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We report a combined experimental and theoretical investigation of electron–molecule interactions using pyrrole as a model system. Experimental two-dimensional electron energy loss spectra (EELS) encode information about the vibrational states of the molecule as well as the position and structure of electronic resonances. The calculations using complex-valued extensions of equation-of-motion coupled-cluster theory (based on non-Hermitian quantum mechanics) facilitate the assignment of all major EELS features. We confirm the two previously described π resonances at about 2.5 and 3.5 eV (the calculations place these two states at 2.92 and 3.53 eV vertically and 2.63 and 3.27 eV adiabatically). The calculations also predict a low-lying resonance at 0.46 eV, which has a mixed character—of a dipole-bound state and σ* type. This resonance becomes stabilized at one quanta of the NH excitation, giving rise to the sharp feature at 0.9 eV in the corresponding EELS. Calculations of Franck–Condon factors explain the observed variations in the vibrational excitation patterns. The ability of theory to describe EELS provides a concrete illustration of the utility of non-Hermitian quantum chemistry, which extends such important concepts as potential energy surfaces and molecular orbitals to states embedded in the continuum.
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This content will become publicly available on June 3, 2026
Exploring potential energy surfaces
Quantum mechanics is central to our understanding of chemistry both qualitatively and quantitatively. Modern electronic structure calculations can yield energies and structures of small to medium size molecules to chemical accuracy, thereby providing a computational model for chemistry. A potential energy surface describes the energy of a molecule as a function of its geometric parameters. The features of potential energy surfaces provide the connections between quantum mechanics and the traditional chemical concepts such as structure, bonding and reactivity. This brief perspective presents an overview of tools for exploring potential energy surfaces such as optimizing equilibrium geometries, finding transition states, following reaction paths and simulating molecular dynamics.
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- Award ID(s):
- 1856437
- PAR ID:
- 10612974
- Publisher / Repository:
- De Gruyter
- Date Published:
- Journal Name:
- Pure and Applied Chemistry
- ISSN:
- 0033-4545
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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