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 ∼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. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008     

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 Mller–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.     

Accurate Coulomb-fitting basis sets for H to Rn

A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented. For each element only one auxiliary basis set is needed to approximate Coulomb energies in conjunction with orbital basis sets of split valence, triple zeta valence and quadruple zeta valence quality with errors of typically below ca. 0.15 kJ mol(-1) per atom; this was demonstrated in conjunction with the recently developed orbital basis sets of types def2-SV(P), def2-TZVP and def2-QZVPP for a large set of small molecules representing (nearly) each element in all of its common oxidation states. These auxiliary bases are slightly more than three times larger than orbital bases of split valence quality. Compared to non-approximated treatments, computation times for the Coulomb part are reduced by a factor of ca. 8 for def2-SV(P) orbital bases, ca. 25 for def2-TZVP and ca. 100 for def2-QZVPP orbital bases.     

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.     

Optimized Slater-type basis sets for the elements 1-118

Seven different types of Slater type basis sets for the elements H (Z = 1) up to E118 (Z = 118), ranging from a double zeta valence quality up to a quadruple zeta valence quality, are tested in their performance in neutral atomic and diatomic oxide calculations. The exponents of the Slater type functions are optimized for the use in (scalar relativistic) zeroth-order regular approximated (ZORA) equations. Atomic tests reveal that, on average, the absolute basis set error of 0.03 kcal/mol in the density functional calculation of the valence spinor energies of the neutral atoms with the largest all electron basis set of quadruple zeta quality is lower than the average absolute difference of 0.16 kcal/mol in these valence spinor energies if one compares the results of ZORA equation with those of the fully relativistic Dirac equation. This average absolute basis set error increases to about 1 kcal/mol for the all electron basis sets of triple zeta valence quality, and to approximately 4 kcal/mol for the all electron basis sets of double zeta quality. The molecular tests reveal that, on average, the calculated atomization energies of 118 neutral diatomic oxides MO, where the nuclear charge Z of M ranges from Z = 1-118, with the all electron basis sets of triple zeta quality with two polarization functions added are within 1-2 kcal/mol of the benchmark results with the much larger all electron basis sets, which are of quadruple zeta valence quality with four polarization functions added. The accuracy is reduced to about 4-5 kcal/mol if only one polarization function is used in the triple zeta basis sets, and further reduced to approximately 20 kcal/mol if the all electron basis sets of double zeta quality are used. The inclusion of g-type STOs to the large benchmark basis sets had an effect of less than 1 kcal/mol in the calculation of the atomization energies of the group 2 and group 14 diatomic oxides. The basis sets that are optimized for calculations using the frozen core approximation (frozen core basis sets) have a restricted basis set in the core region compared to the all electron basis sets. On average, the use of these frozen core basis sets give atomic basis set errors that are approximately twice as large as the corresponding all electron basis set errors and molecular atomization energies that are close to the corresponding all electron results. Only if spin-orbit coupling is included in the frozen core calculations larger errors are found, especially for the heavier elements, due to the additional approximation that is made that the basis functions are orthogonalized on scalar relativistic core orbitals.     

Consistent Gaussian basis sets of triple‐zeta valence with polarization quality for solid‐state calculations

Consistent basis sets of triple‐zeta valence with polarization quality for main group elements and transition metals from row one to three have been derived for periodic quantum‐chemical solid‐state calculations with the crystalline‐orbital program CRYSTAL. They are based on the def2‐TZVP basis sets developed for molecules by the Ahlrichs group. Orbital exponents and contraction coefficients have been modified and reoptimized, to provide robust and stable self‐consistant field (SCF) convergence for a wide range of different compounds. We compare results on crystal structures, cohesive energies, and solid‐state reaction enthalpies with the modified basis sets, denoted as pob‐TZVP, with selected standard basis sets available from the CRYSTAL basis set database. The average deviation of calculated lattice parameters obtained with a selected density functional, the hybrid method PW1PW, from experimental reference is smaller with pob‐TZVP than with standard basis sets, in particular for metallic systems. The effects of basis set expansion by diffuse and polarization functions were investigated for selected systems. © 2012 Wiley Periodicals, Inc.     

Consistent gaussian basis sets of double‐ and triple‐zeta valence with polarization quality of the fifth period for solid‐state calculations

Consistent basis sets of double‐ and triple‐zeta valence with polarization quality for the fifth period have been derived for periodic quantum‐chemical solid‐state calculations with the crystalline‐orbital program CRYSTAL. They are an extension of the pob‐TZVP basis sets, and are based on the full‐relativistic effective core potentials (ECPs) of the Stuttgart/Cologne group and on the def2‐SVP and def2‐TZVP valence basis of the Ahlrichs group. We optimized orbital exponents and contraction coefficients to supply robust and stable self‐consistent field (SCF) convergence for a wide range of different compounds. The computed crystal structures are compared to those obtained with standard basis sets available from the CRYSTAL basis set database. For the applied hybrid density functional PW1PW, the average deviations of calculated lattice constants from experimental references are smaller with pob‐DZVP and pob‐TZVP than with standard basis sets. © 2018 Wiley Periodicals, Inc.     

Accurate evaluation of valence and low-lying Rydberg states with standard time-dependent density functional theory

Using a standard exchange-correlation functional, namely, PBE0, the basis set dependence of time-dependent density functional theory (TD-DFT) calculations has been explored using 33 different bases and five organic molecules as test cases. The results obtained show that this functional can provide accurate (i.e., at convergence) results for both valence and low-lying Rydberg excitations if at least one diffuse function for the heavy atoms is included in the basis set. Furthermore, these results are in fairly good agreement with the experimental data and with those delivered by other functionals specifically designed to yield correct asymptotic/long-range behavior. More generally, the PBE0 calculations show that a greater accuracy can be obtained for both Rydberg and valence excitations if they occur at energies below the epsilonHOMO + 1 eV threshold. This latter value is proposed as a thumb rule to verify the accuracy of TD-DFT/PBE0 applications.     

Augmented Gaussian basis sets of double and triple zeta valence qualities for the atoms K and Sc–Kr: Applications in HF, MP2, and DFT calculations of molecular electric properties

Augmented Gaussian basis sets of double and triple zeta valence qualities plus polarization functions for the atoms K and from Sc to Kr are presented. They were generated from the all-electron unaugmented sets by addition of diffuse functions (s, p, d, f, and g symmetries) that were optimized for the anion ground states. From these sets, Hartree–Fock, second-order Møller–Plesset perturbation theory, and density functional theory electric dipole moment and dipole polarizability calculations for a sample of molecules were carried out. Comparison with theoretical and experimental values available in the literature was done.     

An approximate diatomics in molecules formulation of generalized valence bond theory

The slow computational speed of the generalized valence bond perfect pairing method (GVB-PP) has been an impediment to its routine use. We have addressed this problem by employing a diatomics in molecules Hamiltonian derived from a second quantization perturbation approach. This results in all three- and four-centered two-electron integrals being dropped from the traditional GVB-PP calculation. For moderate sized molecules, as for example C20 computed with a double zeta + polarization basis, there is on average a fifty-fold decrease in computational times. In this article, we present the theory behind our approach and analyze the accuracy and speed of this approximate GVB-PP method for several cases where density functional methods have produced ambivalent results.     

Norbornane: an investigation into its valence electronic structure using electron momentum spectroscopy, and density functional and Green's function theories

We report on the results of an exhaustive study of the valence electronic structure of norbornane (C(7)H(12)), up to binding energies of 29 eV. Experimental electron momentum spectroscopy and theoretical Green's function and density functional theory approaches were all utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among all the tested models, the combination of the Becke-Perdew functional and a polarized valence basis set of triple-zeta quality provides the best representation of the electron momentum distributions for all of the 20 valence orbitals of norbornane. This experimentally validated quantum chemistry model was then used to extract some chemically important properties of norbornane. When these calculated properties are compared to corresponding results from other independent measurements, generally good agreement is found. Green's function calculations with the aid of the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than 22.5 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet photoemission and newly presented (e,2e) ionization spectra, except for the band associated with the 1a(2) (-1) one-hole state, which is probably subject to rather significant vibronic coupling effects, and a band at approximately 25 eV characterized by a momentum distribution of "s-type" symmetry, which Green's function calculations fail to reproduce. We note the vicinity of the vertical double ionization threshold at approximately 26 eV.     

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell pi-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order M?ller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order M?ller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order M?ller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.     

SCF MO CI perturbation calculations of inner shell and valence shell vertical ionization potentials

A CI method for calculating inner and valence shell vertical ionization potentials is presented. It is based on ab initio SCF MO calculations for the neutral closedshell ground state followed by CI perturbation calculations for the ground and ion states including all spin and symmetry adapted singly and doubly excited configurations with respect to the main configurations of the state of interest. The state energy is computed by performing a CI calculation for a set of selected configurations, and then adding the contributions of the remaining configurations as estimated by second order Brillouin-Wigner perturbation theory. The use of the same set of MO's for all states together with the CI perturbation method makes the method rather rapid. The numerical results are, in spite of the limited Gaussian basis sets used, in good agreement with experiment.     

Accurate energetics of small molecules containing third-row atoms Ga-Kr: a comparison of advanced ab initio and density functional theory

Advanced ab initio [coupled cluster theory through quasiperturbative triple excitations (CCSD(T))] and density functional (B3LYP) computational chemistry approaches were used in combination with the standard and augmented correlation consistent polarized valence basis sets [cc-pVnZ and aug-cc-pVnZ, where n=D(2), T(3), Q(4), and 5] to investigate the energetic and structural properties of small molecules containing third-row (Ga-Kr) atoms. These molecules were taken from the Gaussian-2 (G2) extended test set for third-row atoms. Several different schemes were used to extrapolate the calculated energies to the complete basis set (CBS) limit for CCSD(T) and the Kohn-Sham (KS) limit for B3LYP. Zero point energy and spin orbital corrections were included in the results. Overall, CCSD(T) atomization energies, ionization energies, proton affinities, and electron affinities are in good agreement with experiment, within 1.1 kcal/mol when the CBS limit has been determined using a series of two basis sets of at least triple zeta quality. For B3LYP, the overall mean absolute deviation from experiment for the three properties and the series of molecules is more significant at the KS limit, within 2.3 and 2.6 kcal/mol for the cc-pVnZ and aug-cc-pVnZ basis set series, respectively.     

The valence orbitals of NH3 by electron momentum spectroscopy: Quantitative comparisons using Hartree-Fock limit and correlated wavefunctions

The complete valence shell binding energy spectra and valence orbital electron momentum distributions for NH₃ have been measured by high-momentum-resolution electron momentum spectroscopy (EMS). The results are quantitatively compared with theoretical calculations using SCF wavefunctions ranging from DZ quality to a newly developed 126-GTO wavefunction essentially at the Hartree-Fock limit. The 3a₁ and to a lesser extent the 2a₁ valence orbital are not adequately described even at the Hartree-Fock limit with basis set saturation including diffuse functions. The differences between theory and experiment are largely resolved by ion-neutral overlap calculations using CI wavefunctions to incorporate the effects of electron correlation. The 126-G (CI) wavefunctions provide accurate calculation of a wide range of electronic properties of NH₃ and also give good quantitative prediction of the three valence orbital momentum distributions as well as a reasonable prediction of the many-body pole strength distribution observed in the (2a₁)⁻¹ inner valence binding energy spectrum. The present EMS results are compared with recent investigations of wavefunction tails by exterior electron distribution calculations and Penning ionization electron spectroscopy measurements reported by Ohno et al.     

Valence anion of thymine in the DNA pi-stack

Most of theoretical data on the stability of radical anions supported by nucleic acid bases have been obtained for anions of isolated nucleobases, their nucleosides, or nucleotides. This approach ignores the hallmark forces of DNA, namely, hydrogen bonding and pi-stacking interactions. Since these interactions might be crucial for the electron affinities of nucleobases bound in DNA, we report for the first time on the stability of the thymine valence anion in trimers of complementary bases possessing the regular B-DNA geometry but differing in base sequence. In order to estimate the energetics of electron attachment to a trimer, we developed a thermodynamic cycle employing all possible two-body interaction energies in the neutral and anionic duplex as well as the adiabatic electron affinity of isolated thymine. All calculations were carried out at the MP2 level of theory with the aug-cc-pVDZ basis set. The two-body interaction energies were corrected for the basis set superposition error, and in benchmark systems, they were extrapolated to the basis set limit and supplemented with correction for higher order correlation terms calculated at the CCSD(T) level. We have demonstrated that the sequence of nucleic bases has a profound effect on the stability of the thymine valence anion: the anionic 5'-CTC-3' (6.0 kcal/mol) sequence is the most stable configuration, and the 5'-GTG-3' (-8.0 kcal/mol) trimer anion is the most unstable species. On the basis of obtained results, one can propose DNA sequences that are different in their vulnerability to damage by low energy electron.     

Density-functional theory study of electric and magnetic properties of hexafluorobenzene in the vapor phase

A series of electric and magnetic properties of hexafluorobenzene have been calculated, including the electric dipole polarizability, magnetizability, electric quadrupole moment, and nonlinear mixed electric dipole-magnetic dipole-electric quadrupole hyperpolarizabilities needed to obtain estimates of the Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric birefringences in the vapor phase. Time-dependent density-functional theory was employed for the calculation of linear-, quadratic, and cubic response functions. A number of density functionals have been considered, along with Sadlej's triple-zeta basis set and the augmented correlation-consistent polarized valence double zeta and augmented correlation-consistent polarized valence triple zeta basis sets. Comparisons have been made with experiment where possible. The analysis of results allows for an assessment of the capability of time-dependent density-functional theory for high-order electromagnetic properties of an electron-rich system such as hexafluorobenzene.