All-electron Gaussian Basis Sets Research Articles

Ab initio study of the low-lying states of PS molecule

Quantum chemical calculations on the low-lying electronic states of PS correlating with the lowest four dissociation limits are performed by utilizing the internally contracted multireference configuration interaction method (icMRCI) with all-electron Gaussian basis sets. The potential energy curves (PECs) and spectroscopic constants of low-lying bound states are computed. It is of interest to compare the spectroscopic constants of low-lying bound states for the PS molecule with experimental and theoretical results. The detailed information on the properties of the emission 22Π1/2-X12Π1/2, 22Π3/2-X22Π3/2, 12Σ−1/2-X12Π3/2 and 12Σ−1/2-X12Π1/2 bands of PS system, including the transition dipole moments (TDMs), permanent dipole moments (PDMs), Franck-Condon factors (FCFs) and radiative lifetimes, has been identified. We first calculated the f value and radiative lifetime of this radical. Whether the C state is 12Σ− or 12Δ is discussed. According to the calculation results, it is confirmed that the experimental C state is redistributed to 12Δ. Our study should be valuable for further experimental works understanding the spectroscopy and dynamics of the electronic excited states for PS.

Quantum mechanical simulation of various phases of KVF3 perovskite

The relative stability ΔE of the cubic Pm m (C), of the two tetragonal P bm (T1) and I cm (T2), and of the orthorhombic Pbnm (O) phases of KVF3 has been computed both for the ferromagnetic (FM) and antiferromagnetic (AFM) solutions, by using the B3LYP full range hybrid functional and the Hartree–Fock (HF) Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code. The stabilization of the T2 phase with respect to the C one (152 μHa for B3LYP, 180 μHa for HF, per 2 formula units) is due to the rotation of the VF6 octahedra with respect to the c axis, by 4.1–4.6 degrees. The O phase is slightly less stable than the T2 phase (by 6 and 20 μHa for B3LYP and HF); it is, however, a stable structure as the dynamical analysis confirms. The mechanism of the stabilization of the AFM solution with respect to the FM one is discussed through the spin density maps, and is related to the key role of the exact exchange term (20% in B3LYP, 100% in HF). The G-AFM phase (the first six neighbors of the reference V ion with spin reversed) is more stable than the FM one by about 500 (HF) and 1800 (B3LYP) μHa per two formula units. A volume reduction is observed in the C to T passage, and in the FM to AFM one, both being of the order of 0.3–0.5 at the B3LYP level. Atomic charges, magnetic moments and bond populations, evaluated according to a Mulliken partition of the charge a spin density functions, complete the analysis. The IR and Raman spectra of the FM and AFM C, T2 and O cells are discussed; the only noticeable difference between the various space groups appears in the modes with wavenumbers lower than 100 cm−1.

The superexchange mechanism in crystalline compounds. The case of KMF3 (M = Mn, Fe, Co, Ni) perovskites

The ferromagnetic and antiferromagnetic wavefunctions of four KMF3 (M = Mn, Fe, Co and Ni) perovskites have been obtained quantum-mechanically with the CRYSTAL code, by using the Hartree–Fock (HF) Hamiltonian and three flavours of DFT (PBE, B3LYP and PBE0) and an all-electron Gaussian type basis set. In the Fe and Co cases, with d6 and d7 occupation, the Jahn–Teller distortion of the cubic cell is as large as 0.12 Å. Various features of the superexchange interaction energies (SIE), namely additivity, dependence on the M–M distance, on the angle, and on the adopted functional, are explored. The contribution to SIE by the Coulomb, exchange and kinetic energy terms is analyzed. It is shown that, when using density functionals, SIE clearly correlates with the amount of exact (Hartree–Fock) exchange in the functional. The effect of SIE on the equilibrium geometry and volume of the unit cell is discussed, and it is shown that the key quantity is the spin polarization of the (closed shell) F ions along the M–F–M path. The effect of this magneticpressure is evaluated quantitatively for the first time. The superexchange coupling constant J, evaluated at the HF level and through the Ising model, underestimates the experimental values by about 60%–70%. The more sophisticated Yamaguchi model (that takes into account the contamination of the FM and AFM spin states) does not reduce the discrepancy. The B3LYP hybrid functional overestimates the experiments. These last are bracketed by HF and PBE0. For PBE, the overestimation is huge. Finally, Mulliken population data, charge and spin density maps and density of states are used to illustrate the electronic structure.

Explaining improved photocatalytic activity of Double-walled TiO2 Nanotube: A hybrid density functional calculation

The single-walled and double-walled TiO2 NTs rolled up with rectangular anatase (101) slab, have been investigated using modified hybrid density functional (m-B3LYP) with all-electron Gaussian basis set. We have considered single-walled and double-walled TiO2 NTs only with chirality of (0, n) and (0, m)@(0, n), respectively. Their equilibrium geometric structure, stability, electronic structure and band gap edge position relative to water splitting redox potential have been calculated. For single-walled and double-walled TiO2 NTs, the diameters and Ti-O bond lengths remain unchanged compared to TiO2 slab. To analyze the stability of TiO2 NTs, we have calculated the strain energies and formation energies which decrease with the increased diameters, and simulated the binding energies for double-walled ones to describe two walls interaction. when increasing the NTs diameters, the band gap widths of single-walled TiO2 NTs decrease with the valence band and conduction band moving downward. The double-walled TiO2 NTs exhibit II-type band structure characteristics, and their band gap widths are considerable smaller than that of single-walled ones, with the band gap edge straddling the water splitting redox potential. Based on these important findings, we can explain the mechanism of improved photocatalytic activity of double-walled TiO2 NTs as compared to the single-walled ones.

First principles calculations of the vibrational properties of single and dimer F-type centers in corundum crystals.

The present paper investigates the F-type centers in α-Al2O3 through their electronic and vibrational properties from first principle calculations using a periodic supercell approach, a hybrid functional, and all-electron Gaussian basis sets as implemented in the CRYSTAL17 code. Single F-type and dimer F2-type centers related to oxygen vacancies in various charge states were considered. The defect-induced vibrational modes were identified and found to appear mainly in the low (up to 300 cm-1) and high (above 700 cm-1) frequency regions, depending on the defect charge. The perturbation introduced by the defects to the thermal nuclear motion in the crystal lattice is discussed in terms of atomic anisotropic displacement parameters. The calculated Raman spectra are discussed for the first time for such defects in α-Al2O3, suggesting important information for future experimental and theoretical studies and revealing deeper insight into their behavior.

The configuration interaction study on the low-lying electronic states of AsF

High-level ab initio calculation on the 22 Λ-S electronic states of AsF has been performed with all-electron Gaussian basis sets and internally contracted multireference configuration interaction method plus Davidson correction (icMRCI+Q) and scalar relativistic effect. The spin-orbit coupling (SOC) has been investigated in the calculations by using the Breit-Pauli operator. After considering the SOC, the 22 Λ-S states of AsF split into 51 Ω states related to the lowest five dissociation limits. The spectroscopic constants of the bound states were obtained, which are found in better agreement with available experimental and theoretical results. Based on the computed potential energy curves (PECs), permanent dipole moments (PDMs), transition dipole moments (TDMs), Franck-Condon factors (FCFs) and radiative lifetimes have been acquired. This work should enhance our understanding of the electronic structure and spectroscopy information of AsF radical.

Hybrid-functional electronic structure of multilayer graphene

Multilayer graphene with rhombohedral and Bernal stacking are supposed to be metallic, as predicted by density functional theory calculations using semi-local functionals. However recent angular resolved photoemission and transport data have questioned this point of view. In particular, rhombohedral flakes are suggested to be magnetic insulators. Bernal flakes composed of an even number of layers are insulating, while those composed of an odd number of layers are pseudogapped. Here, by systematically benchmarking with plane waves codes, we develop very accurate all-electron Gaussian basis sets for graphene multilayers. We find that, in agreement with our previous calculations, rhombohedral stacked multilayer graphene are gapped for and magnetic. However, the valence band curvature and the details of the electronic structure depend crucially on the basis set. Only substantially extended basis sets are able to correctly reproduce the effective mass of the valence band top at the K point, while the popular POB-TZVP basis set leads to a severe overestimation. In the case of Bernal stacking, we show that exact exchange gaps the flakes composed by four layers and opens pseudogaps for N = 3, 6, 7, 8. However, the gap or pseudogap size and its behaviour as a function of thickness are not compatible with experimental data. Moreover, hybrid functionals lead to a metallic solution for 5 layers and a magnetic ground state for 5, 6 and 8 layers. Magnetism is very weak with practically no effect on the electronic structure and the magnetic moments are mostly concentrated in the central layers. Our hybrid functional calculations on trilayer Bernal graphene multilayers are in excellent agreement with non-magnetic GW calculations. For thicker multilayers, our calculations are a benchmark for manybody theoretical modeling of the low energy electronic structure.

The VN2 negatively charged defect in diamond. A quantum mechanical investigation of the EPR response

The VN2− defect in diamond consists of a vacancy surrounded by two substitutional nitrogen atoms, which lower the local symmetry from Td to C2v. Calculations of the doublet ground state geometry, electronic structure, EPR parameters, and IR spectra of this defect are reported along with a preliminary investigation of the observed optical transition. For the most part our results were obtained using a uniform charge compensated supercell approach together with the B3LYP functional and all-electron Gaussian basis sets designed for the properties studied. In particular, the computed hyperfine and quadrupolar EPR parameters for the carbon and nitrogen atoms adjacent to the vacancy agree very well with the experiments (Fermi contact values are 245 MHz vs 241 for 13C, and 4.1 vs 4.0 for 15N). The accompanying spin distribution may be described as a damped spherical spin wave with little spin density on the nitrogen atoms. IR spectra show some interesting features in the range of approximately 360–1310 cm−1, which are absent in the pristine diamond. Functionals without exact exchange, such as PBE, better reproduce the observed zero phonon line.

Segmented all-electron basis sets of triple zeta quality for the lanthanides: application to structure calculations of lanthanide monoxides.

Nonrelativistic and relativistic (Douglas-Kroll-Hess, DKH) segmented all-electron Gaussian basis sets of valence triple zeta quality plus polarization functions (TZP) for the lanthanides were developed. As some atomic and molecular properties depend on a good description of the electrons far from the nuclei, these basis sets are augmented with diffuse functions, giving rise to the augmented TZP (ATZP) and ATZP-DKH basis sets. At the DKH level of theory, the B3LYP hybrid functional in conjunction with the TZP-DKH basis set were used to calculate the atomic charges and valence orbital populations of the lanthanide and oxygen atoms, the bond lengths, and the equilibrium dissociation energies of lanthanide monoxides. The DKH-B3LYP/ATZP-DKH polarizability of Yb and the DKH-M06/TZP-DKH first ionization energies of the lanthanides are also reported. Compared with the values obtained with a larger all-electron basis set, and theoretical and experimental data found in the literature, data obtained by our compact basis sets are verified to be accurate and reliable. Unlike effective core potential valence basis sets, our basis sets can also be employed in molecular property calculations that involve the simultaneous treatment of core and valence electrons. Graphical abstract ᅟ.

Substitutional nitrogen in diamond: A quantum mechanical investigation of the electronic and spectroscopic properties

This paper reports the fully-relaxed lattice and electronic structures, vibrational spectra, and hyperfine coupling constants of the substitutional Ns defect in diamond, derived from B3LYP calculations constructed from all-electron Gaussian basis sets and based on periodic supercells. Mulliken analyses of the charge and spin distributions indicate that the defect comprises a single unpaired electron distributed very largely over both the negatively-charged substituted site and one of the four nearest-neighbour carbon sites, which relaxes away from the impurity. This leads to a local C3v symmetry, with the nitrogen ‘lone pair’ lying along the C3 axis and pointed towards the ‘dangling’ bond of the shifted carbon neighbour. The calculated band gap is 5.85 eV, within which a singly-occupied, majority spin donor band is found ∼2.9 eV above the valence band, and an unoccupied, minority spin acceptor band ∼0.9 eV below the conduction band. Atom-projected densities of states of the donor and acceptor levels show that, contrary to a widespread description, ∼30% only of the donor band derives from nitrogen states per se, with the majority weight corresponding to states associated with the shifted carbon atom. The defect formation energy is estimated to be ∼3.6 eV. The calculated IR spectrum of the impurity centre shows several features between 800 and 1400 cm−1, all of which are absent in the perfect crystal, for symmetry reasons. These show substantial agreement with recent experimental observations. The calculated hyperfine constants related to the coupling of the unpaired electron spin to the N and C nuclei, for which the Fermi contact terms vary from over 200 MHz to less than 3 MHz, are generally in good agreement with the largest experimental values, both in terms of absolute magnitudes and site assignments. The agreement is less good for the smallest two values, for which the experimental assignments are less certain. The results lend support to previous suggestions that some of the weaker lines in the observed spectra, notably those below ∼7 MHz, which are difficult to assign unambiguously, might result from the overlap of lines from different sites.

Looking for $$sp^2$$ s p 2 carbon atoms in diamond: a quantum mechanical study of interacting vacancies

This paper reports the calculated relaxed lattice configurations and corresponding electronic and magnetic structures, and Raman frequencies of two divacancies in diamond, $$V_2$$ and VC=CV, in which the vacancies are first and third neighbours, respectively. The calculations are formulated within a supercell approach to local defects in crystalline solids, here 64- and 128-atom unit cells and based largely on the B3LYP one-electron approximation constructed from an all-electron Gaussian basis set. Three important findings are first, that, of the four possible spin states, $$S_z=$$ 0, 1, 2, 3, the singlet is predicted to be lowest in energy for both divacancies; second, that the singlet state of $$V_2$$ is $$\sim$$ 1.7 eV lower in energy than that in VC=CV; and third, that the Raman peak at 1628 cm $$^{-1}$$ in defective diamond can be ascribed to the presence of a C=C double bond, as in the singlet state of VC=CV.

Porous silicene and silicon graphenylene-like surfaces: a DFT study

Nanoporous single-layers surfaces derived from silicene, named porous silicene (PS) and silicenylene (SC) have been studied via periodic density functional theory with a modified B3LYP functional combined with an all-electron Gaussian basis set. The structural, elastic, electronic and vibrational properties of these nanoporous surfaces were simulated and analyzed. The results show that both PS and SC structures had a non-null band gap and a buckled structure such as pristine silicene, besides that they are more susceptible to longitudinal and transversal deformation than silicene. The large and well-defined porous diameter of PS and SC can bring new applications, such as gas separation, filtering and as anode material for lithium-ion batteries. These results are a challenge for the experimentalists to synthetize these new nanomaterials, comparing their properties with those described in this work.

Theoretical study of porous surfaces derived from graphene and boron nitride

Porous graphene (PG), graphenylene (GP), inorganic graphenylene (IGP-BN), and porous boron nitride (PBN) single-layer have been studied via periodic density functional theory with a modified B3LYP functional and an all-electron Gaussian basis set. The structural, elastic, electronic, vibrational, and topological properties of the surfaces were investigated. The analysis showed that all porous structures had a nonzero band gap, and only PG exhibited a non-planar shape. All porous structures seem to be more susceptible to longitudinal deformation than their pristine counterparts, and GP exhibits a higher strength than graphene in the transversal direction. In addition, the electron densities of GP and IGP-BN are localized closer to the atoms, in contrast with PG and PBN, whose charge density is shifted towards the pore center; this property could find application in various fields, such as gas adsorption.

Elastic properties of rare earth pyrochlores R2Ti2O7 (R = Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu): Ab initio calculations

The experimental elastic constants of R2Ti2O7 (R = Gd–Lu), in particular for R = Tb, Dy, Ho published in scientific literature up to now are slightly different, so this makes an ab initio investigation of the current elastic constants for the whole rare-earth row R2Ti2O7 (R = Gd-Lu). The aim of this paper is to give the ab initio calculations of the structural and elastic properties for a whole row of rare-earth titanate pyrochlores in terms of the MO LCAO approximation, using hybrid DFT Hamiltonian PBE0, with periodic code CRYSTAL14. First, the geometry optimization was performed using the analytical energy gradients, with respect to atomic coordinates and unit cell parameters. All-electron Gaussian basis sets were adopted for Titanium and Oxygen and for Rare-Earth atoms internal shells up to 4f are replaced by the pseudopotentials. The results obtained are discussed and the agreement between the calculated values and experimental data are quite satisfactory.

Benchmarking the GW Approximation and Bethe-Salpeter Equation for Groups IB and IIB Atoms and Monoxides.

Energies from the GW approximation and the Bethe-Salpeter equation (BSE) are benchmarked against the excitation energies of transition-metal (Cu, Zn, Ag, and Cd) single atoms and monoxide anions. We demonstrate that best estimates of GW quasiparticle energies at the complete basis set limit should be obtained via extrapolation or closure relations, while numerically converged GW-BSE eigenvalues can be obtained on a finite basis set. Calculations using real-space wave functions and pseudopotentials are shown to give best-estimate GW energies that agree (up to the extrapolation error) with calculations using all-electron Gaussian basis sets. We benchmark the effects of a vertex approximation (ΓLDA) and the mean-field starting point in GW and the BSE, performing computations using a real-space, transition-space basis and scalar-relativistic pseudopotentials. While no variant of GW improves on perturbative G0W0 at predicting ionization energies, G0W0ΓLDA-BSE computations give excellent agreement with experimental absorption spectra as long as off-diagonal self-energy terms are included. We also present G0W0 quasiparticle energies for the CuO-, ZnO-, AgO-, and CdO- anions, in comparison to available anion photoelectron spectra.

Segmented all-electron Gaussian basis sets of double and triple zeta qualities for Fr, Ra, and Ac

Segmented all-electron basis sets of valence double and triple zeta qualities plus polarization functions for the elements Fr, Ra, and Ac are generated using non-relativistic and Douglas-Kroll-Hess (DKH) Hamiltonians. The sets are augmented with diffuse functions with the purpose to describe appropriately the electrons far from the nuclei. At the DKH-B3LYP level, first atomic ionization energies and bond lengths, dissociation energies, and polarizabilities of a sample of diatomics are calculated. Comparison with theoretical and experimental data available in the literature is carried out. It is verified that despite the small sizes of the basis sets, they are yet reliable.

The A-center defect in diamond: quantum mechanical characterization through the infrared spectrum

The A-center in diamond, which consists of two nitrogen atoms substituting two neighboring carbon atoms, has been investigated at the quantum mechanical level using an all-electron Gaussian type basis set, hybrid functionals and the periodic supercell approach. In order to simulate different defect concentrations, four supercells have been considered containing 32, 64, 128 and 216 atoms, respectively. The ground state is a closed shell system where the two neighboring nitrogen atoms are separated, as a consequence of the strong repulsive interaction between the lone pairs, by 2.22 Å. The calculated band gap of a perfect diamond is 5.75 eV, which is in very good agreement with the experimental value of 5.80 eV (at 0 °K); the vertical electronic transition energy from the defective band to the conduction band is 4.75 and 4.46 eV for the cells containing 128 and 216 atoms, respectively. The presence of the A-center does not affect the Raman spectrum of diamond. Several intense peaks appear on the contrary in the IR spectrum, which permit (or should permit) the identification of this defect. The four peaks proposed by Sutherland et al. (Nature, 1954, 174, 901-904) and widely accepted as fingerprints of the A-center (at 480, 1093, 1203, 1282 cm-1), and the most important features of the spectrum published by Davies 22 years later (J. Phys. C: Solid State Phys., 1976, 9, 537-542) are very well reproduced by our simulated spectrum with the largest supercell. The modes in which the nitrogen atoms are more involved are identified by the frequency shift due to the 14N → 15N isotopic substitution; the two modes corresponding to the experimental ones at 480 and 1282 cm-1 show the largest isotopic shift. The graphical animation of the modes (available at ) not only confirms this attribution, but permits also the investigation of the nature of the full set of modes.

All-electron Gaussian basis sets of double zeta quality for the actinides.

For the actinides, two segmented all-electron basis sets of valence double zeta quality plus polarization functions (DZP) are developed. One of them must be used along with the non-relativistic Hamiltonian, whereas the other with the Douglas-Kroll-Hess (DKH) one. Adding diffuse functions of s, p, d, f, and g symmetries to the non-relativistic and relativistic sets, augmented basis sets are developed. These functions are essential to describe correctly electrons far away from the nuclei. For some compounds, geometric parameters, atomic charges and valence orbital populations of the actinides, and bond dissociation energies are calculated using the Becke 3-parameter (exchange) and the Lee, Yang, and Parr (correlation) functional in conjunction with the DZP-DKH basis set. For Am and No, the static electric mean dipole polarizabilities are also reported. Comparison with benchmark theoretical and experimental values found in the literature is carried out. It is verified that the performances of the relativistic compact size basis sets generated in this work are regular, efficient, and reliable. They will be extremely helpful in molecular property calculations that need explicitly to consider the core electrons.

Predicting Pt-195 NMR chemical shift using new relativistic all-electron basis set.

Predicting NMR properties is a valuable tool to assist the experimentalists in the characterization of molecular structure. For heavy metals, such as Pt-195, only a few computational protocols are available. In the present contribution, all-electron Gaussian basis sets, suitable to calculate the Pt-195 NMR chemical shift, are presented for Pt and all elements commonly found as Pt-ligands. The new basis sets identified as NMR-DKH were partially contracted as a triple-zeta doubly polarized scheme with all coefficients obtained from a Douglas-Kroll-Hess (DKH) second-order scalar relativistic calculation. The Pt-195 chemical shift was predicted through empirical models fitted to reproduce experimental data for a set of 183 Pt(II) complexes which NMR sign ranges from -1000 to -6000 ppm. Furthermore, the models were validated using a new set of 75 Pt(II) complexes, not included in the descriptive set. The models were constructed using non-relativistic Hamiltonian at density functional theory (DFT-PBEPBE) level with NMR-DKH basis set for all atoms. For the best model, the mean absolute deviation (MAD) and the mean relative deviation (MRD) were 150 ppm and 6%, respectively, for the validation set (75 Pt-complexes) and 168 ppm (MAD) and 5% (MRD) for all 258 Pt(II) complexes. These results were comparable with relativistic DFT calculation, 200 ppm (MAD) and 6% (MRD). © 2016 Wiley Periodicals, Inc.

Periodic density functional theory study of structural and electronic properties of single-walled zinc oxide and carbon nanotubes

Periodic density functional theory calculations with the B3LYP hybrid functional and all-electron Gaussian basis set were performed to simulate the structural and electronic properties as well as the strain and formation energies of single-walled ZnO nanotubes (SWZnONTs) and Carbon nanotubes (SWCNTs) with different chiralities as functions of their diameters. For all SWZnONTs, the band gap, strain energy, and formation energy converge to ~4.5eV, 0.0eV/atom, and 0.40eV/atom, respectively. This result suggests that the nanotubes are formed more easily from the surface than from the bulk. For SWCNTs, the strain energy is always positive, while the formation energy is negative for armchair and zigzag nanotubes, therefore suggesting that these types of nanotubes can be preferentially formed from the bulk. The electronic properties of SWCNTs depend on the chirality; all armchair nanotubes are metallic, while zigzag and chiral nanotubes can be metallic or semiconducting, depending on the n and m vectors.