Strong Correlation Effects Research Articles

Perspective: multi-configurational methods in bio-inorganic chemistry.

Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems. Yet their computational cost has long hindered wider adoption, making methods such as density functional theory (DFT) the method of choice. However, advancements over the past decade have substantially alleviated this limitation, rendering multiconfigurational quantum chemistry methods more accessible and applicable to a wider range of bio-inorganic systems. In this perspective, we discuss some of these developments and how they have already been used to answer some of the most important questions in bio-inorganic chemistry. We also comment on ongoing developments in the field and how the future of the field may evolve.

Research on the electronic phase transitions in strongly correlated oxides and multi-field regulation

External-field-triggered multiple electronic phase transitions within correlated oxides open up a new paradigm to explore exotic physical functionalities and new quantum transitions via regulating the electron correlations and the interplay in the degrees of freedom, which makes the multidisciplinary fields have the promising application prospects, such as neuromorphic computing, magnetoelectric coupling, smart windows, bio-sensing, and energy conversion. This review presents a comprehensive picture of regulating the electronic phase transitions for correlated oxides via multi-field covering the VO<sub>2</sub> and <i>Re</i>NiO<sub>3</sub>, thus highlighting the critical role of external field in exploring the exotic physical property and designing new quantum states. Beyond conventional semiconductors, the complex interplay in the charge, lattice, orbital and spin degrees of freedom within correlated oxides triggers abundant correlated physical functionalities that are rather susceptible to the external field. For example, hydrogen-related electron-doping Mottronics makes it possible to discover new electronic phase and magnetic ground states in the hydrogen-related phase diagram of correlated oxides. In addition, filling-controlled Mottronics by using hydrogenation triggers multiple orbital reconfigurations for correlated oxides away from the correlated electronic ground state that results in new quantum transitions via directly manipulating the d-orbital configuration and occupation, such as unconventional Ni-based superconductivity. The transition metals of correlated oxides are generally substituted by dopants to effectively adjust the electronic phase transitions via introducing the carrier doping and/or lattice strain. Imparting an interfacial strain to correlated oxides introduces an additional freedom to manipulate the electronic phase transition via distorting the lattice framework, owing to the interplay between charge and lattice degrees of freedom. In recent years, the polarization field associated with BiFeO<sub>3</sub> or PMN-PT material triggered by a cross-plane electric field has been used to adjust the electronic phase transition of correlated oxides that enriches the promising correlated electronic devices. The exotic physical phenomenon as discovered in the correlated oxides originates from the non-equilibrium states that are triggered by imparting external fields. Nevertheless, the underneath mechanism as associated with the regulation in the electronic phase transitions of correlated oxides is still in a long-standing puzzle, owing to the strong correlation effect. As a representative case, hydrogen-associated Mottronic transition introduces an additional ion degree of freedom into the correlated oxides that is rather difficult to decouple from the correlated system. In addition, from the perspective of material synthesis, the above-mentioned correlated oxides are expected to be compatible with conventional semiconducting process, by which the prototypical correlated electronic devices can be largely developed. The key point that accurately adjusts and designs the electronic phase transitions for correlated oxides via external fields is presented to clarify the basic relationship between the microscopic degrees of freedom and macroscopic correlated physical properties. On the basis, the multiple electronic phase transitions as triggered by external field within correlated oxides provide new guidance for designing new functionality and interdisciplinary device applications.

Enriching 2D transition metal borides via MB XMenes (M = Fe, Co, Ir): Strong correlation and magnetism.

Recently, two-dimensional (2D) FeSe-like anti-MXenes (or XMenes), composed of late d-block transition metal M and p-block nonmetal X elements, have been both experimentally and theoretically investigated. Here, we select three 2D borides FeB, CoB and IrB for a deeper investigation by including strong correlation effects, as a fertile ground for understanding and applications. Using a combination of Hubbard corrected first-principles calculations and Monte Carlo simulations, FeB and CoB are found to be ferro- and anti-ferro magnetic, contrasting with the non-magnetic nature of IrB. The metallic FeB XMene monolayer, superior to most of the MXenes or MBenes, exhibits robust ferromagnetism, driven by intertwined direct-exchange and super-exchange interactions between adjacent Fe atoms. The predicted Curie temperature (TC) of the FeB monolayer via the Heisenberg model reaches an impressive 425 K, with the easy-axis oriented out-of-plane and high magnetic anisotropic energy (MAE). The asymmetry in the spin-resolved transmission spectrum induces a thermal spin current, providing an opportunity for spin filtration. This novel 2D FeB material is expected to hold great promise as an information storage medium and find applications in emerging spintronic devices.

Effect of Hubbard Potential (U) on Mn Doped BiTeI

In recent years, Bismuth tellurohalide has gained significant attention as a possible candidate for spintronics applications. Among them, BiTeI is one such layered material that shows Rashba spin splitting responsible for transport phenomenon. On the basis of density functional theory calculations using full-potential local-orbital code, we studied the electronic and magnetic properties of Bi2TeMnI2 compound. Our study shows an energy band gap of 1.18 eV for the parent material BiTeI. The main contribution around the Fermi level are from the Bi-6p, I-5p and Te-5p states. Upon doping Mn atom independently to Bi, Te and I site, we found that Te site is energetically most favorable. With Mn doped to Te site, the material is found to transform to ferromagnetic semiconducting state with magnetic easy-axis along [001] with magnetic moment of 3 μB per unit cell. The magnetic moment is found to alter interestingly with the implementation of Hubbard-potential (U). The value first reduces to 1 μB for U = 3 eV and starts changing with increasing value of U. Due to internal ferromagnetic ordering and strong correlation effect, this compound seems to be a promising candidate for spintronics and quantum computing.

Polar NaTaO3/LaAlO3 (001) superlattices: A comparison of PBEsol and PBEsol+[formula omitted] first-principles calculations

The increasing experimental and theoretical interest in two-dimensional charge carrier gases formed at the interfaces of heterostructured perovskite oxide systems has led to a demand for a deeper understanding regarding the influence of exchange–correlation functionals and associated corrections on the systems’ properties. Herein, we investigate the impact of implementing additive Hubbard corrections compared to standard DFT routines using the PBEsol functional in polar NaTaO3/LaAlO3 (001) superlattices. Structural analysis reveals that the qualitative assessment remains consistent regardless of the approach, with slight variations observed for the NaTaO3 phase due to more pronounced polar distortions. Electronically, standard PBEsol fails to accurately describe the electronic structure of the superlattice below the system’s critical thickness, whereas the inclusion of on-site Coulomb interactions through PBEsol+U routines provides the correct semiconductor character of the superlattice, emphasizing the role of strong correlation effects on d and f electrons at the material’s interface. Additionally, our investigation reveals the spatial charge separation in the semiconductor heterostructure, with potential implications for photocatalytic devices. This work not only contributes to demonstrate the importance of the chosen methodology when studying such systems but also sheds light on important electronic and structural properties of NaTaO3/LaAlO3 (001) superlattices, enabling new avenues for future applications.

Iron Vacancy Tunable Superconductor-Insulator Transition in FeSe/SrTiO_{3} Monolayer.

The Fe_{4}Se_{5} with a sqrt[5]×sqrt[5] Fe vacancy order is suggested to be a Mott insulator and the parent state of bulk FeSe superconductor. The iron vacancy ordered state has been considered as a Mott insulator and the parent compound of bulk FeSe-based superconductors. However, for the superconducting FeSe/SrTiO_{3} monolayer (FeSe/STO) with an interface-enhanced high transition temperature (T_{c}), the electronic evolution from its Fe vacancy ordered parent phase to the superconducting state, has not been explored due to the challenge to realize an Fe vacancy order in the FeSe/STO monolayer, even though important to the understanding of superconductivity mechanism. In this study, we developed a new method to generate Fe vacancies within the FeSe/STO monolayer in a tunable fashion, with the assistance of atomic hydrogen. As a consequence, an insulating sqrt[5]×sqrt[5] Fe vacancy ordered monolayer is realized as the parent state. By using scanning tunneling microscopy and scanning tunneling spectroscopy, the spectral evolution from superconductivity to insulator is fully characterized. Surprisingly, a prominent spectral weight transfer occurs, thus implying a strong electron correlation effect. Moreover, the Fe vacancy induced insulating gap exhibits no Mott gap-like features. This work provides new insights in understanding the high-T_{c} superconductivity in FeSe/STO monolayer.

Optimizing phosphate removal by manipulating manganese and cobalt levels in soil aquifer treatment system

Manganese (Mn2+) and cobalt (Co2+) metals have been reported to exhibit complex interactions with phosphate (PO43-) ions, which can influence their mobility, reactivity, and removal behavior in soil aquifer treatment system (SAT). This study aimed to investigate the role of manganese (Mn2+) and cobalt (Co2+) in phosphate (PO43-) removal within a soil aquifer treatment system. A lab-scale column experiment was conducted using sand as the filtration media, and a synthetic wastewater containing 20 mg/L PO43-, 60 mg/L Mn2+, and 40 mg/L Co2+ was used. The breakthrough curves showed efficient removal of PO43- during the infiltration process, with concentrations reaching as low as 1 mg/L. The regression analysis revealed that Mn2+ had a strong negative correlation effect on PO43- concentration, indicating its stimulatory role in PO43- removal. Conversely, Co2+ showed a strong positive correlation effect, suggesting its promoting effect on PO43- concentration. Optimization analysis identified optimal concentrations of 57.4 mg/L for Mn2+ and 4.8 mg/L for Co2+ that interacted with lower PO43- concentrations, achieving the desired outcome of reducing PO43- levels. These findings highlight the importance of considering Mn2+ and Co2+ concentrations in soil aquifer treatment systems for effective phosphate removal.

Thermodynamic behavior of correlated electron-hole fluids in van der Waals heterostructures

Coupled two-dimensional electron-hole bilayers provide a unique platform to study strongly correlated Bose-Fermi mixtures in condensed matter. Electrons and holes in spatially separated layers can bind to form interlayer excitons, composite Bosons expected to support high-temperature exciton condensates. The interlayer excitons can also interact strongly with excess charge carriers when electron and hole densities are unequal. Here, we use optical spectroscopy to quantitatively probe the local thermodynamic properties of strongly correlated electron-hole fluids in MoSe2/hBN/WSe2 heterostructures. We observe a discontinuity in the electron and hole chemical potentials at matched electron and hole densities, a definitive signature of an excitonic insulator ground state. The excitonic insulator is stable up to a Mott density of ~0.8 × 1012 cm−2 and has a thermal ionization temperature of ~70 K. The density dependence of the electron, hole, and exciton chemical potentials reveals strong correlation effects across the phase diagram. Compared with a non-interacting uniform charge distribution, the correlation effects lead to significant attractive exciton-exciton and exciton-charge interactions in the electron-hole fluid. Our work highlights the unique quantum behavior that can emerge in strongly correlated electron-hole systems.

Doubles Connected Moments Expansion: A Tractable Approximate Horn-Weinstein Approach for Quantum Chemistry.

Ab initio methods based on the second-order and higher connected moments, or cumulants, of a reference function have seen limited use in the determination of correlation energies of chemical systems over the years. Moment-based methods have remained unattractive relative to more ubiquitous methods, such as perturbation theory and coupled cluster theory, due in part to the intractable cost of assembling moments of high-order and poor performance of low-order expansions. Many of the traditional quantum chemical methodologies can be recast as a selective summation of perturbative contributions to their energy; using this familiar structure as a guide in selecting terms, we develop a scheme to approximate connected moments limited to double excitations. The tractable Doubles Connected Moments [DCM(N)] approximation is developed and tested against a multitude of common single-reference methods to determine its efficacy in the determination of the correlation energy of model systems and small molecules. The DCM(N) sequence of energies exhibits smooth convergence toward limiting values in the range of N = 11-14, with compute costs that scale as a noniterative O(M6) with molecule size, M. Numerical tests on correlation energy recovery for 55 small molecules comprising the G1 test set in the cc-pVDZ basis show that DCM(N) strongly outperforms MP2 and even CCD with a Hartree-Fock reference. When using an approximate Brueckner reference from orbital-optimized (oo) MP2, the resulting oo:DCM(N) energies converge to values more accurate than CCSD for 49 of 55 molecules. The qualitative success of the method in regions where strong correlation effects begin to dominate, even while maintaining spin purity, suggests this may be a good starting point in the development of methodologies for the description of strongly correlated or spin-contaminated systems while maintaining a tractable single-reference formalism.

Studies on Correlation and Path Analysis of Yield and its Contributing Traits in Sesame (Sesamum indicum)

The purpose of the present investigation was to examine the relationships between seed yield and yield-attributing characters in sesame (Sesamum indicum L.) as well as evaluating their direct and indirect effects. Results indicated that number of capsules per plant (0.806) and 1000-seed weight (0.657) showed positive correlation with seed yield per plant . Path coefficient analysis indicated that number of capsules per plant (0.806) and 1000 seed weight (0.111) exhibited positive direct effect on seed yield. Positive indirect effect was observed through number of branches per plant via number of capsules per plant (0.657). Number of capsules per plant exhibited positive indirect effect via 1000 seed weight (0.111). Since, it showed strong correlation and direct effect on seed yield per plant, selecting for this trait may leads to improvement of seed yield per plant. Present study revealed that the traits viz., number of capsules per plant and 1000 seed weight association was highly desirable as the improvement in any of the yield components results into overall increase in seed yield. Selection among genotypes based on this analyses can be made for further improvement in seed yield per plant and its contributing characters.

Probing the strongly correlated magnetic state of Co2C nanoparticles at low temperatures using μSR

Co2C nanoparticles (NPs) are amongst transition metal carbides whose magnetic properties have not been well explored. An earlier study (Roy et al 2021 J. Phys.: Condens. Matter 33 375804) showed that a pellet made from Co2C NPs exhibits exchange bias (EB) effect below a temperature, T EB = 50 K and a spin glass (SG) feature emerges below T SG = 5 K. In the current study we use magnetic, electrical transport, specific heat, and muon spin rotation (μSR) measurements to explore further the magnetic properties of a pellet made with 40 nm diameter pure Co2C NPs. We uncover the onset of Kondo localization at Kondo temperature T K (= 40.1 K), which is close to the onset temperature (T EB) of the EB effect. A crossover from the Kondo-screened scenario to the Ruderman–Kittel–Kasuya–Yosida interaction-dominated regime is also observed for T < T K. Temperature-dependent specific heat measurement further supports the Kondo localization scenario in the pellet and shows the heavy fermionic nature of the strongly correlated electronic state in Co2C. The zero field μSR asymmetry spectra in the low-temperature regime are characterized by two distinct fast and slow relaxation rates. The spectra show the absence of long-range magnetic order in the sample. However, our analysis suggests the NPs-pellet shows the presence of a dominant magnetically disordered fraction and a smaller fraction with short-range order. Muons in the disordered fraction exhibit a slower relaxation rate, while muons in the smaller fraction with short-range order exhibit a faster relaxation rate. We observe an increase in this fast relaxation rate between T EB and T SG. This increase below T EB ∼ 50 K suggests a slowing down of the fluctuating local magnetic environment around muons. Transverse field-μSR asymmetry spectra show the emergence of a stable, multi-peaked local magnetic field distribution in the pellet below T EB. Longitudinal field μSR spectra shows distinct changes in the dynamics of fluctuations suggesting the presence of a frozen glassy like state below 6 K. Based on our results, we suggest that below T EB, the pellet of Co2C NPs develops a magnetic interface that separates the two magnetic fractions; one is a disordered fraction, and the other is a fraction with short-range order. The exchange interaction that sets in below T EB at the interface couples the two fractions, leading to a suppression of the fluctuations. With the suppression of magnetic fluctuations below T EB, strong correlation effects in the electronic state of Co2C lead to Kondo localization.

Effect of different intensities aerobic exercise to cardiac angiogenesis regulation on Wistar rats

The adaptation response of myocardium angiogenesis stimulated by specific exercise intensities remains unclear. The aims of this study is to explore the effect of different intensities aerobic exercise to cardiac angiogenesis regulation via HIF-1α, PGC-1α, VEGF, and CD34+ in Wistar rats. Wistar rats were divided into control and exercise groups. Exercise groups were trained on a treadmill for 12 weeks, 30 min/day for 5 days with low, moderate, and high-intensity groups. The rats were sacrificed, and the myocardium was collected and preserved at -80°C until used. Cardiac protein samples were extracted and run for Western blotting using the specific antibodies: hypoxia-inducible factor (HIF)-1α, Peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PGC-1α), vascular endothelial growth factor (VEGF), and Cluster of differentiation 34 (CD34+). Results showed that protein expression of HIF-1α, PGC-1α, VEGF, and CD34+ was increased significantly by different intensities in the exercise group compared to the control. A correlation statistics test showed that there was a strong correlation effect of HIF-1α on VEGF protein expression in low (p=0.047) and high intensity exercise groups (p=0.009), but no effect was found in the moderate groups. In addition, there was a significant strong effect of PGC-1α on VEGF protein expression in the moderate groups (p=0.037), but no effect was found in other groups. In conclusion, different exercise intensities induce a different modulation pattern of proteins which might be responsible for cardiac adaptation, especially angiogenesis.

Systems of Strongly Correlated Electrons Interacting with Each Other and with Phonons. Diagram Approach

The features of materials leading to the effect of strong correlation and the phenomena realized in them, namely, the metal-insulator Mott transition and high-temperature superconductivity, were considered. The history of their study was traced. Special attention was paid to the study of the role of the interorbital correlation effect and Hund’s coupling in multi-orbital systems, as well as of the electron-phonon interaction in the systems with both strong electron-phonon and Coulomb interactions. The development of the method of the diagram technique of a strong coupling was analyzed, and the results obtained on the base of that approach are presented.

Emerging Characteristics and Properties of Moiré Materials.

In recent years, scientists have conducted extensive research on Moiré materials and have discovered some compelling properties. The Moiré superlattice allows superconductivity through flat-band and strong correlation effects. The presence of flat bands causes the Moiré material to exhibit topological properties as well. Modulating electronic interactions with magnetic fields in Moiré materials enables the fractional quantum Hall effect. In addition, Moiré materials have ferromagnetic and antiferromagnetic properties. By tuning the interlayer coupling and spin interactions of the Moiré superlattice, different magnetic properties can be achieved. Finally, this review also discusses the applications of Moiré materials in the fields of photocurrent, superconductivity, and thermoelectricity. Overall, Moiré superlattices provide a new dimension in the development of two-dimensional materials.

A comparative investigation on the fundamental physical properties of UX2 (X = O, N, C, Si and S) solid nuclear fuel materials: A DFT + U study

This study investigates and compares the physical properties of various UX2 (X = O, N, C, Si and S) nuclear fuels using a combination of Density Functional Theory (DFT) and Hubbard U correction parameter (U) to accurately model the electronic structure and account for strong correlation effects among 5f orbital electrons. Spin-polarized DFT + U method is employed to optimize the structures of the considered compounds. The computational analysis reveals that UO2 and UN2 exhibit Mott-insulating properties, while the remaining UX2 compounds demonstrate metallic nature. To assess the mechanical aspects of these materials, the study evaluates their mechanical stability, Vickers hardness and machinability index through calculations of elastic constants. Notably, all the UX2 fuels are found to be mechanically stable and possess ductility. Both the two-dimensional (2D) and three-dimensional (3D) depictions of the elastic moduli for the analyzed solid fuels demonstrate the presence of elastic anisotropy. The famous Slack's equation is used to determine the lattice thermal conductivity of the UX2 fuels, providing valuable insights into their thermal properties. Among the investigated materials, UC2 exhibits the highest values of Debye temperature and lattice thermal conductivity, which amount to 412 K and 15.73 Wm−1 K−1 at 300 K, respectively. Furthermore, UN2 demonstrates the highest melting temperature. Among the compounds under investigation, UC2 and UN2 fuels exhibit the most minimal thermal expansion and the greatest heat capacity. Based on these findings, UC2 and UN2 emerge as promising alternative fuel materials to UO2 for potential use in nuclear power reactors. This research contributes to the ongoing efforts in identifying alternative fuel materials.

Thickness and temperature-dependent damping in La0.67Sr0.33MnO3 epitaxial films

Damping of La0.67Sr0.33MnO3 (LSMO) epitaxial films as a function of thickness at different temperatures was studied. The competition between two scattering types (ρ-like and σ-like) with entirely distinct thickness and temperature dependencies resulted in complicated damping behavior. The behavior of σ-like damping in LSMO films is consistent with the behavior in magnetic metal films. However, because ρ-like damping is sensitive to the fine electron structure near the Fermi surface, the distortion of the oxygen octahedra controlled by the film thickness is an important factor in controlling the damping. Our study demonstrates that the complexity of damping in LSMO epitaxial films is a consequence of strong-correlation effects, which are characteristics of complex transition-metal oxides.

Surface-Induced Electronic and Vibrational Level Shifting of [Fe(py)2bpym(NCS)2] on Al(100).

It is essential that one understands how the surface degrees of freedom influence molecular spin switching to successfully integrate spin crossover (SCO) molecules into devices. This study uses density functional theory calculations to investigate how spin state energetics and molecular vibrations change in a Fe(II) SCO compound named [Fe(py)2bpym(NCS)2] when deposited on an Al(100) surface. The calculations consider an environment-dependent U to assess the local Coulomb correlation of 3d electrons. The results show that the adsorption configurations heavily affect the spin state splitting, which increases by 10-40 kJmol-1 on the surface, and this is detrimental to spin conversion. This effect is due to the surface binding energy variation across the spin transition. The preference for the low-spin state originates partly from the strong correlation effect. Furthermore, the surface environment constrains the vibrational entropy difference, which decreases by 8-17 Jmol-1K-1 (at 300 K) and leads to higher critical temperatures. These results suggest that the electronic energy splitting and vibrational level shifting are suitable features for characterizing the spin transition process on surfaces, and they can provide access to high-throughput screening of spin crossover devices.

Quantum Chemical Studies on Possible Molecular Devices Based on Electric Field-Induced Intramolecular Charge Transfer.

We report quantum chemical studies on possible molecular devices working based on electric field-induced intramolecular charge transfer (EFIMCT). In the case of donor-acceptor (DA)-type molecular systems, intramolecular charge transfer (IMCT) can be induced by applying the external electric field to molecular systems along the charge transport direction, providing a possible switching mechanism which does not depend upon the electron-phonon coupling effect and is different from the negative differential resistance mechanism observed in the well-known NO2-substituted phenylene ethynylene oligomers. When the EFIMCT proceeds, the molecular systems have strong static electron correlation effects, where the standard nonequilibrium Green's function-density functional theory (DFT) approach cannot be applied to the molecular junction. As a first step toward practical switching devices, we do quantum chemical studies on the EFIMCT in such molecular systems as an isolated molecule, instead of using the electrode-junction-electrode open quantum system model. A prototype molecule P1 is designed as a tentative candidate molecule where the EFIMCT can proceed. The complete active space self-consistent field (CASSCF) molecular orbital calculations on P1 indicate that the EFIMCT can proceed at the external electric field intensity of 0.003 au, corresponding to about 2.25 V bias voltage. This calculated result strongly suggests that the development of this type of switching devices working at practically low bias voltage is feasible if the molecular system is properly designed. Broken symmetry unrestricted Hartree-Fock and spin-polarized Kohn-Sham DFT calculations also qualitatively reproduce the CASSCF results on P1, to some extent, indicating that these approaches can be employed for rough estimations on the EFIMCT such as the first screening of a large quantity of candidate molecules for this type of molecular devices. The possibility of molecular memory devices based on the EFIMCT is also discussed by analyzing the ground and excited potential energy surface model. Remaining challenges to develop practical molecular devices are discussed.

Nonlocal Functionals Inspired by the Strongly Interacting Limit of DFT: Exact Constraints and Implementation.

Capturing strong correlation effects remains a key challenge for the development of improved exchange-correlation (XC) functionals in density functional theory. The recently proposed multiple radii functional (MRF) [J. Phys. Chem. Lett. 2017, 8, 2799; J. Chem. Theory Comput. 2019, 15, 3580] was designed to capture strong correlation effects seamlessly, as its mathematical structure draws from that of the exact XC functional in the limit of infinite correlations. The MRF functional provides a framework for building approximations along the density-fixed adiabatic connection, delivers accurate XC energy densities in the standard DFT gauge (same as that of the exact exchange energy density), and is free of one-electron self-interaction errors. To facilitate the development of XC functionals based on the MRF, we examine the behavior of the MRF functional when applied to uniform and scaled densities and consider how it can be made exact for the uniform electron gas. These theoretical insights are then used to build improved forms for the fluctuation function, an object that defines XC energy densities within the MRF framework. We also show how the MRF fluctuation function for physical correlation can be easily readjusted to accurately capture the XC functional in the limit of infinite correlations, demonstrating the versatility of MRF for building approximations for different correlation regimes. We describe the implementation of MRF using densities expanded on Gaussian basis sets, which improves the efficiency of previous grid-based MRF implementations.

Observation of Electronic Strong Correlation in VTe_{2}-2sqrt[3]×2sqrt[3] Monolayer.

Strong electron correlation under two-dimensional limit is intensely studied in the transition metal dichalcogenides monolayers, mostly within their charge density wave (CDW) states that host a star of David period. Here, by using scanning tunneling microscopy and spectroscopy and density functional theory calculations with on-site Hubbard corrections, we study the VTe_{2} monolayer with a different 2sqrt[3]×2sqrt[3] CDW period. We find that the dimerization of neighboring Te-Te and V-V atoms occurs during the CDW transition, and that the strong correlation effect opens a Mott-like full gap at Fermi energy (E_{F}). We further demonstrate that such a Mott phenomenon is ascribed to the combination of the CDW transition and on-site Coulomb interactions. Our work provides a new platform for exploring Mott physics in 2D materials.