Embedding Potential Research Articles

Removing artifacts in polarizable embedding calculations of one- and two-photon absorption spectra of fluorescent proteins.

The multiscale calculations involving excited states may suffer from the electron spill-out (ESO) problem. This seems to be especially the case when the environment of the core region, described with the electronic structure method, is approximated by a polarizable force field. The ESO effect often leads to incorrect physical character of electronic excitations, spreading outside the quantum region, which, in turn, results in erroneous absorption spectra. In this work, we investigate means to remove the artifacts in one-photon absorption (OPA) and two-photon absorption (TPA) spectra of green and yellow fluorescent protein representatives. This includes (i) using different basis sets, (ii) extending the core subsystem beyond the chromophore, (iii) modification of polarization interaction between the core region and its environment, and (iv) including the Pauli repulsion through effective core potentials (ECPs). Our results clearly show that ESO is observed when diffuse functions are used to assemble the multielectron wave function regardless of the exchange-correlation functional used. Furthermore, extending the core region, thus accounting for exchange interactions between the chromophore and its environment, leads to even more spurious excited states. Also, damping the interactions between the core subsystem and the polarizable force field is hardly helpful. In contrast, placing ECPs in the position of sites creating the embedding potential leads to the removal of artificious excited states that presumably should not be observed in the OPA and TPA spectra. We prove that it is a reliable and cost-effective approach for systems where the covalent bond(s) between the core region and its environment must be cut.

Revisiting Competing Paths in Electrochemical CO2 Reduction on Copper via Embedded Correlated Wavefunction Theory.

We re-evaluate two key steps in the mechanism of CO2 reduction on copper at a higher level of theory capable of correcting inherent errors in density functional theory (DFT) approximations, namely, embedded correlated wavefunction (ECW) theory. Here, we consider the CO reduction step on Cu(111), which is critical to understanding reaction selectivity. We optimize embedding potentials at the periodic plane-wave DFT level using density functional embedding theory (DFET). All possible adsorption sites (adsites) for each adsorbate then are screened with ECW theory at the catalytically active site to refine the local electronic structure. Unsurprisingly, DFT and ECW theory predict different adsite preferences, largely because of DFT's inability to properly situate the CO 2π* level. Differing preferred adsites suggest that different reaction pathways could emerge from DFT versus ECW theory. Starting from these preferred ECW theory adsites, we then obtain reaction pathways at the plane-wave DFT level using the climbing-image nudged elastic band method to determine minimum energy paths. Thereafter, we perform ECW calculations at the catalytically active site to correct the energetics at each interpolated structure (image) along the reaction pathways. Via this approach, we confirm that the first step in CO reduction via hydrogen transfer on Cu(111) is to form hydroxymethylidyne (*COH) instead of formyl (*CHO). Although the prediction to preferentially form *COH is consistent with that of DFT, the two theories predict quite different structural and mechanistic behaviors, suggesting that verification is needed for other parts of the mechanism of CO2 reduction, which is the subject of ongoing work.

Research of NOx and PM10 pollutants in Cluj-Napoca with the mobile system for mitigating public health risks

The present research is conducted in order to show the possibilities of creating a smart and advanced mobile system capable of investigations regarding the chemical composition of the atmospheric air in the metropolitan areas using flexible technologies and some part of the existing infrastructure. Experimental measurements are made using a mobile station for data recording connected to the internet and with a link to the air quality stations. Taking into consideration the values of different chemical compounds within the atmospheric air, the data processing station may create a chemical map indicating the higher risk of air toxicity. Nitrogen oxides and particulate matter are some of the essential chemical pollutants generated these days by modern industries and transportation activities. By installing the proper technologies and networking capabilities on a current car the research team has made a practical investigation of actual chemical values in the metropolitan area of Cluj-Napoca by accessing the NO, NO2, NOx, and PM 10 data retrieving lines. Necessary changes in hourly retrieved data show that road traffic and other human activities do change the air quality level and its chemical composition. An air map is provided for some moments of the day, including the four stations in Cluj-Napoca city. The practical research is intended to present the technological capability and its embedding potential for the new series models of cars which may thus indicate a proper route in order to avoid critical points and to reduce the toxic chemical overload of some areas.

Analysis of environment response effects on excitation energies within subsystem‐based time‐dependent density‐functional theory

AbstractWe analyze the ability of subsystem time‐dependent density‐functional theory (sTDDFT) to describe environmental response effects. To this end, we utilize the recently proposed “exact” version of sTDDFT relying on projection‐based embedding (PbE), which so far was applied only for the special case of two subsystems. We confirm that PbE‐sTDDFT in combination with supersystem bases yields results equivalent to those of supermolecular TDDFT calculations for systems solvated by many solvent molecules, using the previously studied system of methylene‐cyclopropene⋯(H2O)17 as an example. By means of this exact reference embedding framework, we are able to disentangle solvent effects introduced in terms of the embedding potential from those caused by solvent response couplings, both for the PbE variant and for sTDDFT with approximate non‐additive kinetic energy functionals. Furthermore, we show that the use of a monomer basis introduces significant errors for the environmental response contribution. Employing a virtual‐orbital localization strategy on top of PbE‐sTDDFT, we can also directly assess the impact of inter‐subsystem charge‐transfer excitations on the entire solvent effect, which turn out to play a significant role for the environmental response. Finally, we analyze the response effects introduced by the individual solvent molecules and their interdependence, and show that a simple, pair‐wise additive correction for solvent response yields excellent results in the present example.

Compound-tunable embedding potential: which oxidation state of uranium and thorium as point defects in xenotime is favorable?

Modern strategies for the safe handling of high level waste (HLW) and its long-term disposal in deep geological formations include the immobilization of radionuclides in the form of mineral-like matrices. The most promising matrices for the immobilization of actinides are ceramic forms of waste based on phosphate minerals such as monazite, xenotime, and cheralite. However, the mechanism of substitution of lanthanides and Y by actinides in phosphate minerals is not entirely clear. We formulated a theoretical model, compound-tunable embedding potential (CTEP), that allows one to predict properties of such crystals with point defects. The reliability of the model is validated by a good agreement of calculated geometry parameters with available experimental data. The substitution of Y in the xenotime crystal by Th and U is studied by relativistic DFT in the framework of the CTEP method, based on constructing the embedding potential as the linear combination of short-range "electron-free" spherical "tunable" pseudopotentials. It is shown on the basis of the proposed model that oxidation state +3 is energetically more profitable than +4 not only for thorium but also for uranium as solitary point defects. This atypical oxidation state of U in the mineral is discussed.

Cost-Effective Potential for Accurate Polarizable Embedding Calculations in Protein Environments.

The fragment-based polarizable embedding (PE) model combined with an appropriate electronic structure method constitutes a highly efficient and accurate multiscale approach for computing spectroscopic properties of a central moiety including effects from its molecular environment through an embedding potential. There is, however, a comparatively high computational overhead associated with the computation of the embedding potential, which is derived from first-principles calculations on individual fragments of the environment. To reduce the computational cost associated with the calculation of embedding potential parameters, we developed a set of amino acid-specific transferable parameters tailored for large-scale PE-based calculations that include proteins. The amino acid-based parameters are obtained by simultaneously fitting to a set of reference electric potentials based on structures derived from a backbone-dependent rotamer library. The developed cost-effective polarizable protein potential (CP3) consists of atom-centered charges and isotropic dipole-dipole polarizabilities of the standard amino acids. In terms of reproduction of electric potentials, the CP3 is shown to perform consistently and with acceptable accuracy across both small tripeptide test systems and larger proteins. We show, through applications on realistic protein systems, that acceptable accuracy can be obtained by using a pure CP3 representation of the protein environment, thus altogether omitting the cost associated with the calculation of embedding potential parameters. High accuracy comparable to that of the full fragment-based approach can be achieved through a mixed description where the CP3 is used only to describe amino acids beyond a threshold distance from the central quantum part.

Functional Extrapolations to Tame Unbound Anions in Density-Functional Theory Calculations.

Standard flavors of density-functional theory (DFT) calculations are known to fail in describing anions, due to large self-interaction errors. The problem may be circumvented using localized basis sets of reduced size, leaving no variational flexibility for the extra electron to delocalize. Alternatively, a recent approach exploiting DFT evaluations of total energies on electronic densities optimized at the Hartree-Fock (HF) level has been reported, showing that the self-interaction-free HF densities are able to lead to an improved description of the additional electron, returning affinities in close agreement with the experiments. Nonetheless, such an approach can fail when the HF densities are too inaccurate. Here, an alternative approach is presented, in which an embedding environment is used to stabilize the anion in a bound configuration. Similar to the HF case, when computing total energies at the DFT level on these corrected densities, electron affinities in very good agreement with experiments can be recovered. The effect of the environment can be evaluated and removed by an extrapolation of the results to the limit of vanishing embedding. Apart from the definition of the domain of the embedding potential, the approach is free from parameters and it can be easily applied to DFT calculations with delocalized basis sets, e.g., plane waves, for which alternative approaches are either not viable or more computationally demanding. The proposed extrapolation strategy can be thus applied also to extended systems, as often studied in condensed-matter physics and materials science, and we illustrate how the embedding environment can be exploited to determine the energy of an adsorbing anion, here a chloride ion on a metal surface, whose charge configuration would be incorrectly predicted by standard density functionals.

Reversible data hiding based on novel pairwise PVO and annular merging strategy

Reversible data hiding (RDH) methods aim to reduce the embedding distortion below the required embedding capacity. Concerning this problem, pixel value ordering (PVO)-based methods achieve remarkably good performance as they only modify the minimum and maximum of pixels in each block. In this paper, we further exploit the embedding potential of PVO by merging blocks that cannot be directly used in PVO with neighboring blocks, in order to generate a larger block. The mechanism of PVO is reconsidered and pixel distribution density (PDD) is defined as a metric to control both order and termination of merging strategy. Moreover, a novel two-dimensional prediction-error histogram is generated to enhance the embedding performance. Experimental results verify that the proposed method outperforms previous PVO-based schemes and state-of-the-art methods.

TEnet: target speaker extraction network with accumulated speaker embedding for automatic speech recognition

It is challenging to perform automatic speech recognition when multiple people talk simultaneously. To solve this problem, speaker-aware selective methods have been proposed to extract the speech of the target speaker, relying on the auxiliary speaker characteristics provided by an anchor (a clean audio sample of the target speaker). However, the extraction performance depends on the duration and quality of the anchors, which is unstable. To address this limitation, the authors propose a target speaker extraction network (TEnet) which applies the robust speaker embedding to extract the target speech from the speech mixture. To get more stable speaker characteristics during training, the robust speaker embeddings are accumulated over all the speech of each target speaker, rather than utilising the embedding produced by a single anchor. As for testing, very few anchors are enough to get decent extraction performance. Results show the TEnet trained with accumulated embedding achieves better performance and robustness compared with the single-anchored TEnet. Moreover, to exploit the potential of the speaker embedding, the authors propose to feed the extracted target speech as anchor and train a feedback TEnet, whose results are superior to the short-anchored baseline for 22.5% on word error rate and 15.5% on signal-to-distortion rate.

Reversible data hiding based on novel embedding structure PVO and adaptive block-merging strategy

In data hiding field, pixel-value-ordering (PVO)-based methods yield excellent performances by taking full advantage of correlation in a fixed block. In PVO-based methods, the maximum and minimum of each block are utilized to embed data. The maximal embedding capacity (EC) is achieved by setting embedding block size smaller to generate more basic embedding blocks. In this light, a new three-pixel embedding structure is proposed to improve the maximal EC by reducing the number of pixels in each basic block. Meanwhile, unlike conventional algorithms which take the noise level of current block as complexity, we utilize the correlation information among neighboring blocks to get a better classification on embedding blocks. Moreover, dynamic block partition method is further investigated and an adaptive block-merging strategy is proposed in this paper. In this strategy, a more rational way is provided to exploit the embedding potential than the top-down partition method and the performance is significantly enhanced. With these three new improvements, our scheme exhibits better performance than the state-of-the-art PVO-based methods.

Characterization and embedding potential of bovine serum albumin cold-set gel induced by glucono-δ-lactone and sodium chloride

Bovine serum albumin (BSA) was induced to form cold-set gel by using glucono-δ-lactone (GDL) and sodium chloride (NaCl), and characteristics of the gel and its embedding potential to bioactive molecules were investigated. The results from texture analyzer indicated that hardness and springiness of BSA cold-set gel were improved by increasing GDL or NaCl, but the gel with lower concentration of GDL (1.0%) and NaCl (0.2 M) had better water holding capacity (WHC). GDL had a significant influence on storage modulus (G’) and loss modulus (G″) but it did not appear to be applicable to NaCl. Light transmittance at 500 nm and average particle size were used to characterize formation of BSA cold-set gel as pH values decreased, and the results suggested that BSA molecules had aggregated at the pH value of the gel point. Microstructure and fractal analysis from confocal laser scanning microscope (CLSM) further suggested that electrostatic and hydrophobic interaction played important roles in the formation of the cold-set gel and it could be deduced that structure and properties of the gel were closely related to the forces. BSA cold-set gel showed an excellent embedding performance to encapsulate bioactive molecules (used quercetin as representative), and achieved effective slow-release action, especially in simulated intestinal juice of pH 7.5. BSA cold-set gel may have important potential application in encapsulation, protection, delivery and controlled-release of some fragile bioactive components, so the research provides a theoretical basis for its application.

Combining polarizable embedding with the Frenkel exciton model: applications to absorption spectra with overlapping solute–solvent bands

Modeling of spectral properties of extended chemical systems, such as the case of a solute in a solvent, is often performed based on so-called hybrid models in which only part of the complete system is given a quantum chemical description. The remaining part of the system is represented by an embedding potential treating the environment either by a discrete or continuum model. In order to successfully make use of minimally sized quantum chemical regions, the embedding potential should represent the environment as authentic as possible. Here, the importance of exactly such an accurate description of the embedding potential is investigated by comparing the performance of the polarizable embedding scheme against larger-sized full quantum mechanical calculations. Our main conclusion is that as long as the solute and solvent do not overlap in their absorption spectra, the polarizable embedding approach shows results consistent with full quantum chemical calculations. For partly overlapping absorption spectra, the polarizable embedding approach can furthermore successfully be expanded within a Frenkel exciton approach based on only economical monomeric quantum chemical calculations. Thus, by extending the polarizable embedding scheme to the exciton picture, it is possible to cover computations of the whole absorption spectrum and still reduce the computational cost compared to costly cluster calculations.

Subspace Density Matrix Functional Embedding Theory: Theory, Implementation, and Applications to Molecular Systems.

We introduce the subspace density matrix functional embedding theory (sDMFET), in which optimization of the nonlocal embedding potential and subsequent embedded correlated wave function calculations are carried out within a truncated subspace determined by a Schmidt decomposition. As compared to the original density matrix functional embedding theory [K. Yu and E. A. Carter, Proceedings of the National Academy of Sciences 2017 , 114 , E10861 ], the computational cost of sDMFET is significantly reduced while the accuracy is preserved. We perform test calculations for both covalently and noncovalently bound molecular systems to demonstrate the feasibility of our theory.

Embedded Cluster Density Approximation for Exchange-Correlation Energy: A Natural Extension of the Local Density Approximation.

We developed a local correlation method in the framework of Kohn-Sham density functional theory (KS-DFT). The method is termed ''embedded cluster density approximation'' (ECDA) and is a logical extension of the local density approximation. In ECDA, an embedded cluster is defined for each atom based on the finite-temperature density functional embedding theory. The clusters' exchange-correlation (XC) energy densities are calculated using high-level XC functionals. The system's XC energy is then constructed by patching these locally computed high-level XC energy densities over the system in an atom-by-atom manner. We derive the relationship between the embedding potential and the system's KS potential. We show how to efficiently compute the system's XC potential, which is the functional derivative of the patched XC energy with respect to the system's electron density. The accuracy of ECDA is examined by patching the exact exchange (EXX) and the random phase approximation (RPA) correlation energy densities in a one-dimensional hydrogen chain, as well as by patching EXX energy densities in several molecules. The agreement between ECDA and KS-DFT on total energies, dipole moments, XC potentials, and KS eigenvalues is good in general as the clusters are made larger. Based on these encouraging results, we expect ECDA to be a simple yet effective method to scale up high-level KS-DFT simulations in large systems.

Analytic second derivatives for the efficient electrostatic embedding in the fragment molecular orbital method

The analytic second derivatives of the energy with respect to nuclear coordinates are developed for restricted Hartree-Fock and density functional theory, based on the two-body fragment molecular orbital method (FMO) and combined with the electrostatic embedding potential, self-consistently determined by point charges for far separated fragments and electron densities for near fragments. The accuracy of the method is established with respect to FMO using the exact embedding potential based on electron densities and to full calculations without fragmentation. The computational efficiency of parallelization is measured on the K supercomputer and the method is applied to simulate infrared spectra of two proteins, Trp-cage (PDB: 1L2Y) and crambin (1CRN). The nature of the vibrations in the Amide I peak of crambin and the Tyr symmetric stretch peak in Trp-cage are analyzed in terms of localized vibrations. © 2018 Wiley Periodicals, Inc.

Do Better Quality Embedding Potentials Accelerate the Convergence of QM/MM Models? The Case of Solvated Acid Clusters.

This study examines whether the use of more accurate embedding potentials improves the convergence of quantum mechanics/molecular mechanics (QM/MM) models with respect to the size of the QM region. In conjunction with density functional theory calculations using the ωB97X-D functional, various embedding potentials including the TIP3P water model, the effective fragment potential (EFP), and semi-empirical methods (PM6, PM7, and DFTB) were used to simulate the deprotonation energies of solvated acid clusters. The calculations were performed on solvated neutral (HA) and cationic (HB+) acids clusters containing 160 and 480 water molecules using configurations sampled from molecular dynamics simulations. Consistently, the ωB97X-D/EFP model performed the best when using a minimal QM region size. The performance for the other potentials appears to be highly sensitive to the charge character of the acid/base pair. Neutral acids display the expected trend that semi-empirical methods generally perform better than TIP3P; however, an opposite trend was observed for the cationic acids. Additionally, electronic embedding provided an improvement over mechanical embedding for the cationic systems, but not the neutral acids. For the best performing ωB97X-D/EFP model, a QM region containing about 6% of the total number of solvent molecules is needed to approach within 10 kJ mol−1 of the pure QM result if the QM region was chosen based on the distance from the reaction centre.

Potential Functional Embedding Theory with an Improved Kohn-Sham Inversion Algorithm.

Potential functional embedding theory (PFET) is a rigorous theory that can yield a unique, self-consistent embedding potential shared by different subsystems treated at different levels of theory. Application of PFET has been limited by the time-consuming and sometimes unstable optimized effective potential (OEP) procedure. Here, we improve the performance of PFET by replacing the OEP algorithm with a new method to reconstruct the effective Kohn-Sham (KS) potential. We propose a direct, efficient KS inversion algorithm to solve for the effective KS potential and then employ the resulting algorithm in PFET. We benchmark our KS inversion algorithm against the recently reported modified Ryabinkin-Kohut-Staroverov (mRKS) procedure. Numerical examples show that, with sufficiently large basis sets, our KS inversion algorithm generates almost as accurate results as the mRKS procedure does, except in the vicinity of atomic nuclei, and that it requires less computational time. Three types of chemical interactions then were tested using the new KS inversion algorithm in PFET; the energetics computed from the updated formalism compare well to benchmarks.

Excitation energies of embedded open-shell systems: Unrestricted frozen-density-embedding time-dependent density-functional theory.

Frozen-density-embedding (FDE) linear response time-dependent density functional theory (TDDFT) is generalized to the case of spin-unrestricted reference orbitals. FDE-TDDFT in the uncoupled approximation is applied to calculate vertical excitation energies of diatomic radicals interacting with closed-shell atoms (helium) or molecules like water. Unrestricted FDE-TDDFT can reproduce the vertical valence excitation energies obtained from conventional supermolecular TDDFT with good accuracy, provided that a good embedding potential is available. To investigate the influence of approximate embedding potentials, we also combine the unrestricted FDE-TDDFT formalism with projection-operator and potential reconstruction techniques, thus enabling calculations with accurate ("exact") embedding potentials.

Accurate embedding through potential reconstruction: A comparison of different strategies.

Potential reconstruction is a powerful strategy for deriving accurate (sometimes called "exact") embedding potentials in the context of density-dependent embedding methods. It is particularly useful for partitioning covalent bonds in such fragment-based electronic-structure methods. While the general approach is well defined and easily explained, there are a number of choices to be made in practice, concerning, e.g., the specific reconstruction algorithm, the assignment of electrons to subsystems, or the initial guess potential. A general choice to be made is whether "exact" embedding potentials shall be derived for pre-defined target densities (top-down) or for approximate fragment densities that can be iteratively defined (bottom-up). Here, we compare the pros and cons of a variety of different variants of potential reconstruction, both in terms of conceptual issues and concerning their accuracy and efficiency. We also present several algorithmic improvements that can be crucial in critical cases of potential reconstruction, namely, we show (i) that a combination of basis-set and grid-based potential reconstruction schemes can lead to improved resulting densities, (ii) that similarly the combination of real-space and matrix-representation based potential reconstruction gives great advantages, and (iii) that the potential-matrix reconstruction by Zhang and Carter [J. Chem. Phys. 148, 034105 (2018)] can be made much more efficient by avoiding an explicit Hessian calculation. Additionally, we demonstrated (iv) that a double reconstruction, meaning a reconstruction of both the supersystem potential and the subsystem potential, may lead to beneficial error cancellation. We also address the question of consistent energetics derived from such reconstructed potentials.

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.