Small-core Relativistic Pseudopotentials Research Articles

Correlation consistent basis sets for explicitly correlated wavefunctions: Pseudopotential-based basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements.

New correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements have been developed specifically for use in explicitly correlated F12 calculations. This includes orbital basis sets for valence only (cc-pVnZ-PP-F12, n = D, T, Q) and outer core-valence (cc-pCVnZ-PP-F12) correlation, along with both of these augmented with additional high angular momentum diffuse functions. Matching auxiliary basis sets required for density fitting and resolution-of-the-identity approaches to conventional and F12 integrals have also been optimized. All of the basis sets are to be used in conjunction with small-core relativistic pseudopotentials [Figgen et al., Chem. Phys. 311, 227 (2005)]. The accuracy of the basis sets is determined through benchmark calculation at the explicitly correlated coupled-cluster level of theory for various properties of atoms and diatomic molecules. The convergence of the properties with respect to the basis set is dramatically improved compared to conventional coupled-cluster calculations, with cc-pVTZ-PP-F12 results close to conventional estimates of the complete basis set limit. The patterns of convergence are also greatly improved compared to those observed from the use of conventional correlation consistent basis sets in F12 calculations.

Spectroscopic and theoretical studies of UN and UN.

The low-energy electronic states of UN and UN+ have been examined using high-level electronic structure calculations and two-color photoionization techniques. The experimental measurements provided an accurate ionization energy for UN (IE = 50 802 ± 5 cm-1). Spectra for UN+ yielded ro-vibrational constants and established that the ground state has the electronic angular momentum projection Ω = 4. Ab initio calculations were carried out using the spin-orbit state interacting approach with the complete active space second-order perturbation theory method. A series of correlation consistent basis sets were used in conjunction with small-core relativistic pseudopotentials on U to extrapolate to the complete basis set limits. The results for UN correctly obtained an Ω = 3.5 ground state and demonstrated a high density of configurationally related excited states with closely similar ro-vibrational constants. Similar results were obtained for UN+, with reduced complexity owing to the smaller number of outer-shell electrons. The calculated IE for UN was in excellent agreement with the measured value. Improved values for the dissociation energies of UN and UN+, as well as their heats of formation, were obtained using the Feller-Peterson-Dixon composite thermochemistry method, including corrections up through coupled cluster singles, doubles, triples and quadruples. An analysis of the ab initio results from the perspective of the ligand field theory shows that the patterns of electronic states for both UN and UN+ can be understood in terms of the underlying energy level structure of the atomic metal ion.

Correlation consistent basis sets for explicitly correlated wavefunctions: pseudopotential-based basis sets for the post-d main group elements Ga-Rn.

New correlation consistent basis sets, cc-pVnZ-PP-F12 (n = D, T, Q), for all the post-d main group elements Ga-Rn have been optimized for use in explicitly correlated F12 calculations. The new sets, which include not only orbital basis sets but also the matching auxiliary sets required for density fitting both conventional and F12 integrals, are designed for correlation of valence sp, as well as the outer-core d electrons. The basis sets are constructed for use with the previously published small-core relativistic pseudopotentials of the Stuttgart-Cologne variety. Benchmark explicitly correlated coupled-cluster singles and doubles with perturbative triples [CCSD(T)-F12b] calculations of the spectroscopic properties of numerous diatomic molecules involving 4p, 5p, and 6p elements have been carried out and compared to the analogous conventional CCSD(T) results. In general the F12 results obtained with a n-zeta F12 basis set were comparable to conventional aug-cc-pVxZ-PP or aug-cc-pwCVxZ-PP basis set calculations obtained with x = n + 1 or even x = n + 2. The new sets used in CCSD(T)-F12b calculations are particularly efficient at accurately recovering the large correlation effects of the outer-core d electrons.

Accurate ground-state potential energy surfaces of the C2H2–Kr and C2H2–Xe van der Waals complexes

Accurate ab initio intermolecular potential energy surfaces (IPES) have been obtained for the first time for the ground electronic state of the C2H2–Kr and C2H2–Xe van der Waals complexes. Extensive tests, including complete basis set and all-electron scalar relativistic results, support their calculation at the CCSD(T) level of theory, using small-core relativistic pseudopotentials for the rare-gas atoms and aug-cc-pVQZ basis sets extended with a set of 3s3p2d1f1g mid-bond functions. All results are corrected for the basis set superposition error. The importance of the scalar relativistic and rare-gas outer-core (n–1)d correlation effects is investigated. The calculated IPES, adjusted to analytical functions, are characterized by global minima corresponding to skew T-shaped geometries, in which the Jacobi vector positioning the rare-gas atom with respect to the center of mass of the C2H2 moiety corresponds to distances of 4.064 and 4.229 Å, and angles of 65.22° and 68.67° for C2H2–Kr and C2H2–Xe, respectively. The interaction energy of both complexes is estimated to be −151.88 (1.817 kJ mol−1) and −182.76 cm−1 (2.186 kJ mol−1), respectively. The evolution of the topology of the IPES as a function of the rare-gas atom, from He to Xe, is also discussed.

Molecular core-valence correlation effects involving the post-d elements Ga–Rn: Benchmarks and new pseudopotential-based correlation consistent basis sets

Correlation consistent basis sets that are suitable for the correlation of the outer-core (n-1)spd electrons of the post-d elements Ga-Rn have been developed. These new sets, denoted by cc-pwCVXZ-PP (X=D,T,Q,5), are based on the previously reported cc-pVXZ-PP sets that were built in conjunction with accurate small-core relativistic pseudopotentials (PPs) and designed only for valence nsp correlation. These new basis sets have been utilized in benchmark coupled cluster calculations of the core-valence correlation effects on the dissociation energies and spectroscopic properties of several small molecules. As expected, the most important contribution is the correlation of the (n-1)d electrons. For example, in the case of the group 13 homonuclear diatomics (Ga(2),In(2),Tl(2)), this leads to a dissociation energy increase compared to a valence-only treatment from 1.5 to 3.2 kcal/mol, bond length shortenings from -0.076 to -0.125 Å, and harmonic frequency increases of 7-8 cm(-1). Even in the group 15 cases (As(2),Sb(2),Bi(2)), the analogous effects of (n-1)d electron correlation are certainly not insignificant, the largest values being +4.4 kcal/mol, -0.049 Å, and +9.6 cm(-1) for the effects on D(e), r(e), and ω(e), respectively. In general, the effects increase in magnitude down a group from 4p to 6p. Correlation of the outer-core (n-1)p electrons is about an order of magnitude less important than (n-1)d but larger than that of the (n-1)s. The effect of additional tight functions for Hartree-Fock and valence sp correlation was found to be surprisingly large, especially for the post-4d and post-5d elements. The pseudopotential results for the molecules containing post-3d elements are also compared to the analogous all-electron calculations employing the Douglas-Kroll-Hess Hamiltonian. The errors attributed to the PP approximation are found to be very small.

Two-component relativistic density functional theory modeling of the adsorption of element 114(eka-lead) on gold

A cluster modeling of the interaction of an eka-Pb atom with the stable Au(111) surface using accurate small-core relativistic pseudopotentials and two-component non-collinear DFT is reported. The results obtained with two different types of exchange-correlation functionals (generalized-gradient and hybrid) are generally consistent and give rise to E114/Au(111) adsorption energy estimates within the range 0.4-0.5 eV. Substantial differences between the E114-Au and Pb-Au interactions are further corroborated.

Van der Waals interactions and dipole polarizabilities of lanthanides: Tm(F2)–He and Yb(S1)–He potentials

Anisotropic dipole polarizabilities of Tm(2F), Tm+2(2F), and Yb(1S) are calculated using the finite-field multireference averaged quadratic coupled cluster (MR-AQCC) (Tm and Tm+2) and RCCSD(T) (Yb) methods with small-core relativistic pseudopotentials ECP28MWB combined with the augmented ANO basis sets. The lanthanide atoms are strongly polarizable with the scalar part originating from the 6s electrons and the tensorial part from the open 4f shells. The adiabatic interaction potentials 2Sigma+, 2Pi, 2Delta, and 2Phi of Tm(2F)-He and Tm+2(2F)-He were examined by the multireference approaches, multireference configuration interaction and MR-AQCC, using the basis sets designed in the polarizability calculations. A closed-shell lanthanide system Yb(1S)-He was included for comparison. The Tm-He 2Sigma+, 2Pi, 2Delta, and 2Phi interaction potentials are very shallow and nearly degenerate (within 0.01 cm(-1)), with the well depths in the range of 2.35-2.36 cm(-1) at R=6.17 A. The basis-set saturated well depths are expected to be larger by ca. 25%, as estimated using the bond-function augmented basis set. The interactions of lanthanide atoms with He are one order of magnitude less anisotropic than those involving first-row transition metal atoms. The suppression of anisotropy is chiefly attributed to the screening effected by the 6s shell. When these electrons are removed as in the di-cation complex Tm+2(2F)-He, the potentials deepen to a thousand wave number range and their anisotropy is enhanced 500-fold.

Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements

Sequences of basis sets that systematically converge towards the complete basis set (CBS) limit have been developed for the coinage metals (Cu, Ag, Au) and group 12 elements (Zn, Cd, Hg). These basis sets are based on recently published small-core relativistic pseudopotentials [Figgen D, Rauhut G, Dolg M, Stoll H (2005) Chem Phys 311:227] and range in size from double- through quintuple-ζ. Series of basis sets designed for valence-only and outer-core electron correlation are presented, as well as these sets augmented by additional diffuse functions for the accurate description of negative ions and weak interactions. Selected benchmark calculations at the coupled cluster level of theory are presented for both atomic and molecular properties. The latter include the calculation of both spectroscopic and thermochemical properties of the homonuclear dimers Cu2, Ag2, and Au2, as well as the van der Waals species Zn2, Cd2, and Hg2. The CBS limit results, including the effects of core-valence correlation and spin-orbit coupling, represent some of the most accurate carried out to date and result in new recommendations for the equilibrium bond lengths of the group 12 dimers. Comparisons are also made to a limited number of all-electron Douglas–Kroll–Hess (DKH) calculations (second and third order) carried out using new correlation consistent basis sets of triple-ζ quality.

Microwave spectra of the Xe–N2 van der Waals complex: A comparison of experiment and theory

Rotational transitions for the Xe-N2 complex were measured in the frequency region from 4 to 18 GHz using a pulsed-nozzle Fourier-transform microwave spectrometer. Twelve (four) a-type transitions were recorded for the 132Xe-14N2 and 129Xe-14N2 (131Xe-15N)) isotopomers. In addition, the nuclear quadrupole hyperfine structures due to the presence of the 14N (nuclear-spin quantum number I=1) and 131Xe (I=32) nuclei were detected and analyzed. Two ab initio potential-energy surfaces were calculated at the coupled-cluster level of theory with single, double, and pertubatively included triple excitations. Dunning's augmented correlation-consistent polarized valence triple-zeta basis set was used for the nitrogen atoms. For the first surface, a well-tempered basis set with additional polarization functions was used for the Xe atom; for the second surface, a newly developed augmented correlation-consistent polarized valence quintuple-zeta basis set employing small-core relativistic pseudopotentials was used for the Xe atom. The basis sets were supplemented with bond functions for the van der Waals bond. The counterpoise correction was applied to reduce the basis-set superposition error. The resulting two surfaces both have a single minimum at a T-shaped geometry, with well depths of 122.4 and 119.3 cm(-1), respectively. Bound-state energies supported by the potential-energy surface were determined. The quality of the ab initio potential-energy surfaces was evaluated by comparison of the experimental transition frequencies and rotational and centrifugal distortion constants with those derived from the bound-state energies. A scaled potential-energy surface was obtained which has excellent agreement with the experimental data.

Relativistic effects determined using the Douglas–Kroll contracted basis sets and correlation consistent basis sets with small-core relativistic pseudopotentials

The coupled cluster approximation with single, double, and quasiperturbative triple excitations [CCSD(T)] was used in combination with the Douglas-Kroll contracted correlation consistent basis sets [cc-pVnZ-DK, where n = D(2), T(3), Q(4), and 5] and small-core relativistic pseudopotentials (PP) with correlation consistent polarized valence basis sets (cc-pVnZ-PP and aug-cc-pVnZ-PP) to investigate the impact of scalar relativistic corrections on energetic and structural properties of small molecules containing third-row (Ga-Kr) atoms. These molecules were taken from the Gaussian-2 extended test set for third-row atoms. Atomization energies, ionization energies, electron affinities, and proton affinities for molecules in the test set were determined and compared with nonrelativistic results which were obtained in a recent study in which the standard and augmented correlation consistent basis sets were used in combination with CCSD(T). Several schemes were used to extrapolate the energies to the complete basis set limit.

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 work. Diffuse-augmented basis sets, aug-cc-pVnZ-PP, have also been developed and have been used in calculations of the atomic electron affinities.

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 halogen-containing molecules using basis sets of 5Z quality.