Electron Propagator Methods for Vertical Electron Detachment Energies of Anions: Benchmarks and Case Studies

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.

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.

Electron Propagator Self-Energies versus Improved GW100 Vertical Ionization Energies

Ab initio electron propagator (EP) methods that are free of adjustable parameters in their self-energy formulae and in the generation of their orbital bases have been applied to the calculation of the lowest vertical ionization energies (VIEs) of the GW100 set. An improved set of standard results accompanied by irreducible representation assignments has been produced indirectly with coupled-cluster singles and doubles plus perturbative triples, i.e., CCSD(T), total energy differences at initial-state geometries reoptimized (in 28 cases) with the largest applicable point groups. The best compromises of accuracy and efficiency belong to a new generation of EP self-energies, several members of which may be derived from an intermediately normalized, Hermitized super-operator metric. The following diagonal self-energy methods are optimal: opposite-spin non-Dyson second order (os-nD-D2), approximately renormalized partial third order (P3+), approximately renormalized quasiparticle third order (Q3+), and non-Dyson approximately renormalized linear third order version B (nD-L3+B). Their mean absolute errors (MAEs) in electron volts and arithmetic scaling factors expressed in terms of occupied (O) and virtual (V) orbital dimensions are, respectively, (0.18, OV²), (0.14, O²V³), (0.15, O²V³), and (0.11, OV⁴). The 0.06 eV MAE for the non-diagonal, sixth-power (O²V⁴) Brueckner doubles, triple-field operator (BD-T1) EP method is exceeded by the 0.1 eV MAE with respect to experiments in seventh-power, ΔCCSD(T) calculations and indicates that BD-T1 may serve as a direct, spin-symmetry-conserving alternative in the generation of standard results for VIEs of larger, closed-shell molecules.

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.

High-throughput virtual screening for organic electronics: a comparative study of alternative strategies

We present a review of the field of high-throughput virtual screening for organic electronics materials focusing on the sequence of methodological choices that determine each virtual screening protocol. These choices are present in all high-throughput virtual screenings and addressing them systematically will lead to optimised workflows and improve their applicability. We consider the range of properties that can be computed and illustrate how their accuracy can be determined depending on the quality and size of the experimental datasets. The approaches to generate candidates for virtual screening are also extremely varied and their relative strengths and weaknesses are discussed. The analysis of high-throughput virtual screening is almost never limited to the identification of top candidates and often new patterns and structure-property relations are the most interesting findings of such searches. The review reveals a very dynamic field constantly adapting to match an evolving landscape of applications, methodologies and datasets.

Simulation of Negative Ion Photoelectron Spectroscopy Using a Nuclear Ensemble Approach: Implications from a Nuclear Vibration Effect

The negative ion photoelectron spectroscopy (NIPES) has been proven to be a powerful technique to reveal the electronic structures and spectroscopic properties of various cluster anions/radicals with very high precision. However, direct comparisons of the theoretical NIPES with experimental measurements remain challenging. Particularly the nuclear vibration effect and the ionization probability are typically ignored in reproducing NIPES. In this work, the NIPES of three representative anions (NaS₅^-, P₂N₃^-, and HCPN₃^-) with significantly different spectral features were simulated by combining the nuclear ensemble approach (NEA) and Dyson orbitals (DOs). Overall, the simulated NIPES are in good agreement with the experimentally determined ones, confirming the robustness of such a strategy. The analysis of frontier molecular orbitals (MOs) and DOs further suggests the similar mixed characters for the first ionized doublet (D₀) and adjacent D₁ states of NaS₅^- with distributions on the side sulfur atoms. And the D₀ of P₂N₃* is confirmed as the lowest energy σ radical state; however, the D₀ of HCPN₃* should possess a mixture of π and σ electrons by taking into account the nuclear vibration effect. Next, the broader vibrational distribution and stronger main vibration modes of P₂N₃^- and HCPN₃^- explain why the nuclear vibration possesses a more pronounced influence in reproducing their NIPES while it has little effect on NaS₅^-. Last, the limitations based on the double-harmonic approximation model and density of state method were also discussed, highlighting that the ionization probability and orbital relaxation effect during the ionization process should be reasonably considered.

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.