Electron Propagator Theory Research Articles

Benchmarking model chemistry composite calculations for vertical ionization potential of molecular systems

In chemical science, the vertical ionization potential (VIP) is a crucial metric for understanding the electronegativity, hardness and softness of chemical material systems as well as the electronic structure and stability of molecules. Ever since the last century, the model chemistry composite methods have witnessed tremendous developments in computing the thermodynamic properties as well as the barrier heights. However, their performance in realm of the vertical electron processes of molecular systems has been rarely explored. In this study, we for the first time benchmarked the model chemistry composite methods (e.g., CBS-QB3, G4 and W1BD) in comparison with the commonly used Koopmans's theorem (KT), electron propagator theory (e.g., OVGF, D2, P3 and P3+) and CCSD(T) methods in calculating the VIP for up to 613 molecular systems with available experimental measurements. The large-scale test calculations strongly showed that the CBS-QB3 model chemistry composite technique can be well recommended to calculate VIP from the perspectives of accuracy, economy and applicability. Notably, the VIP values of up to 7 molecules were identified to have the absolute errors of larger than 0.3 eV at all calculation levels, which have strong hints that their VIP experimental values should be re-investigated.

Achieving Accuracy and Economy for Calculating Vertical Detachment Energies of Molecular Anions: A Model Chemistry Composite Methods.

The vertical detachment energy (VDE) is a vital factor for predicting the stability of anions that have important applications in the atom, molecule and cluster science. Due to the synthetic or characterization difficulty of anions, accurate and efficient predictions of VDE independent of laboratory data have always been an appealing task to remedy the experimental deficiencies. Unfortunately, the generally adopted CCSD(T) and electron propagator theory (EPT) methods have respectively been proven to be reliable but very cost-expensive, and cost-effective but sometimes problematic when Koopman's theorem is invalid. Here, we for the first time introduced and benchmarked a series of model chemistry composite methods (e. g., CBS-QB3, G4 and W1BD) on calculating VDE for 57 molecular anions. Notably, CBS-QB3 exceeds the accuracy of CCSD(T) while approaching the economy of EPT. Therefore, we highly recommend the composite method CBS-QB3 to compute VDEs for molecular anions in the attractive "killing two birds with one stone" manner.

Electronic structure analysis and DFT benchmarking of Rydberg-type alkali-metal-crown ether, -cryptand, and -adamanzane complexes.

Density functional theory (DFT) and electron propagator theory (EPT) calculations were performed to study ground and excited electronic structures of alkali-metal (M) coordinated 9-crown-3, 24-crown-8, [2.1.1]cryptand, o-Me2-1.1.1, and 36Adamanzane complexes. Each complex bears an expanded electron in the periphery and occupies diffuse 1p-, 1d-, 1f-type molecular orbitals (or superatomic 1P, 1D, 1F orbitals) in excited electronic states. The calculated superatomic shell model of the M(9-crown-3)2 is 1S, 1P, 1D, 1F, 2S, 2P, 2D, 1G and it is held by all other complexes up to the studied 1F level. Due to the highly diffuse nature of the electron, the ionization energies of these complexes are significantly lower (1.6-2.0 eV) and hence these complexes belong to the superalkali category. The ab initio EPT ionization energy and the excitation energies of the Li(9-crown-3)2 were used to evaluate DFT errors associated with a series of exchange correlation functionals that span multiple rungs of Jacob's ladder (i.e., GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, double-hybrid). Among these, the best performing functional is the range-separated hybrid CAM-B3LYP and the errors are within 6% of high-level ab initio EPT results. The accuracy of CAM-B3LYP is indeed transferable to similar complexes and hence the findings are expected to accelerate the progression of studies of Rydberg-type systems.

Electron binding energies of SO2 at the surface of a water cluster

The electronic properties of SO2 at the surface of a water cluster were investigated by employing a combination of Born–Oppenheimer molecular dynamics and electron propagator theory (EPT). In our work, we utilized a revised version of the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional, which incorporates empirical corrections for dispersion interactions in line with a recent study of the air–water interface conducted by Ohto et al. [J. Phys. Chem. Lett. 10(17), 4914–4919 (2019)]. Polarization effects induce a significant broadening of the electron binding energy distribution, as predicted by EPT. This broadening can result in a substantial increase in electron affinity, impacting the chemical reactivity of SO2 at the air–water interface, a topic of significant and recent research interest. We discuss the relationship between electron binding energies (EBEs) and the specific connections of SO2 to water. The results indicate that configurations involving an OS⋯H bond tend to yield higher electron affinities compared to complex formation through S⋯OW bonds. Surprisingly, SO2 molecules not bound to water molecules according to a specific criterion may also exhibit higher electron affinities. This feature can be explained by the role played by the polarization field from water molecules. Our best estimate for the HOMO–LUMO (H–L) gap of SO2 at the surface of a water cluster is 11.6 eV. Very similar H–L gaps are predicted for isolated and micro-solvated SO2. Fukui functions for the gas phase, and the micro-solvated SO2–H2O complex supports the view that the LUMO is predominantly localized on the SO2 moiety.

Δ-based composite models for calculating x-ray absorption and emission energies

A practical ab initio composite method for modeling x-ray absorption and non-resonant x-ray emission is presented. Vertical K-edge excitation and emission energies are obtained from core-electron binding energies calculated with spin-projected ΔHF/ΔMP and outer-core ionization potentials/electron affinities calculated with electron propagator theory. An assessment of the combined methodologies against experiment is performed for a set of small molecules containing second-row elements.

Ab Initio Approach to the Structure, Vibrational Properties, and Electron Binding Energies of H2S∙∙∙SO2.

The present study employs high-level ab initio calculations to investigate the structure, vibrational frequencies, and electronic properties of H2S∙∙∙SO2. The analysis of vibrational frequencies reveals an intramolecular vibrational energy transfer phenomenon, where energy from the stretching modes of H2S is transferred to the ν1s mode of SO2. At the CCSD(T)/aug-cc-pVQZ level, the interaction energy between H2S and SO2 is predicted to be 2.78 kcal/mol. Electron propagator theory calculations yield a HOMO-LUMO gap of 8.24 eV for H2S∙∙∙SO2. Furthermore, by utilizing ab initio results for the adiabatic ionization energy and electron affinity, the electrophilicity of H2S∙∙∙SO2 is estimated to be 2.01 eV. This value is similar to the electrophilicity of SO2, suggesting comparable reactivity and chemical behavior. The non-covalent interaction (NCI) analysis of the H2S∙∙∙SO2 complex emphasizes the significant contribution of non-covalent van der Waals interactions in its energetic stabilization.

Theoretical investigation of copper clusters using the electron propagator theory

Theoretical investigation of copper clusters using the electron propagator theory

Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides

A new generation of ab initio electron-propagator self-energy approximations that are free of adjustable parameters is tested on a benchmark set of 55 vertical electron detachment energies of closed-shell anions. Comparisons with older self-energy approximations indicate that several new methods that make the diagonal self-energy approximation in the canonical Hartree-Fock orbital basis provide superior accuracy and computational efficiency. These methods and their acronyms, mean absolute errors (in eV), and arithmetic bottlenecks expressed in terms of occupied (O) and virtual (V) orbitals are the opposite-spin, non-Dyson, diagonal second-order method (os-nD-D2, 0.2, OV2), the approximately renormalized quasiparticle third-order method (Q3+, 0.15, O2V3) and the approximately renormalized, non-Dyson, linear, third-order method (nD-L3+, 0.1, OV4). The Brueckner doubles with triple field operators (BD-T1) nondiagonal electron-propagator method provides such close agreement with coupled-cluster single, double, and perturbative triple replacement total energy differences that it may be used as an alternative means of obtaining standard data. The new methods with diagonal self-energy matrices are the foundation of a composite procedure for estimating basis-set effects. This model produces accurate predictions and clear interpretations based on Dyson orbitals for the photoelectron spectra of the nucleotides found in DNA.

Photoionization of poly-nitrosobenzenes

The electronic structures and valence ionizations of seven nitrosobenzene derivatives have been studied using high-level ab initio methods: electron-propagator theory (EPT) and complete active space self-consistent field method/N-electron valence state perturbation theory (CASSCF/NEVPT2). We describe the valence electronic structure as dependent on the number and position of nitroso substituents. We also discuss the electronic structures of azodioxide geometric isomers and their monomers in connection with photodissociation and dimerization reactions.

Photoionization of stable mesoionic compounds

The electronic structures and valence ionizations of three mesoionic compounds: 3-methylsydnone, 3-phenylsydnone and 3-methyl-2-phenyl-1,3,4-thiadiazole-5-thione have been studied using high-level ab initio methods: electron-propagator theory (EPT) and coupled cluster method (IP-EOM-CCSD). We discuss the influence of valence electronic structure on chemical reactivity using global and local electrophilicity indices. We also discuss (non)aromatic character of the studied molecules using information pertaining to photoelectron spectra.

Investigation on the electronic structures of thiamine and related compounds: Free base or salt?

We report the simulated photoelectron spectra of thiamine free base, thiamine and thiamine diphosphate (ThDP) in the gas phase. The structures of eighty conformers of thiamine (vitamin B1) were optimized by DFT method at the B3LYP/6-31+G(d) level. Then population ratios (PRS) with Boltzmann distribution equation were calculated using Gibbs free energy and the stable conformers were obtained. The ionization energies of these conformers were determined by two high-level computational methods. General-R-symmetry adapted cluster-configuration interaction (general-R-SAC-CI) method and electron-propagator theory (EPT) method were used to obtain vertical valence ionization energies (IP). To characterize the nature of ionization processes about different spectral bands, the natural bonding orbital (NBO) method was used to obtain orbital electron densities. The electron correlation was taken into account with SAC-CI method and MOs shapes and ionization assignments given for each spectral band. Results for ThDP show that spectra of two conformers are different: oxygen lone pair ionizations appear at higher ionization energies in the spectrum of conformer II while giving rise to the first ionization band in conformer I. The validity of Koopmans’s approximation was considered for each ionization band and the role of electron correlation was attributed to breaking down of this approximation. The implications of electronic structure results for biological activity of thiamin are discussed. Comparison with the earlier work using aerosol thermodesorption method suggests that free base was present in their photoionization spectra in addition to the deprotonated cation.

Electro-physical properties of GaAs nanoscopic clusters

The electric current through the Cu-GaAs-Cu nanoclusters and their quasi-bandgap widths (HOMO-LUMO differences) are calculated. The ab initio electron propagator theory (Green-Keldysh functions formalism) is implemented for the calculations (that has been never done before for Cu-As-Cu nanoclusters). The calculated current-voltage characteristics exhibit non-linear character with magnitudes of current reaching several pAs. The calculated quasi-bandgap width (HOMO-LUMO difference) of nanocluster exhibits solid-like behavior with the increase of nanocluster's size. The obtained dependencies and characteristics will be useful for semiconductor quantum-dots manufactures and practitioners in the field of semiconductor nanoelectronics and optoelectronics, in particular, for developers of EM radiation sources and detectors with frequency-tuning ability.

A new generation of diagonal self-energies for the calculation of electron removal energies.

A new generation of diagonal self-energy approximations in ab initio electron propagator theory for the calculation of electron removal energies of molecules and molecular ions has been derived from an intermediately normalized, Hermitized super-operator metric. These methods and widely used antecedents such as the outer valence Green's function and the approximately renormalized partial third order method are tested with respect to a dataset of vertical ionization energies generated with a valence, triple-ζ, correlation-consistent basis set and a converged series of many-body calculations whose accuracy approaches that of full configuration interaction. Several modifications of the diagonal second-order self-energy, a version of G0W0 theory based on Tamm-Dancoff excitations and several non-diagonal self-energies are also included in the tests. All new methods employ canonical Hartree-Fock orbitals. No adjustable or empirical parameters appear. A hierarchy of methods with optimal accuracy for a given level of computational efficiency is established. Several widely used diagonal self-energy methods are rendered obsolete by the new hierarchy whose members, in order of increasing accuracy, are (1) the opposite-spin non-Dyson diagonal second-order or os-nD-D2, (2) the approximately renormalized third-order quasiparticle or Q3+, (3) the renormalized third-order quasiparticle or RQ3, (4) the approximately renormalized linear third-order or L3+, and (5) the renormalized linear third-order or RL3 self-energies.

ΔSCF Dyson orbitals and pole strengths from natural ionization orbitals.

The calculation of photoionization cross sections can play a key role in spectral assignments using modeling and simulation. In this work, we provide formal relationships between pole strengths, which are proportional to the photoionization cross section, and terms related to the natural ionization orbital model for ΔSCF calculations. A set of numerical calculations using the developed models is carried out. Pole strength values computed using the two approaches developed for ΔSCF calculations demonstrate excellent agreement with an electron propagator theory model.

The DIRAC code for relativistic molecular calculations.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Experimental and Theoretical Photoemission Study of Indole and Its Derivatives in the Gas Phase

The valence and core-level photoelectron spectra of gaseous indole, 2,3-dihydro-7-azaindole, and 3-formylindole have been investigated using VUV and soft X-ray radiation supported by both an ab initio electron propagator and density functional theory calculations. Three methods were used to calculate the outer valence band photoemission spectra: outer valence Green function, partial third order, and renormalized partial third order. While all gave an acceptable description of the valence spectra, the last method yielded very accurate agreement, especially for indole and 3-formylindole. The carbon, nitrogen, and oxygen 1s core-level spectra of these heterocycles were measured and assigned. The double ionization appearance potential for indole has been determined to be 21.8 ± 0.2 eV by C 1s and N 1s Auger photoelectron spectroscopy. Theoretical analysis identifies the doubly ionized states as a band consisting of two overlapping singlet states and one triplet state with dominant configurations corresponding to holes in the two uppermost molecular orbitals. One of the singlet states and the triplet state can be described as consisting largely of a single configuration, but other doubly ionized states are heavily mixed by configuration interactions. This work provides full assignment of the relative binding energies of the core level features and an analysis of the electronic structure of substituted indoles in comparison with the parent indole.

Dyson Orbitals and Double Rydberg Anions: Methylated, Annulated, and Paramagnetic.

A double Rydberg anion (DRA) consists of a saturated, closed-shell, molecular cation and two electrons that occupy diffuse orbitals. Techniques of ab initio electron propagator theory (EPT) predict the existence and spectra of three new classes of DRAs. The first, with the formula NH4-n(CH3)n-, has vertical electron detachment energies (VEDEs) that vary between 0.24 and 0.39 eV and corresponding Dyson orbitals that accumulate near the periphery of N-H bonds. An internal hydrogen bond that forms a ring with five members occurs in the second class. In paramagnetic DRA isomers, electrons are assigned to two, diffuse, triplet-coupled spin-orbitals that localize outside the N-H bonds of a cationic, tetrahedral center or outside bonds on a nearby amide or methyl group. Effects of delocalization, dispersion, and radial correlation between diffuse electrons on VEDEs are described in terms of Dyson orbitals and their pole strengths. These concepts of EPT connect ground-state and spectral properties to each other and provide a rigorous, systematic, and insightful approach to predicting and characterizing novel patterns of chemical bonding and molecular electronic structure.

Correction to "Electron Propagator Theory Approach to the Electron Binding Energies of a Prototypical Photo-Switch Molecular System: Azobenzene".

The electron binding energies for the trans and cis conformers of azobenzene (AB), a prototypical photoswitch, were investigated by electron propagator theory (EPT). The EPT results are compared with data from photoelectron and electron transmission spectroscopies and complemented by the calculation of the differences between vertical and adiabatic ionization energies and electron affinities of the AB conformers. These differences are discussed in terms of the geometry changes associated with the processes of ionization and electron attachment. The results pointed out a major difference between these processes when we compare trans-AB and cis-AB. For trans-AB, electron attachment leads to a small geometry change, whereas for cis-AB, it is the ionized structure that keeps some similarity with the neutral species. We emphasize the interest of the present results for a better understanding of recent experiments on the dark cis-trans isomerization in different environments, specifically for azobenzenes in interaction with gold nanoparticles, where the proposed cis-trans isomerization mechanism relies on electron transfer induced isomerization.

The Kohn-Sham electronic density of states of liquid HCN: Tuning a long-range corrected exchange-correlation functional for predicting electron binding energies

Abstract The electron binding energies and Kohn-Sham electronic density of states of liquid HCN were calculated by combining Born-Oppenheimer molecular dynamics with electron propagator theory and density functional theory. A modified long-range corrected Perdew-Burke-Ernzerhof exchange-correlation functional (LC-wPBE), where the parameter w was tuned for reproducing the electron binding energies of the HCN monomer and small aggregates was applied in the liquid state calculations. The average HOMO energy of HCN is red-shifted by ∼ 0.8 eV relative to its gas-phase value. The vertical electron affinity of liquid HCN is estimated as 1.08 ± 0.38 eV.

Electron Propagator Theory Approach to the Electron Binding Energies of a Prototypical Photo-Switch Molecular System: Azobenzene.

The electron binding energies for the trans and cis conformers of azobenzene (AB), a prototypical photoswitch, were investigated by electron propagator theory (EPT). The EPT results are compared with data from photoelectron and electron transmission spectroscopies and complemented by the calculation of the differences between vertical and adiabatic ionization energies and electron affinities of the AB conformers. These differences are discussed in terms of the geometry changes associated with the processes of ionization and electron attachment. The results pointed out a major difference between these processes when we compare trans-AB and cis-AB. For trans-AB, electron attachment leads to a small geometry change, whereas for cis-AB, it is the ionized structure that keeps some similarity with the neutral species. We emphasize the interest of the present results for a better understanding of recent experiments on the dark cis-trans isomerization in different environments, specifically for azobenzenes in interaction with gold nanoparticles, where the proposed cis-trans isomerization mechanism relies on electron transfer induced isomerization.