Block Lanczos and many‐body theory: Application to the one‐particle Green’s function

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.

Revealing the Role of N Heteroatoms in Noncovalent Aromatic Interactions by Ultrafast Intermolecular Coulombic Decay

Despite the widely recognized importance of noncovalent interactions involving aromatic rings in many fields, our understanding of the underlying forces and structural patterns, especially the impact of heteroaromaticity, is still incomplete. Here, we investigate the relaxation processes that follow inner-valence ionization in a range of molecular dimers involving various combinations of benzene, pyridine, and pyrimidine, which initiate an ultrafast intermolecular Coulombic decay process. Multiparticle coincidence momentum spectroscopy, combined with ab initio calculations, enables us to explore the principal orientations of these fundamental dimers and, thus, to elucidate the influence of N heteroatoms on the relative preference of the aromatic π-stacking, H-bonding, and CH-π interactions and their dependence on the number of nitrogen atoms in the rings. Our studies reveal a sensitive tool for the structural imaging of molecular complexes and provide a more complete understanding of the effects of N heteroatoms on the noncovalent aromatic interactions at the molecular level.

Two-Sided Impact of Water on the Relaxation of Inner-Valence Vacancies of Biologically Relevant Molecules

After ionization of an inner-valence electron of molecules, the resulting cation-radicals store substantial internal energy which, if sufficient, can trigger ejection of an additional electron in an Auger decay usually followed by molecule fragmentation. In the environment, intermolecular Coulombic decay (ICD) and electron-transfer mediated decay (ETMD) are also operative, resulting in one or two electrons being ejected from a neighbor, thus preventing the fragmentation of the initially ionized molecule. These relaxation processes are investigated theoretically for prototypical heterocycle-water complexes of imidazole, pyrrole, and pyridine. It is found that the hydrogen-bonding site of the water molecule critically influences the nature and energetics of the electronic states involved, opening or closing certain relaxation processes of the inner-valence ionized system. Our results indicate that the relaxation mechanisms of biologically relevant systems with inner-valence vacancies on their carbon atoms can strongly depend on the presence of the electron-density donating or accepting neighbor, either water or another biomolecule.

Concerted Double Hydrogen-Bond Breaking by Intermolecular Coulombic Decay in the Formic Acid Dimer

Hydrogen bonds are ubiquitous in nature and of fundamental importance to the chemical and physical properties of molecular systems in the condensed phase. Nevertheless, our understanding of the structural and dynamical properties of hydrogen-bonded complexes in particular in electronic excited states remains very incomplete. Here, by using formic acid (FA) dimer as a prototype of DNA base pair, we investigate the ultrafast decay process initiated by removal of an electron from the inner-valence shell of the molecule upon electron-beam irradiation. Through fragment-ion and electron coincident momentum measurements and ab initio calculations, we find that de-excitation of an outer-valence electron at the same site can initiate ultrafast energy transfer to the neighboring molecule, which is in turn ionized through the emission of low-energy electrons. Our study reveals a concerted breaking of double hydrogen-bond in the dimer initiated by the ultrafast molecular rotations of two FA⁺ cations following this nonlocal decay mechanism.

Scalable and Predictive Spectra of Correlated Molecules with Moment Truncated Iterated Perturbation Theory

A reliable and efficient computation of the entire single-particle spectrum of correlated molecules is an outstanding challenge in the field of quantum chemistry, with standard density functional theory approaches often giving an inadequate description of excitation energies and gaps. In this work, we expand upon a recently introduced approach that relies on a fully self-consistent many-body perturbation theory coupled to a nonperturbative truncation of the effective dynamics at each step. We show that this yields a low-scaling and accurate method across a diverse benchmark test set that is capable of treating moderate levels of strong correlation effects, and we detail an efficient implementation for applications involving up to ∼1000 orbitals on parallel resources. We then use this method to characterize the spectral properties of the antimalarial drug molecule artemisinin, resolving discrepancies in previous works concerning the active sites of the lowest-energy fundamental excitations of the system.

Valence shell photoelectron angular distributions and vibrationally resolved spectra of imidazole: A combined experimental-theoretical study

Linearly polarized synchrotron radiation has been used to record polarization dependent valence shell photoelectron spectra of imidazole in the photon energy range 21-100 eV. These have allowed the photoelectron angular distributions, as characterized by the anisotropy parameter β, and the electronic state intensity branching ratios to be determined. Complementing these experimental data, theoretical photoionization partial cross sections and β-parameters have been calculated for the outer valence shell orbitals. The assignment of the structure appearing in the experimental photoelectron spectra has been guided by vertical ionization energies and spectral intensities calculated by various theoretical methods that incorporate electron correlation and orbital relaxation. Strong orbital relaxation effects have been found for the 15a', nitrogen lone-pair orbital. The calculations also predict that configuration mixing leads to the formation of several low-lying satellite states. The vibrational structure associated with ionization out of a particular orbital has been simulated within the Franck-Condon model using harmonic vibrational modes. The adiabatic approximation appears to be valid for the X ²A″ state, with the β-parameter for this state being independent of the level of vibrational excitation. However, for all the other outer valence ionic states, a disparity occurs between the observed and the simulated vibrational structure, and the measured β-parameters are at variance with the behavior expected at the level of the Franck-Condon approximation. These inconsistencies suggest that the excited electronic states may be interacting vibronically such that the nuclear dynamics occur over coupled potential energy surfaces.

Koopmans'-Type Theorem in Kohn-Sham Theory with Optimally Tuned Long-Range-Corrected (LC) Functionals

In the present study, we have investigated the applicability of long-range-corrected (LC) functionals to a Kohn-Sham (KS) Koopmans'-type theorem. Specifically, we have examined the performance of optimally tuned LCgau-core functionals (in combination with BOP and PW86-PW91 exchange-correlation functionals) by calculating the ionization potential (IP) within the context of Koopmans' prediction. In the LC scheme, the electron repulsion operator, 1/r₁₂, is divided into short-range and long-range components using a standard error function, with a range separation parameter μ determining the weight of the two ranges. For each system that we have examined (H₂O, CO, benzene, N₂, HF, H₂CO, C₂H₄, and five-membered ring compounds cyclo-C₄H₄X, with X = CH₂, NH, O, and S, and pyridine), the value of μ is optimized to minimize the deviation of the negative HOMO energy from the experimental IP. Our results demonstrate the utility of optimally tuned LC functionals in predicting the IP of outer valence levels. The accuracy is comparable to that of highly accurate ab initio theory. However, our Koopmans' method is less accurate for the inner valence and core levels. Overall, our results support the notion that orbitals in KS-DFT, when obtained with the LC functional, provide an accurate one-electron energy spectrum. This method represents a one-electron orbital theory that is attractive in its simple formulation and effective in its practical application.

Efficient Excitations and Spectra within a Perturbative Renormalization Approach

We present a self-consistent approach for computing the correlated quasiparticle spectrum of charged excitations in iterative O[N5] computational time. This is based on the auxiliary second-order Green's function approach [Backhouse, O. J. Chem. Theory Comput., 2000], in which a self-consistent effective Hamiltonian is constructed by systematically renormalizing the dynamical effects of the self-energy at second-order perturbation theory. From extensive benchmarking across the W4-11 molecular test set, we show that the iterative renormalization and truncation of the effective dynamical resolution arising from the 2h1p and 1h2p spaces can substantially improve the quality of the resulting ionization potential and electron affinity predictions compared to benchmark values. The resulting method is shown to be superior in accuracy to similarly scaling quantum chemical methods for charged excitations in EOM-CC2 and ADC(2), across this test set, while the self-consistency also removes the dependence on the underlying mean-field reference. The approach also allows for single-shot computation of the entire quasiparticle spectrum, which is applied to the benzoquinone molecule and demonstrates the reduction in the single-particle gap due to the correlated physics, and gives direct access to the localization of the Dyson orbitals.

The band 12 issue of norbornane: a study of higher shake-up states

In line with a recent study of the electronic structure of the cage compound norbornane (J. Chem. Phys. 121 (2004), 10525; J. Phys. Chem. A 109 (2005), 4267), symmetry adapted cluster expansion configuration interaction (SAC-CI) general R calculations have been performed and compared with results obtained by the third order algebraic diagrammatic construction scheme [ADC(3)]. Comparison has been made with previously performed electron momentum spectroscopy (EMS) and ultraviolet photo-electron measurements. The region around ~25 eV (band 12), characterized by an elaborated band in the EMS spectrum which is missing in previous Green's function and ADC calculations, is investigated. This study is completed with outer-valence Green's function (OVGF) and SAC-CI/SD-R calculations, and results are obtained by employing (single and double) ionization extended second order ADC [ADC(2)-x]. Since ADC(3) only includes 2h-1p shake-up states, while SAC-CI general-R also includes higher order states, the agreement between both methods assures that the higher order shake-up states do not play an important role in the ionization spectrum of norbornane. While the band-12 issue of norbornane is therefore still open for further discussion, a tentative description in terms of ultrafast nuclear dynamical effects and autoionization processes has become more plausible.

Implementation and use of a direct, partially integral-driven non-Dyson propagator method for molecular ionization

The Green's function ADC(3) scheme has been for many years a successful method to predict theoretically the ionization (and electron affinity) spectrum of molecules. However, a dramatic enhancement of the method's power has come only recently, with the development of an approximation method to the one-particle Green's function which does not make direct use of the Dyson equation. In the present work, we present an efficient computer implementation of this novel approach, with first comparative tests demonstrating its enormous computational advantage over the conventional approach.