Highly accurate relativistic universal Gaussian basis set: Dirac–Fock–Coulomb calculations for atomic systems up to nobelium

Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the 4s, 5s, 6s, and 7s elements

Relativistic basis sets of double-zeta, triple-zeta, and quadruple-zeta quality have been optimized in Dirac-Hartree-Fock calculations for the 4s, 5s, 6s, and 7s elements: K, Ca, Rb, Sr, Cs, Ba, Fr, and Ra. The basis sets include SCF exponents for the occupied spinors and for the np shell, exponents of correlating and polarizing functions for the (n - 1) shell and correlating functions for the (n - 2) shell. For the group 2 elements, correlating functions are given for the ns and np shells, whereas for the group 1 elements, functions for polarization of the ns shell are provided. A finite nuclear size was used in all optimizations. Prescriptions are given for constructing contracted basis sets by addition of primitives to the SCF occupied functions.

Relativistic correlating basis sets for actinide atoms from90Th to103Lr

For 14 actinide atoms from (90)Th to (103)Lr, contracted Gaussian-type function sets are developed for the description of correlations of the 5f, 6d, and 7s electrons. Basis sets for the 6d orbitals are also prepared, since the orbitals are important in molecular environments despite their vacancy in the ground state of some actinides. A segmented contraction scheme is employed for the compactness and efficiency. Contraction coefficients and exponents are so determined as to minimize the deviation from accurate natural orbitals of the lowest term arising from the 5f(n-1)6d(1)7s(2) configuration. The spin-free relativistic effects are considered through the third-order Douglas-Kroll approximation. To test the present correlating sets, all-electron calculations are performed on the ground state of (90)ThO molecule. The calculated spectroscopic constants are in excellent agreement with experimental values.

Dissociation energy of ekaplutonium fluoride E126F: The first diatomic with molecular spinors consisting of g atomic spinors

Our ab initio all-electron fully relativistic Dirac-Fock (DF) and nonrelativistic (NR) Hartree-Fock (HF) self-consistent field (SCF) calculations predict the superheavy diatomic ekaplutonium fluoride E126F to be bound with the calculated dissociation energy of 7.44 and 10.46 eV at the predicted E126-F bond lengths of 2.03 and 2.18 Angstroms, respectively. The antibinding effects of relativity to the dissociation energy of E126F are approximately 3 eV. The predicted dissociation energy with both our NR HF and relativistic DF SCF wave functions is fairly large and is comparable to that for very stable diatomics. This is the first case, where in a diatomic, an atom has g orbital (l = 4) occupied in its ground state electronic configuration and such superheavy diatomics would have occupied molecular spinors (orbitals) consisting of g atomic spinors (orbitals). This opens up a whole new field of chemistry where g atomic spinors (orbitals) may be involved in electronic structure and chemical bonding of systems of superheavy elements with Z> or =122.

Electronic structure and prediction of atomization energy of naked homoleptic uranium hexacarbonyl U(CO)6

Our ab initio all-electron fully relativistic Dirac-Fock and nonrelativistic Hartree-Fock self-consistent field (SCF) calculations predict the octahedral (Oh) uranium hexacarbonyl U(CO)6 to be bound with the calculated atomization energy of 49.84 and 48.76 eV at the predicted U-C bond lengths (assuming the C-O bond distance fixed at 1.17 A) of 2.53 and 2.63 A, respectively. Moreover, our all-electron fully relativistic Dirac-Fock SCF calculations predict U(CO)6 to be lower in energy by 3.90 eV with respect to dissociation into U plus six CO ligands. We predict U(CO)6 (Oh) to be very stable in view of our predicted large atomization energy (approximately 49 eV) and stability (approximately 4 eV) with respect to dissociation into U plus six CO molecules. Innovative techniques should be devised for the synthesis of uranium hexacarbonyl since the usual synthetic methods have failed so far for this naked actinide hexacarbonyl.

Relativistic correlating basis sets for lanthanide atoms from Ce to Lu

Contracted Gaussian-type function (CGTF) sets for the description of the 4f subshell correlation and of the 6s and 5d subshell correlation are developed for lanthanide atoms from Ce to Yb. Also prepared are basis sets for the 5d orbitals, which are vacant in the ground states of most lanthanide atoms but are essential in molecular environments. In addition, correlating CGTF sets for the 4f subshell correlation are supplemented for the Lu atom. A segmented contraction scheme is employed for their compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from accurate natural orbitals generated from configuration interaction calculations that include relativistic effects through the third-order Douglas-Kroll approximation. All-electron and model core potential calculations with the present correlating sets are performed on the ground state of the diatomic CeO molecule. The calculated spectroscopic constants are in good agreement with experimental values.

Gaussian-type function set without prolapse 1H through 83Bi for the Dirac-Fock-Roothaan equation

We have developed prolapse free Gaussian basis sets which can be used for 1H to 83Bi, imposing the condition that the Dirac-Fock-Roothaan (DFR) total energy (TE) decreases monotonically toward the numerical DF (NDF) TE as the expansion term increases. An even-tempered basis set was assumed. The resulting sets gave |TE(DFR) - TE(NDF)| < or = 1 x 10(-6) hartree for any atoms less or equal to 83Bi; TE(NDF) = -21 565.638 345, and TE(DFR) = -21,565.638 345 +/- 0.000 001 hartree for Bi when the expansion terms are in the range (58, 58, 58, 36, 36, 36, and 36) and (72, 72, 72, 36, 36, 36, and 36) for (s+, p-, p+, d-, d+, f-, and f+) symmetries, respectively. A practical set with 44, 44, 44, 36, 36, 32, and 32 for the respective symmetries is also proposed where |TE(DFR) - TE(NDF)| < or = 4 x 10(-5).

Relativistic correlating basis sets for the sixth-period d-block atoms from Lu to Hg

Contracted Gaussian-type function sets to describe valence correlation are developed for the sixth-period d-block atoms Lu through Hg. A segmented contraction scheme is employed for their compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from accurate natural orbitals generated from configuration interaction calculations, in which relativistic effects are incorporated through the third-order Douglas-Kroll approximation. The present basis sets yield more than 99% of atomic correlation energies predicted by accurate natural orbital sets of the same size. Relativistic model core potential calculations with the present correlating sets give the spectroscopic constants of the AuH molecule in excellent agreement with experimental results.

A polynomial version of the generator coordinate Dirac-Fock method

A polynomial version of the Generator Coordinate Dirac-Fock (p-GCDF) method is introduced and applied to develop Adapted Gaussian Basis Sets (AGBS) for helium- and beryllium-like atomic species (He, Ne +8, Ar +16, Sn +48, Be, Ne +6, Ar +14, and Sn +46) and for Kr and Xe atoms. The Dirac-Fock-Coulomb and Dirac-Fock-Breit energies obtained with these basis sets are in excellent agreement with numerical finite-difference calculations. Moreover, the sizes of the AGBS generated here with the p-GCDF method are significantly smaller than the size of previous relativistic Gaussian basis sets.

Gaussian-type function set without prolapse for the Dirac-Fock-Roothaan equation

A Gaussian-type function (GTF) set without a prolapse (variation collapse) is generated for the Dirac-Fock-Roothaan (DFR) equation. The test atom was mercury. The number of primitive GTFs used is between 7 and 62 (abbreviated as 7-62), 6-62, 6-62, 4-36, 4-36, 3-36, and 3-36 for s(+), p(-), p(+), d(-), d(+), f(-), and f(+) symmetries. The respective exponent parameters were determined with even-tempered manner, which requires the minimum and maximum exponents for the respective symmetries. We prepared several sets of these. The total energy (TE) given by the numerical DF (NDF) is -19648.849250 hartree; one of the present sets with largest number of expansion terms gave -19648.849251 hartree. The error (deltaTE) relative to the NDR TE is quite small. We then applied this set to the inert gas atoms Ne (10), Ar (18), Kr (36), Xe (54), Rn (86), and No (102), and also to Es (99) as the representative of the open shell atoms. The absolute values of deltaTE were at most 2.8 x 10(-6) hartree, showing the potential of this set as a universal set.

On 'infinite basis set limits' in molecular electronic structure calculations

Sequences of basis sets can be constructed so as to approach the 'infinite basis set limit' in molecular electronic structure calculations. Extrapolation procedures can also be devized to provide accurate values of this limit. However, some care is required since the 'infinite basis set limit' may not correspond to the limit supported by a complete basis set. Extrapolation procedures can then lead to limiting values, which are not estimates of the exact solutions.