Periodic Reporting for period 4 - T-CUBE (Theoretical Chemistry of Unbound Electrons)
Reporting period: 2024-12-01 to 2025-05-31
The project T-CUBE sought to advance the quantum chemistry of unbound electrons. The overall goal was to develop theoretical methods that can treat the interaction of unbound electrons with extended molecular systems in complex environments such as solutions and biomolecules that are of genuine interest to chemistry and biochemistry.
Traditionally, chemistry has focused on processes in which all electrons remain bound to the nuclei. In a standard chemical reaction driven by heat, the electrons are merely regrouped and chemical bonds are cleaved or formed accordingly. This results in the reactivity patterns known from chemistry textbooks.
When energy is provided in the form of extra electrons or by removal of electrons, different reactivity patterns are observed that are inaccessible otherwise. Until recently, such processes were considered exotic but state-of-the-art experimental techniques have made it possible to create, in a controlled manner, environments where selected electrons are no longer bound to the nuclei. Examples include the cleavage of strong chemical bonds by low-energy electrons, applications of cold plasma, and various nonradiative decay processes following interaction with X rays, for example Auger decay. Together, these processes constitute the chemistry of unbound electrons. Technological applications of these chemical transformations are still at an early stage but hold a lot of promise and could eventually replace processes based on heat-driven traditional chemistry.
Reactions involving unbound electrons are difficult to model theoretically. This is because the short-lived quantum-mechanical states that govern the interaction of unbound electrons with matter are outside the realm of standard quantum-chemical methods, which were designed for bound electrons. T-CUBE contributed to changing that. The project relied on the idea of complex-valued energies, which had been pioneered in the context of nuclear physics to describe radioactivity, and applied it to quantum chemistry. This combination of the concept of complex-valued energy with quantum chemistry enabled a better theoretical description of unbound electrons and, in this way, contributed to their use in novel applications.
Traditionally, chemistry has focused on processes in which all electrons remain bound to the nuclei. In a standard chemical reaction driven by heat, the electrons are merely regrouped and chemical bonds are cleaved or formed accordingly. This results in the reactivity patterns known from chemistry textbooks.
When energy is provided in the form of extra electrons or by removal of electrons, different reactivity patterns are observed that are inaccessible otherwise. Until recently, such processes were considered exotic but state-of-the-art experimental techniques have made it possible to create, in a controlled manner, environments where selected electrons are no longer bound to the nuclei. Examples include the cleavage of strong chemical bonds by low-energy electrons, applications of cold plasma, and various nonradiative decay processes following interaction with X rays, for example Auger decay. Together, these processes constitute the chemistry of unbound electrons. Technological applications of these chemical transformations are still at an early stage but hold a lot of promise and could eventually replace processes based on heat-driven traditional chemistry.
Reactions involving unbound electrons are difficult to model theoretically. This is because the short-lived quantum-mechanical states that govern the interaction of unbound electrons with matter are outside the realm of standard quantum-chemical methods, which were designed for bound electrons. T-CUBE contributed to changing that. The project relied on the idea of complex-valued energies, which had been pioneered in the context of nuclear physics to describe radioactivity, and applied it to quantum chemistry. This combination of the concept of complex-valued energy with quantum chemistry enabled a better theoretical description of unbound electrons and, in this way, contributed to their use in novel applications.
Several important advances of the theory of unbound electrons have been realized, including methodological advances as well as applications:
A first achievement is the development of ab initio molecular dynamics (AIMD) simulations on complex-valued potential energy surfaces. AIMD simulations are in widespread use in computational chemistry and show how the nuclei move in the potential of the electrons. In this way, the progression of a chemical reaction in time can be studied and visualized. However, this was not possible until now for decaying states where electrons can leave the system while the nuclei move. In our work, we devised AIMD simulations for such decaying states and investigated the dissociation of unsaturated halogenated hydrocarbons induced by attachment of slow electrons. Despite a rather crude description of the electronic structure, experimental trends were well reproduced in our simulations.
A second achievement consists in the development of methods for the determination of partial decay widths. Using these new approaches, we were able to model various molecular Auger spectra from first principles. Auger spectroscopy is well established as an analytic technique but the theoretical modeling of molecular Auger spectra has remained a non-routine task for computational chemistry. Already a molecule such as benzene with 12 nuclei and 42 electrons represents a significant challenge. Our theoretical Auger spectrum for benzene, which is based on complex-scaled coupled-cluster theory, is in excellent agreement with experiment. In addition, we used complex-energy methods to investigate a variety of further decay processes: resonant Auger decay, autoionization of Rydberg states, Coster-Kronig decay, super-Coster-Kronig decay, as well as interatomic Coulombic decay.
A third achievement is the application of projection-based quantum embedding to ionization and electron attachment. Quantum embedding is a promising approach for the extension of highly accurate quantum-chemical methods to large molecules and complex systems that is well established for electronic ground states. We showed that the approach delivers good results for ionization and electron attachment as well. Subsequently, we used quantum embedding to model the dissociation of hydrogen chloride on a gold surface and showed that electron attachment facilitates the cleavage of the H-Cl bond as compared to a reaction proceeding through the ground electronic state.
A fourth achievement is the application of density functional theory to decaying states. In the first step, we combined conceptual density functional theory with the charge stabilization method. This allowed us to predict dissociative electron attachment to unsaturated halogenated hydrocarbons through analysis of nuclear and atom-condensed electronic Fukui functions. Additionally, we showed that the electron localization function as well as Berlin's binding function predict dissociative electron attachment as well. In the second step, we combined density functional theory with complex absorbing potentials. We showed that hybrid density functionals are well suited for the characterization of temporary anions of larger molecules.
A fifth achievement is the development of second-order coupled-cluster methods for bound nonvalence anions and temporary anions. Using these new methods, we were able to characterize hitherto unknown dipole-bound anions of larger organic molecules such as progesterone, cortisol, as well as ubiquinone. We also identified a new type of anion, a pi-type quadrupole-bound state, in tetracyanonaphthalene. Furthermore, we showed that the performance of second-order coupled-cluster methods is similar for temporary anions and for bound anions, in particular, the application of spin scaling is advantageous in both cases. Additional developments for anions concerned s-wave scattering that manifests in a characteristic shape of the anionic potential energy surface. We also developed a method for the ab initio computation of nonadiabatic coupling between decaying states.
A first achievement is the development of ab initio molecular dynamics (AIMD) simulations on complex-valued potential energy surfaces. AIMD simulations are in widespread use in computational chemistry and show how the nuclei move in the potential of the electrons. In this way, the progression of a chemical reaction in time can be studied and visualized. However, this was not possible until now for decaying states where electrons can leave the system while the nuclei move. In our work, we devised AIMD simulations for such decaying states and investigated the dissociation of unsaturated halogenated hydrocarbons induced by attachment of slow electrons. Despite a rather crude description of the electronic structure, experimental trends were well reproduced in our simulations.
A second achievement consists in the development of methods for the determination of partial decay widths. Using these new approaches, we were able to model various molecular Auger spectra from first principles. Auger spectroscopy is well established as an analytic technique but the theoretical modeling of molecular Auger spectra has remained a non-routine task for computational chemistry. Already a molecule such as benzene with 12 nuclei and 42 electrons represents a significant challenge. Our theoretical Auger spectrum for benzene, which is based on complex-scaled coupled-cluster theory, is in excellent agreement with experiment. In addition, we used complex-energy methods to investigate a variety of further decay processes: resonant Auger decay, autoionization of Rydberg states, Coster-Kronig decay, super-Coster-Kronig decay, as well as interatomic Coulombic decay.
A third achievement is the application of projection-based quantum embedding to ionization and electron attachment. Quantum embedding is a promising approach for the extension of highly accurate quantum-chemical methods to large molecules and complex systems that is well established for electronic ground states. We showed that the approach delivers good results for ionization and electron attachment as well. Subsequently, we used quantum embedding to model the dissociation of hydrogen chloride on a gold surface and showed that electron attachment facilitates the cleavage of the H-Cl bond as compared to a reaction proceeding through the ground electronic state.
A fourth achievement is the application of density functional theory to decaying states. In the first step, we combined conceptual density functional theory with the charge stabilization method. This allowed us to predict dissociative electron attachment to unsaturated halogenated hydrocarbons through analysis of nuclear and atom-condensed electronic Fukui functions. Additionally, we showed that the electron localization function as well as Berlin's binding function predict dissociative electron attachment as well. In the second step, we combined density functional theory with complex absorbing potentials. We showed that hybrid density functionals are well suited for the characterization of temporary anions of larger molecules.
A fifth achievement is the development of second-order coupled-cluster methods for bound nonvalence anions and temporary anions. Using these new methods, we were able to characterize hitherto unknown dipole-bound anions of larger organic molecules such as progesterone, cortisol, as well as ubiquinone. We also identified a new type of anion, a pi-type quadrupole-bound state, in tetracyanonaphthalene. Furthermore, we showed that the performance of second-order coupled-cluster methods is similar for temporary anions and for bound anions, in particular, the application of spin scaling is advantageous in both cases. Additional developments for anions concerned s-wave scattering that manifests in a characteristic shape of the anionic potential energy surface. We also developed a method for the ab initio computation of nonadiabatic coupling between decaying states.
Several of our developments constitute substantial progress beyond the state of the art: First, ab initio molecular dynamics simulations on complex-valued potential energy surfaces made it for the first time possible to study the interplay of electronic decay and nuclear motion in polyatomic molecules during a chemical reaction triggered by unbound electrons. Second, access to partial decay widths enabled the modeling of molecular Auger and Coster-Kronig spectra from first principles as well as the interpretation of measured spectra. Third, new second-order coupled-cluster and density functional theory methods made it possible to characterize bound nonvalence anions as well as temporary anions in molecules with up to 50 atoms. We expect that further methodological advances will enable applications to even larger systems in the near future. Fourth, the description of unbound electrons in solution and other condensed phases was made possible by means of quantum embedding. In sum, the project T-CUBE has contributed substantially to the advancement of the quantum chemistry of unbound electrons.