Accidental triplet harvesting in donor-acceptor dyads with low spin-orbit coupling.

We present an accidental mechanism for efficient intersystem crossing (ISC) between singlet and triplet states with low spin-orbit coupling (SOC) in molecules having donor-acceptor (D-A) moieties separated by a Sigma bond. Our study shows that SOC between the lowest singlet excited state and the higher-lying triplet states, together with nuclear motion-driven coupling of this triplet state with lower-lying triplet states during the free rotation about a Sigma bond, is one of the possible ways to achieve the experimentally observed ISC rate for a class of D-A type photoredox catalysts. This mechanism is found to be the dominant contributor to the ISC process with the corresponding rate reaching a maximum at a dihedral angle in the range of 72°-78° between the D-A moieties of 10-(naphthalen-1-yl)-3,7-diphenyl-10H-phenoxazine and other molecules included in the study. We have further demonstrated that the same mechanism is operative in a specific spirobis[anthracene]dione molecule, where the D and A moieties are interlocked near to the optimal dihedral angle, indicating the plausible effectiveness of the proposed mechanism. The present finding is expected to have implications in strategies for the synthesis of new generations of triplet-harvesting organic molecules.

Photophysics of uracil: an explicit time-dependent generating function-based method combining both nonadiabatic and spin-orbit coupling effects.

We present a composite framework for calculating the rates of non-radiative deactivation processes, namely internal conversion (IC) and intersystem crossing (ISC), on an equal footing by explicitly computing the non-adiabatic coupling (NAC) and spin-orbit coupling (SOC) constants, respectively. The stationary-state approach uses a time-dependent generating function based on Fermi's golden rule. We validate the applicability of the framework by computing the rate of IC for azulene, obtaining comparable rates to experimental and previous theoretical results. Next, we investigate the photophysics associated with the complex photodynamics of the uracil molecule. Interestingly, our simulated rates corroborate experimental observations. Detailed analyses using Duschinsky rotation matrices, displacement vectors and NAC matrix elements are presented to interpret the findings alongside testing the suitability of the approach for such molecular systems. The suitability of the Fermi's golden rule based method is explained qualitatively in terms of single-mode potential energy surfaces.

New Implementation of an Equation-of-Motion Coupled-Cluster Damped-Response Framework with Illustrative Applications to Resonant Inelastic X-ray Scattering.

We present an implementation of a damped response framework for calculating resonant inelastic X-ray scattering (RIXS) at the equation-of-motion coupled-cluster singles and doubles (CCSD) and second-order approximate coupled-cluster singles and doubles (CC2) levels of theory in the open-source program eT. This framework lays the foundation for future extension to higher excitation methods (notably, the coupled-cluster singles and doubles with perturbative triples, CC3) and to multilevel approaches. Our implementation adopts a fully relaxed ground state and different variants of the core-valence separation projection technique to address convergence issues. Illustrative results are compared with those obtained within the frozen-core core-valence separated approach, available in Q-Chem, as well as with experiment. The performance of the CC2 method is evaluated in comparison with that of CCSD. It is found that, while the CC2 method is noticeably inferior to CCSD for X-ray absorption spectra, the quality of the CC2 RIXS spectra is often comparable to that of the CCSD level of theory, when the same valence excited states are probed. Finally, we present preliminary RIXS results for a solvated molecule in aqueous solution.

Multi-electron excitation contributions towards primary and satellite states in the photoelectron spectrum.

The computation of Dyson orbitals and corresponding ionization energies has been implemented within the equation of motion coupled cluster singles, doubles and perturbative triples (EOM-CC3) method. Coupled to an accurate description of the electronic continuum via a time-dependent density functional approach using a multicentric B-spline basis, this yields highly accurate photoionization dynamical parameters (cross-sections, branching ratios, asymmetry parameters and dichroic coefficients) for primary (1h) states as well as satellite states of (2h1p) character. Illustrative results are presented for the molecular systems H2O, H2S, CS, CS2 and (S)-propylene oxide (a.k.a. methyloxirane).

Behind the scenes of spin-forbidden decay pathways in transition metal complexes.

The interpretation of the ultrafast photophysics of transition metal complexes following photo-absorption is quite involved as the heavy metal center leads to a complicated and entangled singlet-triplet manifold. This opens up multiple pathways for deactivation, often with competitive rates. As a result, intersystem crossing (ISC) and phosphorescence are commonly observed in transition metal complexes. A detailed understanding of such an excited-state structure and dynamics calls for state-of-the-art experimental and theoretical methodologies. In this review, we delve into the inability of non-relativistic quantum theory to describe spin-forbidden transitions, which can be overcome by taking into account spin-orbit coupling, whose importance grows with increasing atomic number. We present the quantum chemical theory of phosphorescence and ISC together with illustrative examples. Finally, a few applications are highlighted, bridging the gap between theoretical studies and experimental applications, such as photofunctional materials.

Vibrationally resolved coupled-cluster x-ray absorption spectra from vibrational configuration interaction anharmonic calculations.

Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the adaptive density-guided approach scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecules.

eT 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods.

The eT program is an open source electronic structure package with emphasis on coupled cluster and multilevel methods. It includes efficient spin adapted implementations of ground and excited singlet states, as well as equation of motion oscillator strengths, for CCS, CC2, CCSD, and CC3. Furthermore, eT provides unique capabilities such as multilevel Hartree-Fock and multilevel CC2, real-time propagation for CCS and CCSD, and efficient CC3 oscillator strengths. With a coupled cluster code based on an efficient Cholesky decomposition algorithm for the electronic repulsion integrals, eT has similar advantages as codes using density fitting, but with strict error control. Here, we present the main features of the program and demonstrate its performance through example calculations. Because of its availability, performance, and unique capabilities, we expect eT to become a valuable resource to the electronic structure community.

Molecular inner-shell photoabsorption/photoionization cross sections at core-valence-separated coupled cluster level: Theory and examples.

Oxygen, nitrogen, and carbon K-shell photoabsorption and photoionization cross sections have been calculated within core-valence-separated coupled cluster (CC) linear response theory for a number of molecular systems, namely, water, ammonia, ethylene, carbon dioxide, acetaldehyde, furan, and pyrrole. The cross sections below and above the K-edge core ionization thresholds were obtained, on the same footing, from L2 basis set calculations of the discrete electronic pseudospectrum yielded by an asymmetric-Lanczos-based formulation of CC linear response theory at the CC singles and doubles (CCSD) and CC singles and approximate doubles (CC2) levels. An analytic continuation procedure for both discrete and continuum cross sections as well as a Stieltjes imaging procedure for the photoionization cross section were applied and the results critically compared.

Intersystem crossing rate dependent dual emission and phosphorescence from cyclometalated platinum complexes: a second order cumulant expansion based approach.

Rates of intersystem crossing (kISC) of two platinum(ii) complexes containing acetylacetonate (acac) and extended cyclometalated ppy (Hppy = 2-phenylpyridine) (1) and thpy (Hthpy = 2-(2' thienyl)pyridine) (2) ligands are calculated using the Condon approximation to the Golden Rule and employing the second-order cumulant expansion method. The emission wavelengths obtained at the RI-CC2 level for the lowest excited singlet (S1) and triplet (T1) states of the two complexes are well in agreement with the experimental results. Our analysis based on kISC evinces that the major pathway involved with the phosphorescence process in complex 1 arises from the S1 → T2 intersystem crossing while the S1 → T1 intersystem crossing is the key step towards the commencement of dual emission in complex 2. Furthermore, it is found that the different pathways are mostly guided by two factors namely, the energy gap and the spin-orbit interaction between the concerned states. Interestingly, the calculated kISC for complex 1 is found to be 107 times larger than that of complex 2, which suggests a rapid depletion of the S1 state population vis-à-vis radiative emission only by phosphorescence from the internally converted lowest excited triplet state while for complex 2, the relatively lower kISC is attributed to the dual emission from this complex.

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy.

First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.

Capturing Correlation Effects on Photoionization Dynamics.

A highly correlated combination of the equation-of-motion coupled cluster (EOM-CC) Dyson orbital and the multicentric B-spline time-dependent density functional theory (TDDFT)-based approach is proposed and implemented within the single-channel approximation to describe molecular photoionization processes. The twofold objective of the approach is to capture interchannel coupling effects, missing in the B-spline DFT treatment, and to explore the response of Dyson orbitals to strong correlation effects and its influence on the photoionization observables. We validate our scheme by computing partial cross sections, branching ratios, asymmetry parameters, and molecular frame photoelectron angular distributions of simple molecules. Finally, the method has been applied to the study of photoelectron spectra of the Ni(C3H5)2 molecule, where giant correlation effects completely destroy the Koopmans picture.

Accurate Description of Photoionization Dynamical Parameters.

Calculation of dynamical parameters for photoionization requires an accurate description of the initial and final states of the system, as well as of the outgoing electron. We show that using a linear combination of atomic orbitals B-spline density functional theory (DFT) method to describe the outgoing electron, in combination with correlated equation of motion coupled cluster singles and double Dyson orbitals, gives good agreement with experiment and outperforms other simpler approaches, like plane and Coulomb waves, used to describe the photoelectron. Results are presented for cross-sections, angular distributions, and dichroic parameters in chiral molecules, as well as for photoionization from excited states. We also present a comparison with the results obtained using Hartree-Fock and DFT molecular orbitals selected according to Koopmans' theorem for the bound states.

Strong Duschinsky Mixing Induced Breakdown of Kasha's Rule in an Organic Phosphor.

We present the novel observation that Duschinsky mixings can lead to the breakdown of Kasha's rule in a white light phosphor molecule, dibenzo[ b, d]thiophen-2-yl (4-chlorophenyl)methanone. Our theoretical analyses show the energy gap between the T1 and T2 states (0.48 eV) is too large to allow for any significant population of the T2 state at room temperature and instead the faster intersystem crossing (ISC) between the S1 and T2 states is rather due to strong Duschinsky mixing, leading to the emission from the T2 state as well. A second-order cumulant-based method has been used for the calculation of the ISC rate, which suggests 2 orders of magnitude faster ISC rates for S1 → T2 compared to those for S1 → T1. We found that the carbonyl moiety of the S1 and T2 states of the molecule is significantly different with respect to bond angle and dihedral angles, engendering large displacements in selective normal modes, thus giving rise to strong Duschinsky mixing.