Theoretical study of lithium ionic conductors by electronic stress tensor density and electronic kinetic energy density

We analyze the electronic structure of lithium ionic conductors, and , using the electronic stress tensor density and kinetic energy density with special focus on the ionic bonds among them. We find that, as long as we examine the pattern of the eigenvalues of the electronic stress tensor density, we cannot distinguish between the ionic bonds and bonds among metalloid atoms. We then show that they can be distinguished by looking at the morphology of the electronic interface, the zero surface of the electronic kinetic energy density. © 2016 Wiley Periodicals, Inc.     

How does the ambiguity of the electronic stress tensor influence its ability to serve as bonding indicator

The electronic stress tensor is not uniquely defined. Possible bonding indicators originating from the quantum stress tensor may inherit this ambiguity. Based on a general formula of the stress tensor this ambiguity can be described by an external parameter λ for indicators derived from the scaled trace of the stress tensor (whereby the scaling function is proportional to the Thomas–Fermi kinetic energy density). The influence of λ is analyzed and the consequences for the representation of chemical bonding are discussed in detail. It is found that the scaled trace of the stress tensor may serve as suitable bonding indicator over a wide range of λ values, excluding the value range between ?0.15 and ?0.48. Focusing on the eigenvalues of the stress tensor, it is found that the sign of the eigenvalues heavily depends on the chosen representation of the stress tensor. Therefore, chemical bonding analyses which are based on the interpretation of the eigenvalue sign (e.g., the spindle structure) are strongly dependent on the chosen form of the stress tensor. © 2014 Wiley Periodicals, Inc.     

How does the ambiguity of the electronic stress tensor influence its ability to reveal the atomic shell structure

The electronic stress tensor is not uniquely defined. Therefore, shell indicators stemming from the quantum stress tensor may inherit this ambiguity. Based on a general formula of the stress tensor this ambiguity can be described by an external parameter λ. Two functions derived from the quantum stress tensor have been evaluated according to their ability to serve as shell indicators. The influence of λ is analyzed and the consequences for the representation of the atomic shell structure are discussed in detail. It is found that the trace of the stress tensor does not fully reveal the atomic shell structure. In contrast, the scaled trace (whereby the scaling function is proportional to the Thomas-Fermi kinetic energy density) produces fairly good representation of the atomic shell structure over a wide range of λ values.     

Study of the kinetic energy densities of electrons as applied to quantum dots in a magnetic field

There are three expressions for the kinetic energy density t( r ) expressed in terms of its quantal source, the single-particle density matrix: t _A( r ) , the integrand of the kinetic energy expectation value; t _B( r ) , the trace of the kinetic energy tensor; t _C( r ) , a virial form in terms of the ‘classical’ kinetic field. These kinetic energy densities are studied by application to ‘artificial atoms‘ or quantum dots in a magnetic field in a ground and excited singlet state. A comparison with the densities for natural atoms and molecules in their ground state is made. The near nucleus structure of these densities for natural atoms is explained. We suggest that in theoretical frameworks which employ the kinetic energy density such as molecular fragmentation, density functional theory, and information-entropic theories, one use all three expressions on application to quantum dots, and the virial expression for natural atoms and molecules. New physics could thereby be gleaned.     

Electronic stress tensor analysis of molecules in gas phase of CVD process for gesbte alloy

We analyze the electronic structure of molecules which may exist in gas phase of chemical vapor deposition process for GeSbTe alloy using the electronic stress tensor, with special focus on the chemical bonds between Ge, Sb, and Te atoms. We find that, from the viewpoint of the electronic stress tensor, they have intermediate properties between alkali metals and hydrocarbon molecules. We also study the correlation between the bond order which is defined based on the electronic stress tensor, and energy‐related quantities. We find that the correlation with the bond dissociation energy is not so strong while one with the force constant is very strong. We interpret these results in terms of the energy density on the “Lagrange surface,” which is considered to define the boundary surface of atoms in a molecule in the framework of the electronic stress tensor analysis. © 2015 Wiley Periodicals, Inc.     

Pointing the way to the products? Comparison of the stress tensor and the second-derivative tensor of the electron density

The eigenvectors of the electronic stress tensor can be used to identify where new bond paths form in a chemical reaction. In cases where the eigenvectors of the stress tensor are not available, the gradient-expansion-approximation suggests using the eigenvalues of the second derivative tensor of the electron density instead; this approximation can be made quantitatively accurate by scaling and shifting the second-derivative tensor, but it has a weaker physical basis and less predictive power for chemical reactivity than the stress tensor. These tools provide an extension of the quantum theory of atoms and molecules from the characterization of molecular electronic structure to the prediction of chemical reactivity.     

libKEDF: An accelerated library of kinetic energy density functionals

Kinetic energy density functionals (KEDFs) approximate the kinetic energy of a system of electrons directly from its electron density. They are used in electronic structure methods that lack direct access to orbitals, for example, orbital‐free density functional theory (OFDFT) and certain embedding schemes. In this contribution, we introduce libKEDF, an accelerated library of modern KEDF implementations that emphasizes nonlocal KEDFs. We discuss implementation details and assess the performance of the KEDF implementations for large numbers of atoms. We show that using libKEDF, a single computing node or (GPU) accelerator can provide easy computational access to mesoscale chemical and materials science phenomena using OFDFT algorithms. © 2017 Wiley Periodicals, Inc.     

Influence of electronic correlation in monoelectronic density in p-space

The radial molecular monoelectronic density and their orbital contributions have been calculated in the momentum space. For these purposes, densities for the ground state of several atoms and molecules, using a cc-pVTZ basis set at HF level, as well as some post-HF and DFT methods are computed. The difference between the radial monoelectronic density computed with each method and that using the HF wave function is used as a tool to study the influence of the electronic correlation in the momentum space. Densities obtained with post HF calculations show a similar behavior around p = 1.0 and 2.0, that are different from the DFT results. Radial momentum densities (p-densities) are more influenced by the electronic correlation than the exchange part of the DFT methods. CISD p-density is more affected than DFT p-density when the intermolecular distance increases. An analysis of the powers of moments calculated with different methods has been carried out. Contribution to the Serafin Fraga Memorial Issue.     

Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn–Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518–2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097–3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn–Sham matrix formation. © 2019 Wiley Periodicals, Inc.     

A theoretical study of the electronic properties of hydrogenated spherical-like SiC quantum dots with C-rich and Si-rich compositions

Quantum dots have many potential applications in opto-electronics, energy storage, catalysis, and medical diagnostics, silicon carbide quantum dots could be very attractive for many biological and technological applications due to their chemical inertness and biocompatibility, however, there are seldom theoretical studies that could boost the development of these applications. In this work, the electronic properties of hydrogenated spherical-like SiC quantum dots with C-rich and Si-rich compositions are investigated using density functional theory calculations. The quantum dots are modeled by removing atoms outside a sphere from an otherwise perfect SiC crystal, the surface dangling bonds are passivated with H atoms. Our results exhibit that the electronic properties of the SiC-QD are strongly influenced by their composition and diameter size. The energy gap is always higher than that of the crystalline SiC, making these SiC QD's suitable for applications at harsh temperatures. The density of states and the energy levels show that the Si-rich quantum dots had a higher density of states near the conduction band minimum, which indicates better conductivity. These results could be used to tune the electronicproperties of SiC quantum dots for optoelectronic applications.     

Electron localization function from density components

This work addresses the decomposition of the Electron Localization Function (ELF) into partial density contributions using an appealing split of kinetic energy densities. Regarding the degree of the electron localization, the relationship between ELF and its usual spin‐polarized formula is discussed. A new polarized ELF formula, built from any subsystems of the density, and a localization function, quantifying the measure of electron localization for only a subpart of the total system are introduced. The methodology appears tailored to describe the electron localization in bonding patterns of subsystems, such as the local nucleophilic character. Beyond these striking examples, this work opens up opportunities to describe any electronic properties that depend only on subparts of the density in atoms, molecules, or solids. © 2016 Wiley Periodicals, Inc.     

Theoretical scrutinization of nine benzoic acid dimers: Stability and energy decomposition analysis

Aromatic carboxylic acids are able to form diverse dimers and multimers due to their hydrogen bond donor and acceptor cites, as well as the aromatic rings. In this work, we examine nine benzoic acid dimers stabilized by hydrogen bonding and stacking interactions. Interacting quantum atoms methodology revealed that dominant attractive interactions in all of them, including hydrogen bonded systems, are due to exchange-correlation. Coulomb interactions are significant only in the most stable dimer with a double hydrogen bond, although the corresponding energy term is almost two times lower compared to the nonclassical one. Since interacting quantum atoms approach treats monomers binding by considering electronic energy only, in order to examine dissociation kinetics we performed density functional theory-based molecular dynamics simulations of selected stacked dimers: in 40% of the studied systems at 300 K thermal energy was sufficient to overpower barrier for dissociation within 1 ps, which resulted in the separation of the monomers, whereas 20% of them remained in the stacked position even after 5 ps. These results highlight the importance of noncovalent interactions, particularly weak stacking interactions, on the structure and dynamics of carboxylic acids and their derivatives.     

Quantum kinetic energy densities: an operational approach

We propose and investigate a procedure to measure, at least in principle, a positive quantum version of the local kinetic energy density. This procedure is based, under certain idealized limits, on the detection rate of photons emitted by moving atoms which are excited by a localized laser beam. The same type of experiment, but in different limits, can also provide other non-positive-definite versions of the kinetic energy density. A connection with quantum arrival time distributions is discussed.     

Use of promolecular ASA density functions as a general algorithm to obtain starting MO in SCF calculations

Atomic shell approximation (ASA) constitutes a way to fit first‐order density functions to a linear combination of spherical functions. The ASA fitting method makes use of positive definite expansion coefficients to ensure appropriate probability distribution features. The ASA electron density is sufficiently accurate for the practical implementation of quantum similarity measures, as was proved in previous published work. Here, a new application of the ASA density formalism is analyzed, and employed to obtain an initial guess of the density matrix for SCF procedures. The number of cycles needed to assess the convergence criterion in electronic energy calculations appears comparable to or less than those obtained by other means. Several molecular structures of different classes, including organic systems and metal complexes, were chosen as representative test cases. In addition, an ASA basis set for atoms Sc‐Kr fitted to an ab initio 6‐311G basis set is also presented. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Performance of the density matrix functional theory in the quantum theory of atoms in molecules

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.     

On the local representation of the electronic momentum operator in atomic systems

The local quantum theory is applied to the study of the momentum operator in atomic systems. Consequently, a quantum-based local momentum expression in terms of the single-electron density is determined. The limiting values of this function correctly obey two fundamental theorems: Kato's cusp condition and the Hoffmann-Ostenhof and Hoffmann-Ostenhof exponential decay. The local momentum also depicts the electron shell structure in atoms as given by its local maxima and inflection points. The integration of the electron density in a shell gives electron populations that are in agreement with the ones expected from the Periodic Table of the elements. The shell structure obtained is in agreement with the higher level of theory computations, which include the Kohn-Sham kinetic energy density. The average of the local kinetic energy associated with the local momentum is the Weizsacker kinetic energy. In conclusion, the local representation of the momentum operator provides relevant information about the electronic properties of the atom at any distance from the nucleus.     

Electronic and Optical Properties of Hydrogenated Si Clusters

The geometric, electronic, and photoabsorption properties of some hydrogenated silicon clusters are investigated. The density functional theory with generalized gradient approximation fimctional is applied. Our study shows that the geometric structures of them relax with their increasing sizes. Synchronously, the polarizations of Si-H bonds become weak slowly but overlap populations increase. In Mulliken population analysis, we find a distinctive passivation effect （some electrons are transferred from outer Si atoms to the central Si with four-coordinate Si atoms）. Owing to the quantum confinement, the energy gap and the lowest excitation energy increase with the decreasing sizes. For nanometer scale cluster, the transition from the highest occupied molecular orbital to the lowest unoccupied molecular orbital state is usually prohibited.