Hartree-Fock with photoionization

Calculations show that cross-sections obtained in the Hartree-Fock approximation utilizing length and velocity forms of the appropriate operator, may essentially differ from each other for transitions between neighbouring outer shells, particularly with the same n. However, they are usually close to each other in the case of photoionization or excitation from an inner shell whose wave function is almost orthogonal with the relevant function of the outer open shell. In dipole approximation an electron from a shell lN may be excited to V = l + 1, but the channel /— / + prevails. For configurations ni/f1 n2l 2 an important role is... 

In the framework of the A-potential model, combined with the frozen-cage approximation, the problem is solved simply. Namely, HF wavefunctions and energies of the encaged atom, solutions of the extended to encaged atoms Hartree-Fock equations (2), must be substituted into corresponding formulae for the photoionization of an nl subshell of the free atom, Equations (18)-(26), thereby turning them into formulae for the encaged atom (to be marked with superscript " A") rrni(o>) —> a A(co), Pni(fi>) Yni o>) - and 8ni((o) - 8 A(co). This accounts... 

One reason for interest in more accurate calculations on HF has been the measured dissociation energy Z)o(HF), which can be obtained from photoionization or photoelectron spectra. Since HF+ dissociates correctly within the Hartree-Fock approximation to H+ and F(2P) in both the X2Tl and 2S+ states, PE curves were calculated by Julienne et a/.,203 and later by Bondybey et a/.,187 both of whom obtained values of Do in good agreement with experiment for the SCF calculation. The bond length in HF+ of 1.000 bohr is less than the experimental result, which the authors call into question. Julienne et al. give a detailed discussion of the adiabatic dissociation process. HF+ was also considered in the calculations of ref. 198. Richards and co-workers have reported several calculations of the PE curves of HF+, including the A2E+ state, which is correctly predicted to be bound.204... 

The ultraviolet photoelectron spectra of diatomic alkali halide molecules are reviewed and interpreted. Data for lithium halide dimers, 112X2> are presented and it is shown that the dimers have significantly larger ionization thresholds than the corresponding monomers. Some historical controversies regarding the presence of dimers and their ionization energies are clarified. Photoionization mass spectrometry is used to determine the adiabatic ionization potential of lithium chloride trimer, in order to probe the trend of I.P. with cluster size. The predictions of Hartree-Fock, Xa and ionic model calculations on this point are presented. 

Theoretical photoelectron spectrum has been calculated by the use of DV-Xa molecular orbital method combined with the calculation of atomic photoionization cross section in Hartree-Fock-Slater model. A calculation of the photoionization cross section has been performed for flexible numerical atomic orbitals including the excited atomic orbitals which are employed for basis functions in the molecular orbital calculation. Some variation of the photoionization cross section is seen when a reconstruction of the atomic orbital due to change in the effective charge takes place. This affects the molecular photoelectron spectrum to a certain extent. 

The calculations of the photoionization cross section of the atomic subshell have previously been performed using Hartree-Fock-Slater one-electron model by several workers. Table 1 compares the photoionization cross sections of the atomic orbital electrons obtained in the present work with those previously reported by Scofield for some atoms. Scofield has used the relativistic wave functions. The... 

Brouwer and Wilbrandt have applied resonance Raman spectroscopy and calculations to questions of structure of amine radical cations [73]. Well-resolved Raman spectra of trialkylamine radical cations that are so short-lived that their electrochemical oxidation waves are irreversible may be obtained at room temperature in solution by photoionization and time-resolved detection. Comparison of the observed spectrum with calculations for various isomers provides a powerful method of answering structural questions. Density-functional calculations prove much easier to apply to open-shell species than Hartree-Fock calculations, which require cumbersome and expensive corrections to introduce suffieient electron correlation to eonsider questions like the charge distribution of disubstituted piperazine (1,4-diazacyclohexane) radical cations. The dimethyl- and diphenyl-substituted piperazine radical cations are delocalized, but charge is localized on one ArN unit of the dianisyl-substituted compound [73dj. 

Concurrent with these developments, the density functional formalism has emerged as an alternative to a Hartree Fock based description of the electronic structure of atoms, molecules and solids. In its most common form as a local density approximation (LDA) the question of atomic photoionization can again be addressed. Here too, one finds that the simplest approach falls to adequately charr-. acterize the experimental results in many cases. However, a recent straightforward generalization of density functional theory to time-dependent phenomena has been applied successfully to the problem of the optical response of atoms. In particular, highly accurate photoionization cross sections can be readily obtained. The purpose of the present article is to review this time-dependent local density approximation (TDLDA), illustrate its scope and limitations and compare it to the more familiar Hartree-Fock based methods. 

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