Absorption Spectra and Chemical Bonding in Complexes by C. K. Jorgensen

By C. K. Jorgensen

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The first-order perturbations are characterized by considering the same wave function before and after the perturbation Ρ in the integral (we use here an integral sign without variables to indicate an integration over all pertinent variables in their whole domain; other authors use the brackets <¥Ί|Ρ| Ψ{> proposed by Dirac). We are here considering the fact that Ρ might contain operators, affecting the kinetic energy. The total energy of a normalized wave function is J ^ H ^ where the Hamiltonian function Η partly produces kinetic energy, necessitating in its definition the indication of a wave function before Η and one after Η ; and partly potential energy, which is simply the integration of the product of with a potential.

5) has a formal resemblance with 2 the potential of a centrifugal force, /(/ + l)/2r , being absent for s-electrons with / = 0. Actually, this is the kinetic contribution from the angular dependence A. It explains the order of increasing orbital energies with increasing / in eqn. (2) (when U(r) decreases -1 more quickly than r for increasing r). It can be shown from eqn. (4) that only s-electrons have a finite probability density close to the nucleus, while the positive /-values prevent a non-vanishing density, due to the "centrifugal" term of the kinetic energy.

Some English authors also use the five letters α, β, γ, δ, c, and use, for example, άγ and d e electrons for y 3 and y 5. The products of different L-values are: 53 MOLECULAR ORBITALS AND MICROSYMMETRY S I\ Ρ D F A Γ3 + Γ5 Γ2 + Γ 4 + Γ 5 G Γ + Γ +Γ +Γ Η I Γ 3 + 2Γ4 + Γ5 Γτ + Γ2 + Γ 3 + Γ 4 + 2 Γ 5 1 Ζ Α Β (44) combined with even or odd parity (as also in spherical symmetry, 4 3 where, for instance, S from p has odd parity, since 3/ = 3 is odd). The orbitals are even for even values of / and odd for odd values, having the same distribution of y n-values as Γ η in eqn.

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