Numerical Atomic Orbitals Research Articles

Crystal structure and hydroxyl group vibrational frequencies of phyllosilicates by DFT methods

A DFT study has been made for the 2 × 2 × 1 supercell of the crystal lattice of low-charge dioctahedral 2:1 phyllosilicates. Norm-conserving pseudopotentials of Al, Si, O, H, Na as well as the basis sets have been optimised. The generalized gradient approximation (GGA) was used with numerical atomic orbitals of the improved basis sets. Crystallographic and spectroscopical properties of some known samples with high charge have been calculated, being consistent with previous computational and experimental results. These results are useful to validate the pseudopotentials and basis set optimised to be applied to study the low-charge samples. Different low-charge dioctahedral 2:1 phyllosilicates have been calculated, revealing good agreement with experimental crystallographic properties.

Implementation of a DFT-Based Method for the Calculation of the Zeeman g-Tensor in Periodic Systems with the Use of Numerical and Slater-Type Atomic Orbitals

The Zeeman g-tensor parameterizes the interaction of an effective electronic spin with the homogeneous external magnetic field in the electron paramagnetic resonance (EPR) experiment. In this article, we describe a Kohn-Sham DFT (KS DFT)-based implementation of the g-tensor for periodic systems. Our implementation can be used, for example, for the first-principles calculation of a g-tensor of paramagnetic defects in solids. Our approach is based on the method of Van Lenthe et al. in which the spin-orbital coupling is taken into account variationally. The method is implemented in the BAND program, a KS DFT implementation for periodic systems. The Bloch states are expanded in the basis of numerical and Slater-type atomic orbitals (NAOs/STOs). Our implementation does not rely on the frozen core approximation tacitly assumed in the pseudopotential schemes. The implementation is validated by calculating the g-tensor for small molecules as well as for paramagnetic defects in solids. In particular, we consider ozonide and hydrogen cyanide anion radicals in a KCl host crystal lattice.

Quasiparticle energy spectra of alkali-metal clusters: All-electron first-principles calculations

A good approximation to the one-electron self-energy operator in the calculation of quasiparticle energy spectra including the first ionization potential (IP) and electron affinity (EA) is to expand it as a simple product of a one-particle Green's function G and a dynamically screened Coulomb interaction W, namely, GW approximation. We developed a spin-polarized version of the all-electron GW approach and applied it to the first-principles calculation of quasiparticle energy spectra of alkali-metal clusters (Na(n) and K(n), n=1-8). Our all-electron mixed basis approach, in which wave functions are expressed as a linear combination of numerical atomic orbitals and plane waves, enables us to compare the absolute values of the singly (or highest) occupied molecular orbital and the lowest unoccupied molecular orbital levels with available experimental IPs and EAs. The agreements with the corresponding experimental values are fairly good. Comparing with the non-spin-polarized results of Na(2n) and K(2n) (n=1-4), we discuss the effect of spin polarization as well as the cluster size dependence of IPs or EAs.

Two-center overlap integrals, three dimensional adaptive integration, and prolate ellipsoidal coordinates

Numerical, adaptive algorithm evaluating the overlap integrals between the Numerical Type Orbitals (NTO) is presented. The described algorithm exploits the properties of the prolate ellipsoidal coordinates, which are the natural choice for two-center overlap integrals. The algorithm is designed for numerical atomic orbitals with the finite support. Since the cusp singularity of the atomic orbitals vanish in the prolate ellipsoidal coordinate system, the adaptive integration algorithm in \({\mathbb{R}^3}\) generates small number of subdivisions. The efficiency and reliability of the algorithm is demonstrated for the overlap integrals evaluated for the selected pairs of Slater Type Orbitals (STO).

Implementation of a Density Functional Theory-Based Method for the Calculation of the Hyperfine A-tensor in Periodic Systems with the Use of Numerical and Slater Type Atomic Orbitals: Application to Paramagnetic Defects

The A-tensor parameterizes the "hyperfine" interaction of an "effective" electronic spin with the magnetic field due to the nuclear spin as monitored in an electron paramagnetic resonance (EPR) experiment. In this account, we describe an implementation for the calculation of the A-tensor in systems with translational invariance based on the Kohn-Sham form of density functional theory (KS DFT). The method is implemented in the periodic program BAND, where the Bloch states are expanded in the basis of numerical and Slater-type atomic orbitals (NAOs/STOs). This basis is well-suited for the accurate representation of the electron density near the nuclei, a prerequisite for the calculation of highly accurate hyperfine parameters. Our implementation does not rely on the frozen core approximation tacitly assumed in the pseudopotential schemes. The implementation is validated by performing calculations on the A-tensor for small atoms and molecules within the supercell approach as well as for paramagnetic defects in solids. In particular, we consider the A-tensor of "normal" and "anomalous" muonium defects in diamond and of the hydrogen cyanide anion radical HCN(-) in a KCl host crystal lattice.

Study on the maximum accuracy of the pseudopotential density functional method with localized atomic orbitals versus plane-wave basis sets

A detailed study on the accuracy attainable with numerical atomic orbitals in the context of pseudopotential first-principles density functional theory is presented. Dimers of first- and second-row elements are analyzed: bond lengths, atomization energies, and Kohn-Sham eigenvalue spectra obtained with localized orbitals and with plane-wave basis sets are compared. For each dimer, the cutoff radius, the shape, and the number of the atomic basis orbitals are varied in order to maximize the accuracy of the calculations. Optimized atomic orbitals are obtained following two routes: (i) maximization of the projection of plane wave results into atomic orbital basis sets and (ii) minimization of the total energy with respect to a set of primitive atomic orbitals as implemented in the OPENMX software package. It is found that by optimizing the numerical basis, chemical accuracy can be obtained even with a small set of orbitals.

Carbon nanotube, graphene, nanowire, and molecule‐based electron and spin transport phenomena using the nonequilibrium Green's function method at the level of first principles theory

Based on density functional theory, we have developed a program code to investigate the electron transport characteristics for a variety of nanometer scaled devices in the presence of an external bias voltage. We employed basis sets comprised of linear combinations of numerical type atomic orbitals, particularly focusing on k-point sampling for the realistic modeling of the bulk electrode. The scheme coupled with the matrix version of the nonequilibrium Green's function method enables calculation of the transmission coefficients at a given energy and voltage in a self-consistent manner as well as the corresponding current-voltage (I-V) characteristics. This scheme has advantages because it is applicable to large systems, easily transportable to different types of quantum chemistry packages, and extendable to time-dependent phenomena or inelastic scatterings. It has been applied to diverse types of practical electronic devices such as carbon nanotubes, graphene nanoribbons, metallic nanowires, and molecular electronic devices. The quantum conductance phenomena for systems involving quantum point contacts and I-V curves for a single molecule in contact with metal electrodes using the k-point sampling method are described.

The formulation and implementation of analytic energy gradients for periodic density functional calculations with STO/NAO Bloch basis set§

Analytic energy gradients with respect to atomic coordinates for systems with translational invariance are formulated within the framework of Kohn–Sham Density Functional Theory. The energy gradients are implemented in the BAND program for periodic DFT calculations which directly employs a Bloch basis set made up of Slater-type (STOs) and numeric atomic orbitals (NAOs). The details of our implementation are described including the use of symmetry in the reciprocal and direct spaces, as well as the application of the frozen core approximation. §Paper is dedicated to Professor Peter Pulay.

Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates. II

AbstractThe efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is presented. On the basis of the prolate spheroidal coordinates, the overlap and the kinetic integral are reduced to the integral over the rectangular domain. The integration over the rectangular domain is performed by the adaptive integration scheme. The developed algorithm is applied to calculate the integrals for the pairs of hydrogen and gallium eigenfunctions. It is demonstrated that high accuracy can be obtained for small number of integrand evaluations what guarantees the efficiency of the presented algorithm. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Numerical evaluation of overlap integrals between atomic orbitals

The algorithm evaluating the overlap integrals for the numerical atomic orbitals is presented. The described algorithm is general and is based on the adaptive integration over the rectangular domain in cylindrical coordinate system. It is designed to apply for Kohn-Sham eigenproblem, which is solved by Linear Combination of Atomic Orbitals with the finite support. Double application of Wigner D-matrix relation, reduces the problem to specific case, where the overlap integral is transformed from R 3 to R 2 . Assuming the finite support of the numerical atomic orbitals, the problem is reformulated in cylindrical coordinate system and simplified to the integration over the rectangular domain. In order to perform the numerical integration over the rectangular domain, the adaptive scheme is applied, based on the seven and five order quadratures. The exemplary results for selected atomic orbitals are presented.

Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates

AbstractThe efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is presented. The described algorithm exploits the properties of the prolate spheroidal coordinates. The overlap and the kinetic integrals in ℝ3 are reduced to the integrals over the rectangular domain in ℝ2, what substantially reduces the complexity of the problem. We prove that the integrand over the rectangular domain is continuous and does not have any slope singularities. For calculation of the integral over the rectangle any adaptive algorithm can be applied. The exemplary results were obtained by application of the adaptive Gauss quadrature. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Efficient quantum mechanical calculation of solvation free energies based on density functional theory, numerical atomic orbitals and Poisson–Boltzmann equation

We have successfully coupled the Kohn–Sham with Poisson–Boltzmann equations to predict the solvation free energy, where the Kohn–Sham equations were solved by implementing the flexible pseudo atomic orbitals as in S iesta package. It was found that the calculated solvation free energy is in good agreement with experimental results for small neutral molecules, and its standard error is 1.33 kcal/mol, the correlation coefficient is 0.97. Due to its high efficiency and accuracy, the proposed model can be a promising tool for computing solvation free energies in computer aided drug design in future.

Optimized atomic-like orbitals for first-principles tight-binding molecular dynamics

We analyze the optimization of atomic-like minimal basis sets for the hydrocarbons and for materials made up only of C atoms, e.g. C-nanotubes. In our approach the optimized numerical atomic orbitals (NAOs) are obtained as a linear combination of only two primitive NAOs. We find that the optimized basis sets yield an important lowering of the total energy, and bondlengths in very good agreement with the experimental evidence. Also, we find that a good “universal” minimal basis set for the hydrocarbons and C-only materials can be obtained using this simple method. The approach discussed in this paper is a promising tool for the simulation of complex organic materials, beyond the hydrocarbons, using optimized minimal basis sets.

Geometric and electronic properties ofSc2C2@C84

The geometric and electronic properties of metal–carbon encaged fullerenesSc2C2@C84 have been studied using the density functional theory at the Becke exchange gradientcorrection and the Perdew–Wang correlation gradient correction function level with thedouble numerical atomic orbitals basis sets augmented by polarization functions. TheSc2C2 cluster was foundto be stable in C84 cage, while the cage expands slightly. TheSc2C2 cluster can rotate freely in the cage around the Sc–Sc axis whichis coincident with the vertical principal axis of the cage. As theSc2C2 cluster is encaged, the degeneracy of energy splits, and theHOMO–LUMO energy gap becomes smaller than that of the pureC84, which suggeststhat Sc2C2@C84 has higherreactivity than C84. Based on our calculated results, the electronic structure ofSc2C2@C84 might be formally describedas (Sc2C2)+1@(C84)−1 due to the chargetransferring from the Sc2C2 cluster to C84 cage.

Computational design ofSi∕SiO2interfaces: Stress and strain on the atomic scale

In this paper, we present results of a comparative computational study of silicon oxide interfaces with (100), (111), and (110) silicon surfaces. Density functional theory (DFT) in the local density approximation (LDA) and generalized gradient approximation with plane wave basis set and in the LDA approximation with localized numerical atomic orbitals are applied to investigate the relation between the structure and topology of chemical bonds and stress and strain effects at different $\mathrm{Si}\text{\ensuremath{-}}\mathrm{Si}{\mathrm{O}}_{2}$ interfaces, which play a crucial role in electronics materials and devices. The resulting stress energies are discussed in terms of chemical, mechanical, and electric polarization components. According to our observations, chemical and mechanical components in the interface energy are not sufficient for description of silicon suboxide systems including $\mathrm{Si}\text{\ensuremath{-}}\mathrm{Si}{\mathrm{O}}_{2}$ interfaces and the long range electrostatic interactions provide a non-negligible contribution. We uncovered computationally an effect of thermodynamic stabilization of oxygen incorporation in silicon lattice, which may have potential implications for nanoscale electronic device design. The trends in the stress energies derived from the results of the calculations are independent from the DFT approaches applied in this study.

Quantum mechanical calculations of trans-vacant and cis-vacant polymorphism in dioctahedral 2:1 phyllosilicates

Trans-vacant and cis-vacant polymorphs of smectites and illites were distinguished by studying different cation substitutions in octahedral and tetrahedral sheets and in the interlayer. The standard Kohn-Sham self-consistent density functional method was used in the generalized gradient approximation (GGA) with numerical atomic orbitals as the basis set. The calculations reproduce the differences in the lattice parameters between the cis-vacant and trans-vacant configurations as observed from experimental studies of phyllosilicates. This theoretical approach is a useful tool for predicting crystallographic properties that must be calculated for smectites and illites because they cannot be determined experimentally in these clay minerals, especially the cis-vacant and trans-vacant configurations. The effect of cation substitutions in the octahedral and tetrahedral sheets on various structural features is also presented. The calculated effects are consistent with experimental results. The energy differences between the cis-vacant and trans-vacant polymorphs for a given composition are lower than the energy changes produced by the relative cation distributions in the octahedral sheet. Nevertheless, in the most illitic samples the trans-vacant arrangement is more stable than the cis-vacant form, in accord with experimental studies.

Variationally optimized basis orbitals for biological molecules

Numerical atomic basis orbitals are variationally optimized for biological molecules such as proteins, polysaccharides, and deoxyribonucleic acid within a density functional theory. Based on a statistical treatment of results of a fully variational optimization of basis orbitals (full optimized basis orbitals) for 43 biological model molecules, simple sets of preoptimized basis orbitals classified under the local chemical environment (simple preoptimized basis orbitals) are constructed for hydrogen, carbon, nitrogen, oxygen, phosphorous, and sulfur atoms, each of which contains double valence plus polarization basis function. For a wide variety of molecules we show that the simple preoptimized orbitals provide well convergent energy and physical quantities comparable to those calculated by the full optimized orbitals, which demonstrates that the simple preoptimized orbitals possess substantial transferability for biological molecules.

Angular momentum in molecular quantum mechanical integral evaluation

Solid-harmonic derivatives of quantum-mechanical integrals over Gaussian transforms of scalar, or radial, atomic basis functions create angular momentum about each center. Generalized Gaunt coefficients limit the amount of cross differentiation for multi-center integrals to ensure that cross differentiation does not affect the total angular momentum. The generalized Gaunt coefficients satisfy a number of other selection rules, which are exploited in a new computer code for computing forces in analytic density-functional theory based on robust and variational fitting of the Kohn–Sham potential. Two-center exponents are defined for four or more solid-harmonic differentiations of matrix elements. Those differentiations can either build up angular momentum about the centers or give forces on molecular potential-energy surfaces, thus generalized Gaunt coefficients of order greater than the number of centers are considered. These 4- j generalized Gaunt coefficients and two-center exponents are used to compute the first derivatives of all integrals involving all the Gaussian exponents on a triplet of centers at once. First all angular factors are contracted with the corresponding part of the linear-combination-of-atomic-orbitals density matrix. This intermediate quantity is then reused for the nuclear attraction integral and the integrals corresponding to each basis function in the analytic fit of the Kohn–Sham potential in the muffin-tin-like, but analytic, Slater–Roothaan method that allows molecules to dissociate into atoms having any desired energy, including the experimental electronic energy. The energy is stationary in all respects and all forces precisely agree with a previous code in tests on small molecules. During geometry optimization of an icosahedral C 720 fullerene computing these angular factors and transforming them via the 4- j generalized Gaunt coefficient takes more than sixty percent of the total computer time. These same angular factors could be used in identical fashion with Gaussian transforms of Slater-type and numerical radial atomic orbitals.

Hydrogen bonding and vibrational properties of hydroxy groups in the crystal lattice of dioctahedral clay minerals by means of first principles calculations

The hydroxy groups of the crystal lattice of dioctahedral 2:1 phyllosilicates were investigated by means of quantum-mechanical calculation. The standard Kohn-Sham self-consistent density functional theory (DFT) method was applied using the generalized gradient approximation (GGA) with numerical atomic orbitals and double-zeta polarized functions as basis set. Isomorphous cation substitution of different cations in the octahedral and tetrahedral sheet was included along with several interlayer cations reproducing experimental crystal lattice parameters. The effect of these substitutions and the interlayer charge on the hydroxyl group properties was also studied. These structures represent different cation pairs among Al3+, Fe3+ and Mg2+ in the octahedral sheet of clays joined to OH groups. The geometrical disposition of the OH bond in the crystal lattice and the hydrogen bonds and other electrostatic interactions of this group were analyzed. The frequencies of different vibrational modes of the OH group [ν(OH), δ(OH) and γ(OH)] were calculated and compared with experimental data, finding a good agreement. These frequencies depend significantly on the nature of cations which are joined with, and the electrostatic interactions with, the interlayer cations. Besides, hydrogen-bonding interactions with tetrahedral oxygens are important for the vibrational properties of the OH groups; however, also the electrostatic interactions of these OH groups with the rest of tetrahedral oxygens within the tetrahedral cavity should be taken into account. The cation substitution effect on the vibration modes of the OH groups was analyzed reproducing the experimental behaviour.

Pyrophyllite dehydroxylation process by First Principles calculations

The crystal structure of triclinic pyrophyllite and its dehydroxylate derivative was studied with quantum mechanical calculations. The standard Kohn-Sham self-consistent density functional theory (DFT) was used through a linear-scaling DFT method with periodical boundary conditions in the generalized gradient approximation (GGA) with numerical atomic orbitals as the basis set. The calculations reproduce the lattice parameters found experimentally in pyrophyllite and its dehydroxylate derivative. The geometrical disposition of the OH bond in the crystal lattice and the hydrogen bonds and other electrostatic interactions of this group were analyzed. The frequencies of different vibration modes were calculated and compared with experimental data; the results show a good agreement. The dehydroxylation process, including different intermediates of this reaction, was investigated theoretically. The energetic differences are according to the thermodynamics of the experimental process. The semidehydroxylate derivative is identified, for the first time, as an important intermediate in this process, clarifying previous questions concerning the mechanism reported from the experimental data.