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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 TURBOMOLEs 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.

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

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 pKa 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 pKa∗ 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 pKa values. For the test set, this approach gives more accurate pKa 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 pKa changes from the ground to the excited state for photoacids and an overestimation for photobases. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present a pair natural orbital (PNO)-based implementation of CC3 excitation energies, which extends our previously published state-specific PNO ansatz for the solution of the excited state eigenvalue problem to methods including connected triple excitations. A thorough analysis of the equations for the excited state triples amplitudes is presented from which we derive a suitable state-specific triple natural orbital basis for the excited state triples amplitudes, which performs equally well for local and non-local excitations. The accuracy of the implementation is evaluated using a large and diverse test set. We find that for states with small contributions from double excitations, a T0 approximation to PNO-CC3 yields accurate results with a mean absolute error (MAE) for TPNO = 10−7 in the range of 0.02 eV. However, for states with larger double excitation contributions, the T0 approximation is found to yield significantly less accurate results, while the Laplace-transformed variant of PNO-CC3 shows a uniform accuracy for singly and doubly excited states (MAE and maximum error of 0.01 eV and 0.07 eV for TPNO = 10−7, respectively). Finally, we apply PNO-CC3 to the calculation of the first excited state of berenil at a S1 minimum geometry, which is shown to be close to a conical intersection. This calculation in the aug-cc-pVTZ basis set (more than 1300 basis functions) is the largest calculation ever performed with CC3 on excitation energies. [ABSTRACT FROM AUTHOR]

In the present work, we report the derivation and implementation of vertical ionization potentials (IPs) and electron affinities (EAs) for embedded wavefunction methods as well as the corresponding analytical nuclear gradients. Vertical transitions have been implemented for CIS(D∞), the second-order algebraic diagrammatic construction [ADC(2)] scheme, and the second-order approximate coupled-cluster singles and doubles method. For all methods, density fitting is applied to facilitate reduced memory and disk storage requirements. Analytical nuclear gradients have been derived and implemented for CIS(D∞) and ADC(2) both with and without frozen-density embedding (FDE). The objective of the reported method is to study the properties of organic semiconductors in which charge is transported along molecular stacks in molecular crystals. The accuracy of the implemented methods is, therefore, assessed using stacked dimers of small model systems. Albeit second-order methods can yield noticeable errors with respect to reference methods in terms of absolute IP and EA values, they show a significantly improved accuracy for the shift of the IP and EA values at different intermolecular distances relative to the monomers. Besides reducing the computational costs, the FDE ansatz introduces furthermore a significant conceptual difference as it enables control over which subsystem is ionized, allowing for the calculation of transfer integrals for the interacting (embedded) systems. The new implementation is finally applied to tetraazaperopyrenes, used as organic semiconductors, to study charge-localization and long-range polarization in particular. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Dioxygen activation pathways on the (001) surfaces of cobalt ferrite, CoFe2O4, 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. [ABSTRACT FROM AUTHOR]

We present the DEC-RIMP2-F12 method where we have augmented the Divide Expand-Consolidate resolution-of-the-identity second-order Møller-Plesset perturbation theory method (DEC-RIMP2) [P. Baudin et al., J. Chem. Phys. 144, 054102 (2016)] with an explicitly correlated (F12) correction. The new method is linear-scaling, massively parallel, and it corrects for the basis set incompleteness error in an efficient manner. In addition, we observe that the F12 contribution decreases the domain error of the DEC-RIMP2 correlation energy by roughly an order of magnitude. An important feature of the DEC scheme is the inherent error control defined by a single parameter, and this feature is also retained for the DEC-RIMP2-F12 method. In this paper we present the working equations for the DEC-RIMP2-F12 method and proof of concept numerical results for a set of test molecules. [ABSTRACT FROM AUTHOR]

We report an implementation of static and frequency-dependent excited state polarizabilities for the approximate coupled cluster single and doubles model CC2 as analytic second derivatives of an excited state quasienergy Lagrangian. By including appropriate conditions for the normalization and the phase of the eigenvectors, divergent secular terms are avoided. This leads to response equations in a subspace orthogonal to the unperturbed eigenvectors. It is shown how these projected equations can be solved without storage of the double excitation part of the eigenvectors. By exploiting the resolution-of-the-identity approximation and a numerical Laplace transformation, the quadratic scaling of the main memory demands of RI-CC2 with the system size could be preserved. This enables calculations of excited state polarizabilities for large molecules, e.g., linear polyacenes up to decacene with almost 2500 basis functions on a single compute node within a few days. For a test set of molecules where measurements are available as reference data, we compare the orbital-relaxed and unrelaxed CC2 approaches with experiment to validate its accuracy. The approach can be easily extended to other response methods, in particular CIS(D8). The latter gives results which, in the orbital-relaxed case, are within a few percent of the CC2 values, while coupled cluster singles results deviate typically by about 20% from orbital-relaxed CC2 and experimental reference data. [ABSTRACT FROM AUTHOR]

We present scaling factors for vibrational frequencies calculated within the harmonic approximation and the correlated wave-function methods coupled cluster singles and doubles model (CC2) and Møller-Plesset perturbation theory (MP2) with and without a spin-component scaling (SCS or spinopposite scaling (SOS)). Frequency scaling factors and the remaining deviations from the reference data are evaluated for several non-augmented basis sets of the cc-pVXZ family of generally contracted correlation-consistent basis sets as well as for the segmented contracted TZVPP basis. We find that the SCS and SOS variants of CC2 and MP2 lead to a slightly better accuracy for the scaled vibrational frequencies. The determined frequency scaling factors can also be used for vibrational frequencies calculated for excited states through response theory with CC2 and the algebraic diagrammatic construction through second order and their spin-component scaled variants. [ABSTRACT FROM AUTHOR]

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 I⋯O 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. [ABSTRACT FROM AUTHOR]

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−. [ABSTRACT FROM AUTHOR]

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We demonstrate how to extend the pair natural orbital (PNO) methodology for excited states, presented in a previous work for the perturbative doubles correction to configuration interaction singles (CIS(D)), to iterative coupled cluster methods such as the approximate singles and doubles model CC2. The original O(N5) scaling of the PNO construction is reduced by using orbital-specific virtuals (OSVs) as an intermediate step without spoiling the initial accuracy of the PNO method. Furthermore, a slower error convergence for charge-transfer states is analyzed and resolved by a numerical Laplace transformation during the PNO construction, so that an equally accurate treatment of local and charge-transfer excitations is achieved. With state-specific truncated PNO expansions, the eigenvalue problem is solved by combining the Davidson algorithm with deflation to project out roots that have already been determined and an automated refresh with a generation of new PNOs to achieve self-consistency of the PNO space. For a large test set, we found that truncation errors for PNO-CC2 excitation energies are only slightly larger than for PNO-CIS(D). The computational efficiency of PNO-CC2 is demonstrated for a large organic dye, where a reduction of the doubles space by a factor of more than 1000 is obtained compared to the canonical calculation. A compression of the doubles space by a factor 30 is achieved by a unified OSV space only. Moreover, calculations with the still preliminary PNO-CC2 implementation on a series of glycine oligomers revealed an early break even point with a canonical RI-CC2 implementation between 100 and 300 basis functions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present an algorithm for computing explicitly correlated second- and third-order Mo\ller-Plesset energies near the basis set limit for large molecules with a cost that scales formally as N4 with system size N. This is achieved through a hybrid approach where locality is exploited first through orbital specific virtuals (OSVs) and subsequently through pair natural orbitals (PNOs) and integrals are approximated using density fitting. Our method combines the low orbital transformation costs of the OSVs with the compactness of the PNO representation of the doubles amplitude vector. The N4 scaling does not rely upon the a priori definition of domains, enforced truncation of pair lists, or even screening and the energies converge smoothly to the canonical values with decreasing occupation number thresholds, used in the selection of the PNO basis. For MP2.5 intermolecular interaction energies, we find that 99% of benchmark basis set limit correlation energy contributions are recovered using an aug-cc-pVTZ basis and that on average only 50 PNOs are required to correlate the significant orbital pairs. [ABSTRACT FROM AUTHOR]

We used ab initio density functional theory in combination with an embedded cluster approach to calculate vibrational spectra and formation enthalpies of possible intermediates and side products (spectator species) in the synthesis of methanol out of syngas on the ZnO([formula]) surface. Our investigations are based upon our previous work on possible reaction pathways and activation barriers for this reaction at oxygen vacancies on ZnO([formula]). We present and discuss calculated vibrational frequencies of short-living formyl, hydroxymethylene, formaldehyde, acetale, and hydroxymethyl intermediates and compare the calculated frequencies of formate and methoxy species as well as CO and CO2 species, at the defect free surface and at oxygen vacancies, with recent experimental findings. All investigated species show characteristic features in their spectra. Therefore, the analysis of their vibrational frequencies is a suitable mean to distinguish them and gain new insights in this reaction which is of recent experimental interest. We are able to identify the structure and characteristics of different surface species, such as monodentate and polydentate carbonate and formate species, in agreement with experimental results. [ABSTRACT FROM AUTHOR]

We explore how in response calculations for excitation energies with wavefunction based (e.g., coupled cluster) methods the number of double excitation amplitudes can be reduced by means of truncated pair natural orbital (PNO) expansions and localized occupied orbitals. Using the CIS(D) approximation as a test model, we find that the number of double excitation amplitudes can be reduced dramatically with minor impact on the accuracy if the excited state wavefunction is expanded in state-specific PNOs generated from an approximate first-order guess wavefunction. As for ground states, the PNO truncation error can also for excitation energies be controlled by a single threshold related to generalized natural occupation numbers. The best performance is found with occupied orbitals which are localized by the Pipek-Mezey localization. For a large test set of excited states we find with this localization that already a PNO threshold of 10-8-10-7, corresponding to an average of only 40-80 PNOs per pair, is sufficient to keep the PNO truncation error for vertical excitation energies below 0.01 eV. This is a significantly more rapid convergence with the number doubles amplitudes than in domain-based local response approaches. We demonstrate that the number of significant excited state PNOs scales asymptotically linearly with the system size in the worst case of completely delocalized excitations and sub-linearly whenever the chromophore does not increase with the system size. Moreover, we observe that the flexibility of state-specific PNOs to adapt to the character of an excitation allows for an almost unbiased treatment of local, delocalized and charge transfer excited states. [ABSTRACT FROM AUTHOR]

We explore using a pair natural orbital analysis of approximate first-order pair functions as means to truncate the space of both virtual and complementary auxiliary orbitals in the context of explicitly correlated F12 methods using localised occupied orbitals. We demonstrate that this offers an attractive procedure and that only 10-40 virtual orbitals per significant pair are required to obtain second-order valence correlation energies to within 1-2% of the basis set limit. Moreover, for this level of virtual truncation, only 10-40 complementary auxiliary orbitals per pair are required for an accurate resolution of the identity in the computation of the three- and four-electron integrals that arise in explicitly correlated methods. [ABSTRACT FROM AUTHOR]

An implementation of scaled opposite-spin CC2 (SOS-CC2) for ground and excited state energies is presented that requires only fourth order scaling computational costs. The SOS-CC2 method yields results with an accuracy comparable to the unscaled method. Furthermore the time-determining fifth order scaling steps in the algorithm can be replaced by only fourth order scaling computational costs using a 'resolution of the identity' approximation for the electron repulsion integrals and a Laplace transformation of the orbital energy denominators. This leads to a significant reduction of computational costs especially for large systems. Timings for ground and excited state calculations are shown and the error of the Laplace transformation is investigated. An application to a chlorophyll molecule with 134 atoms results in a speed-up by a factor of five and demonstrates how the new implementation extends the applicability of the method. A SOS variant of the algebraic diagrammatic construction through second order ADC(2), which arises from a simplification of the SOS-CC2 model, is also presented. The SOS-ADC(2) model is a cost-efficient alternative in particular for future extensions to spectral intensities and excited state structure optimizations. [ABSTRACT FROM AUTHOR]

We propose a novel explicitly correlated coupled-cluster singles and doubles method CCSD(F12*), which retains the accuracy of CCSD-F12 while the computational costs are only insignificantly larger than those for a conventional CCSD calculation. [ABSTRACT FROM AUTHOR]

Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born–Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H2O, CH2O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented. [ABSTRACT FROM AUTHOR]

Coupled-cluster response theory for frequency-dependent optical properties within the coupled-cluster singles-and-doubles model (CCSD) has been derived and implemented for ansatz 2 of the explicitly correlated CCSD(R12) and CCSD(F12) methods as part of the program package DALTON. The basis set convergence of static dipole moments, polarizabilities, and parallel averages of first and second hyperpolarizabilities has been investigated for Ne, BH, N2, CO, and BF. The frequency-dependent results are presented for the electronic second-harmonic generation of N2. With triple-ζ basis sets, the CCSD(F12) correlation contributions using ansatz 2 are close to the basis set limits for dipole moments and second hyperpolarizabilities; the CCSD(R12) results are better than the CCSD results obtained with at least quintuple-ζ basis sets for polarizabilities and first hyperpolarizabilities. The exponent of Slater-type correlation factor for CCSD(F12) ground state energy may not be optimal and has to be re-examined for response properties. We also suggest that the remaining one-electron basis set errors arising within the coupled-cluster singles should be reduced by allowing excitations into the auxiliary orbital space. [ABSTRACT FROM AUTHOR]

The equation-of-motion coupled-cluster method for excited states with the singles-and-doubles model (CCSD) has been implemented for ansatz 2 of the explicitly correlated CCSD(R12) and CCSD(F12) methods as part of the program package Dalton. In this model, an orthonormal complementary auxiliary basis set is used for the resolution-of-identity approximation in order to calculate the three-electron integrals needed for CCSD(R12) and CCSD(F12). The additional CCSD(R12) or CCSD(F12) terms introduced within ansatz 2, which are not present in ansatz 1, are derived and discussed with regard to the extra costs needed for their computation. As a first application the basis set convergence of equilibrium bond lengths and harmonic vibrational frequencies has been investigated for some singlet excited states of the diatomic molecules N2, CO, BF, and BH. The calculated CCSD(F12) results show that the average absolute deviations of the bond lengths and frequencies from the basis set limits are below 0.1 pm and 5 cm-1 as well as 0.05 pm and 1 cm-1 for the triple- and quadruple-ζ basis sets, respectively. These deviations are shown to largely arise from the SCF basis set incompleteness errors. [ABSTRACT FROM AUTHOR]

The overall rotation and internal rotation of p-cresol (4-methyl-phenol) has been studied by comparison of the microwave spectrum with accurate ab initio calculations using the principal axis method in the electronic ground state. Both internal rotations, the torsions of the methyl and the hydroxyl groups relative to the aromatic ring, have been investigated. The internal rotation of the hydroxyl group can be approximately described as the motion of a symmetrical rotor on an asymmetric frame. For the methyl group it has been found that the potential barrier hindering its internal rotation is very small with the first two nonvanishing Fourier coefficients of the potential V3 and V6 in the same order of magnitude. Different splittings of b-type transitions for the A and E species of the methyl torsion indicate a top-top interaction between both internal rotors through the benzene ring. An effective coupling potential for the top-top interaction could be estimated. The hindering barriers of the hydroxyl and methyl rotation have been calculated using second-order Mo\ller-Plesset perturbation theory and the approximate coupled-cluster singles-and-doubles model (CC2) in the ground state and using CC2 and the algebraic diagrammatic construction through second order in the first electronically excited state. The results are in excellent agreement with the experimental values. [ABSTRACT FROM AUTHOR]

Response theory up to infinite order is combined with the explicitly correlated coupled-cluster singles and doubles model including linear-r12 corrections, CCSD(R12). The additional terms introduced by the linear-r12 contributions, not present in the conventional CCSD calculation, are derived and discussed with respect to the extra costs required for their evaluation. An implementation is presented up to the cubic response function for one-electron perturbations, i.e., up to frequency-dependent second hyperpolarizabilities. As first applications the authors computed the electronic polarizabilities and second hyperpolarizabilities of BH, N2, and formaldehyde and show that the improvement in the one-electron basis set convergence known from the R12 method for ground state energies is retained for higher-order optical properties. Frequency-dependent results are presented for the second hyperpolarizability of N2. [ABSTRACT FROM AUTHOR]