Zeta Valence Quality Research Articles

All-electron basis sets for H to Xe specific for ZORA calculations: Applications in atoms and molecules

Abstract A segmented basis set of quadruple zeta valence quality plus polarization functions (QZP) for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian. This set was augmented with diffuse functions to describe electrons farther away from the nuclei adequately. Using the ZORA-CCSD(T)/QZP-ZORA theoretical model, atomic ionization energies and bond lengths, harmonic vibrational frequencies, and atomization energies of some molecules were calculated. The addition of core-valence corrections has been shown to improve the agreement between theoretical and experimental results for molecular properties. For atomization energies, a similar observation emerges when considering spin-orbit couplings. With the augmented QZP-ZORA set, static mean dipole polarizabilities of a set of atoms were calculated and compared with previously published recommended and experimental values. Performance evaluations of the ZORA and Douglas–Kroll–Hess Hamiltonians were made for each property studied.

All-electron ZORA triple zeta basis sets for the elements Cs–La and Hf–Rn

Segmented all-electron basis set of triple zeta valence quality plus polarization functions (TZP) for the elements of the fifth row to be used together with the zero-order regular approximation (ZORA) is carefully constructed. To correctly describe electrons distant from atomic nuclei, the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA. At the ZORA-B3LYP theoretical level, these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms, bond length, dissociation energy, and harmonic vibrational frequency of diatomic molecules. Then, these results are compared with the theoretical and experimental data found in the literature. Even considering that our sets are relatively compact, they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell. The performances of the ZORA and second-order Douglas–Kroll–Hess Hamiltonians are evaluated and the results are also discussed.

ZORA double zeta basis sets for fifth row elements: Application in studies of electronic structures of atoms and molecules

Segmented all-electron basis set of double zeta valence quality plus polarization functions (DZP) to be used with the zero-order regular approximation (ZORA) scalar relativistic Hamiltonian was developed for the elements Cs, Ba, La, and from Hf to Rn. This set was augmented with diffuse functions for the purpose of describing electrons distant from atomic nuclei. Using the ZORA-B3LYP method, some atomic and molecular properties are computed. Benchmark theoretical results and experimental data were used to evaluate the performance of the DZP-ZORA and ADZP-ZORA basis sets. Despite their small sizes, these sets have proven to be accurate and reliable and can also be used in property calculations involving electrons not only from the outer shells, but also from the inner shells. Comparison of second order Douglas-Kroll-Hess and ZORA results was made.

ZORA all-electron double zeta basis sets for the elements from H to Xe: application in atomic and molecular property calculations

From the segmented all-electron basis set of double zeta valence quality plus polarization functions (DZP) for the elements from H to Xe, the zeroth-order regular approximation (ZORA) is used to generate a DZP-ZORA basis set, i.e., the contraction coefficients of the DZP set are re-optimized using the minimum ZORA energy criterion. To properly describe electrons distant from the nuclei, a diffuse function is added to each atomic symmetry (s, p, d, and f). The later basis set is designated as DZP-ZORA augmented. To test the effectiveness of the basis sets developed in this work, calculations of ionization energies and mean dipole polarizabilities of some elements are performed using the ZORA-CCSD(T) method. At the same level of theory, bond lengths, dissociation energies, and harmonic vibrational frequencies of some diatoms are also reported. Comparison with experimental data and recommended values available in the literature is made. Except for polarizability, scalar relativistic effects are estimated for the other properties. The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated.

All-electron triple zeta basis sets for ZORA calculations: Application in studies of atoms and molecules

Segmented all-electron basis set of triple zeta valence quality plus polarization functions for the elements from H to Xe to be used together with the ZORA Hamiltonian is developed. This set was augmented with diffuse functions in order to properly describe electrons distant from the nuclei. At the ZORA-CCSD(T) level of theory, ionization energies and mean dipole polarizabilities of some atoms as well as bond lengths, dissociation energies, and harmonic vibrational frequencies of a set of molecules are calculated. Scalar relativistic effects are estimated for all properties. The performances of the ZORA and DKH2 Hamiltonians are also assessed.

All-electron segmented contraction basis sets of triple zeta valence quality for the fifth-row elements

All-electron contracted Gaussian basis set of triple zeta valence quality plus polarisation functions (TZP) for the elements Cs, Ba, La, and from Hf to Rn is presented. Douglas–Kroll–Hess (DKH) basis set for fifth-row elements is also reported. We have recontracted the original TZP basis set, i.e., the values of the contraction coefficients are re-optimised using the second-order DKH Hamiltonian. By addition of diffuse functions (s, p, d, f, and g symmetries), which are optimised for the anion ground states, an augmented TZP basis set is constructed. Using the B3LYP hybrid functional, the performance of the TZP–DKH basis set is assessed for predicting atomic ionisation energy as well as spectroscopy constants of some compounds. Despite its compact size, this set demonstrates consistent, efficient, and reliable performance and will be especially useful in calculations of molecular properties that require explicit treatment of the core electrons.

Segmented contracted basis sets for one- and two-component Dirac–Fock effective core potentials

Segmented contracted basis sets for 4d, 5d, 5s, and 6s elements of split (double zeta) valence to quadruple zeta valence quality optimized for Dirac-Fock effective core potentials (ECPs) are presented. They were obtained from previous bases optimized for Wood-Boring ECPs by comparably small modifications and reoptimizations. Additionally extensions for two-component self-consistent-field treatments accounting for spin-orbit (SO) coupling were designed and optimized. Reliability for chemical applications was assessed by comparing results to those obtained with a very large (19s16p17d7f6g) reference basis for a set of more than 80 representatively chosen 5s-5d compounds. Moreover, the effect of different types of ECPs and that of the SO-coupling at the basis set limit of density functional theory is documented for the above set of molecules extended by 40 5p-6p compounds.

Gaussian basis set of double zeta quality for atoms Rb through Xe: application in non-relativistic and relativistic calculations of atomic and molecular properties

The all-electron contracted Gaussian basis set of double zeta valence quality plus polarization functions (DZP) for the atoms from Rb to Xe is presented. The Douglas–Kroll–Hess (DKH) basis set for fourth-row elements is also reported. The original DZP basis set has been recontracted, i.e. the values of the contraction coefficients were re-optimized using the relativistic DKH Hamiltonian. This extends earlier works on segmented contracted DZ basis set for atoms H-Kr. These sets along with ab initio methods were used to calculate ionization energies of some atoms and spectroscopic constants of a sample of molecules and, then, comparison with results obtained with other basis sets was made. It was shown that experimental and benchmark bond lengths and harmonic vibrational frequencies can be reproduced satisfactorily with DZP-DKZ.

Augmented Gaussian basis set of double zeta valence quality for the atoms Rb and Y–Xe: Application in DFT calculations of molecular electric properties

Augmented Gaussian basis set of double zeta valence quality plus polarization functions for the atoms Rb and from Y to Xe is presented. It was generated from the all-electron unaugmented set by addition of diffuse functions (s, p, d, and f symmetries) that were optimized for the anion ground states. From this set, density functional theory electric dipole moment and dipole polarizability for a sample of molecules were calculated and compared with theoretical and experimental values available in the literature. Our results give good agreement with experimental and benchmark values.

Gaussian basis set of triple zeta valence quality for the atoms from K to Kr: Application in DFT and CCSD(T) calculations of molecular properties

A contracted basis set of triple zeta (TZ) valence quality for the atoms from K to Kr was constructed from fully-optimized Gaussian basis sets generated in this work. Gaussian polarization functions (d, f, and g symmetries), which were optimized at the second-order Mφller–Plesset level, were added to the TZ set. This extends earlier work on segmented contracted TZ basis set for atoms H-Ar. This set along with the BP86 non-hybrid and B3LYP hybrid functionals were used to calculate geometric parameters, dissociation energy, harmonic vibrational frequency, and electric dipole moment of a sample of molecules and, then, comparison with results obtained with other basis sets and with experimental data reported in the literature is done. CCSD(T) atomic excitation energies and bond lengths, dissociation energies, and harmonic vibrational frequencies of some diatomics were also evaluated. Using density functional theory and gauge-including atomic orbitals, 57Fe and 77Se nuclear magnetic resonance chemical shifts in Fe(C5H5)2, H2Se, (CH3)SeH, CSe2, SeCO, H2CSe, and SeF6 were calculated. Comparison with theoretical and experimental values previously published in the literature was done. It is verified that in general these results give good agreement with experimental and benchmark values.

Some considerations about Gaussian basis sets for electric property calculations

Recently, segmented contracted basis sets of double, triple, and quadruple zeta valence quality plus polarization functions (XZP, X = D, T, and Q, respectively) for the atoms from H to Ar were reported. In this work, with the objective of having a better description of polarizabilities, the QZP set was augmented with diffuse (s and p symmetries) and polarization (p, d, f, and g symmetries) functions that were chosen to maximize the mean dipole polarizability at the UHF and UMP2 levels, respectively. At the HF and B3LYP levels of theory, electric dipole moment and static polarizability for a sample of molecules were evaluated. Comparison with experimental data and results obtained with a similar size basis set, whose diffuse functions were optimized for the ground state energy of the anion, was done. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Augmented Gaussian basis set of quintuple zeta valence quality for H and from Li to Ar: Applications in DFT calculations of molecular electric properties

Augmented Gaussian basis set of quintuple zeta valence quality plus polarization functions (A5ZP) for H and Li–Ar is presented. It was determined from the 5ZP basis set by addition of diffuse (s and p symmetries) and polarization (p, d, f, g, and h symmetries) functions that were optimized for the anion at the Hartree–Fock and Mϕller–Plesset second-order levels, respectively. It was shown that in general this basis set in combination with the density functional theory can be used with success to predict electric properties for a sample of molecules. Comparison with theoretical and experimental values available in the literature is done.

Basis set convergence of electric properties in HF and DFT calculations of nucleic acid bases

AbstractRecently, a hierarchical sequence of augmented basis sets of double, triple, and quadruple zeta valence quality plus polarization functions (AXZP, X = D, T, and Q) for the atoms from H to Ar were presented by Jorge et al. We report a systematic study of basis sets required to obtain accurate values of several electric properties for benzene, pyridine, the five common nucleic acid bases (uracil, cytosine, thymine, guanine, and adenine), and three related bases (fluorouracil, 5‐methylcytosine, and hypoxanthine) at their full optimized geometries. Two methods were examined: Hartree‐Fock (HF) and density functional theory (DFT). Including electron correlation decreases the magnitude of the dipole moment and increases the mean polarizability and also the polarizability anisotropy for every molecule. Calculated B3LYP/ADZP dipole moments and dipole polarizabilities show good agreement with both experimental and ab initio results based on second‐order Møller‐Plesset perturbation theory calculations. We have also showed that a basis set of double zeta quality is enough to obtain reliable and accurate electric property results for this kind of compounds. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Basis-set convergence of nuclear magnetic shielding constants in molecular HF and MP2 calculations

Recently, segmented contracted basis sets of double, triple, quadruple and quintuple zeta valence quality plus polarization functions (XZP, X = D, T, Q and 5) for the atoms from H to Ar were presented by Jorge et al. We report a systematic study of basis sets required to obtain accurate values for nuclear magnetic shielding tensors for 20 molecules at their experimental equilibrium geometries. Two methods were examined: Hartree–Fock (HF) and second-order Møller–Plesset perturbation theory (MP2). Gauge-invariant atomic orbitals were used to guarantee origin-independent values of magnetic properties. By direct calculations or by fitting the directly calculated values through two extrapolation schemes, estimates of the HF and MP2 complete basis-set limit have been obtained. Comparison with experiment and benchmark results reported in the literature is made.

Scaling factors for fundamental vibrational frequencies and zero-point energies obtained from HF, MP2, and DFT/DZP and TZP harmonic frequencies

Recently, segmented contracted basis sets of double, triple, and quadruple zeta valence quality plus polarization functions (XZP, X = D, T, and Q) for the atoms from H to Ar were presented by Jorge et al. Scaling factors for the fundamental vibrational frequencies, low-frequency vibrations, and zero-point vibrational energies (ZPVEs) evaluated at 14 levels of theory are reported. The ab initio Hartree–Fock (HF) and second-order Møller–Plesset perturbation theory (MP2) methods, and several variants of density functional theory (DFT: B1LYP, B3LYP, B3P86, B3PW91, and BP86) have been examined in conjunction with the DZP and TZP basis sets. The experimental fundamental vibrational frequencies of 63 small molecules and the ZPVEs of 24 small molecules are used to determine the scaling factors through the least-square fitting procedure. Scaling factors suitable for low-frequency vibrations were obtained from least-squares fits of inverse frequencies. For each model used in this work, a recommended scale factor is presented. Overall, the most successful method to estimate fundamental frequencies and ZPVEs is B3LYP along with the TZP and DZP sets, respectively.

Hartree–Fock exchange fitting basis sets for H to Rn †

For elements H to Rn (except Lanthanides), a series of auxiliary basis sets fitting exchange and also Coulomb potentials in Hartree-Fock treatments (RI-JK-HF) is presented. A large set of small molecules representing nearly each element in all its common oxidation states was used to assess the quality of these auxiliary bases. For orbital basis sets of triple zeta valence and quadruple zeta valence quality, errors in total energies arising from the RI-JK approximation are below approximately 1 meV per atom in molecular compounds. Accuracy of RI-JK-approximated HF wave functions is sufficient for being used for post-HF treatments like Møller-Plesset perturbation theory, MP2. Compared to nonapproximated treatments, RI-JK-HF leads to large computational savings for quadruple zeta valence orbital bases and, in case of small to midsize systems, to significant savings for triple zeta valence bases.

Augmented Gaussian basis sets of triple and quadruple zeta valence quality for the atoms H and from Li to Ar: Applications in HF, MP2, and DFT calculations of molecular dipole moment and dipole (hyper)polarizability

Recently, segmented contracted basis sets of triple and quadruple zeta valence quality plus polarization functions for the atoms from H to Ar were reported. In this work, with the objective of having a better description of electron affinities, polarizabilities, and hydrogen bonding, each of these sets was augmented with diffuse (s and p symmetries) and polarization (p, d, f, and g symmetries) functions that were optimized for the anion at the Hartree–Fock (HF) and M ϕller–Plesset second-order (MP2) levels, respectively. This extends earlier work on segmented contracted double zeta valence basis set. In order to assess the quality of these sets, HF, MP2, and density functional theory calculations of electric dipole moment and static dipole polarizability and hyperpolarizability for a sample of molecules were carried out. The results are compared with theoretical and experimental values reported in the literature.

Density functional theory calculations of optical rotation: Employment of ADZP and its comparison with other basis sets

Density function theory calculations of frequency dependent optical rotations ([alpha]omega) for 30 rigid chiral molecules are reported. Calculations have been carried out at the sodium D line frequency, using the augmented double zeta valence quality plus polarization functions (ADZP) basis set and the BP86 nonhybrid and B3LYP hybrid functionals. Gauge-invariant atomic orbitals were used to guarantee origin-independent values of [alpha]D. Comparison between corresponding results obtained with nonhybrid and hybrid functionals as well as with theoretical optical rotations reported in the literature is done. Excited electronic states of three molecules are also discussed in light of circular dichroism spectra and B3LYP and BP86 calculated excitation energies and rotatory strengths. One verifies that the B3LYP/ADZP results are in better agreement with experiment.

Gaussian basis sets of 5 zeta valence quality for correlated wave functions

Contracted Gaussian basis set of 5 zeta valence quality plus polarization functions for the atoms from H to Ar are presented. We assess the performance of the basis set comparing total HF and second order correlation energies of a sample of diatomic molecules with results obtained numerically or using basis sets reported in the literature. By fitting the directly calculated values through an extrapolation scheme, estimates of the complete basis set limits for second order correlation energy have been obtained. In addition, using some correlated methods, dissociation energies are evaluated and compared with experimental data.

Gaussian basis sets of triple and quadruple zeta valence quality for correlated wave functions

Contracted basis sets of triple and quadruple zeta (TZ and QZ, respectively) valence quality for the atoms from H to Ar are presented. They have been determined from fully-optimized basis sets of primitive Gaussian-type functions generated in atomic Hartree–Fock (HF) calculations. Sets of Gaussian polarization functions optimized at the Møller–Plesset second-order (MP2) level were added to the TZ and QZ basis sets. This extends earlier work on segmented contracted double zeta valence basis sets. The performance of the basis sets are assessed in molecular HF and MP2 calculations for a sample of diatomic molecules by a comparison of energies, dissociation energies, and dipole moments with results obtained numerically or using basis sets reported in the literature. By fitting the directly calculated values through two extrapolation schemes, estimates of the complete basis set limit for second order correlation energy have been obtained. In addition, results for MP2-R12/A calculations to establish the basis set convergence for the standard calculations are also presented.