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.

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.

Double Rydberg anions, Rydberg radicals and micro-solvated cations with ammonium-water kernels

Highly accurate ab initio electron-propagator and coupled-cluster methods are employed to predict the vertical electron attachment energies (VEAEs) of NH₄⁺(H₂O)_n (n = 1-4) cationic clusters. The VEAEs decrease with increasing n and the corresponding Dyson orbitals are diffused over peripheral, non-hydrogen bonded protons. Clusters formed from NH₄^- double Rydberg anions (DRAs) and stabilized by hydrogen bonding or electrostatic interactions are studied through calculations on NH₄^-(H₂O)_n complexes and are compared with more stable H^-(NH₃)(H₂O)_n isomers. Structures that have cationic and anionic congeners have notable changes in geometry. For all values of n, the hydride-molecule complex H^-(NH₃)(H₂O)_n is always the most stable, with large vertical electron detachment energies (VEDEs). NH₄^-(H₂O)_n DRA isomers are predicted to have VEDEs that correspond to energetically well-separated peaks in an anion photoelectron spectrum. Less stable DRA isomers display proton donation from the tetrahedral NH₄^- fragment to water molecules and VEDEs close to those of previously discovered DRAs. The most stable DRA isomers feature tetrahedral NH₄^- fragments without H bridges to water molecules and VEDEs that increase with n. Dyson orbitals of NH₄^-(H₂O)_n DRAs occupy regions beyond the exterior non-bridging O-H and N-H bonds. Thus, the Rydberg electrons in the uncharged Rydberg radicals and DRAs are held near the outer protons of the water and ammonia molecules. 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.

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.

Complete-active-space extended Koopmans theorem method

The complete-active-space (CAS) extended Koopmans theorem (EKT) method is defined as a special case of the EKT in which the reference state is a CAS configuration interaction (CI) expansion and the electron removal operator acts only on the active orbitals. With these restrictions, the EKT is equivalent to the CI procedure involving all hole-state configurations derived from the active space of the reference wavefunction and has properties analogous to those of the original Koopmans theorem. The equivalence is used to demonstrate in a transparent manner that the first ionization energy predicted by the EKT is in general not exact, i.e., not equal to the difference between the full CI energies of the neutral and the ion, but can approach the full CI result with arbitrary precision even within a finite basis set. The findings also reconcile various statements about the EKT found in the literature.

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.

Excess electrons bound to H2S trimer and tetramer clusters

We have prepared the hydrogen sulfide trimer and tetramer anions, (H2S)3− and (H2S)4−, measured their anion photoelectron spectra, and applied high-level quantum chemical calculations to interpret the results.

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.

Transition-metal solvated-electron precursors: diffuse and 3d electrons in V(NH3)0,±6

Ground and excited electronic states of V(NH₃)0,±6 complexes, investigated with ab initio electronic structure theory, consist of a V(NH₃)₆²⁺ core with up to three electrons distributed over its periphery.

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.

Assessment of Electron Propagator Methods for the Simulation of Vibrationally Resolved Valence and Core Photoionization Spectra

The analysis of photoelectron spectra is usually facilitated by quantum mechanical simulations. Because of the recent improvement of experimental techniques, the resolution of experimental spectra is rapidly increasing, and the inclusion of vibrational effects is usually mandatory to obtain a reliable reproduction of the spectra. With the aim of defining a robust computational protocol, a general time-independent formulation to compute different kinds of vibrationally resolved electronic spectra has been generalized to also support photoelectron spectroscopy. The electronic structure data underlying the simulation are computed using different electron propagator approaches. In addition to the more standard approaches, a new and robust implementation of the second-order self-energy approximation of the electron propagator based on a transition operator reference (TOEP2) is presented. To validate our implementation, a series of molecules has been used as test cases. The result of the simulations shows that, for ultraviolet photoionization spectra, the more accurate nondiagonal approaches are needed to obtain a reliable reproduction of vertical ionization energies but that diagonal approaches are sufficient for energy gradients and pole strengths. For X-ray photoelectron spectroscopy, the TOEP2 approach, besides being more efficient, is also the most accurate in the reproduction of both vertical ionization energies and vibrationally resolved bandshapes.

Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules I. Reference Data at the CCSD(T) Complete Basis Set Limit

In designing organic materials for electronics applications, particularly for organic photovoltaics (OPV), the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor play key roles. This makes OPV design an appealing application for computational chemistry since IPs and EAs are readily calculable from most electronic structure methods. Unfortunately reliable, high-accuracy wave function methods, such as coupled cluster theory with single, double, and perturbative triples [CCSD(T)] in the complete basis set (CBS) limit are too expensive for routine applications to this problem for any but the smallest of systems. One solution is to calibrate approximate, less computationally expensive methods against a database of high-accuracy IP/EA values; however, to our knowledge, no such database exists for systems related to OPV design. The present work is the first of a multipart study whose overarching goal is to determine which computational methods can be used to reliably compute IPs and EAs of electron acceptors. This part introduces a database of 24 known organic electron acceptors and provides high-accuracy vertical IP and EA values expected to be within ±0.03 eV of the true non-relativistic, vertical CCSD(T)/CBS limit. Convergence of IP and EA values toward the CBS limit is studied systematically for the Hartree-Fock, MP2 correlation, and beyond-MP2 coupled cluster contributions to the focal point estimates.

Valence-bound and diffuse-bound anions of 5-azauracil

Structures, isomerization energies, and electron binding energies of 5-azauracil and its anions have been calculated ab initio with perturbative, coupled-cluster, and electron-propagator methods. Tautomeric structures, including those produced by proton transfer to a CH group, have been considered. Dyson orbitals and pole strengths from electron-propagator calculations validated a simple, molecular-orbital picture of anion formation. In one case, an electron may enter a delocalized π orbital, yielding a valence-bound (VB) anion with a puckered ring structure. The corresponding electron affinity is 0.27 eV; the vertical electron detachment energy (VEDE) of this anion 1.05 eV. An electron also may enter a molecular orbital that lies outside the nuclear framework, resulting in a diffuse-bound (DB) anion. In the latter case, the electron affinity is 0.06 eV and the VEDE of the DB anion is 0.09 eV. Another VB isomer that is only 0.02 eV more stable than the neutral molecule has a VEDE of 2.0 eV.

Computational tests of models for kinetic parameters of unimolecular reactions of organophosphorus and organosulfur compounds

A computational study of the kinetics of isomerization and elimination reactions of organophosphorus and organosulfur reactions is presented with a view to characterizing the predictive capabilities of widely applied techniques for processes that pertain to the destruction of chemical warfare agents. A set of 22 reactions has been studied, and the results have been compared to experimentally derived data. The BMK functional and the MG3S basis set have been used to compute minimum energy paths. Corrections have been added from CBS-QB3, CASSCF, and CASMP2 calculations. Thermal rate constants at experimental temperatures have been calculated with canonical variational transition state theory and small-curvature tunneling theory. The quality of these results may depend on recrossing of the variational transition state, the amount of radical or diradical character found in the minimum energy paths, or the accuracy of barrier heights.

Electron propagator and coupled-cluster calculations on the photoelectron spectra of thiouracil and dithiouracil anions

Electron affinities, vertical electron detachment energies, and isomerization energies of 4-thiouracil, 2-thiouracil, and 2,4-dithiouracil and their valence anions have been calculated with ab initio electron propagator and other many-body methods. Anions in which protons have been transferred to the C5 from the N1 or N3 ring positions have been considered, but the canonical forms are most stable for the 4-thiouracil and 2,4-dithiouracil anions. Electron affinities of 0.61, 0.26, and 0.87 eV have been determined for 4-thiouracil, 2-thiouracil, and 2,4-dithiouracil, respectively. Electron propagator calculations on the canonical anions yield vertical electron detachment energies that are in close agreement with experimental peaks at 1.05, 3.21, and 3.32 eV for 4-thiouracil and at 1.4 eV for 2,4-dithiouracil.

Computational tests of quantum chemical models for structures, vibrational frequencies, and heats of formation of molecules with phosphorus and sulfur atoms

The Gaussian-n, complete basis set, and Weizmann-1 quantum chemical models for heats of formation are applied to a set of molecules with relevance to the combustion or pyrolysis of chemical warfare materials. Most of these models generate standard deviations from experiment that are less than 2 kcal/mol. The structures and vibrational frequencies that are generated in the course of these calculations are in good agreement with experimental data. Detailed comparisons with respect to structural types indicate that the present computational models are likely to generate useful data for complex models of combustion and pyrolysis of chemical warfare materials.

Second-order, two-electron Dyson propagator theory: Comparisons for vertical double ionization potentials

The second-order, two-electron Dyson propagator is derived using superoperator theory with a spin-adapted formulation. To include certain ladder diagrams to all orders, the shifted-denominator (SD2) approximation is made. Formal and computational comparisons with other approximations illustrate the advantages of the SD2 procedure. Vertical double ionization potentials (DIPs) for a set of closed-shell molecules are evaluated with the second-order propagator and the SD2 method. The results of the SD2 approximation are in good agreement with experiment. To systematically examine the quality of the results, we compared SD2 and equation-of-motion, coupled-cluster predictions. The average absolute discrepancy is 0.26 eV for 36 doubly ionized states.

Base and phosphate electron detachment energies of deoxyribonucleotide anions

Photoelectron spectra of deoxyribonucleotide anions are interpreted with ab initio, electron propagator calculations. Ground-state structures display hydrogen bonds which are not present in less stable minima that resemble Watson-Crick fragment geometries. For the adenosine and thymidine anions, there are two vertical electron detachment energies (VEDEs) within 0.1 eV of each other that correspond to phosphate- and base-centered Dyson orbitals (DOs). The first VEDE of the cytidine anion belongs to a phosphate-centered DO. The anomalously low VEDE of the guanosine anion is assigned to a base-centered, pi DO. Higher VEDEs of all four anions also are assigned.

Removing Electrons Can Increase the Electron Density: A Computational Study of Negative Fukui Functions

Ab initio and density-functional theory calculations for a family of substituted acetylenes show that removing electrons from these molecules causes the electron density along the C-C bond to increase. This result contradicts the predictions of simple frontier molecular orbital theory, but it is easily explained using the nucleophilic Fukui function-provided that one is willing to allow for the Fukui function to be negative. Negative Fukui functions emerge as key indicators of redox-induced electron rearrangements, where oxidation of an entire molecule (acetylene) leads to reduction of a specific region of the molecule (along the bond axis, between the carbon atoms). Remarkably, further oxidization of these substituted acetylenes (one can remove as many as four electrons!) causes the electron density along the C-C bond to increase even more. This work provides substantial evidence that the molecular Fukui function is sometimes negative and reveals that this is due to orbital relaxation.

OH3− and O2H5− double Rydberg anions: Predictions and comparisons with NH4− and N2H7−

A low barrier in the reaction pathway between the double Rydberg isomer of OH(3) (-) and a hydride-water complex indicates that the former species is more difficult to isolate and characterize through anion photoelectron spectroscopy than the well known double Rydberg anion (DRA), tetrahedral NH(4) (-). Electron propagator calculations of vertical electron detachment energies (VEDEs) and isosurface plots of the electron localization function disclose that the transition state's electronic structure more closely resembles that of the DRA than that of the hydride-water complex. Possible stabilization of the OH(3) (-) DRA through hydrogen bonding or ion-dipole interactions is examined through calculations on O(2)H(5) (-) species. Three O(2)H(5) (-) minima with H(-)(H(2)O)(2), hydrogen-bridged, and DRA-molecule structures resemble previously discovered N(2)H(7) (-) species and have well separated VEDEs that may be observable in anion photoelectron spectra.

Surface Green’s function calculations: A nonrecursive scheme with an infinite number of principal layers

A novel computational method for a surface Green's function matrix is introduced for the calculation of electrical current in molecular wires. The proposed nonrecursive approach includes an infinite number of principal layers and yields the second-order matrix equation for the transformed Green's function matrix. The solution is found by the direct diagonalization of the auxiliary matrix without any iteration process. As soon as complex roots of the auxiliary matrix (approximately GS) are calculated, the gaps and the bands in the surface electronic structure are found. It is shown that the solution of a second-order matrix equation determines the spectral density matrix, that is, the density of states for noninteracting electrons. Single and double principal layer models are studied both analytically and numerically. The energy interval for nonvanishing spectral matrices is determined. This method is applicable to matrices of any rank.

Sequential addition of H2O, CH3OH, and NH3 to Al3O3−: A theoretical study

Photoelectron spectra of two species, Al3O3(H2O)2- and Al3O3(CH3OH)2-, that are produced by the addition of two water or methanol molecules to Al3O3- are interpreted with density-functional geometry optimizations and electron propagator calculations of vertical electron detachment energies. In both cases, there is only one isomer that is responsible for the observed spectral features. A high barrier to the addition of a second molecule may impede the formation of Al3O3N2H6- clusters in an analogous experiment with NH3.

Electronic Structure Analysis and Electron Detachment Energies of Polynitrogen Pentagonal Aromatic Anions

Various decouplings of the electron propagator have been employed to provide theoretical comparison to experimental electron detachment energies for the pyrrolide, imidazolide, and pyrazolide anions. Predictions for isoelectronic anions in which CH groups are replaced by N atoms also are reported. The ab initio electron propagator results agree closely with experimental values, and the associated Dyson orbitals provide a detailed catalog of bonding changes as the number and positions of N atoms vary within the set of pentagonal aromatic anions.

Deprotonated Cytosine Anions: A Theoretical Prediction of Photoelectron Spectra

Predictions on the photoelectron spectra of deprotonated cytosine anions (cytosinate, Cye(-)) have been made with ab initio electron propagator methods. Two imino-oxo forms are most stable, but four other isomers have energies within 10 kcal/mol. The first vertical electron detachment energies (VEDEs) for the three most stable Cye(-) isomers are approximately 3.4 eV. Imino-oxy VEDEs are about 0.3 eV smaller. For each anion, the lowest VEDE corresponds to a pi Dyson orbital. The order of higher final states is changed when relaxation and correlation effects are considered. Considerable mixing between lone-pair and bonding lobes occurs in the sigma Dyson orbitals.

Are structures with Al–H bonds represented in the photoelectron spectrum of Al3O4H2−?

Photoelectron spectra of Al3O4H2- clusters formed by reactions of Al3O3- with water molecules have been interpreted recently in terms of dissociative absorption products with hydroxide and oxide anions that are coordinated to aluminum cations. Alternative isomers with Al-H bonds have lower energies, but barriers to hydrogen migrations that break O-H bonds and create Al-H bonds are high. Ab initio electron propagator calculations of the vertical electron detachment energies of the anions indicate that the species with hydrides cannot be assigned to the chief features in the photoelectron spectrum. Therefore, the previously studied dissociative absorption products are the structures that are most likely to be probed in the photoelectron spectra.

Ab initioelectron propagator theory of molecular wires. II. Multiorbital terminal description

Correlated, ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical formalism is developed for the calculation of retarded and advanced Green functions in terms of the electron propagator matrix for a bridge molecule. The calculation of the current requires integration in a complex half-plane for a trace that involves terminal and Green function matrices that may have any rank. Because the latter arrays have poles represented by matrices, an alternative expression is developed in terms of ordinary poles which are (n-1)-fold degenerate or nondegenerate. For an arbitrary number of terminal orbitals, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator, i.e., the parameters that are found in the output of numerical calculations.

Ab initioelectron propagator theory of molecular wires: I. Formalism

Ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical approach is developed for the calculation of the retarded and advanced Green functions in terms of the electron propagator matrix for the bridge molecule. The calculation of the current requires integration in a complex half plane for a trace that involves terminal and Green's-function matrices. Because the Green's-function matrices have complex poles represented by matrices, a special scheme is developed to express these "matrix poles" in terms of ordinary poles. An expression for the current is derived for a terminal matrix of arbitrary rank. For a single terminal orbital, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator. It is shown that Dyson orbitals with high pole strengths and overlaps with terminal orbitals are most responsible for the conduction of electrical current.

Ab Initio Electron Propagator Calculations on the Ionization Energies of Free Base Porphine, Magnesium Porphyrin, and Zinc Porphyrin

Ab initio electron propagator methods are applied to the prediction, assignment, and interpretation of the valence photoelectron spectra of free base porphine and of magnesium and zinc porphyrins. Tests of various approximate self-energies, including the partial third (P3), the outer valence Green's function, and the nondiagonal, renormalized second-order (NR2) methods are performed. Basis set effects and reduced active orbital spaces are examined as well. The P3 method and the one-electron picture of ionization that accompanies it are validated for the first two cationic states and for states with sigma holes that are localized in nitrogen, lone pair regions. In the remaining pi-hole states, there is significant shake-up character and NR2 results provide useful diagnostics of correlation effects.

Pseudopotential and electron propagator methods for the calculation of the photoelectron spectra of anionic silicon clusters: predictions on Si10-

Photoelectron spectra of anionic clusters of silicon require reliable theoretical calculations for their assignment and interpretation. Electron propagator calculations in the outer valence Green's-function approximation with two well-characterized, all-electron basis sets on vertical electron detachment energies (VEDEs) of anions are compared to similar calculations that employ Stuttgart pseudopotentials. Tests on Si(n) (-) clusters with n=3-7 exhibit an encouraging agreement between the all-electron and pseudopotentials results and between electron propagator predictions and experiments and values obtained from coupled-cluster calculations. To illustrate the capabilities of the new approach based on a Si pseudopotential and electron propagator methods, VEDE calculations on Si(10) (-) are presented.

Molecular photoionization cross sections in electron propagator theory: Angular distributions beyond the dipole approximation

Corrections to dipole approximation results for angular distributions in photoionization of first-row hydrides have determined by using Dyson orbitals calculated with ab initio electron propagator theory and by considering the full multipole expansion for the incident photon representation. The relative importance of first-order corrections which consist of electric quadrupole and magnetic dipole terms and of higher-order terms has been estimated as a function of photon energy. Multipole corrections to the dipole approximation depend on photon energy and on the characteristics of the Dyson orbitals.

Ground and excited states of the Rydberg radical H3O: Electron propagator and quantum defect analysis

Vertical excitation energies of the Rydberg radical H(3)O are inferred from ab initio electron propagator calculations on the electron affinities of H(3)O(+). The adiabatic ionization energy of H(3)O is evaluated with coupled-cluster calculations. These predictions provide optimal parameters for the molecular-adapted quantum defect orbital method, which is used to determine oscillator strengths. Given that the experimental spectrum of H(3)O does not seem to be available, comparisons with previous calculations are discussed. A simple model Hamiltonian, suitable for the study of bound states with arbitrarily high energies is generated by these means.

Addition of water, methanol, and ammonia to Al3O3− clusters: Reaction products, transition states, and electron detachment energies

Products of reactions between the book and kite isomers of Al3O3- and three important molecules are studied with electronic structure calculations. Dissociative adsorption of H2O or CH3OH is highly exothermic and proton-transfer barriers between anion-molecule complexes and the products of these reactions are low. For NH3, the reaction energies are less exothermic and the corresponding barriers are higher. Depending on experimental conditions, Al3O3- (NH3) coordination complexes or products of dissociative adsorption may be prepared. Vertical electron detachment energies of stable anions are predicted with ab initio electron propagator calculations and are in close agreement with experiments on Al3O3- and its products with H2O and CH3OH. Changes in the localization properties of two Al-centered Dyson orbitals account for the differences between the photoelectron spectra of Al3O3- and those of the product anions.

Electron Propagator Calculations Show that Alkyl Substituents Alter Porphyrin Ionization Energies

The effect of alkyl substituents on the four lowest vertical ionization energies of porphyrins is determined with ab initio electron propagator calculations on porphine and octamethylporphyrin. With the use of the partial third-order approximation, predicted ionization energies are in close agreement with recent photoelectron spectra. These data and the associated Dyson orbitals, which describe changes in electronic structure that accompany photoionization, enable assignment of photoelectron spectra and determination of alkyl-induced shifts. Hyperconjugation is most evident in the Dyson orbitals associated with the third and fourth ionization energies of octamethylporphyrin and is least prominent in the Dyson orbital of the second ionization energy. There is a positive correlation between the shift in an ionization energy produced by alkyl substitution and the degree of hyperconjugation in the associated Dyson orbital. Alkyl substitutions, therefore, may be employed to adjust the ionization energies of porphyrins and, consequently, their reactivity patterns that depend on charge-transfer capabilities and disposition to electrophilic attack.

Silicon−Nitrogen Bonding in Silatranes: Assignment of Photoelectron Spectra

Silicon-nitrogen bonding and the photoelectron spectra of hydro-silatrane and methyl-silatrane, XSi[OCH2CH2]3N (X = H and Me), were studied with ab initio electron propagator theory, many-body methods, and density functional models. A linear vibronic coupling (LVC) model was employed to estimate vibrational widths of the ionization bands and to study the dependence of the ionization energies on the molecular geometry. Particular attention was given to coordinates that change the Si-N distance and the strength of the donor-acceptor interaction between these two atoms. The ionization energy of the highest occupied molecular orbital has a very strong geometrical dependence which leads to an unusually large vibrational width in the corresponding photoelectron band. The assignment of this band in methyl-silatrane, which was controversial for a long time, is resolved by the present study. The calculated photoelectron spectra allow for clear assignment of at least three more bands in the observed spectra. The present results demonstrate the important role of electrostatic interactions in Si <-- N bonding and in the outer-valence ionization energies of the silatranes.