Generator coordinate Hartree–Fock method applied to the choice of a contracted Gaussian basis for the second-row atoms

The generator coordinate Hartree–Fock (GCHF) method is employed as a criterion for the selection of a 18s12p Gaussian basis for the atoms Na–Ar. The role of the weight functions in the assessment of the numerical integration range of the GCHF equations is shown. The extended basis is then contracted to (10s6p) by a standard procedure and in combination with the previously contracted (7s5p) Gaussian basis for the atoms Li–Ne is enriched with polarization functions. This basis is tested for AlF, SiO, PN, BCl, and P₂. The properties of interest were HF total energies, MP2 dipolar moments, bond distances, and dissociation energies. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 927–934, 1997     

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.     

Valence p functions for alkali and alkaline-earth atoms

Contracted Gaussian-type function (CGTF) basis sets are reported for valence p orbitals of the six alkali and alkaline-earth atoms Li, Be, Na, Mg, K, and Ca for molecular applications. These sets are constructed by Roothaan–Hartree–Fock calculations for the ns → np excited states of atoms, in which both linear and nonlinear parameters of CGTFs are variationally optimized. The present CGTF sets reproduce well the numerical Hartree–Fock ns → np excitation energies: the largest error is 0.0009 hartrees for Li. New CGTFs are tested with diatomic Li₂, Na₂, K₂, and MH molecules, where M = Li, Be, Na, Mg, K, and Ca, by self-consistent-field (SCF) and multiconfiguration SCF calculations. The resultant spectroscopic constants compare well with those of more elaborate calculations and are sufficiently close to experimental values, supporting the efficiency of the present set for the valence p orbitals. Received: 9 July 1998 / Accepted: 17 September 1998 / Published online: 1 February 1999     

Long range interaction energies using Gaussian basis sets and a one center method

A one center method, based on the work of Karplus and Kolker, is discussed and used to calculate the induction energy, through O(R^?8), for the H(ls) – H⁺ interaction employing two types of Gaussian basis sets constructed from functions of the form {r^je^?αr2}. The effective hydrogen atom excitation energies and transition multipole moment matrix elements generated in these calculations are used to calculate the dispersion energy for the H(ls) – H(ls) interaction, through O(R^?10), and the R^?9 triple dipole energy corresponding to the interaction of three H(ls) atoms. The results indicate that Gaussian functions can form good basis sets for obtaining long range forces for a variety of multipole interaction energies.     

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.     

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

Summary Generally contracted basis sets for second 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 17s12p5d4f for the second row atoms Na-Ar. Corresponding ANO basis sets for first row atoms have recently been published.     

Electronic structure of first and second row atoms under harmonic confinement

Atoms under pressure undergo a number of modifications of their electronic structure. Good examples are the spontaneous ionization, stabilization of excited-state configurations, and contraction of atomic-shells. In this work, we study the effects of confinement with harmonic potentials on the electronic structure of atoms from H to Ne. Dynamic and static correlation is taken into account with coupled cluster with single and double excitations and CASSCF calculations. Because the strength of harmonic confinement cannot be translated into pressure, we envisioned a “calibration” method to transform confinement into pressure. We focused on the effect of confinement on: (a) changes of electron distribution and localization within the K and L shells, (b) confinement-induced ionization pressure, (c) level crossing of electronic states, and (d) correlation energy. We found that contraction of valence and core-shells are not negligible and that the use of standard pseudopotentials might be not adequate to study solids under extreme pressures. The critical pressure at which atoms ionize follows a periodic trend, and it ranges from 28 GPa for Li to 10.8 TPa for Ne. In Li and Be, pressure induces mixing of the ground state configuration with excited states. At high pressure, the ground states of Li and Be become a doublet and a triplet with configurations 1s²2p and 1s²2s2p, respectively, which could change the chemistry of Be. Finally, it is observed that atoms with fewer electrons correlation increases, but for atoms with more electrons, the increasing of kinetic energy dominates over electron correlation.     

Theoretical study of LiK and LiK+ in adiabatic representation

The potential energy curves have been calculated for the electronic states of the molecule LiK within the range 3 to 300 a.u., of the internuclear distance R. Using an ab initio method, through a semiempirical spin-orbit pseudo-potential for the Li (1s ²) and K (1s ²2s ²2p ⁶3s ²3p ⁶) cores and core valence correlation correction added to the electrostatic Hamiltonian with Gaussian basis sets for both atoms. The core valence effects including core-polarization and core-valence correlation are taken into account by using an l-dependent core-polarization potential. The molecular orbitals have been derived from self-consistent field (SCF) calculation. The spectroscopic constants, dipole moments and vibrational levels of the lowest electronic states of the LiK molecule dissociating into K (4s, 4p, 5s, 3d, and 5p) + Li (2s, 2p, 3s, and 3p) in ^{1, 3}Σ, ^{1, 3}Π, and ^{1, 3}Δ symmetries. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiK⁺ dissociating into Li (2s, 2p, 3s, and 3p) + K⁺ and Li⁺ + K (4s, 4p, 5s, 3d, and 5p). The comparison of the present results with those available in the literature shows a very good agreement in spectroscopic constants of some lowest states of the LiK and LiK⁺ molecules, especially with the available theoretical works. The existence of numerous avoided crossing between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺K and LiK⁺.     

Uniform quality gaussian basis sets for molecular calculations. III. Charge optimized basis sets

Gradient optimized constrained (2s ≠ 2p) and unconstrained (2s ≠ 2p) Gaussian 3G basis sets are reported for the first-row atoms and ions X^O, for Q = ?2 to +4. Analytic equations have been fitted to the logarithm of the exponents as a function of the nuclear charge Z and formal charge Q. Consequently only two parameters Z and Q have to be specified in order to completely define a basis set.     

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.     

Valence 4p functions for the first-row transition metal atoms

For the valence 4p orbitals of the first-row transition metal atoms Sc through Zn, Gaussian-type basis functions are developed referring to excited 3d ^m 4s ¹4p ¹ electronic configurations. Molecular tests of the present work 4p sets are performed for the Cu atom, the diatomic Cu₂ molecule, and Cu₉ and Cu₁₃ clusters, and the results are compared with those from two literature sets. Received: 17 January 2000 / Accepted: 30 May 2000 / Published Online: 11 September 2000     

Collision spectroscopy with aligned and oriented atoms

Neutralisation processes in 0.15–1.5 keV collisions of H^? with Na atoms in the 3s ground state or in the excited 3p state have been investigated by means of time-of-flight analysis of the neutral H atoms produced. The H^? - Na(3p) system, investigated here for the first time, is particularly interesting since the entrance channel is embedded in the [H - Na(3s)] +e ^? continuum, enabling Penning detachment to occur. The measured relative neutralisation cross section ratios σ(3p)/σ(3s) decrease from 3 to 1.6 with increasing energy. Based on earlier published results for σ(3s), σ(3p) total cross sections exceeding 100 Ų are estimated.     

Theoretical study of Na(4p2P) + Na(3s2S) and Cd(5p3P0) + Na(3s2S) collisions and their role in the energy transfer between Cd.* and Na

We have computed the cross sections for the energy transfer process Cd(5p³P₀) + Na(3s²S) → Cd(5s¹S) + Na(4p²P) and for the state changing collision Na(4p²P) + Na(3s²S) → Na(3d²D) + Na(3s²S), based on theoretical interaction potentials for the NaCd and Na2 systems, respectively. Our calculations shed light on the interpretation of experiments with laser excited Na+Cd vapour mixtures [1]. It turns out that Cd(5p³P₀), in rapid equilibrium with the doorway state Cd(5p³P₁), efficiently transfers energy to Na, populating the 4p²P state. The collisions with ground state Na cause a very fast conversion of the 4p³P₁ to the 3d²D state, from which the strongest emission is observed.     

SCF calculations for H 2 + , Li 2 + and LiH+ with atomic basis sets enlarged by bond functions

To simulate the charge distortion in the formation of a molecule from the separated atoms, a set of concentrics-type Gaussian functions is placed on the internuclear axis in addition to thes-type atomic basis functions to construct the molecular orbital for the one valence-electron systems H ₂ ⁺ , Li ₂ ⁺ and LiH⁺. This simple model gives 90.1%, 75.2% and 61.7%, respectively, of the improvement over minimal basis relative to Hartree-Fock energies.Supported in part by a research grant to Rice University from the Robert A. Welch Foundation.     

A systematic preparation of new contracted Gaussian-type orbital sets. III. Second-row atoms from Li through ne

Four minimal Gaussian basis sets are generated for the second-row atoms Li through Ne. The first one, MINI-1, consists of a 3-term contraction of primitive Gaussian-type orbitals for 1s, 2s, and 2p atomic orbitals. The convenient shorthand notation would be (3,3) for Li? Be and (3,3/3) for B? Ne. The second one, MINI-2, can be represented by (3,3/4) for B? Ne. In the same way, MINI-3 is described as (4,3) for Li? Be, and MINI-3 and MINI-4 are represented by (4,3/3) and (4,3/4) for B? Ne, respectively. Although the four basis sets are the minimal type, they give the valence shell orbital energies which are close to those of DZ. These four and other sets derived from them are tested for the hetero- and homodiatomic molecules and some organic molecules. They are found to give the orbital energies that agree well with those given by extended calculations. Atomization energies and other spectroscopic constants are also calculated and compared with those of extended calculations. The results clearly indicate that the present basis sets can be used very effectively in the molecular calculations.     

Gaussian basis sets for transition metals of the second series

A Gaussian basis set consisting of (15s, 9p, 8d) Gaussian functions has been optimized for the transition metal atoms of the second series (fourth-row atoms).     

Accurate nonrelativistic energies for 2Pe states of the Li isoelectronic series

Highly accurate upper bounds for several ²P^e states of the Li isoelectronic series obtained by extensive Hylleraas-Cl calculations are given. The best value for the 2²P^e state (1s2p²) of Li is −5.2137392₀ au. The evaluation of the occurring integrals is given explicitly. Additionally, we present some expectation values and isotope energies of the Li isoelectronic series. © 1997 John Wiley & Sons, Inc.     

Molecular orbital theory of electron donor-acceptor complexes

A Gaussian basis set consisting of 12s-type, 6p-type and 4d-type functions has been optimized for the third row atoms, together with a 9s, 5p, 3d set for the corresponding dipositive ion. The applicability of these atomic sets for molecular calculation is discussed.

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Zusammenfassung Ein Basissatz von 12s-, 6p- und 4d-Funktionen für die Atome der dritten Reihe des periodischen Systems ist optimalisiert worden; das gleiche gilt für einen entsprechenden Satz für die zweifach positiven Ionen aus 9s-, 5p- und 3d-Funktionen. Ferner wird ihre Anwendbarkeit bei Rechnungen an Molekülen diskutiert.

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Résumé On présente un ensemble optimal de fonctions de base gaussiennes pour les atomes et les ions de la troisième ligne. Cet ensemble est constitué de 12 fonctions du type s, 6 fonctions du type p et 4 fonctions du type d pour l'atome neutre et de 9 fonctions s, 5 fonctions p et 3 fonctions d pour l'ion M²⁺. On discute l'emploi de ces bases pour des calculs moléculaires.