Pseudopotential Research Articles

Automated model discovery for tensional homeostasis: Constitutive machine learning in growth and remodeling.

We present a built-in physics neural network architecture, known as inelastic Constitutive Artificial Neural Network (iCANN), to discover the inelastic phenomenon of tensional homeostasis. In this course, identifying the optimal model and material parameters to accurately capture the macroscopic behavior of inelastic materials can only be accomplished with significant expertise, is often time-consuming, and prone to error, regardless of the specific inelastic phenomenon. To address this challenge, built-in physics machine learning algorithms offer significant potential. We introduce the incorporation of kinematic growth and homeostatic surfaces into the iCANN to discover the Helmholtz free energy and the pseudo potential. The latter describes the state of homeostasis in a smeared sense. To this end, we additionally propose a novel design of the corresponding feed-forward network in terms of principal stresses. We evaluate the ability of the proposed network to learn from experimentally obtained tissue equivalent data at the material point level, assess its predictive accuracy beyond the training regime, and discuss its current limitations when applied at the structural level. Our source code, data, examples, and an implementation of the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.13946282.

Numerical simulation of common envelope stage in close binary systems: comparison between Newtonian and modified gravity

We consider the important stage in evolution of close binary system namely common envelope phase in framework of various models of modified gravity. The comparison of results between calculations in Newtonian gravity and modified gravity allows to estimate possible observational imprints of modified gravity. Although declination from Newtonian gravity should be negligible we can propose that due to the long times some new effects can appear. We use the moving-mesh code AREPO for numerical simulation of binary system consisting of ∼ M ⊙ white dwarf and a red giant with mass ∼ 2M ⊙. For implementing modified gravity into AREPO code we apply the method of (pseudo)potential, assuming that modified gravity can be described by small corrections to usual Newtonian gravitational potential. As in Newtonian case initial orbit has to shrink due to the energy transfer to the envelope of a giant. We investigated evolution of common envelope in a case of simple model of modified gravity with various values of parameters and compared results with simulation in frames of Newtonian gravity.

Norm-Conserving 5f-in-Core Pseudopotentials and Gaussian Basis Sets Optimized for Tri- and Tetra-Valent Actinides (An = Pa-Lr).

Relativistic pseudopotentials (PPs) and basis sets are the workhorses for modeling heavy elements of lanthanides and actinides. The norm-conserving Goedecker-Teter-Hutter (GTH) PP is advantageous for modeling lanthanide and actinide compounds and condensed systems because of its transferability and accuracy. In this work, we develop a set of well-benchmarked GTH-type 5f-in-core PPs with scalar-relativistic effects together with associated Gaussian basis sets for the most commonly encountered trivalent and tetravalent actinides [An(III), An(IV); An = Pa-Lr]. The 5f-in-core GTH PPs are constructed by placing 5f-subconfiguration 5fn of An(III) and 5fn-1 of An(IV) (n = 2-14) into the atomic core in the core-valence separation. The formalism of 5f-in-core GTH PPs circumvents the computational difficulty arising from the 5f open valence shell. The different performances of 5f-in-core GTH PPs for trivalent and tetravalent actinides are further analyzed from the chemical bonding features of actinides. We anticipate that the optimized 5f-in-core GTH PPs and Gaussian basis sets can be used to accelerate the costly first-principles modeling of structure-complicated actinide compounds and condensed-phase actinide systems.

Exploring the Theoretical Kinetic Analysis of Halogen Monoxide (XO, X = Cl, Br, I) Reactivity with Isoprene across Diverse Temperatures.

The rate coefficients for the reactions for XO (XO, X = Cl, Br, I) + isoprene were calculated using the RRKM and ILT approach in master equation simulation (MESMER) in the temperature range of 200-400 K at 1 atm pressure. The thermochemical and energy parameters for ClO + isoprene were calculated using the CCSD(T)/aug-cc-pVDZ//B3LYP/6-31g(2df,p) theory. In the case of the BrO and IO radical reaction, all thermochemical parameters were calculated using CCSD(T)/AVDZ//M06-2X/AVDZ (AVDZ = aug-cc-pVDZ for C, H, and O atoms and aug-cc-pVDZ-pp for the Br atom with effective core potential (ECP) approximation) and CCSD(T)/AVDZ_ecp//M06-2X/AVDZ_ecp (AVDZ_ecp = aug-cc-pVDZ for C, H, and O atoms and Def2SVP for I atom with ECP), respectively. The rate coefficient for the reaction ClO + isoprene was calculated as k(T)200-400KClO+isoprene = (3.63 ± 0.35) × 10-13 exp - (32.5 ± 30.2)/T cm3 molecule-1 s-1 at 1 atm. The rate coefficients for isoprene + BrO and isoprene + IO were calculated in the temperature range of 200-400 K at 1 atm as k(T)200-400KBrO+isoprene = (2.33 ± 0.07) × 10-13 exp(431.8 ± 8.1)/T cm3 molecule-1 s-1 and k(T)200-400KIO+isoprene = (5.71 ± 0.12) × 10-13 exp(678.8 ± 6.2)/T cm3 molecule-1 s-1. The rate coefficients measured for BrO and IO radicals show a negative temperature dependence over 200-400 K.

DFT-based accurate and efficient bandgap prediction of CsSnI3-xBrx and parameter optimization for enhanced perovskite solar cell performance

This article analyzes the bandgap (Eg) of tin-based metal halide perovskites CsSnI3-xBrx (x = 0, 1, 2, 3) using density functional theory (DFT). For the first time, the study evaluates various exchange-correlation (XC) families—LDA, GGA, MGGA, and HSE—along with key DFT parameters such as pseudopotentials (PP), K-point densities, and basis sets. The investigation identifies the optimal combination of parameters that most accurately matches experimental Eg values for different mole fractions. The study reports average deviations from experimental Eg values of 6.48% for LDA, 8.08% for GGA, 3.44% for MGGA, and 3.07% for HSE. While HSE shows the smallest deviation, MGGA demonstrates better consistency across mole fractions with lower computational costs. Additionally, the band structure and Eg trends for each mole fraction are examined, providing valuable insights for future computational studies on perovskite materials.

Molecular line lists for the singlet states in gaseous YN at high temperature

ABSTRACT Our aim in this study is to investigate the electronic structure of the gaseous YN molecule and provide an accurate molecular line list of spectroscopic transitions between the five lowest singlet states. The calculations were done by using large basis set for yttrium aug-cc-pVQZ-PP with relativistic effective core potentials at the spin-free level. We first used the method of complete active space self-consistent field, which was followed by the multireference singles and doubles configuration interaction. Potential energy curves and permanent and transition dipole moments were calculated at the internuclear distance range of 1.3–2.96 Å. For each state, we calculated the spectroscopic constants (Te, ωe, ωexe, ωeye, Be, αe, Re). The calculated values of the spectroscopic constants are in excellent agreement with the experimental constants available, with a relative difference of less than 5 cm−1. We further calculated the transition intensities of allowed transitions, and we provided the absorption spectra up to a temperature of 4000 K. The computed molecular line list contains 2.6 million transitions calculated between almost 18 186 vibro-rotational energy levels. It covers the frequency range between 0 and 30 000 cm−1. The effect of temperature on the spectra of hot YN was investigated with partition functions calculated between 298 and 4000 K. This study should help in identifying the singlet state spectrum of the hot YN molecule, which is possibly found in the atmospheres of cool stars and hot rocky super-Earths.

Speciation and formation constants of aqueous lanthanum (III) chloride complexes from 5 to 80 °C by Raman spectroscopy

Lanthanum chloride solutions were studied both computationally and by polarized Raman spectroscopy to determine the aqueous species present and their equilibrium constants. Four species were predicted from Gaussian 16 computations using density functional theory: La(H2O)9 3+, LaCl(H2O)8 2+, LaCl2(H2O)6 2+, and LaCl3(H2O)4 0. Both LaCl(H2O)8 2+ and LaCl2(H2O)6 + were identified in the reduced isotropic solvent-subtracted Raman spectra from their La–Cl vibrational bands at 234 and 221 cm−1, respectively. The spectra did not change significantly with temperature from 5 to 80 °C, and the Raman bands for each species could not be fitted with sufficient accuracy to determine the scattering coefficients directly from the experimental data. Instead, the computed scattering coefficients from Gaussian 16 (B3LYP with the Los Alamos National Laboratory 2-double-zeta effective core potential and 6-311+G(d,p) basis set) were to be used to obtain the equilibrium concentrations of LaCl(H2O)8 2+ and LaCl2(H2O)6 +, from which the concentration of La(H2O)9 3+ was determined. The concentration dependent formation quotients were fitted with the specific ion interaction (SIT) activity coefficient model to determine the stepwise formation constants K0, 1 and K1, 2, from 5 to 80 °C. Both K0, 1 and K1, 2 showed minor increases with temperature.

Polyconvex inelastic constitutive artificial neural networks

AbstractThe characterization of the material behavior of inelastic materials requires a high degree of expert knowledge to identify and constitutively describe the material response. In addition, specific models are usually pre‐selected in the course of characterization and only the best parameters for these specific models are determined, but therefore not necessarily the best models. Unfortunately, a more general description of these pre‐selected models results in an increased effort during characterization, which is barely practicable by hand. This is where machine learning algorithms may help us. To get the best of both worlds, powerful machine learning and sound thermodynamic considerations, inelastic Constitutive Artificial Neural Networks (iCANNs) discover generic formulations of the Helmholtz free energy and pseudo potential. Constitutive relations guide us towards thermodynamically consistent descriptions of stresses and inelastic strains; a concept that is applicable to a wide range of inelastic phenomena from viscoelasticity, elastoplasticity, phase transformations to growth and remodeling of living tissues. Here, we equip the original iCANN framework to guarantee polyconvexity a priori, which ensures at least one minimizing deformation. We investigate the ability of our iCANN to identify the material behavior of a viscoelastic polymer at different stretch levels and strain rates. We made our source code, data, and example accessible to the public at https://doi.org/10.5281/zenodo.11084354.

Rearrangement of Proline Complexes with Zn2+: An Infrared Multiple Photon Dissociation and Theoretical Investigation.

Complexes of proline (Pro) cationized with Zn2+ and Cd2+ were examined by infrared multiple photon dissociation (IRMPD) action spectroscopy using light generated from a free electron laser. Complexes of intact Pro with CdCl+, CdCl+(Pro), a complex of (Zn+Pro-H)+ where a proton has been lost, as well as Zn+(Pro-H)(Pro) were formed by electrospray ionization. In order to identify the structures formed experimentally, the IRMPD spectra were compared to those calculated from optimized structures at the B3LYP/6-311+G(d,p) level for zinc complexes and B3LYP/def2-TZVP level with an effective core potential on cadmium for the CdCl+(Pro) system. For the latter complex, the main binding motif observed has a zwitterionic proline ligand structure, [CO2-]cc, where the metal binds to the two carboxylate oxygens. In contrast, for Zn+(Pro-H)(Pro), both ligands interact with zinc via a [N,CO-][N,CO] binding motif, where binding is observed at the carbonyl oxygens and nitrogens for both ligands, consistent with previous work. In both cases, contributions from different puckers of the proline ring may contribute. For (Zn+Pro-H)+, we identify that the structure is actually ZnH+(Pro-2H), in which the proline has been dehydrogenated and one of the hydrogens has migrated to form a covalent bond with Zn, which verifies a previous report relying on a single OH stretch band.

A DFT investigation of Li substitution in CsCaY3 (Y[dbnd]F, Cl, Br) having admirable optoelectronic characteristics as a viable candidate for photocatalytic water splitting

In this study we investigated pristine and Li substituted Cs1-xLixCaY3 (YF, Cl, Br) lead free halide perovskite with different concentrations x = 0, 0.11, 0.33, 0.55, 0.77, and 1 using CASTEP under Density functional theory (DFT) has been employed under Perdew Burke Ernzerhof generalized gradient approximation (GGA-PBE) and Ultrasoft pseudo potential (USSP) approaches. Understudy pristine materials have a cubic phase Pm3 m space group. At the same time, doped compositions show a tetragonal phase structure except those in which Li completely swaps out Cs, so both end materials own a cubic nature. Li introduced at the Cs site is more effective than Ca because additional gamma points formed, influencing the electronic formation of pristine CsCaF3, CsCaCl3, and CsCaBr3 minimized band gap from 6.299 to 4.152 eV, 5.261–3.613 eV and 4.338–2.752 eV respectively. All compositions are thermodynamically stable, as suggested by the negative values of the formation energy. For all compositions, the Fermi level resides near the valence band which confirms the p-type behavior of the semiconductors. All of the materials retain the indirect bandgap. The total/partial/elemental density of states calculated has been approximated to provide a full picture of the band structure. Although elastic constants for all compounds, whether cubic or tetragonal, are used to predict mechanical parameters such as bulk modulus, shear modulus, young modulus, Poisson ratio, and Pugh's ratio, materials were first developed to support born stability criteria. From all of the compositions Cs1-xLixCaF3 for x = (0.11, 0.55, 0.77, and 1) and Cs0.23Li0.77CaCl3 are found to be mechanically unstable. All other combinations are stable, whether cubic or tetragonal. We evaluated and contrasted many optical properties like absorption spectra, refractive index, dielectric function, reflectivity, and energy loss function of pristine CsCaY3 (YF, Cl, Br) in comparison with Li substitution concentrations. For both pristine and Li substituted CsCaY3 (YF, Cl, Br) the overall water splitting was explored. All the compositions can be used for hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and overall water splitting reactions but Cs0.23Li0.77CaBr3 is a good catalyst among all. It is proposed that the aforementioned materials have a bandgap range suitable for solar cell applications in addition to being lead-free for environmentally conscious applications in photocatalytic activity.

Measurement of core electron binding energies of silver nanoparticles and their modeling with electron propagator calculations of silver clusters

Silver nanoparticles were synthesized by ionic exchange with zeolites and further reduction with hydrogen flux. Core electron binding energies were determined by X-ray photoelectron spectroscopy at different times of the reduction process. Electron propagator calculations of core electron binding energies were performed including scalar relativistic effects using effective core potentials and zero order regular approximation. Theoretical results were compared to the experiment to get insight into the origin of the experimental signals for carbon, oxygen, silicon, aluminum and silver. Small model molecules and zeolite fragments were used for the calculation of core electron binding energies. It is evidenced that although binding energies tend to converge, fluctuations of more than 1 eV are found for non-symmetric structures in neutral and cationic silver clusters. Detailed analysis shows that these fluctuations originate on the different coordination numbers of ionized silver atoms and charge fluctuations.

Theoretical modeling of electronic absorption spectra of ionized species of β-diketones.

Direct DFT evaluation of negatively charged or highly π-delocalized systems is intrinsically problematic. Single ionized (anionic) forms of β-diketones combine both these issues. In this article, we have summarized and analyzed the experimental and theoretical spectral dataset for anionic forms of different substituted perfluorinated β-diketones that were obtained by our team during the past few years. Using previously collected experimental data, spectra of anion of diketones containing phenol, 2-furoyl, 2-thiophen, 2-selenophen, 2-tellorphe, 2-pyridin, 2-naphthyl, and N-methyl-pyrrole substituted rings were considered and chosen for the simulation. The X3LYP density functional demonstrates good results in both ultraviolet and visible parts of the diketones spectra. Minnesota family show predictable ability within the reasonable errors. The linear correlation between the Hartree-Fock exchange and the errors of estimation has been observed. Density functionals with a low contribution of HF weight (0-30%) provide better prediction accuracy. Quantum chemistry calculations were performed under eighteen density functionals (Slater, Becke, OPTX, LYP, PW91C, BPE0, B3LYP, CAM-B3LYP, X3LYP, TPSS, revTPSS, TPSSh, M06-L, M06, M06-2X, M06-HF, M11-L, MN15-L), paired with the SMD solvation model implemented in GAMESS US program package. Def2-SVP basis set functions were applied to light atoms, and CRENBL effective core potential was used to Tellurium.

The Use of Effective Core Potentials with Multiconfiguration Pair-Density Functional Theory.

The reliable and accurate prediction of chemical properties is a key goal in quantum chemistry. Transition-metal-containing complexes can often pose difficulties to quantum mechanical methods for multiple reasons, including many electron configurations contributing to the overall electronic description of the system and the large number of electrons significantly increasing the amount of computational resources required. Often, multiconfigurational electronic structure methods are employed for such systems, and the cost of these calculations can be reduced by the use of an effective core potential (ECP). In this work, we explore both theoretical considerations and performances of ECPs applied in the context of multiconfiguration pair-density functional theory (MC-PDFT). A mixed-basis set approach is used, using ECP basis sets for transition metals and all-electron basis sets for nonmetal atoms. We illustrate the effects that an ECP has on the key parameters used in the computation of MC-PDFT energies, and we explore how ECPs affect the prediction of physical observables for chemical systems. The dissociation curve for a metal dimer was explored, and ionization energies for transition metal-containing diatomic systems were computed and compared to experimental values. In general, we find that ECP approaches employed with MC-PDFT are able to predict ionization energies with improved accuracy compared to traditional Kohn-Sham density functional theory approaches.

Exchange-correlation kernel for perturbation dependent auxiliary functions in auxiliary density perturbation theory

ContextAnalytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses.MethodAll calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (Pt3Cu)n cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores.

Molecular relaxation by reverse diffusion with time step prediction

Abstract Molecular relaxation, finding the equilibrium state of a non-equilibrium structure, is an essential component of computational chemistry to understand reactivity. Classical force field (FF) methods often rely on insufficient local energy minimization, while neural network FF models require large labeled datasets encompassing both equilibrium and non-equilibrium structures. As a remedy, we propose MoreRed, molecular relaxation by reverse diffusion, a conceptually novel and purely statistical approach where non-equilibrium structures are treated as noisy instances of their corresponding equilibrium states. To enable the denoising of arbitrarily noisy inputs via a generative diffusion model, we further introduce a novel diffusion time step predictor. Notably, MoreRed learns a simpler pseudo potential energy surface (PES) instead of the complex physical PES. It is trained on a significantly smaller, and thus computationally cheaper, dataset consisting of solely unlabeled equilibrium structures, avoiding the computation of non-equilibrium structures altogether. We compare MoreRed to classical FFs, equivariant neural network FFs trained on a large dataset of equilibrium and non-equilibrium data, as well as a semi-empirical tight-binding model. To assess this quantitatively, we evaluate the root-mean-square deviation between the found equilibrium structures and the reference equilibrium structures as well as their energies.

Fixed-node diffusion Monte Carlo shows promise for modeling reaction thermochemistry of hydrocarbon-based radicals.

Reliable thermodynamic and kinetic properties of free radical polymerization reactions are essential for synthesizing both primary polymeric materials and specialty polymers. The computational generation of these data from quantum chemistry requires a time-efficient method capable of capturing the essential physics. One such method, fixed-node diffusion Monte Carlo (FN-DMC) (using single Slater-Jastrow trial wavefunctions), has demonstrated the capability to recover 90%-95% of missing dynamic correlation energy for typical systems. In this study, methyl radical addition to ethylene serves as a simple model to test FN-DMC's ability to calculate enthalpies of reaction and activation energies with different time steps, antisymmetric trial wavefunctions, basis set sizes, and effective core potentials. The FN-DMC computational protocol thus defined for methyl radical addition to ethylene is subsequently benchmarked against Weizmann-1 and experimental reaction enthalpies from Lin et al.'s test set of 21 radical addition and 28 hydrogen abstraction enthalpies. Our findings reveal that FN-DMC consistently generates reaction enthalpies with chemical accuracy, exhibiting mean absolute deviation of 3.5(7) and 1.4(8) kJ/mol from the Weizmann-1 reference for radical addition and hydrogen abstraction reactions, respectively. Given its favorable computational scaling and high degree of parallelizability, we, therefore, recommend more comprehensive testing of FN-DMC with effective core potentials to address more extensive and intricate polymerization reactions and reactions with other radicals.

Quadruple bonds in MoC: Accurate calculations and precise measurement of the dissociation energy of low-lying states of MoC.

In the present work, the electronic structure and chemical bonding of the MoC X3Σ- ground state and the six lowest excited states, A3Δ, a1Γ, b5Σ-, c1Δ, d1Σ+, and e5Π, have been investigated in detail using multireference configuration interaction methods and basis sets, including relativistic effective core potentials. In addition, scalar relativistic effects have been considered in the second order Douglas-Kroll-Hess approximation, while spin-orbit coupling has also been calculated. Five of the investigated states, X3Σ-, A3Δ, a1Γ, c1Δ, and d1Σ+, present quadruple σ2σ2π2π2 bonds. Experimentally, the predissociation threshold of MoC was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the dissociation energy of the ground state. Theoretically, the complete basis set limit of the calculated dissociation energy with respect to the atomic ground state products, including corrections for scalar relativistic effects, De(D0), is computed as 5.13(5.06) eV, in excellent agreement with our measured value of D0(MoC) of 5.136(5) eV. Furthermore, the calculated dissociation energies of the states having quadruple bonds with respect to their adiabatic atomic products range from 6.22 to 7.23eV. The excited electronic states A3Δ2 and c1Δ2 are calculated to lie at 3899 and 8057 cm-1, also in excellent agreement with the experimental values of DaBell et al., 4002.5 and 7834 cm-1, respectively.

Exploring Heusler superconducting properties for Ni2ZrAl and Ni2ZrGa Heusler compounds: First principal insight

This paper presents a theoretical study of structural, mechanical, electronic, vibrational and superconducting properties of full Heusler compounds Ni2ZrZ (Z= Al and Ga) using the norm conserving pseudo potential within the framework of Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT). Our finding reveal that the non-magnetic L21 phase structure is energetically more stable for both compounds. The band structure shows that these compounds have a metallic behavior with a saddle point (Van Hove Singularity) at L-point. Elastic and vibrational properties analysis confirm the mechanical and dynamical stability of our studied compounds. The Ni2ZrAl and Ni2ZrGa exhibit BCS weak coupling superconductivity with critical temperatures of 1.78 K and 2.68 K, respectively. The study extends to explore the impact of Hf concentrations, providing valuable insights into the superconducting properties of Ni2Zr(1-x)HfxGa alloys.

Density functional simulation of water molecule with Ab-initio pseudo potential

Density functional simulation of water molecule with Ab-initio pseudo potential

Performance assessment of the effective core potentials under the fermionic neural network: First and second row elements.

The rapid development of deep learning techniques has driven the emergence of a neural network-based variational Monte Carlo (VMC) method (referred to as FermiNet), which has manifested high accuracy and strong predictive power in the electronic structure calculations of atoms, molecules, and some periodic systems. Recently, the implementation of the effective core potential (ECP) scheme has further facilitated more efficient calculations in practice. However, there is still a lack of comprehensive assessments of the ECP's performance under the FermiNet. In this work, we set sail to fill this gap by conducting extensive tests on the first two row elements regarding their atomic, spectral, and molecular properties. Our major finding is that, in general, the qualities of ECPs have been correctly reflected under FermiNet. Two recently built ECP tables, namely, correlation consistent ECP (ccECP) and energy consistent correlated electron pseudopotential (eCEPP), seem to prevail in terms of overall performance. In particular, ccECP performs slightly better on spectral precision and covers more elements, while eCEPP is more systematically built from both shape and energy consistency and better treats the core polarization. On the other hand, the high accuracy of the all-electron calculations is hindered by the absence of relativistic effects as well as the numerical instabilities in some heavier elements. Finally, with further in-depth discussions, we generate possible directions for developing and improving FermiNet in the near future.