Kirk A. Peterson

Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton

Valence correlation consistent and augmented correlation consistent basis sets have been determined for the third row, main group atoms gallium through krypton. The methodology, originally developed for the first row atoms, was first applied to the selenium atom, resulting in the expected natural groupings of correlation functions (although higher angular momentum functions tend to be relatively more important for the third row atoms as they were for the second row atoms). After testing the generality of the conclusions for the gallium atom, the procedure was used to generate correlation consistent basis sets for all of the atoms gallium through krypton. The correlation consistent basis sets for the third row main group atoms are as follows: cc-pVDZ: (14s11p6d)/[5s4p2d]; cc-pVTZ: (20s13p9d1f )/[6s5p3d1f]; cc-pVQZ: (21s16p12d2 f1g)/[7s6p4d2 f1g]; cc-pV5Z: (26s17p13d3f2g1h)/[8s7p5d3f2g1h]. Augmented sets were obtained by adding diffuse functions to the above sets (one for each angular momentum present in th...

Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16–18 elements

A series of correlation consistent basis sets have been developed for the post-d group 16–18 elements in conjunction with small-core relativistic pseudopotentials of the energy-consistent variety. The latter were adjusted to multiconfiguration Dirac–Hartree–Fock data based on the Dirac–Coulomb–Breit Hamiltonian. The outer-core (n−1)spd shells are explicitly treated together with the nsp valence shell with these PPs. The accompanying cc-pVnZ-PP and aug-cc-pVnZ-PP basis sets range in size from DZ to 5Z quality and yield systematic convergence of both Hartree–Fock and correlated total energies. In addition to the calculation of atomic electron affinities and dipole polarizabilities of the rare gas atoms, numerous molecular benchmark calculations (HBr, HI, HAt, Br2, I2, At2, SiSe, SiTe, SiPo, KrH+, XeH+, and RnH+) are also reported at the coupled cluster level of theory. For the purposes of comparison, all-electron calculations using the Douglas–Kroll–Hess Hamiltonian have also been carried out for the haloge...

A comparison of the efficiency and accuracy of the quadratic configuration interaction (QCISD), coupled cluster (CCSD), and Brueckner coupled cluster (BCCD) methods

Abstract The coupled-cluster method restricted to single and double excitations from a closed-shell reference function (CCSD) and the corresponding quadratic configuration interaction method (QCISD) are formulated in terms of quantities which can be computed directly from the two-electron integrals in AO basis. A simple yet effective method to accelerate convergence in Brueckner coupled-cluster (BCCD) calculations is also described. Using this procedure BCCD calculations require no more effort than CCSD calculations. In order to compare the accuracy of all three methods potential energy functions and spectroscopic constants have been calculated for N 2 , CO, F 2 , and HF using large basis sets.

Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2→H2+H reaction

Using systematic sequences of correlation consistent Gaussian basis sets from double to sextuple zeta quality, the classical barrier height of the H+H2 exchange reaction has been calculated by multireference configuration interaction (MRCI) methods. The MRCI calculations for collinear H3 have also been calibrated against large basis set full CI (FCI) results, which demonstrate that the MRCI treatment leads to energies less than 1 μhartree (≤0.001 kcal/mol) above the FCI energies. The dependence of both the H2 and H3 total energies on the basis set is found to be very regular, and this behavior has been used to extrapolate to the complete basis set (CBS) limits. The resulting estimate of the H–H–H CBS limit yields a classical barrier height, relative to exact H+H2, of 9.60±0.02 kcal/mol; the best directly calculated value for the barrier is equal to 9.62 kcal/mol. These results are in excellent agreement with recent quantum Monte Carlo calculations.

Accurate correlation consistent basis sets for molecular core–valence correlation effects: The second row atoms Al–Ar, and the first row atoms B–Ne revisited

Correlation consistent basis sets for accurately describing core–core and core–valence correlation effects in atoms and molecules have been developed for the second row atoms Al–Ar. Two different optimization strategies were investigated, which led to two families of core–valence basis sets when the optimized functions were added to the standard correlation consistent basis sets (cc-pVnZ). In the first case, the exponents of the augmenting primitive Gaussian functions were optimized with respect to the difference between all-electron and valence–electron correlated calculations, i.e., for the core–core plus core–valence correlation energy. This yielded the cc-pCVnZ family of basis sets, which are analogous to the sets developed previously for the first row atoms [D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 103, 4572 (1995)]. Although the cc-pCVnZ sets exhibit systematic convergence to the all-electron correlation energy at the complete basis set limit, the intershell (core–valence) correlation energ...

Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited

For molecules containing second row atoms, unacceptable errors have been found in extrapolating dissociation energies calculated with the standard correlation consistent basis sets to the complete basis set limit. By carefully comparing the convergence behavior of De(O2) and De(SO), we show that the cause of these errors is a result of two inter-related problems: near duplication of the exponents in two of the d sets and a lack of high-exponent functions in the early members of the sets. Similar problems exist for the f sets (and probably in higher angular momentum sets), but have only a minor effect on the calculated dissociation energies. A number of approaches to address the problems in the d sets were investigated. Well behaved convergence was obtained by augmenting the (1d) and (2d) sets with a high-exponent function and by replacing the (3d) set by the (4d) set and the (4d) set by the (5d) set and so on. To ensure satisfactory coverage of both the L and M shell regions, the exponents of the new d se...

Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn.

Sequences of basis sets that systematically converge towards the complete basis set (CBS) limit have been developed for the first-row transition metal elements Sc-Zn. Two families of basis sets, nonrelativistic and Douglas-Kroll-Hess (-DK) relativistic, are presented that range in quality from triple-zeta to quintuple-zeta. Separate sets are developed for the description of valence (3d4s) electron correlation (cc-pVnZ and cc-pVnZ-DK; n = T,Q, 5) and valence plus outer-core (3s3p3d4s) correlation (cc-pwCVnZ and cc-pwCVnZ-DK; n = T,Q, 5), as well as these sets augmented by additional diffuse functions for the description of negative ions and weak interactions (aug-cc-pVnZ and aug-cc-pVnZ-DK). Extensive benchmark calculations at the coupled cluster level of theory are presented for atomic excitation energies, ionization potentials, and electron affinities, as well as molecular calculations on selected hydrides (TiH, MnH, CuH) and other diatomics (TiF, Cu2). In addition to observing systematic convergence towards the CBS limits, both 3s3p electron correlation and scalar relativity are calculated to strongly impact many of the atomic and molecular properties investigated for these first-row transition metal species.

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.

Systematically convergent basis sets with relativistic pseudopotentials. I. Correlation consistent basis sets for the post-d group 13–15 elements

New correlation consistent-like basis sets have been developed for the post-d group 13–15 elements (Ga–As, In–Sb, Tl–Bi) employing accurate, small-core relativistic pseudopotentials. The resulting basis sets, which are denoted cc-pVnZ-PP, are appropriate for valence electron correlation and range in size from (8s7p7d)/[4s3p2d] for the cc-pVDZ-PP to (16s13p12d3f2g1h)/[7s7p5d3f2g1h] for the cc-pV5Z-PP sets. Benchmark calculations on selected diatomic molecules (As2, Sb2, Bi2, AsN, SbN, BiN, GeO, SnO, PbO, GaCl, InCl, TlCl, GaH, InH, and TlH) are reported using these new basis sets at the coupled cluster level of theory. Much like their all-electron counterparts, the cc-pVnZ-PP basis sets yield systematic convergence of total energies and spectroscopic constants. In several cases all-electron benchmark calculations were also carried out for comparison. The results from the pseudopotential and all-electron calculations were nearly identical when scalar relativity was accurately included in the all-electron wo...

Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y-Pd

Scalar-relativistic pseudopotentials and corresponding spin-orbit potentials of the energy-consistent variety have been adjusted for the simulation of the [Ar]3d(10) cores of the 4d transition metal elements Y-Pd. These potentials have been determined in a one-step procedure using numerical two-component calculations so as to reproduce atomic valence spectra from four-component all-electron calculations. The latter have been performed at the multi-configuration Dirac-Hartree-Fock level, using the Dirac-Coulomb Hamiltonian and perturbatively including the Breit interaction. The derived pseudopotentials reproduce the all-electron reference data with an average accuracy of 0.03 eV for configurational averages over nonrelativistic orbital configurations and 0.1 eV for individual relativistic states. Basis sets following a correlation consistent prescription have also been developed to accompany the new pseudopotentials. These range in size from cc-pVDZ-PP to cc-pV5Z-PP and also include sets for 4s4p correlation (cc-pwCVDZ-PP through cc-pwCV5Z-PP), as well as those with extra diffuse functions (aug-cc-pVDZ-PP, etc.). In order to accurately assess the impact of the pseudopotential approximation, all-electron basis sets of triple-zeta quality have also been developed using the Douglas-Kroll-Hess Hamiltonian (cc-pVTZ-DK, cc-pwCVTZ-DK, and aug-cc-pVTZ-DK). Benchmark calculations of atomic ionization potentials and 4d(m-2)5s(2)-->4d(m-1)5s(1) electronic excitation energies are reported at the coupled cluster level of theory with extrapolations to the complete basis set limit.