New Relativistic Atomic Natural Orbital Basis Sets for Lanthanide Atoms with Applications to the Ce Diatom and LuF3

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are inluded as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.

Crystal and molecular structures of three 2-sulphur-substituted cyclohexanones studied by X-ray crystallography and by ab initio molecular orbital calculations

The conformational features of three 2-sulphur-substituted cyclohexanone derivatives, which differ in the number of sulphur-bound oxygen atoms, i.e. zero (I), one (II) and two (III), were investigated by single crystal X-ray crystallography and geometry optimized structures determined using Hartree-Fock method. In each of (I)-(III) an intramolecular S center dot center dot center dot O(carbonyl) interaction is found with the magnitude correlated with the oxidation state of the sulphur atom, i.e. 2.838(3) angstrom in (I) to 2.924(2) angstrom in (II) to 3.0973(18) angstrom in (III). There is an inverse relationship between the strength of this interaction and the magnitude of the carbonyl bond. The supramolecular aggregation patterns are primarily determined by C-H center dot center dot center dot O contacts and are similarly influenced by the number of oxygen atoms in the molecular structures. Thus, a supramolecular chain is found in the crystal structure of (I). With an additional oxygen atom available to participate in C-H center dot center dot center dot O interactions, as in (II), a two-dimensional array is found. Finally, a three-dimensional network is found for (III). Despite there being differences in conformations between the experimental structures and those calculated in the gas-phase, the S center dot center dot center dot O interactions persist. The presence of intermolecular C-H center dot center dot center dot O interactions involving the cyclohexanone-carbonyl group in the solid-state, disrupts the stabilising intramolecular C-H center dot center dot center dot O interaction in the energetically-favoured conformation. (I): C(12)H(13)NO(3)S, triclinic space group P (1) over bar with a = 5.392(3) angstrom b = 10.731(6) angstrom, c = 11.075(6) angstrom, alpha = 113.424(4)degrees, beta = 94.167(9)degrees, gamma = 98.444(6)degrees, V = 575.5(6) angstrom(3), Z = 2, R(1) = 0.052; (II): C(12)H(13)NO(4)S, monoclinic P2(1)/n, a = 7.3506(15) angstrom, b = 6.7814(14) angstrom, c = 23.479(5) angstrom, beta = 92.94(3)degrees, V = 1168.8(4) angstrom(3), Z = 4, R(1) = 0.046; (III): C(12)H(13)NO(5)S, monoclinic P2(1)/c, a = 5.5491(11) angstrom, b = 24.146(3) angstrom, c = 11.124(3) angstrom, beta = 114.590(10)degrees, V = 1355.3(5) angstrom(3), Z = 4, R(1) = 0.051.