Electron impact electronic excitation of benzene: Theory and experiment.

We report experimental differential cross sections (DCSs) for electron impact excitation of bands I to V of benzene at incident energies of 10, 12.5, 15, and 20 eV. They are compared to calculations using the Schwinger multichannel method while accounting for up to 437 open channels. For intermediate scattering angles, the calculations reveal that the most intense band (V) emerges from surprisingly similar contributions from all its underlying states (despite some preference for the dipole-allowed transitions). They further shed light on intricate multichannel couplings between the states of bands I to V and higher-lying Rydberg states. In turn, the measurements support a vibronic coupling mechanism for excitation of bands II and IV and also show an unexpected forward peak in the spin-forbidden transition accounting for band III. Overall, there is decent agreement between theory and experiment at intermediate angles and at lower energies and in terms of the relative DCSs of the five bands. Discrepancies between the present and previous experiment regarding bands IV and V draw attention to the need of additional experimental investigations. We also report measured DCSs for vibrational excitation of combined C-H stretching modes.

Electron Scattering from 1-Methyl-5-Nitroimidazole: Cross-Sections for Modeling Electron Transport through Potential Radiosensitizers.

In this study, we present a complete set of electron scattering cross-sections from 1-Methyl-5-Nitroimidazole (1M5NI) molecules for impact energies ranging from 0.1 to 1000 eV. This information is relevant to evaluate the potential role of 1M5NI as a molecular radiosensitizers. The total electron scattering cross-sections (TCS) that we previously measured with a magnetically confined electron transmission apparatus were considered as the reference values for the present analysis. Elastic scattering cross-sections were calculated by means of two different schemes: The Schwinger multichannel (SMC) method for the lower energies (below 15 eV) and the independent atom model-based screening-corrected additivity rule with interferences (IAM-SCARI) for higher energies (above 15 eV). The latter was also applied to calculate the total ionization cross-sections, which were complemented with experimental values of the induced cationic fragmentation by electron impact. Double differential ionization cross-sections were measured with a reaction microscope multi-particle coincidence spectrometer. Using a momentum imaging spectrometer, direct measurements of the anion fragment yields and kinetic energies by the dissociative electron attachment are also presented. Cross-sections for the other inelastic channels were derived with a self-consistent procedure by sampling their values at a given energy to ensure that the sum of the cross-sections of all the scattering processes available at that energy coincides with the corresponding TCS. This cross-section data set is ready to be used for modelling electron-induced radiation damage at the molecular level to biologically relevant media containing 1M5NI as a potential radiosensitizer. Nonetheless, a proper evaluation of its radiosensitizing effects would require further radiobiological experiments.

Anion states of halocamphor molecules: insights into chirally sensitive dissociative electron attachment.

Recent measurements of spin-polarized electron collisions with halocamphor molecules have observed intriguing trends in their dissociative electron attachment (DEA) chiral asymmetries. While the differences between the DEA asymmetries of 3-bromocamphor (3BrC) and 3-iodocamphor (3IC) were consistent with the larger atomic number of iodine, the even higher chiral asymmetry reported for 10-iodocamphor (10IC) was unexpected. In fact, the helicity densities and the distances from the iodine atoms to the closest chiral centers would suggest smaller asymmetries for 10IC compared to 3IC. To better understand the observed trends, we performed electron scattering and bound state calculations, as well as Born-Oppenheimer molecular dynamics simulations for the three halocamphors. Our results indicate that the DEA signals stem exclusively from halide ions produced by the fast dissociation of low-lying σ* anion states. While we also found dipole bound states and higher-lying shape resonances, we do not expect those states to significantly contribute to the observed yields. Despite the fact that we do not account for the spin-orbit interactions or reaction dynamics, the energies and autoionization lifetimes of the σ* resonances strongly support larger DEA yields for 10IC than 3BrC. The more efficient dissociation could explain the fourfold difference between the maximum DEA chiral asymmetries, since the difference in the atomic numbers of iodine and bromine only accounts for a factor of two. Additionally, our calculations suggest that the twofold difference between the DEA asymmetries of the iodocamphor isomers could be related to the partial suppression of the cross section for electron attachment to 3IC, compared to 10IC.

Variational coupled cluster for ground and excited states.

In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes that are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations that may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC and we compare it with its (projected) traditional version in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear H4 molecule and the continuous deformation of the square H4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of variational pCCD (VpCCD) and traditional pCCD is gauged against their configuration interaction (CI) equivalent, known as doubly occupied CI, for reference Slater determinants made of ground- or excited-state Hartree-Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated.

Accurate full configuration interaction correlation energy estimates for five- and six-membered rings.

Following our recent work on the benzene molecule [P.-F. Loos, Y. Damour, and A. Scemama, J. Chem. Phys. 153, 176101 (2020)], motivated by the blind challenge of Eriksen et al. [J. Phys. Chem. Lett. 11, 8922 (2020)] on the same system, we report accurate full configuration interaction (FCI) frozen-core correlation energy estimates for 12 five- and six-membered ring molecules (cyclopentadiene, furan, imidazole, pyrrole, thiophene, benzene, pyrazine, pyridazine, pyridine, pyrimidine, s-tetrazine, and s-triazine) in the standard correlation-consistent double-ζ Dunning basis set (cc-pVDZ). Our FCI correlation energy estimates, with an estimated error smaller than 1 millihartree, are based on energetically optimized-orbital selected configuration interaction calculations performed with the configuration interaction using a perturbative selection made iteratively algorithm. Having at our disposal these accurate reference energies, the respective performance and convergence properties of several popular and widely used families of single-reference quantum chemistry methods are investigated. In particular, we study the convergence properties of (i) the Møller-Plesset perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), (ii) the iterative approximate coupled-cluster series CC2, CC3, and CC4, and (iii) the coupled-cluster series CCSD, CCSDT, and CCSDTQ. The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized CC model, CR-CC(2,3), is also investigated. We show that MP4 provides an interesting accuracy/cost ratio, while MP5 systematically worsens the correlation energy estimates. In addition, CC3 outperforms CCSD(T) and CR-CC(2,3), as well as its more expensive parent CCSDT. A similar trend is observed for the methods including quadruple excitations, where the CC4 model is shown to be slightly more accurate than CCSDTQ, both methods providing correlation energies within 2 millihartree of the FCI limit.

Excited States of Bromopyrimidines Probed by VUV Photoabsorption Spectroscopy and Theoretical Calculations.

We report absolute photoabsorption cross sections for gas-phase 2- and 5-bromopyrimidine in the 3.7-10.8 eV energy range, in a joint theoretical and experimental study. The measurements were carried out using high-resolution vacuum ultraviolet synchrotron radiation, with quantum chemical calculations performed through the nuclear ensemble approach in combination with time-dependent density functional theory, along with additional Franck-Condon Herzberg-Teller calculations for the first absorption band (3.7-4.6 eV). The cross sections of both bromopyrimidines are very similar below 7.3 eV, deviating more substantially from each other at higher energies. In the 7.3-9.0 eV range where the maximum cross-section is found, a single and broad band is observed for 5-bromopyrimidine, while more discernible features appear in the case of 2-bromopyrimidine. Several π* ← π transitions account for the most intense bands, while weaker ones are assigned to transitions involving the nitrogen and bromine lone pairs, the antibonding σ*Br orbital, and the lower-lying Rydberg states. A detailed comparison with the available photo-absorption data of bromobenzene is also reported. We have found significant differences regarding the main absorption band, which is more peaked in bromobenzene, becoming broader and shifting to higher energies in both bromopyrimidines. In addition, there is a significant suppression of vibrational structures and of Rydberg states in the pair of isomers, most noticeably for 2-bromopyrimidine.

Low-energy electron scattering by cyanamide: anion spectra and dissociation pathways.

The low-energy anion spectra of cyanamide and its rare tautomer carbodiimide were surveyed with elastic electron scattering calculations. Our assignments differ qualitatively and quantitatively from a previous theoretical report. We support that both tautomers present two π* and two shape resonances, while cyanamide should also display a dipole bound state and a shape resonance. Available dissociative electron attachment measurements have shown several structures for dehydrogenation below 4 eV, but no sharp peaks related to vibrational Feshbach resonances. The absence of these resonances is explained by the lack of a potential barrier for tunneling of the hydrogen atom, despite the coupling between dipole bound and states. We found that the π* resonances initiate the dynamics that lead to hydrogen loss at 1.5, 2.5 and 3 eV. The later two structures arise from the anion states of cyanamide, while carbodiimide should account for the lower-lying one. The rarity of the second tautomer would be offset by its larger dissociative electron attachment cross section, enough to leave a distinct signature in the measured ion yield spectra. Low-energy electrons should thus decompose carbodiimide much more efficiently than cyanamide.

Electronic excitation of ethanol by low-energy electron impact.

We report computed differential cross sections (DCSs) for electron impact excitation of the lower-lying states of both trans and gauche tautomers of ethanol, as well as total cross sections for the 15 eV-50 eV energy range. The Schwinger multichannel (SMC) method with pseudopotentials has been employed, and in our most sophisticated calculation in terms of multichannel coupling, 431 open target states have been considered. We found an overall good agreement with the available experimental data at intermediate scattering angles and at higher impact energies. Although we have used a Born-closure scheme for the higher partial waves, we have found discrepancies in the forward direction that were assigned to a poor description of the long-range component of the lower partial waves. Meanwhile, the lack of more Rydberg states could be related to the overestimated DCSs at lower energies. Missing open channels are usually evoked to explain the remaining discrepancies to experiment, but here, we argue that other factors should also be involved. Aiming at an improved description of the target states, we have proposed a simple procedure for selecting the pairs of hole and particle orbitals while keeping the single excitation prescription of the current SMC implementation. A quantitative assessment of the collision process should further consider the individual contribution of each tautomer, which presented quite distinct DCSs in some cases. Our computed excitation energies also support that the second absorption band of ethanol is comprised of three singlet states of each tautomer, rather than the previously suggested two or four states.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry.

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

Reference Energies for Double Excitations: Improvement and Extension.

In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

State-Specific Coupled-Cluster Methods for Excited States.

We reexamine ΔCCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain in which the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here to evaluate the effectiveness of ΔCCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the ΔCCSD and EOM-CCSD methods for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our data set, consisting of 276 excited states stemming from the quest database [Véril et al., WIREs Comput. Mol. Sci. 2021, 11, e1517], provides a significant base to draw general conclusions concerning the accuracy of ΔCCSD. Except for the doubly excited states, we found that ΔCCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of 0.10 and 0.07 eV) is less pronounced than that obtained for singly excited states of closed-shell systems (MAEs of 0.15 and 0.08 eV). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for ΔCCSD. We also found typically small improvements by employing state-specific optimized orbitals.

State-Specific Configuration Interaction for Excited States.

We introduce and benchmark a systematically improvable route for excited-state calculations, labeled state-specific configuration interaction (ΔCI), which is a particular realization of multiconfigurational self-consistent field and multireference configuration interaction. Starting with a reference built from optimized configuration state functions, separate CI calculations are performed for each targeted state (hence, state-specific orbitals and determinants). Accounting for single and double excitations produces the ΔCISD model, which can be improved with second-order Epstein-Nesbet perturbation theory (ΔCISD+EN2) or a posteriori Davidson corrections (ΔCISD+Q). These models were gauged against a vast and diverse set of 294 reference excitation energies. We have found that ΔCI is significantly more accurate than standard ground-state-based CI, whereas close performances were found between ΔCISD and EOM-CC2 and between ΔCISD+EN2 and EOM-CCSD. For larger systems, ΔCISD+Q delivers more accurate results than EOM-CC2 and EOM-CCSD. The ΔCI route can handle challenging multireference problems, singly and doubly excited states, from closed- and open-shell species, with overall comparable accuracy and thus represents a promising alternative to more established methodologies. In its current form, however, it is reliable only for relatively low-lying excited states.

Seniority and Hierarchy Configuration Interaction for Radicals and Excited States.

Hierarchy configuration interaction (hCI) has recently been introduced as an alternative configuration interaction (CI) route combining excitation degree and seniority number and has been shown to efficiently recover both dynamic and static correlations for closed-shell molecular systems [ J. Phys. Chem. Lett. 2022, 13, 4342]. Here we generalize hCI for an arbitrary reference determinant, allowing calculations for radicals and excited states in a state-specific way. We gauge this route against excitation-based CI (eCI) and seniority-based CI (sCI) by evaluating how different ground-state properties of radicals converge to the full CI limit. We find that hCI outperforms or matches eCI, whereas sCI is far less accurate, in line with previous observations for closed-shell molecules. Employing second-order Epstein-Nesbet (EN2) perturbation theory as a correction significantly accelerates the convergence of hCI and eCI. We further explore various hCI and sCI models to calculate the excitation energies of closed- and open-shell systems. Our results underline that the choice of both the reference determinant and the set of orbitals drives the fine balance between correlation of ground and excited states. State-specific hCI2 and higher-order models perform similarly to their eCI counterparts, whereas lower orders of hCI deliver poor results unless supplemented by the EN2 correction, which substantially improves their accuracy. In turn, sCI1 produces decent excitation energies for radicals, encouraging the development of related seniority-based coupled-cluster methods.

Reference Vertical Excitation Energies for Transition Metal Compounds.

To enrich and enhance the diversity of the quest database of highly accurate excitation energies [Véril, M.; et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], we report vertical transition energies in transition metal compounds. Eleven diatomic molecules with a singlet or doublet ground state containing a fourth-row transition metal (CuCl, CuF, CuH, ScF, ScH, ScO, ScS, TiN, ZnH, ZnO, and ZnS) are considered, and the corresponding excitation energies are computed using high-level coupled-cluster (CC) methods, namely, CC3, CCSDT, CC4, and CCSDTQ, as well as multiconfigurational methods such as CASPT2 and NEVPT2. In many cases, to provide more comprehensive benchmark data, we also provide full configuration interaction estimates computed with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. Based on these calculations, theoretical best estimates of the transition energies are established in both the aug-cc-pVDZ and aug-cc-pVTZ basis sets. This allows us to accurately assess the performance of the CC and multiconfigurational methods for this specific set of challenging transitions. Furthermore, comparisons with experimental data and previous theoretical results are also reported.

Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality.

We report ground- and excited-state dipole moments and oscillator strengths (computed in different "gauges" or representations) of full configuration interaction (FCI) quality using the selected configuration interaction method known as Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI). Thanks to a set encompassing 35 ground- and excited-state properties computed in 11 small molecules, the present near-FCI estimates allow us to assess the accuracy of high-order coupled-cluster (CC) calculations including up to quadruple excitations. In particular, we show that incrementing the excitation degree of the CC expansion (from CC with singles and doubles (CCSD) to CC with singles, doubles, and triples (CCSDT) or from CCSDT to CC with singles, doubles, triples, and quadruples (CCSDTQ)) reduces the average error with respect to the near-FCI reference values by approximately 1 order of magnitude.

Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree.

We propose a novel partitioning of the Hilbert space, hierarchy configuration interaction (hCI), where the excitation degree (with respect to a given reference determinant) and the seniority number (i.e., the number of unpaired electrons) are combined in a single hierarchy parameter. The key appealing feature of hCI is that each hierarchy level accounts for all classes of determinants whose number shares the same scaling with system size. By surveying the dissociation of multiple molecular systems, we found that the overall performance of hCI usually exceeds or, at least, parallels that of excitation-based CI. For higher orders of hCI and excitation-based CI, the additional computational burden related to orbital optimization usually does not compensate the marginal improvements compared with results obtained with Hartree-Fock orbitals. The exception is orbital-optimized CI with single excitations, a minimally correlated model displaying the qualitatively correct description of single bond breaking at a very modest computational cost.

Observation of Transient Anions That Do Not Decay through Dissociative Electron Attachment: New Pathways for Radiosensitization.

Low-energy electrons (LEEs) can very efficiently induce bond breaking via dissociative electron attachment (DEA). While DEA is ubiquitous, the importance of other reactions initiated by LEEs remains much more elusive. Here, we looked into this question by measuring highly accurate total cross sections for electron scattering from 1-methyl-5-nitroimidazole (1M5NI), a model radiosensitizer. The small uncertainty and high energy resolution allow us to identify many resonant features related to the formation of transient anions. In addition to novel insights about DEA reactions through the lower-lying resonances, our key finding is that the higher-lying resonances do not undergo DEA, implying alternative decay channels with significant cross sections. In particular, dissociation into two neutral fragments is probably involved in the case of 1M5NI. This finding has direct implications for the understanding of LEE-induced chemistry, particularly in the fundamental processes underlying the radiosensitization activity.

Newton-X Platform: New Software Developments for Surface Hopping and Nuclear Ensembles.

Newton-X is an open-source computational platform to perform nonadiabatic molecular dynamics based on surface hopping and spectrum simulations using the nuclear ensemble approach. Both are among the most common methodologies in computational chemistry for photophysical and photochemical investigations. This paper describes the main features of these methods and how they are implemented in Newton-X. It emphasizes the newest developments, including zero-point-energy leakage correction, dynamics on complex-valued potential energy surfaces, dynamics induced by incoherent light, dynamics based on machine-learning potentials, exciton dynamics of multiple chromophores, and supervised and unsupervised machine learning techniques. Newton-X is interfaced with several third-party quantum-chemistry programs, spanning a broad spectrum of electronic structure methods.

Excited States from State-Specific Orbital-Optimized Pair Coupled Cluster.

The pair coupled cluster doubles (pCCD) method (where the excitation manifold is restricted to electron pairs) has a series of interesting features. Among others, it provides ground-state energies very close to what is obtained with doubly occupied configuration interaction (DOCI), but with a polynomial cost (compared with the exponential cost of the latter). Here, we address whether this similarity holds for excited states by exploring the symmetric dissociation of the linear H4 molecule. When ground-state Hartree-Fock (HF) orbitals are employed, pCCD and DOCI excited-state energies do not match, a feature that is assigned to the poor HF reference. In contrast, by optimizing the orbitals at the pCCD level (oo-pCCD) specifically for each excited state, the discrepancies between pCCD and DOCI decrease by 1 or 2 orders of magnitude. Therefore, the pCCD and DOCI methodologies still provide comparable energies for excited states, but only if suitable, state-specific orbitals are adopted. We also assessed whether a pCCD approach could be used to directly target doubly excited states, without having to resort to the equation-of-motion (EOM) formalism. In our Δoo-pCCD model, excitation energies are extracted from the energy difference between separate oo-pCCD calculations for the ground state and the targeted excited state. For a set comprising the doubly excited states of CH+, BH, nitroxyl, nitrosomethane, and formaldehyde, we found that Δoo-pCCD provides quite accurate excitation energies, with root-mean-square deviations (with respect to full configuration interaction results) lower than those of CC3 and comparable to those of EOM-CCSDT, two methods with a much higher computational cost.

Nonadiabatic dynamics in multidimensional complex potential energy surfaces.

Despite the continuous development of theoretical methodologies for describing nonadiabatic dynamics of molecular systems, there is a lack of approaches for processes where the norm of the wave function is not conserved, i.e., when an imaginary potential accounts for some irreversible decaying mechanism. Current approaches rely on building potential energy surfaces of reduced dimensionality, which is not optimal for more involving and realistic multidimensional problems. Here, we present a novel methodology for describing the dynamics of complex-valued molecular Hamiltonians, which is a generalisation of the trajectory surface hopping method. As a first application, the complex surface fewest switches surface hopping (CS-FSSH) method was employed to survey the relaxation mechanisms of the shape resonant anions of iodoethene. We have provided the first detailed and dynamical picture of the π*/σ* mechanism of dissociative electron attachment in halogenated unsaturated compounds, which is believed to underlie electron-induced reactions of several molecules of interest. Electron capture into the π* orbital promotes C[double bond, length as m-dash]C stretching and out-of-plane vibrations, followed by charge transfer from the double bond into the σ* orbital at the C-I bond, and, finally, release of the iodine ion, all within only 15 fs. On-the-fly dynamics simulations of a vast class of processes can be envisioned with the CS-FSSH methodology, including autoionisation from transient anions, core-ionised and superexcited states, Auger and interatomic coulombic decay, and time-dependent luminescence.