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We present a non-Dyson fourth-order algebraic diagrammatic construction formulation of the electron propagator, featuring the distinct IP- and EA-ADC(4) schemes for the treatment of ionization and electron attachment processes. The algebraic expressions have been derived automatically using the intermediate state representation approach and implemented in the Q-Chemquantum-chemical program package. The performance of the novel methods is assessed with respect to high-level reference data for ionization potentials and electron affinities of closed- and open-shell systems. While only minor improvements over the corresponding third-order methods are observed for one-hole ionization and one-particle electron attachment processes from closed-shell systems (MAEIP-ADC(4)= 0.27 eV and MAEEA-ADC(4)= 0.05 eV), a significantly enhanced performance is found in case of open-shell reference states (MAEIP-ADC(4)= 0.11 eV and MAEEA-ADC(4)= 0.02 eV). A particularly appealing feature of the novel methods is their accurate treatment of satellite transitions. For closed-shell reference states, we obtain accuracies of MAEIP-ADC(4)= 0.81 eV and MAEEA-ADC(4)= 0.27 eV, while in case of open-shell reference states, mean absolute errors of MAEIP-ADC(4)= 0.15 eV and MAEEA-ADC(4)= 0.27 eV are found.

Benzobisthiadiazoles (BBTs) are promising organic semiconductors for applications in field effect transistors and solar cells since they possess a strong electron-accepting characteristic. Thereby, the electronic structure of organic/metal interfaces and within thin films is essential for the performance of organic electronic devices. Here, we study the structural and electronic properties of two BBTs, with different core substitution patterns, a phenyl (BBT-Ph) and a thiophene (BBT-Th) derivative adsorbed on Au(111) using vibrational and electronic high-resolution electron energy loss spectroscopy in combination with state-of-the-art quantum chemical calculations. In the mono- and multilayer, both BBTs adopt a planar adsorption geometry with the molecular backbone, as well as the phenyl and thiophene side groups are oriented parallel to the gold substrate. The energies of the lowest excited electronic singlet states (S) and the first triplet state (T1) are determined. The optical gap (S0→ S1transition) is found to be 2.2 eV for BBT-Ph and 1.6 eV for BBT-Th. The energy of T1is identified to be 1.2 eV in BBT-Ph and in the case of BBT-Th 0.7 eV. Thus, both the optical gap size as well as the T1energy are drastically reduced in BBT-Th compared to BBT-Ph. Based on our quantum chemical calculations, this is attributed to the electron-rich nature of the five-membered thiophene rings in conjunction with their preference for planar geometries. Variation of the substitution pattern in BBTs opens an opportunity for tailoring their electronic properties.

We present the implementation of an efficient matrix-folded formalism for the evaluation of complex response functions and the calculation of transition properties at the level of the second-order algebraic-diagrammatic construction (ADC(2)) scheme. The underlying algorithms, in combination with the adopted hybrid MPI/OpenMP parallelization strategy, enabled calculations of the UV/vis spectra of a guanine oligomer series ranging up to 1032 contracted basis functions, thereby utilizing vast computational resources from up to 32,768 CPU cores. Further analysis of the convergence behavior of the involved iterative subspace algorithms revealed the superiority of a frequency-separated treatment of response equations even for a large spectral window, including 101 frequencies. We demonstrate the applicability to general quantum mechanical operators by the first reported electronic circular dichroism spectrum calculated with a complex polarization propagator approach at the ADC(2) level of theory.

The photophysics of organic semiconductor (OSC) thin films or crystals has garnered significant attention in recent years since a comprehensive theoretical understanding of the various processes occurring upon photoexcitation is crucial for assessing the efficiency of OSC materials. To date, research in this area has relied on methods using Frenkel–Holstein Hamiltonians, calculations of the GW-Bethe–Salpeter equation with periodic boundaries, or cluster-based approaches using quantum chemical methods, with each of the three approaches having distinct advantages and disadvantages. In this work, we introduce an optimally tuned, range-separated time-dependent density functional theory approach to accurately reproduce the total and polarization-resolved absorption spectra of pentacene, tetracene, and perylene thin films, all representative OSC materials. Our approach achieves excellent agreement with experimental data (mostly ≤0.1 eV) when combined with the utilization of clusters comprising multiple monomers and a standard polarizable continuum model to simulate the thin-film environment. Our protocol therefore addresses a major drawback of cluster-based approaches and makes them attractive tools for OSC investigations. Its key advantages include its independence from external, system-specific fitting parameters and its straightforward application with well-known quantum chemical program codes. It demonstrates how chemical intuition can help to reduce computational cost and still arrive at chemically meaningful and almost quantitative results.

We present the open-source responsefunpackage, which implements a universally applicable procedure for computing molecular response properties within the algebraic diagrammatic construction (ADC) framework, exploiting the intermediate state representation (ISR) approach. With symbolic mathematics, the user can simply enter textbook sum-over-states (SOS) expressions from time-dependent perturbation theory, which are then automatically translated into the corresponding symbolic ADC/ISR formulations. Using the data structures provided by the hybrid Python/C++ module adccfor calculating excited states with ADC, the specified response property is directly evaluated, and the result is returned to the user. Employing the novel responsefunpackage, we present the first ADC/ISR calculations of second-order hyperpolarizability tensors and three-photon-absorption matrix elements.

The eChem project features an e-book published as a web page (10.30746/978-91-988114-0-7), collecting a repository of Jupyter notebooks developed for the dual purpose of explaining and exploring the theory underlying computational chemistry in a highly interactive manner as well as providing a tutorial-based presentation of the complex workflows needed to simulate embedded molecular systems of real biochemical and/or technical interest. For students ranging from beginners to advanced users, the eChem book is well suited for self-directed learning, but workshops led by experienced instructors and targeting student bodies with specific needs and interests can readily be formed from its components. This has been done by using eChem as the base for a workshop directed toward graduate students learning the theory and practices of quantum chemistry, resulting in very positive assessment of the interactive nature of this framework. The members of the eChem team are engaged in both education and research, and as a mirroring activity, we develop the open-source software upon which this e-book is predominantly based. The overarching vision and goal of our work is to provide a science- and education-enabling software platform for quantum molecular modeling on contemporary and future high-performance computing systems, and to document the resulting development and workflows in the eChem book.

A synthetic route to new gold(III) complexes was developed. From a [(tBuC∧N∧C)AuCl] complex as a precursor, a substitution by different azulene moieties was achieved. Because of the extraordinary photophysical properties of both substituted [(C∧N∧C)Au] compounds and azulene building blocks, the fusion of these generated organometallic azulene/gold(III) pincer hybrids. The isolated complexes were fully characterized and investigated, including X-ray single-crystal structure analysis, the electrochemical properties, and UV–vis spectra.

Research on materials facilitating efficient singlet fission (SF) is driven by a possible reduction of thermalization losses in organic photovoltaic devices. Intramolecular SF (iSF) is in this context of special interest, as the targeted modification of either chromophores or linkers enables gradual variations of molecular properties. In this combined synthetic, spectroscopic, and computational work, we present and investigate nine novel spiro-linked azaarene dimers, which undergo efficient iSF with triplet yields up to 199%. Additional molecular braces enhance the rigidity of these tailor-made dimers (TMDs), resulting in great agreement between crystal structures and predicted optimal geometries for iSF in solution. Regardless of the employed chromophores and linkages, the dynamics of all nine TMDs are perfectly described by a unified kinetic model. Most notably, an increase in the orbital overlap of the π-systems by decreasing the twist angle between the two chromophores does not only increase the rate of formation of the correlated triplet pair but also further promotes its decorrelation. This new structure–function relationship represents a promising strategy toward TMDs with high triplet lifetimes to be utilized in optoelectronic devices.

The extension of the frozen-density embedding theory for nonvariational methods [J. Chem. Theory Comput.2020,16,6880] was utilized to evaluate intermolecular interaction energies for complexes in the Zhao–Truhlar basis set. In the applied method (FDET-MP2-FAT-LDA), the same auxiliary system is used to evaluate the correlation energy by means of the second-order Møller–Plesset perturbation theory (MP2), as in our previous work [J. Chem. Phys.2019,150,121101]. Local density approximation is used for ExcTnad[ρA,ρB] in both cases. Additionally, the contribution to the energy due to the neglected correlation potential was evaluated and analyzed. The domain of applicability of the local density approximation for ExcTnad[ρA,ρB] was determined based on deviations from the interaction energies from the conventional MP2 calculations. The local density approximation for ExcTnad[ρA,ρB] performs well for hydrogen- or dipole-bound complexes. The relative errors in the interaction energy lie within 3–30%. While for charge-transfer complexes, this approximation fails consistently, and for other types of complexes, the performance of this approximation is not systematic. The sources of error are discussed in detail.

We present open-source implementations of the linear-scaling fast multipole method (FMM) within the polarizable embedding (PE) model for efficient treatment of large polarizable environments in computational spectroscopy simulations. The implementations are tested for accuracy, efficiency, and usability on model systems as well as more realistic biomolecular systems. We explain how FMM parameters affect the calculation of molecular properties and show that PE calculations employing FMM can be carried out in a black-box manner. The efficiency of the linear-scaling approach is demonstrated by simulating the UV/vis spectrum of a chromophore in an environment of more than 1 million polarizable sites. Our implementations are interfaced to several open-source quantum chemistry programs, making computational spectroscopy simulations within the PE model and FMM available to a large variety of methods and a broad user base.

We investigate the basis set requirements for the accurate calculation of core excitations and core ionizations using correlated wave functions of coupled cluster type and linear response methods for describing the excitation. When a core excitation is described as an energy difference calculated using density functional theory, the basis set can be tailored to provide a balanced description of the reference- and excited-hole states. When the core excitation process is described by coupled cluster linear response methods, however, the basis set requirements are somewhat different. A systematic study of the sensitivity of the result to the basis set parameters suggests that a relatively large set of s- and p-type basis functions in combination with a careful selection of valence and core polarization functions is required. Based on these results, we propose a hierarchical sequence of basis sets, denoted ccX-nZ (n= D, T, Q, 5) for the atoms B–Ne, which are suitable for the calculation of core excitations by the correlated wave function linear response and equation-of-motion methods. The ccX-nZ series provides lower basis set errors for a given cardinal number or number of basis functions than other existing basis sets. For large systems, the ccX-nZ basis sets can be combined with the standard basis sets by placing the ccX-nZ only on the atoms where core excitations are of interest, but the accuracy of such mixed basis sets appears to be system-dependent.

The derivation and implementation of analytical gradients for methods based on the non-Dyson algebraic diagrammatic construction for the electron propagator, IP-ADC and EA-ADC, up to the third order is presented. Using nuclear gradients, ground-state equilibrium structures for small open-shell systems are calculated. In addition, we investigated the performance of IP/EA-ADC methods for the calculation of adiabatic ionization potentials and electron affinities for medium-sized organic molecules.

N-Heterotriangulenes (N-HTAs) represent a class of functional molecules with high potential for optoelectronic materials, for example, as electron donating compounds in donor/acceptor (D/A) systems. The capability of two different N-HTAs, N-HTA 550 and N-HTA 557, the latter containing an additional 7-membered ring, to act as electron donors at interfaces with strong tetracyanoquinodimethane (TCNQ and F4TCNQ) acceptors is studied using high-resolution electron energy loss spectroscopy in combination with state-of-the-art quantum chemical calculations. For TCNQ/N-HTA bilayer systems adsorbed on Au(111), low-energy (<2.5 eV) electronic transitions which are attributed to charge transfer (CT) states for all four D/A combinations are identified. Based on substantial quantum chemical calculations, a generation of ground state CT complexes is excluded. Instead, CT in the excited state, in which an electron-stimulated CT from the N-HTAs to TCNQs is the underlying process, is proposed. The energies of the CT states are determined by the values of the ionization potential and electron affinity of the involved donor and acceptor.

While the conventional variants of the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator are generally incapable of correctly describing the topology of S1/S0conical intersections (CIs), its corresponding spin-flip (SF) variant of third-order ADC (ADC(3)) is herein demonstrated to successfully reproduce the S1/S0minimum-energy CI (MECI) of twisted formaldinium (H2CNH2+). Analytical nuclear excited-state gradients of ADC have been used in combination with the CIOpt program for the optimization of the MECI without the need for nonadiabatic-coupling vectors. For comparison, MS-CASPT2 calculations were performed via conventional CI optimization employing analytical nonadiabatic-coupling vectors. It is shown that SF-ADC(3) yields the correct dimensionality of the CI and overall compares very favorably to the MS-CASPT2 results.

Naphthothiadiazoles are promising electron acceptors for applications in organic semiconductor-based (opto)electronic devices. Here, we studied the structural and electronic properties of naphthothiadiazole (NTD) derivatives adsorbed on Au(111) in the monolayer and thin films using temperature-programmed desorption as well as vibrational and electronic high-resolution electron energy loss spectroscopy. In addition, we performed state-of-the-art quantum chemical calculations to further illuminate electronic properties. In the monolayer and multilayer coverage regime, the NTD derivatives adsorbed in a planar fashion with the molecular backbone oriented parallel to the gold surface. Several singlet and the first triplet transition energies are determined. The optical gap (S0→ S1transition) in the nonhalogenated parent NTD is found to be 2.6 eV, whereas it is reduced by 200 meV in the chlorinated and brominated NTD. All experimentally observed singlet and triplet transition energies are reduced due to halogenation, which is underlined by theory.

The performance of several standard and popular approaches for calculating X-ray absorption spectra at the carbon, nitrogen, and oxygen K-edges of 40 primarily organic molecules up to the size of guanine has been evaluated, focusing on the low-energy and intense 1s → π* transitions. Using results obtained with CVS-ADC(2)-x and fc-CVS-EOM-CCSD as benchmark references, we investigate the performance of CC2, ADC(2), ADC(3/2), and commonly adopted density functional theory (DFT)-based approaches. Here, focus is on precisionrather than on accuracyof transition energies and intensities—in other words, we target relative energies and intensities and the spread thereof, rather than absolute values. The use of exchange–correlation functionals tailored for time-dependent DFT calculations of core excitations leads to error spreads similar to those seen for more standard functionals, despite yielding superior absolute energies. Long-range corrected functionals are shown to perform particularly well compared to our reference data, showing error spreads in energy and intensity of 0.2–0.3 eV and ∼10%, respectively, as compared to 0.3–0.6 eV and ∼20% for a typical pure hybrid. In comparing intensities, state mixing can complicate matters, and techniques to avoid this issue are discussed. Furthermore, the influence of basis sets in high-level ab initiocalculations is investigated, showing that reasonably accurate results are obtained with the use of 6-311++G**. We name this benchmark suite as XABOOM (X-ray absorption benchmark of organic molecules) and provide molecular structures and ground-state self-consistent field energies and spectroscopic data. We believe that it provides a good assessment of electronic structure theory methods for calculating X-ray absorption spectra and will become useful for future developments in this field.

The computational modeling of molecules under high pressure is a growing research area that augments experimental high-pressure chemistry. Here, a new electronic structure method for modeling atoms and molecules under pressure, Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) approach, is introduced. In this method, a set of Gaussian potentials is distributed evenly on the van der Waals surface of the investigated chemical system, leading to a compression of the electron density and the atomic scaffold. Since no parameters other than pressure need to be specified, GOSTSHYP allows straightforward geometry optimizations and ab initiomolecular dynamics simulations of chemical systems under pressure for nonexpert users. Calculated energies, bond lengths, and dipole moments under pressure fall within the range of established computational methods for high-pressure chemistry. A Diels–Alder reaction and the cyclotrimerization of acetylene showcase the ability of GOSTSHYP to model pressure-induced chemical reactions. The connection to mechanochemistry is pointed out.

Homoconjugation and intramolecular “through-space” charge transfers are molecular phenomena that have been studied since the 1960s. A detailed understanding and control of these effects would provide a tool to tune the optoelectronic properties of organic molecules in respect of the necessities for applications such as for organic electronics. Triptycene is a perfect candidate to investigate homoconjugation effects due to its three-dimensional alignment of three aromatic phenylene units, separated by two methine bridges. Here, a series of 16 π-extended triptycenes with up to three different permuted electron-accepting units and an electron-rich veratrole unit are studied in detail by UV/vis spectroscopy and cyclovoltammetry in combination with DFT calculations to get a deeper understanding of homoconjugation and charge-transfer processes of triptycenes. Furthermore, the gained knowledge can be exploited to construct triptycene-based electron acceptors with fine-tuned adjustment of electronic properties, such as electron affinities, by thorough choice of the aromatic blades that interact through homoconjugation.

Singlet fission (SF) has the potential to dramatically increase solar cell efficiency by converting one singlet exciton to two free triplet excitons via a correlated triplet pair intermediate. Identification and characterization of excited states involved in SF are of great importance for understanding the fundamentals of SF. Despite their importance, it is still nontrivial to distinguish various species in transient absorption spectra due to their spectral overlaps and ultrashort lifetimes. Theoretical modeling of SF and its electronically excited state absorption (ESA) is generally challenging due to the multiexciton nature of the correlated triplet pair, which usually requires description by expensive high-level ab initiomethods. In this work, taking the bis((triisopropylsilyl)ethynyl) (TIPS)-pentacene monomer and its covalently linked dimer as representative examples, we demonstrate the use of single-reference DFT-based approaches to simulate the ESA spectra during SF. In particular, the singlet and triplet ESA are evaluated by TDDFT, QR-TDDFT, SLR-TDDFT, SF-TDDFT, and UTDDFT, in combination with ten different exchange–correlation functionals. The correlated triplet pair and its ESA are characterized by broken-symmetry DFT and TDDFT, and the role of orbital relaxation is highlighted. With a rational choice of exchange–correlation functionals, we found the resulting spectra to show good agreement with transient absorption experiments and certain improvements over high-order CI methods.

Singlet fission (SF) has the potential to boost solar energy conversion. Research has focused on designing new strategies to tune the electrochemistry, photophysics, and device architecture at the molecular level to improve the efficiency of SF sensitizers. These studies indicate that SF efficiency strongly depends on morphology, packing, and chemical structure. In this work, we use time-resolved spectroscopy to study intramolecular SF in three covalently linked azaarene dimers. Their rigid structure makes them promising model systems to investigate the effect of chemical modification on intramolecular SF without any potential contributions from geometrical factors. Our experimental results along with theoretical calculations show that SF occurs in all three dimers, confirming SF in perpendicularly oriented chromophores with negligible overlapping π-systems. Additionally, a complex branching mechanism is discovered for the evolution of the singlet (S0S1) and the correlated triplet pair 1(T1T1) states. Although chemical modification has only a minor effect on SF rate and generation of the correlated triplet pair, it plays a critical role in the evolution toward the formation of free triplets. Finally, comparison of deaerated and aerated solutions underpins the effect of oxygen in altering the 1(T1T1) dynamics by opening new decay pathways.

The electronic structure of organic/metal interfaces and thin films is essential for the performance of organic-molecule-based field effect transistors and solar cells. Here, we investigated the adsorption and electronic properties of the N-heteropolycyclic aromatic compound 6,13-diazapentacene (DAP), a potential electron-transporting semiconductor on Au(111), using temperature-programmed desorption, vibrational and electronic high-resolution electron energy loss spectroscopy, two-photon photoemission spectroscopy, and state-of-the-art quantum chemical methods. In the mono- and multilayer regime DAP adsorbs in a planar fashion with the molecular backbone oriented parallel to the gold substrate. The energetic position of transport levels (electron affinities and ionization potentials) and singlet (S) as well as triplet (T) transition energies are quantitatively determined. The lowest affinity level is located at 3.48 eV, whereas the energetic position of the first excitonic state is at 4.00 eV, resulting in an exciton binding energy of 0.52 eV. Compared to pentacene, the optical gap is reduced by 0.1 eV and the α-band gains substantially in intensity, which is explained by a detailed analysis of the electronic structure. The optical gap, i.e., the S1excitation energy, is determined to be 2.0 eV, and the T1transition energy is 0.9 eV, making an exothermic singlet fission process relevant in organic photovoltaics feasible.

The efficient implementation of the third-order unitary coupled-cluster scheme (UCC3) for the calculation of excited electronic states is reported. The UCC3 scheme and its second-order UCC2 variant have been benchmarked and compared to Jacquemin’s recently introduced, as well as Thiel’s well-established, benchmark sets for excitation energies and oscillator strengths. For the latter, the calculation of 134 excited singlet and 71 excited triplet states of 28 small- to medium-sized organic molecules has revealed that UCC2 exhibits a mean error and standard deviation of 0.36 ± 0.41 eV for singlet states and 0.22 ± 0.21 eV for triplet states, whereas UCC3 revealed an accuracy of 0.06 ± 0.27 eV for singlet and −0.22 ± 0.15 eV for triplet states. In addition, the oscillator strengths obtained with effective transition moments correct through second order in perturbation theory are in very good agreement with literature data.

N-Heteropolycyclic aromatic compounds are promising organic electron-transporting semiconductors for applications in field effect transistors. Here, we studied the structural and the electronic properties of an arrow-shaped N-heteropentacene derivative (triisopropylsilyl-dibenzodiazapentacene, TIPS-BAP) adsorbed on Au(111) in the monolayer and thin films using temperature-programmed desorption, vibrational and electronic high-resolution electron energy loss spectroscopy, and two-photon photoemission spectroscopy. In addition, we performed state-of-the-art quantum chemical calculations to further elucidate electronic properties. TIPS-BAP adopted an adsorption geometry in which the molecular backbone is oriented parallel to the Au(111) surface. We quantitatively determined the energetic position of several unoccupied as well as occupied molecular electronic states (transport states) with respect to the Fermi level of the gold substrate and resolved the optical gap (S0→ S1transition) to be 1.9 eV. Compared to the corresponding polycyclic aromatic hydrocarbon TIPS-dibenzodipentacene (TIPS-BP), the optical gap is reduced by 0.2 eV due to nitrogen substitution. Based on our quantum chemical calculations, we attributed this effect to a stabilization of the first excited singlet state (S1) in the polar environment. Furthermore, an intense α-band (S0→ S2) in TIPS-BAP compared to TIPS-BP is observed due to an enhanced oscillator strength in the N-heteropolycyclic aromatic compound.

Vibrational spectroscopies, such as Raman and Fourier-transform infrared spectroscopy (FT-IR), are powerful tools for the characterization of organic semiconductor thin films and crystals in addition to X-ray diffraction and scanning atomic force microscopy. They enable the investigation of molecular orientation, polymorphism, doping levels, and intra- as well as intermolecular vibrational modes albeit without much spatial resolution. Two fundamentally different scanning probe techniques offer two-dimensional mapping of infrared-active modes with a spatial resolution below 100 nm: scattering-type scanning near-field optical microscopy (IR s-SNOM) and atomic force microscopy-infrared spectroscopy (AFM-IR). Here, we compare these two techniques with each other and to conventional FT-IR spectroscopy measurements with regard to their applicability to highly ordered molecular semiconductors. For this purpose, we use organic single crystals of rubrene, perfluorobutyldicyanoperylene carboxydiimide (PDIF-CN2), TIPS-pentacene, and TIPS-tetraazapentacene as model systems. We find significant spectral differences depending on the technique and polarization that are related to the anisotropy of the crystals and the fundamentally different working principles of the applied methods. The spatial and spectral resolution of IR s-SNOM and AFM-IR are further tested and compared for a polycrystalline thin film of PDIF-CN2.

The oxadi-π-methane rearrangement of 2,4-cyclohexadienones to bicyclic ketones was found to proceed with high enantioselectivity (92–97% ee) in the presence of catalytic amounts of a chiral Lewis acid (15 examples, 52–80% yield). A notable feature of the transformation is the fact that it proceeds on the singlet hypersurface and that no triplet intermediates are involved. Rapid racemic background reactions were therefore avoided, and the catalyst loading could be kept low (10 mol %). Computational studies suggest that the enantioselectivity is determined within a Lewis acid bound singlet intermediate via a conical intersection. The utility of the method was demonstrated by a concise synthesis of the natural product trans-chrysanthemic acid.

Generating two long-living low-energy excitations after absorption of a single high-energy photon has stoked interest in singlet fission (SF) to enhance solar energy conversion in photovoltaics. To this end, survival of the triplet states is critical. This process is investigated in diethynylbenzene-linked tetraaza-triisopropylsilylethynyl-pentacene dimers, for which SF is energetically feasible and facilitated by the close distances between the azapentacenes. The orthoand metaconnectivities are explored and compared with the tetraazapentacene molecule and the (1,3,5) trimer. Efficient SF (potential ΦT≥ 160%) is demonstrated in all oligomers by quantitative kinetic analysis of broadband transient absorption and fluorescence signals. Together with dynamics of the starting singlet, the triplet pair, and the final free triplet state, our results show an intermediate component with spectral properties compatible with a biexcitonic state. Long-living triplets represent only a fraction of the high number of transient triplet pair intermediates, which undergo triplet–triplet annihilation as well as fusion between neighboring pentacenes. Therefore, our work provides new insight into the SF in covalent dimers and paves the way for the application of these materials for carrier multiplication.

In this Article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the Article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

We present a modular open-source library for polarizable embedding (PE) named CPPE. The library is implemented in C++, and it additionally provides a Python interface for rapid prototyping and experimentation in a high-level scripting language. Our library integrates seamlessly with existing quantum chemical program packages through an intuitive and minimal interface. Until now, CPPE has been interfaced to three packages, Q-Chem, Psi4, and PySCF. Furthermore, we show CPPE in action using all three program packages for a computational spectroscopy application. With CPPE, host program interfaces only require minor programming effort, paving the way for new combined methodologies and broader availability of the PE model.

Quantum chemistry and time-resolved spectroscopy are applied to rationalize how singlet fission (SF) is affected by systematic chemical modifications introduced into phenazinothiadiazoles (PTD). Substitution of the terminal aromatic ring of TIPS-tetracene by a thiadiazole group leads to a considerable change in the relative energies of its S1and T1states. Thus, in contrast to TIPS-tetracene, SF becomes exothermic for various PTD derivatives, which show S1–2T1energy differences as high as 0.15 eV. This enables SF in PTD as corroborated by femtosecond transient absorption spectroscopy and TD-DFT calculations. The latter report T-T spectra consistent with thin film UV–vis femtosecond transient absorption of PTDs at long delays. TD-DFT calculations also show that the S1–T1energy gap can be rationally tuned by introducing N atoms into the aromatic scaffold and by the halogenation of one side ring of the PTD. In addition, the specific S1-to-1(T1T1) electronic coupling depends on the crystal morphology and the electronic properties simultaneously. Thus, both of them govern the strength and the interplay between direct and superexchange couplings, which in the most favorable cases accelerate SF to rate constants beyond (100 fs)−1. Remarkably, direct coupling was found to contribute considerably to the total effective coupling and even to dominate it for some PTDs investigated here. A quantum yield of 200% is obtained on the early picosecond time scale for all compounds studied here, which is reduced to 100% due to triplet–triplet annihilation after a few nanoseconds.

The calculation of X-ray emission spectra has been addressed with the algebraic diagrammatic construction (ADC) scheme, using a core-ionized wave function as the reference state. With this, the valence-to-core transitions are found as the first eigenstates with negative eigenvalues. The performance of the ADC hierarchical methods ADC(2), ADC(2)-x, and ADC(3/2) has been investigated on 17 transition of second-row elements (C, N, O, F, and Ne), and 5 transitions of third-row elements (S and Cl). We report ADC(2) results within 0.20 ± 0.36 eV of experimental values with an appropriate choice of basis set and when accounting for relativistic effects, with a slight tendency toward underestimating emission energies. By comparison, ADC(2)-x yields a similar spread in relative energies, but a consistent overestimation of approximately 1.5 eV. Going to ADC(3/2), we now observe an underestimation of emission energies and a larger error spread. By comparison, calculations of X-ray absorption spectra have been reported to favor the ADC(2)-x method, with ADC(2) showing the largest error when comparing to experimental values. The difference in ADC performance trends between these core spectroscopies are attributed to the different electron rearrangement effects in X-ray absorption and emission processes.

Upon irradiation at λ = 366 nm, tertiary N-alkoxycarbonyl-N-aryl-β-enaminones furnished exclusively the trans-hexahydrocarbazol-4-ones by a conrotatory [6π] photocyclization but epimerized on silica to cis-hexahydrocarbazol-4-ones (14 examples, 44–98% yield). The acceptor substitution on the nitrogen atom enhanced the stability of the cyclized products compared to N-alkyl-N-aryl-β-enaminones reported previously. The mechanism of the [6π] photocyclization was investigated by quenching experiments, deuterium-labeling experiments, and DFT calculations, suggesting a triplet pathway for the conrotatory ring closure followed by a suprafacial [1,4] hydrogen migration.

The light-activated cleavage of cyclobutane-based systems via [2 + 2] cycloreversions, such as thymine and coumarin dimers, is an important but still poorly understood ultrafast photochemical reaction. Systems displaying reversible cycloreversion have found various uses in cross-linked polymers, enhancing gas adsorption affinities in inorganics, and light-activated medical therapies. We report the identification of a heterogeneous mode of cycloreversion for a rarely examined coumarin analogue system. Quinolinone monomers and dimers were probed using ultraviolet pumped, transient absorption spectroscopy and demonstrated radically different photophysical properties than coumarins. Monomers displayed enhanced intersystem crossing at almost 1:1 versus the combined nonradiative and radiative singlet decay, while the dimers underwent cycloreversion to a one excited–one ground state monomer photoproduct pair. The change in both systems was directly linked to the lactame group in the quinolinone motif. This discovery highlights the dramatic effects that small chemical changes can have on photoreaction pathways and opens up a new means to produce and develop more efficient cycloaddition–cycloreversion systems.

We present a variant of the algebraic diagrammatic construction (ADC) scheme by combining ADC with the polarizable embedding (PE) model. The presented PE-ADC method is implemented through second and third order and is designed with the aim of performing accurate calculations of excited states in large molecular systems. Accuracy and large-scale applicability are demonstrated with three case studies, and we further analyze the importance of both state-specific and linear-response-type corrections to the excitation energies in the presence of the polarizable environment. We demonstrate how our combined method can be readily applied to study photoinduced biochemical processes as we model the charge-transfer (CT) excitation which is key to the photoprotection mechanism in the dodecin protein with PE-ADC(2). Through direct access to state-of-the-art excited state analysis, we find that the polarizable environment plays a decisive role by significantly increasing the CT character of the electronic excitation in dodecin. PE-ADC is thus suited to decipher photoinduced processes in complex, biomolecular systems at high precision and at reasonable computational cost.

We present a thorough investigation of the errors in results obtained with the combination of frozen-density embedding theory and the algebraic diagrammatic construction scheme for the polarization propagator of second order (FDE-ADC(2)). The study was carried out on a set of 52 intermolecular complexes with varying interaction strength, each consisting of a chromophore of fundamental interest and a few small molecules in its environment. The errors emerging in frozen-density embedding theory-based methods originate from (a) the solver of the quantum many-body problem used to obtain the embedded wave function (ΨAemb), (b) the approximation for the explicit density functional for the embedding potential, and (c) the choice of the density representing the environment (ρB(r⃗)). The present work provides a comprehensive analysis of the errors in the excitation energies based on the last two factors. Furthermore, a density-overlap-based parameter is proposed to be used as an a priori criterion of applicability.

Benchmarking is an every-day task in computational chemistry, yet making meaningful comparisons between different methods is nontrivial. Benchmark studies often focus on the most obvious quantities such as energy differences. But to gain insight, it is desirable to explain the discrepancies between theoretical methods in terms of underlying wave functions and, consequently, physically relevant quantities. We present a new strategy of benchmarking excited-state calculations, which goes beyond excitation energies and oscillator strengths and involves the analysis of exciton properties based on the one-particle transition density matrix. By using this approach, we compare the performance of many-body excited-state methods (equation-of-motion coupled-cluster and algebraic diagrammatic construction) and time-dependent density functional theory. The selected examples illustrate the utility of different exciton descriptors in assigning state character and explaining the discrepancies among different methods. The examples include Rydberg, valence, and charge-transfer states, as well as delocalized excitonic states in large conjugated systems and states with substantial doubly excited character.

Density-based wave function analysis enables unambiguous comparisons of the electronic structure computed by different methods and removes ambiguity of orbital choices. We use this tool to investigate the performance of different spin-flip methods for several prototypical diradicals and triradicals. In contrast to previous calibration studies that focused on energy gaps between high- and low spin-states, we focus on the properties of the underlying wave functions, such as the number of effectively unpaired electrons. Comparison of different density functional and wave function theory results provides insight into the performance of the different methods when applied to strongly correlated systems such as polyradicals. We show that canonical molecular orbitals for species like large copper-containing diradicals fail to correctly represent the underlying electronic structure due to highly non-Koopmans character, while density-based analysis of the same wave function delivers a clear picture of the bonding pattern.

High-level multireference computations on electronically excited and charged states of tetracene are performed, and the results are analyzed using an extensive wave function analysis toolbox that has been newly implemented in the Molcasprogram package. Aside from verifying the strong effect of dynamic correlation, this study reveals an unexpected critical influence of the atomic orbital basis set. It is shown that different polarized double-ζ basis sets produce significantly different results for energies, densities, and overall wave functions, with the best performance obtained for the atomic natural orbital (ANO) basis set by Pierloot et al. Strikingly, the ANO basis set not only reproduces the energies but also performs exceptionally well in terms of describing the diffuseness of the different states and of their attachment/detachment densities. This study, thus, not only underlines the fact that diffuse basis functions are needed for an accurate description of the electronic wave functions but also shows that, at least for the present example, it is enough to include them implicitly in the contraction scheme.

A scheme has been derived and implemented to gain computational access to the full electronic part of the Kramers–Heisenberg–Dirac (KHD) expression for resonant and nonresonant inelastic scattering amplitudes. Our implementation of this scheme is based on the complex polarization propagator in the algebraic diagrammatic construction (ADC) framework and within its intermediate state representation (ISR). The hierarchy of the second- and third-order ADC/ISR computational schemes known as ADC(2), ADC(2)-x, and ADC(3/2) is considered, and the calculated resonant inelastic X-ray scattering (RIXS) amplitudes and transition strengths for water are in excellent agreement with recent experimental data.

Implementation, benchmarking, and representative applications of the new FDE-ADC(3) method for describing environmental effects on excited states as a combination of frozen density embedding (FDE) and the algebraic-diagrammatic construction scheme for the polarization propagator of third order (ADC(3)) are presented. Results of FDE-ADC(3) calculations are validated with respect to supersystem calculations on test systems with varying molecule–environment interaction strengths from dispersion up to multiple hydrogen bonds. The overall deviation compared to the supersystem calculations is as small as 0.029 eV for excitation energies, which is even smaller than the intrinsic error of ADC(3). The dependence of the accuracy on the choice of method and functional for the calculation of the environment and the nonelectrostatic part of the system–environment interaction is evaluated. In three representative examples, the FDE-ADC method is applied to investigate larger systems and to analyze excited state properties using visualization of embedded densities and orbitals.

We investigate intramolecular singlet fission (iSF) of spiro-linked azaacene heterodimers by time-resolved spectroscopy and quantum chemical calculations. Combining two different azaacenes through a nonconjugated linker using condensation chemistry furnishes azaacene heterodimers. Compared to their homodimers, iSF quantum yields are improved at an extended absorption range. The driving force of iSF, the energy difference ΔEiSFbetween the S1state and the correlated triplet pair 1(TT), is tuned by the nature of the heterodimers. iSF is exothermic in all of the herein studied molecules. The overall quantum yield for triplet exciton formation reaches approximately 174%. This novel concept exploits large energy differences between singlet electronic states in combination with spatially fixed chromophores, which achieves efficient heterogeneous iSF, if the through-space interaction between the chromophores is minimal.

A multistate formulation of the recently developed quantum Monte Carlo (QMC) algebraic diagrammatic construction (ADC) method, QMCADC, is presented. QMCADC solves the Hermitian eigenvalue problem of the second-order ADC scheme for the polarization propagator stochastically by combining ADC schemes with projector quantum Monte Carlo (PQMC). It allows for massively parallel distributed computing and exploits the sparsity of the effective ADC matrix, thereby relaxing memory and processing requirements of ADC methods significantly. Here, the theory and implementation of the multistate variant of QMCADC are described, and our first proof-of-principle calculations for various molecular systems are shown. Indeed, multistate QMCADC enables sampling of an arbitrary number of low-lying excited states and can reproduce their vertical excitation energies with a marginal controllable error. The performance of multistate QMCADC is examined in terms of state-wise and overall accuracy as well as with respect to the balance in the treatments of excited states relatively to each other. The results are very promising as they show bias and imbalances among excited states to diminish as the number of sampling points increases. Furthermore, the impact of the quality of trial wave functions on the vertical excitation energies is investigated. A black-box approach for the generation of high quality trial wave functions internally is given.

The Hula-Twist (HT) photoreaction represents a fundamental photochemical pathway for bond isomerizations and is defined by the coupled motion of a double bond and an adjacent single bond. This photoreaction has been suggested as the defining motion for a plethora of light-responsive chromophores such as retinal within opsins, coumaric acid within photoactive yellow protein, or vitamin D precursors, and stilbenes in solution. However, due to the fleeting character of HT photoproducts a direct experimental observation of this coupled molecular motion was severely hampered until recently. To solve this dilemma, the Dube group has designed a molecular framework able to deliver unambiguous experimental evidence of the HT photoreaction. Using sterically crowded atropisomeric hemithioindigo (HTI) the HT photoproducts are rendered thermally stable and can be observed directly after their formation. However, following the ultrafast excited state process of the HT photoreaction itself has not been achieved so far and thus crucial information for an elementary understanding is still missing. In this work, we present the first ultrafast spectroscopy study of the HT photoreaction in HTI and probe the competition between different excited state processes. Together with extensive excited state calculations a detailed mechanistic picture is developed explaining the significant solvent effects on the HT photoreaction and revealing the intricate interplay between productive isomerizations and unproductive twisted intramolecular charge transfer (TICT) processes. With this study essential insights are thus gained into the mechanism of complex multibond rotations in the excited state, which will be of primary importance for further developments in this field.

The Cotton-Mouton effect is theoretically investigated for a selected set of molecules by using a novel computational methodology based on algebraic diagrammatic construction (ADC) schemes in the intermediate state representation (ISR) formulation. Therefore, the electronic contributions to the frequency-dependent polarizabilities and, for the first time, to the magnetizabilities as well as mixed electric and magnetic hypermagnetizabilities have been computed in the ADC/ISR framework. In addition to calculation of the Cotton-Mouton constant and the birefringence, the gauge origin dependence of the computed tensors and the applied methodology are thoroughly investigated. The new ADC/ISR methodology, employing the recently presented responsefunpackage, is applied to a test set of Ne and small molecules (H2, HF, O2, CO2, and benzene) and compared to data from the experiment as well as other ab initiomethods. The presented theoretical ab initioADC/ISR approach is a substantial extension of the available computational methods for the investigation of complex nonlinear properties, however, with a gauge origin dependence inherent to the method that decreases with increasing perturbation order.