Research

The article compares electron-propagator (EP) methods with experimental ionization energies, showing that some achieve high accuracy with mean absolute errors as low as 0.075 eV. It identifies the most efficient and accurate EP models, such as Q3+, RL3, and NRL3, and introduces composite approaches that enhance computational efficiency without sacrificing accuracy. These findings establish EP methods as reliable tools for predicting vertical ionization energies in computational chemistry.

This work examines the predictive capabilities of the new-generation diagonal self-energies when they are generalized to unrestricted Hartree–Fock (UHF) theory. Predictive accuracy is assessed against experimental data on open-shell atomic and molecular electron binding energies. By adhering to our established guidelines, MAEs increase by ~0.05 eV relative to results obtained with closed-shell reference orbitals.

New-generation non-diagonal methods have been tested on VEAs for the first time using a new benchmark standard of small closed-shell molecules, facilitating rapid and cost-effective evaluations at the complete-basis-set limit. This enabled the assessment of both new-generation diagonal and non-diagonal methods for VEAs in a CBS limit, as well as on VEAs of OPV molecules. Fifth-power arithmetic scaling methods achieve MAEs below 0.1 eV, while the best non-diagonal sixth power scaling methods achieve a MAE of approximately 0.05 eV.

In this work, the new non-diagonal electron-propagator methods are evaluated on VEDEs for the first time. Numerical tests indicate that explicitly renormalized, diagonal self-energies are needed when Dyson orbitals have large valence nitrogen, oxygen or fluorine components. Also, greater accuracy can be realized with the new non-diagonal methods that do not employ the diagonal self-energy approximation in the canonical Hartree–Fock basis. Composite models based on the new methods have been used to assign the photoelectron spectra of the green fluorescent protein (GFP) chromophore anions. Predictions for the lowest VEDEs in these anions are in excellent agreement with experimental data.  

This project was an invited featured article. The main aim of the article was to review the theory and performance of all the new-generation diagonal and non-diagonal electron propagator methods developed for vertical ionization energies (VIEs), vertical electron affinities (VEAs) and vertical electron detachment energies (VEDEs) of molecular anions. 

New-generation parameter-free ab initio electron-propagator methods achieved improved accuracy and efficiency than their predecessors for  vertical ionization energies (VIEs) of small and medium sized closed-shell molecules. In this work, these advancements are extended to include vertical electron affinities (VEAs), with calculations performed on a set of 24 conjugated organic photovoltaic (OPV) molecules featuring diverse functional groups. This set comprises larger molecules than those used in prior VIE tests. Several new methods obtain mean absolute errors (MAEs) below 0.1 eV when compared with benchmark VIEs and VEAs. Composite models achieve MAEs near 0.05 eV relative to reference values with an established error margin of approximately 0.03 eV. 

New non-diagonal electron-propagator methods namely NRL3, NRQ3 and NRP3 have been developed for calculating electron binding energies. These methods are extensions of the recent advances in diagonal self-energies for calculating electron removal energies in molecules ions. The non-diagonal methods allow Dyson orbitals to be expressed as linear combinations of canonical HF orbitals. Comparative tests show that the new non-diagonal, renormalized methods offer a slight accuracy improvement, with mean absolute errors between 0.10 and 0.06 eV, although they require more computational resources. Despite this, they outperform their non-diagonal predecessors in both accuracy and efficiency.

New ab initio electron-propagator self-energy approximations, evaluated using 55 vertical electron detachment energies of closed-shell anions, show enhanced accuracy and efficiency. These methods use diagonal self-energy approximations in the canonical Hartree–Fock orbital basis. Notable methods anf their MAEs include os-nD-D2 (0.2 eV), Q3+ (0.15 eV), and nD-L3+ (0.1 eV), with BD-T1 showing significant agreement with ΔCCSD(T). The new methods methods offer precise predictions and clear insights into the photoelectron spectra of DNA nucleotides.

Ab initio electron propagator (EP) methods with no adjustable parameters have been used to calculate the lowest vertical ionization energies (VIEs) of the GW100 set. Improved standard results, derived indirectly with CCSD(T) total energy differences, were produced at initial-state geometries optimized with the largest applicable point groups. The best accuracy and efficiency are achieved by a new generation of EP self-energies, derived from an intermediately normalized, Hermitized super-operator metric, including optimal methods like os-nD-D2, P3+, Q3+, and nD-L3+B. The Brueckner doubles, triple-field operator (BD-T1) EP method, with a mean absolute error (MAE) of 0.06 eV, surpasses seventh-power ΔCCSD(T) calculations, suggesting its potential for generating standard VIEs for larger, closed-shell molecules.

A new generation of parameter-free ab initio diagonal self-energy approximations for calculating electron removal energies in molecules has been developed using an intermediately normalized, Hermitized super-operator metric. These methods, along with their antecedents such as the outer valence Green's function and approximately renormalized partial third-order method, have been tested against a dataset of vertical ionization energies. The new methods are more accurate and efficient than their predecessors.

A new benchmark standard, named NIST-50-EA, for vertical electron affinities (VEAs) has been established in a complete basis set limit. This standard is based on small closed-shell molecules with bound, stable final anionic states. The benchmark has been utilized to evaluate the performance of new electron-propagator methods for calculating VEAs. Additionally, it is suitable for calibrating other many-body methods for determining electron affinities. 

The section of this work on the photoelectron spectra of GFP (Green Fluorescent Protein) anions describes the application of new-generation electron-propagator methods to analyze model GFP chromophores. The study specifically examines the chromophoric center, which is responsible for GFP’s fluorescence, focusing on the p-hydroxybenzylidene-2,3-dimethylimidazoline (p-HBDI) anion and two variants with fluorine or methoxy substitutions. These methods yield highly accurate predictions for the vertical electron detachment energies (VEDEs), matching experimental results closely. Improved computational techniques, like explicitly renormalized self-energies, enhance accuracy by accounting for electron correlation and orbital relaxation, particularly when the electrons are localized near electronegative centers. This section highlights the potential of these computational methods to replicate and predict the behavior of GFP-related molecules, showcasing the efficiency and accuracy of these advanced models for understanding biological fluorescence at the molecular level. 

The VEAs and VIEs of organic photovoltaic molecules relevant for the optimization of solar energy devices have been calculated with exceptional accuracy and efficiency using new-generation electron-propagator methods. 

The section of this work on the photoelectron spectra of DNA nucleotides discusses the application of advanced electron-propagator methods to analyze the electronic properties of DNA components. The study focuses on predicting vertical electron detachment energies, which are crucial for understanding how DNA nucleotides respond to ionization. Advanced methods, like non-Dyson approximations and renormalized self-energy calculations, have been employed to estimate the impact of electron correlation on these energies, leading to accurate photoelectron spectra predictions for DNA bases. The analysis covers various nucleotides, highlighting differences in electron binding energies between the phosphate groups and the aromatic bases like adenine, guanine, thymine, and cytosine. It emphasizes how accurate calculations help identify the localization of electron density changes, which is vital for understanding chemical reactivity and radiation damage in DNA. These findings align closely with experimental data, validating the computational models used and demonstrating their capability to predict DNA behavior at the molecular level accurately. 

Highly accurate ab initio methods predict vertical electron attachment energies (VEAEs) of NH₄⁺(H₂O)ₙ clusters, showing a decrease with increasing nn. NH₄⁻ double Rydberg anions (DRAs) stabilized by hydrogen bonding or electrostatic interactions are compared to more stable H⁻(NH₃)(H₂O)ₙ isomers. Geometric changes are notable. H⁻(NH₃)(H₂O)ₙ complexes are the most stable for all nn, with large vertical electron detachment energies (VEDEs). NH₄⁻(H₂O)ₙ DRA isomers have distinct VEDEs and Dyson orbitals beyond non-bridging O–H and N–H bonds. Rydberg electrons reside near exterior protons, with various low-lying excited states following the Aufbau principle. Several bound low-lying excited states of the doublet Rydberg radicals have single electrons occupying delocalized Dyson orbitals of s-like, p-like, d-like, or f-like nodal patterns with the following Aufbau principle: 1s, 1p, 1d, 2s, 2p, 1f. 

Ab initio electron propagator methods predict the vertical electron attachment energies of OH₃⁺(H₂O)ₙ clusters, showing a decrease with increasing n. Dyson orbitals are diffused over exterior, non-hydrogen-bonded protons. Studied clusters include OH₃⁻ double Rydberg anions (DRAs) stabilized by hydrogen bonding or electrostatic interactions, compared to more stable H⁻(H₂O)ₙ₊₁ isomers. Anionic hydronium–water clusters exhibit significant geometric changes from their cationic counterparts, with Rydberg electrons near exterior protons. H⁻(H₂O)ₙ₊₁ complexes are the most stable, with high vertical electron detachment energies (VEDEs). OH₃⁻(H₂O)ₙ DRAs have well-separated VEDEs, potentially visible in anion photoelectron spectra, and distinct Dyson orbitals. 

• Electron propagator theory of condensed-phase matter

• Polarization propagator theory of molecular excitation energies

• Double electron propagator theory of double-electron binding energies and Auger spectra

• Relativistic electron propagator methods for calculating relativistic electron binding energies and spin-orbit splitting

• Multireference electron propagator methods 

• Development and analysis of chemical bonding concepts

• Qualitative theories of molecular structure, spectra, and reactivity

• Approximate Monte Carlo many-body Green’s function methods 

• Density fitting and Cholesky decomposition integral approximations in many-body Green’s function methods 

• Non-Dyson quasiparticle propagator 

• Quantum chemistry of macromolecules and solids

• Sustainable Energy: photovoltaic molecules, heterocyclic acenes, fullerenes, etc. 

• Bioactive Molecules: steroids, narcotics, analgesics, benzodiazepins, nitroimidazoles, amino acids, polypeptides, DNA and RNA fragments, thiooxamines, etc.

• Bioimaging: green and yellow fluorescent proteins anions, luciferin, and infraluciferin anions, photoactive proteins ions, etc.

• Catalysis: superhalogens, superalkalis, anthracenophane, stable mesoionic compounds, phosphate esters, arylboronic acids, sumanene, superacids, superbases, metal oxide clusters, etc.

• Organic Pollutants: galvinoxyl radical, Atrazine, bromoxynil, lindane, dieldrin, DDT, DDE, DDD, chlorophenols, etc.

• Macromolecules: quinonechloroimides, phenyloxiranes, quinoxalines, polypodanes, metalloporphyrins, etc.

• Exotic Anions: Multiple Rydberg anions, solvated electron precursors, dipole, and diffuse-bound anions, metastable anions, etc.

• Materials Science: metal-oxide anions and other clusters of interest in materials science research

• Molecular Clusters: Supermolecules, solvated clusters, anions that interact strongly with solvents

• The mechanisms of oxidation of olefins with transition metal oxo complexes

• Spin forbidden reactions in transition metal chemistry

• Thermal cycloaddition reactions to produce complex carbocyclic frameworks in a single step

• Mechanistic studies on homogeneous transition metal and base catalyzed reactions 

• Water oxidation catalysis

• NHC catalysis

• Photochemistry and excited states

• Mechanistic elucidation of tandem/domino reactions