Electron Exchange-correlation Research Articles

Quantum mechanical analysis of yttrium-stabilized zirconia and alumina: implications for mechanical performance of esthetic crowns

BackgroundYttrium-stabilized zirconia (YSZ) and alumina are the most commonly used dental esthetic crown materials. This study aimed to provide detailed information on the comparison between yttrium-stabilized zirconia (YSZ) and alumina, the two materials most often used for esthetic crowns in dentistry.MethodologyThe ground-state energy of the materials was calculated using the Cambridge Serial Total Energy Package (CASTEP) code, which employs a first-principles method based on density functional theory (DFT). The electronic exchange–correlation energy was evaluated using the generalized gradient approximation (GGA) within the Perdew (Burke) Ernzerhof scheme.ResultsOptimization of the geometries and investigation of the optical properties, dynamic stability, band structures, refractive indices, and mechanical properties of these materials contribute to a holistic understanding of these materials. Geometric optimization of YSZ provides important insights into its dynamic stability based on observations of its crystal structure and polyhedral geometry, which show stable configurations. Alumina exhibits a distinctive charge, kinetic, and potential (CKP) geometry, which contributes to its interesting structural framework and molecular-level stability. The optical properties of alumina were evaluated using pseudo-atomic computations, demonstrating its responsiveness to external stimuli. The refractive indices, reflectance, and dielectric functions indicate that the transmission of light by alumina depends on numerous factors that are essential for the optical performance of alumina as a material for esthetic crowns. The band structures of both the materials were explored, and the band gap of alumina was determined to be 5.853 eV. In addition, the band structure describes electronic transitions that influence the conductivity and optical properties of a material. The stability of alumina can be deduced from its bandgap, an essential property that determines its use as a dental material. Refractive indices are vital optical properties of esthetic crown materials. Therefore, the ability to understand their refractive-index graphs explains their transparency and color distortion through how the material responds to light..The regulated absorption characteristics exhibited by YSZ render it a highly attractive option for the development of esthetic crowns, as it guarantees minimal color distortion.ConclusionThe acceptability of materials for esthetic crowns is strongly determined by mechanical properties such as elastic stiffness constants, Young's modulus, and shear modulus. YSZ is a highly durable material for dental applications, owing to its superior mechanical strength.

Review of electron emission and electrical breakdown in nanogaps

With the continual miniaturization of electronic devices, there is an urgent need to understand the electron emission and the mechanism of electrical breakdown at nanoscale. For a nanogap, the complete process of the electrical breakdown includes the nano-protrusion growth, electron emission and thermal runaway of the nano-protrusion, and plasma formation. This review summarizes recent theories, experiments, and advanced atomistic simulation related to this breakdown process. First, the electron emission mechanisms in nanogaps and their transitions between different mechanisms are emphatically discussed, such as the effects of image potential (of different electrode's configurations), anode screening, electron space-charge potential, and electron exchange-correlation potential. The corresponding experimental results on electron emission and electrical breakdown are discussed for fixed nanogaps on substrate and adjustable nanogaps, including space-charge effects, electrode deformation, and electrical breakdown characteristics. Advanced atomistic simulations about the nano-protrusion growth and the nanoelectrode or nano-protrusion thermal runaway under high electric field are discussed. Finally, we conclude and outline the key challenges for and perspectives on future theoretical, experimental, and atomistic simulation studies of nanoscale electrical breakdown processes.

Employing neural density functionals to generate potential energy surfaces.

With the union of machine learning (ML) and quantum chemistry, amid the debate between machine-learned functionals and human-designed functionals in density functional theory (DFT), this paper aims to demonstrate the generation of potential energy surfaces using computations with machine-learned density functional approximation (ML-DFA). A recent research trend is the application of ML in quantum sciences in the design of density functionals such as DeepMind's Deep Learning model (DeepMind21, DM21). Though science reported the state-of-the-art performance of DM21, the opportunity to utilize DeepMind's pretrained DM21 neural networks in computations in quantum chemistry has not yet been tapped. So far in the literature, the Deep Learning density functionals (DM21) have not been applied to generate potential energy surfaces. While the superior accuracy of DM21 has been reported, there is still a scarcity of publications that apply DM21 in calculations in the field. In this context, for the first time in literature, neural density functionals inferring 2D potential energy surfaces (ML-DFA-PES) based on machine-learned DFA-based computational method is contributed in this paper. This paper reports the ML-DFA-generated PES for C4H8, H2O, H2, and H2+ by employing a pretrained DM21m TensorFlow model with cc-pVDZ basis set. In addition, we also analyze the long-range behavior of DM21 based PES to investigate the ability to describe a system at long ranges. Furthermore, we compare PES diagrams from DM21 with popular DFT functionals (b3lyp/ PW6B95) and CCSD(T). In this method, 2D potential energy surfaces are obtained using a method that relies upon the neural network's ability to accurately learn the mapping between 3D electron density and exchange-correlation potential. By inserting Deep Learning inference in DFT with a pretrained neural network, self-consistent field (SCF) energy at different geometries along the coordinates of interest is computed, and then, potential energy surfaces are plotted. In this method, first, the electron density is computed mathematically, and this computed 3D electron density is used as a ML feature vector to predict the exchange correlation potential as a ML inference computed by a forward pass of pre-trained DM21 TensorFlow computational graph, followed by the computation of self-consistent field energy at multiple geometries, and then, SCF energies at different bond lengths/angles are plotted as 2D PES. We implement this in a python source code using frameworks such as PySCF and DM21. This paper contributes this implementation in open source. The source code and DM21-DFA-based PES are contributed at https://sites.google.com/view/MLfunctionals-DeepMind-PES .

Application of density functional theory for evaluating the mechanical properties and structural stability of dental implant materials

BackgroundTitanium is a commonly used material for dental implants owing to its excellent biocompatibility, strength-to-weight ratio, corrosion resistance, lightweight nature, hypoallergenic properties, and ability to promote tissue adhesion. However, alternative materials, such as titanium alloys (Ti–Al-2 V) and zirconia, are available for dental implant applications. This study discusses the application of Density Functional Theory (DFT) in evaluating dental implant materials' mechanical properties and structural stability, with a specific focus on titanium (Ti) metal. It also discusses the electronic band structures, dynamic stability, and surface properties. Furthermore, it presents the mechanical properties of Ti metal, Ti–Al-2 V alloy, and zirconia, including the stiffness matrices, average properties, and elastic moduli. This research comprehensively studies Ti metal's mechanical properties, structural stability, and surface properties for dental implants.MethodsWe used computational techniques, such as the CASTEP code based on DFT, GGA within the PBE scheme for evaluating electronic exchange–correlation energy, and the BFGS minimization scheme for geometry optimization. The results provide insights into the structural properties of Ti, Ti–Al-2 V, and zirconia, including their crystal structures, space groups, and atomic positions. Elastic properties, Fermi surface analysis, and phonon studies were conducted to evaluate the tensile strength, yield strength, ductility, elastic modulus, Poisson's ratio, hardness, fatigue resistance, and corrosion resistance.ResultsThe findings were compared with those of Ti–Al-2 V and zirconia to assess the advantages and limitations of each material for dental implant applications. This study demonstrates the application of DFT in evaluating dental implant materials, focusing on titanium, and provides valuable insights into their mechanical properties, structural stability, and surface characteristics.ConclusionsThe findings of this study contribute to the understanding of dental implant material behavior and aid in the design of improved materials with long-term biocompatibility and stability in the oral environment.

DFT study of SF6 adsorption by Pd-doped hydroxyl-terminal modified Ti3C2Tx MXene.

SF6 gas has a strong greenhouse effect, and how to treat SF6 in an environmentally friendly way has been a hot topic of current research. In this paper, the adsorption behavior of SF6 on the surface of Pd-doped hydroxyl-terminated modified Ti3C2Tx (i.e., Ti3C2(OH)2) was investigated based on the density functional theory using two-dimensional MXene as the catalyst. The structures of different Pd-doped Ti3C2(OH)2 were analyzed and the most structurally stable doped structures were selected as the basis for subsequent calculations. A large number of adsorption configurations were constructed and geometrically optimized, and the adsorption energy, charge transfer, differential charge density, and density of states of the systems were calculated in order to analyze the gas-solid interactions and find the surface active sites; compared with the adsorption performance of undoped Ti3C2(OH)2 on SF6, it was found that Pd doping played a less inhibitory role in the adsorption of SF6 on the Ti3C2(OH)2 surface. The results of this study can provide theoretical support for the use of Pd-doped Ti3C2(OH)2 as a catalyst for the degradation of SF6. In this paper, simulations of SF6 adsorption on Ti3C2Tx surfaces are based on density functional theory and are carried out in the Dmol3 module of Material Studio. To better describe the non-uniform electron density of the actual system, the PBE functional in the generalized gradient approximation (GGA) was chosen for the optimization of the structure of the gas-solid interface system and the calculation of the relevant electronic properties, combined with the Grimme dispersion correction in the DFT-D dispersion correction for the electron exchange correlation term. Because both Pd and Ti are transition metal elements, the mode-conserving pseudopotential DNP basis set containing relativistic effects was chosen for the electronic wave function expansion. In this paper, an all-electron model is used for the inner core treatment of gas molecules and a density generalized semi-nuclear pseudopotential DSSP is used for the solid surface treatment.

The co-adsorption of sulfate and metal ions on Al-doped graphene: a first principles study.

The co-adsorption of sulfate and metal ions on intrinsic and Al-doped graphene is investigated through first principles calculations. When SO42- ions exist only, both of intrinsic and Al-doped graphene can form stable adsorption configurations with SO42-. However, the presence of Cu2+/Ca2+/Zn2+/Mg2+ ions attenuates the interaction between intrinsic graphene and SO42-, resulting in weak physical adsorption between them, while Al-doped graphene can still constitute co-adsorption chemically with both SO42- and Cu2+/Ca2+/Zn2+/Mg2+ ions simultaneously. The sensitivity of Al-doped graphene towards co-adsorbed ions is in the order of SO42--Cu2+ > SO42--Zn2+ > SO42--Ca2+ > SO42--Mg2+. The research indicates Al-doped graphene could be a promising material for sensing sulfate ions under the presence of various metal ions. All of the calculations were carried out by using a first principles method based on density functional theory (DFT). The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional was selected to describe electron exchange-correlation energy. The double numerical plus polarization (DNP) was employed as the basis set. The conductor-like screening model (COSMO) was implemented to simulate the aqueous solvent effect.

Shift current response in elemental two-dimensional ferroelectrics

A bulk material without inversion symmetry can generate a direct current under illumination. This interface-free current generation mechanism, referred to as the bulk photovoltaic effect (BPVE), does not rely on p-n junctions. Here, we explore the shift current generation, a major mechanism responsible for the BPVE, in single-element two-dimensional (2D) ferroelectrics represented by phosphorene-like monolayers of As, Sb, and Bi. The strong covalency, small band gap, and large joint density of states afforded by these elemental 2D materials give rise to large shift currents, outperforming many state-of-the-art materials. We find that the shift current, due to its topological nature, depends sensitively on the details of the Bloch wave functions. It is crucial to consider the electronic exchange-correlation potential beyond the generalized gradient approximation as well as the spin-orbit interaction in density functional theory calculations to obtain reliable frequency-dependent shift current responses.

Computational evaluation of transport parameters and logic circuit designing of L-Lysine amino acid stringed to Au, Ag, Cu, Pt, and Pd electrodes

The integrants of proteins, i.e., amino acids, have grossed exceptional recognition for their applications towards designing imminent switching devices. Among 20 amino acids, L-Lysine (i.e., positively charged) has the highest number of CH2 chains, and such chains affect the rectification ratio in several biomolecules. Towards molecular rectification, we investigate the transport parameters of L-Lysine in conjunction with five different coinage metal electrodes, i.e., Au, Ag, Cu, Pt and Pd to form five distinct devices. We deputize the NEGF-DFT formulism for computing conductance, frontier molecular orbitals, current-voltage, and molecular projected self-Hamiltonian calculations using a self-consistent function. We focus on the most widely used electron exchange correlation combination, i.e., the PBE version of GGA with DZDP basis set. The molecular devices under inquisition exhibit phenomenal rectification ratios (RR) in conjunction with negative differential resistance (NDR) regimes. The nominated molecular device offers a substantial rectification ratio of 45.6 with platinum electrodes and a prominent peak to valley current ratio of 1.78 with copper electrodes. We deduce from these findings that L-Lysine based molecular devices would implicit in future bio-nanoelectronic devices. The OR and AND logic gates are also proposed hinged on highest rectification ratio of L-Lysine-based devices.

The effects of experimentally obtained electron correlation and polarization on electron densities and exchange-correlation potentials.

In X-ray constrained wavefunction (XCW) fitting, external information, such as electron correlation and polarization, is included into a single-determinantal isolated-molecule wavefunction. In a first step, we show that the extraction of these two physical effects by XCW fitting is complete and accurate by comparing to theoretical reference calculations. In a second step, we show that fitting to data from single-crystal x-ray diffraction measurements provides the same results qualitatively and how the physical effects can be separated, although always inherently convolved in the experiment. We further demonstrate that exchange-correlation potentials are systematically affected by XCW fitting in a physically meaningful way, which could be exploited for method development in quantum chemistry, subject to some remaining challenges that we also outline.

Ab Initio Static Exchange-Correlation Kernel across Jacob's Ladder without Functional Derivatives.

The electronic exchange─correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of properties such as the dielectric characteristics, the thermal and electrical conductivity, or the response to an external perturbation. In this work, we present a formally exact methodology for the computation of the system specific static XC kernel exclusively within the framework of density functional theory (DFT) and without employing functional derivatives─no external input apart from the usual XC-functional is required. We compare our new results with exact quantum Monte Carlo (QMC) data for the archetypical uniform electron gas model under both ambient and warm dense matter conditions. This gives us unprecedented insights into the performance of different XC functionals, and it has important implications for the development of new functionals that are designed for the application at extreme temperatures. In addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as it occurs in fusion applications and astrophysical objects. The observed excellent agreement to the QMC reference data demonstrates that presented framework is capable to capture nontrivial effects such as XC-induced isotropy breaking in the density response of hydrogen at large wave numbers.

Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions.

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ion configurations from density functional theory molecular dynamics (DFT-MD) simulations to solve the electronic problem for hydrogen under warm dense matter conditions [Böhme et al., Phys. Rev. Lett. 129, 066402 (2022)0031-900710.1103/PhysRevLett.129.066402]. The problem of path collapse due to the Coulomb attraction is avoided by utilizing the pair approximation, which is compared against the simpler Kelbg pair potential. We find very favorable convergence behavior towards the former. Since we do not impose any nodal restrictions, our PIMC simulations are afflicted with the notorious fermion sign problem, which we analyze in detail. While computationally demanding, our results constitute an exact benchmark for other methods and approximations within DFT. Our setup gives us the unique capability to study important properties of warm dense hydrogen such as the electronic static density response and exchange-correlation kernel without any model assumptions, which will be very valuable for a variety of applications such as the interpretation of experiments and the development of new XC functionals.

Exploring the structural, electronic, magnetic, and magneto-optical properties of double perovskites Ca2TMIrO6 (TM = Fe, Co) through first principles study

This study is aimed at exploring the electronic, magnetic, and magneto-optical properties of double perovskites Ca2FeIrO6 and Ca2CoIrO6 with monoclinic structure (space group P21/c) in order to examine their potential applications in spintronic and photovoltaic devices. The calculations were done using the full-potential linearized augmented plane wave within the density functional theory. For the electronic exchange-correlation function, we used the generalized gradient approximation (GGA) and GGA+U (Hubbard potential), and spin-orbit coupling (SOC). The study showed that Ca2FeIrO6 and Ca2CoIrO6 exhibit a monoclinic structure (space group P21/c). The structure relaxation shows an antiferromagnetic behavior in both systems with a magnetic moment of about 6.00 μB for Ca2FeIrO6 and 4.00 μB for Ca2CoIrO6 by using GGA+U approximation. The results of GGA and GGA+U predict the half-metallic behavior of Ca2FeIrO6 and Ca2CoIrO6. The magneto-optical polar Kerr effect (MOKE) was examined by studying the variation of Kerr and ellipticity rotation. The Kerr rotation angle is 1.3º at 4.82 eV and -1.21º at 4.3 eV, and the ellipticity angle is -1.21º at 4.3 eV for Ca2FeIrO6. In the case of Ca2CoIrO6, the Kerr rotation angle is -1.04º at 4.05 eV; the significant Kerr rotation in both compounds may suggest the application of these materials in optoelectronics bias. The named compounds have a potential application in the field of spintronics and its devices, such as in optoelectronics technologies.

How does electron exchange correlation influence reactivity of metallo-β-lactamase L1 against cephalosporin antibiotics

Cephalosporin hydrolysis by the metallo-β-lactamase L1 is a reaction where electron delocalization in the substrate-protein complex affects the reaction rate: the more cephalosporin lone pairs are localized on the N atom, the higher hydrolysis rates are. We show that high Fermi holevariability is responsible for the stipulation of the electron lone pairs’ localization.One-electron potentials reveal that higher lone pairs’ localization is expressed in the dominance of the static exchange correlation (reflected in theaverage Fermi hole depth) in theN atomvicinity. However, this dominance was found to be defined by the height of the kinetic exchange potential barriers (expressing the Fermi holevariability and the response of the exchange correlation hidden in the kinetic potential to electron density variations), rather than by the features of the static exchange correlation itself. The need to account both static and kinetic exchange correlations for the reliable description of the electron delocalization explains inapplicability of the simple geometric criteria for the chemical bonding study in the considered systems.

Charting C–C coupling pathways in electrochemical CO2 reduction on Cu(111) using embedded correlated wavefunction theory

The electrochemical CO2 reduction reaction (CO2RR) powered by excess zero-carbon-emission electricity to produce especially multicarbon (C2+) products could contribute to a carbon-neutral to carbon-negative economy. Foundational to the rational design of efficient, selective CO2RR electrocatalysts is mechanistic analysis of the best metal catalyst thus far identified, namely, copper (Cu), via quantum mechanical computations to complement experiments. Here, we apply embedded correlated wavefunction (ECW) theory, which regionally corrects the electron exchange-correlation error in density functional theory (DFT) approximations, to examine multiple C-C coupling steps involving adsorbed CO (*CO) and its hydrogenated derivatives on the most ubiquitous facet, Cu(111). We predict that two adsorbed hydrogenated CO species, either *COH or *CHO, are necessary precursors for C-C bond formation. The three kinetically feasible pathways involving these species yield all three possible products: *COH-CHO, *COH-*COH, and *OCH-*OCH. The most kinetically favorable path forms *COH-CHO. In contrast, standard DFT approximations arrive at qualitatively different conclusions, namely, that only *CO and *COH will prevail on the surface and their C-C coupling paths produce only *COH-*COH and *CO-*CO, with a preference for the first product. This work demonstrates the importance of applying qualitatively and quantitatively accurate quantum mechanical method to simulate electrochemistry in order ultimately to shed light on ways to enhance selectivity toward C2+ product formation via CO2RR electrocatalysts.

Quantum machine learning corrects classical forcefields: Stretching DNA base pairs in explicit solvent.

In order to improve the accuracy of molecular dynamics simulations, classical forcefields are supplemented with a kernel-based machine learning method trained on quantum-mechanical fragment energies. As an example application, a potential-energy surface is generalized for a small DNA duplex, taking into account explicit solvation and long-range electron exchange-correlation effects. A long-standing problem in molecular science is that experimental studies of the structural and thermodynamic behavior of DNA under tension are not well confirmed by simulation; study of the potential energy vs extension taking into account a novel correction shows that leading classical DNA models have excessive stiffness with respect to stretching. This discrepancy is found to be common across multiple forcefields. The quantum correction is in qualitative agreement with the experimental thermodynamics for larger DNA double helices, providing a candidate explanation for the general and long-standing discrepancy between single molecule stretching experiments and classical calculations of DNA stretching. The new dataset of quantum calculations should facilitate multiple types of nucleic acid simulation, and the associated Kernel Modified Molecular Dynamics method (KMMD) is applicable to biomolecular simulations in general. KMMD is made available as part of the AMBER22 simulation software.

Total, state-selective, and angular-differential cross sections for electron capture in He2++H collisions in warm dense plasmas

The total, state-selective, and angular-differential cross sections for He2++H collision system in warm dense plasmas are studied by using the two-center atomic orbital close-coupling method in the energy range 0.1–300 keV/u. The calculations are performed for plasma density and temperature ranges ne ∼1018 to ∼1021 cm−3, Te = 0.3 eV–1.2 eV, typical for the H- and He-rich white dwarfs. The plasma environments are described by a unified screened potential involving electron degeneracy, finite-temperature gradient, and exchange-correlation effects. The results for H++H cases with the same plasma parameters are also presented for comparison to elucidate the discrepancies of plasma screening effects on the electron capture dynamics for collision systems with different nuclear symmetries. Moreover, classical Debye screening results are also given for comparison to clarify the effects of quantum correlations in warm dense plasmas on the electron capture dynamics. The present work is expected to provide theoretical and data support for the astrophysical plasmas.

Kinetic studies of exchange-correlation effect on the collective excitations of warm dense plasmas.

The exchange-correlation of electrons, as a fundamental effect in quantum mechanics, plays an important role in the collective motions of electrons in warm dense matter. We derive the quantum kinetic equationsbased on the time-dependent Kohn-Sham equation. By using a temperature-dependent functional for the exchange correlation, the excitations of electrostatic waves are analyzed under the adiabatic local density approximation (ALDA). We find that the influences of the exchange-correlation effect on the group velocity of electrostatic waves can be as high as 10% when both the density and temperature are low. Moreover, we also compare the results obtained by using ALDA-based kinetic theory, exchange kinetic theory, and quantum hydrodynamics, and discuss the differences among them.

Structural, elastic, mechanical, electronic, magnetic and optical properties of half-Heusler compounds CoFeZ (Z = P, As, Sb): A GGA+U approximation

The first-principles study technique is implemented to explore Co-based H–H compounds, namely CoFeP, CoFeAs, and CoFeSb. In this study we have investigated the structural, elastic, electronic, magnetic, and optical properties using DFT as a fundamental approach within simulation package WIEN2k, utilizing linearized augmented plane wave method with full potential. Calculations for electronic exchange–correlation energy are performed using GGA (Generalized Gradient Approximation) approach together with the on-site Coulomb interactions effect as (GGA + U). Using Phono3py code, we have calculated the phonon spectrum of CoFeZ compounds and there is no negative frequency in the phonon spectrum which shows the dynamic stability of CoFeZ (Z = P, As, Sb) compounds. Large lattice constants are seen for all three compounds CoFeP, CoFeAs, and CoFeSb. Elastically, the former two compounds CoFeP and CoFeAs are ductile while the latter one, CoFeSb is brittle. All the compounds show small band gaps for spin-down channels hence confirming half-metallic character. It is found that magnetic moments follow the Slater–Pauling 18Mt=Zt-18 electron rule with the high total magnetic moments. Also, optical properties such as refractive index, absorption coefficient, dielectric function, conductivity, and reflectivity are calculated and discussed, which show that all the compounds are highly active at intermediate energy spectra.

Evidence for multiple liquid–liquid phase transitions in carbon, and the Friedel ordering of its liquid state

Carbon, the fourth most abundant element in the universe, forms a metallic fluid with transient covalent bonds on melting. Its liquid–liquid phase transitions, intensely sought using simulations, had been elusive. Here, we use density functional theory (DFT) simulations with up to 108 atoms using molecular dynamics, as well as one-atom DFT as implemented in the neutral pseudo-atom method where multi-atom effects are treated by ion–ion correlation functionals. Both methods use electron–electron exchange correlation functionals for electron many-body effects. Here, we show using both methods that liquid carbon displays multiple liquid–liquid transitions linked to changes in coordination number in the density range 3–6 g/cm3 when a coordination number of 12 is reached. The transitions disappear by 4 eV in temperature. The calculated pressures and transition densities are shown to be sensitive to the exchange-correlation functionals used. Significantly, we find that a simple metallic model yields the structure factors and thermodynamics with quantitative accuracy, without invoking any covalent-bonding features. The ion–ion structure factor for these densities and temperatures is found to have a subpeak tied to twice the Fermi wavevector, constraining the fluid in momentum space. The dominant Friedel oscillations forming the pair interactions correlate the ions and drive the multiple liquid–liquid phase transitions. Our results suggest that liquid carbon typifies a class of fluids whose structure is ordered by the long-ranged Friedel oscillations in the pair-potentials. These results are critical to terrestrial and astrophysical studies, inertial fusion using carbon drivers, refined shock experiments, and in seeking new carbon-based materials.

Two-component density functional theory for muonic molecules: Inclusion of the electron-positive muon correlation functional.

It is well-known experimentally that the positively charged muon and the muonium atom may bind to molecules and solids, and through muon's magnetic interaction with unpaired electrons, valuable information on the local environment surrounding the muon is deduced. Theoretical understanding of the structure and properties of resulting muonic species requires accurate and efficient quantum mechanical computational methodologies. In this paper, the two-component density functional theory (TC-DFT), as a first principles method, which treats electrons and the positive muon on an equal footing as quantum particles, is introduced and implemented computationally. The main ingredient of this theory, apart from the electronic exchange-correlation functional, is the electron-positive muon correlation functional that is foreign to the purely electronic DFT. A Wigner-type local electron-positive muon correlation functional, termed eμc-1, is proposed in this paper and its capability is demonstrated through its computational application to a benchmark set of muonic organic molecules. The TC-DFT equations containing eμc-1 are not only capable of predicting the muon's binding site correctly, but they also reproduce muon's zero-point vibrational energies and the muonic densities much more accurately than the TC-DFT equations lacking eμc-1. Thus, this study sets the stage for developing accurate electron-positive muon functionals, which can be used within the context of the TC-DFT to elucidate the intricate interaction of the positive muon with complex molecular systems.