Advances in quantum chemistry. / Volume 3 by Per-Olov (Editor); Lowdin

By Per-Olov (Editor); Lowdin

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S(1) is, for example, the integral over spin coordinates for the spin functions on electron 1 and is unity if both spin functions are the same; otherwise it is zero. We therefore have : w= H, 1 = 2zs + 2Ip + 2rpx+ 21py+ 2zp, +Jss + Js*s* + J p x p x + Jpypy + Jpzpz + 2(2Jss*- Kss*)+ 2(2Jspx- Ksp,) + 2(2Jspy- Kspy) + 2(2Jspz - Kp,)+ 2(2Js*px- Ks*px)+ 2(2Js*py- Ks*py) + 2(2Js*pz- Ks'p,) + 2(2Jpxpy- Kpxpy)+ 2(2Jp p - K p x p ) + 2(2Jpypz- K p p ). X I Y Z Each of the one-electron integrals, Ii, is composed of three parts, a kinetic energy term : s a nitrogen-electron potential energy term : ZiN = [:I $i*(1) - - 4i(l) dt, and a proton-electron potential energy term : 31 Single-Center Molecular Wave Functions Evaluation of ZiT and Zr is straightforward and leads to the expressions: and ZiT = C i 2 [ni + Zi(Zi + 1)]/[2ni(2ni- I)] ZiN = -7Ci/ni.

80 au for methane, a result inferior to both Albasiny’s and Bishop’s value. 74D) for the dipole moment of HF in a calculation similar to the one of Moccia, which will be described next. Perhaps the greatest justification, certainly in the quality and the extent of the results, for single-center expansions has come from the work of Moccia. Using the Roothaan SCF method to determine the correct linear combinations of atomic orbitals and energy minimization to determine the orbital exponents (ni had integral values only), he was able to calculate bond distances, angles, dipole moments, ionization potentials, and molecular energies for a whole range of molecules to a high degree of accuracy (see Table VII).

Phys. 38, 1347. MCLEAN,A. D. (1963b). J. Chem. Phys. 39,2653. MCLEAN,A. D. (1964). J. Chem. Phys. 40,2774. MERRYMAN, P. M. (1959). Unpublished work. MOCCIA,R. (1962). J. Chem. Phys. 37, 910. MOCCIA,R. (1 964a). J . Chem. Phys. 40, 2164. MOCCIA,R. (1964b). J. Chem. Phys. 40, 2176. MOCCIA,R. J. Chem. Phys. 40,2186. MBLLER, C . , and PLESSET, M. S. (1934). Phys. Rev. 46, 618. MOSKOWITZ, J. W. (1965). J. Chem. Phys. 43, 60. MOSKOWITZ, J. , and HARRISON, M. C. (1965). J. Chem. Phys. 42, 1726. MULLIKEN, R.

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