Electron Propagator Theory

A multiphoton ionisation photoelectron imaging study of thiophene

Thiophene is a prototype for the excited state photophysics that lies at the heart of many technologies within the field of organic electronics. Here, we report a multiphoton ionisation photoelectron imaging study of gas-phase thiophene using a range of photon energies to excite transitions from the ground electronic state to the first two electronically excited singlet states, from the onset of absorption to the absorption maximum. Analysis of the photoelectron spectra and angular distributions reveal features arising from direct photoionisation from the ground electronic state, and resonance-enhanced photoionisation via the electronically excited singlet states. The first two ionisation energies from the ground electronic state were confirmed to be 8.8 eV (adiabatic) and 9.6 eV (vertical). The ionisation energies from the first two electronically excited singlet states were found to be 3.7 eV (adiabatic) and 4.4 eV (vertical).

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.

Superalkalis with Hydrogen as Central Electronegative Atom and their Possible Applications: Ab Initio and DFT Study

Superalkalis are unusual species having ionization energies lower than that of the alkali metals. These species with various applications are of great importance in chemistry due to their low ionization energies and strong reducing property. A typical superalkali contains a central electronegative core decorated with excess metal ligands. In the quest for novel superalkalis, we have designed the superalkalis HLi2, HLiNa and HNa2 using hydrogen as central electronegative atom for the first time employing high level ab initio (CCSD(T), MP2) and density functional theory (ωB97X-D) methods. The superalkalis exhibit very low ionization energies, even lower than that of cesium. Stability of these species is verified from binding energy and dissociation energy values. The superalkalis are capable of reducing SO2, NO, CO2, CO and N2 molecules by forming stable ionic complexes and therefore can be used as catalysts for the reduction or activation of systems possessing very low electron affinities. The superalkalis form stable supersalts with tailored properties when interact with a superhalogen. They also show remarkably high non-linear optical responses, hence could have industrial applications. It is hoped that this work will enrich the superalkali family and spur further theoretical and experimental research in this direction.

New-Generation Electron-Propagator Methods for Molecular Electron-Binding Energies

A new generation of electron-propagator methods for the calculation of electron binding energies has surpassed its antecedents with respect to accuracy, efficiency, and interpretability. No adjustable parameters are introduced in these fully ab initio procedures. Numerical tests versus several databases of valence, vertical electron binding energies of closed-shell molecules and atoms have been performed. Easily interpreted self-energy approximations with cubic arithmetic scaling produce mean absolute errors (MAEs) of 0.2 and 0.3 eV for electron detachments and attachments, respectively. The most accurate explicitly renormalized methods with fifth-power arithmetic scaling yield MAEs below 0.1 eV for detachments and attachments. Approximate renormalization leads to more efficient fifth-power alternatives for electron detachments that achieve similar accuracy with fewer bottleneck operations. Composite protocols generate excellent predictions versus highly accurate basis-extrapolated standards and experiments. The validity of the diagonal self-energy approximation and the accuracy of the approximate renormalizations are confirmed. The success of these perturbative methods based on canonical Hartree-Fock orbitals rests on a Hermitized, intermediately normalized superoperator metric. The results of all of the new-generation calculations may be analyzed in terms of final-state orbital relaxation and differential correlation effects.

XPS and quantum chemical analysis of 4Me-BODIPY derivatives

The results of a X-ray photoelectron spectroscopy (XPS) and steady-state absorption spectroscopy study of the electronic structure, and cationic and excited states of a series of 1,3,5,7-tetramethyl-substituted BODIPYs (4Me,2R-BODIPYs) are presented. The experimental data were interpreted using high-level ab initio quantum chemical computations, including the algebraic diagrammatic construction method for the polarization propagator of the second order (ADC(2)), the outer-valence Green's function (OVGF) method, the density functional (DFT) approach, and the time-dependent DFT (TD-DFT) approach. Substitution effects on the XPS and absorption spectra were determined for 2,6-positions of 4Me,2R-BODIPY pyrrole nuclei (R = H, Br, Bu, benzyl). A very satisfactory performance of the DFT Koopmans theorem analogue was demonstrated with respect to the energy intervals between the electronic levels of 4Me,2R-BODIPY above 13 eV (BHHLYP functional) and the values of the HOMO-LUMO energy gap (ωB97X functional).

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.

Accurate Prediction of Vertical Ionization Potentials and Electron Affinities from Spin-Component Scaled CC2 and ADC(2) Models

The CC2 and ADC(2) wave function models and their spin-component scaled modifications are adopted for predicting vertical ionization potentials (VIPs) and electron affinities (VEAs). The ionic solutions are obtained as electronic excitations in the continuum orbital formalism, making possible the use of existing, widespread quantum chemistry codes with minimal modifications, in full consistency with the treatment of charge transfer excitations. The performance of different variants is evaluated via benchmark calculations on various sets from previous works, containing small- and medium-sized systems, including the nucleobases. It is shown that with the spin-scaled approximate methods, in particular the scaled opposite-spin variant of the ADC(2) method, the accuracy of EOM-CCSD is achievable at a fraction of the computational cost, also outperforming many common electron propagator approaches.

Investigation of Ionization Potential in Quantum Dots Using the Stratified Stochastic Enumeration of Molecular Orbitals Method

The overarching goal of this work is to investigate the size-dependent characteristics of the ionization potential of PbS and CdS quantum dots. The ionization potentials of quantum dots provide critical information about the energies of occupied states, which can then be used to quantify the electron-removal characteristics of quantum dots. The energy of the highest-occupied molecular orbital is used to understand electron-transfer processes when invesigating the energy-level alignment between quantum dots and electron-accepting ligands. Ionization potential is also important for investigating and interpreting electron-detachment processes induced by light (photoelectron spectra), external voltage (chemiresistance), and collision with other electrons (impact ionization). Accurate first-principles calculations of ionization potential continue to be challenging because of the computational cost associated with the construction of the frequency-dependent self-energy operator and the numerical solution of the associated Dyson equation. The computational cost becomes prohibitive as the system size increases because of the large number of 2particle-1hole (2p1h) and 1particle-2hole (1p2h) terms needed for the calculation. In this work, we present the Stratified Stochastic Enumeration of Molecular Orbitals (SSE-MO) method for efficient construction of the self-energy operator. The SSE-MO method is a real-space method and the central strategy of this method is to use stochastically enumerated sampling of molecular orbitals and molecular-orbital indices for the construction of the 2p1h and 1p2h terms. This is achieved by first constructing a composite MO-index Cartesian coordinate space followed by transformation of the frequency-dependent self-energy operator to this composite space. The evaluation of both the real and imaginary components of the self-energy operator is performed using a stratified Monte Carlo technique. The SSE-MO method was used to calculate the ionization potentials and the frequency-dependent spectral functions for a series of PbS and CdS quantum dots by solving the Dyson equation using both single-shot and iterative procedures. The ionization potentials for both PbS and CdS quantum dots were found to decrease with increasing dot size. Analysis of the frequency-dependent spectral functions revealed that for PbS quantum dots the intermediate dot size exhibited a longer relative lifetime whereas in CdS the smallest dot size had the longest relative lifetime. The results from these calculations demonstrate the efficacy of the SSE-MO method for calculating accurate ionization potentials and spectral functions of chemical systems.

The anti-corrosive behavior of benzo-fused N-heterocycles: an in silico study toward developing organic corrosion inhibitors

The work provides a computational protocol to predict the anti-corrosive performance of organic molecules through three successive phases of calculations; electron propagator theory (EPT), Monte Carlo (MC) simulations, and the density functional based tight-binding (DFTB) method. The protocol was applied to investigate the influence of two structural factors on the anti-corrosive performance of benzo fused-N-heterocycles (BFNHs) against the Fe(110) surface in an acidic medium; positional isomerism and the gradual insertion of nitrogen atoms in the heterocycle ring. The choice of BFNHs is attributed to their anti-corrosion activity and their use as building blocks in the molecular structure of many organic inhibitors. The findings indicate that EPT is a safe method for calculating the quantum chemical descriptors of the isolated molecules. Besides, the current work recommends using MC simulations and the DFTB method to describe the physical and chemical adsorption, respectively. Unexpected results were observed, as the gradual insertion of nitrogen atoms is not a specific factor for improving the inhibition efficiency of BFNHs. The findings were crystallized in equations linking the physical and chemical adsorption energies with the quantum chemical descriptors with a correlation exceeding 0.75. Besides, the peri steric hindrance plays an influential role in chemical adsorption. Intriguingly, the continuous introduction of nitrogen atoms does not increase the efficiency of the inhibitor along the way. For example, phthalazine exhibited better efficiency than benzotetrazine. In light of the above, the present protocol helps understand the anti-corrosive behavior of organic inhibitors and provides a feasible method to develop novel corrosion inhibitors.

Ground and Electronically Excited States of Main-Group-Metal-Doped B20 Double Rings

Ab initio coupled-cluster, electron propagator, and Møller-Plesset second-order perturbation theory calculations are utilized to analyze the low-lying electronic states of several metal-doped B₂₀. In the ground state, the presently focused AB₂₀/EB₂₀ (A = Li, Na, and K; E = Mg and Ca) consist of charge-separated A⁺B₂₀^-/E²⁺B₂₀^2- frameworks. The excited electronic states of AB₂₀ and EB₂₀⁺ were analyzed by computing the vertical electron attachment energies (VEAEs) of AB₂₀⁺ and EB₂₀²⁺. In several excited states, the radical electron is predominantly localized on the B₂₀ frames, which are counterparts of the low-lying states of bare B₂₀^-. A variety of basis sets were tested on obtaining VEAEs, and the aug-cc-pVDZ/_A,E d-aug-cc-pVDZ/_B combination provided the best accuracy-efficiency compromise on them. Furthermore, this work analyzes the Rydberg-like excited states of AB₂₀ and EB₂₀⁺ and will serve as a guide for future studies on similar metal-doped boron systems.

Superatomic Chelates: The Cases of Metal Aza-Crown Ethers and Cryptands

Li, Na, and Mg⁺-coordinated hexaaza-18-crown-6 ([18]aneN₆) and 1,4,7-triazacyclononane ([9]aneN₃), Li[1.1.1]cryptand, and Na[2.2.2]cryptand species possess a diffuse electron in a quasispherical s-type orbital. They populate expanded p-, d-, f-, and g-shape orbitals in low-lying excited states and hence are identified as "superatoms". By means of quantum calculations, their superatomic shell models are revealed. The observed orbital series of M([9]aneN₃)₂ and M[18]aneN₆ (M = Li, Na, Mg⁺) are identical to the 1s, 1p, 1d, 1f, 2s, and 2p. The electronic spectra of Li[1.1.1]cryptand and Na[2.2.2]cryptand were analyzed up to the 1f¹ configuration, and their transitions were found to occur at lower energies compared to their aza-crown ethers. The introduced superatomic shell models in this work closely resemble the Aufbau principle of "solvated electrons precursors". All reported alkali metal complexes bear lower ionization potentials than any atom in the periodic table; thus, they can also be recognized as "superalkalis".

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.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Intermediate state representation approach to physical properties of molecular electron-attached states: Theory, implementation, and benchmarking

Computational schemes for comprehensive studies of molecular electron-attached states and the calculation of electron affinities (EAs) are formulated and implemented employing the intermediate state representation (ISR) formalism and the algebraic-diagrammatic construction approximation for the electron propagator (EA-ADC). These EA-ADC(n)/ISR(m) schemes allow for a consistent treatment of not only electron affinities and pole strengths up to third-order of perturbation theory (n = 3) but also one-electron properties of electron-attached states up to second order (m = 2). The EA-ADC/ISR equations were implemented in the Q-Chem program for Ŝ_z-adapted intermediate states, allowing also open-shell systems to be studied using unrestricted Hartree-Fock references. For benchmarking of the EA-(U)ADC/ISR schemes, EAs and dipole moments of various electron-attached states of small closed- and open-shell molecules were computed and compared to full configuration interaction data. As an illustrative example, EA-ADC(3)/ISR(2) has been applied to the thymine-thymine (6-4) DNA photolesion.

Electron binding energies and Dyson orbitals of OnH2n+1 +,0,- clusters: Double Rydberg anions, Rydberg radicals, and micro-solvated hydronium cations

Ab initio electron propagator methods are employed to predict the vertical electron attachment energies (VEAEs) of OH₃ ⁺(H₂O)_n clusters. The VEAEs decrease with increasing n, and the corresponding Dyson orbitals are diffused over exterior, non-hydrogen bonded protons. Clusters formed from OH₃ ^- double Rydberg anions (DRAs) and stabilized by hydrogen bonding or electrostatic interactions between ions and polar molecules are studied through calculations on OH₃ ^-(H₂O)_n complexes and are compared with more stable H^-(H₂O)_n+1 isomers. Remarkable changes in the geometry of the anionic hydronium-water clusters with respect to their cationic counterparts occur. Rydberg electrons in the uncharged and anionic clusters are held near the exterior protons of the water network. For all values of n, the anion-water complex H^-(H₂O)_n+1 is always the most stable, with large vertical electron detachment energies (VEDEs). OH₃ ^-(H₂O)_n DRA isomers have well separated VEDEs and may be visible in anion photoelectron spectra. Corresponding Dyson orbitals occupy regions beyond the peripheral O-H bonds and differ significantly from those obtained for the VEAEs of the cations.

Ionization Energies and Dyson Orbitals of the Iso-electronic SO2, O3, and S3 Molecules from Electron Propagator Calculations

Adiabatic and vertical ionization energies corresponding to the X̃ A12, à B22, and B̃ A22 final states of SO₂⁺, O₃⁺, and S₃⁺ have been calculated with a variety of electron-propagator and coupled-cluster methods. The BD-T1 electron-propagator method for vertical ionization energies and coupled-cluster adiabatic and zero-point corrections yield agreement with experiment to within 0.1 eV in all cases but one. The remaining discrepancies for the à B22 state of SO₂⁺ indicate a need for higher levels of theory in determining cationic minima and their accompanying vibrational frequencies. Predictions for the still unobserved à B22 and B̃ A22 final states of S₃⁺ are included. To account for increased biradical character in O₃ and S₃, highly correlated reference states are required to produce the correct order of final states. Electron correlation plays a subtle role in determining the contours of the Dyson orbitals obtained with BD-T1 and NR2 electron-propagator calculations.

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 NH_4-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.

Orbitals and the Interpretation of Photoelectron Spectroscopy and (e,2e) Ionization Experiments

Electron momentum spectroscopy, scanning tunneling microscopy, and photoelectron spectroscopy provide unique information about electronic structure, but their interpretation has been controversial. This essay discusses a framework for interpretation. Although this interpretation is not new, we believe it is important to present this framework in light of recent publications. The key point is that these experiments provide information about how the electron distribution changes upon ionization, not how electrons behave in the pre-ionized state. Therefore, these experiments do not lead to a "selection of the correct orbitals" in chemistry and do not overturn the well-known conclusion that both delocalized molecular orbitals and localized molecular orbitals are useful for interpreting chemical structure and dynamics. The two types of orbitals can produce identical total molecular electron densities and therefore molecular properties. Different types of orbitals are useful for different purposes.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

Aufbau Rules for Solvated Electron Precursors: Be(NH3)40,± Complexes and Beyond

Tetra-amino beryllium complexes and ions, Be(NH₃)₄^0,±, have a tetrahedral Be(NH₃)₄²⁺ core with one, two, or three outer electrons orbiting its periphery. Our calculations reveal a new class of molecular entities, solvated electron precursors, with Aufbau rules (1s, 1p, 1d, 2s, 1f, 2p, 2d) that differ from their familiar hydrogenic counterparts and resemble those of jellium or nuclear-shell models. The core's radial electrostatic potential suffices to reproduce the chief features of the ab initio results. Wave function and electron-propagator methods combined with diffuse basis sets are employed to calculate accurate geometries, ionization energies, electron affinities, and excitation energies.

Molecules mimicking atoms: monomers and dimers of alkali metal solvated electron precursors

Tetra-amino lithium and sodium complexes M(NH₃)0,−4 (M = Li, Na) have one or two electrons that occupy diffuse hydrogenic type orbitals distributed chiefly outside the M(NH₃)₄⁺ core. Two such neutral species can bind to form a dimer which can be seen as the analogue of molecular hydrogen.