N-representability violations in truncated equation-of-motion coupled-cluster methods.

One-electron reduced density matrices (1RDMs) from equation-of-motion (EOM) coupled-cluster with single and double excitations (CCSD) calculations are analyzed to assess their N-representability (i.e., whether they are derivable from a physical N-electron state). We identify EOM-CCSD stationary states whose 1RDMs violate either ensemble-state N-representability conditions or pure-state conditions known as generalized Pauli constraints. As such, these 1RDMs do not correspond to any physical N-electron state. Unphysical states are also encountered in the course of time-dependent EOM-CC simulations; when an external field drives transitions between a pair of stationary states with pure-state N-representable 1RDMs, the 1RDM of the time-dependent state can violate ensemble-state conditions. These observations point to potential challenges in interpreting the results of time-dependent EOM-CCSD simulations.

Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian.

Simulations of laser-induced electron dynamics in a molecular system are performed using time-dependent (TD) equation-of-motion (EOM) coupled-cluster (CC) theory. The target system has been chosen to highlight potential shortcomings of truncated TD-EOM-CC methods [represented in this work by TD-EOM-CC with single and double excitations (TD-EOM-CCSD)], where unphysical spectroscopic features can emerge. Specifically, we explore driven resonant electronic excitations in magnesium fluoride in the proximity of an avoided crossing. Near the avoided crossing, the CCSD similarity-transformed Hamiltonian is defective, meaning that it has complex eigenvalues, and oscillator strengths may take on negative values. When an external field is applied to drive transitions to states exhibiting these traits, unphysical dynamics are observed. For example, the stationary states that make up the time-dependent state acquire populations that can be negative, exceed one, or even complex-valued.

Benchmarking the semi-stochastic CC(P;Q) approach for singlet-triplet gaps in biradicals.

We recently proposed a semi-stochastic approach to converging high-level coupled-cluster (CC) energetics, such as those obtained in the CC calculations with singles, doubles, and triples (CCSDT), in which the deterministic CC(P;Q) framework is merged with the stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)]. In this work, we investigate the ability of the semi-stochastic CC(P;Q) methodology to recover the CCSDT energies of the lowest singlet and triplet states and the corresponding singlet-triplet gaps of biradical systems using methylene, (HFH)-, cyclobutadiene, cyclopentadienyl cation, and trimethylenemethane as examples.

Femtosecond intramolecular rearrangement of the CH3NCS radical cation.

Strong-field ionization, involving tunnel ionization and electron rescattering, enables femtosecond time-resolved dynamics measurements of chemical reactions involving radical cations. Here, we compare the formation of CH3S+ following the strong-field ionization of the isomers CH3SCN and CH3NCS. The former involves the release of neutral CN, while the latter involves an intramolecular rearrangement. We find the intramolecular rearrangement takes place on a single picosecond timescale and exhibits vibrational coherence. Density functional theory and coupled-cluster calculations on the neutral and singly ionized species help us determine the driving force responsible for intramolecular rearrangement in CH3NCS. Our findings illustrate the complexity that accompanies radical cation chemistry following electron ionization and demonstrate a useful tool for understanding cation dynamics after ionization.

Steric effects in light-induced solvent proton abstraction.

The significance of solvent structural factors in the excited-state proton transfer (ESPT) reactions of Schiff bases with alcohols is reported here. We use the super photobase FR0-SB and a series of primary, secondary, and tertiary alcohol solvents to illustrate the steric issues associated with solvent to photobase proton transfer. Steady-state and time-resolved fluorescence data show that ESPT occurs readily for primary alcohols, with a probability proportional to the relative -OH concentration. For secondary alcohols, ESPT is greatly diminished, consistent with the barrier heights obtained using quantum chemistry calculations. ESPT is not observed in the tertiary alcohol. We explain ESPT using a model involving an intermediate hydrogen-bonded complex where the proton is "shared" by the Schiff base and the alcohol. The formation of this complex depends on the ability of the alcohol solvent to achieve spatial proximity to and alignment with the FR0-SB* imine lone pair stabilized by the solvent environment.

Isoenergetic two-photon excitation enhances solvent-to-solute excited-state proton transfer.

Two-photon excitation (TPE) is an attractive means for controlling chemistry in both space and time. Since isoenergetic one- and two-photon excitations (OPE and TPE) in non-centrosymmetric molecules are allowed to reach the same excited state, it is usually assumed that they produce similar excited-state reactivity. We compare the solvent-to-solute excited-state proton transfer of the super photobase FR0-SB following isoenergetic OPE and TPE. We find up to 62% increased reactivity following TPE compared to OPE. From steady-state spectroscopy, we rule out the involvement of different excited states and find that OPE and TPE spectra are identical in non-polar solvents but not in polar ones. We propose that differences in the matrix elements that contribute to the two-photon absorption cross sections lead to the observed enhanced isoenergetic reactivity, consistent with the predictions of our high-level coupled-cluster-based computational protocol. We find that polar solvent configurations favor greater dipole moment change between ground and excited states, which enters the probability for TPE as the absolute value squared. This, in turn, causes a difference in the Franck-Condon region reached via TPE compared to OPE. We conclude that a new method has been found for controlling chemical reactivity via the matrix elements that affect two-photon cross sections, which may be of great utility for spatial and temporal precision chemistry.

Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations.

The recently proposed idea of identifying the most important higher-than-doubly excited determinants in the ground-state coupled-cluster (CC) calculations through stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua et al., Phys. Rev. Lett. 119, 223003 (2017)] is extended to excited electronic states via the equation-of-motion (EOM) CC methodology. The advantages of the new approach are illustrated by calculations aimed at recovering the ground- and excited-state energies of the CH+ molecule at the equilibrium and stretched geometries resulting from the EOMCC calculations with a full treatment of singles, doubles, and triples.

Approximate Exponential Integrators for Time-Dependent Equation-of-Motion Coupled Cluster Theory.

With a growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schrödinger equation is of keen interest in modern electronic structure theory. In this work, we present two approaches for the formation of the quantum propagator for time-dependent equation-of-motion coupled cluster theory based on the Chebyshev and Arnoldi expansions of the complex, nonhermitian matrix exponential, respectively. The proposed algorithms are compared with the short-iterative Lanczos method of Cooper et al. [J. Phys. Chem. A 2021 125, 5438-5447], the fourth-order Runge-Kutta method, and exact dynamics for a set of small but challenging test problems. For each of the cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency relative to the reference simulations.

Intramolecular Relaxation Dynamics Mediated by Solvent-Solute Interactions of Substituted Fluorene Derivatives. Solute Structural Dependence.

Several fluorene derivatives exhibit excited-state reactivity and relaxation dynamics that remain to be understood fully. We report here the spectral relaxation dynamics of two fluorene derivatives to evaluate the role of structural modification in the intramolecular relaxation dynamics and intermolecular interactions that characterize this family of chromophores. We have examined the time-resolved spectral relaxation dynamics of two compounds, NCy-FR0 and MK-FR0, in protic and aprotic solvents using steady-state and time-resolved emission spectroscopy and quantum chemical computations. Both compounds exhibit spectral relaxation characteristics similar to those seen in FR0, indicating that hydrogen bonding interactions between the chromophore and solvent protons play a significant role in determining the relaxation pathways available to three excited electronic states.

Excited-State Dynamics of a Substituted Fluorene Derivative. The Central Role of Hydrogen Bonding Interactions with the Solvent.

Substituted fluorene structures have demonstrated unusual photochemical properties. Previous reports on the substituted fluorene Schiff base FR0-SB demonstrated super photobase behavior with a ΔpKb of ∼14 upon photoexcitation. In an effort to understand the basis for this unusual behavior, we have examined the electronic structure and relaxation dynamics of the structural precursor of FR0-SB, the aldehyde FR0, in protic and aprotic solvents using time-resolved fluorescence spectroscopy and quantum chemical calculations. The calculations show three excited singlet states in relatively close energetic proximity. The spectroscopic data are consistent with relaxation dynamics from these electronic states that depend on the presence and concentration of solvent hydroxyl functionality. These results underscore the central role of solvent hydrogen bonding to the FR0 aldehyde oxygen in mediating the relaxation dynamics within this molecule.

Quantum computation solves a half-century-old enigma: Elusive vibrational states of magnesium dimer found.

The high-lying vibrational states of the magnesium dimer (Mg2), which has been recognized as an important system in studies of ultracold and collisional phenomena, have eluded experimental characterization for half a century. Until now, only the first 14 vibrational states of Mg2 have been experimentally resolved, although it has been suggested that the ground-state potential may support five additional levels. Here, we present highly accurate ab initio potential energy curves based on state-of-the-art coupled-cluster and full configuration interaction computations for the ground and excited electronic states involved in the experimental investigations of Mg2. Our ground-state potential unambiguously confirms the existence of 19 vibrational levels, with ~1 cm-1 root mean square deviation between the calculated rovibrational term values and the available experimental and experimentally derived data. Our computations reproduce the latest laser-induced fluorescence spectrum and provide guidance for the experimental detection of the previously unresolved vibrational levels.

Proton Abstraction Mediates Interactions between the Super Photobase FR0-SB and Surrounding Alcohol Solvent.

We report on the motional and proton transfer dynamics of the super photobase FR0-SB in the series of normal alcohols C1 (methanol) through C8 (n-octanol) and ethylene glycol. Steady-state and time-resolved fluorescence data reveal that the proton abstraction dynamics of excited FR0-SB depend on the identity of the solvent and that the transfer of the proton from solvent to FR0-SB*, forming FR0-HSB+*, fundamentally alters the nature of interactions between the excited molecule and its surroundings. In its unprotonated state, solvent interactions with FR0-SB* are consistent with slip limit behavior, and in its protonated form, intermolecular interactions are consistent with a much stronger interaction of FR0-HSB+* with the deprotonated solvent RO-. We understand the excited-state population dynamics in the context of a kinetic model involving a transition state wherein FR0-HSB+* is still bound to the negatively charged alkoxide, prior to solvation of the two charged species. Data acquired in ethylene glycol confirm the hypothesis that the rotational diffusion dynamics of FR0-SB* are largely mediated by solvent viscosity while proton transfer dynamics are mediated by the lifetime of the transition state. Taken collectively, our results demonstrate that FR0-SB* extracts solvent protons efficiently and in a predictable manner, consistent with a ca. 3-fold increase in dipole moment upon photoexcitation as determined by ab initio calculations based on the equation-of-motion coupled-cluster theory.

Efficacy of Density Functionals and Relativistic Effective Core Potentials for Lanthanide-Containing Species: The Ln54 Molecule Set.

The utility of 22 density functionals paired with relativistic effective core potentials (RECPs) for the prediction of thermodynamic properties was investigated for the Ln54 set of lanthanide-containing molecules. The Ln54 set includes lanthanide oxides, fluorides, and chlorides with the lanthanide formally in the +1, + 2, or +3 oxidation state. The density functionals were chosen to span the gamut of complexity from the local density approximation to double hybrids. Computed enthalpies of formation and bond dissociation energies were compared to experimental data and to previous calculations performed with all electron basis sets. The performance of the functionals was then assessed for each class of molecules in the Ln54 set. Overall, SVWN was found to be the best-performing functional having the lowest MAD of 22.1 kcal mol-1 and the most systematic deviation in comparison to the other functionals.