Energy-adjusted pseudopotentials for the rare earth elements

Nonrelativistic and quasirelativistic energy-adjusted pseudopotentials and optimized (7s6p5d)/[5s4p3d]-GTO valence basis sets for use in molecular calculations for fixed f-subconfigurations of the rare earth elements, La through Lu, have been generated. Atomic excitation and ionization energies from numerical HF, as well as SCF pseudopotential calculations using the derived basis sets, differ by less than 0.1 eV from numerical HF all-electron results. Corresponding values obtained from CI(SD), CEPA-1, as well as density functional calculations using the quasirelativistic pseudopotentials, are in reasonable agreement with experimental data.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd ⁿ ,d ^n–1 s, andd ^n–2 s ² for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.     

Energy-adjustedab initio pseudopotentials for the second and third row transition elements: Molecular test for M2 (M=Ag,Au) and MH (M=Ru,Os)

Summary Recently published nonrelativistic and quasirelativistic energy-adjustedab initio pseudopotentials representing the M^(Z–28)+ cores of the second row transition metal atoms and the M^(Z–60)+ cores of the third row transition metal atoms have been tested in SCF, CI(SD) and CEPA1 calculations of the spectroscopic constants (R _e ,D _e , and _e ) of the ground states of the neutral and singly charged silver and gold dimers, and in state averaged CASSCF and multi-reference CI(SD) calculations of the spectroscopic constants (R _e ,D _e , _e , _e , /R). Comparison is made with experimental and reliable theoretical data where available; in the case of the hydrides, additional calculations with pseudopotentials published by other groups have been made for comparison.     

The well-tempered model core potentials for the main-group elements Li–Rn

The well-tempered model core potential (wtMCP) parameters and valence basis sets, based on the well-tempered basis set expansion, were developed for the main-group elements Li–Rn. For the s–block elements, the valence space comprises the ns valence shell and the outermost core (n–1)p shell. For the p-block elements, the ns and np shells together with the (n–1)d shell make up the valence space. Nonrelativistic wtMCPs were developed for all atoms. Scalar-relativistic wtMCPs were prepared for all atoms heavier than Ar by using the relativistic elimination of small components to obtain the reference and core orbitals. The new potentials were tested at the restricted Hartree–Fock, second-order Mø øller–Plesset perturbation theory and density functional theory with Beckes three-parameter hybrid functional combined with Perdews 1991 gradient-corrected correlation functional levels for several diatomic molecules and the results were compared with those obtained from all-electron calculations and experimental values. Excellent agreement between the results was obtained.     

Accurate Ab Initio Calculations for LiH and its Ions, LiH+ and LiH−

Ab initio calculations were performed for LiH using a pseudopotential approach with CPP corrections and huge basis sets on both atoms. A wide range of ^1,3Σ⁺ electronic adiabatic states have been investigated, from the ground state up to those dissociating into Li(5p)+H. Permanent and transition electric dipole moments are also considered for the first few excited states. Comparison with experiments and recent all-electron calculations, reveals an excellent global accuracy, only the bottom of the ground state being better described by all-electron approaches. Using almost identical basis sets, coupled cluster all-electron calculations are performed for the ground states of LiH⁺, LiH⁻ and LiH. High care has been given to the correct relative position of the asymptotes, allowing for this rather complete set of accurate ab initio data to be useful for further molecular physics studies.     

Compact basis sets for LCAO-LSD calculations. Part I: Method and bases for Sc to Zn

A method for preparing compact orbital and auxiliary basis sets for LCAO-LSD calculations has been developed. The method has been applied to construct basis sets for first row transition metal atoms from Sc to Zn for the 3d^n?14s¹ and 3d^n?24s² configurations. The properties of different expansion patterns have been tested in atomic calculations for the chromium atom.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Summary Generally contracted basis sets for first row atoms have been constructed using the Atomic Natural Orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over several atomic states, positive and negative ions, and atoms in an external electric field. The contracted basis sets give virtually identical results as the corresponding uncontracted sets for the atomic properties, which they have been designed to reproduce. The design objective has been to describe the ionization potential, the electron affinity, and the polarizability as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations. The starting primitive sets are 8s4p3d for hydrogen, 9s4p3d for helium, and 14s9p4d3f for the heavier first row atoms.     

A note on the importance of d orbitals in the calculation of effective interactions and the excitation spectra of atoms and molecules

The focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation-cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen-like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the ³P → ¹D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.     

Why do the second row transition metal atoms prefer 5s14dm+1 to 5s24dm?

Numerical Hartree-Fock (NHF) calculations have been performed for 332 ground and low-lying excited states of the fifth period atoms Rb through Xe, with our special interest in the states arising from the 5s ²4d ^m , 5s ¹4d ^m +1, and 5s ⁰ 4d ^m +2 configurations of the second row transition metal atoms. Among various properties, orbital energies and mean values ofr of the outermost orbitals of each symmetry are presented as well as total energies. It is discussed in some detail why the second row transition metal atoms have a tendency to prefers ¹ d ^m +1 as the ground configuration in contrast to the preferreds ² d ^m configuration in the first row transition metal atoms. Our systematic NHF computations reported in this and the previous papers conclude that the Hartree-Fock method correctly predicts the experimental ground state of the atoms He through Xe with the sole exception for Zr.     

Large atomic natural orbital basis sets for the first transition row atoms

Large atomic natural orbital (ANO) basis sets are tabulated for the Sc to Cu atoms. The primitive sets are taken from the large sets optimized by Partridge, namely (21s13p8d) for Sc and Ti and (20s12p9d) for V to Cu. These primitive sets are supplemented with threep, oned, sixf, and fourg functions. The ANO sets are derived from configuration interaction density matrices constructed as the average of the lowest states derived from the 3d ⁿ 4s ² and 3d ⁿ⁺¹4s ¹ occupations. For Ni, the¹ S(3d ¹⁰) state is included in the averaging. The choice of basis sets for molecular calculations is discussed.     

Atomic SCF valence orbitals for first transition series metals

A consistent set of 4s, 4p, and 3d orbitals are reported that are linear combinations of Slatertype functions for the highest multiplicity term of the configurations 3d ⁿ–2 4s ¹4p ¹ for the metals titanium through copper.Research supported by the National Science Foundation, Grant No.NSF-GP-5498.NIH Predoctoral Fellow (1968–1970).Research Engineer; Dow Chemical Company, Freeport, Texas 77541.     

Core projection effects in atomic frozen-core calculations: A numerical analysis

Frozen-core calculations on the (He) 2s²2p⁶ – ¹S state of the F^? ion and the (Ar) 3d⁴4s² – ⁵D state of the Cr atom, obtained with differently reduced basis sets and different core-projection schemes, are presented and compared with the corresponding all-electron results in order to analyze the behavior of the core projection under these circumstances. Severe truncation of the valence basis set can give frozen-core results noticeably deviated from the all electron values if the regular projection (projection factors x_g = 2.0) is adopted. Much better results are obtained in these cases if a softer projection (x_g = 1.0) is used for those core orbitals having high electronic density in regions where the valence basis set has low flexibility. In these circumstances the expectation value of the core projector becomes a nonvanishing correction to the valence energy because the core-valence orthogonality is incomplete after core projection.     

High-quality Gaussian basis sets for fourth-row atoms

Summary Energy-optimized Gaussian basis sets of triple-zeta quality for the atoms Rb-Xe have been derived. Two series of basis sets are developed; (24s 16p 10d) and (26s 16p 10d) sets which we expand to 13d and 19p functions as the 4d and 5p shells become occupied. For the atoms lighter than Cd, the (24s 16p 10d) sets with triple-zeta valence distributions are higher in energy than the corresponding double-zeta distribution. To ensure a triple-zeta distribution and a global energy minimum the (26s 16p 10d) sets were derived. Total atomic energies from the largest basis sets are between 198 and 284E _H above the numerical Hartree-Fock energies.     

Recursion formulae for calculation of overlap integrals

Multi-ζ Slater-type orbitals are frequently used in molecular orbital calculations. Master formulae and numerical tables are available in literature for overlap integrals between s, p, and d atomic orbitals up to principal quantum number (n) = 3 and for some other selected quantum numbers. However, no master formula or numerical table is available for quantum numbers n = 5 and above and involving ? orbitals. In this article recursion formulae have been presented for the calculation of the overlap integral between any two s, p, d, and ? atomic orbitals formed by a linear combination of Slater-type orbitals. These formulae, when expanded, would give rise to all the master formulae reported in the literature as well as formulae hitherto unreported.