Dyson Orbitals Research Articles

CaH Rydberg series, oscillator strengths and photoionization cross sections from Molecular Quantum Defect and Dyson Orbital theories

In this work, electron-propagator methods are applied to the calculation of the ionization potential and vertical excitation energies for several Rydberg series of the CaH molecule. The present calculations cover more highly excited states than those previously reported. In particular, excitation energies for ns (n>5), np (n>5), nd (n>4) and nf Rydberg states are given. Oscillator strengths for electronic transitions involving Rydberg states of CaH, as well as photoionization cross sections for Rydberg channels, also have been determined by using the Molecular Quantum Defect Orbital approach. Good agreement has been found with the scarce comparative data that are available for oscillator strengths. To our knowledge, predictions of photoionization cross sections from the outermost orbital of CaH are made here for the first time. A Cooper minimum and mixed atomic orbital character in some of the Dyson orbitals are among the novel features of these present calculations.

Electron propagators based on generalised density operators

ABSTRACTElectron binding energies and Dyson orbitals may be obtained from the poles and residues of the electron propagator. The Dyson quasiparticle equation provides a convenient route to computing this information. Systematic approximations to the latter equation's self-energy, wherein electron correlation and final-state orbital relaxation are described, may be expressed in terms of the elements of the superoperator Hamiltonian matrix. Perturbative methods of electron propagator theory in wide use are based on a reference determinant constructed with canonical, Hartree–Fock orbitals. Generalised matrix elements of the superoperator Hamiltonian that accommodate non-integer occupation numbers associated with general, orthogonal spin orbitals are presented for the first time. Non-Hermitian terms may be systematically eliminated with perturbative corrections to generalised reference density operators. The structure of self-energy approximations that are complete through second, third, fourth or fifth order is presented in terms of superoperator Hamiltonian matrix elements. The present extensions pertain when generalised, zeroth-order density operators expressed in terms of orthonormal spin orbitals are employed.

Generalized average local ionization energy and its representations in terms of Dyson and energy orbitals.

Ryabinkin and Staroverov [J. Chem. Phys. 141, 084107 (2014)] extended the concept of average local ionization energy (ALIE) to correlated wavefunctions by defining the generalized ALIE as Ī(r)=-∑jλj|fj(r)|(2)/ρ(r), where λj are the eigenvalues of the generalized Fock operator and fj(r) are the corresponding eigenfunctions (energy orbitals). Here we show that one can equivalently express the generalized ALIE as Ī(r)=∑kIk|dk(r)|(2)/ρ(r), where Ik are single-electron removal energies and dk(r) are the corresponding Dyson orbitals. The two expressions for Ī(r) emphasize different physical interpretations of this quantity; their equivalence enables one to calculate the ALIE at any level of ab initio theory without generating the computationally expensive Dyson orbitals.

Theoretical investigation of alignment-dependent intense-field fragmentation of acetylene

We analyze the alignment-dependent dissociative and nondissociative ionization of acetylene, ${\mathrm{C}}_{2}{\mathrm{H}}_{2}$. Numerical models describing the yield of the singly and doubly charged ions $({\mathrm{C}}_{2}{\mathrm{H}}_{2}{}^{+},{\mathrm{C}}_{2}{\mathrm{H}}_{2}{}^{2+})$ and several fragmentation and isomerization channels $({\mathrm{C}}_{2}{\mathrm{H}}^{+}+{\mathrm{H}}^{+},{\mathrm{CH}}^{+}+{\mathrm{CH}}^{+},{\mathrm{CH}}_{2}{}^{+}+{\mathrm{C}}^{+})$ as a function of the relative alignment angle between the laser polarization axis and the molecular axis are presented. We apply and compare two different approaches. The first is based on time-dependent density functional theory. The second is a quasi-single-particle approach using the Dyson orbitals. We find good agreement between the results of both methods. A comparison of our theoretical predictions with experimental data allows us to show that the alignment-dependent yield of most reaction channels is described to high accuracy assuming sequential ionization. However, for some of the fragmentation channels, namely, ${\mathrm{CH}}^{+}+{\mathrm{CH}}^{+}$ and ${\mathrm{C}}_{2}{\mathrm{H}}^{+}+{\mathrm{H}}^{+}$, we find non-negligible influence of recollisional ionization.

Photoionization of furan from the ground and excited electronic states

Here we present a comparative computational study of the photoionization of furan from the ground and the two lowest-lying excited electronic states. The study aims to assess the quality of the computational methods currently employed for treating bound and continuum states in photoionization. For the ionization from the ground electronic state, we show that the Dyson orbital approach combined with an accurate solution of the continuum one particle wave functions in a multicenter B-spline basis, at the density functional theory (DFT) level, provides cross sections and asymmetry parameters in excellent agreement with experimental data. On the contrary, when the Dyson orbitals approach is combined with the Coulomb and orthogonalized Coulomb treatments of the continuum, the results are qualitatively different. In excited electronic states, three electronic structure methods, TDDFT, ADC(2), and CASSCF, have been used for the computation of the Dyson orbitals, while the continuum was treated at the B-spline/DFT level. We show that photoionization observables are sensitive probes of the nature of the excited states as well as of the quality of excited state wave functions. This paves the way for applications in more complex situations such as time resolved photoionization spectroscopy.

Characterizing metastable states beyond energies and lifetimes: Dyson orbitals and transition dipole moments.

The theoretical description of electronic resonances is extended beyond calculations of energies and lifetimes. We present the formalism for calculating Dyson orbitals and transition dipole moments within the equation-of-motion coupled-cluster singles and doubles method for electron-attached states augmented by a complex absorbing potential (CAP-EOM-EA-CCSD). The capabilities of the new methodology are illustrated by calculations of Dyson orbitals of various transient anions. We also present calculations of transition dipole moments between transient and stable anionic states as well as between different transient states. Dyson orbitals characterize the differences between the initial neutral and final electron-attached states without invoking the mean-field approximation. By extending the molecular-orbital description to correlated many-electron wave functions, they deliver qualitative insights into the character of resonance states. Dyson orbitals and transition moments are also needed for calculating experimental observables such as spectra and cross sections. Physically meaningful results for those quantities are obtained only in the framework of non-Hermitian quantum mechanics, e.g., in the presence of a complex absorbing potential (CAP), when studying resonances. We investigate the dependence of Dyson orbitals and transition moments on the CAP strength and illustrate how Dyson orbitals help understand the properties of metastable species and how they are affected by replacing the usual scalar product by the so-called c-product.

Time-dependent Dyson orbital theory.

Although time-dependent density functional theory (TDDFT) has become the tool of choice for real-time propagation of the electron density ρ(N)(t) of N-electron systems, it also encounters problems in this application. The first problem is the neglect of memory effects stemming from the, in TDDFT virtually unavoidable, adiabatic approximation, the second problem is the reliable evaluation of the probabilities P(n)(t) of multiple photoinduced ionization, while the third problem (which TDDFT shares with other approaches) is the reliable description of continuum states of the electrons ejected in the process of ionization. In this paper time-dependent Dyson orbital theory (TDDOT) is proposed. Exact TDDOT equations of motion (EOMs) for time-dependent Dyson orbitals are derived, which are linear differential equations with just static, feasible potentials of the electron-electron interaction. No adiabatic approximation is used, which formally resolves the first TDDFT problem. TDDOT offers formally exact expressions for the complete evolution in time of the wavefunction of the outgoing electron. This leads to the correlated probability of single ionization P(1)(t) as well as the probabilities of no ionization (P(0)(t)) and multiple ionization of n electrons, P(n)(t), which formally solves the second problem of TDDFT. For two-electron systems a proper description of the required continuum states appears to be rather straightforward, and both P(1)(t) and P(2)(t) can be calculated. Because of the exact formulation, TDDOT is expected to reproduce a notorious memory effect, the "knee structure" of the non-sequential double ionization of the He atom.

Theory of pump–probe ultrafast photoemission and X-ray absorption spectra

Keldysh Green's function approach is extensively used in order to derive practical formulas to analyze pump–probe ultrafast photoemission and X-ray absorption spectra. Here the pump pulse is strong enough whereas the probe X-ray pulse can be treated by use of a perturbation theory. We expand full Green's function in terms of renormalized Green's function without the interaction between electrons and probe pulse. The present theoretical formulas allow us to handle the intrinsic and extrinsic losses, and furthermore resonant effects in X-ray Absorption Fine Structures (XAFS). To understand the radiation field screening in XPS spectra, we have to use more sophisticated theoretical approach. In the ultrafast XPS and XAFS analyses the intrinsic and extrinsic loss effects can interfere as well. In the XAFS studies careful analyses are necessary to handle extrinsic losses in terms of damped photoelectron propagation. The nonequilibrium dynamics after the pump pulse irradiation is well described by use of the time-dependent Dyson orbitals. Well above the edge threshold, ultrafast photoelectron diffraction and extended X-ray absorption fine structure (EXAFS) provide us with transient structural change after the laser pump excitations. In addition to these slow processes, the rapid oscillation in time plays an important role related to pump electronic excitations. Near threshold detailed information could be obtained for the combined electronic and structural dynamics. In particular high-energy photoemission and EXAFS are not so influenced by the details of excited states by pump pulse. Random-Phase Approximation (RPA)-boson approach is introduced to derive some practical formulas for time-dependent intrinsic amplitudes.

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.

Theoretical study of photo-double ionization of CO2 in the equal energy sharing regime using Dyson orbitals and the parameterized three center continuum wave function

The theoretical procedure for the determination of the multiply differential cross sections (MDCS) applied recently [, ] to the vertical photo-double ionization of a diatomic N2 molecule is extended to the three center CO2 molecule producing dissociative dication. Dyson orbitals for the bound active electrons are introduced, and the parameterized three-center continuum wave function in its correlated form is used to describe the two ejected electrons. The variation of the MDCS for the coincidence detection of the two ejected electrons, for a randomly orientated internuclear axis is studied. The comparison of our results to those obtained by the Gaussian parametrization formula shows the similarities and the differences between the behavior of an atomic target and CO2.

Mapping the dissociative ionization dynamics of molecular nitrogen with attosecond resolution

SynopsisWe wish to understand the processes underlying the ionization dynamics of N2 as experimentally induced and studied by recording the kinetic energy release (KER) in a XUV-pump/IR-probe setup. To this end a theoretical model was developed describing the ionization process using Dyson Orbitals and, subsequently, the dissociation process using a large set of diabatic potential energy surfaces (PES) on which to propagate. From said set of PES, a small subset is extracted allowing for the identification of one and two photon processes chiefly responsible for the experimentally observed features.

Strong field ionization of small hydrocarbon chains with full 3D momentum analysis

SynopsisStrong field ionization of small hydrocarbon chains is studied in a kinematic complete experiment using a reaction microscope. By coincidence detection of ions and electrons different ionization continua populated during the ionization process are identified. In addition, photoelectron momentum distributions from laser-aligned molecules allow to characterize the electron wavepackets emerging from different Dyson orbitals.

The three-center parameterized continuum wave function and Dyson orbitals for the determination of the triply differential cross section of the simple ionization of CO2 by electron impact

Synopsis(e,2e) ionization of the linear three center CO2 molecules by fast electron impact.

Angle-Dependent Ionization of Small Molecules by Time-Dependent Configuration Interaction and an Absorbing Potential.

The angle-dependence of strong field ionization of O2, N2, CO2, and CH2O has been studied theoretically using a time-dependent configuration interaction approach with a complex absorbing potential (TDCIS-CAP). Calculation of the ionization yields as a function of the direction of polarization of the laser pulse produces three-dimensional surfaces of the angle-dependent ionization probability. These three-dimensional shapes and their variation with laser intensity can be interpreted in terms of ionization from the highest occupied molecular orbital (HOMO) and lower lying orbitals, and the Dyson orbitals for the ground and excited states of the cations.

First-principles photoemission spectroscopy and orbital tomography in molecules from koopmans-compliant functionals.

The determination of spectral properties from first principles can provide powerful connections between microscopic theoretical predictions and experimental data, but requires complex electronic-structure formulations that fall outside the domain of applicability of common approaches, such as density-functional theory. We show here that Koopmans-compliant functionals, constructed to enforce piecewise linearity and the correct discontinuity derivative in energy functionals with respect to fractional occupation-i.e., with respect to charged excitations-provide molecular photoemission spectra and momentum maps of Dyson orbitals that are in excellent agreement with experimental ultraviolet photoemission spectroscopy and orbital tomography data. These results highlight the role of Koopmans-compliant functionals as accurate and inexpensive quasiparticle approximations to the spectral potential.

(e,2e) simple ionization of CO2 by fast electron impact: use of three-center parameterized continuum wave function and Dyson orbitals

The variation of the triple differential cross section of the (e,2e) simple ionization of CO2 with the direction of the ejected electron is studied. The calculations are performed in the frame of a perturbative first Born procedure, using a three-center Dyson type description for the 1πg bound electron and an approximate three-center continuum solution of the corresponding Schrödinger equation for a specific wave vector for the free ejected electron, which satisfies the correct asymptotic boundary condition up to the order . Empirical values for the screening of the three nuclei of the target and for the Sommerfeld parameters of the three-center Coulomb continuum function are introduced. The results are compared to existing experimental results and a theoretical result obtained by the same approach, using a Hartree–Fock Slater type orbital.

Angle resolved photoemission from organic semiconductors: orbital imaging beyond the molecular orbital interpretation

Fascinating pictures that can be interpreted as showing molecular orbitals have been obtained with various imaging techniques. Among these, angle resolved photoemission spectroscopy (ARPES) has emerged as a particularly powerful method. Orbital images have been used to underline the physical credibility of the molecular orbital concept. However, from the theory of the photoemission process it is evident that imaging experiments do not show molecular orbitals, but Dyson orbitals. The latter are not eigenstates of a single-particle Hamiltonian and thus do not fit into the usual simple interpretation of electronic structure in terms of molecular orbitals. In a combined theoretical and experimental study we thus check whether a Dyson-orbital and a molecular-orbital based interpretation of ARPES lead to differences that are relevant on the experimentally observable scale. We discuss a scheme that allows for approximately calculating Dyson orbitals with moderate computational effort. Electronic relaxation is taken into account explicitly. The comparison reveals that while molecular orbitals are frequently good approximations to Dyson orbitals, a detailed understanding of photoemission intensities may require one to go beyond the molecular orbital picture. In particular we clearly observe signatures of the Dyson-orbital character for an adsorbed semiconductor molecule in ARPES spectra when these are recorded over a larger momentum range than in earlier experiments.

Valence-Bound and Diffuse-Bound Anions of 5-Azauracil

Structures, isomerization energies, and electron binding energies of 5-azauracil and its anions have been calculated ab initio with perturbative, coupled-cluster, and electron-propagator methods. Tautomeric structures, including those produced by proton transfer to a CH group, have been considered. Dyson orbitals and pole strengths from electron-propagator calculations validated a simple, molecular-orbital picture of anion formation. In one case, an electron may enter a delocalized π orbital, yielding a valence-bound (VB) anion with a puckered ring structure. The corresponding electron affinity is 0.27 eV; the vertical electron detachment energy (VEDE) of this anion 1.05 eV. An electron also may enter a molecular orbital that lies outside the nuclear framework, resulting in a diffuse-bound (DB) anion. In the latter case, the electron affinity is 0.06 eV and the VEDE of the DB anion is 0.09 eV. Another VB isomer that is only 0.02 eV more stable than the neutral molecule has a VEDE of 2.0 eV.

Exploring ultrafast dynamics of pyrazine by time-resolved photoelectron imaging.

We present the simulation of time-resolved photoelectron imaging spectra of pyrazine in the gas phase. The approach we have adopted is based on the combination of the ab initio nonadiabatic molecular dynamics "on the fly" with an approximate treatment of the photoionization process using Dyson orbitals and Coulomb functions to describe the bound and ionized states of the photoelectron. The method has been implemented (Humeniuk, A.; et al. J. Chem. Phys 2013, 139, 134104) in the framework of the time-dependent density functional theory and has been applied here to interrogate the ultrafast internal conversion between the S2 and S1 states in pyrazine. Conventional time-resolved photoelectron spectra without angular resolution fail to locate the S2 → S1 internal conversion, because the ionization potentials relevant for the photoionization channels S2 → D1 (π(-1)) and S1 → D0 (n(-1)) are almost identical. Introducing the angular resolution in the photoelectron spectra reveals evidence of such ultrafast internal conversion and provides a more detailed picture of the overall dynamics. The simulated time- and energy-dependent anisotropy map obtained within the Dyson/time-dependent density functional theory approach is in good agreement with its experimental counterpart provided by Horio et al. (Horio, T.; et al. J. Am. Chem. Soc. 2009, 131, 10932). Our theoretical approach represents a general tool for mapping the time- and angle-resolved photoelectron spectra in complex systems and thus can be used to investigate the ultrafast relaxation processes occurring in isolated molecules.

Attosecond electronic and nuclear quantum photodynamics of ozone: time-dependent Dyson orbitals and dipole

A nonadiabatic scheme for the description of the coupled electron and nuclear motions in the ozone molecule was proposed recently (Halász et al 2013 Phys. Rev. A 88 023425). An initial coherent nonstationary state was prepared as a superposition of the ground state and the excited Hartley band. In this situation neither the electrons nor the nuclei are in a stationary state. The multiconfiguration time-dependent Hartree method was used to solve the coupled nuclear quantum dynamics in the framework of the adiabatic separation of the time-dependent Schrödinger equation. The resulting wave packet shows an oscillation of the electron density between the two chemical bonds. As a first step for probing the electronic motion we computed the time-dependent molecular dipole and the Dyson orbitals. The latter play an important role in the explanation of the photoelectron angular distribution. Calculations of the Dyson orbitals are presented both for the time-independent as well as the time-dependent situations. We limited our description of the electronic motion to the Franck–Condon region only due to the localization of the nuclear wave packets around this point during the first 5–6 fs.