Computational methods for the one-particle green's function

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.

A meshless stochastic method for Poisson-Nernst-Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson-Nernst-Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift-diffusion process with time- and space-varying drift. We leverage Green's functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method's convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

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.

Quantum Algorithm for Imaginary-Time Green's Functions

Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H2 and H4 on quantum simulators and on IBM's quantum devices.

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.

Signatures of Conical Intersections in Extreme Ultraviolet Photoelectron Spectra of Furan Measured with 15 fs Time Resolution

Ultrafast internal conversion of furan upon deep UV excitation at 200 nm is studied by using extreme ultraviolet time-resolved photoelectron spectroscopy with a time resolution of 15 fs. Ballistic nuclear wavepacket motion from the 1B2(ππ*) state to the ground state is fully observed using 21.7 eV probe pulses. Through the performance of a comparison with the results of electronic structure calculations at the MS(3)-CASPT2(10,10)/cc-pVTZ level of theory, the photoelectron signals from the conical intersection regions are identified.

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.

CP-AFM Molecular Tunnel Junctions with Alkyl Backbones Anchored Using Alkynyl and Thiol Groups: Microscopically Different Despite Phenomenological Similarity

In this paper, we report results on the electronic structure and transport properties of molecular junctions fabricated via conducting probe atomic force microscopy (CP-AFM) using self-assembled monolayers (SAMs) of n-alkyl chains anchored with acetylene groups (CnA; n = 8, 9, 10, and 12) on Ag, Au, and Pt electrodes. We found that the current-voltage (I-V) characteristics of CnA CP-AFM junctions can be very accurately reproduced by the same off-resonant single-level model (orSLM) successfully utilized previously for many other junctions. We demonstrate that important insight into the energy-level alignment can be gained from experimental data of transport (processed via the orSLM) and ultraviolet photoelectron spectroscopy combined with ab initio quantum chemical information based on the many-body outer valence Green's function method. Measured conductance GAg < GAu < GPt is found to follow the same ordering as the metal work function ΦAu < ΦAu < ΦPt, a fact that points toward a transport mediated by an occupied molecular orbital (MO). Still, careful data analysis surprisingly revealed that transport is not dominated by the ubiquitous HOMO but rather by the HOMO-1. This is an important difference from other molecular tunnel junctions with p-type HOMO-mediated conduction investigated in the past, including the alkyl thiols (CnT) to which we refer in view of some similarities. Furthermore, unlike in CnT and other junctions anchored with thiol groups investigated in the past, the AFM tip causes in CnA an additional MO shift, whose independence of size (n) rules out significant image charge effects. Along with the prevalence of the HOMO-1 over the HOMO, the impact of the "second" (tip) electrode on the energy level alignment is another important finding that makes the CnA and CnT junctions different. What ultimately makes CnA unique at the microscopic level is a salient difference never reported previously, namely, that CnA's alkyne functional group gives rise to two energetically close (HOMO and HOMO-1) orbitals. This distinguishes the present CnA from the CnT, whose HOMO stemming from its thiol group is well separated energetically from the other MOs.

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.

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 Perspective on Sustainable Computational Chemistry Software Development and Integration

The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.

Induced photoelectron circular dichroism onto an achiral chromophore

An achiral chromophore can acquire a chiral spectroscopic signature when interacting with a chiral environment. This so-called induced chirality is documented in electronic or vibrational circular dichroism, which arises from the coupling between electric and magnetic transition dipoles. Here, we demonstrate that a chiroptical response is also induced within the electric dipole approximation by observing the asymmetric scattering of a photoelectron ejected from an achiral chromophore in interaction with a chiral host. In a phenol-methyloxirane complex, removing an electron from an achiral aromatic π orbital localised on the phenol moiety results in an intense and opposite photoelectron circular dichroism (PECD) for the two enantiomeric complexes with (R) and (S) methyloxirane, evidencing the long-range effect (~5 Å) of the scattering chiral potential. This induced chirality has important structural and analytical implications, discussed here in the context of growing interest in laser-based PECD, for in situ, real time enantiomer determination.

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 ionization induced fragmentation pathways of trichloroanisole

Trichloroanisole (TCA) is one of the most significant contaminants in cork stoppers. The presence of TCA leads to an unpleasant odor known as "cork taint", resulting in high economic losses for the cork and wine industries. Hence, the detection, quantification, and characterization of TCA are essential to address this concern. The present study investigates the electron-driven fragmentation pathways of TCA through electron ionization mass spectrometry as a function of electron energy (0-100 eV), and the results are supported by theoretical characterization of ionization potentials, dissociation thresholds, and electron ionization cross sections. The appearance energies of ten cations were measured, including the first experimental evaluation of the molecule's ionization energy at 8.8 ± 0.3 eV, in excellent agreement with the calculations (8.83 eV). For lower energies, around 20 eV, the parent cation accounted for more than 60% of the total ion signal, followed by its demethylated fragment. Taken together, these ion signals could be used as fingerprints of TCA in industrial quality control by low-energy electron ionization mass spectrometry. Fifty other fragments have been identified at higher electron energies, revealing the very rich fragmentation pattern of TCA.

State-specific frozen natural orbital for reduced-cost algebraic diagrammatic construction calculations: The application to ionization problem

We have developed a reduced-cost algebraic diagrammatic construction (ADC) method based on state-specific frozen natural orbital and natural auxiliary functions. The newly developed method has been benchmarked on the GW100 test set for the ionization problem. The use of state-specific natural orbitals drastically reduces the size of the virtual space with a systematically controllable accuracy and offers a significant speedup over the standard ionization potential (IP)-ADC(3) method. The accuracy of the method can be controlled by two thresholds and nearly a black box to use. The inclusion of the perturbative correction significantly improves the accuracy of the calculated IP values, and the efficiency of the method has been demonstrated by calculating the IP of a molecule with 60 atoms and more than 2216 basis functions.

Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation

Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.

A study of the valence photoelectron spectrum of uracil and mixed water-uracil clusters

The valence ionization of uracil and mixed water-uracil clusters has been studied experimentally and by ab initio calculations. In both measurements, the spectrum onset shows a red shift with respect to the uracil molecule, with the mixed cluster characterized by peculiar features unexplained by the sum of independent contributions of the water or uracil aggregation. To interpret and assign all the contributions, we performed a series of multi-level calculations, starting from an exploration of several cluster structures using automated conformer-search algorithms based on a tight-binding approach. Ionization energies have been assessed on smaller clusters via a comparison between accurate wavefunction-based approaches and cost-effective DFT-based simulations, the latter of which were applied to clusters up to 12 uracil and 36 water molecules. The results confirm that (i) the bottom-up approach based on a multilevel method [Mattioli et al. Phys. Chem. Chem. Phys. 23, 1859 (2021)] to the structure of neutral clusters of unknown experimental composition converges to precise structure-property relationships and (ii) the coexistence of pure and mixed clusters in the water-uracil samples. A natural bond orbital (NBO) analysis performed on a subset of clusters highlighted the special role of H-bonds in the formation of the aggregates. The NBO analysis yields second-order perturbative energy between the H-bond donor and acceptor orbitals correlated with the calculated ionization energies. This sheds light on the role of the oxygen lone-pairs of the uracil CO group in the formation of strong H-bonds, with a stronger directionality in mixed clusters, giving a quantitative explanation for the formation of core-shell structures.

Electronic structure, cationic, and excited states of nitrogen-containing spiroborates

CONTEXT

This paper presents the results of the study of the electronic structure and cationic and excited states of three spiroborate complexes (2-acetylacetonato-1,3,2-benzodioxaborol, its NH- and NMe-derivatives) and three corresponding ligands (acetylacetone, 4-aminopent-3-en-2-one, and 4-methylaminopent-3-en-2-one). Materials based on spiroborates are used in medicine, for example, as a drug carrier. In industry, spiroborate anions are used in ionic liquids and as alternative high performance lubricants. Analysis of experimental and calculated data allowed determining the influence of functional groups on the parameters of the electronic structure and energy of electronic transitions. Compared to acetylacetone and its NH- and NMe-derivatives, the upper filled molecular orbitals of the corresponding spiroborates are stabilized at 0.4-1.7 eV, which is due to the positive charge of the ligand due to the acceptor properties of the dioxyphenylene fragment. Among the studied compounds, when replacing the oxygen atom in the α-position with the NH- or NMe-group, a bathochromic shift of intense bands in the absorption spectra is observed, since the energy intervals between the orbitals of the π₃ and π₄ ligand are reduced. In addition, in a number of spiroborates, the violation of C_2v symmetry when replacing an oxygen atom leads to the appearance of a low-intensity maximum in the long-wave part of the absorption spectrum, due to the π₂^X → π₄ transition.

METHOD

Complexes were studied by photoelectron spectroscopy, absorption spectroscopy, and high-level ab initio quantum chemical computations, including the algebraic diagrammatic construction method for the polarization propagator of the second order (ADC(2)), the outer-valence Green's function (OVGF), the density functional theory (DFT), the time-dependent density functional theory (TDDFT) and the domain-based local pair natural orbital (EOM-DLPNO) methods. X-ray photoelectronic spectra of two spiroborates in the condensed state were measured using a two-chamber high-vacuum system MXPS XP (Omicron, Germany). UV-visible absorption spectra were recorded using a spectrophotometer 2550 (Shimadzu-UV, Japan). The geometry of all studied compounds was optimized by the DFT/B3LYP/Def2-SVP method. The energy of electron levels in the S₀ state and the distribution of electron density at each MO were obtained by the DFT/CAMB3LYP/cc-pVDZ method. The energies of excited states were obtained by the TDDFT/CAMB3LYP/cc-pVDZ, ADC(2)/cc-pVDZ and EOM-DLPNO/cc-pVDZ methods. All DFT and TDDFT calculations were carried out in the GAMESS (US) software computing package. ADC(2) calculations of excited states were performed using the Orca 4.0.1 software package. EOM-DLPNO and OVGF calculations were carried out in the Gaussian 16 software package.

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.

XPS and quantum chemical analysis of 4Me-BODIPY derivatives

The results of a X-ray photoelectron spectroscopy (XPS) and steady-state absorption spectroscopy study of the electronic structure, and cationic and excited states of a series of 1,3,5,7-tetramethyl-substituted BODIPYs (4Me,2R-BODIPYs) are presented. The experimental data were interpreted using high-level ab initio quantum chemical computations, including the algebraic diagrammatic construction method for the polarization propagator of the second order (ADC(2)), the outer-valence Green's function (OVGF) method, the density functional (DFT) approach, and the time-dependent DFT (TD-DFT) approach. Substitution effects on the XPS and absorption spectra were determined for 2,6-positions of 4Me,2R-BODIPY pyrrole nuclei (R = H, Br, Bu, benzyl). A very satisfactory performance of the DFT Koopmans theorem analogue was demonstrated with respect to the energy intervals between the electronic levels of 4Me,2R-BODIPY above 13 eV (BHHLYP functional) and the values of the HOMO-LUMO energy gap (ωB97X functional).

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.

The Role of Molecular Structure in Monte Carlo Simulations of the Secondary Electron Yield and Backscattering Coefficient from Methacrylic Acid

In this paper, we show the influence of the chemical structure of four different conformers on the secondary electron emission and backscattering of an electron beam from a gel of methacrylic acid. The conformers have different permanent dipole moments, which determines the cross sections for elastic collisions with electrons. The cross sections are used in Monte Carlo simulations of an electron beam, which enters the gel of methacrylic acid. The secondary electron yield and the backscattering coefficient are computed as a function of the beam energy.

The ionic and ground states of gamma-pyrone. The photoionization spectrum studied by synchrotron radiation and interpreted by configuration interaction and density functional calculations

A synchrotron-based photoionization spectrum up to 27 eV represents a considerable improvement in resolution over early He(I) and He(II) spectra. Symmetry-adapted coupled cluster calculations of the ionic state sequence give the sequence of state vertical ionization energies (VIE) as 1²B₂ < 1²B₁ < 1²A₂ < 2²B₁ < 1²A₁. Generally, these symmetry-adapted cluster configuration interactions VIE match reasonably well with the experimental spectrum over this wide energy range. Density functional calculations of the corresponding adiabatic terms (AIE) were also performed. Higher energy ionic states were determined by complete active space self-consistent field methods; these include all π-ionizations and some σ-ionic states. These were analyzed by Franck-Condon (FC) procedures and compared with an experiment. The spectral onset is complex, where two states, later shown to be the 1²B₂ and 1²B₁ states, are strongly overlapping. The superposition of the FC vibrational structure in the 1²B₂ and 1²B₁ states accounts for most of the peaks arising at the onset of the photoelectron spectra. However, the small separation between these two ionic states makes vibronic interaction fairly inevitable. In the absence of Herzberg-Teller analyses for ionic states, we have sought and determined a transition state between the 1²B₂ and 1²B₁ states, showing that vibronic coupling does occur. The lack of degradation in the vibrational envelope of the higher of the two states contrasts with our previous work on the halogenobenzenes, where overlapping state envelopes led to considerable widening of the line width at half-height of the higher energy states.

Dehydrogenation of Ammonia Borane Impacts Valence and Core Electrons: A Photoemission Spectroscopic Study

Ammonia borane (H₃BNH₃) is a promising material for hydrogen storage and release. Dehydrogenation of ammonia borane produces small boron-nitrogen hydrides such as aminoborane (H₂BNH₂) and iminoborane (HBNH). The present study investigates ammonia borane and its two dehydrogenated products for the first time using calculated photoemission spectra of the valence and core electrons. It is found that a significant decrease in the dipole moment was observed associated with the dehydration from 5.397 D in H₃BNH₃, to 1.942 D in H₂BNH₂, and to 0.083 D in HBNH. Such reduction in the dipole moment impacts properties such as hydrogen bonding, dihydrogen bonding, and their spectra. Dehydrogenation of H₃BNH₃ impacts both the valence and core electronic structure of the boron-nitrogen hydrides. The calculated valence vertical ionization energy (VIE) spectra of the boron-nitrogen hydrides show that valence orbitals dominated by 2p-electrons of B and N atoms exhibit large changes, whereas orbitals dominated by s-electrons, such as (3a₁4a₁5a₁/3σ4σ5σ) remain less affected. The first ionization energy slightly increases from 10.57 eV for H₃BNH₃ to 11.29 eV for both unsaturated H₂BNH₂ and HBNH. In core space, the oxidative dehydrogenation of H₃BNH₃ affects the core electron binding energy (CEBE) of borane and nitrogen oppositely. The B1s binding energies increase from 194.01 eV in H₃BNH₃ to 196.93 eV in HBNH, up by 2.92 eV, whereas the N1s binding energies decrease from 408.20 eV in H₃BNH₃ to 404.88 eV in HBNH, dropped by 3.32 eV.

Periodic Coupled-Cluster Green's Function for Photoemission Spectra of Realistic Solids

We present an efficient implementation of the coupled-cluster Green's function (CCGF) method for simulating photoemission spectra of periodic systems. We formulate the periodic CCGF approach with Brillouin zone sampling in the Gaussian basis at the coupled-cluster singles and doubles (CCSD) level. To enable CCGF calculations of realistic solids, we propose an active-space self-energy correction scheme by combining CCGF with the cheaper many-body perturbation theory (GW) and implement the model order reduction (MOR) frequency interpolation technique. We find that the active-space self-energy correction and MOR techniques significantly reduce the computational cost of CCGF while maintaining the high accuracy. We apply the developed CCGF approaches to compute spectral properties and band structure of silicon (Si) and zinc oxide (ZnO) crystals using triple-ζ Gaussian basis sets and medium-size k-point sampling and find good agreement with experimental measurements.

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.

Electron-impact ionization cross sections of small molecules containing Fe and Cr∗

We present the electron-impact ionization cross sections (EICSs) of iron and chromium hydrides, nitrides, and oxides. The motivation of this work stems from the fact that chemical sputtering from a steel surface exposed to a hot plasma can create these molecules which in turn influence the composition and energy balance of the plasma. The latter influence is quantified by the EICS which we derive by using two semi-empirical methods which can be employed in the relevant energy range of 10-1000 eV. They are important molecular properties for plasma- and materials science. We discuss the foundations of the methods and present the cross sections of the high- and low-spin states of the species in their neutral ground states and of their cations.

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.

Boron Oxide B5O6− Cluster as a Boronyl-Based Inorganic Analog of Phenolate Anion

Boron oxide clusters have structural richness and exotic chemical bonding. We report a quantum chemical study on the binary B5O6− cluster, which is relatively oxygen-rich. A global structural search reveals planar C2v (1A1) geometry as the global minimum structure, featuring a heteroatomic hexagonal B3O3 ring as its core. The three unsaturated B sites are terminated by two boronyl (BO) groups and an O− ligand. The B5O6− cluster can be faithfully formulated as B3O3(BO)2O−. This structure is in stark contrast to that of its predecessors, Cs B5O5− and Td B5O4−, both of which have a tetrahedral B center. Thus, there exists a major structural transformation in B5On− series upon oxidation, indicating intriguing competition between tetrahedral and heterocyclic structures. The chemical bonding analyses show weak 6π aromaticity in the B5O6− cluster, rendering it a boronyl analog of phenolate anion (C6H5O−) or boronyl boroxine. The calculated vertical detachment energy of B5O6− cluster is 5.26 eV at PBE0, which greatly surpasses the electron affinities of halogens (Cl: 3.61 eV), suggesting that the cluster belongs to superhalogen anions.

Photoelectron Circular Dichroism as a Signature of Subtle Conformational Changes: The Case of Ring Inversion in 1-Indanol

Chirality plays a fundamental role in the molecular recognition processes. Molecular flexibility is also crucial in molecular recognition, allowing the interacting molecules to adjust their structures and hence optimize the interaction. Methods probing simultaneously chirality and molecular conformation are therefore crucially needed. Taking advantage of a possible control in the gas phase of the conformational distribution between the equatorial and axial conformers resulting from a ring inversion in jet-cooled 1-indanol, we demonstrate here the sensitivity of valence-shell photoelectron circular dichroism (PECD) to both chirality and subtle conformational changes, in a case where the photoelectron spectra of the two conformers are identical. For the highest occupied orbital, we observe a dramatic inversion of the PECD-induced photoelectron asymmetries, while the photoionization cross-section and usual anisotropy (β) parameter are completely insensitive to conformational isomerism. Such a sensitivity is a major asset for the ongoing developments of PECD-based techniques as a sensitive chiral (bio)chemical analytical tool in the gas phase.

Multi-electron excitation contributions towards primary and satellite states in the photoelectron spectrum

The computation of Dyson orbitals and corresponding ionization energies has been implemented within the Equation of Motion Coupled Cluster Singles, Doubles and Perturbative Triples (EOM-CC3) method. Coupled to an accurate...

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.

Quantitative analysis of weak current rectification in molecular tunnel junctions subject to mechanical deformation reveals two different rectification mechanisms for oligophenylene thiols versus alkane thiols

Metal-molecule-metal junctions based on alkane thiol (CnT) and oligophenylene thiol (OPTn) self-assembled monolayers (SAMs) and Au electrodes are expected to exhibit similar electrical asymmetry, as both junctions have one chemisorbed Au-S contact and one physisorbed, van der Waals contact. Asymmetry is quantified by the current rectification ratio RR apparent in the current-voltage (I-V) characteristics. Here we show that RR < 1 for CnT and RR > 1 for OPTn junctions, in contrast to expectation, and further, that RR behaves very differently for CnT and OPTn junctions under mechanical extension using the conducting probe atomic force microscopy (CP-AFM) testbed. The analysis presented in this paper, which leverages results from the previously validated single level model and ab initio quantum chemical calculations, allows us to explain the puzzling experimental findings for CnT and OPTn in terms of different current rectification mechanisms. Specifically, in CnT-based junctions the Stark effect creates the HOMO level shifting necessary for rectification, while for OPTn junctions the level shift arises from position-dependent coupling of the HOMO wavefunction with the junction electrostatic potential profile. On the basis of these mechanisms, our quantum chemical calculations allow quantitative description of the impact of mechanical deformation on the measured current rectification. Additionally, our analysis, matched to experiment, facilitates direct estimation of the impact of intramolecular electrostatic screening on the junction potential profile. Overall, our examination of current rectification in benchmark molecular tunnel junctions illuminates key physical mechanisms at play in single step tunneling through molecules, and demonstrates the quantitative agreement that can be obtained between experiment and theory in these systems.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.