MolecularK-shell photoionization cross sections in the relaxed-core Hartree-Fock approximation

Abstract

The relaxed-core Hartree-Fock (RCHF) approach to the calculation of E-shell photoionization cross sections is analyzed and applied to I(-shell single-hole ionization in CO. A direct method based on the Schwinger variational principle and single-center-expansion techniques is used to generate the continuum orbitals associated with the motion of the photoelectron in the direct and exchange potential of the relaxed ion. A method is presented for evaluating the ¹lectron transition moment, a step that has posed a considerable computational obstacle due to the lack of orthogonality between the frozen and relaxed orbitals in the initial and final ¹lectron states, respectively. Besides being very practical and efficient, this formulation establishes the distinction between the "direct" and "conjugate" part of the transition moment, introducing bound-free dipole and overlap integrals, respectively.Whereas for large photoelectron energies the conjugate terms can be neglected, they become important near threshold, contributing, for example, up to 30% to the 1s cross sections in CO. An analysis by means of low-order perturbation theory shows that the RCHF model correctly describes the e6'ect of ionic relaxation, that is, essentially the screening of the 1s hole by the valence electrons. As a consequence the 0 shape resonance is substantially shifted to higher energy and broadened compared with the frozen-core Hartree-Fock picture where the more attractive unscreened 1s-hole potentials are used. The remaining discrepancies with the experimental results are attributed to the neglect of target polarization in the RCHF model.

Vibrational Feshbach resonances in near-threshold HOCO−photodetachment: A theoretical study

“…For example, in C 1s photoionization of neutral CO 2 , the cross sections computed using the ion molecular orbitals or averaged (Slater's transition-state [33]) orbitals give much better agreement with experimental observations than those obtained with CO 2 molecular orbitals [34][35][36]. Slater's transition-state orbitals have been used extensively in core-level photoionization studies and have been shown to give results consistent with experimental measurements [34,35,37,38]. To investigate the orbital relaxation effects in the case of photodetachment, here we compute the cross sections using anion, neutral and Slater's transition-state orbitals.…”

Vibrational branching ratios in the photoelectron spectra of N2 and CO: interference and diffraction effects

“…At higher energies the RCHF approximation has also been used (CO 43,44,50,52,54,67,[115][116][117][118][119][120] , N 2 3 ). This is in contrast with the frozen core Hartree Fock (FCHF) approximation, which has widely been used in most earlier and some recent works (CO 42,48,58,74,75,106,121 , N 2 22,27,32,58,74,75,106 ).…”

“…Another single channel approach is the Stieltjes-Tchebycheff moment theory (STMT) (CO 47,101 ; N 2 10,30,101,102 ) which is able to describe shape resonances near the ionization threshold (see results below) but suffers from limited energy resolution and range. The Schwinger iterative approach that has been implemented at the frozen core (FCHF) 32,46,48 and relaxed core (RCHF) 14,42,[103][104][105][106] levels for polyatomic molecules can instead produce accurate solutions of the molecular electronic continuum. Another method that has been shown to provide accurate results for large systems is the present multicenter Bspline static-exchange DFT method 17,24,33,49,107 , which makes use of the Kohn-Sham density functional theory to describe the molecular ionic states and the Galerkin approach to evaluate the continuum electron wave function in the field of the corresponding Kohn-Sham density.…”

“…This is especially important in the vicinity of shape and Feshbach resonances, which lead to the peaks observed just above the ionization threshold. Previous theoretical methods also lead to reasonable results, although they were obtained in the fixed nuclei approximation and, in some cases, they do not 47 , Maroon dashed: random phase approximation (RPA) 44 , Blue dashed: RPA with the fractional charge basis set RCHF(0.7) 44 , Maroon points: frozen-core Hartree-Fock (FCHF) in the length gauge 42 , Blue points: relaxed core Hartree-Fock (RCHF) in the length gauge 42 , Orange solid: logarithmic derivative version of the Kohn vartiational principle Lobatto technique (LDKL) 12 , Black thick solid: DFT method using a LB94 functional (this work), Black dashed thick: DFT method using a LDA functional (this work), Red thick solid: TDDFT method using a LDA functional (this work). (Experimental data 142 and 55 were renormalized to our theoretical ones).…”

“…In particular, a wealth of experimental and theoretical data has been published for total cross sections corresponding to core as well as valence-shell photoionization of the prototype N 2 1-35 and CO 1,2,5,6,12,13,34,[36][37][38][39][40][41][42][43][44][45][46][47][48][49] molecules, from the ionization threshold up to a few tens of eV above it. More recently, the advent of high-brilliance 3rd-generation synchrotron radiation sources in combination with high energy-resolution detection techniques has opened the way for the determination of vibrationally resolved photoionization spectra of these molecules, both at low and high photon energies 30,35,38,39,[50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] .…”