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.     

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     

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.     

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.     

Automatically generated Coulomb fitting basis sets: design and accuracy for systems containing H to Kr

For intermediate sized chemical systems the use of an auxiliary basis set (ABS) to fit the charge density provides a useful means of accelerating the performance of various quantum chemical methods. As a consequence much effort has been devoted to the design of various ABSs. This paper explores a fundamentally new approach where the ABS is created dynamically based on the specific orbital basis set (OBS) being used. The new approach includes a parameter that is used to coalesce candidate fitting functions together but which can also be used to provide some coarse grain control over the number of functions in the ABS. The accuracy of the new automatically generated ABS (auto-ABS) is systemically studied for a variety of small systems containing the elements H-Kr. Errors in the Coulomb energy computed using auto-ABS and with a variety of OBSs are shown to be small compared to errors in the Hartree-Fock energy due to incompleteness in the OBS. In contrast to fixed size ABSs, the use of auto-ABS is shown to lead to smaller errors as the size (quality) of the OBS is expanded. The performance of auto-ABS is also compared with the use of the recently proposed universal fitting sets [Weigend, Phys. Chem. Chem. Phys. 8, 1057 (2006)] for 180 compounds containing atoms from H to Kr.     

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.     

Some valence bond calculations for H2 with 1s and 2p basis sets

Summary The results ofab initio valence bond calculations are reported for H₂, with up to 16 nuclear centred and eight midbond 1s and 2p AOs included in them. The 24 AO calculation, with 116S=0 spin structures, gives an STO-6G energy of –1.17237 a.u., which is close to an MP4 estimate of –1.17256 a.u.     

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.     

BSSE-correction scheme for consistent gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations

Revised versions of our published pob-TZVP [Peintinger, M. F.; Oliveira, D. V. and Bredow, T., J. Comput. Chem., 2013, 34 (6), 451–459.] and unpublished pob-DZVP basis sets, denoted as pob-TZVP-rev2 and pob-DZVP-rev2, have been derived for the elements H Br. It was observed that the pob basis sets suffer from the basis set superposition error (BSSE). In order to reduce this effect, we took into account the counterpoise energy of hydride dimers as an additional parameter in the basis set optimization. The overall performance, portability, and SCF stability of the resulting rev2 basis sets are significantly improved compared to the original pob basis sets. © 2019 Wiley Periodicals, Inc.     

Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn

The introduction of the resolution-of-the-identity (RI) approximation for electron repulsion integrals in quantum chemical calculations requires in addition to the orbital basis so-called auxiliary or fitting basis sets. We report here such auxiliary basis sets optimized for second-order Møller–Plesset perturbation theory for the recently published (Weigend and Ahlrichs Phys Chem Chem Phys, 2005, 7, 3297–3305) segmented contracted Gaussian basis sets of split, triple-ζ and quadruple-ζ valence quality for the atoms Rb–Rn (except lanthanides). These basis sets are designed for use in connection with small-core effective core potentials including scalar relativistic corrections. Hereby accurate resolution-of-the-identity calculations with second-order Møller–Plesset perturbation theory (MP2) and related methods can now be performed for molecules containing elements from H to Rn. The error of the RI approximation has been evaluated for a test set of 385 small and medium sized molecules, which represent the common oxidation states of each element, and is compared with the one-electron basis set error, estimated based on highly accurate explicitly correlated MP2–R12 calculations. With the reported auxiliary basis sets the RI error for MP2 correlation energies is typically two orders of magnitude smaller than the one-electron basis set error, independent on the position of the atoms in the periodic table.     

Polarized basis sets of Slater-type orbitals: H to Ne atoms

We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree-Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H(2) or Li(2)) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions.     

Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar

Correlation consistent basis sets have been optimized for use with explicitly correlated F12 methods. The new sets, denoted cc-pVnZ-F12 (n=D,T,Q), are similar in size and construction to the standard aug-cc-pVnZ and aug-cc-pV(n+d)Z basis sets, but the new sets are shown in the present work to yield much improved convergence toward the complete basis set limit in MP2-F12/3C calculations on several small molecules involving elements of both the first and second row. For molecules containing only first row atoms, the smallest cc-pVDZ-F12 basis set consistently recovers nearly 99% of the MP2 valence correlation energy when combined with the MP2-F12/3C method. The convergence with basis set for molecules containing second row atoms is slower, but the new DZ basis set still recovers 97%-99% of the frozen core MP2 correlation energy. The accuracy of the new basis sets for relative energetics is demonstrated in benchmark calculations on a set of 15 chemical reactions.     

Correlating basis sets for the H atom and the alkali-metal atoms from Li to Rb

 Contracted Gaussian-type function sets are developed for correlating p, d, and f functions for a valence electron of the hydrogen atom and alkali-metal atoms from Li to Rb. A segmented contraction scheme is used for its compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from the K orbitals of the atoms. The present basis sets yield an accuracy comparable to the correlation-consistent basis set for the hydrogen atom and also give a similar high accuracy for the alkali-metal atoms. In the calculations of spectroscopic constants of alkali hydrides, the decontraction of the p function plays an important role, especially for LiH. The contributions of d and f functions are nontrivial for KH and RbH. Received: 6 September 2002 / Accepted: 13 November 2002 / Published online: 19 March 2003 Acknowledgements. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. Correspondence to: T. Noro e-mail: tashi@sci.hokudai.ac.jp     

Uniform quality gaussian basis sets for molecular calculations. V. Property optimization: A study on H2O

Energy optimization (Eo) and property optimization (PO) were performed on the H₂O molecule. A definition of the “optimality” κ, a dimensionless quantity of the form has been proposed where ω_i is a weighting factor, 〈ǒ〉_i is the computed observable, and O_i is the corresponding property measured experimentally. The minimization of κ leads to property optimization methods (POM) which is a useful alternative to energy optimization methods (EOM).     

Electrically polarized valence basis sets for the SBKJC effective core potential developed for calculations of dynamic polarizabilities and Raman intensities

Sadlej’s electric polarization method of Gaussian basis functions was applied to the double-zeta effective core potential basis sets of Stevens, Basch, Krauss, Jasien and Cundari to generate a new augmented polarized valence double-zeta set, named as pSBKJC, which is appropriate for the calculation of dynamic polarizabilities and Raman intensities. The pSBKJC basis set was developed for the atoms of families 14–17 (from C to F, Si to Cl, Ge to Br and Sn to I). In order to assess the performance of this new basis set, these properties were compared to those evaluated using Sadlej’s set, available in the EMSL online library under the name of Sadlej-pVTZ. In these tests, Hartree-Fock/pSBKJC calculations have proved to be less demanding of the computer than the Hartree-Fock/Sadlej-pVTZ ones but give results in excellent agreement with those from the Sadlej-pVTZ basis set. Since the Stevens et al. pseudopotential can represent the scalar relativistic effects, the results obtained at the Hartree-Fock/pSBKJC level show a better agreement with the results of Dirac-Hartree-Fock/Sadlej-pVTZ relativistic calculations using Dyall’s spin-free Hamiltonian. When comparing Hartree-Fock/pSBKJC data of Raman scattering activities, at the excitation wavelength of 488 nm, with those of spin-free Dirac-Hartree-Fock/Sadlej-pVTZ calculations, a very good agreement is observed, where the RMS error is 8.5 Å⁴a.m.u.^?1 and the averaged percentage error is 3.4%. In terms of computer savings in calculations of dynamic Raman intensities, a 20% reduction in the CPU time in the coupled cluster singles and doubles intensities of C₆H₆ and about 40% reduction in the time-dependent Hartree-Fock intensities for C₆F₆ molecules were attained.     

Ab initio calculations on sulfur-containing compounds. I. Uniform quality basis sets for sulfur: Total energies and geometries of H2S

Uniform quality basis sets (UQ-NG ; N=3, 4, 5), with s = p and s ≠ p, and a 6-31 G^* basis set have been optimized for the sulfur atom. These uniform quality basis sets in their uncontracted and contracted forms were used, together with other basis sets reported in the literature (a total of 40 basis sets), to study their accuracy in predicting the bond length and bond angle of H₂S.     

GF calculation with minimal and extended basis sets for H2O,NH3, CH4 and H2O2

A method is proposed for applying the theory of generalized group functions to SCF-GF calculations with large basis sets. A simple procedure for localising the SCF-MO's resulting from a standard SCF calculation is described, with applications to H₂O, NH₃, CH₄ and H₂O₂. Results compare quite favourably with those obtained by the usual GF method. It is shown that when basis functions are the SCF-MO's and there are only two functions per group, the GF approach is practically equivalent to a configuration interaction treatment where only double excitations within the groups are considered.

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Zusammenfassung Es wird eine Methode zur Anwendung von verallgemeinerten Gruppenfunktionen auf SCF-GF-Rechnungen mit großen Basissätzen vorgeschlagen. Ferner wird ein einfaches Verfahren zur Lokalisierung von SCF-MO's angegeben und auf H₂O, NH₃, CH₄ und H₂O₂ angewendet. Die Resultate sind denen üblicher GF-Methoden ähnlich. Wenn als Basisfunktionen SCF-Funktionen, und zwar nur zwei je Gruppe, angewendet werden, ist der GF-Ansatz praktisch einer CI-Rechnung mit maximal Zweifachanregungen äquivalent.

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Résumé On propose une méthode pour appliquer la théorie des fonctions de groupes généralisés à des calculs SCF GF dans des bases de grande dimension. Un procédé de localisation simple est décrit, il permet de localiser les orbitales SCF ordinaires et est appliqué à H₂O,NH₃, CH₄ et H₂O₂. Les résultats obtenus sont comparables à ceux fournis par la méthode GF ordinaire. Lorsque les fonctions de base sont les O.M. S.C.F. et qu'il n'y a que deux fonctions par groupe, la méthode GF est pratiquement équivalente à une interaction de configuration où seules seraient prises en considération les diexcitations à l'intérieur des groupes.