Pseudopotential Research Articles

ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set.

A new composite density functional theory (DFT) method is presented. It is based on ωB97X-V as one of the best-performing density functionals for the GMTKN55 thermochemistry database and completes the family of "3c" methods toward range-separated hybrid DFT. This method is consistently available for all elements up to Rn (Z = 1-86). Its further key ingredients are a polarized valence double-ζ (vDZP) Gaussian basis set, which was fully optimized in molecular DFT calculations, in combination with large-core effective core potentials and a specially adapted D4 dispersion correction. Unlike most existing double-ζ atomic orbital sets, vDZP shows only small basis set superposition errors (BSSEs) and can compete with standard sets of triple-ζ quality. Small residual BSSE effects are efficiently absorbed by the D4 damping scheme, which overall eliminates the need for an explicit treatment or empirical corrections for BSSE. Thorough tests on a variety of thermochemistry benchmark sets show that the new composite method, dubbed ωB97X-3c, is on par with or even outperforms standard hybrid DFT methods in a quadruple-zeta basis set at a small fraction of the computational cost. Particular strengths of this method are the description of non-covalent interactions and barrier heights, for which it is among the best-performing density functionals overall.

Greater transferability and accuracy of norm-conserving pseudopotentials using nonlinear core corrections.

We present an investigation into the transferability of pseudopotentials (PPs) with a nonlinear core correction (NLCC) using the Goedecker, Teter, and Hutter (GTH) protocol across a range of pure GGA, meta-GGA and hybrid functionals, and their impact on thermochemical and non-thermochemical properties. The GTH-NLCC PP for the PBE density functional demonstrates remarkable transferability to the PBE0 and ωB97X-V exchange-correlation functionals, and relative to no NLCC, improves agreement significantly for thermochemical benchmarks compared to all-electron calculations. On the other hand, the B97M-rV meta-GGA functional performs poorly with the PBE-derived GTH-NLCC PP, which is mitigated by reoptimizing the NLCC parameters for this specific functional. The findings reveal that atomization energies exhibit the greatest improvements from use of the NLCC, which thus provides an important correction needed for covalent interactions relevant to applications involving chemical reactivity. Finally we test the NLCC-GTH PPs when combined with medium-size TZV2P molecularly optimized (MOLOPT) basis sets which are typically utilized in condensed phase simulations, and show that they lead to consistently good results when compared to all-electron calculations for atomization energies, ionization potentials, barrier heights, and non-covalent interactions, but lead to somewhat larger errors for electron affinities.

A neural network potential energy surface for the Li + LiNa → Li2 + Na reaction and quantum dynamics study from ultracold to thermal energies.

An improved fundamental invariant neural network (FI-NN) approach for representing a potential energy surface (PES) involving permutation symmetry is introduced in this work. In this approach, FIs are regarded as symmetric neurons, thus avoiding complex preprocessing of training set data, especially when the training set contains gradient data. In this work, the improved FI-NN method, combined with simultaneous fitting of the energy and gradient strategy, is used for constructing a global accurate PES of a Li2Na system (root-mean-square error of 12.20 cm-1). The potential energies and the corresponding gradients are calculated by a UCCSD(T) method with effective core potentials. Based on the new PES, the vibrational energy levels and the corresponding wave functions of Li2Na molecules are calculated using an accurate quantum mechanics method. To accurately describe the cold or ultracold reaction dynamics of the Li + LiNa(v = 0, j = 0) → Li2(v', j') + Na reaction, the long-range region of the PES in both the reactant and product asymptotes is represented by an asymptotically correct form. A statistical quantum model (SQM) is used to study the dynamics of the ultracold Li + LiNa reaction. The calculated results are in good agreement with the exact quantum dynamics results (B. K. Kendrick, J. Chem. Phys., 2021, 154, 124303), which indicates that the dynamics of the ultracold Li + LiNa reaction can be well described by the SQM approach. The time-dependent wave packet calculations are performed for the Li + LiNa reaction at thermal energies, and the characteristic of differential cross-sections confirms that the reaction follows the complex-forming reaction mechanism.

Elastic Constants of Tetragonal Cu2ZnSnS4 Semiconductor: AB-Initio Calculation

Abstract In this work, an ab-initio calculation is used to investigate the elastic constants and some other mechanical and thermal parameters of tetragonal Cu2ZnSnS4 (CZTS) quaternary semiconducting bulk material in Kesterite (KS) and Stannite (ST) phases. The Quantum Espresso code within the Ultra Soft pseudo potentials (USPP) and the local density approximation (LDA) approach were used in the calculation. Firstly,, studies are started with the prediction of the elastic stiffness constants Cij and the normal and shear anisotropy factors. Then some other mechanical moduli, especially the isotropic bulk modulus B, the shear modulus G, the Young modulus E, the Poisson’s ratio ν, and the Pugh’s criteria (G/B) are delivered. The analysis of the mechanical stability criteria at equilibrium shows that our elastic stiffness constants Cij of CZTS material obey all the stability conditions. Additionally, some other parameters of the CZTS semiconductor, especially: the Vickers hardness HV , the sound velocity, the Debye temperature θD and the melting temperature Tm were also calculated. The obtained values of the elastic constants Cij and other mechanical and thermal parameters agree well with experimental and other theoretical results of the literature. The Debye temperature θD of the KS phase was found at around 332.7 K, and that of the stannite phase was found equal to 329.1 K, respectively.

Global Full-Dimensional Potential Energy Surface for the Reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 and the Formation Rate and Lifetime of the 23Na287Rb2 Collision Complex.

A full-dimensional global potential energy surface (PES) for the reaction 23Na87Rb + 23Na87Rb → 23Na2 + 87Rb2 was constructed based on high-level ab initio calculations. The short-range part was expressed as a permutation invariant polynomial-neural network (PIP-NN) fit of 22 003 ab initio points calculated using a coupled cluster method with the one-electron basis 5s5p5d2f plus effective core potentials and core polarizability potentials, while the long-range part was represented in an asymptotically correct form based on multipole expansion. The formation rate of the 23Na287Rb2 complex calculated using a quantum statistical method is in good agreement with experiment, while the estimated 19.20 μs lifetime of the complex from Rice-Ramsperger-Kassel-Marcus (RRKM) theory is significantly shorter than the measured millisecond decay rate, signaling either the inadequacy of RRKM theory or a yet unresolved loss mechanism.

Ab initio relativistic potential energy surface with analytical long-range part of benzene-Rn complex and its application to intermolecular vibrations

We study the benzene-Rn (BzRn) complex in its electronic ground state using an ab initio scalar relativistic method in the framework of the coupled-cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)]. Two different approaches to treat the scalar relativistic effects have been tested — the small-core pseudopotential (PP) and the Douglas–Kroll–Hess (DKH) Hamiltonian. These methods were used with the augmented Dunning’s double zeta basis set for C and H atoms, and the augmented triple PP basis set for Rn supplemented by midbond functions. Additionally, the effects of the basis extension for C and H atoms and the extension of the correlation space to include the internal orbitals of Rn and C have been tested. The comparison of the binding energy De and the equilibrium coordinate ze found with different methods has allowed to choose the optimal one based on PP for the construction of the analytical potential energy surface (PES). The long-range part of the potential has been fitted separately and the obtained long-range coefficients have been compared to their counterparts calculated from the first principles using the CCSD polarization propagator. The vibrational energy level pattern of BzRn has been studied, and the revealed polyad structure of the complex has been compared to the previously studied benzene-Kr and benzene-Xe complexes. A Python code that yields the interaction energy at any Rn position is provided.

Experimental and DFT study of structural and optical properties of Ni-doped ZnO nanofiber thin films for optoelectronic applications

As an important metal oxide semiconductor, transition metal-doped zinc oxide (ZnO) has attracted great interest for various applications in optoelectronic, spintronic photovoltaic and photodetectors due to its significant chemical and physical properties. In this research study, pure and nickel (Ni)-doped ZnO nanostructured films were synthesized via the sol-gel method using the spin coating technique on glass substrates. The structural results revealed that all samples exhibited a polycrystalline wurtzite structure and a (002) plane preferred orientation. The crystallite size was reduced by Ni doping. The morphology micrographs indicate that the surface of thin films shows nanofiber structures. An optical study revealed the high transparency of the films. The photoluminescence (PL) showed one ultraviolet (UV) emission at 387 nm and different defect emissions for all films. The absorption, band gap and PL emissions intensities were influenced by Ni doping. Ni-doped ZnO nanostructured thin films revealed high UV sensitivity and photoresponse. Therefore, these thin films are a promising material for a UV photodetector. The dielectric function, absorption coefficient and energy band gap were also calculated and discussed by density functional theory (DFT), using the Ultra Soft Pseudo Potential (US-PP) approach implemented in the CASTEP code.

Correlation consistent effective core potentials for late 3d transition metals adapted for plane wave calculations.

We construct a new modification of correlation consistent effective core potentials (ccECPs) for late 3d elements Cr-Zn with Ne-core that are adapted for efficiency and low energy cut-offs in plane wave calculations. The decrease in accuracy is rather minor, so that the constructions are in the same overall accuracy class as the original ccECPs. The resulting new constructions work with energy cut-offs at or below ≈400 Ry and, thus, make calculations of large systems with transition metals feasible for plane wave codes. We also provide the basic benchmarks for atomic spectra and molecular tests of this modified option that we denote as ccECP-soft.

Quantum chemical and experimental thermodynamic studies of HfO(g).

Hafnium dioxide vaporizes primarily to HfO(g) in a reducing environment. The thermochemistry of HfO(g) is calculated from quantum methods and measured via Knudsen effusion mass spectrometry. For the computations, all-electron and relativistic effective core potential calculations are used. The calculation of an accurate dissociation energy and an entire potential energy curve is reported. These calculations lead to ΔfH°(298) = 63.19 ± 10 kJ/mol, S°(298) = 235.52 J/mol K, and Cp(298-2500K) = (2.741 × 10-9)T3 - (9.853 × 10-6)T2 + (1.295 × 10-2)T + 2.761 × 10-1 J/mol K. Experimentally, HfO(g) is generated from the reaction of Hf(s) and HfO2(s) in a specially made Hf Knudsen cell. A third law treatment of the data leads to ΔfH°(298) of 58.4 ± 12.3 kJ/mol, in good agreement with the calculated value.

Conical Intersections in Solution with Polarizable Embedding: Integral-Exact Direct Reaction Field.

A common strategy to exploring the properties and reactivity of complex systems is to use quantum mechanics/molecular mechanics (QM/MM) embedding, wherein a QM region is defined and treated with electronic structure theory, and the remainder of the system is treated with a force field. Important to the description of electronic excited states, especially those of charge-transfer character, is the treatment of the coupling between the QM and MM subsystems. The state of the art is to use a polarizable force field for the MM region and mutually couple the QM wavefunction and MM induced dipoles, in addition to the usual electrostatic embedding, yielding a polarizable embedding (QM/MM-Pol) approach. However, we showed previously that current popular QM/MM-Pol approaches exhibit issues of root flipping and/or incorrect descriptions of electronic crossings in multistate calculations [J. Chem. Theory Comput. 14, 2137 (2018)]. Here, we demonstrate a solution to these problems with an integral-exact reformulation of the direct reaction field approach of Thole and Van Duijnen (QM/MM-IEDRF). The resulting embedding potential includes one- and two-electron operators and many-body dipole-induced dipole interactions and thus includes a natural description of the screening of electron-electron interactions by the MM induced dipoles. Pauli repulsion from the environment is mimicked by effective core potentials on the MM atoms. Inherent to the DRF approach is the assumption that MM dipoles respond instantaneously to the positions of the QM electrons; therefore, dispersion interactions are captured approximately. All electronic states are eigenfunctions of the same Hamiltonian, while the polarization induced in the environment and the associated energetic stabilization are unique to each state. This allows for a consistent definition of transition properties and state crossings. We demonstrate QM/MM-IEDRF by exploring the influence of a (polarizable) inert xenon matrix environment on the conical intersection underlying the photoisomerization of ethylene.

Iron-Catalyzed Cross-Electrophile Coupling of Inert C–O Bonds with Alkyl Bromides

Iron-Catalyzed Cross-Electrophile Coupling of Inert C–O Bonds with Alkyl Bromides

Two pressure boundary conditions for multi-component multiphase flow simulations using the pseudo-potential lattice Boltzmann model

In this study, two boundary condition (BC) schemes are proposed for the pseudo-potential (PP) lattice Boltzmann method (LBM). The two BC schemes include a modified Convective Boundary Condition (mCBC) and a modified Non-equilibrium Bounceback (mNEBB), and their development is aimed at treating pressure-driven outflow problems for fluids with similar and different density ratios in multi-component multiphase (MCMP) environments. It is the first attempt to incorporate interaction force at boundaries for MCMP fluids. Key limitations of existing LBM boundary schemes for MCMP flow are alleviated. In particular, the constraint of zero-velocity specification at tangential direction is removed by applying the proposed mCBC scheme. In addition, it is demonstrated that multiphase outflow performance is improved with the application of either scheme, while alleviating the nonphysical distortions introduced by the available BC schemes. Three numerical case studies have been conducted to test the proposed scheme. Results have been validated using uncut-off extended domains. These cases are designed to test the induced distortion to the fluids exiting boundaries, examine the scheme’s capability to treat the pressure boundary condition, and explore whether the model can make physically meaningful predictions when these modified BCs are applied. The mCBC scheme is shown to be more capable to correctly treat such pressure specified boundary conditions.

Relativistic versus Jahn-Teller effects in tantalum and tungsten clusters

We juxtapose the interplay of relativistic and Jahn-Teller effects in small tantalum and tungsten clusters. We employ relativistic techniques to study the low-lying electronic states of Tan for 2 ≤ n ≤ 6. We have used the complete active space MCSCF (CASSCF) techniques for the low-lying electronic states of Ta2 together with DFT techniques including spin–orbit corrections for large clusters that employed relativistic effective core potentials. The results thus obtained were compared with CASSCF/MRCI computations together with the inclusion of spin–orbit coupling for the tungsten trimer. Our computations reveal that unlike clusters containing lighter atoms, the spin–orbit effects overcome Jahn-Teller stabilization effects resulting in more symmetrical structures for tantalum and tungsten clusters. We have also computed the 3D-potential energy surfaces of different interesting regions of the Mexican hat surfaces. Whereas for the trimer and tetramer spin–orbit stabilization seems to overtake Jahn-Teller stabilization, thus resulting in the stabilization of symmetric structures, the Jahn-Teller stabilizations are larger than spin–orbit effects for larger clusters, thus resulting in distorted structures for larger clusters. We have provided a double group and graph-theoretical analysis of the electronic states of tantalum clusters to gain insights into the effect of spin–orbit coupling and pseudorotation on the electronic states of these clusters. The absorption spectra for these clusters are computed using time dependent density functional theory (TDDFT).

Optimization of Large Determinant Expansions in Quantum Monte Carlo.

We present a new method for the optimization of large configuration interaction (CI) expansions in the quantum Monte Carlo (QMC) framework. The central idea here is to replace the nonorthogonal variational optimization of CI coefficients performed in usual QMC calculations by an orthogonal non-Hermitian optimization thanks to the so-called transcorrelated (TC) framework, the two methods yielding the same results in the limit of a complete basis set. By rewriting the TC equations as an effective self-consistent Hermitian problem, our approach requires the sampling of a single quantity per Slater determinant, leading to minimal memory requirements in the QMC code. Using analytical quantities obtained from both the TC framework and the usual CI-type calculations, we also propose improved estimators which reduce the statistical fluctuations of the sampled quantities by more than an order of magnitude. We demonstrate the efficiency of this method on wave functions containing 105-106 Slater determinants, using effective core potentials or all-electron calculations. In all the cases, a sub-milli-Hartree convergence is reached within only two or three iterations of optimization.

Correlation Consistent Basis Sets and Core Polarization Potentials for Al-Ar with ccECP Pseudopotentials.

New correlation consistent basis sets for the second-row atoms (Al–Ar) to be used with the neon-core correlation consistent effective core potentials (ccECPs) have been developed. The basis sets, denoted cc-pV(n+d)Z-ccECP (n = D, T, Q), include the “tight”-d functions that are known to be important for second-row elements. Sets augmented with additional diffuse functions are also reported. Effective core polarization potentials (CPPs) to account for the effect of core–valence correlation have been adjusted for the same elements, and two different forms of the CPP cutoff function have been analyzed. The accuracy of both the basis sets and the CPPs is assessed through benchmark calculations at the coupled-cluster level of theory for atomic and molecular properties. Agreement with all-electron results is much improved relative to the basis sets that originally accompanied the ccECPs; moreover, the combination of cc-pV(n+d)Z-ccECP and CPPs is found to be a computationally efficient and accurate alternative to including core electrons in the correlation treatment.

DFT Calculations Using Quantum ESPRESSO for Optical and Electronic Properties of Si Crystal

The DFT calculations were performed to study the structural, electronic and optical properties of Si. The open source computer code, Quantum ESPRESSO used is for first-principles electronic structure modeling based on density functional theory. The optimized crystal lattice constant, band gap, density of states (DOS) and band structure were calculated. The calculated value of lattice constant was in good agreement with reported value. The band gap was calculated using three different pseudo potentials. The HSE hybrid functional provided best agreement of band gap calculations with literature values. The pseudo-dielectric functions was also calculated to estimate the optical properties including refractive indices, extinction coefficients, reflectivities and absorption coefficients in the spectral energy ranges from 0 eV to 10 eV.

Electronic structure of α−RuCl3 by fixed-node and fixed-phase diffusion Monte Carlo methods

Layered material $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ has caught wide attention due to its possible realization of Kitaev's spin liquid and its electronic structure that involves the interplay of electron-electron correlations and spin-orbit effects. Several $\mathrm{DFT}+U$ studies have suggested that both electron-electron correlations and spin-orbit effects are crucial for accurately describing the band gap. This work studies the importance of these two effects using fixed-node and fixed-phase diffusion Monte Carlo calculations both in spin-averaged and explicit spin-orbit formalisms. In the latter, the Slater-Jastrow trial function is constructed from two-component spin orbitals using our recent quantum Monte Carlo (QMC) developments and thoroughly tested effective core potentials. Our results show that the gap in the ideal crystal is already accurately described by the spin-averaged case, with the dominant role being played by the magnetic ground state with significant exchange and electron correlation effects. We find qualitative agreement between hybrid DFT, $\text{DFT}+U$, and QMC. In addition, QMC results agree very well with available experiments, and we identify the values of exact Fock exchange mixing that provide comparable gaps. Explicit spin-orbit QMC calculations reveal that the effect of spin-orbit coupling on the gap is minor, of the order of 0.2 eV, which corresponds to the strength of the spin orbit of the Ru atom.

A new generation of effective core potentials from correlated and spin-orbit calculations: Selected heavy elements.

We introduce new correlation consistent effective core potentials (ccECPs) for the elements I, Te, Bi, Ag, Au, Pd, Ir, Mo, and W with 4d, 5d, 6s, and 6p valence spaces. These ccECPs are given as a sum of spin-orbit averaged relativistic effective potential (AREP) and effective spin-orbit (SO) terms. The construction involves several steps with increasing refinements from more simple to fully correlated methods. The optimizations are carried out with objective functions that include weighted many-body atomic spectra, norm-conservation criteria, and SO splittings. Transferability tests involve molecular binding curves of corresponding hydride and oxide dimers. The constructed ccECPs are systematically better and in a few cases on par with previous effective core potential (ECP) tables on all tested criteria and provide a significant increase in accuracy for valence-only calculations with these elements. Our study confirms the importance of the AREP part in determining the overall quality of the ECP even in the presence of sizable spin-orbit effects. The subsequent quantum Monte Carlo calculations point out the importance of accurate trial wave functions that, in some cases (mid-series transition elements), require treatment well beyond a single-reference.

Study of the Structural, Electronic and Optical Properties of 1T-ZrX<sub>2</sub> Materials (X=S, Se, Te)

The Electronic and optical properties of zirconium dichalcogenides (ZrS2,ZrSe2, andZrTe2),have been explored via ab-initio methods based on the density functionaltheory (DFT) within the frame of generalized gradient approximation (GGA) and a couplingtechnique between the plane wave (PW) and the pseudo-potential (PP) approaches. Theobtained results showed that ZrS2 and ZrSe2 are semiconducting materials with energy gapsof 1.15 eV and 0.3 eV respectively from the valence band maximum located at G point andthe conduction band minimum located at L point, while ZrTe2 showed a metallic characterwith a density of states at the Fermi level of about 0.8 states/eV. Based on a Kramers–Kroniganalysis of the reflectivity, we have obtained the spectral dependence of the real andimaginary parts of the complex dielectric function (ε1 and ε2, respectively) and the refractiveindex (n). The collected data were used for the calculation of absorption coefficient,reflectivity index, conductivity, and electron energy loss function of ZrS2, ZrSe2, and ZrTe2 forradiation up to 20 eV. All three chalcogenides were found to be good absorbers of ultravioletradiation. The reflectivity of ZrS2 is low in the visible and near-ultraviolet region butincreases sharply for higher photon energies and approaches 96% at ~18.5 eV. The R(ω) spectrum of ZrTe2, on the other hand, is non-selective and remains above 50% over a widerange of energies from infrared to ultraviolet which suggeststhe potential application of thismaterial as an effective solar reflector. On the other hand, the refractive indices of ZrS2, ZrSe2,and ZrTe2 in the visible range are high. The optical spectra show moderate anisotropy concerning the electric field polarization of the incident light.

Self-consistent calculations of charge self-trapping energies: A comparative study of polaron formation and migration in PbTiO3

This study presents a systematic assessment of the behavior of self-trapped electrons in ${\mathrm{PbTiO}}_{3}$, which is a prototypical ferroelectric material with a wide range of technological applications. Since modeling of polarons depends sensitively on the applied method, the goal of this work is to identify the parameters used in density functional theory (DFT), which allow to predict the properties of polarons with high accuracy. The $\mathrm{DFT}+U$ method is employed to benchmark how the choice of $k$-mesh grids, lattice parameters, and pseudopotential (PP) affects the polaron trapping energy. Then, the appropriate parameters were used to study polaron trapping energy and its optical transition using the HSE06 hybrid functional. It is shown that the magnitude of the trapping energy is highly sensitive to the choice of the PP and the applied lattice parameters. A comparison of polaron trapping energies using the two functionals indicates proximity of the $\mathrm{DFT}+U$ result to the HSE06 result. Finally, configuration coordinate diagrams for the polaron-associated absorption and luminescence peaks in ${\mathrm{PbTiO}}_{3}$ are presented and compared to experiments.