Molecular Photoionization Cross Sections Research Articles

Tiresia: A code for molecular electronic continuum states and photoionization

The Tiresia program [1] provides access to numerically accurate solutions of the one-particle Schrödinger equation for highly excited states of complex polyatomic molecules, both bound and continuum, that cannot be described by conventional Quantum Chemistry approaches. It is based on an expansion of the required solution in a local multicentric basis set, with primitive functions built as products of a radial B-spline times a real spherical harmonic. In conjunction with Density Functional Theory (DFT), it has been extensively employed in a large variety of photoionization studies, also for rather large systems. Highly excited bound states as well as wavepacket propagation can also be accurately described. In fact, the flexibility of the basis essentially allows accurate solutions of linear operator equations, like Poisson or inhomogeneous perturbative equations, which are employed in the code. The program is parallelized with standard MPI-I instructions and makes extensive use of the Scalapack linear algebra library. Ancillary programs are available for the evaluation of photoionization cross sections and angular distributions from randomly to fully oriented molecules. Program summaryProgram Title: TiresiaCPC Library link to program files:https://doi.org/10.17632/fcrjxwgjxh.1Licensing provisions: GPLv3Programming language: Fortran77, Fortran90, MPISupplementary material: Program manual documentNature of problem: Accurate solutions for highly excited and continuum electronic states in complex polyatomic molecules. Molecular photoionization cross sections and angular distributions under high energy, high-intensity radiation pulses from Synchrotron radiation and laser sources, photoelectron imaging in pump-probe experiments, basis for electronic wavepackets under ultrafast or nonperturbative excitation.Solution method: Solution of the Schrödinger and similar linear operator equations in a finite domain is obtained via basis set expansion. Flexible basis set, that may approach practical completeness within the domain, is obtained as a multicenter set of B-spline radial functions times spherical harmonics. Accurate numerical integration is employed for the evaluation of matrix elements, and conventional diagonalization for bound states, or Galerkin approach for the full multichannel solution in the continuum. Full hamiltonian and dipole matrices in the spectral basis are available for time propagation. DFT many-body description is available, and strong correlations in the bound states may be incorporated via Dyson orbitals.Additional comments including restrictions and unusual features: The code is noted for computational efficiency, which allows fast yet reasonably accurate photoionization calculations for medium-sized molecules, allowing, e.g., calculations at many molecular geometries as required to describe time-resolved photoelectron spectra in pump-probe experiments.

Machine Learning for Ionization Potentials and Photoionization Cross Sections of Volatile Organic Compounds.

Molecular ionization potentials (IP) and photoionization cross sections (σ) can affect the sensitivity of photoionization detectors (PIDs) and other sensors for gaseous species. This study employs several methods of machine learning (ML) to predict IP and σ values at 10.6 eV (117 nm) for a dataset of 1251 gaseous organic species. The explicitness of the treatment of the species electronic structure progressively increases among the methods. The study compares the ML predictions of the IP and σ values to those obtained by quantum chemical calculations. The ML predictions are comparable in performance to those of the quantum calculations when evaluated against measurements. Pretraining further reduces the mean absolute errors (ε) compared to the measurements. The graph-based attentive fingerprint model was most accurate, for which εIP = 0.23 ± 0.01 eV and εσ = 2.8 ± 0.2 Mb compared to measurements and computed cross sections, respectively. The ML predictions for IP correlate well with both the measured IPs (R 2 = 0.88) and with IPs computed at the level of M06-2X/aug-cc-pVTZ (R 2 = 0.82). The ML predictions for σ correlated reasonably well with computed cross sections (R 2 = 0.66). The developed ML methods for IP and σ values, representing the properties of a generalizable set of volatile organic compounds (VOCs) relevant to industrial applications and atmospheric chemistry, can be used to quantitatively describe the species-dependent sensitivity of chemical sensors that use ionizing radiation as part of the sensing mechanism, such as photoionization detectors.

Photoelectron Spectroscopy of Molecules Beyond the Electric Dipole Approximation.

A methodology implemented to compute photoionization cross sections beyond the electric dipole approximation using Gaussian type orbitals for the initial state and plane waves for the final state is applied to molecules of various sizes. The molecular photoionization cross sections computed for valence molecular orbitals as a function of photon energy present oscillations due to the wave-like nature of both the outgoing photoelectron and of the incoming photon. These oscillations are damped by rotational and vibrational averaging or by performing a k-point summation for the solid state case. For core orbitals, the corrections introduced by going beyond the electric dipole approximation are comparable to the atomic case. For valence orbitals, nondipole corrections to the total photoinization cross sections can reach up to 20% at photon energies above 1 keV. The corrections to the differential cross sections calculated at the magic angle are larger, reaching values between 30% and 50% for all molecules included. Our findings demonstrate that photoelectron spectroscopy, especially angle-resolved, on, e.g., molecules and clusters on surfaces, using high photon energies, must be accompanied by theories that go beyond the electric dipole approximation.

Photoelectron wave function in photoionization: plane wave or Coulomb wave?

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

Total photoionization cross-sections of excited electronic states by the algebraic diagrammatic construction-Stieltjes-Lanczos method

Here, we extend the L2 ab initio method for molecular photoionization cross-sections introduced in Gokhberg et al. [J. Chem. Phys. 130, 064104 (2009)] and benchmarked in Ruberti et al. [J. Chem. Phys. 139, 144107 (2013)] to the calculation of total photoionization cross-sections of molecules in electronically excited states. The method is based on the ab initio description of molecular electronic 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. The intermediate state representation of the dipole operator in the ADC basis is used to compute the transition moments between the excited states of the molecule. We compare the results obtained using different levels of the many-body theory, i.e., ADC(1), ADC(2), and ADC(2)x for the first two excited states of CO, N2, and H2O both at the ground state and the excited state equilibrium or saddle point geometries. We find that the single excitation ADC(1) method is not adequate even at the qualitative level and that the inclusion of double electronic excitations for description of excited state photoionization is essential. Moreover, we show that the use of the extended ADC(2)x method leads to a substantial systematic difference from the strictly second-order ADC(2). Our calculations demonstrate that a theoretical modelling of photoionization of excited states requires an intrinsically double excitation theory with respect to the ground state and cannot be achieved by the standard single excitation methods with the ground state as a reference.

Total molecular photoionization cross-sections by algebraic diagrammatic construction-Stieltjes-Lanczos method: Benchmark calculations

In [K. Gokhberg, V. Vysotskiy, L. S. Cederbaum, L. Storchi, F. Tarantelli, and V. Averbukh, J. Chem. 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, NH3, H2O, CO2, H2CO, CH4, C2H2, and C2H4. 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.

Autoionization of Molecular Hydrogen: Where do the Fano Lineshapes Go?

Atomic autoionization following photoabsorption is a typical example of quantum interferences governed by electron-electron correlation. Coherence between direct photoionization and autoionization paths results in "Fano profiles", widely explored in atoms in the last 60 years. The advent of femto- and attosecond laser technology made time-resolved images of the delayed electron ejection in autoionization accessible, leading to the reemergence of such studies in atomic systems. The counterpart molecular phenomena show the richness, as well as the complexity, added by nuclear motion, which may proceed on similar time scales. However, Fano profiles are usually absent in measured molecular photoionization cross sections and an unequivocal parametrization of molecular autoionization signatures, similar to that introduced by Fano in atoms [U. Fano, Phys. Rev. 1961, 124, 1866] has not yet been achieved. In this work we introduce a simple semiclassical model that accounts for all the features observed in H2 photoionization and demonstrate that the interference structures observed in dissociative ionization spectra are almost exclusively due to the phase accumulated in the nuclear motion. Furthermore, we show that the temporal build-up of these structures in the energy-differential cross sections is also determined by nuclear motion. We validate our models by comparing with full-dimensional ab initio calculations solving the time-dependent Schrödinger equation.

Angular distribution of photoelectrons in small molecules: A molecular quantum defect calculation

The molecular quantum defect orbital (MQDO) method, previously used in the determination of molecular photoionization cross sections, is applied here to calculate the angular distribution of photoelectrons arising from the molecular photoionization. Calculations are performed for the ionization from outer valence orbitals of HF, H(2)O, NH(3), N(2)O, and H(2)CO molecules. The results are compared with previous measurements and with theoretical curves found in the literature. Profiles of the angular distribution parameter as a function of photoelectron energy covering a range from the photoionization threshold to 120 eV are presented for the above molecules. The energy dependence of the angular distributions predicted by the MQDO calculations agrees fairly well with predictions from more sophisticated theories and with observed results.

Non-physical consequences of the muffin-tin-type intra-molecular potential

Abstract We demonstrate, using a simple model, that, in the frame of muffin-tin-like potential, non-physical peculiarities appear in molecular photoionization cross-sections that are a consequence of “jumps” in the potential and its first derivative at some radius. The magnitude of non-physical effects is of the same order as the physical oscillations in the cross-section of a diatomicmolecule. The role of the size of these “jumps” is illustrated by choosing three values for it. The results obtained are connected to the previously studied effect of non-analytic behavior as a function of r, the potential V(r) acting upon a particle on its photoionization cross-section. In reality, such potential has to be analytic in magnitude and have a first derivative function in r. The introduction of non-analytic features in model V(r) leads to non-physical features — oscillations, additional maxima, and so forth — in the corresponding cross-section.

Molecular photoionization cross sections by Stieltjes–Chebyshev moment theory applied to Lanczos pseudospectra

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.

Electron propagator theory calculations of molecular photoionization cross sections: the first-row hydrides.

Together with ionization potentials, cross sections provide valuable information for the interpretation of photoelectron spectra. We have developed a program to perform ab initio calculations of photoionization cross sections within the electric dipole approximation using electron propagator theory. Applications to the first-row hydrides CH(4), NH(3), H(2)O, and HF, using several approximations for the propagator self-energy and the plane-wave and orthogonalized-plane-wave approximations to represent the photoelectron, as well as comparison to experimental data, are presented. This program is implemented within the quantum chemistry package GAUSSIAN.

On the angular distributions of electrons photoejected from fixed-in-space and randomly oriented molecules

Abstract New theoretical expressions are devised from a dynamical perspective for molecular photoionization cross sections differential in electron ejection angles which facilitate comparisons between theory and experiment and provide a convenient basis for ab initio calculations. The cross sections obtained for fixed-in-space molecules, including the lowest-order (nondipole) effects of retardation, are given in terms of invariant molecular body-frame transition moments and related normalized angular-distribution amplitudes which can be calculated employing interaction-prepared states without reference to specific scattering boundary conditions. Corresponding expressions for molecular dipole and nondipole anisotropy factors appropriate for randomly oriented molecules are obtained in closed forms involving expectation values of harmonic polynomials over the fixed-in-space body-frame angular-distribution amplitudes. The expressions are seen to be in the spirit of corresponding results for atomic photoionization anisotropy factors, to which they reduce in appropriate limits. Interpretations of recently measured angular distributions of photoelectrons from the K-shell of molecular nitrogen illustrate how the development relates measurements on randomly oriented molecules to those performed on fixed-in-space molecules. The theoretical formalism provides results in excellent accord with measurements of the molecular nitrogen K-shell dipole anisotropy factor, and accounts for the origins of large nondipole effects observed at relatively low photon energies (ℏω≤500 eV) in the measured angular distributions.

Time-dependent density functional calculations of molecular photoionization cross sections: N2 and PH3

A method based on the time-dependent density functional theory (TD-DFT) is proposed to calculate the photoionization cross section employing the explicit continuum wave-function, within a One Center Expansion and B-Splines radial basis set. The LB94 exchange-correlation potential with correct asymptotic behavior is employed. The results obtained for N2 and PH3 are in excellent agreement with the experimental data and are of comparable accuracy of ab initio methods. A deterioration is still present in the inner valence. For PH3 the effect of TD-DFT is dramatic and recovers completely the Kohn–Sham deficiency. The method has proven efficient for both valence and core ionization.

Algebraic variational approach to atomic and molecular photoionization cross sections: Removing the energy dependence from the basis

We describe a variational method for calculating photoionization cross sections from a matrix element of the resolvent operator. Scattering boundary conditions are enforced by expanding the resolvent in a basis of square-integrable (${\mathrm{L}}^{2}$ ) and outgoing wave continuum basis functions. By employing several continuum basis functions, with overlaps defined by a suitable analytic continuation, we can, in a single calculation, express the cross section over a continuous range of energies without explicitly resolving the variational equations at each desired energy. The method is illustrated by calculation of the photoionization cross section of atomic Be in the autoionizing region between the ${1\mathrm{s}}^{2}$ 2s and ${1\mathrm{s}}^{2}$ 2p states of ${\mathrm{Be}}^{+}$ .

Interchannel coupling and ground state correlation effects in the photoionization of CO

We describe a general procedure for applying the complex Kohn variational method to the calculation of molecular photoionization cross sections and asymmetry parameters. In this initial application of the method, we examine the effects of interchannel coupling and ground state correlation on the X 2Σ+(5σ−1), A 2Π(1π−1), and B 2Σ+(4σ−1) partial photoionization cross sections and asymmetry parameters for the CO molecule. We find that the dominant effect of interchannel coupling is to remove a spurious π→π* resonance feature from the continuum that appears at the frozen-core Hartree–Fock level. We also find that it appears to be important to combine the effects of final channel coupling with a correlated initial target state to achieve quantitatively correct cross sections.

The correlation states of furan and thiophene by high resolution synchrotron photoelectron spectroscopy

The high resolution synchrotron photoelectron spectra (PES) of furan and thiophene are obtained at 90–200 eV photon energy. Several ionization peaks attributed to inner valence orbitals and correlation (satellite) states are resolved for the first time. By using the photon energy dependence of the ionization cross sections of the valence orbitals and the correlation states, significant insight into the dominant character of the valence orbitals and correlation states of furan and thiophene is attained. Two classes of a 1-type molecular orbitals in furan, two classes of b 2-type molecular orbitals in furan and two types of correlation (satellite) states in thiophene are distinguished by the present procedure. Some limitations of the photon energy dependence of molecular photoionization cross sections are also discussed.

A GTO basis set calculation of properties of the continuum. Photoionization and resonances of He

By using the K-matrix technique for the continuum states that was previously employed with particularly diffuse L2 basis sets, it is shown that GTO bases are also capable of yielding accurate values for the properties belonging to the electronic continuum. The method has been tested for helium and proved of satisfactory accuracy also for the analysis of the autoionizing states. The results include the phase shifts of the continuum states of the 1Seand 1P° manifolds, the properties of the lowest resonances of these symmetries, the ground state photoionization cross section, and the S contribution to the 1s2p1P° photoionization cross section. The results obtained suggest that the proposed technique should be useful for computing molecular differential photoionization cross sections by exploiting the widely used codes that employ GTO bases. Keywords: photoionization, Gaussian basis sets, helium, autoionizing states.

Representation of electronic wavefunctions by Lobatto shape functions: application to the photoionization cross section of H +2

It is shown that a convenient and flexible representation of molecular electronic continuum wavefunctions may be constructed from Lobatto shape functions, especially in combination with conventional Gaussian-type basis functions. When used in the logarithmic derivative version of the Kohn variational principle, an efficient procedure for calculating molecular photoionization cross sections is obtained. As a first example, the method is applied to the benchmark system H + 2. Excellent results are found with rather moderate effort for the full investigated range of photoelectron energies (up to 200 eV).

A program for calculating partial molecular photoionization cross sections

A program for calculating partial molecular photoionization cross sections

Method to compute atomic and molecular photoionization cross sections by use of basis sets.

An alternative approach is presented to the problem of computing atomic and molecular photoionization cross sections by use of basis sets. The present method is based on a simple integral equation that relates the real polarizability on the imaginary frequency axis to the photoionization cross section. Hence the computational work consists in obtaining polarizabilities for imaginary frequencies. Many-body perturbation theory is used for that purpose, and the perturbation expansion is complete to second order in the Coulomb interaction. In that way there is a comprehensive inclusion of correlation effects. Techniques to invert the integral equation to obtain photoionization cross sections from the computed polarizabilities are discussed, and results are given for the atomic systems neon and argon as test cases.