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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.

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.

This work applies the thermodynamic Förster cycle to theoretically investigate the pKa*, i.e., excited-state pKavalues 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 pKaand the electronic excitation energies. We use the conductor-like screening model for real solvents (COSMO-RS) to compute the ground-state pKaand the correlated wavefunction-based methods ADC(2) and CC2 with the continuum solvation model COSMO to calculate the pKachange 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 pKajump upon excitation decreases with increasing solvent polarity, as rationalized based on the Förster cycle.

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.

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.

The process of hydrogen spillover on metal nanoparticle decorated carbon surfaces has been discussed for many years due to its importance for heterogeneous catalysis and hydrogen storage. The present density functional theory (DFT) study supports recent experimental observations of the hydrogen spillover process. By use of model systems of carbon-supported palladium nanoparticles, the details of hydrogen spillover are investigated and the effects of nitrogen doping on such processes are elucidated. It is found that graphitic nitrogen atoms and water molecules significantly facilitate the hydrogen spillover reaction and serve as anchoring sites for the spillover hydrogen atoms.

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.

The effects of biomolecular embedding on the photoinduced relaxation process of the DNA-minor-groove binder berenil, diminazene aceturate, are studied with quantum mechanics/molecular mechanics, QM/MM, calculations that employ the algebraic diagrammatic construction through second-order, ADC(2), for the quantum mechanical part and an atomistic polarizable embedding for the classical part. The lowest singlet excitation to the S1state is a bright transition with a ππ* character and a perichromatic red shift, due to the interactions with the solvent and DNA. The excited-state relaxation pathway is a two-step mechanism, an N═N azo-bond stretch followed by a volume-conserving bicycle-pedal twist. The DNA confinement and the coupling to solvent molecules via hydrogen bonds lead, for the excited-state relaxation process, only to small deviations from the ideal bicycle-pedal relaxation. Because of its volume-conserving character, the S1excited-state relaxation proceeds almost unhindered, even in a fully rigid minor-groove confinement. With a fully frozen DNA minor groove and solvent, the energy gap for deexcitation from S1to the ground state increased to 2.0 eV compared to 0.16 eV in aqueous solution. When the relaxation of the first solvation shell is included, the relaxation process on the S1potential energy surface proceeds to a region on the potential energy surface, where only a small gap to the ground-state potential energy surface remains, 0.43 eV. These results show that the solvent relaxation has a significant effect in controlling the energy gap between the ground and S1electronically excited states, which explains the experimental observations of the fluorescence characteristics of berenil in DNA confinement.

We address in this work the question to which extend reaction field schemes for correlated wave function methods give accurate excitation energies and, at the same time, physically consistent potential energy surfaces. The performance of the perturbation on energy (PTE), perturbation on energy and density (PTED), and post-SCF reaction field schemes is compared for the algebraic diagrammatic construction through second-order, ADC(2), as electronic structure and the conductor-like screening model COSMO as solvation model. The conditions on reaction field schemes to give physically consistent potential energies surfaces are discussed at the example of 4-(N,N-dimethylamino)benzonitrile, which is used as a test case to assess the artifacts introduced by state-specific contributions to the effective Hamiltonian. To evaluate the accuracy for excitation energies, we use two benchmark sets with data in gas phase and solution for ππ* and nπ* electronic transitions. The experimental solvatochromic shifts are compared to the corresponding calculated values at the COSMO-ADC(2) level with the PTE scheme within the frozen solvent approximation, PTED with the linear response (LR) and corrected linear response (cLR) and post-SCF with LR schemes and with the approximate coupled-cluster singles and doubles method CC2 combined with COSMO in the post-SCF (LR) scheme. The PTE scheme gives at the COSMO-ADC(2) level less accurate solvent shifts than the PTED(LR), PTED(cLR), and post-SCF(LR) schemes. The most accurate prediction of solvatochromism is obtained with the post-SCF(LR) scheme. In most cases, PTED(cLR) performs similar to post-SCF, although its nonlinear perturbative correction causes problems for potential energy surfaces.

QM/MM calculations of electronic excitations with diffuse basis sets often have large errors due to spill-out of electrons from the quantum subsystem. The Pauli repulsion of the electrons by the environment has to be included to avoid this. We propose transferable atomic all-electron pseudopotentials that can readily be combined with most MM force fields to avoid electron spill-out. QM/MM excitation energies computed with time-dependent Hartree–Fock and the algebraic diagrammatic construction through second-order are benchmarked against supermolecular calculations to validate these new pseudopotentials. The QM/MM calculations with pseudopotentials give accurate results that are stable with augmentation of the basis set with diffuse functions. We show that the largest contribution to residual deviations from full QM calculations is caused by the missing London dispersion interaction.

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-tBuand 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→ S1transition 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-tBuin 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-tBuand P1.

The absorption and magnetic circular dichroism (MCD) spectra of purine and of the purine nucleobases adenine and guanine have been calculated in gas phase at the Coupled Cluster Singles and Doubles (CCSD) and Resolution-of-Identity Singles and Approximate Doubles (RI-CC2) levels of theory. Exploiting a new development in the TURBOMOLE program package for computing vertical excitation energies and Faraday Bterms in an implicit solvent approximated by the conductor-like screening model (COSMO) at the CC2 level, we have investigated the solvent effects on the relative positions of the ππ* and nπ* electronic transitions in these three molecules and compared them to the corresponding vacuum results. In the case of adenine, we also included specific solvent effects with a small water cluster. The spectra obtained with the implicit model COSMO are in qualitative agreement with those obtained with explicit water molecules both with and without the inclusion of the bulk solvent effects via the continuum solvent model. This suggests that the inclusion of the electrostatic contributions of the solvent can provide a sufficiently accurate description of the absorption spectra for adenine. The results for purine, adenine, and guanine show that, after the inclusion of bulk solvation, the ππ* states shift to lower energies while at the same time nπ* states show a reversed behavior. The computed MCD spectra show the characteristic bisignate profile found experimentally in all cases, despite, for adenine, remarkable differences in the origin of the individual peaks for different computational methods. Therefore, the ability (or inability) of MCD to determine the relative stability of the Laand Lbstates is critically reassessed. According to our best estimate for adenine in aqueous solution, the Lastate is more stable than Lb.

An implementation of a QM/MM embedding in a polarizable environment is presented for second-order Møller–Plesset perturbation theory, MP2, for ground state energies and molecular gradients and for the second-order Algebraic Diagrammatic Construction, ADC(2), for excitation energies and excited state molecular gradients. In this implementation of PE-MP2 and PE-ADC(2), the polarizable embedded Hartree–Fock wave function is used as uncorrelated reference state. The polarization-correlation cross terms for the ground and excited states are included in this model via an approximate coupling density. A Lagrangian formulation is used to derive the relaxed electron densities and molecular gradients. The resolution-of-the-identity approximation speeds up the calculation of four-index electron repulsion integrals in the molecular orbital basis. As a first application, the method is used to study the photophysical properties of host–guest complexes where the accuracy and weaknesses of the model are also critically examined. It is demonstrated that the ground state geometries of the full quantum mechanical calculation for the supermolecule can be well reproduced. For excited state geometries, the deviations from the supermolecular calculation are slightly larger, but still the environment effects are captured qualitatively correctly, and energy gaps between the ground and excited states are obtained with sufficient accuracy.

In this work, we present a new pair natural orbitals (PNO)-based incremental scheme to calculate CCSD(T) and CCSD(T0) reaction, interaction, and binding energies. We perform an extensive analysis, which shows small incremental errors similar to previous non-PNO calculations. Furthermore, slight PNO errors are obtained by using TPNO= TTNOwith appropriate values of 10–7to 10–8for reactions and 10–8for interaction or binding energies. The combination with the efficient MP2 focal-point approach yields chemical accuracy relative to the complete basis-set (CBS) limit. In this method, small basis sets (cc-pVDZ, def2-TZVP) for the CCSD(T) part are sufficient in case of reactions or interactions, while some larger ones (e.g., (aug)-cc-pVTZ) are necessary for molecular clusters. For these larger basis sets, we show the very high efficiency of our scheme. We obtain not only tremendous decreases of the wall times (i.e., factors >102) due to the parallelization of the increment calculations as well as of the total times due to the application of PNOs (i.e., compared to the normal incremental scheme) but also smaller total times with respect to the standard PNO method. That way, our new method features a perfect applicability by combining an excellent accuracy with a very high efficiency as well as the accessibility to larger systems due to the separation of the full computation into several small increments.

In recent years PNO-based local correlation methods have gained popularity since they allow Coupled Cluster (CC) calculations with reduced computational costs, yet only a few systematic studies concerning their accuracy are available, in particular for the explicitly correlated versions. In this work we take a deeper look at the explicitly correlated local PNO-CCSD(F12*)(T0) and PNO-CCSD(F12*)(T) methods. The first variant uses the so-called semicanonical triples correction (T0) which neglects off-diagonal elements in the occupied block of the Fock matrix. In PNO-CCSD(F12*)(T) this approximation is avoided by means of Laplace transformation techniques and convergence to the canonical results in the limit of no PNO truncation is restored. We assess the accuracy of both methods using well established benchmark sets for reaction energies and weak molecular interactions and take a look at a system with strong cooperative many-body effects. For reaction energies a close agreement with canonical methods is observed, and chemical accuracy can be reached. Also for weak intermolecular interactions the accuracy is easily controlled, and the methods even allow for improving existing benchmark data.

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 Aterm 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.

Chlorophylls are light-capturing units found in photosynthetic proteins. We study here the ground and excited state properties of monomeric, dimeric, and tetrameric models of the special chlorophyll/bacteriochlorophyll (Chl/BChl) pigment (P) centers P700 and P680/P870 of type I and type II photosystems, respectively. In the excited state calculations, we study the performance of the algebraic diagrammatic construction through second-order (ADC(2)) method in combination with the reduced virtual space (RVS) approach and the recently developed Laplace-transformed scaled-opposite-spin (LT-SOS) algorithm, which allows us, for the first time, to address multimeric effects at correlated ab initiolevels using large basis sets. At the LT-SOS-RVS-ADC(2)/def2-TZVP level, we obtain vertical excitation energies (VEEs) of 2.00–2.07 and 1.52–1.62 eV for the P680/P700 and the P870 pigment models, respectively, which agree well with the experimental absorption maxima of 1.82, 1.77, and 1.43 eV for P680, P700, and P870, respectively. In the P680/P870 models, we find that the photoexcitation leads to a π → π* transition in which the exciton is delocalized between the adjacent Chl/BChl molecules of the central pair, whereas the exciton is localized to a single chlorophyll molecule in the P700 model. Consistent with experiments, the calculated excitonic splittings between the central pairs of P680, P700, and P870 models are 80, 200, and 400 cm–1, respectively. The calculations show that the electron affinity of the radical cation of the P680 model is 0.4 V larger than for the P870 model and 0.2 V larger than for P700. The chromophore stacking interaction is found to strongly influence the electron localization properties of the light-absorbing pigments, which may help to elucidate mechanistic details of the charge separation process in type I and type II photosystems.

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

We present a novel polarizable embedded resolution-of-identity coupled cluster singles and approximate doubles (PERI-CC2) method for calculation of two-photon absorption (TPA) spectra of large molecular systems. The method was benchmarked for three types of systems: a water-solvated molecule of formamide, a uracil molecule in aqueous solution, and a set of mutants of the channelrhodopsin (ChR) protein. The first test case shows that the PERI-CC2 method is in excellent agreement with the PE-CC2 method and in good agreement with the PE-CCSD method. The uracil test case indicates that the effects of hydrogen bonding on the TPA of a chromophore with the nearest environment is well-described with the PERI-CC2 method. Finally, the ChR calculation shows that the PERI-CC2 method is well-suited and efficient for calculations on proteins with medium-sized chromophores.

The noncovalent interaction of the formic acid dimer (FAD) with pyrene and single-walled carbon nanotubes (SWCNTs) is studied using both density functional theory with an empirical dispersion correction as well spin-component-scaled and F12 variants of second-order Møller–Plesset perturbation theory. For the FAD–pyrene model system, it is shown that the dispersion-corrected DFT methods provide similar accurate results for the noncovalent interaction of carboxylic acid dimers with large conjugated π-systems such as MP2 and SCS-MP2. The binding energy of FAD in SWCNTs is found to be sensitive to the radius of the nanotube. It amounts to ca. 22 kcal/mol in the armchair (6,6) SWCNT and decreases with increasing tube radius. In the armchair (8,8) SWCNT, the binding energy is already 25% smaller. To facilitate an experimental identification of FAD inside SWCNTs, we report results for the shifts of the vibrational frequency, where we could identify intense C–O, CO and O–H stretch modes as promising infrared signatures for an experimental detection of such complexes.

An implementation of analytic second derivatives for the approximate coupled cluster singles and doubles model CC2 and for second-order Møller–Plesset perturbation theory (MP2) will be presented. The RI approximation for the two-electron repulsion integrals is used to reduce memory demands, operation count, and I/O requirements. During the calculation, the storage of N4quantities (where Nis a measure for the system size) can completely be avoided. It is shown that with the MP2 method and an appropriate scaling of the harmonic frequencies, especially C–F stretch frequencies are reproduced much better in comparison to experiments than with the B3LYP density functional. Similar advantages are observed for molecules with strong, internal van der Waals interactions. Spin scaling offers additional improvements in these cases. The implementation has been tested for molecules with up to 81 atoms and 684 basis functions.

We present a combination of the polarizable embedding (PE) method with the resolution-of-the-identity implementation of the approximate coupled-cluster singles and doubles method CC2. The new approach, termed PERI–CC2, allows one to study excited state phenomena of large solvated molecular systems with an accurate correlated wave function method. Central to the PE approach is the advanced description of the environmental electrostatic potential and inclusion of polarization, and the quintessence of RI-CC2 is efficient access to excited state properties while retaining the accuracy associated with CC theory. To maintain efficiency, an approximate truncated CC2 density is introduced to calculate the PE contributions. Explicitly, we derive the central equations and outline an implementation of polarizable embedding for the RI-CC2 approach. The new method is tested against previous PE–CC2 and PE–CCSD results for solvatochromic shifts, demonstrating how the important effects of polarization are incorporated well with PERI–CC2 but with a dramatically reduced overall computational cost. A follow-up investigation of the solvatochromic shift of uracil in aqueous solution further illustrates the potential of PERI–CC2. We discuss the need to explicitly incorporate several water molecules into the region treated by quantum mechanics in order to obtain a reliable and accurate description of the physical effects when specific solute/solvent interactions as, e.g., hydrogen-bonds are involved.

The oxidation of 2-propanol by titanium peroxo complexes is investigated in a combined synthetic, spectroscopic, and computational study. We find in quantum chemical calculations for the thermal reaction in protic solvents that the temporary protonation of the peroxo group activates the latter as electrophile. This transient species is amenable to a concerted transfer of two electrons and a proton from the secondary C atom of 2-propanol. Simultaneously, the carbonyl group is formed and the alcoholic proton is transferred to the solvent. In line with the results of the calculations, we find experimentally that the activity of the titanium peroxo complexes as oxidant depends on the pH value of the reaction medium.

The derivation of coupled-cluster response theory for explicitly correlated wavefunctions with terms linear in the interelectronic distance r12(CC-R12) or a function f12thereof (CC-F12) is reviewed and an implementation at the CCSD(R12) and CCSD(F12) for excitation energies and the linear, quadratic and cubic reponse functions is reported for ansätze 1 and 2. We discuss the results of first applications for vertical excitation energies, excited state equilibrium structures and vibrational frequencies, polarizabilities and first and second hyperpolarizabilities with focus on present limitations and future prospects of the approach. We show in particular that the standard choice of the geminal functions and wavefunction expansion can in certain cases lead to a bias towards the unperturbed ground state and how this can be avoided by extending the geminal space. If taken care of this, in particular CCSD(F12)/ansatz 2 shows for the potential energy curves of excited states and for optical properties a similar enhanced basis set convergence of the correlation contribution due to connected double excitations as for ground state energies. For diffuse excited states and hyperpolarizbilities the correlation contribution converges with CCSD(F12)/ansatz 2 often faster than orbital relaxation contributions. The convergence of the latter can be improved by allowing single excitations into a space spanned by a complementary auxiliary basis set.

Formulae are derived and implemented for the analytic calculation of first-order molecular properties at the level of explicitly-correlated second-order Møller-Plesset perturbation theory. In this theory, which is denoted as MP2-F12 theory, Slater-type geminals are used to expand the first-order wave function. A second-order perturbation theory correction for single excitations into a complementary auxliary basis set is also included. At the MP2-F12 level, it seems sufficient to restrict the analytic calculation of energy derivatives to the level of standard approximation A of MP2-F12 theory and to assume the extended Brillouin condition to hold. Smooth and rapid convergence towards the basis-set limit is observed for the dipole moments of a selection of small closed- and open-shell molecules when calculated at the RI-MP2-F12/2A*[T+V] + CABS singles level in augmented correlation-consistent polarized valence double-, triple-, and quadruple-zeta basis sets that have been optimized especially for use in MP2-F12 theory.

The elementary steps of the methanol synthesis reaction at oxygen vacancies on the polar ZnO(0001̅) surface have been studied with density functional theory. We report results for reaction and activation energies for the most important elementary steps of the methanol synthesis reaction on this surface. At these oxygen vacancies the barriers for heterolytic cleavage of H2into protons, bound in surface OH groups, and hydrides, trapped in the vacancies, is low. The stabilized hydride facilitates the reduction of CO to formyl (stabilized in the vacancy) with a low barrier ≲100 kJ/mol. After a fast rearrangement to formaldehyde and hydroxymethylene species, a second reduction step leads probably to a surface-bound methoxide which at reducing conditions desorbs from the surface under regeneration of an oxygen vacancy. Beside formate, which appears as a side product, and formyl species, oxygen-bound hydroxymethylene might be another observable intermediate of the methanol synthesis reaction at oxygen vacancy sites on the ZnO(0001̅) surface.

In der theoretischen bioanorganischen Chemie hat sich die Berechnung spektroskopischer Parameter mit Dichtefunktionalmethoden im Zusammenspiel mit Experimenten als besonders fruchtbar erwiesen. Inzwischen entsprechen gerechnete Geschwindigkeitskonstanten für Reaktionen mit mehratomigen Molekülen experimentellen Werten. Dimensionsreduzierte quantenmechanische Studien geben Einsicht in die Bedeutung einzelner Schwingungsmoden. Coupled‐Cluster‐Methoden sind heute ein Standard für genaue Berechnungen von Energien von Grund‐ und angeregten Zuständen sowie elektrischen und magnetischen Eigenschaften. In der bioanorganischen Chemie hat sich die Berechnung spektroskopischer Parameter mit Dichtefunktionalmethoden als fruchtbar erwiesen. Inzwischen entsprechen gerechnete Geschwindigkeitskonstanten experimentellen Werten. Coupled‐Cluster‐Methoden sind Standard für Berechnungen der Energien von Grund‐ und angeregten Zuständen.

We present a parallel implementation of second-order Møller–Plesset perturbation theory with the resolution-of-the-identity approximation (RI-MP2). The implementation is based on a recent improved sequential implementation of RI-MP2 within the Turbomole program package and employs the message passing interface (MPI) standard for communication between distributed memory nodes. The parallel implementation extends the applicability of canonical MP2 to considerably larger systems. Examples are presented for full geometry optimizations with up to 60 atoms and 3300 basis functions and MP2 energy calculations with more than 200 atoms and 7000 basis functions.

An implementation of analytic basis set gradients is reported for the optimization of auxiliary basis sets in resolution-of-the-identity second-order Møller–Plesset perturbation theory RI-MP2 and approximate coupled-cluster singles-and-doubles RI-CC2 calculations. The analytic basis set gradients are applied in the optimization of auxiliary basis sets for a number of large one-electron orbital basis sets which provide correlation energies close to the basis set limit: the core–valence basis sets cc-pwCVXZ B–Ne, Al–Ar with X D, T, Q, 5, the quintuple-ζbasis sets cc-pV5Z H–Ar and cc-pV5 dZ Al–Ar and the doubly-polarized valence quadruple-ζbasis sets QZVPP for Li–Kr. The quality of the optimized auxiliary basis sets is evaluated for several test sets with small and medium sized molecules.

OPEP is a suite of FORTRAN programs targeted at the optimal partitioning of molecular electric properties. It includes an interactive module for the construction of Cartesian grids of points, on which either the molecular electrostatic potential or the induction energy is mapped. The generation of distributed multipoles and polarizabilities is achieved using either the formalism of the normal equations of the least‐squares problem, which restates the fitting procedure in terms of simple matrix operations, or a statistical approach, which provides a pictorial description of the distributed models of multipoles and polarizabilities, thereby allowing the pinpointing of pathological cases. Molecular symmetry is accounted for by means of local atomic frames, which are generated in an automated fashion. A Tcl/Tk graphical user interface wraps the suite of programs, thereby making OPEP a user‐friendly package for building models of distributed multipoles and polarizabilities. OPEP is an open‐source suite of programs distributed free of charge under the GNU general public license (GPL) at . © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 997–1008, 2003

Triplet excitation energies within the approximate coupled cluster singles and doubles model CC2 have been implemented using an explicitly spin coupled basis and the resolution of the identity approximation for two-electron integrals. This approach reduces substantially the requirements for CPU time, disk space and memory, and extends the applicability of CC2 for triplet excited states to molecules that could not be studied before with this method. We report an application to the lowest singlet and triplet vertical excitation energies of trans-azobenzene. An accurate ab initio geometry optimized at the MP2/cc-pVTZ level is presented, and CC2 calculations in the aug-cc-pVTZ basis set with 874 basis functions are combined with coupled cluster singles and doubles (CCSD) calculations in modest basis sets to obtain the best possible estimates for the vertical excitation energies. The results show that recently reported SOPPA calculations are unreliable. Good agreement with experiment is obtained for the lowest excited singlet state S₁, but for the lowest triplet state T₁ the results indicate a large difference between the vertical excitation energy and the experimentally observed transition.

A new derivation is presented for the orientation-dependent interaction tensors which describe the electrostatic interaction between two multipole or multipole polarizability distributions both given in their own molecule-fixed coordinate system. This derivation leads to an explicit equations that allows easy and direct evaluation of formulae for the components of the double-tensors and also for high ranks. Such an equation is given for the real, complex spherical, and cartesian moments. The formula is suitable for providing stable computer-generated expressions for tensor operators of any rank.

Abstract.: The frequency dependence of third-order properties can in the normal dispersion region be expanded in a Taylor series in the frequency arguments. The dispersion coefficients thus obtained provide an efficient way of expressing the dispersion of frequency-dependent properties and are transferable between different optical processes. We derive analytic expressions for the dispersion coefficients of third-order properties in coupled cluster quadratic response theory and report an implementation for the three coupled cluster models CCS, CC2, and CCSD. Calculations are performed for the first hyperpolarizability of the NH3 molecule. The convergence of the dispersion expansion with the order of the coefficients is examined and we find good convergence up to about half the frequency at which the first pole in the hyperpolarizability occurs. Pad approximants improve the convergence dramatically and extend the application range of the dispersion expansion to frequencies close to the first pole. The sensitivity of the dispersion coefficients on the dynamic correlation treatment and on the choice of the one-electron basis set is investigated. The results demonstrate that, contrary to presumptions in the literature, the dispersion coefficients are sensitive to basis set effects and correlation treatment similar to the static hyperpolarizabilities.

Frequency-dependent distributed polarizabilities have been determined from time-dependent Hartree–Fock calculations, using the partitioning of the molecular space suggested by Bader's topological theory of atoms in molecules. The basis set dependence of the distributed dynamic polarizabilities is analyzed in terms of the first few Cauchy moments, for the carbon monoxide, water, cyanogen, urea and benzene molecules. Two alternative relocalization schemes have been considered in order to reduce the number of distributed dynamic polarizability parameters. The first one, closely related to the atomic polarizability model of Bader, leads to atomic charge–dipole and dipole–dipole polarizabilities, describing the response of the molecular charge distribution to a uniform external field, in terms of atomic charges and dipoles. The second scheme, similar to that suggested by Stone, retains the fully distributed description of the dynamic charge-flow polarizabilities, while all two-center dipole–dipole and charge–dipole contributions are condensed in one-center dynamic dipole–dipole polarizabilities. Keywords: Bader-partitioning, distributed dynamic polarizabilities, Cauchy-moments, benzene, polarizability of; urea, polarizability of.

It is demonstrated that frequency-dependent response functions can conveniently be derived from the time-averaged quasienergy. The variational criteria for the quasienergy determines the time-evolution of the wave-function parameters and the time-averaged time-dependent Hellmann–Feynman theorem allows an identification of response functions as derivatives of the quasienergy. The quasienergy therefore plays the same role as the usual energy in time-independent theory, and the same techniques can be used to obtain computationally tractable expressions for response properties, as for energy derivatives in time-independent theory. This includes the use of the variational Lagrangian technique for obtaining expressions for molecular properties in accord with the 2n+1 and 2n+2 rules. The derivation of frequency-dependent response properties becomes a simple extension of variational perturbation theory to a Fourier component variational perturbation theory. The generality and simplicity of this approach are illustrated by derivation of linear and higher-order response functions for both exact and approximate wave functions and for both variational and nonvariational wave functions. Examples of approximate models discussed in this article are coupled-cluster, self-consistent field, and second-order Møller–Plesset perturbation theory. A discussion of symmetry properties of the response functions and their relation to molecular properties is also given, with special attention to the calculation of transition- and excited-state properties. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 1–52, 1998

Cobalt ferrite, CoFe2O4(CFO), nanocrystals are efficient and competitive anode materials in the field of electrochemical water splitting. Using density functional theory with on-site Hubbard Ucorrections (DFT+U), we have investigated the structural, electronic, and magnetic properties of CFO (001)/(100) surfaces, as well as their reactivities toward water adsorption. Special attention has been focused on the formation of oxygen vacancies (VO), due to their key role in the oxidation activity of metal oxides, often based on the Mars–van Krevelen mechanism. Our results show that vacancy formation is easiest at oxygen sites that are not bound to tetrahedrally coordinated Fe. Water adsorbs mainly in molecular form on the Co/Fe metal cations, whereas it dissociates at defects. In comparison to other spinels, CFO is similar to NiFe2O4, exhibiting relatively low energy cost of VOformation and a strong affinity of the vacancies toward water. These findings suggest that CFO may be a more promising oxidation catalyst than NiCo2O4and Co3O4.