Role of Singles Amplitudes in ADC(2) and CC2 for Low-Lying Electronically Excited States.

The closely related second-order methods CC2 and ADC(2) usually perform very similarly for single excitations of organic molecules. However, as rationalized in this work, significant deviations between these two methods can arise if the ground state and a low-lying singly excited state arise from a strong coupling between their leading configurations. Such a configuration mixing is partially accounted for in CC2 through the ground-state singles amplitudes but is omitted in ADC(2). This can cause unusual deviations between the results obtained with these methods. In this work, we study how severe this effect can become at the example of two solvatochromic dyes: the negatively solvatochromic betaine dye N1-tBu and the positively solvatochromic bithiophene P1. These two dyes allow one to study the limits of both small and somewhat larger excitation energies and configuration mixing by tuning the S0 → S1 transition energy through the polarity of the environment. Higher-level calculations at the CC3 level provide information on the accuracy of ADC(2) and CC2 in these cases. The most extreme deviation between ADC(2) and CC2 is found for N1-tBu in vacuum, where the ADC(2) result is 0.45 eV below that of CC2. In this case, the methodical error of CC2 with respect to CC3 is only 0.05 eV. With increasing excitation energy in polar solvents, the CC2-ADC(2) deviation decreases and reaches a value of only 0.15 eV. For P1, which has larger excitation energies, these effects are reversed due to the opposite solvatochromism but also smaller in magnitude: the deviation increases from 0.08 eV in vacuum to 0.16 eV in the so-called conductor limit of the continuum solvation model. Although for these two dyes larger deviations are observed for smaller excitation energies, the extent of configuration mixing does not generally correlate with only the size of excitation energy. For example, s-triazine (0.15 eV), formamide (0.19 eV), and formaldehyde (0.23 eV) also show large deviations between CC2 and ADC(2) despite their much higher excitation energies compared to those of N1-tBu and P1.

Insights into localization, energy ordering, and substituent effect in excited states of azobenzenes from coupled cluster calculations of nuclear spin-induced circular dichroism.

Nuclear spin-induced circular dichroism (NSCD) is a molecular effect of differential absorption of left- and right-circularly polarized light due to nuclear spins in the molecule. In this work, new tools for its calculation are presented. Specifically, analytic expressions for the computation of the K term of NSCD have been derived and implemented for the second-order coupled cluster singles and doubles (CC2) model. NSCD results obtained thereby for three derivatives of azobenzenes have been compared with results from time-dependent density functional theory (TD-DFT). The complementary information that could be obtained from NSCD measurements compared to NMR for these three species is discussed.

Efficient Protocol for Computing MCD Spectra in a Broad Frequency Range Combining Resonant and Damped CC2 Quadratic Response Theory.

Coupled cluster response theory offers a path to high-accuracy calculations of spectroscopic properties, such as magnetic circular dichroism (MCD). However, divergence or slow convergence issues are often encountered for electronic transitions in high-energy regions with a high density of states. This is here addressed for MCD by an implementation of damped quadratic response theory for resolution-of-identity coupled cluster singles-and-approximate-doubles (RI-CC2), along with an implementation of the MCD A term from resonant response theory. Combined, damped and resonant response theory calculations provide an efficient strategy to obtain MCD spectra over a broad frequency range and for systems that include highly symmetric molecules with degenerate excited states. The protocol is illustrated by application to zinc tetrabenzoporphyrin in the energy region of 2-8 eV and comparison to experimental data. Timings are reported for the resonant and damped approaches, showing that a greater part of the calculation time is consumed by the construction of the building blocks for the final MCD ellipticity. A recommendation on how to use the procedure is outlined.

Performance of the COSMO solvation model for photoacidity and basicity in water.

The possibilities and problems to predict excited-state acidities and basicities in water with electronic structure calculations combined with a continuum solvation model are investigated for a test set of photoacids and photobases. Different error sources, like errors in the ground-state p K a values, the excitation energies in solution for the neutral and (de-)protonated species, basis set effects, and contributions beyond implicit solvation are investigated and their contributions to the total error in p K a ∗ are discussed. Density functional theory in combination with the conductor like screening model for real solvents and an empirical linear Gibbs free energy relationship are used to predict the ground-state p K a values. For the test set, this approach gives more accurate p K a values for the acids than for the bases. Time-dependent density-functional theory (TD-DFT) and second-order wave function methods in combination with the conductor like screening model are applied to compute excitation energies in water. Some TD-DFT functionals fail for several species to predict correctly the order of the lowest excitations. Where experimental data for absorption maxima in water is available, the implicit solvation model leads with the applied electronic structure methods in most cases for the excitation energies in water to an overestimation for the protonated and to an underestimation for the deprotonated species. The magnitude and sign of the errors depend on the hydrogen bond donating and accepting ability of the solute. We find that for aqueous solution this results generally in an underestimation in the p K a changes from the ground to the excited state for photoacids and an overestimation for photobases.

TURBOMOLE: Today and Tomorrow.

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Computational investigation of explicit solvent effects and specific interactions of hydroxypyrene photoacids in acetone, DMSO, and water.

This work employs the correlated wavefunction-based methods ADC(2) and CC2 in combination with the implicit solvent model COSMO to calculate the UV/Vis absorption and fluorescence emission energies of particularly strong hydroxypyrene photoacids in acetone. According to the Förster cycle, the electronic transition energies are first used to compute , i.e., the pKa change upon excitation and then the excited-state pKa (labeled ) with ground-state pKa values based on COSMO-RS as additional inputs. Furthermore, for the strongest photoacid of that class, namely tris(1,1,1,3,3,3-hexafluoropropan-2-yl)-8-hydroxypyrene-1,3,6-trisulfonate, the need to go beyond implicit solvation and to account for explicit solvent effects on the electronic transition energies and the resulting ΔpKa is investigated in the solvents acetone, dimethyl sulfoxide (DMSO), and water. For this, a hybrid implicit-explicit approach is followed by comparing micro-solvated structures that are generated based on Kamlet-Taft considerations. While implicit solvent effects are mostly sufficient for the aprotic solvent acetone, one explicit solvent molecule seems relevant for DMSO due to its stronger hydrogen-bond (HB) acceptance and hence larger interaction with the photoacid OH group as a HB donor. For the protic solvent water, the situation is more complicated, involving at least one water molecule at the OH group and up to three water molecules at the O- group of the corresponding base. Finally, these results are used to rationalize the experimentally observed spectral evolution of the photoacid absorption band in acetone-water solvent mixtures.

Structural Sampling and Solvation Models for the Simulation of Electronic Spectra: Pyrazine as a Case Study.

The impact of sampling methods on spectral broadening in the gas phase and on the convergence of spectra in aqueous solution when using microsolvation, continuum solvation, and hybrid models is studied using pyrazine as a test case. For the sake of comparing classical Maxwell-Boltzmann and Wigner samplings in the gas phase, static and time-resolved X-ray absorption spectra after photoexcitation to the lowest 1B2u(ππ*) state, as well as the static UV-vis absorption spectrum, are considered. In addition, the UV-vis absorption spectrum of pyrazine in aqueous solution is also computed in order to systematically investigate its convergence with the number of explicitly included solvent shells with and without taking bulk solvation effects into account with the conductor-like screening model to represent implicit water beyond such explicit solute complexes. Concerning the static and time-resolved X-ray absorption spectra of pyrazine at the carbon K-edge as well as its UV-vis absorption spectrum in the gas phase, we find that these spectra obtained with Wigner and Maxwell-Boltzmann samplings substantially agree. For the UV-vis absorption spectrum in the aqueous solution, only the first two energetically low-lying bands converge quickly with the size of the explicitly included solvation shells, either with or without an additional continuum solvation taken into account. In stark contrast, calculations of the higher-lying excitations relying on finite microsolvated clusters without additional continuum solvation severely suffer from unphysical charge-transfer excitations into Rydberg-like orbitals at the cluster/vacuum interface. This finding indicates that computational UV-vis absorption spectra covering sufficiently high-lying states converge only if continuum solvation of the explicitly microsolvated solutes is included in the models.

Pushing the limits: Efficient wavefunction methods for excited states in complex systems using frozen-density embedding.

Frozen density embedding (FDE) is an embedding method for complex environments that is simple for users to set up. It reduces the computation time by dividing the total system into small subsystems and approximating the interaction by a functional of their densities. Its combination with wavefunction methods is, however, limited to small- or medium-sized molecules because of the steep scaling in computation time of these methods. To mitigate this limitation, we present a combination of the FDE approach with pair natural orbitals (PNOs) in the TURBOMOLE software package. It combines the uncoupled FDE (FDEu) approach for excitation energy calculations with efficient implementations of second-order correlation methods in the ricc2 and pnoccsd programs. The performance of this combination is tested for tetraazaperopyrene (TAPP) molecular crystals. It is shown that the PNO truncation error on environment-induced shifts is significantly smaller than the shifts themselves and, thus, that the local approximations of PNO-based wavefunction methods can without the loss of relevant digits be combined with the FDE method. Computational wall times are presented for two TAPP systems. The scaling of the wall times is compared to conventional supermolecular calculations and demonstrates large computational savings for the combination of FDE- and PNO-based methods. Additionally, the behavior of excitation energies with the system size is investigated. It is found that the excitation energies converge quickly with the size of the embedding environment for the TAPPs investigated in the current study.

Interactions of water and short-chain alcohols with CoFe2O4(001) surfaces at low coverages.

Iron and cobalt-based oxides crystallizing in the spinel structure are efficient and affordable catalysts for the oxidation of organics, yet, the detailed understanding of their surface structure and reactivity is limited. To fill this gap, we have investigated the (001) surfaces of cobalt ferrite, CoFe2O4, with the A- and B-layer terminations using density functional theory (DFT/PBE0) and an embedded cluster model. We have considered the five-fold coordinated Co2+/3+ (Oh), two-fold coordinated Fe2+ (Td), and an oxygen vacancy, as active sites for the adsorption of water and short-chain alcohols: methanol, ethanol, and 2-propanol, in the low coverage regime. The adsorbates dissociate upon adsorption on the Fe sites whereas the adsorption is mainly molecular on Co. At oxygen vacancies, the adsorbates always dissociate, fill the vacancy and form (partially) hydroxylated surfaces. The computed vibrational spectra for the most stable configurations are compared with results from diffuse reflectance infrared Fourier transform spectroscopy.

Theoretical Study on the Photoacidity of Hydroxypyrene Derivatives in DMSO Using ADC(2) and CC2.

This work applies the thermodynamic Förster cycle to theoretically investigate the pKa*, i.e., excited-state pKa values of pyranine-derived superphotoacids developed by Jung and co-workers. The latter photoacids are strong enough to transfer a proton to the aprotic solvent dimethyl sulfoxide (DMSO). The Förster cycle provides access to pKa* via the ground-state pKa and the electronic excitation energies. We use the conductor-like screening model for real solvents (COSMO-RS) to compute the ground-state pKa and the correlated wavefunction-based methods ADC(2) and CC2 with the continuum solvation model COSMO to calculate the pKa change upon excitation. A comparison of the calculated UV/Vis absorption and fluorescence emission energies to the experimental results leads us to infer that this approach allows for a proper description of the electronic excitations. In particular, implicit solvation by means of the COSMO model appears to be sufficient for the treatment of these photoacids in DMSO. The calculations confirm the presumption that a charge redistribution from the hydroxy group to the aromatic ring and the electron-withdrawing substituents is the origin of photoacidity for these photoacids. Moreover, the calculations with the continuum solvation model predict that the pKa jump upon excitation decreases with increasing solvent polarity, as rationalized based on the Förster cycle.

Prediction of acid pKa values in the solvent acetone based on COSMO-RS.

In this contribution we extent the use of the conductor-like screening model for realistic solvation (COSMO-RS) to the prediction of pKa values in acetone, a commonly used dipolar aprotic solvent. For this, we calculated the Gibbs free energy of dissociation of 120 organic acids (nine acrylic acids, 87 benzoic acids, nine phenols, and 15 benzenesulfonamides) using COSMO-RS at the two levels BP-TZVP and BP-TZVPD-FINE and determined the parameters for a linear free energy relation for the pKa prediction by performing linear fits to experimental values. Our results suggest that the data set dissects into two groups, with the phenols being different from the other three subsets. The acrylic and benzoic acids and the sulfonamides can be treated together and yield an excellent linear correlation ( r2>0.95 ) with an RMSD of only ~0.3. The slope is found to be significantly smaller than the theoretical value ( 1/RTln10 ), only 45% of it, which is in accordance with findings in the literature. The phenols, however, while similarly well correlated in their own subset with an RMSD of 1.7-1.9, exhibit a slope larger than one. We discuss both a higher uncertainty in the reference values as well as physical origins as possible reasons.

Employing Pseudopotentials to Tackle Excited-State Electron Spill-Out in Frozen Density Embedding Calculations.

In frozen density embedding (FDE), the properties of a target molecule are computed in the presence of an effective embedding potential, which accounts for the attractive and repulsive contributions of the environment. The formally exact embedding potential, however, is in practice calculated using explicit kinetic-energy functionals for which the resulting potentials are in many cases not repulsive enough to account fully for Pauli repulsion by the electrons of the environment and to compensate thereby the strong electron-nuclear attraction. For the excited states on the target molecule, this leads to charge spill-out when diffuse basis functions are included, which allow that valence electrons are excited to those regions of the environment where the strong nuclear attraction is not sufficiently compensated by repulsive contributions. To reduce this insufficiency, we propose in the present work the inclusion of atomic all-electron pseudopotentials for all environment atoms on top of the conventional embedding potential. In the current work, the pseudopotentials are applied for computing vertical excitation energies of local excited states in complex systems employing the second-order algebraic diagrammatic construction (ADC(2)) scheme. The proposed approach leads to significantly reduced charge spill-out and an improved agreement of FDE and supermolecular calculations in the frozen solvent approximation. In particular, when diffuse functions are employed, the mean absolute deviation (MAD) is reduced from 0.27 to 0.05 eV for the investigated cases.

Activation of Molecular O2 on CoFe2 O4 (001) Surfaces: An Embedded Cluster Study.

Dioxygen activation pathways on the (001) surfaces of cobalt ferrite, CoFe2 O4 , were investigated computationally using density functional theory and the hybrid Perdew-Burke-Ernzerhof exchange-correlation functional (PBE0) within the periodic electrostatic embedded cluster model. We considered two terminations: the A-layer exposing Fe2+ and Co2+ metal sites in tetrahedral and octahedral positions, respectively, and the B-layer exposing octahedrally coordinated Co3+ . On the A-layer, molecular oxygen is chemisorbed as a superoxide on the Fe monocenter or bridging a Fe-Co cation pair, whereas on the B-layer it is adsorbed at the most stable anionic vacancy. Activation is promoted by transfer of electrons provided by the d metal centers onto the adsorbed oxygen. The subsequent dissociation of dioxygen into monoatomic species and surface reoxidation have been identified as the most critical steps that may limit the rate of the oxidation processes. Of the reactive metal-O species, [FeIII -O]2+ is thermodynamically most stable, while the oxygen of the Co-O species may easily migrate across the A-layer with barriers smaller than the associative desorption.

An automatized workflow from molecular dynamic simulation to quantum chemical methods to identify elementary reactions and compute reaction constants.

We present an automatized workflow which, starting from molecular dynamics simulations, identifies reaction events, filters them, and prepares them for accurate quantum chemical calculations using, for example, Density Functional Theory (DFT) or Coupled Cluster methods. The capabilities of the automatized workflow are demonstrated by the example of simulations for the combustion of some polycyclic aromatic hydrocarbons (PAHs). It is shown how key elementary reaction candidates are filtered out of a much larger set of redundant reactions and refined further. The molecular species in question are optimized using DFT and reaction energies, barrier heights, and reaction rates are calculated. The setup is general enough to include at this stage configurational sampling, which can be exploited in the future. Using the introduced machinery, we investigate how the observed reaction types depend on the gas atmosphere used in the molecular dynamics simulation. For the re-optimization on the DFT level, we show how the additional information needed to switch from reactive force-field to electronic structure calculations can be filled in and study how well ReaxFF and DFT agree with each other and shine light on the perspective of using more accurate semi-empirical methods in the MD simulation.

Solvent Effects in the Ultraviolet and X-ray Absorption Spectra of Pyridazine in Aqueous Solution.

Electrostatic interaction of the solvent with the solute and fluctuations of the solvent configurations may make excitation energies of the solute different from those in the gas phase. These effects may dominate photoinduced or chemical reaction dynamics in solution systems and can be observed as shifts or broadening of peaks in absorption spectra. In this work, the nitrogen K-edge X-ray absorption spectra were measured for pyridazine in the gas phase and in aqueous solution. The ultraviolet and X-ray absorption spectra of pyridazine in aqueous solution, as well as those in the gas phase, were then calculated with models based on the algebraic-diagrammatic construction through second order [ADC(2)] with the resolution-of-identity (RI) approximation and compared with the spectra obtained in experiments. For aqueous solution, explicit local solvation structures were extracted from an ab initio molecular dynamics (AIMD) trajectory of pyridazine in bulk water, and RI-ADC(2) was combined with the conductor-like screening model (COSMO). The experimental absorption spectra of pyridazine in aqueous solution were reproduced with good accuracy by theoretical treatment of an ensemble containing the explicit local solvation structures of pyridazine with relevant water molecules combined with the COSMO solvation model of water for long-range solvation.

Tracing absorption and emission characteristics of halogen-bonded ion pairs involving halogenated imidazolium species.

We investigate how the absorption and fluorescence of halogenated imidazolium compounds in acetonitrile solution is influenced by the presence of counterions and the ability to act as halogen-bond donors. Experimental measurements and quantum chemical calculations with correlated wavefunction methods are applied to study three monodentate halogen-bond complexes of iodo-imidazolium, iodo-benzimidazolium and bromo-benzimidazolium cations with triflate counterions, and a bidentate complex of bis(iodo-benzimidazolium) dications with chloride as counterion. The three monodentate complexes with triflate counterions relax after photoexcitation to minima on the S1 potential energy surface where the C-I bond and the IO halogen bond are partially broken. For the bidentate complex with the smaller chloride counterion the halogen-bond interaction stays intact in the S1 minimum that is reached by relaxation from the Franck-Condon point. In a complementing experimental approach, stationary absorption and emission as well as transient fluorescence spectra are recorded for iodo- and bromo-benzimidazolium in acetonitrile. Variation of the counterion, substitution of the iodine by bromine, hydrogen, or methyl, and the comparison to theory allows the identification of spectroscopic signatures and photoinduced dynamics associated with ion-pairing.

Damped (linear) response theory within the resolution-of-identity coupled cluster singles and approximate doubles (RI-CC2) method.

An implementation of a complex solver for the solution of the linear equations required to compute the complex response functions of damped response theory is presented for the resolution-of-identity (RI) coupled cluster singles and approximate doubles (CC2) method. The implementation uses a partitioned formulation that avoids the storage of double excitation amplitudes to make it applicable to large molecules. The solver is the keystone element for the development of the damped coupled cluster response formalism for linear and nonlinear effects in resonant frequency regions at the RI-CC2 level of theory. Illustrative results are reported for the one-photon absorption cross section of C60, the electronic circular dichroism of n-helicenes (n = 5, 6, 7), and the C6 dispersion coefficients of a set of selected organic molecules and fullerenes.

Formic Acid-Assisted Selective Hydrogenolysis of 5-Hydroxymethylfurfural to 2,5-Dimethylfuran over Bifunctional Pd Nanoparticles Supported on N-Doped Mesoporous Carbon.

Biomass-derived 5-hydroxymethylfurfural (HMF) is regarded as one of the most promising platform chemicals to produce 2,5-dimethylfuran (DMF) as a potential liquid transportation fuel. Pd nanoparticles supported on N-containing and N-free mesoporous carbon materials were prepared, characterized, and applied in the hydrogenolysis of HMF to DMF under mild reaction conditions. Quantitative conversion of HMF to DMF was achieved in the presence of formic acid (FA) and H2 over Pd/NMC within 2 h. The reaction mechanism, especially the multiple roles of FA, was explored through a detailed comparative study by varying hydrogen source, additive, and substrate as well as by applying in situ ATR-IR spectroscopy. The major role of FA is to shift the dominant reaction pathway from the hydrogenation of the aldehyde group to the hydrogenolysis of the hydroxymethyl group via the protonation by FA at the C-OH group, lowering the activation barrier of the C-O bond cleavage and thus significantly enhancing the reaction rate. XPS results and DFT calculations revealed that Pd2+ species interacting with pyridine-like N atoms significantly enhance the selective hydrogenolysis of the C-OH bond in the presence of FA due to their high ability for the activation of FA and the stabilization of H- .

Can Small Polyaromatics Describe Their Larger Counterparts for Local Reactions? A Computational Study on the H-Abstraction Reaction by an H-Atom from Polyaromatics.

Hydrogen abstraction is one of the crucial initial key steps in the combustion of polycyclic aromatic hydrocarbons. For an accurate theoretical prediction of heterogeneous combustion processes, larger systems need to be treated as compared to pure gas phase reactions. We address here the question on how transferable activation and reaction energies computed for small molecular models are to larger polyaromatics. The approximate transferability of energy contributions is a key assumption for multiscale modeling approaches. To identify efficient levels of accuracy, we start with accurate coupled-cluster and density functional theory (DFT) calculations for different sizes of polyaromatics. More approximate methods as the reactive force-field ReaxFF and the extended semi-empirical tight binding (xTB) methods are then benchmarked against these data sets in terms of reaction energies and equilibrium geometries. Furthermore, we analyze the role of bond-breaking and relaxation energies, vibrational contributions, and post-Hartree-Fock correlation corrections on the reaction, and for the activation energies, we analyze the validity of the Bell-Evans-Polanyi and Hammond principles. First, we find good transferability for this process and that the predictivity of small models at high theoretical levels is way superior than any approximate method can deliver. Second, ReaxFF can serve as a qualitative exploration method, whereas GFN2-xTB in combination with GFN1-xTB appears as a favorable tool to bridge between DFT and ReaxFF so that we propose a multimethod scheme with employing ReaxFF, GFN1/GFN2-xTB, DFT, and coupled cluster to cope effectively with such a complex reactive system.

Anchoring of palladium nanoparticles on N-doped mesoporous carbon.

Pd nanoparticles deposited on nitrogen-doped mesoporous carbon are promising catalysts for highly selective and effective catalytic hydrogenation reactions. To design and utilize these novel catalysts, it is essential to understand the effect of N doping on the metal-support interactions. A combined experimental (X-ray photoelectron spectroscopy) and computational (density functional theory) approach is used to identify preferential adsorption sites and to give detailed explanations of the corresponding metal-support interactions. Pyridinic N atoms turned out to be the preferential adsorption sites for Pd nanoparticles on nitrogen-doped mesoporous carbon, interacting through their lone pairs (LPs) with the Pd atoms via N-LP - Pd dσ and N-LP - Pd s and Pd dπ - π* charge transfer, which leads to a change in the Pd oxidation state. Our results evidence the existence of bifunctional palladium nanoparticles containing Pd0 and Pd2+ centers.