Ground states optimized exponents

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

Several low-lying quartet states of NJ have been studied using valence-shell Cl with up to 270 configurations per symmetry.248 The 2s and 2p exponents for the ground state of N2 were optimized for the molecule. Several states were found to be bound, and they have lower energies and larger Re than previously assumed, particularly the 4nff state. 

A. He/H2 and Ha.—It is convenient to consider first these species. Tsapline and Kutzelnigg375 have applied the IEPA-PNO method, previously described, to the ground state of the He/Ha system. The van der Waals minimum was computed, using a gaussian lobe basis set with carefully optimized exponents. The collinear arrangement with a depth of 21 K was found for the van der Waals minimum, with a saddle point of 14 K for the Czv geometry. The computed surface was compared with experiment and with the R 6 term. The anisotropy of the potential is larger than that predicted asymptotically. 

Examine now the determination of exponents for polarization functions. Obviously, the atomic ground state calculations that are so useful in the optimization of valence shell exponents cannot help us. There is a possibility of performing calculations for excited states of atoms. This approach is, however, not appropriate. The role of polarization functions is to polarize valence orbitals in bonds so that the excited atomic orbitals are not very suitable for this purpose. Chemically, more well-founded polarization functions are obtained by direct exponent optimization in molecules. Actually, this was done for a series of small molecules in both Slater and Gaussian basis sets. Among the published papers, we cite. Since expo-... 

Magnasco, V. (2008) Orbital exponent optimization in elementary VB calculations of the chemical bond in the ground state of simple molecular systems. J. Chem. Edu., 85, 1686-1691. 

The ground state energies (in a.u.) of a few members of He-isoelectronic sequence obtained by SAM-based optimization of all the linear parameters and (ala single exponent, (b) all the exponents, in 10-term 0 using STOs as basis functions... 

The GVB method gives a of 4.12 eV for ground-state H2, as compared with 3.15 eV for the Heitler-London VB function, 3.78 eV for the Heitler-London-Wang function with an optimized orbital exponent, 4.03 eV for the Weinbaum function (13.110) that includes an ionic term, and 4.75 eV for the experimental value. At very large intemuclear distance R, the GVB functions / and g approach the atomic orbitals s and Hj,. Thus, like the VB (but unlike the MO ), the GVB wave function shows the correct behavior on dissociation. At intermediate distances, / is a linear combination of AOs that has its most important contribution fi"om but that has a significant contribution from and lesser contributions fi om the other AOs (these contributions reflect the polarization of the AO that occurs on molecule formation). 

Calculations were originally carried out (2 ) for the lowest states of Hz, LiH, BH, NH, and HF and the corresponding deuterated molecules with the LCAO-MO wavefunction of Coulson for Hz (11) and the LCAO-MO-SCF functions of Hansil (12) for the other molecules. These wavefunctions contain a minimum basis set of inner and valence shell Slater-type orbitals with the orbital exponents optimized at the experimental equilibrium intemuclear distance. The S states are the ground states of the respective molecules except in the case of NH. 

Another way to form contracted Gaussians is to start with atomic GTE SCF calculations. Huzinaga used a (9s5p) basis set of uncontracted Gaussians to do SCF calculations on the atoms Li-Ne. For example, for the ground state of the O atom, the optimized orbital exponents of the nine i-type basis GTFs were found to be [S. Huzinaga, J. Chem. Phys., 42, 1293 (1965)]... 

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