Nonlocal Pseudopotentials Research Articles

Effects of nonlocal pseudopotentials on the electrical and thermal transport properties of aluminum: A density functional theory study

Effects of nonlocal pseudopotentials on the electrical and thermal transport properties of aluminum: A density functional theory study

On the excitonic effects of the 1T and 1O[formula omitted] phases of PdS2, PdSe2, and PdSSe monolayers

We report the excitonic effects in the 1T and 1OT phases of PdS2, PdSe2, and PdSSe monolayers. Using fully relativistic norm-conserving non-local PBE pseudopotentials and including the spin–orbit (SOC) coupling, the 1T geometries are indirect band gap semiconductors; conversely, the 1OT structures are semimetallic. The band gaps were corrected using the HSE06 hybrid functional, making all structures semiconductors. Maximally localized Wannier functions were utilized to fit the bands of all six structures. The excitonic band structures were obtained using the Bethe–Salpeter equation (BSE), and the absorption coefficients were estimated at both the BSE and the independent particle approximation (IPA) levels. While the 1OT monolayers are more inclined to absorb light polarized in the y-direction, the 1T structures absorb light equally, independent of the polarization direction. We perceive that the 1T phase is the most promising candidate for photovoltaic devices; in particular, the 1T PdSSe system possesses a maximum power conversion efficiency (PCE) of 29.31% if light trapping techniques are used to enhance absorbance. Amongst the 1OT materials, PdS2 features the highest PCE of 8.38%. Our results constitute the first step to encourage experimental studies towards the fabrication of Pd-based regular and Janus transition metal dichalcogenides photoabsorbers and give hints of how to increase the PCE of such materials.

Implementation of Nuclear Velocity Perturbation and Magnetic Field Perturbation Theory in CP2K and Their Application to Vibrational Circular Dichroism

We present the implementation of nuclear velocity perturbation theory (NVPT), using a pioneering combination of atom-centered (velocity-dependent) Gaussian basis functions and plane waves in the CP2K package. The atomic polar tensors (APTs) and atomic axial tensors (AATs) are evaluated in the velocity representation using efficient density functional perturbation theory. The presence of nonlocal pseudopotentials, the representation of potentials on numerical integration grids, and effects arising from the basis functions being centered on the atoms have been considered in the implementation. The Magnetic Field Perturbation Theory (MFPT) using gauge-including atomic orbitals is implemented in the same code and compared to the NVPT. Our implementation is the first to compare both approaches (MFPT and NVPT) in the same code. The implementation has been verified via sum rules and by investigating the gauge origin dependence of the AATs for a set of small molecules, oxirane, and fluoro-oxirane. We also present vibrational circular dichroism spectra that are related to the APTs and AATs, applying both theories.

Nonlocal pseudopotential energy density functional for orbital-free density functional theory

Orbital-free density functional theory (OF-DFT) is an electronic structure method with a low computational cost that scales linearly with the number of simulated atoms, making it suitable for large-scale material simulations. It is generally considered that OF-DFT strictly requires the use of local pseudopotentials, rather than orbital-dependent nonlocal pseudopotentials, for the calculation of electron-ion interaction energies, as no orbitals are available. This is unfortunate situation since the nonlocal pseudopotentials are known to give much better transferability and calculation accuracy than local ones. We report here the development of a theoretical scheme that allows the direct use of nonlocal pseudopotentials in OF-DFT. In this scheme, a nonlocal pseudopotential energy density functional is derived by the projection of nonlocal pseudopotential onto the non-interacting density matrix (instead of “orbitals”) that can be approximated explicitly as a functional of electron density. Our development defies the belief that nonlocal pseudopotentials are not applicable to OF-DFT, leading to the creation for an alternate theoretical framework of OF-DFT that works superior to the traditional approach.

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

We present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.

Radial and three-dimensional nonlocal pseudopotential calculations in gradient-corrected Kohn–Sham density functional theory based on higher-order finite element methods

Kohn–Sham density functional theory is an ab initio framework for electronic structure calculation that offers a basis for nonphenomenological multiscale approaches. In this work, higher-order finite element methods are applied in the context of this theory, with a particular focus on the use of nonlocal pseudopotentials. Specifically, an accurate class of pseudopotentials which are based on the generalized gradient approximation of the exchange–correlation functional with nonlinear core corrections are targeted. To this end, the suitable weak formulation of the underlying nonlinear eigenvalue problem is derived and additionally cast in a radial form. The weak forms are discretized through traditional Lagrange elements in addition to isogeometric analysis based on B-splines in order to explore alternative means of achieving faster routes to the solution of the resulting generalized eigenvalue problems with O(106–107) degrees of freedom. Numerical investigations on single atoms and larger molecules validate the computational framework where stringent accuracy requirements are met through convergence at optimal rates.

Split representation of adaptively compressed polarizability operator

The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The cost of computing the polarizability operator generally scales as $${\mathcal {O}}(N_{e}^4)$$ where $$N_e$$ is the number of electrons in the system. The recently developed adaptively compressed polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying, Multiscale Model. Simul. 2017] reduces such complexity to $${\mathcal {O}}(N_{e}^3)$$ in the context of phonon calculations with a large basis set for the first time, and demonstrates its effectiveness for model problems. In this paper, we improve the performance of the ACP formulation by splitting the polarizability into a near singular component that is statically compressed, and a smooth component that is adaptively compressed. The new split representation maintains the $${\mathcal {O}}(N_e^3)$$ complexity, and accelerates nearly all components of the ACP formulation, including Chebyshev interpolation of energy levels, iterative solution of Sternheimer equations, and convergence of the Dyson equations. For simulation of real materials, we discuss how to incorporate nonlocal pseudopotentials and finite temperature effects. We demonstrate the effectiveness of our method using one-dimensional model problem in insulating and metallic regimes, as well as its accuracy for real molecules and solids.

Nonlocal pseudopotentials and time-step errors in diffusion Monte Carlo.

We present a version of the T-moves approach for treating nonlocal pseudopotentials in diffusion Monte Carlo, which has much smaller time-step errors than the existing T-moves approaches, while at the same time preserving desirable features such as the upper-bound property for the energy. In addition, we modify the reweighting factor of the projector used in diffusion Monte Carlo to reduce the time-step error. The latter is applicable not only to pseudopotential calculations but also to all-electron calculations.

A new form of pseudopotential for the study of lattice mechanical properties of transition metals

ABSTRACT The study of lattice mechanical properties of transition metals using pseudopotential is burdensome as the presence of d-band in these metals complicates their electronic structure. The use of pseudopotential for the study of physical properties can be justified if it accounts for the effect of d-band. The local form of the pseudopotentials is widely used to study the physical properties of materials due to their computational simplicity, physical transparency, and transferability to other environments. It is a well-established fact that non-local pseudopotentials should be preferred to the local ones. But, non-local pseudopotentials are proven to be at a higher computational cost. Inspired by such requirements, we, in the present communication, propose a pseudopotential comprising of one non-local (energy-dependent) and another local term in q-space. The non-local (energy-dependent) term accounts for s-p interaction, while the other term is used to account for the effect of s-d hybridisation. The Generalized Pseudopotential Theory (GPT) has been used to formulate the pseudopotential. Further, the pseudopotential has been used to study static binding energy, lattice dynamics, lattice mechanical properties and second-order elastic constants in the long-wavelength limit (q→0) for transition metals γ-Fe (fcc), Co and α-Fe (bcc). Computed results are found to be in good agreement with experimental and other theoretical results, which proves that the proposed pseudopotential itself accounts for the effect of d-band without using additional short-ranged Born–Mayer type potential and effective valency.

Analytic calculation and analysis of atomic polar tensors for molecules and materials using the Gaussian and plane waves approach.

The evaluation of atomic polar tensors and Born Effective Charge (BEC) tensors from Density Functional Perturbation Theory (DFPT) has been implemented in the CP2K code package. This implementation is based on a combination of the Gaussian and plane wave approach for the description of basis functions and arising potentials. The presence of non-local pseudo-potentials has been considered, as well as contributions arising from the basis functions being centered on the atoms. Simulations of both periodic and non-periodic systems have been implemented and carried out. Dipole strengths and infrared absorption spectra have been calculated for two isomers of the tripeptide Ser-Pro-Ala using DFPT and are compared to the results of standard vibrational analyses using finite differences. The spectra are then decomposed into five subsets by employing localized molecular orbitals/maximally localized Wannier functions, and the results are discussed. Moreover, group coupling matrices are employed for visualization of results. Furthermore, the BECs and partial charges of the surface atoms of a periodic (101) anatase (TiO2) slab have been investigated in a periodic framework.

Hybridizing pseudo-Hamiltonians and non-local pseudopotentials in diffusion Monte Carlo.

An accurate treatment of effective core potentials (ECPs) requires care in continuum quantum Monte Carlo (QMC) methods. While most QMC studies have settled on the use of familiar non-local (NL) pseudopotentials with additional localization approximations, these approaches have been shown to result in moderate residual errors for some classes of molecular and solid state applications. In this work, we revisit an idea proposed early in the history of QMC ECPs that does not require localization approximations, namely, a differential class of potentials referred to as pseudo-Hamiltonians. We propose to hybridize NL potentials and pseudo-Hamiltonians to reduce residual non-locality of existing potentials. We derive an approach to recast pseudopotentials for 3d elements as hybrid pseudo-Hamiltonians with optimally reduced NL energy. We demonstrate the fidelity of the hybrid potentials by studying atomic ionization potentials of Ti and Fe and the binding properties of TiO and FeO molecules with diffusion Monte Carlo (DMC). We show that localization errors have been reduced relative to potentials with the same NL channels for Sc-Zn by considering the DMC energy change with respect to the choice of approximate localization. While localization error decreases proportionate to the reduced NL energy without a Jastrow, with a Jastrow, the degree of reduction decreases at higher filling of the d-shell. Our results suggest that a subset of existing ECPs may be recast in this hybrid form to reduce the DMC localization error. They also point to the prospect of further reducing this error by generating ECPs within this hybrid form from the start.

Evaluating Hellmann–Feynman forces within non-local pseudopotentials

A new approach for evaluating Hellmann–Feynman forces within a non-local potential is introduced. Particularly, the case of Hellmann–Feynman theorem applied within density functional theory in combination with nonlocal ab-initio pseudopotentials, discretized by the finite-element method, is discussed in detail. The validity of the new approach is verified using test calculations on simple molecules and the convergence properties (w.r.t. the DFT loop) are analyzed. A comparison to other previously published approaches to Hellmann–Feynman forces calculations is shown to document that the new approach mitigates, for l-dependent as well as for separable forms of nonlocal pseudopotentials, the efficiency and/or accuracy problems arising in the methods published so far.

Ab initio calculation of the shift photocurrent by Wannier interpolation

We describe and implement a first-principles algorithm based on maximally-localized Wannier functions for calculating the shift-current response of piezoelectric crystals in the independent-particle approximation. The proposed algorithm presents several advantages over existing ones, including full gauge invariance, low computational cost, and a correct treatment of the optical matrix elements with nonlocal pseudopotentials. Band-truncation errors are avoided by a careful formulation of $k\cdot p$ perturbation theory within the subspace of wannierized bands. The needed ingredients are the matrix elements of the Hamiltonian and of the position operator in the Wannier basis, which are readily available at the end of the wannierization step. If the off-diagonal matrix elements of the position operator are discarded, our expressions reduce to the ones that have been used in recent tight-binding calculations of the shift current. We find that this `diagonal' approximation can introduce sizeable errors, highlighting the importance of carefully embedding the tight-binding model in real space for an accurate description of the charge transfer that gives rise to the shift current.

Contour integral method for obtaining the self-energy matrices of electrodes in electron transport calculations

We propose an efficient computational method for evaluating the self-energy matrices of electrodes to study ballistic electron transport properties in nanoscale systems. To reduce the high computational cost incurred in large systems, a contour integral eigensolver based on the Sakurai-Sugiura method combined with the shifted biconjugate gradient method is developed to solve exponential-type eigenvalue problem for complex wave vectors. A remarkable feature of the proposed algorithm is that the numerical procedure is very similar to that of conventional band structure calculations. We implement the developed method in the framework of the real-space higher-order finite difference scheme with nonlocal pseudopotentials. Numerical tests for a wide variety of materials validate the robustness, accuracy, and efficiency of the proposed method. As an illustration of the method, we present the electron transport property of the free-standing silicene with the line defect originating from the reversed buckled phases.

Quantitative estimation of localization errors of 3d transition metal pseudopotentials in diffusion Monte Carlo.

The necessarily approximate evaluation of non-local pseudopotentials in diffusion Monte Carlo (DMC) introduces localization errors. We estimate these errors for two families of non-local pseudopotentials for the first-row transition metal atoms Sc-Zn using an extrapolation scheme and multideterminant wavefunctions. Sensitivities of the error in the DMC energies to the Jastrow factor are used to estimate the quality of two sets of pseudopotentials with respect to locality error reduction. The locality approximation and T-moves scheme are also compared for accuracy of total energies. After estimating the removal of the locality and T-moves errors, we present the range of fixed-node energies between a single determinant description and a full valence multideterminant complete active space expansion. The results for these pseudopotentials agree with previous findings that the locality approximation is less sensitive to changes in the Jastrow than T-moves yielding more accurate total energies, however not necessarily more accurate energy differences. For both the locality approximation and T-moves, we find decreasing Jastrow sensitivity moving left to right across the series Sc-Zn. The recently generated pseudopotentials of Krogel et al. [Phys. Rev. B 93, 075143 (2016)] reduce the magnitude of the locality error compared with the pseudopotentials of Burkatzki et al. [J. Chem. Phys. 129, 164115 (2008)] by an average estimated 40% using the locality approximation. The estimated locality error is equivalent for both sets of pseudopotentials when T-moves is used. For the Sc-Zn atomic series with these pseudopotentials, and using up to three-body Jastrow factors, our results suggest that the fixed-node error is dominant over the locality error when a single determinant is used.

Auxiliary-field quantum Monte Carlo calculations with multiple-projector pseudopotentials

We have implemented recently developed multiple-projector pseudopotentials into the plane-wave-based auxiliary-field quantum Monte Carlo (pw-AFQMC) method. Multiple-projector pseudopotentials can yield smaller plane-wave cutoffs while maintaining or improving transferability. This reduces the computational cost of pw-AFQMC, increasing its reach to larger and more complicated systems. We discuss the use of nonlocal pseudopotentials in the separable Kleinman-Bylander form, and the implementation in pw-AFQMC of the multiple-projector optimized norm-conserving pseudopotential ONCVPSP of Hamann. The accuracy of the method is first demonstrated by equation-of-state calculations of the ionic insulator NaCl and more strongly correlated metal Cu. The method is then applied to calibrate the accuracy of density-functional theory (DFT) predictions of the phase stability of recently discovered high temperature and pressure superconducting sulfur hydride systems. We find that DFT results are in good agreement with pw-AFQMC, due to the near cancellation of electron-electron correlation effects between different structures.

A spectral scheme for Kohn–Sham density functional theory of clusters

Starting from the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane-wave method – is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn–Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn–Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.

Introducing PROFESS 3.0: An advanced program for orbital-free density functional theory molecular dynamics simulations

Orbital-free density functional theory (OFDFT) is a linear-scaling first-principles quantum mechanics method used to calculate the ground-state energy of a given system. Here we present a new version of PRinceton Orbital-Free Electronic Structure Software (PROFESS) with new features. First, PROFESS 3.0 provides a set of new kinetic energy density functionals (KEDFs) which are designed to model semiconductors or transition metals. Specifically, PROFESS 3.0 includes the Huang–Carter (HC) KEDF [1], a density decomposition method with fixed localized electronic density [2], the Wang–Govind–Carter (WGC) decomposition KEDF [3], and the Enhanced von Weizsacker (EvW)-WGC KEDF [4]. Other major new functions are included, such as molecular dynamics with different statistical mechanical ensembles and spin-polarized density optimizers.

Deriving k·p parameters from full-Brillouin-zone descriptions: A finite-element envelope function model for quantum-confined wurtzite nanostructures

We present a multiband envelope-function model for wurtzite nanostructures based on a rigorous numerical procedure to determine operator ordering and band parameters from nonlocal empirical pseudopotential calculations. The proposed approach, implemented within a finite-element scheme, leads to well-posed, numerically stable envelope equations that accurately reproduce full-Brillouin-zone subband dispersions of quantum systems. Although demonstrated here for III-nitride nonlocal empirical pseudopotentials, the model provides a general theoretical framework applicable to ab initio electronic structures of wurtzite semiconductors.

The pressure dependences of elastic and lattice dynamic properties of AlAs from ab initio calculations

Ab initio calculations, based on norm-conserving nonlocal pseudopotentials and density functional theory (DFT), are performed to investigate the structural, elastic, dielectric, and vibrational properties of aluminum arsenide (AlAs) with a zinc-blende (B3) structure and a nickel arsenide (B81) structure under hydrostatic pressure. Firstly, the path for the phase transition from B3 to B81 is confirmed by analyzing the energies of different structures, which is in good agreement with previous theoretical results. Secondly, we find that the elastic constants, bulk modulus, static dielectric constants, and the optical phonon frequencies vary in a nearly linear manner under hydrostatic pressure. What is more, the softening mode of the transversal acoustic mode at the X point supports the phase transition in AlAs.