Kohn-Sham atomic orbitals

Larsen H, Jorgensen P, Olsen J, Helgaker T. Hartree-Fock and Kohn-Sham atomic-orbital based time-dependent response theory. J Chem Phys 2000 113 8908-8917. 

There is, of course, much that remains to be understood with regard to the physical interpretation. For example, the correlation-kinetic-energy field Z, (r) and potential W, (r) need to be investigated further. However, since accurate wavefunctions and the Kohn-Sham theory orbitals derived from the resulting density now exist for light atoms [40] and molecules [54], it is possible to determine, as for the Helium atom, the structure of the fields P(r), < P(r), and Zt (r), and the potentials WjP(r), W (r), W (r), and W (r) derived from them, respectively. A study of these results should lead to insights into the correlation and correlation-kinetic-energy components, and to the numerical determination of the asymptotic power-law structure of these fields and potentials. The analytical determination of the asymptotic structure of either [Z, (r), W, (r)] or [if (r), WP(r)] would then lead to the structure of the other. 

The work interpretation of Kohn-Sham theory is in terms of the wavefunction T (xi,...Xn) and the Kohn-Sham spin-orbitals ( j x). The structure of the exchange, correlation and correlation-kinetic-energy components of the fields and potentials are as such most readily determined for the He atom ground-state, since by the choice of an accurate wavefunction P, the Kohn-Sham orbitals are simultaneously also known as i(x) = [p(r)/2] . The results [28] given in this section are those obtained for the accurate analytical 39-parameter correlated wavefunction of Kinoshita [37]. 

Pig. 15 Kohn-Sham molecular orbitals of [Mo(ZnH)i2] (61H) with significant coefficients at the molybdenum atom... 

Fig. 18 Occupied Kohn-Sham molecular orbitals of [Ru(ZnH),o] (65H) with coefficients at the central ruthenium atom...

The collision of an atom of gold and a molecule of butane includes some extra challenges compared with the previous case. Instead of two electrons, now we have a total of 113 electrons. By using pseudopotentials, the number of electrons treated explicitly can be reduced to 37. The gold atom being spin-polarized, we have to treat independently each spin channel. The total number of Kohn-Sham spin orbitals to be handled is thus 37. 

The wavevector is a good quantum number e.g., the orbitals of the Kohn-Sham equations [21] can be rigorously labelled by k and spin. In tln-ee dimensions, four quantum numbers are required to characterize an eigenstate. In spherically syimnetric atoms, the numbers correspond to n, /, m., s, the principal, angular momentum, azimuthal and spin quantum numbers, respectively. Bloch s theorem states that the equivalent... 

To solve the Kohn-Sham equations a number of different approaches and strategies have been proposed. One important way in which these can differ is in the choice of basis set for expanding the Kohn-Sham orbitals. In most (but not all) DPT programs for calculating the properties of molecular systems (rather than for solid-state materials) the Kohn-Sham orbitals are expressed as a linear combination of atomic-centred basis functions ... 

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