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The equation-of-motion coupled-cluster singles and doubles method with double electron attachment (EOM-DEA-CCSD) is capable of computing reliable energies, wave functions, and first-order properties of excited states in diradicals and polyenes that have a significant doubly excited character with respect to the ground state, without the need for including the computationally expensive triple excitations. Here, we extend the capabilities of the EOM-DEA-CCSD method to the calculations of a multiphoton property, two-photon absorption (2PA) cross sections. Closed-form expressions for the 2PA cross sections are derived within the expectation-value approach using response wave functions. We analyze the performance of this new implementation by comparing the EOM-DEA-CCSD energies and 2PA cross sections with those computed using the CC3 quadratic response theory approach. As benchmark systems, we consider transitions to the states with doubly excited character in twisted ethene and in polyenes, for which EOM-EE-CCSD (EOM-CCSD for excitation energies) performs poorly. The EOM-DEA-CCSD 2PA cross sections are comparable with the CC3 results for twisted ethene; however, the discrepancies between the two methods are large for hexatriene. The observed trends are explained by configurational analysis of the 2PA channels. 

We present a new implementation for computing spin–orbit couplings (SOCs) within a time-dependent density-functional theory (TD-DFT) framework in the standard spin-conserving formulation as well in the spin–flip variant (SF-TD-DFT). This approach employs the Breit–Pauli Hamiltonian and Wigner–Eckart’s theorem applied to the reduced one-particle transition density matrices, together with the spin–orbit mean-field treatment of the two-electron contributions. We use a state-interaction procedure and compute the SOC matrix elements using zero-order non-relativistic states. Benchmark calculations using several closed-shell organic molecules, diradicals, and a single-molecule magnet illustrate the efficiency of the SOC protocol. The results for organic molecules (described by standard TD-DFT) show that SOCs are insensitive to the choice of the functional or basis sets, as long as the states of the same characters are compared. In contrast, the SF-TD-DFT results for small diradicals (CH 2 , [Formula: see text], SiH 2 , and [Formula: see text]) show strong functional dependence. The spin-reversal energy barrier in a Fe(III) single-molecule magnet computed using non-collinear SF-TD-DFT (PBE0, ωPBEh/cc-pVDZ) agrees well with the experimental estimate. 

We present an ab initio computational study of the Auger electron spectrum of benzene. Auger electron spectroscopy exploits the Auger–Meitner effect, and although it is established as an analytic technique, the theoretical modeling of molecular Auger spectra from first principles remains challenging. Here, we use coupled-cluster theory and equation-of-motion coupled-cluster theory combined with two approaches to describe the decaying nature of core-ionized states: (i) Feshbach–Fano resonance theory and (ii) the method of complex basis functions. The spectra computed with these two approaches are in excellent agreement with each other and also agree well with experimental Auger spectra of benzene. The Auger spectrum of benzene features two well-resolved peaks at Auger electron energies above 260 eV, which correspond to final states with two electrons removed from the 1 e 1 g and 3 e 2 g highest occupied molecular orbitals. At lower Auger electron energies, the spectrum is less well resolved, and the peaks comprise multiple final states of the benzene dication. In line with theoretical considerations, singlet decay channels contribute more to the total Auger intensity than the corresponding triplet decay channels. 

This computational study characterises charge-transfer-to-solvent (CTTS) states of aqueous thiocyanate anion using equation-of-motion coupled-cluster methods combined with electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) scheme. Equilibrium sampling was carried out using classical molecular dynamics (MD) with standard force-fields and QM/MM ab initio molecular dynamics (AIMD) using density functional theory. The two calculations yield significantly different local structure around solvated SCN− . Because of the diffuse character of CTTS states, they are very sensitive to the local structure of solvent around the solute and its dynamic fluctuations. Owing to this sensitivity, the spectra computed using MD and AIMD based snapshots differ considerably. This sensitivity suggests that the spectroscopy exploiting CTTS transitions can provide an experimental handle for assessing the quality of force-fields and density functionals. By combining CTTS-based spectroscopies with reliable theoretical modeling, detailed microscopic information of the solvent structure can be obtained. We present a robust computational protocol for modeling spectra of solvated anions and emphasise the use of an ab initio characterization of individual electronic transitions as CTTS or local excitations. 

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. 

Photoelectron angular distributions (PADs) in SO − photodetachment using linearly polarized 355 nm (3.49 eV), 532 nm (2.33 eV), and 611 nm (2.03 eV) light were investigated via photoelectron imaging spectroscopy. The measurements at 532 and 611 nm access the X 3 Σ − and a 1 Δ electronic states of SO, whereas the measurements at 355 nm also access the b 1 Σ + state. In aggregate, the photoelectron anisotropy parameter values follow the general trend with respect to electron kinetic energy (eKE) expected for π*-orbital photodetachment. The trend is similar to O 2 − , but the minimum of the SO − curve is shifted to smaller eKE. This shift is mainly attributed to the exit-channel interactions of the departing electron with the dipole moment of the neutral SO core, rather than the differing shapes of the SO − and O 2 − molecular orbitals. Of the several ab initio models considered, two approaches yield good agreement with the experiment: one representing the departing electron as a superposition of eigenfunctions of a point dipole-field Hamiltonian, and another describing the outgoing electron in terms of Coulomb waves originating from two separated charge centers, with a partial positive charge on the sulfur and an equal negative charge on the oxygen. These fundamentally related approaches support the conclusion that electron–dipole interactions in the exit channel of SO − photodetachment play an important role in shaping the PADs. While a similar conclusion was previously reached for photodetachment from σ orbitals of CN − (Hart, Lyle, Spellberg, Krylov, Mabbs, J. Phys. Chem. Lett. , 2021, 12 , 10086–10092), the present work includes the first extension of the dipole-field model to detachment from π* orbitals.