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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]

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]

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 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]

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]

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 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]

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]

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]

As known since about two decades, R12 methods, which include terms linear in the interelectronic distance r12 in the wave function, improve substantially the basis set convergence of the ground state correlation energy. In a previous study, however, it was found that the same approach does not give a similar systematic improvement if applied to excited states in the framework of coupled cluster response theory. In the present work, we examine the reason for this behavior and show that the inclusion of additional orbitals in the construction of the r12 pair functions leads to an enhanced basis set convergence (and thus a balanced description) also for the excited states. [ABSTRACT FROM AUTHOR]

The microwave spectrum of m-cresol (3-methylphenol) has been investigated using a molecular beam Fourier transform microwave spectrometer in the frequency range from 3 to 26.5 GHz. The rotation of the hydroxy group into two different unequal energetic minima leads to different spectra for the syn- and anticonformers. Because of a high potential barrier both conformers can be analyzed independently. The methyl group is undergoing an almost free internal rotation which is only hindered by small barriers and splits the vibrational ground state in two states of internal rotation denoted as A and E species. The spacing between the species is found to be up to 10 GHz. The potential for the internal rotation can be determined from the spectra and analyzed in terms of the Fourier components V3 and V6. For syn-m-cresol these parameters were determined as V3=673(3) GHz and V6=-335(24) GHz and for anti-m-cresol V3=95(5) GHz and V6=-416(46) GHz. The barriers to internal rotation were furthermore calculated with second-order Mo\ller-Plesset perturbation theory and second-order coupled-cluster singles- and-doubles model (CC2) in the electronic ground state and with CC2 in the first excited state. The CC2 method is found to be an appropriate method to calculate potential barriers in electronic excited states of such compounds. [ABSTRACT FROM AUTHOR]

Coupled-cluster response theory for vertical excitation energies within the second-order approximate coupled-cluster singles-and-doubles model CC2, including linear-r12 corrections, is derived and implemented for Ansätze 1 and 2 of R12 theory. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation in order to calculate the three- and four-electron integrals needed in R12 theory. The basis set convergence is investigated for a selected set of atoms and small molecules and it is found that in many cases the convergence is not improved. An analysis of the different contributions to excitation energies shows that the present scheme for the construction of the R12 pair functions leads in response theory to an unbalanced description of ground- and excited-state wave functions and needs to be generalized to carry the high accuracy of R12 methods over to response theory. [ABSTRACT FROM AUTHOR]

The derivation and implementation of excited state gradients is reported for the approximate coupled-cluster singles and doubles model CC2 employing the resolution-of-the-identity approximation for electron repulsion integrals. The implementation is profiled for a set of examples with up to 1348 basis functions and exhibits no I/O bottlenecks. A test set of sample molecules is used to assess the performance of the CC2 model for adiabatic excitation energies, excited state structure constants and vibrational frequencies. We find very promising results, especially for adiabatic excitation energies, though the need of a single-reference ground state and a single-replacement dominated excited state puts some limits on the applicability of the method. Its reliability, however, can always be tested on grounds of diagnostic measures. As an example application, we present calculations on the π[sup *]←π excited state of trans-azobenzene.© 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An implementation of the gradient for the second-order coupled-cluster singles-and-doubles model CC2 is reported, which employs the resolution-of-the-identity (RI) approximation for electron repulsion integrals. The performance of the CC2 model for ground state equilibrium geometries and harmonic frequencies is investigated and compared with experiment and other ab initio methods. It is found that CC2 equilibrium geometries have a similar accuracy to those calculated with second-order Møller-Plesset perturbation theory (MP2), but the bond lengths are larger. In particular, double and triple bonds and bonds in electron-rich compounds are elongated by 0.5-1.5 pm. Thereby CC2 slightly outperforms MP2 for single bonds, in particular in electron-rich compounds, but for strong double and triple bonds CC2 is somewhat inferior to MP2. The results for harmonic frequencies go in parallel with the results for equilibrium structures. The error introduced by the RI approximation is found to be negligible compared to the remaining one-electron basis set error, if optimized auxiliary basis sets are used. Typically, the RI error in bond lengths is of the order of 10[SUP-3] pm and the error in angles 10[SUP-3]-1[SUP-2] deg. Applications are reported for the geometry of trans-azobenzene and for the geometry and harmonic frequencies of cis,trans-1,4-difluorobutadiene. [ABSTRACT FROM AUTHOR]

An implementation of transition moments and excited-state first-order properties is reported for the approximate coupled-cluster singles-and-doubles model (CC2) using the resolution of the identity (RI) approximation. In parallel to the previously reported code for the ground- and excited-state amplitude equations, we utilize a partitioned form of the CC2 equations and thus eliminate the need to store any N[SUP4] intermediates. This opens the perspective for applications on molecules with 30 and more atoms. The accuracy of the RI approximation is tested for a set of 29 molecules for the aug-cc-pVXZ (X = D, T, Q) basis sets in connection with the recently optimized auxiliary basis sets. These auxiliary basis sets are found to be sufficient even for the description of diffuse states. The RI error is compared to the usual basis set error and is demonstrated to be insignificant. [ABSTRACT FROM AUTHOR]

Abstract To provide a qualitative analysis on how the reaction energies and mechanisms of initial steps of char combustion depend on a) the size of polycyclic aromatic hydrocarbons (PAHs) and b) the reaction sites, we investigate the initial steps of the individual reactions of thirteen PAHs with atomic oxygen with density functional theory. Specifically, we have studied three elementary steps: i) O(3P) addition, ii) subsequent oxyradical formation through H abstraction, and iii) CO elimination from the oxyradicals. We find that the CO elimination from the oxyradicals follows either a three, two, or single step mechanism, depending on the geometrical strain at the reaction site. In accordance, we observe that as the geometrical strain at the reaction site increases, the activation energy of the first step of the CO elimination from the oxyradicals increases. Important findings that are relevant for a multiscale modeling of the oxidation of large PAHs, e.g. during char burnout, are that the activation energies for these reactions can be related to the reaction energies through Bell-Evans-Polanyi (BEP) fits, and that for the O addition and the last step of the three or two step CO elimination mechanisms, i.e. the CO elimination from carbonyl radicals, the reaction energies are correlated with the stabilization energies calculated from the Hückel molecular orbital theory. [ABSTRACT FROM AUTHOR]

In order to test the performance of the recently developed time-dependent second-order Mo\ller–Plesset perturbation theory (TDMP2) for anisotropic frequency-dependent multipole polarizabilities, we have studied the isoelectronic series CO, N2, CN-, and NO+. The polarizabilities of these triple-bonded diatomics are an interesting test for the TDMP2 method, because it is known that Mo\ller–Plesset perturbation theory has its difficulties describing multiple bonds. We selected these molecules as test systems because, especially for N2 and CO, accurate experimental and other ab initio data are available to compare with and their dynamical polarizabilities are needed for dispersion coefficients of van der Waals complexes, which are presently under intensive investigation. To get reliable results near the TDMP2 basis set limit we used large one-particle basis sets, optimized for polarizability calculations at the coupled Hartree–Fock level. The results show that the TDMP2 method is capable to improve for the isotropic as well as for the anisotropic polarizabilities considerably on the TDHF approximation, with the exception of the dipole polarizabilities of N2 and NO+, for which the static correlation effects are too strong to be treated by second-order Mo\ller–Plesset perturbation theory. However, we find, that the TDMP2 method, due to the use of coupled (TDHF) first-order orbital rotation parameters, is somewhat more stable with respect to static correlation effects than the singles-doubles-triples many-body perturbation theory to second order [SDT-MBPT(2)] double perturbation theory. Where reference data are available, the TDMP2 results for static polarizabilities and for the first Cauchy moments are in good agreement with the best theoretical and experimental data. We also calculated dispersion coefficients for the (N2)2 and the (CO)2 dimer and, utilizing the results of previous TDMP2 studies for the atoms He through Xe, also for the... [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 coupled cluster singles and doubles (CCSD) excitation energies that builds upon the previously proposed state-specific PNO approach to the excited state eigenvalue problem. We construct the excited state PNOs for each state separately in a truncated orbital specific virtual basis and use a local density-fitting approximation to achieve an at most quadratic scaling of the computational costs for the PNO construction. The earlier reported excited state PNO construction is generalized such that a smooth convergence of the results for charge transfer states is ensured for general coupled cluster methods. We investigate the accuracy of our implementation by applying it to a large and diverse test set comprising 153 singlet excitations in organic molecules. Already moderate PNO thresholds yield mean absolute errors below 0.01 eV. The performance of the implementation is investigated through the calculations on alkene chains and reveals an at most cubic cost-scaling for the CCSD iterations with the system size. [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]

An improved formulation of pair natural orbital (PNO)-based explicitly correlated Møller-Plesset second-order perturbation theory is presented. Increased efficiency has been achieved by modifying the representation of the strong orthogonality projector used in the evaluation of the F12 intermediates. We demonstrate two simple relationships between the truncation errors arising from PNOs in the virtual space and those arising from the PNOs in the strong orthogonality operators. This permits robust error control through a single parameter. [ABSTRACT FROM AUTHOR]

Abstract: An implementation of analytical gradients, transition moments and excited state properties for scaled opposite-spin (SOS) CC2 and a SOS variant of the algebraic diagrammatic construction through second order ADC(2) is presented. The time-determining fifth order scaling steps in the algorithms are replaced by schemes with only fourth order scaling computational costs using a “resolution of the identity” approximation for the electron repulsion integrals and a numerical Laplace transformation of the orbital energy denominators. This leads to a significant reduction of the computational costs for geometry optimizations of large systems. This work is an extension to the recently presented quartic scaling algorithm for SOS–CC2 energies for ground and excited states. The Laplace error for adiabatic electronic excitation energies and excited state structures is found to be very small. SOS–ADC(2) provides for adiabatic electronic excitation energies, excited state structure parameters, harmonic vibrational frequencies as well as dipole moments and transition strengths an accuracy similar to SOS–CC2. Timings for ground and excited state calculations are reported and applications to a chlorophyll molecule and a ditopic 2,2′:6′,2″-bis(terpyridine) with 160 atoms demonstrate how the new implementation extends the applicability of these methods for large systems. [Copyright &y& Elsevier]

Abstract: The excited-state potential-energy surfaces of the lowest-energy conformer of the tryptophan–glycine dipeptide have been investigated with ab initio electronic-structure methods. The calculations reveal a potentially very efficient excited-state deactivation mechanism via conical intersections of the excited states of the indole chromophore with locally-excited and charge-transfer states of the peptide backbone. These findings suggest that the excited-state lifetime of the lowest-energy conformer of the Trp-Gly dipeptide may be too short to allow the detection of a resonant two-photon ionization signal. It is proposed that the efficient excited-state deactivation enhances the photostability of the dipeptide. [Copyright &y& Elsevier]

The introduction of the resolution-of-the-identity (RI) approximation for electron repulsion integrals in quantum chemical calculations requires in addition to the orbital basis so-called auxiliary or fitting basis sets. We report here such auxiliary basis sets optimized for second-order Møller–Plesset perturbation theory for the recently published (Weigend and Ahlrichs Phys Chem Chem Phys, 2005, 7, 3297–3305) segmented contracted Gaussian basis sets of split, triple-ζ and quadruple-ζ valence quality for the atoms Rb–Rn (except lanthanides). These basis sets are designed for use in connection with small-core effective core potentials including scalar relativistic corrections. Hereby accurate resolution-of-the-identity calculations with second-order Møller–Plesset perturbation theory (MP2) and related methods can now be performed for molecules containing elements from H to Rn. The error of the RI approximation has been evaluated for a test set of 385 small and medium sized molecules, which represent the common oxidation states of each element, and is compared with the one-electron basis set error, estimated based on highly accurate explicitly correlated MP2–R12 calculations. With the reported auxiliary basis sets the RI error for MP2 correlation energies is typically two orders of magnitude smaller than the one-electron basis set error, independent on the position of the atoms in the periodic table. [ABSTRACT FROM AUTHOR]

Quantum-chemical calculations with the approximate coupled-cluster singles-and-doubles model CC2 have been carried out for 1-tert-butyl-6-cyano-1,2,3,4-tetrahydroquinoline (NTC6). For this molecule dual fluorescence was experimentally observed, raising the discussion about the importance of the amino twist angle for this process. The calculations suggest that both the ground state and the normal fluorescent state are significantly twisted by 300–40° and that the molecule is flexible enough to move into an even stronger twisted conformation (600–70°) in its intramolecular charge-transfer (ICT) state which is responsible for the anomalous fluorescence band. Such a conformation both minimizes the total energy in the S1 state and maximizes the dipole moment. The barrier from the normal fluorescent state to the ICT state region is very small. Comparison to the situation in the 1-methyl-derivative NMC6 suggests that a large alkyl substituent makes the preferably planar normal fluorescent state energetically unfavorable compared to the ICT state and thus promotes the occurrence of dual fluorescence. [ABSTRACT FROM AUTHOR]

The recently developed singles-and-doubles linear-r12 corrected coupled-cluster model CCSD(R12) has been extended by inclusion of triples corrections in exactly the same manner as in the popular CCSD(T) model. The resulting model is denoted CCSD(T)(R12). An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation to calculate the three- and four-electron integrals needed in the linear-r12 Ansatz. CCSD(T)(R12) reaction energies are calculated for a test set of 15 chemical reactions involving 23 small molecules. The CCSD(T)(R12), CCSD(R12), and MP2-R12 results are compared with experimental data obtained by correcting experimental enthalpies of reaction for zero-point vibrational energies and finite temperature contributions. Conventional MP2, CCSD, and CCSD(T) results are presented for comparison. An estimate of the basis set limit is obtained by an aug-cc-pV(Q + d)Z/aug-cc-pV(5 + d)Z CCSD(T) extrapolation for a subset of 12 reactions. All CCSD(T) results are compared with the extrapolated values, and the errors are analyzed for the CCSD(T) and CCSD(T)(R12) models in various basis sets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [ABSTRACT FROM AUTHOR]

4-(N-N-Dimethyl-amino)benzonitrile (DMABN) is a prototype molecule for dual fluorescence. The anomalous emission has been attributed to an intramolecular charge-transfer (ICT) state, and the structure of the latter is still subject to some controversy. We applied a recently developed analytical gradient code for the approximate coupled-cluster singles-and-doubles method CC2 in combination with accurate basis sets to address this problem. Fully optimized excited state structures are presented for the ICT state and the so-called locally excited state, and recent transient IR and Raman measurements on the excited states are interpreted by means of calculated harmonic frequencies. Strong evidence is found for an electronic decoupling of the phenyl and the dimethyl-amino moiety, resulting in a minimum structure for the Id state with a twisted geometry. In contrast to previous findings, the structure of this state is, at least in the gas phase, not C2v symmetric but distorted towards Cs symmetry. The distortion coordinate is a pyramidalization of the phenyl carbon atom carrying the dimethyl-amino group. The results from the CC2 model are supported by single-point calculations using more elaborate coupled-cluster models (CCSD, CCSDR(3)) and by CASSCF calculations. [ABSTRACT FROM AUTHOR]

Second virial coefficients for the density dependence of a number of electric properties are calculated for neon gas. Employing an accurate CCSD(T) potential for the Ne 2 van der Waals dimer and interaction-induced electric dipole polarizabilities and hyperpolarizabilities obtained from CCSD response theory, we evaluated the dielectric, refractivity, Kerr and ESHG second virial coefficients using both a semiclassical and a quantum statistical approach. The results cover a wide range of temperatures and are expected to be more reliable than the available experimental and empirical data. Quantum effects are found to be important only for temperatures below 100 K. The frequency-dependence of the refractivity virial coefficient is found to be small, but not negligible. For frequencies in the visible region it accounts for a few percent of the final results. For the ESHG virial coefficient of neon, frequency dependence is found to be very important, accounting for 20-25% of the second virial coefficient at the typical frequencies employed in experiments. [ABSTRACT FROM AUTHOR]

Accuracy and efficiency of the resolution of the identity approximation in second-order Møller–Plesset perturbation theory (RI-MP2) are reassessed in the light of the new MP2 code by Pulay et al. It is demonstrated that with the RI approximation considerable computational savings can be achieved, especially for larger basis sets of triple-zeta and higher quality. The error introduced by the RI approximation has to be viewed in comparison with the one-electron basis set error. It is shown that this error is insignificant if optimized auxiliary basis sets are used. [Copyright &y& Elsevier]

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]

The adsorption of N2 on the rutile TiO2 (110) surface in the limit of low coverage has been studied as a prototype example for the adsorption of non-polar molecules on strongly ionic oxide surfaces. We employed for this study an embedded cluster ansatz in combination with density functional theory and wavefunction methods. Both, clusters saturated with hydrogen atoms and electrostatically embedded clusters have been applied and methods and basis sets have been varied to test their reliability and accuracy for describing the electrostatic potential on the surface and its interaction with the non-polar N2 molecule. Quantum clusters consisting of up to 342 atoms have been used to converge the results with respect to the cluster size. For electrostatically embedded clusters, the convergence can considerably be enhanced by optimizing the charges for the point charge embedding. On the rutile (110) surface an accurate account of the long ranging interaction of the adsorbate with the bridging oxygen atoms is important for quantitative adsorption energies of weakly bound molecules. In addition the geometric relaxation of the surface has a marked influence on the results, whereas the basis set-dependence is small. Of all methods investigated (HF, DFT/PBE, DFT/B3LYP, MP2), only MP2 and DFT/B3LYP were able to describe the adsorption of N2 on the rutile surface properly. After including the zeropoint vibrational energy, the calculated adsorption energy is close to experimental results. The approach is thus promising for future investigations on adsorption energies and structures of non-polar molecules on ionic oxide surfaces. [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 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 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]

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]

We have measured pump/probe photoelectron spectra of mass-selected, near room temperature C60- in the gas phase. The lifetime of the vibrationally excited B-(2Eg) state at a calculated energy of 1.26 eV was found to be τ=2.2±0.2 ps. The dominant decay process corresponds to intramolecular radiationless transitions into ground state C60-. This is in contrast to C60 for which pumping at the absorption onset (1.95 eV) leads to predominantly intersystem crossing. [ABSTRACT FROM AUTHOR]

A simplified singles-and-doubles linear-r12 corrected coupled-cluster model, denoted CCSD(R12), is proposed and compared with the complete singles-and-doubles linear-r12 coupled-cluster method CCSD-R12. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation to calculate three-electron integrals needed in the linear-r12 Ansatz. Basis-set convergence is investigated for a selected set of atoms and small molecules. In a large basis, the CCSD(R12) model provides an excellent approximation to the full linear-r12 energy contribution, whereas the magnitude of this contribution is significantly overestimated at the level of second-order perturbation theory. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A preliminary implementation of a gradient for MP2 based on the pair natural orbital approximation (PNO–MP2) is presented. The accuracy of the PNO approximation for geometries is investigated by comparing bond lengths and bond angles of the PNO–MP2 structures with results from canonical MP2. Special emphasis is put on the optimisation of weakly bound complexes, such as differently sized water clusters. It is found that the error introduced by the PNO approximation is already for moderate PNO thresholds negligible compared to the inherent error of MP2. However, too loose PNO thresholds lead to convergence difficulties in geometry optimisations. This is observed in particular for floppy groups as, for example, methyl groups with low rotational barriers. Compared to optimisations with canonical MP2, the convergence thresholds have to be mainly energy and less coordinate based to comply with the slight roughness of the potential energy surface which is introduced by the PNO selection. [ABSTRACT FROM AUTHOR]

The excited state dipole moments of two positional isomers of dicyanobenzene have been determined from thermochromic shifts of the absorption and fluorescence emission spectra in ethyl acetate solution and compared to the results of ab initio calculations. We found that the dipole moments of excited states from thermochromic shifts closely resemble the ab initio values of the isolated molecule, while the results of conductor-like screening model (COSMO) using the same wave function model as for the isolated molecule, shows considerable deviations from the experimental values. It is shown that the dipole moments of the two cyano groups add up vectorially for both the ground and excited states. • Dipole moment of two isomeric dicyanobenzenes determined in ground and excited state from thermochromic shifts. • Comparison of the experimental results to SCS-CC2 calculations shows a very good agreement for excited state dipole moments of the isolated molecules. • Bad agreement with the results of COSMO calculations. • Additivity rule for dipole increments works in the ground state and the excited state. [Display omitted] [ABSTRACT FROM AUTHOR]

Oxygen functional groups (OFGs) within char play an important role during char burnout. They either already exist in the solid fuel and facilitate initiation reactions or they are formed as intermediates that open up fast reaction pathways with low barriers. This study aims to provide an atomistic-level understanding of the evolution of OFGs during char burnout. One of the major motivations behind this study is to provide functional group-specific reaction mechanisms which can be used to develop predictive physicochemical models of char oxidation. For our investigation of char burnout reactions at the OFGs, we use an automated reaction discovery tool based on reactive molecular dynamics simulations and quantum mechanical refinement of the reactions. The model OFGs comprise aldehydes, carboxylic acids, alcohols, anhydrides, quinones, furans, dioxins, pyrones, and lactones. We observe that radicals play an important role in initiating the combustion of these species. OFGs perturb the aromaticity of carbon rings and facilitate their opening and the decomposition into smaller carbon-containing species, such as CO, CO 2 , formyl radicals and formaldehyde, leaving behind free radical sites, which can further react with less reactive gas-phase species such as O 2. [Display omitted] • Automated workflow for atomistic simulation and refinement of combustion reactions. • Oxygen-containing functional groups facilitate the formation of reactive radicals. • Oxygen-heteroatoms in aromatic rings facilitate break-down of aromatic frameworks. • Reaction rates for decomposition of a variety of oxygen functional groups obtained. [ABSTRACT FROM AUTHOR]

In this study, we predict vibronic two-photon absorption (TPA) spectra for 4-nitroaniline in vacuo. The simulations are performed using density functional theory and the approximate second-order coupled-cluster singles and doubles model CC2. Thereby we also demonstrate the possibility of simulations of vibronic TPA spectra with ab initio wavefunction methods that include electron correlation for medium-sized systems. A special focus is put on the geometric derivatives of the second-order transition moment and the dipole moment difference between the charge-transfer excited state and the ground state. The results of CC2 calculations bring new insight into the vibronic coupling mechanism in TPA spectra of 4-nitroniline and demonstrate that the mixed term is quite large and that it also exhibits a negative interference with the Franck-Condon contribution. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We present an implementation of pair natural orbital second-order Møller–Plesset perturbation theory with computational costs that scale only cubically with the system size. The low cost-scaling is achieved by combining a hybrid approach, where the pair natural orbitals are build from orbital-specific virtuals OSVs, with an iterative block Davidson algorithm for solving the equations for OSVs. We thereby avoid a complete diagonalisation of amplitude matrices and the explicit construction of the corresponding exchange integral matrices. This reduces the cost-scaling for the generation of the OSVs and of the pair natural orbitals towithouta prioriassumptions about locality. The costs can be further reduced by combining the approach with a local resolution-of-the-identity approximation for the exchange integrals. The errors introduced by these approximations are negligible and do not affect the final accuracy of the correlation energy. Test calculations on a set of organic and inorganic molecules demonstrate that the additional errors are at least one order of magnitude smaller than the truncation error for the pair natural orbital space and that the accuracies for all steps can be controlled by a single threshold parameter. Calculations on glycine chainswithn= 1, 2, 4, 8, 16, 32 in the aug-cc-pVTZ basis set reveal an early break even point between the-scaling and the non-iterative-scaling implementation that uses a full diagonalisation and with canonical RI-MP2. We present applications to systems, which are of interest in the field of nano machines: afullerene acceptor system with over 8000 basis functions and a foldamer with nearly 8000 basis functions. [ABSTRACT FROM PUBLISHER]

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]