Linear Combination Of Gaussian-type Orbitals Research Articles

Energy Bands in Ferromagnetic Iron

Results of a self-consistent tight-binding calculation of the band structure of body-centered-cubic iron are reported. The basis set consisted of atomic wave functions for the $1s$, $2s$, $3s$, $4s$, $2p$, $3p$, and $4p$ states, expressed as linear combinations of Gaussian-type orbitals (GTO), and five individual GTO for each $3d$ state. The Coulomb part of the crystal potential in the first iteration was constructed from a superposition of overlapping neutral-atom charge densities; the atoms being in the $3{d}^{7}4{s}^{1}$ configuration. Exchange potentials for both spins were calculated utilizing the $X\ensuremath{\alpha}$ method. Self-consistent band structures were obtained for different values of the exchange parameter $\ensuremath{\alpha}$. Best results appear to be obtained for $\ensuremath{\alpha}=0.64$. In this case, 140 points in $\frac{1}{48}$ of the Brillouin zone (BZ) were used to determine the charge density. The resulting self-consistent potentials were then utilized to compute energy levels at 819 regularly spaced points in $\frac{1}{48}$ of the BZ. The results thus obtained are discussed and compared with other reported band-structure results for the same metal. The Fermi surface is analyzed in detail. The density of states has been computed. Magnetic and x-ray form factors are presented. The results are found to be in reasonably good agreement with experiment.

Utility of Gaussian-Type Orbitals in Molecular Collisions: Electronic Excitation of the First Positive System of the Nitrogen Molecule

The use of gaussian-type orbitals (GTO) as basis sets of electronic wave functions of molecules for calculating electron-collision excitation cross sections is discussed. A test calculation of the electron excitation cross section of the 2p state of atomic hydrogen at 60-1000 eV in which the hydrogenic wave functions were expressed as linear combinations of GTO indicates that an expansion of the is wave function by six GTO's and the 2p by four GTO's gives quite accurate results. Methods for evaluating the multicenter integrals which appear in the expressions of electron-excitation cross section (by the Born-type approximation) of diatomic molecules are described. Cross sections of direct electron excitation of the B(3)II(g) state (the first positive bands) of the N(2) molecule are calculated by this scheme, and the results are in good agreement with experiments.

Integral-Transformation Trial Functions of the Fractional-Integral Class

We propose fractional integrals (Euler transforms) of conventional quantum-mechanical functions as special integral-transform trial functions. Calculations on the first four members of the He isoelectronic sequence with three different-order Euler transforms of both Slater and Gaussian $1s$ orbitals are reported. A pilot calculation for ${\mathrm{H}}_{2}$ with an Euler transform of an LCGTO (linear combination of Gaussian-type orbitals) molecular orbital gives a total energy $E=\ensuremath{-}1.10903$ a.u. at $R=1.4$ a.u. (exact value is -1.17444 a.u.). A generalization of the shape function used in this work is given and the general applicability of Euler transforms discussed.

Gaussian-Type Functions for Polyatomic Systems. II

The use of a linear combination of Gaussian-type orbitals (CGTO), instead of an individual Gaussian-type orbital (GTO), as a unit of basis functions for large-scale molecular calculations, is discussed. A systematic construction of the CGTO basis functions is attempted and the results for the atoms from Li through Ar are reported.

Ab Initio Studies of Small Molecules Using 1s Gaussian Basis Functions. III. LCGTO SCF MO Wavefunctions of the Three- and Four-Electron Systems He2+, He2, and Linear H3, H4+, H4

The ground states of the three- and four-electron systems He2+, He2, and linear symmetric H3, H4+, and H4 are investigated using the linear combinations of Gaussian-type orbitals (LCGTO) self-consistent-field molecular-orbital (SCF MO) approach. The basis functions are 1s GTO's, not necessarily located at nuclear positions. Optimized, near-Hartree–Fock (HF) wavefunctions are presented for the isoelectronic H3 and He2+ systems, for which such results were not previously available. They are found to have similar correlation energies. With simpler wavefunctions, E-vs-R plots for H3 and He2+ give good bond lengths and shapes of the energy curve. It is found that previous SCF MO studies have not closely approximated the true HF function for He2. The H4+ calculations are the first SCF MO results available for the species, and indicate its instability with respect to H3+ + H, in agreement with recent experimental data. The GTO studies for H4 are the only rigorously executed ab initio calculations yet done for the system. E-vs-R data derived for H4 refute the best previous studies, which used integral approximations. The interaction potential of two H2 molecules (end to end) is derived from these H4 energies.