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.

Can the absolute configuration of cyclic peptides be determined with vibrational circular dichroism?

Cyclic peptides show a wide range of biological activities, among others as antibacterial agents. These peptides are often large and flexible with multiple chiral centers. The determination of the stereochemistry of molecules with multiple chiral centers is a challenging and important task in drug development. Chiroptical spectroscopies such as vibrational circular dichroism (VCD) can distinguish between different stereoisomers. The absolute configuration (AC) of a stereoisomer can be determined by comparing its experimental spectra to computed spectra of stereoisomers with known AC. In this way, the AC of rigid molecules with up to seven chiral centers has been assigned (Bogaerts et al., Phys. Chem. Chem. Phys., 2020, 22, 18014). The question arises whether this is possible with more conformationally flexible molecules such as cyclic peptides. We here investigate to what extent the AC of cyclic peptides can be determined with VCD. More specifically, we investigate the maximum number of chiral centers a cyclic peptide can have in order to be able to unambiguously assign the AC with VCD. We present experimental and computed IR and VCD spectra for a series of eight tetrapeptides and hexapeptides with two, three and four chiral centers. We use our recently developed computational protocol with a conformational search based on sampling with meta-dynamics. We use visual inspection to compare the computed spectra of different stereoisomers with an experimental spectrum of the corresponding cyclic peptide with known AC. We find that the AC of the investigated cyclic peptides with two chiral centers can be unambiguously assigned with VCD. This is however not possible for all of the cyclic peptides with three chiral centers and for none of those with four chiral centers. At best, one can limit the number of possible stereoisomers in those cases. Our work shows that other techniques are needed to assign the AC of cyclic peptides with three or more chiral centers. Our study also constitutes a warning that the spectra of all stereoisomers should be computed before attempting to match to an experimental spectrum, to avoid an accidental erroneous match.

Exact Two-Component TDDFT with Simple Two-Electron Picture-Change Corrections: X-ray Absorption Spectra Near L- and M-Edges of Four-Component Quality at Two-Component Cost.

X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivities. However, the theoretical modeling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchange-correlation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on L- and M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modeling XAS.

Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory.

The simulation of X-ray absorption spectra requires both scalar and spin-orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac-Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L2,3- and M4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange-correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee-Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L2,3-edge X-ray absorption spectra of [RuCl2(DMSO)2(Im)2] and [WCl4(PMePh2)2], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.

Vibrational Corrections to NMR Spin-Spin Coupling Constants from Relativistic Four-Component DFT Calculations.

Zero-point vibrational (ZPV) corrections to the nuclear spin-spin coupling constants have been calculated using four-component Dirac-Kohn-Sham DFT for H2X (where X = O, S, Se, Te, Po), XH3 (where X = N, P, As, Sb, Bi), and XH4 (where X = C, Si, Ge, Sn, and Pb) molecules and for HC≡CPbH3. The main goal was to study the influence of relativistic effects on the ZPV corrections and thus results calculated at relativistic and nonrelativistic approaches have been compared. The effects of relativity become notable for the ZPV corrections to the spin-spin coupling constants for compounds with lighter elements (selenium and germanium) than for the spin-spin coupling constants themselves. In the case of molecules containing heavier atoms, for instance BiH3 and PbH4, relativistic effects play a crucial role on the results and approximating ZPV corrections by the nonrelativistic results may lead to larger errors than omitting ZPV corrections altogether.

A Computational Protocol for Vibrational Circular Dichroism Spectra of Cyclic Oligopeptides.

Cyclic peptides are a promising class of compounds for next-generation antibiotics as they may provide new ways of limiting antibiotic resistance development. Although their cyclic structure will introduce some rigidity, their conformational space is large and they usually have multiple chiral centers that give rise to a wide range of possible stereoisomers. Chiroptical spectroscopies such as vibrational circular dichroism (VCD) are used to assign stereochemistry and discriminate enantiomers of chiral molecules, often in combination with electronic structure methods. The reliable determination of the absolute configuration of cyclic peptides will require robust computational methods than can identify all significant conformers and their relative population and reliably assign their stereochemistry from their chiroptical spectra by comparison with ab initio calculated spectra. We here present a computational protocol for the accurate calculation of the VCD spectra of a series of flexible cyclic oligopeptides. The protocol builds on the Conformer-Rotamer Ensemble Sampling Tool (CREST) developed by Grimme and co-workers ( Phys. Chem. Chem. Phys. 2020, 22, 7169-7192 and J. Chem. Theory. Comput. 2019, 15, 2847-2862) in combination with postoptimizations using B3LYP and moderately sized basis sets. Our recommended computational protocol for the computation of VCD spectra of cyclic oligopeptides consists of three steps: (1) conformational sampling with CREST and tight-binding density functional theory (xTB); (2) energy ranking based on single-point energy calculations as well as geometry optimization and VCD calculations of conformers that are within 2.5 kcal/mol of the most stable conformer using B3LYP/6-31+G*/CPCM; and (3) VCD spectra generation based on Boltzmann weighting with Gibbs free energies. Our protocol provides a feasible basis for generating VCD spectra also for larger cyclic peptides of biological/pharmaceutical interest and can thus be used to investigate promising compounds for next-generation antibiotics.

Spin-vibronic interaction induced reverse intersystem crossing: A case study with TXO-TPA and TXO-PhCz molecules.

We highlight the important roles the direct spin-orbit (DSO) coupling, the spin-vibronic (SV) coupling, and the dielectric constant of the medium play on the reverse intersystem crossing (RISC) mechanism of TXO-TPA and TXO-PhCz molecules. To understand this complex phenomenon, we have calculated the RISC rate constant, kRISC, using a time-dependent correlation function-based method within the framework of second-order perturbation theory. Our computed kRISC in two different solvents, toluene and chloroform, suggests that in addition to the DSO, a dielectric medium-dependent SV mechanism may also have a significant impact on the net enhancement of the rate of RISC from the lowest triplet state to the first excited singlet state. Whereas we have found that kRISC of TXO-TPA is mostly determined by the DSO contribution independent of the choice of the solvent, the SV mechanism contributes more than 30% to the overall kRISC of TXO-PhCz in chloroform. In toluene, however, the SV mechanism is less important for the RISC process of TXO-PhCz. An analysis of mode-specific nonadiabatic coupling (NAC) between T2 and T1 of TXO-PhCz and TXO-TPA suggests that the NAC values in certain normal modes of TXO-PhCz are much higher than those of TXO-TPA, and it is more pronounced with chloroform as a solvent. The findings demonstrate the role of the solvent-assisted SV mechanism toward the net RISC rate constant, which in turn maximizes the efficiency of thermally activated delayed fluorescence.

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.

Relativistic Four-Component DFT Calculations of Vibrational Frequencies.

We investigate the effect of relativity on harmonic vibrational frequencies. Density functional theory (DFT) calculations using the four-component Dirac-Coulomb Hamiltonian have been performed for 15 hydrides (H2X, X = O, S, Se, Te, Po; XH3, X = N, P, As, Sb, Bi; and XH4, X = C, Si, Ge, Sn, Pb) as well as for HC≡CPbH3. The vibrational frequencies have been calculated using finite differences of the molecular energy with respect to geometrical distortions of the nuclei. The influences of the choice of basis set, exchange-correlation functional, and step length for the numerical differentiation on the calculated harmonic vibrational frequencies have been tested, and the method has been found to be numerically robust. Relativistic effects are noticeable for the heavier congeners H2Te and H2Po, SbH3 and BiH3, and SnH4 and PbH4 and are much more pronounced for the vibrational modes with higher frequencies. Spin-orbit effects constitute a very small fraction of the total relativistic effects, except for H2Te and H2Po. For HC≡CPbH3 we find that only the frequencies of the modes with large contributions from Pb displacements are significantly affected by relativity.

A generalized few-state model for the first hyperpolarizability.

The properties of molecules depend on their chemical structure, and thus, structure-property relations help design molecules with desired properties. Few-state models are often used to interpret experimental observations of non-linear optical properties. Not only the magnitude but also the relative orientation of the transition dipole moment vectors is needed for few-state models of the non-linear optical properties. The effect of the relative orientation of the transition dipole moment vectors is called dipole alignment, and this effect has previously been studied for multiphoton absorption properties. However, so far, no such studies are reported for the first hyperpolarizability. Here, we present a generalized few-state model for the static and dynamic first hyperpolarizability ß, accounting for the effect of dipole alignment. The formulas derived in this work are general in the sense that they can be used for any few-state model, i.e., a two-state model, a three-state model, or, in general, an n-state model. Based on the formulas, we formulate minimization and maximization criteria for the alignment of transition dipole moment vectors. We demonstrate the importance of dipole alignment by applying the formulas to the static first hyperpolarizability of ortho-, meta-, and para-nitroaniline. The formulas and the analysis provide new ways to understand the structure-property relationship for ß and can hence be used to fine-tune the magnitude of ß in a molecule.

ReSpect: Relativistic spectroscopy DFT program package.

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac-Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin-spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program's website http://www.respectprogram.org.

Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems.

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

Relativistic four-component linear damped response TDDFT for electronic absorption and circular dichroism calculations.

We present a detailed theory, implementation, and a benchmark study of a linear damped response time-dependent density functional theory (TDDFT) based on the relativistic four-component (4c) Dirac-Kohn-Sham formalism using the restricted kinetic balance condition for the small-component basis and a noncollinear exchange-correlation kernel. The damped response equations are solved by means of a multifrequency iterative subspace solver utilizing decomposition of the equations according to Hermitian and time-reversal symmetry. This partitioning leads to robust convergence, and the detailed algorithm of the solver for relativistic multicomponent wavefunctions is also presented. The solutions are then used to calculate the linear electric- and magnetic-dipole responses of molecular systems to an electric perturbation, leading to frequency-dependent dipole polarizabilities, electronic absorption, circular dichroism (ECD), and optical rotatory dispersion (ORD) spectra. The methodology has been implemented in the relativistic spectroscopy DFT program ReSpect, and its performance was assessed on a model series of dimethylchalcogeniranes, C4H8X (X = O, S, Se, Te, Po, Lv), and on larger transition metal complexes that had been studied experimentally, [M(phen)3]3+ (M = Fe, Ru, Os). These are the first 4c damped linear response TDDFT calculations of ECD and ORD presented in the literature.

Resolution-of-identity accelerated relativistic two- and four-component electron dynamics approach to chiroptical spectroscopies.

We present an implementation and application of electron dynamics based on real-time time-dependent density functional theory (RT-TDDFT) and relativistic 2-component X2C and 4-component Dirac-Coulomb (4c) Hamiltonians to the calculation of electron circular dichroism and optical rotatory dispersion spectra. In addition, the resolution-of-identity approximation for the Coulomb term (RI-J) is introduced into RT-TDDFT and formulated entirely in terms of complex quaternion algebra. The proposed methodology was assessed on the dimethylchalcogenirane series, C4H8X (X = O, S, Se, Te, Po, Lv), and the spectra obtained by non-relativistic and relativistic methods start to disagree for Se and Te, while dramatic differences are observed for Po and Lv. The X2C approach, even in its simplest one-particle form, reproduces the reference 4c results surprisingly well across the entire series while offering an 8-fold speed-up of the simulations. An overall acceleration of RT-TDDFT by means of X2C and RI-J increases with system size and approaches a factor of almost 25 when compared to the full 4c treatment, without compromising the accuracy of the final spectra. These results suggest that one-particle X2C electron dynamics with RI-J acceleration is an attractive method for the calculation of chiroptical spectra in the valence region.

Interplay of twist angle and solvents with two-photon optical channel interference in aryl-substituted BODIPY dyes.

Channel interference plays a crucial role in understanding the physics behind multiphoton absorption processes. In this work, we study the role of channel interference and solvent effects on the two-photon absorption in aryl-substituted boron dipyrromethene (BODIPY) dyes, a class of intramolecular charge-transfer (ICT) molecules. For this purpose, we consider fourteen dyes of this class with various donor/acceptor substitutions at the para position of the phenyl ring and with or without methyl (-CH3) substitution on the BODIPY moiety. The presence of a methyl group on the BODIPY moiety affects the dihedral angle significantly, which in turn affects the one- (OPA) and two-photon absorption (TPA) properties of the molecules. Among the molecules studied, the one having the strong electron-donating dimethylamino group and no methyl substitution at the BODIPY moiety is found to have the highest TPA cross section. Our few-state model analysis shows that the large TPA activity of this molecule is due to the all positive contributions from different channel interference terms. Change in dielectric constant of the medium is found to have a profound impact on both the magnitude and sign of the channel interference terms. The magnitude of destructive channel interference gradually decreases with decreasing solvent polarity and becomes constructive in a low-polarity solvent. We also study the effect of rotating the phenyl ring with respect to the BODIPY moiety on the TPA activity. In the gas phase and in different solvents, we found that channel interference is changed from destructive to constructive on twisting the molecule. These results are explained by considering different dipole-, energy- and angle-terms appearing in the expression of a two-state model.

Cryptophanes for Methane and Xenon Encapsulation: A Comparative Density Functional Theory Study of Binding Properties and NMR Chemical Shifts.

The host-guest chemistry of cryptophanes is an active research area because of its applications in sensor design, targeting small molecules and atoms in environmental and medical sciences. As such, the computational prediction of binding energies and nuclear magnetic resonance (NMR) properties of different cryptophane complexes are of interest to both theoreticians and experimentalists working in host-guest based sensor development. Herein we present a study of 10 known and some newly proposed cryptophanes using density functional theory (DFT) calculations. We benchmark the description of nonbonding interactions by different DFT functionals against spin-component-scaled, second-order Møller-Plesset theory (SCS-MP2) and predict novel host molecules with enhanced affinity toward methane and Xenon, two representative systems of high interest. We demonstrate the power and limitations of the different computational methods in describing the binding and NMR properties of these established and novel host systems. The results show the importance of including dispersion corrections in the DFT functionals. The overall analysis of the dispersion corrections indicated that results obtained from pure DFT functionals should be used cautiously when conclusions are drawn for molecular systems with considerable weak interactions. Proposed analogues of cryptophane-A, where the alkoxy bridges are replaced by alkyl chains, are predicted to display enhanced affinity toward both methane and Xenon.

Channel interference in multiphoton absorption.

We extend the theory of channel interference to higher-order multiphoton absorption processes. We derive an explicit expression for channel interference in a three-photon absorption process and propose a general scheme for deriving such expressions for multiphoton absorption processes of any order. Based on this general scheme, we derive and analyze the simplest few-state models for multiphoton absorption in centrosymmetric molecules and discuss the criteria for maximizing the corresponding multiphoton absorption strengths.

Complete analytic anharmonic hyper-Raman scattering spectra.

We present the first computational treatment of the complete second-order vibrational perturbation theory applied to hyper-Raman scattering spectroscopy. The required molecular properties are calculated in a fully analytic manner using a recently developed program [Ringholm, Jonsson and Ruud, J. Comp. Chem., 2014, 35, 622] that utilizes recursive routines. For some of the properties, these calculations are the first analytic calculations of their kind at their respective levels of theory. We apply this approach to the calculation of the hyper-Raman spectra of methane, ethane and ethylene and compare these to available experimental data. We show that the anharmonic corrections have a larger effect on the vibrational frequencies than on the spectral intensities, but that the inclusion of combination and overtone bands in the anharmonic treatment can improve the agreement with the experimental data, although the quality of available experimental data limits a detailed comparison.

Three-photon circular dichroism: towards a generalization of chiroptical non-linear light absorption.

We present the theory of three-photon circular dichroism (3PCD), a novel non-linear chiroptical property not yet described in the literature. We derive the observable absorption cross section including the orientational average of the necessary seventh-rank tensors and provide origin-independent expressions for 3PCD using either a velocity-gauge treatment of the electric dipole operator or a length-gauge formulation using London atomic orbitals. We present the first numerical results for hydrogen peroxide, 3-methylcyclopentanone (MCP) and 4-helicene, including also a study of the origin dependence and basis set convergence of 3PCD. We find that for the 3PCD-brightest low-lying Rydberg state of hydrogen peroxide, the dichroism is extremely basis set dependent, with basis set convergence not being reached before a sextuple-zeta basis is used, whereas for the MCP and 4-helicene molecules, the basis set dependence is more moderate and at the triple-zeta level the 3PCD contributions are more or less converged irrespective of whether the considered states are Rydberg states or not. The character of the 3PCD-brightest states in MCP is characterized by a fairly large charge-transfer character from the carbonyl group to the ring system. In general, the quadrupole contributions to 3PCD are found to be very small.