Orbital Basis Sets Research Articles

Проектирование однодетерминантных решений спин-поляризованных уравнений самосогласованного поля в базисе парных орбиталей

Представлена новая схема получения чистого спинового состояния для однодетерминантной волновой функции, построенной на орбиталях Хартри—Фока или Кона—Шэма. В основе лежит разложение неограниченного детерминанта по ограниченным детерминантам, построенным в базисе парных орбиталей. Проектирование позволяет выделить компоненты спиновой плотности, соответствующие чистым спиновым состояниям, и оценить вес спиновых контаминантов в спиновой плотности. Эффективность нового подхода продемонстрирована на примере реакции окисления метана. Показано, что самосогласованные решения уравнений Хартри—Фока или Кона—Шэма с нарушенной спиновой симметрией (broken spin symmetry) — это не артефакт однодетерминантного приближения, уравнения отражают реальную спиновую поляризацию, приводящую к появлению отрицательной спиновой плотности в некоторых частях молекулярной системы.

Quantum chemical calculations for elucidating chiral resolution mechanism of chiral covalent organic frameworks 6 chromatographic stationary phase

With the aim of exploring the chiral resolution mechanism of the chiral covalent organic frameworks 6 (CCOF6) chromatographic stationary phase, the ORCA program was used to optimize the structures of CCOF6 and four pairs of enantiomers. Then the molecular docking of CCOF6 with each enantiomer was performed by AutoDock program to obtain the initial interaction configurations of CCOF6 with four pairs of enantiomers. Energy calculations of the initial configurations were performed by ORCA program (B3LYP functional with DFT-D3 correction, def2-TZVP orbital basis set, def2/J auxiliary basis set, and RIJCOSX used to accelerate the calculation) to determine the interaction configurations of CCOF6 with four pairs of enantiomers and to obtain the corresponding binding free energy and binding free energy difference. Wave function analyses of ORCA calculation results were performed by Multiwfn program, and the weak interactions between CCOF6 and the four pairs of enantiomers were visualized by Visual Molecular Dynamics program. The results showed the following:① for calculating the binding free energies of CCOF6 and the four pairs of enantiomers, the ORCA method with the solvation effect was more accurate than the AutoDock method as well as the ORCA method without the solvation effect; ② the greater the absolute value of the binding free energy difference between the CCOF6 stationary phase and enantiomers, the greater was the selectivity factor of the enantiomers but not the resolution of the enantiomers; ③ the hydroxyl group of S-1-phenyl-1-propanol interacted with the ether bond of CCOF6, but the hydroxyl groups of the other enantiomers all interacted with the carbonyl groups of CCOF6, and the binding force between S-1-phenyl-1-propanol and CCOF6 was the weakest; ④ from the peak time of the enantiomer and its binding free energy with CCOF6, it was confirmed that the elution ability of n-hexane/isopropanol for 1-phenyl-1-propanol was the weakest, followed by the elution ability for 1-phenyl-2-propanol; ⑤ the peak time of S-1-phenyl-1-propanol was longer than that of R-1-phenyl-1-propanol, while for the other enantiomers, the peak time of the R-enantiomers was longer than that of the S-enantiomers.

Potential-energy curve for the a3Σu+ state of a lithium dimer with Slater-type orbitals

We report state-of-the-art ab initio calculations of the potential energy curve for the $a^3\Sigma_u^+$ state of the lithium dimer conducted to achieve spectroscopic accuracy ($<$1cm$^{-1}$) without any prior adjustment to fit the corresponding experimental data. The nonrelativistic clamped-nuclei component of the interaction energy is calculated with a composite method involving six-electron coupled cluster and full configuration interaction theories combined with basis sets of Slater-type orbitals ranging in quality from double- to sextuple-zeta. To go beyond the nonrelativistic Born-Oppenheimer picture we include both the leading-order relativistic and adiabatic corrections, and find both of these effects to be non-negligible within the present accuracy standards. The potential energy curve developed by us allowed to calculate molecular parameters ($D_e$, $D_0$, $\omega_e$ etc.) for this system, as well as the corresponding vibrational energy levels, with an error of only a few tenths of a wavenumber ($0.2-0.4\,$cm$^{-1}$). We also report an ab initio value for the scattering length of two $^2S$ lithium atoms which determines the stability of the related Bose-Einstein condensate.

Smart local orbitals for efficient calculations within density functional theory and beyond.

Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs that provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time, it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.

An improved seminumerical Coulomb and exchange algorithm for properties and excited states in modern density functional theory.

A seminumerical algorithm capable of performing large-scale (time-dependent) density functional theory (TD-DFT) calculations to extract excitation energies and other ground-state and excited-state properties is outlined. The algorithm uses seminumerical integral techniques for evaluating Coulomb and exchange parts for a set of density matrices as occurring in standard TD-DFT or similar methods for the evaluation of vibrational frequencies. A suitable optimized de-aliasing procedure is introduced. The latter does not depend on further auxiliary quantities and retains the symmetry of a given density matrix. The algorithm is self-contained and applicable to any orbital basis set available without the need for further auxiliary basis sets or optimized de-aliasing grids. Relativistic two-component excited-state TD-DFT calculations are reported for the first time using the developed seminumerical algorithm for standard and local hybrid density functional approximations. Errors are compared with the widely used "resolution of the identity" (RI) approximations for Coulomb (RI-J) and exchange integrals (RI-K). The fully seminumerical algorithm does not exhibit an enlarged error for standard DFT functionals compared to the RI approximation. For the more involved local hybrid functionals and within strong external fields, accuracy is even considerably improved.

Calculation of magnetic properties with density functional approximations including rung 3.5 ingredients.

Density functional theory is widely used for modeling the magnetic properties of molecules, solids, and surfaces. Rung-3.5 ingredients, based on the expectation values of nonlocal one-electron operators, are new promising tools for the construction of exchange-correlation functional approximations. We present the formal extension of rung-3.5 ingredients to the calculation of magnetic properties. We add to the underlying nonlocal operators a dependence on the gauge of the magnetic field, and we derive the working equations for rung-3.5 expectation values in basis sets of gauge-including atomic orbitals. We demonstrate that the gauge corrections are significant. We conclude with an initial study of chemical shifts, optical rotatory dispersion, and Raman optical activity spectra predicted by M11plus, a range-separated hybrid meta functional incorporating nonlocal rung-3.5 correlation. M11plus proves to be reasonably accurate, further motivating the incorporation of nonlocal rung-3.5 ingredients in new density functional approximations.

First-principles study of topologically protected vortices and ferroelectric domain walls in hexagonal YGaO3

Ferroelectric behavior on the meso- and macroscopic scale depends on the formation and dynamics of domains and controlling the domain patterns is imperative to device performance. While density functional theory (DFT) calculations have successfully described the basic properties of ferroelectric domain walls, the necessarily small cell sizes used for the calculations hampers DFT studies of complex domain patterns. Here, we simulate large-scale complex ferroelectric domain patterns in ferroelectric ${\mathrm{YGaO}}_{3}$ using multisite local orbitals as implemented in the DFT code conquest. The multisite local orbital basis set gives similar bulk structural and electronic properties, and atomic domain wall structures and energetics as those obtained with conventional plane-wave DFT. With this basis set model, 3600-atom cells are used to simulate topologically protected vortices. The local atomic structure at the vortex cores is subtly different from the domain walls, with a lower electronic band gap suggesting enhanced local conductance at these cores.

Tsallis q‐exponentials as atomic orbitals in two‐electron systems

AbstractThe use of simple q‐exponential functions, derived from Tsallis entropy distribution, as basis set of atomic orbitals, is explored within the non‐relativistic limit. As compared to Gaussian or to STO (Slater type orbitals) basis set, considering q as variational parameter, q‐exponentials functions lower considerably the energy of two electron systems, always respecting the Ritz variation principle, where E ≥ E0, with E0 being the true energy. The q parameter attains the highest value of 1.209 for Z = 1 (H−) slowly going down toward 1 as Z grows (for Z = 36 q = 1.005225, Kr+34). Interestingly, the correlation energy as determined considering the exact solution by the calculations of Pekeris with the current ones, shows a regular variation as a function of the q parameter. Moreover, the study confirms the link between correlation energy and Shannon information entropy.

INFLUENCE OF PRESSURE ON STRUCTURAL, ELECTRONIC, AND OPTICAL PROPERTIES OF CHOLINE IODIDE

The influence of pressure on structural, electronic, and optical properties of choline iodide is studied within the density functional theory approach using the РВЕ gradient functional, the D3(BJ) dispersion correction, and a basis set of localized orbitals. Elastic constants, parameters of the Birch–Murnaghan equation of state, density of electronic states, and frequencies of normal longwave vibrations are calculated. It is shown that the immediate environment of the iodine atom contains 12 carbon atoms with the shortest O–H⋯I distance equal to 2.486 A. The О–H distance increases slightly together with pressure, and the I–H distance decreases while its linear modulus is an order of magnitude smaller than the bulk modulus under 97 GPa. In contrast to intramolecular vibrations, the pressure shifts of lattice vibrations exceed 10 cm–1/GPa, and their modal Gruneisen parameters are an order of magnitude larger.

A Self-Consistent Crank-Nicolson Method for Solving Time-Dependent Kohn-Sham Equation in a Localized Atomic Orbital Basis Set

A Self-Consistent Crank-Nicolson Method for Solving Time-Dependent Kohn-Sham Equation in a Localized Atomic Orbital Basis Set

Unfolding optical transition weights of impurity materials for first-principles LCAO electronic structure calculations

A method to analyze optical transitions is developed by combining the Kubo-Greenwood formula with the unfolding method to construct an unfolded electronic band structure with optical transition weights, which allows us to investigate how optical transitions are perturbed by imperfections such as impurity, vacancy, and structural distortions. Based on the Kubo-Greenwood formula, we first calculate frequency-dependent optical conductivity based on the first-principles electronic structure calculations using the linear combinations of atomic orbitals. Benefiting from the atomic orbital basis sets, the frequency-dependent optical conductivity can be traced back to their individual components before summations over all of $k$ points and bands. As a result, optical transition weights of the material can be put on the unfolded electronic band structure to show contributions at different $k$ points and bands. This method is especially useful to study the effects of broken symmetry in the optical transitions due to presence of impurities in the materials. As a demonstration, decomposed optical transition weights of a monolayer Si-doped graphene are shown in the electronic band structure.

Simulated infrared and Raman spectroscopy, complex dielectric function and refractive index dataset of monoclinic C2/m stoichiometric clinochlore Mg6Si4O10(OH)8 as obtained from Density Functional Theory.

This article reports a simulated dataset of the vibrational (infrared and Raman) and optical properties (complex dielectric function and refractive index) of clinochlore, an important mineral belonging to the phyllosilicate family [1]. The data here reported were calculated from ab initio Density Functional Theory (DFT) simulations at B3LYP level, including a correction for the dispersive forces (B3LYP-D* approach) and all-electron Gaussian-type orbitals basis sets. This dataset was calculated between 0 cm–1 and 4000 cm–1 and comprises infrared, reflectance and Raman spectra, frequency-dependent complex dielectric function and complex refractive index of clinochlore. The data was validated against available experimental spectroscopic results reported in literature and can be of help in several application fields, for instance fundamental georesource exploration and exploitation, in applied mineralogy, geology, material science, and as a reference to assess the quality of other theoretical approaches.

Extended tight‐binding quantum chemistry methods

AbstractThis review covers a family of atomistic, mostly quantum chemistry (QC) based semiempirical methods for the fast and reasonably accurate description of large molecules in gas and condensed phase. The theory is derived from a density functional (DFT) perturbation expansion of the electron density in fluctuation terms to various orders similar to the original density functional tight binding model. The term “eXtended” in their name (xTB) emphasizes the parameter availability for almost the entire periodic table of elements (Z ≤ 86) and improvements of the underlying theory regarding, for example, the atomic orbital basis set, the level of multipole approximation and the treatment of the important electrostatic and dispersion interactions. A common feature of most members is their consistent parameterization on accurate gas phase theoretical reference data for geometries, vibrational frequencies and noncovalent interactions, which are the primary properties of interest in typical applications to systems composed of up to a few thousand atoms. Further specialized versions were developed for the description of electronic spectra and corresponding response properties. Besides a provided common theoretical background with some important implementation details in the efficient and free xtb program, various benchmarks for structural and thermochemical properties including (transition‐)metal systems are discussed. The review is completed by recent extensions of the model to the force‐field (FF) level as well as its application to solids under periodic boundary conditions. The general applicability together with the excellent cost‐accuracy ratio and the high robustness make the xTB family of methods very attractive for various fields of computer‐aided chemical research.This article is categorized under: Electronic Structure Theory &gt; Ab Initio Electronic Structure Methods Electronic Structure Theory &gt; Semiempirical Electronic Structure Methods Software &gt; Quantum Chemistry

Comparative Analysis of the Interaction Potentials of the Ozone Molecule with Atoms of Noble Gases: O3–Ar and O3–He Complexes

The interaction energy of the ozone molecule with atoms of noble gases (Ar and He) is analyzed. The coupled cluster methods CCSD(T) and CCSD(T)-F12 with orbital basis sets including electrons from diffuse orbitals (aug-cc-pVXZ for X = D, T, Q, 5, … CBS) have been used. The geometrical configurations corresponding to the structures with global minima are established. The full three-dimensional grids of the interaction potentials with more than 4800(5300) points have been fitted for the O3–Ar(He) complexes with root-mean-square values of 0.421(0.567) cm–1. The interaction energy was additionally calculated for the O3–He complex with one internal coordinate r1 of ozone stretched to Δr1 = 0.2 and 0.4a0.

Reaction mechanism for hydrogen production using the Pd4 cluster and formic acid by DFT

A systematic study was conducted on the production of hydrogen from formic acid with a Pd4 cluster using density functional theory (DFT) with the B3LYP and the 6-31G** orbital basis set for the C, H and O atoms, while a LANL2DZ effective core potential was used for palladium atoms. The thermodynamic results obtained show a favorable reaction mechanism for producing hydrogen with energy barriers lower than 30 kcal/mol. Moreover, the nature of the bonds involved in all system were analyzed using the theory of atoms in molecules (AIM) identifying the non-covalent interactions in this type of system.

DFT COMPUTATION OF THE BAND STRUCTURE AND DENSITY OF STATE FOR ZnO HALITE STRUCTURE USING FHI-aims CODE.

This research work is on Density Functional Theory (DFT) within Local Density Approximation as parameterised by Perdew and Wang (pw-lda).The calculation was performed using Fritz Haber Institute Ab-initio Molecular Simulations (FHI-aims) code based on numerical atomic-centered orbital basis sets. The electronic band structure, density of state (DOS) and band gap energy were calculated for ZnO compound. The band structure and Density of States (DOS) diagrams are plotted from the calculated equilibrium lattice parameters. The experimentally lattice constant values were used to calculate the minimum total energy. The calculated electronic band structure results show that ZnO (Halite) is an indirect semiconductor with energy band gap of 0.89 eV. Hence, the HOMO is -0.863382 eV at L_symmetry point and LUMO is 0.0239417 eV at ᴦ- point. The DOS energy level within the compound shows considerable high state of electron occupation and the DOS observed around the Fermi level at zero level indicate that it has conducting properties. In general, FHI-aims code has shown better accuracy and prediction of band structure calculation within reasonable computational methods.

Static Polarizabilities at the Basis Set Limit: A Benchmark of 124 Species.

Benchmarking molecular properties with Gaussian-type orbital (GTO) basis sets can be challenging, because one has to assume that the computed property is at the complete basis set (CBS) limit, without a robust measure of the error. Multiwavelet (MW) bases can be systematically improved with a controllable error, which eliminates the need for such assumptions. In this work, we have used MWs within Kohn–Sham density functional theory to compute static polarizabilities for a set of 92 closed-shell and 32 open-shell species. The results are compared to recent benchmark calculations employing the GTO-type aug-pc4 basis set. We observe discrepancies between GTO and MW results for several species, with open-shell systems showing the largest deviations. Based on linear response calculations, we show that these discrepancies originate from artifacts caused by the field strength and that several polarizabilies from a previous study were contaminated by higher order responses (hyperpolarizabilities). Based on our MW benchmark results, we can affirm that aug-pc4 is able to provide results close to the CBS limit, as long as finite difference effects can be controlled. However, we suggest that a better approach is to use MWs, which are able to yield precise finite difference polarizabilities even with small field strengths.

A library of ab initio Raman spectra for automated identification of 2D materials

Raman spectroscopy is frequently used to identify composition, structure and layer thickness of 2D materials. Here, we describe an efficient first-principles workflow for calculating resonant first-order Raman spectra of solids within third-order perturbation theory employing a localized atomic orbital basis set. The method is used to obtain the Raman spectra of 733 different monolayers selected from the Computational 2D Materials Database (C2DB). We benchmark the computational scheme against available experimental data for 15 known monolayers. Furthermore, we propose an automatic procedure for identifying a material based on an input experimental Raman spectrum and apply it to the cases of MoS2 (H-phase) and WTe2 (T{}^{prime}-phase). The Raman spectra of all materials at different excitation frequencies and polarization configurations are freely available from the C2DB. Our comprehensive and easily accessible library of ab initio Raman spectra should be valuable for both theoreticians and experimentalists in the field of 2D materials.

Unusual and Conventional Dative Bond Formation by s2 Lone Pair Donation from Alkaline Earth Metal Atoms to BH3, AlH3, and GaH3.

Using ab initio electronic structure methods with flexible atomic orbital basis sets, we examined the nature of the bonding arising from donation of an ns2 electron pair on an alkaline earth atom (Mg or Ca) into a vacant n'p orbital on the group 13 atom of BH3, AlH3, or GaH3. We also examined what happens when an excess electron is attached to form corresponding molecular anions. Although the geometries of MgBH3, MgAlH3, MgGaH3, and CaBH3 are found to be much as one would expect for datively bound molecules, CaAlH3 and CaGaH3 were found to have very unusual geometries in that their Al-H or Ga-H bonds are directed toward the Ca atom rather than away, as in the other compounds. Internal electrostatic Coulomb attractions between the partially positively charged Ca center and the partially negatively charged H centers were suggested as a source of these unusual geometries. The other novel finding is that the electron affinities (EAs) of all six M'-MH3 species lie in the 0.7-1.0 eV range, which is suggestive of ionic electronic structures for the neutrals even though the partial charges on the alkaline earth centers are as low as 0.3 atomic units. Partial positive charge on the alkaline earth atoms combined with substantial electron affinities of the BH3, AlH3, and GaH3 groups, but only when distorted from planar geometries, were suggested to be the primary contributors to the large EAs.

The pseudoatomic orbital basis: electronic accuracy and soft-mode distortions in ABO3 perovskites

The perovskite oxides are known to be susceptible to structural distortions over a long wavelength when compared to their parent cubic structures. From an ab initio simulation perspective, this requires accurate calculations including many thousands of atoms; a task well beyond the remit of traditional plane wave-based density functional theory (DFT). We suggest that this void can be filled using the methodology implemented in the large-scale DFT code, CONQUEST, using a local pseudoatomic orbital (PAO) basis. Whilst this basis has been tested before for some structural and energetic properties, none have treated the most fundamental quantity to the theory, the charge density n(r) itself. An accurate description of n(r) is vital to the perovskite oxides due to the crucial role played by short-range restoring forces (characterised by bond covalency) and long range Coulomb forces as suggested by the soft-mode theory of Cochran and Anderson. We find that modestly sized basis sets of PAOs can reproduce the plane-wave charge density to a total integrated error of better than 0.5% and provide Bader partitioned ionic charges, volumes and average charge densities to similar degree of accuracy. Further, the multi-mode antiferroelectric distortion of PbZrO3 and its associated energetics are reproduced by better than 99% when compared to plane-waves. This work suggests that electronic structure calculations using efficient and compact basis sets of pseudoatomic orbitals can achieve the same accuracy as high cutoff energy plane-wave calculations. When paired with the CONQUEST code, calculations with high electronic and structural accuracy can now be performed on many thousands of atoms, even on systems as delicate as the perovskite oxides.