Gaussian-type Basis Sets Research Articles

Sapporo-(DKH3)-nZP (n = D, T, Q) sets for the sixth period s-, d-, and p-block atoms

For the sixth period s-, d-, and p-block atoms, we report Sapporo-DKH3-nZP (n = D, T, Q) sets, which are compact and efficient segmented contracted Gaussian-type basis sets for relativistic molecular calculations. In the construction of the present sets, we consider the correlation effects among the 5s and 5p outer core and the 5d, 6s, and 6p valence electrons. Test calculations on four hydrides and three oxides are carried out at the CCSD(T) level. Despite the compactness of the present basis sets, the calculated spectroscopic constants show good agreements with the experimental values.

The vibrational features of hydroxylapatite and type A carbonated apatite: A first principle contribution

In this work, the vibrational spectra of hexagonal hydroxylapatite OHAp (space group P63) and type A carbonated apatite [Ca10(PO4)6(CO3), space group P1] have been calculated with an ab initio approach by the density function method using the hybrid B3LYP functional and an all-electron polarized double-ζ quality Gaussian-type basis set using the CRYSTAL09 computer program. The effect on the vibrational properties due to improving the Ca pseudopotential, usually adopted in previous studies on hydroxylapatite, toward the present all-electron basis set has also been briefly addressed. The anharmonic correction for hydroxyl groups in OHAp has also been considered. The results of the modeling are in good agreement with the available FTIR and Raman data presented in the literature and can be useful to experimental researchers to assign unequivocally the bands in infrared and Raman spectra to specific fundamental vibrational modes.

Ab InitioPeriodic Simulation of the Spectroscopic and Optical Properties of Novel Porous Graphene Phases

We present a detailed periodic ab initio quantum-mechanical simulation of two recently proposed systems, namely hydrogenated porous graphene (HPG) and biphenyl carbon (BPC), using hybrid HF-DFT functionals and all-electron Gaussian-type basis sets. The equilibrium geometry, the vibrational spectrum (including IR intensities), the full set of components of the polarizability and hyperpolarizability tensors are provided, the latter evaluated through a coupled-perturbed KS/HF scheme. IR and Raman spectra for the two systems are quite different, and differ also from graphene, thus permitting their experimental identification. It is then shown that small defects inserted into the graphene sheet lead to finite values for the in-plane components of the static (hyper)polarizability tensors, spanning a relatively large range of values. By dehydrogenation of porous graphene into biphenyl carbon, a noteworthy enhancement of the nonlinear optical properties through the static second dipole hyperpolarizability can be ...

The vibrational spectrum of CaCO3 aragonite: A combined experimental and quantum-mechanical investigation

The vibrational properties of CaCO(3) aragonite have been investigated both theoretically, by using a quantum mechanical approach (all electron Gaussian type basis set and B3LYP HF-DFT hybrid functional, as implemented in the CRYSTAL code) and experimentally, by collecting polarized infrared (IR) reflectance and Raman spectra. The combined use of theory and experiment permits on the one hand to analyze the many subtle features of the measured spectra, on the other hand to evidentiate limits and deficiencies of both approaches. The full set of TO and LO IR active modes, their intensities, the dielectric tensor (in its static and high frequency components), and the optical indices have been determined, as well as the Raman frequencies. Tools such as isotopic substitution and graphical animation of the modes are available, that complement the analysis of the spectrum.

The electronic structure of MgO nanotubes. An ab initio quantum mechanical investigation

The structural, vibrational and response properties of the (n,0) and (m,m) MgO nanotubes are computed by using a Gaussian type basis set, a hybrid functional (B3LYP) and the CRYSTAL09 code. Tubes in the range 6 ≤ n ≤ 140 and 3 ≤ m ≤ 70 were considered, being n = 2 × m the number of MgO units in the unit cell (so, the maximum number of atoms is 280). Tubes are built by rolling up the fully relaxed 2-D conventional cell (2 MgO units, with oxygen atoms protruding from the Mg plane alternately up and down by 0.38 Å). The relative stability of the (n,0) with respect to the (m,m) family, the relaxation energy and equilibrium geometry, the band gap, the IR vibrational frequencies and intensities, and the electronic and ionic contributions to the polarizability are reported. All these properties are shown to converge smoothly to the monolayer values. Absence of negative vibrational frequencies confirms that the tubes have a stable structure. The parallel component of the polarizability α(∥) converges very rapidly to the monolayer value, whereas α(⊥) is still changing at n = 140; however, when extrapolated to very large n values, it coincides with the monolayer value to within 1%. The electronic contribution to α is in all cases (α(∥) and α(⊥); 6 ≤ n ≤ 140) smaller than the vibrational contribution by about a factor of three, at variance with respect to more covalent tubes such as the BN ones, for which the ratio between the two contributions is reversed.

On the basis set convergence of electron–electron entanglement measures: helium-like systems

A systematic investigation of three different electron–electron entanglement measures, namely the von Neumann, the linear and the occupation number entropy at full configuration interaction level has been performed for the four helium-like systems hydride, helium, Li+ and Be2+ using a large number of different basis sets. The convergence behavior of the resulting energies and entropies revealed that the latter do in general not show the expected strictly monotonic increase upon increase of the one–electron basis. Overall, the three different entanglement measures show good agreement among each other, the largest deviations being observed for small basis sets. The data clearly demonstrates that it is important to consider the nature of the chemical system when investigating entanglement phenomena in the framework of Gaussian type basis sets: while in case of hydride the use of augmentation functions is crucial, the application of core functions greatly improves the accuracy in case of cationic systems such as Li+ and Be2+. In addition, numerical derivatives of the entanglement measures with respect to the nucleic charge have been determined, which proved to be a very sensitive probe of the convergence leading to qualitatively wrong results (i.e., the wrong sign) if too small basis sets are used.

Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis

In this paper, the problem of efficient grid-based computation of the two-electron integrals (TEI) in a general basis is considered. We introduce the novel multiple tensor factorizations of the TEI unfolding matrix which decrease the computational demands for the evaluation of TEI in several aspects. Using the reduced higher-order SVD the redundancy-free product-basis set is constructed that diminishes dramatically the initial number $O(N_b^2)$ of three-dimensional ($3$D) convolutions, defined over cross products of $N_b$ basis functions, to $O(N_b)$ scaling. The tensor-structured numerical integration with the $3$D Newton convolving kernel is performed in one-dimensional ($1$D) complexity, thus enabling high resolution over fine $3$D Cartesian grids. Furthermore, using the quantized approximation of long vectors ensures the logarithmic storage complexity in the grid size. Finally, we present and analyze two approaches to compute the Cholesky decomposition of the TEI matrix based on two types of precomputed factorizations. We show that further compression is possible via columnwise quantization of the Cholesky factors. Our “black-box” approach essentially relaxes limitations on the traditional Gaussian-type basis sets, giving an alternative choice of rather general low-rank basis functions represented only by their $1$D samplings on a tensor grid. Numerical tests for some moderate size compact molecules demonstrate the expected asymptotic performance.

Ab initio analytical infrared intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method

A fully analytical method for calculating Born charges and, hence, infrared intensities of periodic systems, is formulated and implemented in the CRYSTAL program, which uses a local gaussian type basis set. Our efficient formalism combines integral gradients with first-order coupled perturbed Hartree-Fock/Kohn Sham electronic response to an electric field. It avoids numerical differentiation with respect to wave vectors, as in some Berry phase approaches, and with respect to atomic coordinates. No perturbation equations for the atomic displacements need to be solved. Several tests are carried out to verify numerical stability, consistency in one, two, and three dimensions, and applicability to large unit cells. Future extensions to piezoelectricity and Raman intensities are noted.

Assessing modern GGA functionals for solids

We present periodic calculations carried out with Gaussian-type basis sets on a test set of 21 solids with nine exchange-correlation functionals, extending previous works performed with two parameter-free correlation functionals (TCA and revTCA) which showed promising results for molecules in terms of key structural and energetic properties. Two LDAs and seven GGAs were considered for the prediction of equilibrium lattice constants, bulk moduli, and cohesive energies, using the same test set for all properties when possible. The effect of combining the TCA correlation with exchange potentials other than the PBE form originally used is also addressed. We find that the previously noted good accuracy of the parameter-free TCA functional for molecules also holds for solids, as long as a modified form of the exchange potential that is more biased towards solids than PBE is taken into account. In particular, the PBEsolTCA functional performs well overall for the three key structural and energetic properties considered here.

Determination of Kohn–Sham effective potentials from electron densities using the differential virial theorem

We present an accurate method for constructing the Kohn-Sham effective potential corresponding to a given electron density in one-dimensional and spherically symmetric systems. The method is based on the differential virial theorem--an exact relation between the effective potential, the electron density, and the kinetic energy density. A distinctive feature of the proposed technique is that it employs a size-consistent bosonic reference potential to ensure the correct asymptotic behavior of the resulting Kohn-Sham potential. We describe a practical implementation of our method and use it to obtain high-quality exchange-correlation and correlation potentials of the neon and argon atoms from ab initio densities generated in large Slater- and Gaussian-type basis sets.

Elastic and Vibrational Properties of α- and β-PbO.

The structure, electronic and dynamic properties of the two layered alpha (litharge) and beta (massicot) phases of PbO have been studied by density functional methods. The role of London dispersion interactions as leading component of the total interaction energy between layers has been addressed by using the Grimme's approach, in which new parameters for Pb and O atoms have been developed. Both gradient corrected and hybrid functionals have been adopted using Gaussian-type basis sets of polarized triple zeta quality for O atoms and small core pseudo-potential for the Pb atoms. Basis set superposition error (BSSE) has been accounted for by the Boys-Bernardi correction to compute the interlayer separation. Cross check with calculations adopting plane waves that are BSSE free have also been performed for both structures and vibrational frequencies. With the new set of proposed Grimme's type parameters structures and dynamical parameters for both PbO phases are in good agreement with experimental data.

Molecular Electrical Properties from Quantum Monte Carlo Calculations: Application to Ethyne

We used Quantum Monte Carlo (QMC) methods to study the polarizability and the quadrupole moment of the ethyne molecule using the Jastrow-Antisymmetrised Geminal Power (JAGP) wave function, a compact and strongly correlated variational ansatz. The compactness of the functional form and the full optimization of all its variational parameters, including linear and exponential coefficients in atomic orbitals, allow us to observe a fast convergence of the electrical properties with the size of the atomic and Jastrow basis sets. Both variational results on isotropic polarizability and quadrupole moment based on Gaussian type and Slater type basis sets are very close to the Lattice Regularized Diffusion Monte Carlo values and in very good agreement with experimental data and with other quantum chemistry calculations. We also study the electronic density along the C≡C and C-H bonds by introducing a generalization for molecular systems of the small-variance improved estimator of the electronic density proposed by Assaraf et al. (Assaraf, R.; Caffarel, M.; Scemama, A. Phys. Rev. E, 2007, 75, 035701).

Ab initio modelling of protein–biomaterial interactions: influence of amino acid polar side chains on adsorption at hydroxyapatite surfaces

The adsorption from the gas phase of five different amino acids (AAs), namely Gly, Ser, Lys, Gln and Glu, on three surface models of hexagonal hydroxyapatite (HA) has been studied at B3LYP level with Gaussian type basis set within a periodic approach. The AA adsorption was simulated on the (001) and (010) stoichiometric surfaces, the latter both in its pristine and water-reacted form. Low/high AA coverage has been studied by doubling the HA unit cell size. The AAs have been docked to the HA surfaces following the electrostatic complementarity between the electrostatic potentials of AA and the bare HA. Gly adsorbs as a zwitterion at the (001) surface, whereas at the (010) ones, the proton of the COOH group is transferred to the surface resulting in an HA(+)/Gly(-) ion pair. For the other AAs, the common COOH-CH-NH(2) moiety behaves like in Gly, while the specific side-chain functionalities adsorb at the HA surfaces by maximizing electrostatic and H-bond interactions. The interactions between the side chains and the HA surface impart a higher stability compared with the Gly case, with Glu being the strongest adsorbate owing to its high Ca affinity and H-bond donor propensity. For AAs of large size, the adsorption is more favourable in conditions of low coverage as repulsion between adjacent AAs is avoided. For all considered AAs, the strongest interaction is always established on the (010) faces rather than on the (001) one, therefore suggesting an easier growth along the c-direction of HA crystals from AA solutions.

Ab initio Quantum Mechanical Study of Crystalline Nitric Acid Hydrates: Structures and Vibrational Spectra

The vibrational spectra of crystalline nitric acid hydrates have been investigated at the periodic ab initio quantum level by using a Gaussian type basis set and the hybrid B3LYP Hamiltonian with CRYSTAL06 code. Using as input the X-ray structures of crystalline nitric acid monohydrate NAM, dihydrate α-NAD and trihydrate β-NAT, the inner coordinates within each unit cell have been optimized. The calculated structures of these atmospherically relevant systems are used in the evaluation of their vibrational normal modes. The obtained theoretical results show in general a good agreement compared to the observed spectra in the range 4000- 600 cm-1 and 200-20 cm-1 for infrared and Low-Frequency Raman spectra, respectively.

Segmented contracted basis sets for atoms H through Xe: Sapporo-(DK)-nZP sets (n = D, T, Q)

For the 54 atoms from H to Xe, compact yet accurate segmented Gaussian-type basis sets have been constructed for all electron calculations. Non-relativistic nZP (Sapporo-nZP) sets for Li–Xe and relativistic nZP (Sapporo-DK-nZP) sets for K–Xe are developed (n = D, T, Q), which efficiently incorporate valence and core electron correlations. Test calculations at the coupled-cluster level of theory are performed for spectroscopic constants of 12 hydrides of s- and d-block atoms and 12 diatomics of p-block atoms in their ground states. For all molecules, the calculated spectroscopic constants approach to the experimental values smoothly as the basis set quality increases.

Exchange-only optimized-effective-potential calculations using Slater-type basis functions: Atoms and diatomic molecules

The exchange-only optimized-effective-potential method is implemented with the use of Slater-type basis functions, seeking an alternative to the standard methods of solution with some computational advantages. This procedure has been tested in a small group of closed-shell atoms and diatomic molecules, for which numerical solutions are available. The results obtained with this implementation have been compared to the exact numerical solutions and to the results obtained when the optimized effective equations are solved using the Gaussian-type basis sets. This Slater-type basis approach leads to a more compact expansion space for representing the potential of the optimized-effective-potential method and to considerable computational savings when compared to both the numerical solution and the more traditional one in terms of the Gaussian basis sets.

The infrared spectrum of ortho-enstatite from reflectance experiments and first-principle simulations

Infrared (IR) spectra provide a rich amount of information concerning chemical composition, lattice structure, size and shape of circumstellar dust. Accurate reference data are then required for the analysis of the various detected components. This study provides the IR characterization of one of the most frequently observed compounds, MgSiO3 ortho-enstatite, and shows that IR experiments and ab initio techniques can be used synergically to obtain high-quality data concerning crystalline materials. The IR reflectance spectrum of synthetic ortho-enstatite was collected and compared to ab initio results (Gaussian-type basis set, PBE0 hybrid density functional theory (DFT) functional). An excellent agreement is observed both for vibrational frequencies (ν) and intensities, the latter estimated through the oscillator strength. The mean absolute difference between experimental and calculated ν is of the order of 7–8 cm−1 (43 out of 65 peaks differ by less than 10 cm−1, only four peaks differ by 15–19 cm−1). The static dielectric tensor and its components (electronic and ionic contributions) were measured and compared to calculated data: differences are in the 2–5 per cent range.

Optimized Basis Sets for Calculation of Electron Paramagnetic Resonance Hyperfine Coupling Constants: aug-cc-pVTZ-J for the 3d Atoms Sc-Zn.

The hyperfine coupling tensor of electron paramagnetic resonance (EPR), describing the interaction between an electron and a given nuclei, depends strongly on the electron density at the nucleus. With standard Gaussian-type orbital basis sets (GTOs), employed in most calculations, it is difficult to obtain converged results of the hyperfine coupling tensor, and basis sets with more flexible core regions have therefore been devised. To this class of core property basis sets belong the aug-cc-pVTZ-J basis sets developed for the s- and p-block atoms. Here, we extend the aug-cc-pVTZ-J basis sets to include the 3d elements Sc-Zn. The converged optimal basis sets are throughout the series described by a (25s17p10d3f2g)/[17s10p7d3f2g] contraction scheme, where four tight s-, one tight p-, and one tight d-type function have been added to the original aug-cc-pVTZ basis sets. The basis sets are generally contracted, and molecular orbital coefficients are used as contraction coefficients. By validation studies with different functionals and compounds, it is shown that the values of the contraction coefficient are effectively independent of the compound used in their generation and the exchange-correlation functional employed in the calculation.

H-Bond Network in Amino Acid Cocrystals with H2O or H2O2. The DFT Study of Serine–H2O and Serine–H2O2

The structure, IR spectrum, and H-bond network in the serine-H(2)O and serine-H(2)O(2) crystals were studied using DFT computations with periodic boundary conditions. Two different basis sets were used: the all-electron Gaussian-type orbital basis set and the plane wave basis set. Computed frequencies of the IR-active vibrations of the titled crystals are quite different in the range of 10-100 cm(-1). Harmonic approximation fails to reproduce IR active bands in the 2500-2800 frequency region of serine-H(2)O and serine-H(2)O(2). The bands around 2500 and 2700 cm(-1) do exist in the anharmonic IR spectra and are caused by the first overtone of the OH bending vibrations of H(2)O and a combination vibration of the symmetric and asymmetric bendings of H(2)O(2). The quantum-topological analysis of the crystalline electron density enables us to describe quantitatively the H-bond network. It is much more complex in the title crystals than in a serine crystal. Appearance of water leads to an increase of the energy of the amino acid-amino acid interactions, up to ~50 kJ/mol. The energy of the amino acid-water H-bonds is ~30 kJ/mol. The H(2)O/H(2)O(2) substitution does not change the H-bond network; however, the energy of the amino acid-H(2)O(2) contacts increases up to 60 kJ/mol. This is caused by the fact that H(2)O(2) is a much better proton donor than H(2)O in the title crystals.

The IR vibrational properties of six members of the garnet family: A quantum mechanical ab initio study

The IR vibrational properties and the corresponding reflectance spectra of the six most common members of the garnet family (pyrope Mg3Al2Si3O12, almandine Fe3Al2Si3O12, spessartine Mn3Al2Si3O12, grossular Ca3Al2Si3O12, uvarovite Ca3Cr2Si3O12, and andradite Ca3Fe2Si3O12) were simulated at the ab initio level with the CRYSTAL09 code by using a large all-electron Gaussian-type basis set and the B3LYP hybrid functional. The 17 IR active F1u transverse optical (TO) and longitudinal optical (LO) frequencies, the oscillator strengths, the high frequency and static dielectric constants, and the reflectance spectrum were computed. The agreement with experiments for the TO and LO peaks is always excellent, the mean absolute difference for the whole set of data (overall 178 peaks) being 5 cm-1. Oscillator strengths, calculated from the mass-weighted effective Born charges, are found in semi-quantitative agreement with the experimental data. The reflectance spectra, simulated through the classical dispersion relation, reproduce the experimental curves extremely well. The availability of the full set of simulated frequencies and intensities, obtained by using uniform computational tools (computer code, variational basis sets, density functional), permits the establishment of correlations between IR wavenumbers and structural features suggested, but only partially documented, in the past