Electron Propagator Self-Energies versus Improved GW100 Vertical Ionization Energies

Electron-propagator methods versus experimental ionization energies

Select electron-propagator (EP) methods agree as closely with experimental standards for molecular vertical ionization energies as they do with computational data of nearly full-configuration-interaction quality. Several EP methods consistently attain higher accuracy than alternatives with equal arithmetic bottlenecks expressed in terms of occupied (O) and virtual (V) orbital dimensions. The cubically scaling methods realize a mean absolute error (MAE) below 0.2 eV and are feasible whenever conventional self-consistent-field calculations are performed. O2V3-scaling EP self-energies achieve an MAE slightly above 0.1 eV and are as feasible as conventional second-order perturbative calculations of total energies. OV4 methods are more accurate (MAEs ∼0.075 eV) than ΔCCSD(T) and are more efficient than third-order total-energy calculations. An equally accurate generalization with full self-energy matrices and non-iterative O2V4 contractions produces Dyson orbitals in their most general form. Composite EP models that accurately estimate the effects of basis-set saturation drastically improve efficiency without sacrificing accuracy. No adjustable parameters are employed in the self-energy formulas or in the generation of reference-state orbitals. When Dyson-orbital probability factors indicate that Koopmans's theorem is qualitatively valid, simple perturbative corrections suffice to approach chemical accuracy.

Electron Binding Energies of Open-Shell Species from Diagonal Electron-Propagator Self-Energies with Unrestricted Hartree-Fock Spin-Orbitals

For closed-shell molecules, valence electron binding energies may be calculated accurately and efficiently with ab initio electron-propagator methods that have surpassed their predecessors. Advantageous combinations of accuracy and efficiency range from cubically scaling methods with mean errors of 0.2 eV to quintically scaling methods with mean errors of 0.1 eV or less. The diagonal self-energy approximation in the canonical Hartree-Fock basis is responsible for the enhanced efficiency of several methods. This work examines the predictive capabilities of diagonal self-energy approximations when they are generalized to the canonical spin-orbital basis of unrestricted Hartree-Fock (UHF) theory. Experimental data on atomic electron binding energies and high-level, correlated calculations in a fixed basis for a set of open-shell molecules constitute standards of comparison. A review of the underlying theory and analysis of numerical errors lead to several recommendations for the calculation of electron binding energies: (1) In calculations that employ the diagonal self-energy approximation, Koopmans's identity for UHF must be qualitatively correct. (2) Closed-shell reference states are preferable to open-shell reference states in calculations of molecular ionization energies and electron affinities. (3) For molecular electron binding energies between doublets and triplets, calculations of electron detachment energies are more accurate and efficient than calculations of electron attachment energies. When these recommendations are followed, mean absolute errors increase by approximately 0.05 eV with respect to their counterparts obtained with closed-shell reference orbitals.

Ab Initio Electron Propagators with an Hermitian, Intermediately Normalized Superoperator Metric Applied to Vertical Electron Affinities

New-generation ab initio electron propagator methods for calculating electron detachment energies of closed-shell molecules and anions have surpassed their predecessors' accuracy and computational efficiency. Derived from an Hermitian, intermediately normalized superoperator metric, these methods contain no adjustable parameters. To assess their versatility, a standard set (NIST-50-EA) of 50 vertical electron affinities of small closed-shell molecules based on NIST reference data has been created. Errors with respect to reference data on 23 large, conjugated organic photovoltaic (OPV23) molecules have also been analyzed. All final states are valence anions that correspond to electron affinities between 0.2 and 4.2 eV. For a given scaling of the arithmetic bottleneck, the new-generation methods obtain the lowest mean absolute errors (MAEs). The best methods with fifth-power arithmetic scaling realize MAEs below 0.1 eV. Composite models comprising cubically and quintically scaling calculations executed with large and small basis sets, respectively, produce OPV23 MAEs near 0.05 eV. The accuracy of quintically scaling methods executed with large basis sets is thereby procured with reduced computational effort. New-generation results obtained with and without the diagonal self-energy approximation in the canonical Hartree-Fock basis have been compared. These results indicate that Dyson orbitals closely resemble canonical Hartree-Fock orbitals multiplied by the square root of a probability factor above 0.85.

New-generation electron-propagator methods for vertical electron detachment energies of molecular anions: benchmarks and applications to model green-fluorescent-protein chromophores

Ab initio electron-propagator calculations continue to be useful companions to experimental investigations of electronic structure in molecular anions. A new generation of electron-propagator methods recently has surpassed its antecedents' predictive accuracy and computational efficiency. Interpretive clarity has been conserved, for no adjustable parameters have been introduced in the preparation of molecular orbitals or in the formulation of approximate self-energies. These methods have employed the diagonal self-energy approximation wherein each Dyson orbital equals a canonical Hartree-Fock orbital times the square root of a probability factor. Numerical tests indicate that explicitly renormalized, diagonal self-energies are needed when Dyson orbitals have large valence nitrogen, oxygen or fluorine components. They also demonstrate that even greater accuracy can be realized with generalizations that do not employ the diagonal self-energy approximation in the canonical Hartree-Fock basis. Whereas the diagonal methods have fifth-power arithmetic scaling factors, the non-diagonal generalizations introduce only non-iterative sixth-power contractions. Composite models conserve the accuracy of the most demanding combinations of self-energy approximations and flexible basis sets with drastically reduced computational effort. Composite-model results on anions that resemble the chromophore of the green fluorescent protein illustrate the interpretive capabilities of explicitly renormalized self-energies. Accurate predictions on the lowest vertical electron detachment energy of each anion confirm experimental data and the utility of the diagonal self-energy approximation.

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.

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.

New-Generation Electron-Propagator Methods for Calculations of Electron Affinities and Ionization Energies: Tests on Organic Photovoltaic Molecules

A new generation of ab initio electron-propagator self-energies recently superseded its antecedents' accuracy and computational efficiency in calculating vertical ionization energies (VIEs) of closed-shell molecules. (See J. Chem. Phys. 2021, 155, 204107, J. Chem. Theory Comput. 2022, 18, 4927, J. Chem. Phys. 2023, 159, 124109.) No adjustable parameters were introduced in the generation of reference orbitals or in the construction of self-energies. The same approach has been extended in this work to vertical electron affinities (VEAs). Calculations were performed on 24 conjugated, organic photovoltaic molecules with diverse functional groups. These molecules are considerably larger than those studied in previous tests on VIEs. Several new-generation self-energies produce mean absolute errors (MAEs) below 0.1 eV versus ΔCCSD(T) (i.e., total energy differences from the coupled-cluster singles, doubles, and perturbative triples method) VIEs and VEAs obtained with identical basis sets. A composite model employs cubically and quintically scaling algorithms and power-law basis-set extrapolations based on augmented double-triple or triple-quadruple ζ data. Its MAEs are near 0.05 eV versus benchmark values, with 0.03 eV error bars for the lowest VIE and the highest VEA of each molecule. A more efficient and equally accurate composite model for calculating VIEs avoids full transformations of electron repulsion integrals to the molecular orbital basis. High probability factors support the diagonal self-energy approximation, wherein Dyson orbitals are proportional to canonical, Hartree-Fock orbitals.

A new generation of non-diagonal, renormalized self-energies for calculation of electron removal energies

A new generation of diagonal self-energies for the calculation of electron removal energies of molecules and molecular ions that has superseded its predecessors with respect to accuracy, efficiency, and interpretability is extended to include non-diagonal self-energies that permit Dyson orbitals to be expressed as linear combinations of canonical Hartree-Fock orbitals. In addition, an improved algorithm for renormalized methods eliminates the convergence difficulties encountered in the first studies of the new, diagonal self-energies. A dataset of outer-valence, vertical ionization energies with almost full-configuration-interaction quality serves as a standard of comparison in numerical tests. The new non-diagonal, renormalized methods are slightly more accurate than their diagonal counterparts, with mean absolute errors between 0.10 and 0.06 eV for outer-valence final states. This advantage is procured at the cost of an increase in the scaling of arithmetic bottlenecks that accompany the inclusion of non-diagonal self-energy terms. The new, non-diagonal, renormalized self-energies are also more accurate and efficient than their non-diagonal predecessors.

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.