Atomic Orbital Basis Research Articles

Superhalogen Anions Supported by the Systems Comprising Alternately Aligned Boron and Nitrogen Central Atoms.

Using DFT/(B3LYP/wB97XD/B2PLYPD) and OVGF electronic structure methods with flexible atomic orbital basis sets, we examined the series of polynuclear superhalogen anions matching the (BF3(BN) n F4n+1)– formula (for n = 1-10,13,18-20) containing alternately aligned boron and nitrogen central atoms decorated with fluorine ligands. It was found that the equilibrium structures of these anions correspond to fully extended chains (with each B and N central atom surrounded by four substituents arranged in a tetrahedral manner) and thus mimic the globally stable fully extended (all-trans) conformations of higher n-alkanes. The vertical electron detachment energies of the (BF3(BN) n F4n+1)– anions were found to exceed 8 eV in all cases and gradually increase with the increasing number of n. The approximate limiting value of vertical electron binding energy that could be achieved for such polynuclear superhalogen anions was estimated as equal to ca. 10.7 eV.

Bonding character of intermediates in on-surface Ullmann reactions revealed with energy decomposition analysis.

On-surface synthesis has become a thriving topic in surface science. The Ullmann coupling reaction is the most applied synthetic route today, but the nature of the organometallic intermediate is still under discussion. We investigate the bonding nature of prototypical intermediate species (phenyl, naphthyl, anthracenyl, phenanthryl, and triphenylenyl) on the Cu(111) surface with a combination of plane wave and atomic orbital basis set methods using density functional theory calculations with periodic boundary conditions. The surface bonding is shown to be of covalent nature with a polarized shared-electron bond supported by π-back donation effects using energy decomposition analysis for extended systems (pEDA). The bond angle of the intermediates is determined by balancing dispersion attraction and Pauli repulsion between adsorbate and surface. The latter can be significantly reduced by adatoms on the surface. We furthermore investigate how to choose computational parameters for pEDA of organic adsorbates on metal surfaces efficiently and show that bonding interpretation requires consistent choice of the density functional.

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Edge Effect in Electronic and Transport Properties of 1D Fluorinated Graphene Materials.

A systematic examination of the electronic and transport properties of 1D fluorine-saturated zigzag graphene nanoribbons (ZGNRs) is presented in this article. One publication (Withers et al., Nano Lett., 2011, 11, 3912–3916.) reported a controlled synthesis of fluorinated graphene via an electron beam, where the correlation between the conductivity of the resulting materials and the width of the fluorinated area is revealed. In order to understand the detailed transport mechanism, edge-fluorinated ZGNRs with different widths and fluorination degrees are investigated. Periodic density functional theory (DFT) is employed to determine their thermodynamic stabilities and electronic structures. The associated transport models of the selected structures are subsequently constructed. The combination of a non-equilibrium Green’s function (NEGF) and a standard Landauer equation is applied to investigate the global transport properties, such as the total current-bias voltage dependence. By projecting the corresponding lesser Green’s function on the atomic orbital basis and their spatial derivatives, the local current density maps of the selected systems are calculated. Our results suggest that specific fluorination patterns and fluorination degrees have significant impacts on conductivity. The conjugated system is the dominate electron flux migration pathway, and the edge effect of the ZGNRs can be well observed in the local transport properties. In addition, with an asymmetric fluorination pattern, one can trigger spin-dependent transport properties, which shows its great potential for spintronics applications.

Robust Pipek-Mezey Orbital Localization in Periodic Solids.

We describe a robust method for determining Pipek-Mezey (PM) Wannier functions (WF), recently introduced by Jónsson et al. (J. Chem. Theor. Chem. 2017, 13, 460), which provide some formal advantages over the more common Boys (also known as maximally-localized) Wannier functions. The Broyden-Fletcher-Goldfarb-Shanno-based PMWF solver is demonstrated to yield dramatically faster convergence compared to the alternatives (steepest ascent and conjugate gradient) in a variety of one-, two-, and three-dimensional solids (including some with vanishing gaps) and can be used to obtain Wannier functions robustly in supercells with thousands of atoms. Evaluation of the PM functional and its gradient in periodic linear combination of atomic orbital representation used a particularly simple definition of atomic charges obtained by Moore-Penrose pseudoinverse projection onto the minimal atomic orbital basis. An automated "canonicalize phase then randomize" method for generating the initial guess for WFs contributes significantly to the robustness of the solver.

Local perturbations of periodic systems. Chemisorption and point defects by GoGreenGo.

We present a software package GoGreenGo-an overlay aimed to model local perturbations of periodic systems due to either chemisorption or point defects. The electronic structure of an ideal crystal is obtained by worldwide-distributed standard quantum physics/chemistry codes, and then processed by various tools performing projection to atomic orbital basis sets. Starting from this, the perturbation is addressed by GoGreenGo with use of the Green's functions formalism, which allows evaluating its effect on the electronic structure, density matrix, and energy of the system. In the present contribution, the main accent is made on processes of chemical nature, such as chemisorption or doping. We address a general theory and its computational implementation supported by a series of test calculations of the electronic structure perturbations for benchmark model solids: simple, face-centered, and body-centered cubium systems. In addition, more realistic problems of local perturbations in graphene lattice, such as lattice substitution, vacancy, and "on-top" chemisorption, are considered.

Straightforward and Accurate Automatic Auxiliary Basis Set Generation for Molecular Calculations with Atomic Orbital Basis Sets.

Density fitting (DF), also known as the resolution of the identity (RI), is a widely used technique in quantum chemical calculations with various types of atomic basis sets─Gaussian-type orbitals, Slater-type orbitals, as well as numerical atomic orbitals─to speed up density functional, Hartree-Fock (HF), and post-HF calculations. Traditionally, custom auxiliary basis sets are hand-optimized for each orbital basis set; however, some automatic schemes have also been suggested. In this work, we propose a simple yet numerically stable automated scheme for forming auxiliary basis sets with the help of a pivoted Cholesky decomposition, which is applicable to any type of atomic basis function. We exemplify the scheme with proof-of-concept calculations with Gaussian basis sets and show that the proposed approach leads to negligible DF/RI errors in HF and second-order Møller-Plesset (MP2) total energies of the non-multireference part of the W4-17 test set when used with orbital basis sets of at least polarized triple-ζ quality. The results are promising for future applications employing Slater-type orbitals or numerical atomic orbitals, as well as schemes based on the use of local fitting approaches. Global fitting approaches can also be used, in which case the high-angular-momentum functions produced by the present scheme can be truncated to minimize the computational cost.

Considering Density Functional Approaches for Actinide Species: The An66 Molecule Set.

The importance of spin-orbit effects on the predictions of energetic properties of actinide compounds has been considered for 18 different density functionals, comparing the spin-orbit and non-spin-orbit ("standard") forms of density functional theory (DFT). A set of enthalpies of formation for 66 small actinide (Th-Am) compounds-the An66 set, for which experimental data are available-have been investigated. The set includes actinide halides, oxides, and oxohalides in the general form AnOmXn, where n = 0-6, m = 0-3, and X = F, Cl, Br, or I. The impact of basis set choice was investigated, and to help account for the impact of relativity, the Stuttgart general and segmented contracted atomic natural orbital (ANO) basis sets paired with small core relativistic effective core potentials (RECP) as well as all-electron calculations utilizing the third-order Douglas-Kroll-Hess were considered.

Hybrid Atomic Orbital Basis from First Principles: Bottom-Up Mapping of Self-Energy Correction to Large Covalent Systems.

Construction of hybrid atomic orbitals is proposed as the approximate common eigenstates of finite first moment matrices. Their hybridization and orientation can be a priori tuned as per their anticipated neighborhood. Their Wannier function counterparts constructed from the Kohn-Sham (KS) single particle states constitute an orthonormal multiorbital tight binding (TB) basis resembling hybrid atomic orbitals locked to their immediate atomic neighborhood, while spanning the subspace of KS states. The proposed basis thus renders predominantly single TB parameters from first principles for each nearest neighbor bond involving no more than two orbitals irrespective of their orientation and also facilitates an easy route for the transfer of such TB parameters across isostructural systems exclusively through mapping of neighborhoods and projection of orbital charge centers. With hybridized 2s, 2p and 3s, 3p valence electrons, the spatial extent of the self-energy correction (SEC) to TB parameters in the proposed basis is found to be localized mostly within the third nearest neighborhood, thus allowing effective transfer of self-energy-corrected TB parameters from smaller reference systems to much larger target systems, with nominal additional computational cost beyond that required for explicit computation of SEC in the reference systems. The proposed approach promises inexpensive estimation of the quasi-particle structures of large covalent systems with workable accuracy.

Calculation of Berry curvature using non-orthogonal atomic orbitals

We present a derivation of the full formula to calculate the Berry curvature on non-orthogonal numerical atomic orbital (NAO) bases. Because usually, the number of NAOs is larger than that of the Wannier bases, we use a orbital contraction method to reduce the basis sizes, which can greatly improve the calculation efficiency without significantly reducing the calculation accuracy. We benchmark the formula by calculating the Berry curvature of ferroelectric BaTiO3 and bcc Fe, as well as the anomalous Hall conductivity for Fe. The results are in excellent agreement with the finite-difference and previous results in the literature. We find that there are corrections terms to the Kubo formula of the Berry curvature. For the full NAO base, the differences between the two methods are negligibly small, but for the reduced bases sets, the correction terms become larger, which may not be neglected in some cases. The formula developed in this work can readily be applied to the non-orthogonal generalized Wannier functions.

Strategy for constructing compact numerical atomic orbital basis sets by incorporating the gradients of reference wavefunctions

We develop an algorithm to construct high-quality numerical atomic orbital (NAO) basis sets suitable for large-scale, efficient density-functional calculations. The key idea behind this algorithm is that, in addition to fitting the reference wavefunctions themselves generated by plane-wave based calculations of chosen target systems, the first derivatives of the reference wavefunctions are also taken into account as the fitting target. By doing so, the quality of the generated NAO basis sets is significantly improved in the sense that the same level of numerical precision can be achieved with smaller basis set sizes or with reduced cutoff radii of the NAOs.

Research of cation dependences of structural and elastic properties of metal carbonates series by density functional theory calculations

Using the density functional theory methods with the PBE gradient functional, and taking into account the van der Waals interaction in the basis of localized atomic orbitals, using the CRYSTAL 17 program code, calculations of the structure and elastic constants for MgCO3, ZnCO3, CdCO3 CaCO3 in the calcite structure, CdMg(CO3)2, CaMg(CO3)2, CaZn(CO3)2 in the dolomite structure, BaMg(CO3)2 – norsethite, and CaCO3, SrCO3, PbCO3, BaCO3 in the aragonite structure are calculated. It is shown that the lattice constants, interatomic distances linearly depend on the cation radius RM, and the band gap, atomic charges, overlap populations of electron shells, and crystal density depend on cation electronegativity χM. Elastic compression constants and linear elastic moduli along the c axis are also described by RM. For polycrystalline bulk modulus BH, shear modulus GH, and Young's modulus EH, linear dependences with a good correlation coefficient were obtained: BH (GPa) = 175.95−84.89·RM, GH (GPa) = 87.57−46.05·RM, EH (GPa) = 224.36−103.59·RM. Similar dependences are established for the longitudinal and transverse speeds of sound, the Debye temperature and the coefficient of minimum thermal lattice conductivity. These results can be used to predict the elastic and mechanical characteristics of carbonates with the chemical formula MCO3 and solid solutions based on them.

Accurate stress calculations based on numerical atomic orbital bases: Implementation and benchmarks

We present the detailed formalism for stress calculations within the framework of numerical atomic orbital (NAO) bases, as implemented in the first-principles electronic code package ABACUS. The validity and numerical precision of our implementation are benchmarked against reference results obtained using the finite difference method as well as those calculated using plane wave (PW) bases. The equation of state for α-quartz calculated using our NAO-based implementation is in excellent agreement with the experimental data. We further show that the stresses calculated in terms of NAO bases converge much faster with respect to the energy cutoff than those calculated using PW bases. This enables accurate stress calculations at relatively low cost. An analysis is provided to elucidate the origin of this behavior.

Formulation and Implementation of Density Functional Embedding Theory Using Products of Basis Functions.

The representation of embedding potential using products of atomic orbital basis functions has been developed in the context of density functional embedding theory. The formalism allows to treat pseudopotential and all-electron calculations on the same footing and enables simple transfer of the embedding potential in a compact matrix form. In addition, a cost-reduction procedure for the basis set and potential reduction based on population analysis has been proposed. Implemented for the condensed-phase and molecular systems within Gaussian and plane-waves and Gaussian and augmented plane-waves formalisms, the scheme has been tested for proton-transfer reactions in the cluster and the condensed phase and projected density of states of carbon monoxide adsorbed on platinum surface. With the computational scaling of the embedding potential optimization similar to that of hybrid density functional theory with a significantly reduced prefactor, the method allows for large-scale applications to extended systems.

Identification of the Mott Insulating Charge Density Wave State in 1T-TaS_{2}.

We investigate the low-temperature charge density wave (CDW) state of bulk TaS_{2} with a fully self-consistent density-functional theory with the Hubbard U potential, over which the controversy has remained unresolved regarding the out-of-plane metallic band. By examining the innate structure of the Hubbard U potential, we reveal that the conventional use of atomic-orbital basis could seriously misevaluate the electron correlation in the CDW state. By adopting a generalized basis, covering the whole David star, we successfully reproduce the Mott insulating nature with the layer-by-layer antiferromagnetic order. Similar consideration should be applied for description of the electron correlation in molecular solid.

Advances in methods and applications of nonadiabatic quantum dynamics simulation of condensed matters

First-principles molecular dynamics simulations, which can reveal the microscopic mechanisms and the macroscopic properties of molecules and condensed systems, have become a significant driving force in the development of physics. In the past decades, the ground state electronic properties of various materials can be accurately described using the first-principles method based on the Born-Oppenheimer approximation. However, in nonadiabatic processes, such as the ultrafast excited-state dynamics where laser interacts with molecules and condensed matters, the Born-Oppenheimer approximation evolving nuclear wave function on the ground state potential energy plane is no longer valid because of the nonnegligible nonadiabatic couplings between electrons and nuclei. In order to investigate the novel physical phenomena in nonadiabatic processes, many nonadiabatic molecular dynamics methods have been proposed, for instance, full quantum dynamics and mixed quantum-classical dynamics. When the nuclear quantum effects are trivial, the mixed quantum-classical dynamics is effective, which solves the time-dependent electron Schrodinger equation and describes the motion of the nuclei in the form of Newtonian mechanics. Two methods based on the mixed quantum-classical dynamics, the fewest-switches trajectory surface-hopping method (FSSH) and Ehrenfest dynamics, have accepted much attention since they could be easily implemented and combined with real-time time-dependent density functional theory (rt-TDDFT) for high-precision calculations. The combination of quantum and classical dynamics reduces the computational cost and allows the applications for real materials. At low temperatures, the nuclear quantum effects, including quantum tunneling and zero-point vibrations, cannot be ignored. Ring-polymer molecular dynamics (RPMD) based on the imaginary-time path integral is widely used to consider the nuclear quantum effects, which describes the quantum behavior of atomic nuclei by sampling a larger number of quantum configurations and paths. By combining RPMD and mixed quantum-classical nonadiabatic dynamics, one can describe quantum motions of nuclei and the excited electrons in quantum nonadiabatic dynamics simulations. Here, we summarize the recent progress of the rt-TDDFT methods based on numerical atomic orbital basis and plane- wave basis set, as well as highly efficient RP-TDAP method combining rt-TDDFT and RPMD towards a quantum description of electronic-nuclear dynamics. Finally, we show several representative applications employing these methods, including high harmonic generation modulated by two-color light, charge density wave dynamics, photocatalytic water decomposition as well as the quantum evolution of nuclear wave packets. These applications are in good agreement with experimental measurements, which demonstrates the reliability of these methods and their advantages in the corresponding research areas. These developments and applications are in a significant step from ground state methods to full quantum simulation of the coupled motion of electrons and nuclei, providing a new perspective for understanding and predicting the quantum interactions and dynamical behavior of condensed materials in the degree of atomic spatial scales and attosecond time scales.

Electron attachment to representative cations composing ionic liquids.

Using ab initio electronic structure methods with flexible atomic orbital basis sets, we investigated the electronic structure and stability of reduction products of selected representative cations (C+) constituting ionic liquids. We found that an electron attachment to such cations leads to the neutral radicals, whereas a subsequent attachment of another (i.e., excess) electron leads to adiabatically stable anions only in two cases {[P(CH3)4]- and [MeMePyr]-}. The possibility of the formation of various dimers (such as CC+, CC, and CC-) was also considered, and the resulting systems were characterized by predicting their lowest energy structures, ionization potentials, electron affinities, and susceptibilities to the fragmentation process. Among the cations studied, only the [MeMePyr]+ was found to form a typical Rydberg radical (MeMePyr) and double-Rydberg anion ([MeMePyr]-), whereas the remaining cations were predicted to form neutral radicals of a primarily valence (MeMeIm and MePy) or mixed Rydberg-valence [P(CH3)4] character. Our calculations confirmed the stability of all CC+ and CC dimers against fragmentation yielding the corresponding monomers (the binding energies of 12.2-20.5 kcal/mol and 11.3-72.3 kcal/mol were estimated for CC+ and CC dimers, respectively). [(MeMePyr)2]- was identified as the only adiabatically stable CC- dimeric anion having its vertical electron detachment energy of 0.417 eV. We also found that in the [(MeMePyr)2]- anionic state, three outermost electrons are described by Rydberg orbitals, which results in the (σ)2(σ*)1 configuration.

R2SCAN-3c: A "Swiss army knife" composite electronic-structure method.

The recently proposed r2SCAN meta-generalized-gradient approximation (mGGA) of Furness and co-workers is used to construct an efficient composite electronic-structure method termed r2SCAN-3c. To this end, the unaltered r2SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error. The performance of the new method is evaluated for the GMTKN55 database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for non-covalent interactions, organometallic reactions, and lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r2SCAN-3c: It by far surpasses its predecessor B97-3c at only twice the cost and provides one of the best results of all semi-local density-functional theory (DFT)/QZ methods ever tested for the GMTKN55 database at one-tenth of the cost. Specifically, for reaction and conformational energies as well as non-covalent interactions, it outperforms prominent hybrid-DFT/QZ approaches at two to three orders of magnitude lower cost. Perhaps, the most relevant remaining issue of r2SCAN-3c is self-interaction error (SIE), owing to its mGGA nature. However, SIE is slightly reduced compared to other (m)GGAs, as is demonstrated in two examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous composite DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.

All-electron periodic G0W0 implementation with numerical atomic orbital basis functions: Algorithm and benchmarks

We present an all-electron, periodic ${G}_{\text{0}}{W}_{\text{0}}$ implementation within the numerical atomic orbital (NAO) basis framework. A localized variant of the resolution-of-the-identity (RI) approximation is employed to significantly reduce the computational cost of evaluating and storing the two-electron Coulomb repulsion integrals. We demonstrate that the error arising from localized RI approximation can be reduced to an insignificant level by enhancing the set of auxiliary basis functions, used to expand the products of two single-particle NAOs. An efficient algorithm is introduced to deal with the Coulomb singularity in the Brillouin zone sampling that is suitable for the NAO framework. We perform systematic convergence tests and identify a set of computational parameters, which can serve as the default choice for most practical purposes. Benchmark calculations are carried out for a set of prototypical semiconductors and insulators, and compared to independent reference values obtained from an independent ${G}_{\text{0}}{W}_{\text{0}}$ implementation based on linearized augmented plane waves (LAPWs) plus high-energy localized orbitals (HLOs) basis set, as well as experimental results. With a moderate (FHI-aims tier 2) NAO basis set, our ${G}_{\text{0}}{W}_{\text{0}}$ calculations produce band gaps that typically lie in between the standard LAPW and the $\mathrm{LAPW}+\mathrm{HLO}$ results. Complementing tier 2 with highly localized Slater-type orbitals (STOs), we find that the obtained band gaps show an overall convergence towards the $\mathrm{LAPW}+\mathrm{HLO}$ results. The algorithms and techniques developed in this work pave the way for efficient implementations of correlated methods within the NAO framework.

Structural and Electronic Calculations of CdTe Using DFT: Exchange–Correlation Functionals and DFT-1/2 Corrections

Ab initio calculations were performed to investigate the structural and electronic properties of bulk CdTe using various exchange–correlation (XC) functionals available. Among the selected XC functionals include the local density approximation (LDA), generalized gradient approximation (GGA), meta-generalized gradient approximation (MGGA) (using the linear combination of atomic orbitals basis scheme) and Heyd–Scuseria–Ernzerhof-06 (HSE06) (using the plane-wave basis scheme). Further computational studies were performed based on the local density approximation-1/2 (LDA-1/2) and generalized gradient approximation-1/2 (GGA-1/2) self-energy correction schemes to verify their effect on the CdTe band gap in comparison to the other traditional XC functionals. The lattice parameter values obtained using different XC functionals (LDA, GGA and MGGA) were well in agreement with experimental value, with LDA predicting 6.548 A. This is 1.02% greater than the experimental value of 6.482 A. The electronic structure of CdTe was calculated for the fixed 6.482 A lattice parameter of bulk CdTe and resulted in a band gap ranging between 0.68 and 1.56 eV for LDA, GGA, MGGA, and HSE06. The band gap values predicted by the LDA-1/2 and GGA-1/2 corrections were 1.47 eV and 1.50 eV, respectively, and are found to be in good agreement with experimental values. The influence of XC functionals and semi-empirical correction schemes are expected to have important implications on the prediction and understanding of bulk CdTe thin-films found in photovoltaic applications.