All-electron basis sets of quintuple and sextuple zeta valence qualities plus polarization functions (5ZP and 6ZP) for the elements from H to Ar, to be used together with the zero-order regular approximation (ZORA), have been developed. To describe electrons distant from the nuclei, diffuse functions were added to the 6ZP non-relativistic set, giving rise to the set designated as augmented 6ZP (A6ZP). A5ZP-ZORA, A6ZP-ZORA, and A6ZP-DKH (Douglas–Kroll–Hess) basis sets were also generated. In order to have a better description of some molecular properties, d-symmetry functions with high exponents were added to the ZORA basis sets for the elements of the second-row. Using these basis sets together with the couple cluster method, ionization energies and static mean dipole polarizabilities of some atoms and geometric parameters, harmonic vibrational frequencies, atomization energies, and electric dipole moments of a set of molecules were calculated and compared with recommended and experimental values found in the literature. The performances of the ZORA and DKH Hamiltonians were evaluated.

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.

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.

Segmented all-electron basis sets of double and triple zeta valence qualities plus polarization functions (DZP and TZP) for the elements Fr, Ra, and Ac to be used with the zeroth-order regular approximation (ZORA) were presented. These sets were constructed from the reoptimization of the contraction coefficients of the corresponding non-relativistic basis sets. In order to adequately describe electrons distant from the atomic nuclei, these sets were augmented with diffuse functions and were, respectively, designated as ADZP-ZORA and ATZP-ZORA. At the ZORA-B3LYP theory level, the relativistic sets were employed to calculate ionization energies of Fr, Ra, and Ac as well as bond lengths, dissociation energies, harmonic vibrational frequencies, and static mean dipole polarizabilities of some diatomics. Comparing with benchmark theoretical results and with experimental data available in the literature, it can be verified that our basis sets are able to produce reliable and accurate results. Evaluation of the performances of ZORA and second-order Douglas-Kroll-Hess Hamiltonians was performed.

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.

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.

Non-relativistic and Douglas-Kroll-Hess (DKH) basis sets augmented with diffuse functions for He, Ca, Sr, Ba, and lanthanides are generated. These sets are appropriated to describe electrons away from the nuclei. Using the DKH augmented sets along with the B3LYP functional, bond lengths, dissociation energies, harmonic vibrational frequencies, adiabatic ionization potentials, adiabatic electron affinities, and dipole moments for CaH, SrH, and BaH are computed. These results agree well with the most recent experimental and benchmark theoretical data published in the literature. The DKH mean dipole polarizabilities reported in this work for some elements are close to the recommended values. Scalar relativistic effects are also estimated.

Douglas-Kroll-Hess calculations of bond lengths, binding energies, HOMO-LUMO energy gaps, vertical ionization potentials and electron affinities, dissociation energies, second-order difference of total energies, polarizabilities, and spin magnetic moments of small rhodium cluster are carried out using the BLYP functional along with the all-electron TZP + 1d-DKH basis set. Our results agree well with the experimental values available in the literature. Overall, the spin magnetic moments computed in this work are the best published to date. These findings certainly add credibility to the ground state geometrical structures reported by us, which do not always coincide with the structures found earlier. Rh-8 and Rh-12 are the most stable clusters, while Rh-5 and Rh-7 are the most reactive. Mean dipole polarizabilities and polarizability anisotropies are also reported. It is the first time that these electrical properties are calculated and they are useful for understanding the electronic structures of the Rh-n clusters.

A new method for optimizing a set of numerical parameters is presented. This method does not depend on prior knowledge of the goal function and of its derivatives. Besides, it is robust and does not require any other method to achieve result near the global extreme (maximum/minimum) of the goal function. However, as the computational time spent by our method increases with the number of numerical parameters and with the size of each parameter to be optimized, in this work, it is applied together with the IGCHF method to construct accurate uncontracted basis sets to describe the ground states of some atoms. In these cases, the parameters to be optimized are the exponents of the Gaussian functions and the minimum total HF energy criterion is guaranteed by the variational principle. It is verified that the results calculated with the proposed new method are better than those obtained with the Monte Carlo and particle swarm methods, although the computational times spent in some cases by it are larger than those of the other two methods.

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.

At the Douglas-Kroll-Hess level, the B3PW91 hybrid functional along with relativistic all-electron basis sets are used to evaluate geometric parameters, binding energies, vertical ionization potentials and electron affinities, and HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) energy gaps of the small golden clusters (Au-n, n <= 8). The so expected odd-even oscillations of the experimental ionization potentials and electron affinities are confirmed in this work and the Au-7 cluster is predicted to be the most reactive cluster. Using the optimized geometries, DKH2 static mean dipole polarizability and polarizability anisotropy are also computed. From n >= 2, the mean dipole polarizabilities per atom present an odd-even oscillatory characteristic, whereas the polarizability anisotropies increase with the cluster size. At the non-relativistic level, the second hyperpolarizabilities are calculated. It is the first time that hyperpolarizabilities of gold clusters are reported. Comparisons with theoretical results obtained previously for the copper and silver clusters at the same level of theory are made.

Segmented all-electron basis sets of valence triple zeta qualities plus polarization functions for the elements Fr to Lr 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, bond lengths and dissociation energies of a sample of diatomics are calculated for Fr, Ra and Ac. For the actinide monoxides, bond distances and dissociation energies are calculated with the B3LYP/ TZP-DKH procedure. 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.

At the second order Douglas-Kroll-Hess (DKH2) level, the B3PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute bond lengths, dissociation energies, vertical ionization potentials, and the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the small iridium clusters (Ir-n, n <= 8). These results are compared with the experimental and theoretical data available in the literature. Our results confirm the theoretical predictions made by Feng et al. about the catalytic activities of the Ir-4 and Ir-6 clusters. From the optimized geometries, DKH2 calculations of static electric mean dipole polarizabilities and polarizability anisotropies are also carried out. It is the first time that the polarizabilities of small iridium clusters have been studied. For n <= 4, the mean dipole polarizabilities per atom present an odd-even oscillatory behavior, whereas from Ir-5 to Ir-8, they decrease with the cluster size increasing. The dependence of the polarizability anisotropy on the structure symmetry of the iridium cluster is verified.

Non-relativistic and Douglas-Kroll-Hess (DKH) segmented all-electron basis sets of valence triple zeta quality plus polarization functions (TZP) for the actinides are developed. To describe accurately the properties that depend on a good description of the electrons far away from the nuclei, the corresponding augmented sets (ATZP and ATZP-DKH) are reported as well. For the actinide monoxides, bond distances, dissociation energies, natural charges and populations of the valence orbitals of the actinides, and bond indices are calculated with the B3LYP/TZP-DKH procedure. For Am and No, the B3LYP/ATZP-DKH static mean dipole polarizabilities are also computed. To assess the performance of these small size all-electron basis sets, comparison with theoretical and experimental data reported previously in the literature is done. These sets must be also helpful on calculations of properties involving simultaneously core and valence electrons.

Time-dependent density functional theory (TDDFT) calculations of electronic transitions have been widely used to determine molecular structures. The excitation wavelengths and oscillator strengths obtained with the hybrid exchange-correlation functional B3LYP in conjunction with the ADZP basis set are employed to simulate the UV–Vis spectra of eight phenolic acids. Experimental and theoretical UV–Vis spectra reported previously in the literature are compared with our results. The fast, sensitive and non-destructive technique of photoacoustic spectroscopy (PAS) is used to determine the UV–Vis spectra of four Brazilian tropical fresh fruits in natura. Then, the PAS along with the TDDFT results are for the first time used to investigate and identify the presence of phenolic acids in the fruits studied in this work. This theoretical method with this experimental technique show to be a powerful and cheap tool to detect the existence of phenolic acids in fruits, vegetables, cereals, and grains. Comparison with high performance liquid chromatography results, when available, is also carried out.

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.

At the Douglas-Kroll-Hess (DKH) level, the B3PW91 functional along with the all-electron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and electronic properties of the small silver clusters (Agn, n <= 7). The results presented in this study are in good agreement with the experimental data and theoretical values obtained at a higher level of theory from the literature. Static polarizability and hyperpolarizability are also reported. It is verified that the mean dipole polarizability per atom exhibits an odd-even oscillation and that the polarizability anisotropy is directly related to the cluster shape. In this article, the first study of hyperpolarizabilities of small silver clusters is presented. Except for the monomer, the second hyperpolarizabilities of the silver clusters are significantly larger than those of the copper clusters.

A hierarchical sequence of basis sets along with one long‐range corrected functional (CAM‐B3LYP) were used to calculate electronic optical rotations (OR) at three wavelengths (355.0, 589.3, and 633.0 nm) of 14 rigid chiral molecules whose experimental values are available in the literature. As the results showed to be sensitive to the basis set quality, complete basis set limits were estimated. Special attention was given to five particularly difficult compounds. In these cases, one verifies that vibrational corrections (taken from the literature) must be added to the CAM‐B3LYP equilibrium OR to correct signs. In general, the complete basis set limits reported in this work are in good agreement with the experimental data and with those obtained at a higher level of theory. For some compounds, solvent effects are taken into account by means of the polarizable continuum model. For the solvated systems, the dependence between OR and cavity size is also examined. © 2015 Wiley Periodicals, Inc.

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.