Total photoionization cross-sections of excited electronic states by the algebraic diagrammatic construction-Stieltjes-Lanczos method (original) (raw)
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The Journal of Chemical Physics, 2013
Phys. 130, 064104 (2009)] we introduced a new L 2 ab initio method for the calculation of total molecular photoionization cross-sections. The method is based on the ab initio description of discretized photoionized molecular states within the many-electron Green's function approach, known as algebraic diagrammatic construction (ADC), and on the application of Stieltjes-Chebyshev moment theory to Lanczos pseudospectra of the ADC electronic Hamiltonian. Here we establish the accuracy of the new technique by comparing the ADC-Lanczos-Stieltjes cross-sections in the valence ionization region to the experimental ones for a series of eight molecules of first row elements: HF, NH 3 , H 2 O, CO 2 , H 2 CO, CH 4 , C 2 H 2 , and C 2 H 4. We find that the use of the second-order ADC technique [ADC(2)] that includes double electronic excitations leads to a substantial systematic improvement over the first-order method [ADC(1)] and to a good agreement with experiment for photon energies below 80 eV. The use of extended second-order ADC theory [ADC(2)x] leads to a smaller further improvement. Above 80 eV photon energy all three methods lead to significant deviations from the experimental values which we attribute to the use of Gaussian single-electron bases. Our calculations show that the ADC(2)-Lanczos-Stieltjes technique is a reliable and efficient ab initio tool for theoretical prediction of total molecular photo-ionization cross-sections in the valence region.
Physical Review A, 2010
The quantum regime of highly doubly excited states in two-electron atoms has, so far, been largely inaccessible both to numerical methods as well as to experiments. Recent advances in semiclassical closed orbit theory in combination with a quantum mapping approach have shown a new way into this region of high dynamical complexity. In particular, new scaling laws near the double-ionization threshold as well as the dominant semiclassical contributions to the total photoionization cross section can be identified. We will present this new approach here in all its detail. It is based on representing the photoionization cross section in terms of quantum maps. These quantum maps or quantum propagators are used as a starting point for developing an efficient numerical method for calculating cross sections. Furthermore, by writing the quantum operators in semiclassical approximations, it is possible to interpret the quantum results in terms of classical triple collision orbits and to derive threshold laws near the three-particle breakup point. Semiclassical and numerical quantum results show excellent agreement for a model system, namely collinear helium.
Multicentered Theory of Molecular Photoionization
Surface Review and Letters, 2002
A new theory for near-threshold photoionization of inner electrons of atoms confined in multicentered atomic formations, e.g. molecules or clusters, is developed. The formulas for fixed-in-space molecules have been derived. The interaction of the photoelectron in the continuum with atoms that surround the atom being ionized, is replaced by the suitable boundary conditions imposed on the photoelectron wave function at the location of nuclei of these atoms in the molecule. The general formulas derived are used to calculate photoelectron angular distributions of diatomic molecules. The calculated data are in qualitative agreement with experimental data and results of other calculations.
On the Accurate Description of Photoionization Dynamical Parameters
Calculation of dynamical parameters for photoionization requires an accurate descriptionof both initial and final states of the system, as well as of the outgoing electron.We here show, that using a linear combination of atomic orbitals (LCAO) B-spline densityfunctional (DFT) method to describe the outgoing electron, in combination withcorrelated equation-of-motion coupled cluster singles and double (EOM-CCSD) Dysonorbitals, gives good agreement with experiment and outperforms other simpler approaches,like plane and Coulomb waves, used to describe the photoelectron. Resultsare presented for cross sections, angular distributions and dichroic parameters in chiralmolecules, as well as for photoionization from excited states. We also present a comparisonwith the results obtained using Hartree-Fock (HF) and density-functional theorymolecular orbitals selected according to Koopmans’ theorem for the bound states.
A complex Gaussian approach to molecular photoionization
Journal of Computational Chemistry, 2021
We develop and implement a Gaussian approach to calculate partial cross-sections and asymmetry parameters for molecular photoionization. Optimal sets of complex Gaussian-type orbitals (cGTOs) are first obtained by non-linear optimization, to best fit sets of Coulomb or distorted continuum wave functions for relevant orbital quantum numbers. This allows us to represent the radial wavefunction for the outgoing electron with accurate cGTO expansions. Within a time-independent partial wave approach, we show that all the necessary transition integrals become analytical, in both length and velocity gauges, thus facilitating the numerical evaluation of photoionization observables. Illustrative results, presented for NH 3 and H 2 O within a one-active-electron monocentric model, validate numerically the proposed strategy based on a complex Gaussian representation of continuum states.
The Journal of Chemical Physics, 2009
Stieltjes imaging technique is widely used for the ab initio computation of photoionization cross sections and decay widths. The main problem hampering the application of the standard Stieltjes imaging algorithms in conjunction with high-level ab initio methods to polyatomic molecules is the requirement of full diagonalization of excessively large Hamiltonian matrices. Here we show that the full diagonalization bottleneck can be overcome by applying the Stieltjes imaging procedure to Lanczos pseudospectrum of the atomic or molecular Hamiltonian. Using the helium and neon atoms as examples, we demonstrate that the Lanczos pseudospectrum obtained after only a relatively small number of iterations can be used for Stieltjes-type calculations of photoionization cross sections essentially without loss of accuracy. The new technique is applied to the calculation of the total photoionization cross section of benzene within an ab initio approach explicitly taking into account single and double electronic excitations. Good agreement with experimental results is obtained.
Single and Double Photoionization from Dipole Response Function
Physical Review Letters, 1997
¥ A ¦ method for including the correlated motion of the electrons in the calculation of single and double ionization of atomic and molecular systems by the absorption of a single photon is described. The correlated § dipole response function is central to the formulation. The single and double photoionization cross § sections of helium are calculated. We show that the method accurately corrects for the error thaẗ is present at high energies when the length gauge is used to characterize the photon interaction. The cross sections obtained from the length, velocity, and acceleration gauges are brought into agreement © with each other and with cross sections calculated from the many-body perturbation theory.