Description of spin–orbit coupling in excited states with two-component methods based on approximate coupled-cluster theory

Stochastic Resolution of Identity to CC2 for Large Systems: Excited State Properties

We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for the excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O(N3), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O(N5) to O(N3). We test the sRI-CC2 for different molecular systems and basis sets, and we show that our sRI-CC2 method can accurately reproduce the results of the deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O(N2.59) for a series of olefin chains, allowing us to calculate systems with nearly thousands of electrons.

A Photoswitchable Metallocycle Based on Azobenzene: Synthesis, Characterization, and Ultrafast Dynamics

The novel photoswitchable ligand 3,3'-Azobenz(metPA)2 (1) is used to prepare a [Cu2(1)2](BF4)2 metallocycle (2), whose photoisomerization was characterized using static and time-resolved spectroscopic methods. Optical studies demonstrate the highly quantitative and reproducible photoinduced cyclic E/Z switching without decay of the complex. Accordingly and best to our knowledge, [Cu2(1)2](BF4)2 constitutes the first reversibly photoswitchable (3d)-metallocycle based on azobenzene. The photoinduced multiexponential dynamics in the sub-picosecond to few picosecond time domain of 1 and 2 have been assessed. These ultrafast dynamics as well as the yield of the respective photostationary state (PSSZ = 65 %) resemble the behavior of archetypical azobenzene. Also, the innovative pump-probe laser technique of gas phase transient photodissociation (τ-PD) in a mass spectrometric ion trap was used to determine the intrinsic relaxation dynamics for the isolated complex. These results are consistent with the results from femtosecond UV/Vis transient absorption (fs-TA) in solution, emphasizing the azobenzene-like dynamics of 2. This unique combination of fs-TA and τ-PD enables valuable insights into the prevailing interplay of dynamics and solvation. Both analyses (in solution and gas phase) and quantum chemical calculations reveal a negligible effect of the metal coordination on the switching mechanism and electronic pathway, which suggests a non-cooperative isomerization process.

Electronic spectroscopy of homo- and heterometallic binuclear coinage metal phosphine complexes in isolation

Binuclear coinage metal phosphine complexes are examined under ion trap isolation in order to elucidate their noncovalent binding, structural properties and intrinsic electronic spectra. Our survey shows an intriguing order of electronic transitions obtained by in situ synthesis and mass-spectrometrically supported UV photodissociation spectroscopy on a series of six isolated homo- and heterobinuclear complexes of type [MM'(dcpm)2]2+ (M, M' = CuI, AgI, AuI; dcpm = bis(dicyclohexyl-phosphino)methane). This approach provides the unique opportunity to study all possible coinage metal interactions within a fixed ligand framework. A successive blue-shift (33 700-38 500 cm-1; 297-260 nm) of the lowest-energy bright electronic transition energy in gas phase was observed in the order of Cu2 < CuAu < CuAg < Au2 < AgAu < Ag2. This order was reproduced by quantum chemical calculations using a scalar-relativistic GW-Bethe-Salpeter-equation (GW-BSE) approach. Theory ascribes the electronic bands of all complexes to metal-centered 1MC(dσ*-pσ) transitions revealing a strengthening of metal-metal' (M-M') binding upon excitation, in agreement to mass spetrometric results. A test of the correlation of transition energies with M-M' distance by quantum chemical calculations of single point energies as a function of intermetallic distance indicates qualitative agreement with experimental results. However, the experimentally observed high sensitivity of spectroscopic shifts towards metal composition cannot be accounted for solely by M-M' distance variation. The differences in electronic transitions are qualitatively rationalized by the varying (n + 1)s (n = 3, 4, 5) orbital contributions (increase from Cu2via CuAu/CuAg to Au2/AgAu/Ag2) within the nd(n + 1)s/p-hybridization for the ground electronic state of the different complexes, whereas the excited state (of (n + 1)p orbital character) shows significantly less variation in energy. In particular, the observed spectroscopic and mass spectrometric sequence for the Ag/Au complexes is traced back to the interplay of Pauli repulsion and variation in metal-ligand bond strength within the orbital hybridization model.

Molecular Dynamics of Linear Molecules in Strong Magnetic Fields

Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born-Oppenheimer potential energy surfaces are calculated at the Hartree-Fock and MP2 levels of theory, using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges.

The GW/BSE Method in Magnetic Fields

The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.

New Cationic fac-[Re(CO)3(deeb)B2]+ Complex, Where B2 Is a Benzimidazole Derivative, as a Potential New Luminescent Dye for Proteins Separated by SDS-PAGE

Sodium-dodecyl-sulfate polyacrylamide gel electrophoresis (SDS-PAGE) can be used to separate proteins based mainly on their size such as in denaturing gels. Different staining methods have been reported to observe proteins in the gel matrix, where the most used dyes are generally anionic. Anionic dyes allow for interactions with protonated amino acids, retaining the dye in the proteins. Fluorescent staining is an alternative technique considered to be sensitive, safe, and versatile. Some anionic complexes based on d⁶ transition metals have been used for this purpose, where cationic dyes have been less explored in this context. In this work, we synthesized and characterized a new monocationic rhenium complex fac-[Re(CO)₃(deeb)B2]⁺ (where deeb is 4,4′-bis(ethoxycarbonyl)-2,2′-bpy and B2 is 2,4-di-tert-butyl-6-(3H-imidazo[4,5-c]pyridine-2-yl)phenol). We carried out a structural characterization of this complex by MS⁺, FTIR, ¹H NMR, D₂O exchange, and HHCOSY. Moreover, we carried out UV-Vis, luminescence, and cyclic voltammetry experiments to understand the effect of ligands on the complex’s electronic structure. We also performed relativistic theoretical calculations using the B3LYP/TZ2P level of theory and R-TDDFT within a dielectric continuum model (COSMO) to better understand electronic transitions and optical properties. We finally assessed the potential of fac-[Re(CO)₃(deeb)B2]⁺ (as well as the precursor fac-Re(CO)₃(deeb)Br and the free ligand B2) to stain proteins separated by SDS-PAGE. We found that only fac-[Re(CO)₃(deeb)B2]⁺ proved viable to be directly used as a luminescent dye for proteins, presumably due to its interaction with negatively charged residues in proteins and by weak interactions provided by B2. In addition, fac-[Re(CO)₃(deeb)B2]⁺ seems to interact preferentially with proteins and not with the gel matrix despite the presence of sodium dodecyl sulfate (SDS). In future applications, these alternative cationic complexes might be used alone or in combination with more traditional anionic compounds to generate counterion dye stains to improve the process.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Natural transition orbitals for complex two-component excited state calculations

While the natural transition orbital (NTO) method has allowed electronic excitations from time-dependent Hartree-Fock and density functional theory to be viewed in a traditional orbital picture, the extension to multicomponent molecular orbitals such as those used in relativistic two-component methods or generalized Hartree-Fock (GHF) or generalized Kohn-Sham (GKS) is less straightforward due to mixing of spin-components and the inherent inclusion of spin-flip transitions in time-dependent GHF/GKS. An extension of single-component NTOs to the two-component framework is presented, in addition to a brief discussion of the practical aspects of visualizing two-component complex orbitals. Unlike the single-component analog, the method explicitly describes the spin and frequently obtains solutions with several significant orbital pairs. The method is presented using calculations on a mercury atom and a CrO₂ Cl₂ complex.

Analytical energy gradients for ionized states using equation-of-motion coupled-cluster theory with spin-orbit coupling

Spin-orbit coupling (SOC) may have a significant effect on the structure and harmonic frequencies of particularly heavy p-block element compounds. However, reports on analytical energy gradients with SOC are scarce, especially for excited states. In this work, we implemented analytical energy gradients for ionized states using the equation-of-motion coupled-cluster (CC) theory at the CC singles and doubles level (EOM-IP-CCSD) with SOC. Effects of SOC on structure and harmonic frequencies as well as properties for both the ground and some excited states of open-shell compounds with one unpaired electron can be investigated efficiently with the present implementation. A closed-shell reference is required in the calculations, and SOC is included in post-Hartree-Fock treatment. Relativistic effective core potentials are employed in dealing with both scalar relativistic effects and SOC, and we treat perturbations that are even under time reversal in this work. Both time-reversal symmetry and double point group symmetry for D_2h ^* and its subgroups are exploited in the implementation. The method is applicable to states which can be reached by removing one electron from a closed-shell reference state. The results of some open-shell cations indicate the importance of SOC on structures and harmonic frequencies of heavy element compounds.

Circularly polarised fluorescence and phosphorescence calculations on organic molecules using the approximate coupled-cluster model CC2

We report the first calculations of rotational strengths for circularly polarised phosphorescence at the coupled cluster level. The rotational strengths for circular dichroism (CD), circularly polarised fluorescence (CPF) and circularly polarised phosphorescence (CPP) were calculated for β,γ-enones and ketones with conjugated double bonds using the CC2 model. To compute spin-forbidden CPP, spin-orbit coupling with perturbation theory is employed within a response theory framework (SOC-PT-CC2). For closed-shell molecules containing only light elements, a spin-free formalism is used to treat the singlet-triplet transitions. It is verified that the simplification obtained in the spin-free formulation from the Wigner-Eckart theorem for spin-forbidden oscillator strengths is also valid for the rotational strengths. Our implementation utilises the resolution of identity (RI) approximation for two-electron integrals which facilitates applications to larger molecules. In the current study, the rotational strength for spin-forbidden circularly-polarised phosphorescence was calculated for a chiral aromatic system, S-DMBDA, containing 44 atoms.

Floppy molecules as candidates for achieving optoelectronic molecular devices without skeletal rearrangement or bond breaking

Molecular species investigated as possible candidates for molecular photoswitches often toggle between two (low and high conductance) conformations implying skeletal rearrangement, bond breaking, and substantial changes of molecular length. All these represent shortcomings that impede the switching speed and straightforward incorporation in nanodevices. In the present paper we propose a mechanism wherein the photoinduced switching is from a nonplanar conformation to a planar conformation, and involves neither skeletal rearrangement nor bond breaking or significant molecular length changes. Specifically, by choosing typical floppy molecules consisting of two benzene or benzene-like rings that can easily rotate relative to each other, we present results of both ab initio and DFT quantum chemical calculations demonstrating that the lowest electronic excitation corresponds to a planar molecular conformation (φ = 0), in contrast to the nonplanar ground state characterized by φ ≠ 0. Because the low bias conductance scales as G ∝ cos² φ, the planar conformation has a higher conductance than the non-planar conformation, acting therefore as ON and OFF states of the molecular switch, respectively. We analyze recent experimental data on illuminated single-molecule junctions (E.-D. Fung et al., Nano Lett., 2017, 17, 1255) and show that the measured photoinduced conductance enhancement is consistent with the presently proposed mechanism. Furthermore, based on recent results demonstrating the substantial impact of the SAM coverage on the twisting angle (I. Bâldea, Faraday Discuss., 2017, 204, 35) we show that a photoinduced conductance enhancement can be much stronger than the rather modest enhancement obtained in the aforementioned experiment.

Approaching Phosphorescence Lifetimes in Solution: The Two-Component Polarizable-Embedding Approximate Coupled-Cluster Method

Theoretical description of phosphorescence lifetimes in the condensed phase requires a method that takes into account both spin-orbit coupling and solvent-solute interactions. To obtain such a method, we have coupled our recently developed two-component coupled-cluster method with singles and approximated doubles to a polarizable environment. With this new method, we investigate how different solvents effect the electronic phosphorescence energies and lifetimes of 4H-pyran-4-thione.

Spin-Free CC2 Implementation of Induced Transitions between Singlet Ground and Triplet Excited States

In most organic molecules, phosphorescence has its origin in transitions from triplet exited states to the singlet ground state, which are spin-forbidden in nonrelativistic quantum mechanics. A sufficiently accurate description of phosphorescence lifetimes for molecules that contain only light elements can be achieved by treating the spin-orbit coupling (SOC) with perturbation theory (PT). We present an efficient implementation of this approach for the approximate coupled cluster singles and doubles model CC2 in combination with the resolution-of-the-identity approximation for the electron repulsion integrals. The induced oscillator strengths and phosphorescence lifetimes from SOC-PT are computed within the response theory framework. In contrast to previous work, we employ an explicitly spin-coupled basis for singlet and triplet operators. Thereby, a spin-orbital treatment can be entirely avoided for closed-shell molecules. For compounds containing only light elements, the phosphorescence lifetimes obtained with SOC-PT-CC2 are in good agreement with those of exact two-component (X2C) CC2, whereas the calculations are roughly 12 times faster than with X2C. Phosphorescence lifetimes computed for two thioketones with the SOC-PT-CC2 approach agree very well with reference results from experiment and are similar to those obtained with multireference spin-orbit configuration interaction and with X2C-CC2. An application to phosphorescent emitters for metal-free organic light-emitting diodes (OLEDs) with almost 60 atoms and more than 1800 basis functions demonstrates how the approach extends the applicability of coupled cluster methods for studying phosphorescence. The results indicate that other decay channels like vibrational relaxation may become important in such systems if lifetimes are large.