems, with QM/MM being the prime example. A challenge arises when trying to apply embedding methodology to systems with diffusible particles, e.g. solvents, if some of them must be included in the QM region, for example in the description of solvent-supported electronic states or reactions involving proton transfer or charge-transfer-to-solvent: without a special treatment, inter-diffusion of QM and MM particles will lead eventually to a loss of QM/MM separation. We have developed a new method called Flexible Boundary Layer using Exchange (FlexiBLE) that solves the problem by adding a biasing potential to the system that closely maintains QM/MM separation. The method rigorously preserves ensemble averages by leveraging their invariance to exchange of identical particles. With a careful choice of the biasing potential, and the use of a tree algorithm to include only important QM and MM exchanges, we find the method has an MM-forcefield-like computational cost and thus adds negligible overhead to a QM/MM simulation. Furthermore, we show that molecular dynamics with the FlexiBLE bias conserves total energy and remarkably, dynamical quantities in the QM region are unaffected by the applied bias. FlexiBLE thus widens the range of chemistry that can be studied with embedding theory.

Excited States of Crystalline Point Defects with Multireference Density Matrix Embedding Theory

Accurate and affordable methods to characterize the electronic structure of solids are important for targeted materials design. Embedding-based methods provide an appealing balance in the trade-off between cost and accuracy - particularly when studying localized phenomena. Here, we use the density matrix embedding theory (DMET) algorithm to study the electronic excitations in solid-state defects with a restricted open-shell Hartree--Fock (ROHF) bath and multireference impurity solvers, specifically, complete active space self-consistent field (CASSCF) and n-electron valence state second-order perturbation theory (NEVPT2). We apply the method to investigate an oxygen vacancy (OV) on a MgO(100) surface and find absolute deviations within 0.05 eV between DMET using the CASSCF/NEVPT2 solver, denoted as CAS-DMET/NEVPT2-DMET, and the non-embedded CASSCF/NEVPT2 approach. Next, we establish the practicality of DMET by extending it to larger supercells for the OV defect and a neutral silicon-vacancy in diamond where the use of non-embedded CASSCF/NEVPT2 is extremely expensive.