A band‐Lanczos method for computing matrix elements of a resolvent

Efficient Full-Frequency GW Calculations Using a Lanczos Method

The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical mean-field theory. However, full-frequency GW calculations for large systems with hundreds of atoms remain computationally challenging, even after years of efforts to reduce the prefactor and improve scaling. We propose a method that reformulates the correlation part of the GW self-energy as a resolvent of a Hermitian matrix, which can be efficiently and accurately computed using the standard Lanczos method. This method enables full-frequency GW calculations of material systems with a few hundred atoms on a single computing workstation. We further demonstrate the efficiency of the method by calculating the defect-state energies of silicon quantum dots with diameters up to 4 nm and nearly 2,000 silicon atoms using only 20 computational nodes.

Revealing the Role of N Heteroatoms in Noncovalent Aromatic Interactions by Ultrafast Intermolecular Coulombic Decay

Despite the widely recognized importance of noncovalent interactions involving aromatic rings in many fields, our understanding of the underlying forces and structural patterns, especially the impact of heteroaromaticity, is still incomplete. Here, we investigate the relaxation processes that follow inner-valence ionization in a range of molecular dimers involving various combinations of benzene, pyridine, and pyrimidine, which initiate an ultrafast intermolecular Coulombic decay process. Multiparticle coincidence momentum spectroscopy, combined with ab initio calculations, enables us to explore the principal orientations of these fundamental dimers and, thus, to elucidate the influence of N heteroatoms on the relative preference of the aromatic π-stacking, H-bonding, and CH-π interactions and their dependence on the number of nitrogen atoms in the rings. Our studies reveal a sensitive tool for the structural imaging of molecular complexes and provide a more complete understanding of the effects of N heteroatoms on the noncovalent aromatic interactions at the molecular level.

Concerted Double Hydrogen-Bond Breaking by Intermolecular Coulombic Decay in the Formic Acid Dimer

Hydrogen bonds are ubiquitous in nature and of fundamental importance to the chemical and physical properties of molecular systems in the condensed phase. Nevertheless, our understanding of the structural and dynamical properties of hydrogen-bonded complexes in particular in electronic excited states remains very incomplete. Here, by using formic acid (FA) dimer as a prototype of DNA base pair, we investigate the ultrafast decay process initiated by removal of an electron from the inner-valence shell of the molecule upon electron-beam irradiation. Through fragment-ion and electron coincident momentum measurements and ab initio calculations, we find that de-excitation of an outer-valence electron at the same site can initiate ultrafast energy transfer to the neighboring molecule, which is in turn ionized through the emission of low-energy electrons. Our study reveals a concerted breaking of double hydrogen-bond in the dimer initiated by the ultrafast molecular rotations of two FA⁺ cations following this nonlocal decay mechanism.

Interatomic and Intermolecular Coulombic Decay

Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed.

Beyond structure: ultrafast X-ray absorption spectroscopy as a probe of non-adiabatic wavepacket dynamics

The excited state non-adiabatic dynamics of polyatomic molecules, leading to the coupling of structural and electronic dynamics, is a fundamentally important yet challenging problem for both experiment and theory. Ongoing developments in ultrafast extreme vacuum ultraviolet (XUV) and soft X-ray sources present new probes of coupled electronic-structural dynamics because of their novel and desirable characteristics. As one example, inner-shell spectroscopy offers localized, atom-specific probes of evolving electronic structure and bonding (via chemical shifts). In this work, we present the first on-the-fly ultrafast X-ray time-resolved absorption spectrum simulations of excited state wavepacket dynamics: photo-excited ethylene. This was achieved by coupling the ab initio multiple spawning (AIMS) method, employing on-the-fly dynamics simulations, with high-level algebraic diagrammatic construction (ADC) X-ray absorption cross-section calculations. Using the excited state dynamics of ethylene as a test case, we assessed the ability of X-ray absorption spectroscopy to project out the electronic character of complex wavepacket dynamics, and evaluated the sensitivity of the calculated spectra to large amplitude nuclear motion. In particular, we demonstrate the pronounced sensitivity of the pre-edge region of the X-ray absorption spectrum to the electronic and structural evolution of the excited-state wavepacket. We conclude that ultrafast time-resolved X-ray absorption spectroscopy may become a powerful tool in the interrogation of excited state non-adiabatic molecular dynamics.

The band 12 issue of norbornane: a study of higher shake-up states

In line with a recent study of the electronic structure of the cage compound norbornane (J. Chem. Phys. 121 (2004), 10525; J. Phys. Chem. A 109 (2005), 4267), symmetry adapted cluster expansion configuration interaction (SAC-CI) general R calculations have been performed and compared with results obtained by the third order algebraic diagrammatic construction scheme [ADC(3)]. Comparison has been made with previously performed electron momentum spectroscopy (EMS) and ultraviolet photo-electron measurements. The region around ~25 eV (band 12), characterized by an elaborated band in the EMS spectrum which is missing in previous Green's function and ADC calculations, is investigated. This study is completed with outer-valence Green's function (OVGF) and SAC-CI/SD-R calculations, and results are obtained by employing (single and double) ionization extended second order ADC [ADC(2)-x]. Since ADC(3) only includes 2h-1p shake-up states, while SAC-CI general-R also includes higher order states, the agreement between both methods assures that the higher order shake-up states do not play an important role in the ionization spectrum of norbornane. While the band-12 issue of norbornane is therefore still open for further discussion, a tentative description in terms of ultrafast nuclear dynamical effects and autoionization processes has become more plausible.

LANCZOS ALGORITHMS AND CROSS CORRELATION FUNCTIONS Cif(E)

Cross correlation (CC) functions Cif(E) play an important role in chemical physics. They appear in the description of reactive scattering, photo-dissociation, photo-electron spectroscopy and electron transfer to mention a few. In this paper, we discuss two methods based on the Lanczos algorithm to compute the CC function for several initial and final states at the same time, without diagonalization. The property of the coupled two-term recursions variant of the Lanczos algorithm that yields a decomposition [Formula: see text] of the tridiagonal Lanczos matrix is crucial. The first method, the quasi minimal-recursive residue generation method (QM-RRGM) is based on solving a set of linear equations whereas the second method is based on a band-Lanczos method. The computational cost is of the same order of magnitude for both methods and is given by the number of matrix-vector multiplications in the underlying Lanczos method. Only a small set of scalars needs to be updated each recursion. The methods are compared for a model problem, the continuum resonance Raman cross section for a collinear model of CH2IBr . Both methods shows similar convergence properties. By adding a pre-conditioner, the rate of convergence can be increased dramatically.

Reduced-Order Modeling, Error Estimation, and the Role of the Start-Vector: The Recursive Residue Generation Method Revisited

The recursive residue generation method (RRGM) [Wyatt, R. E. Adv. Chem. Phys. 1989, 73, 231] is re-derived using the formalism of reduced-order modeling [Bai, Z. Appl. Numerical Math. 2002, 43, 9]. A stopping criteria for the RRGM recursions is proposed, on the basis of an expression for an upper bound to the absolute error [Bai, Z.; Ye, Q. Electron. Trans. Numerical Anal. 1998, 7, 1]. It is further pointed out that, in general, the start-vector has a negligible effect on the convergence of the RRGM.

Imaging Momentum Orbital Densities of Conformationally Versatile Molecules: A Benchmark Theoretical Study of the Molecular and Electronic Structures of Dimethoxymethane

The main purpose of the present work is to predict from benchmark many-body quantum mechanical calculations the results of experimental studies of the valence electronic structure of dimethoxymethane employing electron momentum spectroscopy, and to establish once and for all the guidelines that should systematically be followed in order to reliably interpret the results of such experiments on conformationally versatile molecules. In a first step, accurate calculations of the energy differences between stationary points on the potential energy surface of this molecule are performed using Hartree-Fock (HF) theory and post-HF treatments of improving quality (MP2, MP3, CCSD, CCSD(T), along with basis sets of increasing size. This study focuses on the four conformers of this molecule, namely the trans-trans (TT), trans-gauche (TG), gauche-gauche (G+G+), and gauche-gauche (G+G-) structures, belonging to the C2v, C1, C2, and Cs symmetry point groups, respectively. A focal point analysis supplemented by suited extrapolations to the limit of asymptotically complete basis sets is carried out to determine how the conformational energy differences at 0 K approach the full CI limit. In a second step, statistical thermodynamics accounting for hindered rotations is used to calculate Gibbs free energy corrections to the above energy differences, and to evaluate the abundance of each conformer in the gas phase. It is found that, at room temperature, the G+G+ species accounts for 96% of the conformational mixture characterizing dimethoxymethane. In a third step, the valence one-electron and shake-up ionization spectrum of dimethoxymethane is analyzed according to calculations on the G+G+ conformer alone by means of one-particle Green's function [1p-GF] theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. A complete breakdown of the orbital picture of ionization is noted at electron binding energies above 22 eV. A comparison with available (e,2e) ionization spectra enables us to identify specific fingerprints of through-space orbital interactions associated with the anomeric effect. At last, based on our 1p-GF/ADC(3) assignment of spectral bands, accurate and spherically averaged (e,2e) electron momentum distributions at an electron impact energy of 1200 eV are computed from the related Dyson orbitals. Very significant discrepancies are observed with momentum distributions obtained for several outer-valence levels using standard Kohn-Sham orbitals.

Ionization and double ionization of small water clusters

The valence ionization and double ionization spectra of the water molecule, of the water dimer, and the cyclic water clusters (H2O)3 and (H2O)4 are calculated by ab initio Green's function methods and discussed in some detail. Particular attention is paid to the analysis of the development of the spectra with increasing cluster size. Electronic decay following inner valence ionization is addressed and a crude estimate for the kinetic energy spectrum of the secondary electrons is given for the clusters.

Spectral convergence of the quadrature discretization method in the solution of the Schrödinger and Fokker-Planck equations: Comparison with sinc methods

Spectral methods based on nonclassical polynomials and Fourier basis functions or sinc interpolation techniques are compared for several eigenvalue problems for the Fokker-Planck and Schrodinger equations. A very rapid spectral convergence of the eigenvalues versus the number of quadrature points is obtained with the quadrature discretization method (QDM) and the appropriate choice of the weight function. The QDM is a pseudospectral method and the rate of convergence is compared with the sinc method reported by Wei [J. Chem. Phys., 110, 8930 (1999)]. In general, sinc methods based on Fourier basis functions with a uniform grid provide a much slower convergence. The paper considers Fokker-Planck equations (and analogous Schrodinger equations) for the thermalization of electrons in atomic moderators and for a quartic potential employed to model chemical reactions. The solution of the Schrodinger equation for the vibrational states of I2 with a Morse potential is also considered.

Green's function study of the one-electron and shake-up ionization spectra of unsaturated hydrocarbon cage compounds

The valence one-electron and shake-up ionization spectra of stella-2,6-diene, stella-2,6-dione, bicyclo-[2.2.2]-octane-2,5-dione, and bicyclo-[2.2.1]-heptane-2,5-dione have been exhaustively studied, up to the double ionization threshold and beyond, by means of one-particle Green's function theory. This study is based on calculations employing the outer-valence Green's function and the third-order algebraic diagrammatic construction schemes, along with a variety of basis sets. A comparison is made with available ultraviolet (He I) photoelectron and (e, 2e) electron-impact ionization spectra, with main focus on the identification of spectral fingerprints for cyclic strains and through-bond pi-conjugation. As a byproduct, our results demonstrate that it is impossible to reliably assign complex (e, 2e) ionization spectra by resorting only to Hartree-Fock or Kohn-Sham orbital energies and to the related electron momentum distributions.

Quasiparticle band structure of infinite hydrogen fluoride and hydrogen chloride chains

We study the quasiparticle band structure of isolated, infinite (HF)(infinity) and (HCl)(infinity) bent (zigzag) chains and examine the effect of the crystal field on the energy levels of the constituent monomers. The chains are one of the simplest but realistic models of the corresponding three-dimensional crystalline solids. To describe the isolated monomers and the chains, we set out from the Hartree-Fock approximation, harnessing the advanced Green's function methods local molecular orbital algebraic diagrammatic construction (ADC) scheme and local crystal orbital ADC (CO-ADC) in a strict second order approximation, ADC(2,2) and CO-ADC(2,2), respectively, to account for electron correlations. The configuration space of the periodic correlation calculations is found to converge rapidly only requiring nearest-neighbor contributions to be regarded. Although electron correlations cause a pronounced shift of the quasiparticle band structure of the chains with respect to the Hartree-Fock result, the bandwidth essentially remains unaltered in contrast to, e.g., covalently bound compounds.

Study of the molecular structure, ionization spectrum, and electronic wave function of 1,3-butadiene using electron momentum spectroscopy and benchmark Dyson orbital theories

The scope of the present work is to reconcile electron momentum spectroscopy with elementary thermodynamics, and refute conclusions drawn by Saha et al. in J. Chem. Phys. 123, 124315 (2005) regarding fingerprints of the gauche conformational isomer of 1,3-butadiene in electron momentum distributions that were experimentally inferred from gas phase (e,2e) measurements on this compound [M. J. Brunger et al., J. Chem. Phys. 108, 1859 (1998)]. Our analysis is based on thorough calculations of one-electron and shake-up ionization spectra employing one-particle Green's function theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. Accurate spherically averaged electron momentum distributions are correspondingly computed from the related Dyson orbitals. The ionization spectra and Dyson orbital momentum distributions that were computed for the trans-conformer of 1,3-butadiene alone are amply sufficient to quantitatively unravel the shape of all available experimental (e,2e) electron momentum distributions. A comparison of theoretical ADC(3) spectra for the s-trans and gauche energy minima with inner- and outer-valence high-resolution photoelectron measurements employing a synchrotron radiation beam [D. M. P. Holland et al., J. Phys. B 29, 3091 (1996)] demonstrates that the gauche structure is incompatible with ionization experiments in high-vacuum conditions and at standard temperatures. On the other hand, outer-valence Green's function calculations on the s-trans energy minimum form and approaching basis set completeness provide highly quantitative insights, within approximately 0.2 eV accuracy, into the available experimental one-electron ionization energies. At last, analysis of the angular dependence of relative (e,2e) ionization intensities nicely confirms the presence of one rather intense pi(-2) pi(*+1) satellite at approximately 13.1 eV in the ionization spectrum of the s-trans conformer.

Double ionization of fluorinated benzenes: hole localization and delocalization effects

The dense double ionization spectra of all the twelve fluoro-substituted benzene molecules are investigated in great detail by Green's function ADC2 calculations and a two-hole density mapping. Double ionization is shown to provide an extremely sensitive tool of electronic structure analysis. The calculations evidence and measure quantitatively how the charge distribution is dictated by the complex interplay between the resilience of the aromatic ring electronic structure and the disruptive effect of the electronegative halogen substituents. Successive substitutions are found not to have any synergic effect, but affect the spectra in very identifiable ways. The Auger spectra of the fluorobenzenes are interpreted in the light of the charge distribution results, using the foreign-imaging model. The double charge transfer spectra are also analyzed and discussed.

Investigation into the Valence Electronic Structure of Norbornene Using Electron Momentum Spectroscopy, Green's Function, and Density Functional Theories

Results of a study of the valence electronic structure of norbornene (C(7)H(10)), up to binding energies of 30 eV, are reported. Experimental electron momentum spectroscopy (EMS) and theoretical Green's function and density functional theory approaches were utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among the tested models, the combination of the Becke-Perdew functional and a polarized valence basis set of triple-zeta quality provides the best representation of the electron momentum distributions for all 19 valence orbitals of norbornene. This experimentally validated model was then used to extract other molecular properties of norbornene (geometry, infrared spectrum). When these calculated properties are compared to corresponding results from independent measurements, reasonable agreement is typically found. Due to the improved energy resolution, EMS is now at a stage to very finely image the effective topology of molecular orbitals at varying distances from the molecular center, and the way the individual atomic components interact with each other, often in excellent agreement with theory. This will be demonstrated here. Green's Function calculations employing the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than about 22 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet emission and newly presented (e,2e) ionization spectra. Finally, limitations inherent to calculations of momentum distributions based on Kohn-Sham orbitals and employing the vertical depiction of ionization processes are emphasized, in a formal discussion of EMS cross sections employing Dyson orbitals.

Effect of relativity on the ionization spectra of the xenon fluorides XeFn (n=2, 4, 6)

Noble gas compounds exhibit special chemical bonding situations and have been investigated by various spectroscopic and theoretical techniques. In this work we calculate the ionization spectra of the xenon fluorides (XeF2,XeF4, and XeF6) in the valence and subvalence (down to Xe 4d) areas by application of the recently developed Dirac-Hartree-Fock one-particle propagator technique. In this technique, the relativistic (four-component) and electron correlation effects are computed simultaneously. The xenon compounds show considerable spin-orbit splitting strongly influencing the photoelectron spectrum not reproducible in prior calculations. Comparison to one-component methods is made and the occurring satellite structures are interpreted. The satellite structures can be attributed either to the breakdown of the one-particle picture or to a reflection of intra-atomic and interatomic Auger decay processes within the molecule.