Ab Initio Electron Propagator Research Articles

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.

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.

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.

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.

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.

Double Rydberg anions with solvated ammonium kernels: Electron binding energies and Dyson orbitals

Ab initio electron-propagator calculations on the electron detachment energies and associated Dyson orbitals of NnH3n+1− for n = 1–5 confirm the assignment of low-energy peaks in anion photoelectron spectra to double Rydberg anions, species in which a closed-shell cation binds a diffuse pair of electrons. The most stable double Rydberg anions contain NnH3n+1+ cores, wherein the NH4+ kernel forms n − 1 hydrogen bonds with ammonia molecules. Other low-energy peaks for a given n pertain to double Rydberg anions of lower n that are weakly bound to ammonia molecules. High-energy peaks arise from the most stable isomers which consist of hydrides bound to N–H bonds of coordinating ammonia molecules. Dyson orbitals of electron detachment are distributed over the periphery of the bonding regions of the NnH3n+1+ cores. For n = 2–4, negative charge accumulates mostly outside the N–H bonds of the NH4+ kernels that are not engaged in hydrogen bonds. For the tetrahedral cases, where n = 1, 5, Dyson orbitals are diffuse, symmetric functions that are orthogonalized to occupied a1 orbitals of the cationic core. Shake-up features in spectra have been assigned to doublet states with a single diffuse electron in an s, p, d, or f orbital.

Carborane superhalide bases and their conjugate Brønsted-Lowry Superacids: Electron binding energies and Dyson orbitals

Superacidity in protonated carboranes arises from properties of conjugate anions: shallow, uniform electrostatic potentials, large electron detachment energies and nodal structure in Dyson orbitals. Vertical electron detachment energies (VEDEs) and Dyson orbitals of closo CHB11X11− (X = H, F, Cl) carboranes calculated with ab initio electron-propagator theory in the renormalized partial third order (P3+) and non-diagonal, renormalized, second-order (NR2) approximations are in close agreement with anion photoelectron spectra. Whereas first VEDEs to 2E2 final states of all three of these superhalide anions exceed 6 eV, a more promising strategy for enhancing superacidity is increasing the anionic base’s second VEDE to the lowest 2E1 final state.

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

Ab initio electron propagator methods are efficient and accurate means of calculating vertical electron detachment energies of closed-shell, molecular anions with nuclei from the first three periods. Basis set extrapolations enable definitive comparisons between electron propagator results and benchmarks defined by total energy differences obtained with coupled-cluster, single, double, plus perturbative triple substitution theory. The best compromises of accuracy and efficiency are provided by the renormalized, partial third-order, diagonal (P3+) self-energy and by the nondiagonal, renormalized, second-order (NR2) approximation. The outer-valence Green function, the two-particle-one-hole Tamm-Dancoff approximation, the third-order algebraic diagrammatic construction, and the renormalized third-order methods also are examined. A detailed analysis of errors for small anions is performed. Case studies include F-(H2O) and Cl-(H2O) complexes, C5H5-, two P2N3- pentagonal rings, and a superhalide, Al(BO2)4-, whose electron detachment energy is more than double those of the halide anions. These applications illustrate the versatility of electron propagator methods, their utility for interpreting negative-ion photoelectron spectra, and their promise in the discovery of unusual properties and patterns of chemical bonding. Composite methods, which combine basis set effects calculated at the relatively efficient diagonal, second-order level and higher correlation effects calculated with small basis sets, provide excellent estimates of basis set-extrapolated P3+ or NR2 results and facilitate applications to large molecules. In the P3+ and NR2 methods, a judicious choice of low-order couplings between hole operators that correspond to the assumptions of Koopmans's theorem and operators that describe final-state relaxation and polarization and initial-state correlation leads to predictive accuracy, computational efficiency, and interpretive lucidity.

Assignment of photoelectron spectra of intramolecular silicon complexes: 1-vinyl- and 1-phenylsilatranes.

The problematic experimental photoelectron spectra of silatranes XSi[OCH2CH2]3N (X = vinyl and Ph) were theoretically studied. The ab initio electron propagator theory, many-body methods, and model vibrational Hamiltonian were employed to establish the nature of bands in the energetically lowest part of the photoelectron spectrum of these intramolecular silicon complexes. The first vertical ionization energy corresponds to a nitrogen atom lone pair, nN, in 1-vinylsilatrane, and the essentially doubly degenerate π-orbitals πPh and πPh' of the aromatic ring in 1-phenylsilatrane. Peaks at 9.6 and 9.9 eV in the spectra of both compounds, previously associated with the removal of an electron from the lone pair level of the equatorial oxygens, should actually be assigned to the bonding orbital HV1 of their 3c-4e axial CSi←N moiety. Taking silatranes with X = H, Me, OEt, F, vinyl, and Ph as examples, it was found that the length of the dative Si←N contact and the ionization energy of HV2 (formally nN) were in a good linear relationship. Regardless of the nature of the X substituent, this relationship could be used for the identification of orbitals that participate in the formation of the coordination Si←N bond in the wide series of XSi[OCH2CH2]3N and their structural analogs.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules IV: Electron-Propagator Methods.

Comparison of ab initio electron-propagator predictions of vertical ionization potentials and electron affinities of organic, acceptor molecules with benchmark calculations based on the basis set-extrapolated, coupled cluster single, double, and perturbative triple substitution method has enabled identification of self-energy approximations with mean, unsigned errors between 0.1 and 0.2 eV. Among the self-energy approximations that neglect off-diagonal elements in the canonical, Hartree-Fock orbital basis, the P3 method for electron affinities, and the P3+ method for ionization potentials provide the best combination of accuracy and computational efficiency. For approximations that consider the full self-energy matrix, the NR2 methods offer the best performance. The P3+ and NR2 methods successfully identify the correct symmetry label of the lowest cationic state in two cases, naphthalenedione and benzoquinone, where some other methods fail.

Ab initio electron propagator calculations of transverse conduction through DNA nucleotide bases in 1-nm nanopore corroborate third generation sequencing

BackgroundThe conduction properties of DNA molecule, particularly its transverse conductance (electron transfer through nucleotide bridges), represent a point of interest for DNA chemistry community, especially for DNA sequencing. However, there is no fully developed first-principles theory for molecular conductance and current that allows one to analyze the transverse flow of electrical charge through a nucleotide base. MethodsWe theoretically investigate the transverse electron transport through all four DNA nucleotide bases by implementing an unbiased ab initio theoretical approach, namely, the electron propagator theory. ResultsThe electrical conductance and current through DNA nucleobases (guanine [G], cytosine [C], adenine [A] and thymine [T]) inserted into a model 1-nm Ag–Ag nanogap are calculated. The magnitudes of the calculated conductance and current are ordered in the following hierarchies: gA>gG>gC>gT and IG>IA>IT>IC correspondingly. The new distinguishing parameter for the nucleobase identification is proposed, namely, the onset bias magnitude. Nucleobases exhibit the following hierarchy with respect to this parameter: Vonset(A)<Vonset(T)<Vonset(G)<Vonset(C). ConclusionsThe difference in current magnitudes and onset voltages implies the possibility of nucleobases electrical identification by virtue of DNA translocation through an electrode-equipped nanopore. General significanceThe results represent interest for the theorists and practitioners in the field of third generation sequencing techniques as well as in the field of DNA chemistry.

Excitation energies, photoionization cross sections, and asymmetry parameters of the methyl and silyl radicals.

Vertical excitation energies of the methyl and silyl radicals were inferred from ab initio electron propagator calculations on the electron affinities of CH3(+) and SiH3(+). Photoionization cross sections and angular distribution of photoelectrons for the outermost orbitals of both CH3 and SiH3 radicals have been obtained with the Molecular Quantum Defect Orbital method. The individual ionization cross sections corresponding to the Rydberg channels to which the excitation of the ground state's outermost electron gives rise are reported. Despite the relevance of methyl radical in atmospheric chemistry and combustion processes, only data for the photon energy range of 10-11 eV seem to be available. Good agreement has been found with experiment for photoionization cross section of this radical. To our knowledge, predictions of the above mentioned photoionization parameters on silyl radical are made here for the first time, and we are not aware of any reported experimental measurements. An analysis of our results reveals the presence of a Cooper minimum in the photoionization of the silyl radical. The adequacy of the two theoretical procedures employed in the present work is discussed.

Microsolvation effects on the electron binding energies of halide anions

Ab initio electron propagator calculations in the partial third order (P3) and P3+ approximations were performed to obtain vertical electron detachment energies (VEDEs) of fluoride and chloride clusters with one through three molecules of water. Larger clusters of F− and Cl− with six water molecules were also treated with and without the polarisable continuum model (PCM). For the smaller clusters, good agreement between calculated VEDEs and peak positions in photoelectron spectra is achieved. Large shifts in VEDEs are observed for both hexameric fluoride–water and chloride–water complexes when the PCM is applied. Significant changes in coordination geometries about the chloride anion also occur in this model. In all fluoride complexes, Dyson orbitals for the lowest VEDEs are delocalised over oxygen atoms. On the contrary, for the case of chloride–water clusters, the Dyson orbitals corresponding to the lowest VEDEs are localised on the anion.

Assignment of photoelectron spectra of halide–water clusters: Contrasting patterns of delocalization in Dyson orbitals

Ab initio electron propagator calculations in various self-energy approximations provide accurate assignments of peaks observed in the photoelectron spectra of complexes that comprise a fluoride or chloride anion and two or three water molecules. More than one minimum structure is found in all four cases. When the halide anion is Cl(-), the first three final states may be described as quasi-degenerate (2)P chlorine atoms coordinated to water molecules. Higher final states consist of a chloride anion juxtaposed to a positive charge that is delocalized over the water molecules. For the clusters with fluoride anions, most of the final states correspond to Dyson orbitals that are delocalized over the F and O nuclei. A variety of F-O σ and π bonding and antibonding patterns are evident in the Dyson orbitals. The assignment of low-lying spectral peaks to halide p orbital vacancies or to delocalized solvent orbitals is more valid for the chloride clusters than for the fluoride clusters, where a delocalized picture arises from strong bonding interactions between F 2p and H2O 1b1 orbitals.

Valence and diffuse-bound anions of noble-gas complexes with uracil

Valence-bound (VB) and diffuse-bound (DB) anions of noble-gas (Ar, Kr, and Xe) complexes with uracil have been studied with ab initio methods. MP2 optimizations revealed minima corresponding to anions of both kinds in each case. Coupled-cluster singles and doubles with perturbative triples, CCSD(T), and electron propagator single-point calculations were performed in order to assess vertical and adiabatic electron detachment energies of these complexes. Ab initio electron propagator calculations employed the outer valence Green's function and partial third-order approximations, and the algebraic diagrammatic construction in third order. Basis set effects have been systematically examined. DB anions of all three complexes were adiabatically bound, with calculated adiabatic electron attachment energies below 0.06 eV. Corresponding vertical electron detachment energies were below 0.1 eV. As to VB anions, only the Xe complex had a positive adiabatic electron detachment energy, of 0.01 eV, with a corresponding vertical electron detachment energy of 0.6 eV. These computational findings are consistent with the interpretation of results previously obtained experimentally by Hendricks et al.

Ab initio Study on Ionization Energies of 1-Methyl-hypoxanthine

Six low-lying tautomers of 1-methyl-hypoxanthine have been studied at the B3LYP/aug-cc-pVDZ level. Two tautomers N7H and N9H with the comparable energies are far more stable than the others. The vertical ionization energies of the tautomers calculated with ab initio electron propagator theory in the P3/aug-cc-pVDZ approximation are in agreement with the experimental data from photoelectron spectroscopy. According to the calculated relative energies and the comparison between the simulated and the experimental photoelectron spectra, it demonstrates that there are at least two tautomers of 1-methyl-hypoxanthine in the gas-phase experiments.