More Stable Template Localization for an Incremental Focal-Point Approach-Implementation and Application to the Intramolecular Decomposition of Tris-perfluoro-tert-butoxyalane.

We present a new implementation of the template localization for the fully automated and parallizable incremental method, which excludes failures of this important step within the domain-specific basis set approach and thus ensures a higher reliability of the scheme, preserving its very high accuracy. Furthermore, we combine our method with an efficient focal-point ansatz to reach the complete basis set limit and carefully assess this approach for the first time with regard to reaction energies. For a test set of 51 reactions the incremental focal-point method with a basis set of moderate size provides a very high accuracy with respect to the complete basis set limit. That way, we are finally able to apply the scheme as a benchmark method (e.g., for density functionals) in the context of a relevant chemical topic, the intramolecular decomposition of tris-perfluoro-tert-butoxyalane (43 heavy atoms, 352 electrons).

Combining Accuracy and Efficiency: An Incremental Focal-Point Method Based on Pair Natural Orbitals.

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

Kinetics of Electrophilic Alkylations of Barbiturate and Thiobarbiturate Anions.

Second-order rate constants (k2) of the reactions of various barbiturate anions such as the parent barbiturate, 1,3-dimethylbarbiturate, 2-thiobarbiturate, and 1,3-diethyl-2-thiobarbiturate with diarylcarbenium ions and Michael acceptors have been determined in dimethyl sulfoxide solution at 20 °C. The reactivity parameters N and sN of the barbiturate anions were derived from the linear plots of log k2 versus the electrophilicity parameters E of these reference electrophiles, according to the linear-free-energy relationship log k2 (20 °C) = sN (E + N). Several reactions of these nucleophiles with benzylidenemalononitriles and quinone methides proceeded with reversible formation of the new C-C-bond followed by rate-determining proton shift. No evidence for initial attack of the electrophiles at the enolate oxygens of these nucleophiles was found by the kinetic measurements, in line with quantum chemical DFT calculations, which showed that in all cases C-attack is kinetically and thermodynamically preferred over O-attack. The nucleophilic reactivities of barbiturate anions were compared with those of structurally related carbanions, e.g., Meldrum's acid and dimedone anions.

Molecular Dipole Moments within the Incremental Scheme Using the Domain-Specific Basis-Set Approach.

We present the first implementation of the fully automated incremental scheme for CCSD unrelaxed dipole moments using the domain-specific basis-set approach. Truncation parameters are varied, and the accuracy of the method is statistically analyzed for a test set of 20 molecules. The local approximations introduce small errors at second order and negligible ones at third order. For a third-order incremental CCSD expansion with a CC2 error correction, a cc-pVDZ/SV domain-specific basis set (tmain = 3.5 Bohr), and the truncation parameter f = 30 Bohr, we obtain a mean error of 0.00 mau (-0.20 mau) and a standard deviation of 1.95 mau (2.17 mau) for the total dipole moments (Cartesian components of the dipole vectors). By analyzing incremental CCSD energies, we demonstrate that the MP2 and CC2 error correction schemes are an exclusive correction for the domain-specific basis-set error. Our implementation of the incremental scheme provides fully automated computations of highly accurate dipole moments at reduced computational cost and is fully parallelized in terms of the calculation of the increments. Therefore, one can utilize the incremental scheme, on the same hardware, to extend the basis set in comparison to standard CCSD and thus obtain a better total accuracy.

Understanding Stacking Interactions between an Aromatic Ring and Nucleobases in Aqueous Solution: Experimental and Theoretical Study.

Stacking interactions between aromatic compounds and nucleobases are crucial in recognition of nucleotides and nucleic acids, but a comprehensive understanding of the strength and selectivity of these interactions in aqueous solution has been elusive. To this end, model complexes have been designed and analyzed by experiment and theory. For the first time, stacking free energies between five nucleobases and anthracene were determined experimentally from thermodynamic double mutant cycles. Three different experimental methods were proposed and evaluated. The dye prefers to bind nucleobases in the order (kcal/mol): G (1.3) > T (0.9) > U (0.8) > C (0.5) > A (0.3). The respective trend of interaction free energies extracted from DFT calculations correlates to that obtained experimentally. Analysis of the data suggests that stacking interactions dominate over hydrophobic effects in an aqueous solution and can be predicted with DFT calculations.

Optimized Basis Sets for the Environment in the Domain-Specific Basis Set Approach of the Incremental Scheme.

Minimal basis sets, denoted DSBSenv, based on the segmented basis sets of Ahlrichs and co-workers have been developed for use as environmental basis sets for the domain-specific basis set (DSBS) incremental scheme with the aim of decreasing the CPU requirements of the incremental scheme. The use of these minimal basis sets within explicitly correlated (F12) methods has been enabled by the optimization of matching auxiliary basis sets for use in density fitting of two-electron integrals and resolution of the identity. The accuracy of these auxiliary sets has been validated by calculations on a test set containing small- to medium-sized molecules. The errors due to density fitting are about 2-4 orders of magnitude smaller than the basis set incompleteness error of the DSBSenv orbital basis sets. Additional reductions in computational cost have been tested with the reduced DSBSenv basis sets, in which the highest angular momentum functions of the DSBSenv auxiliary basis sets have been removed. The optimized and reduced basis sets are used in the framework of the domain-specific basis set of the incremental scheme to decrease the computation time without significant loss of accuracy. The computation times and accuracy of the previously used environmental basis and that optimized in this work have been validated with a test set of medium- to large-sized systems. The optimized and reduced DSBSenv basis sets decrease the CPU time by about 15.4% and 19.4% compared with the old environmental basis and retain the accuracy in the absolute energy with standard deviations of 0.99 and 1.06 kJ/mol, respectively.

Quantum cluster equilibrium model of N-methylformamide-water binary mixtures.

The established quantum cluster equilibrium (QCE) approach is refined and applied to N-methylformamide (NMF) and its aqueous solution. The QCE method is split into two iterative cycles: one which converges to the liquid phase solution of the QCE equations and another which yields the gas phase. By comparing Gibbs energies, the thermodynamically stable phase at a given temperature and pressure is then chosen. The new methodology avoids metastable solutions and allows a different treatment of the mean-field interactions within the gas and liquid phases. These changes are of crucial importance for the treatment of binary mixtures. For the first time in a QCE study, the cis-trans-isomerism of a species (NMF) is explicitly considered. Cluster geometries and frequencies are calculated using density functional theory (DFT) and complementary coupled cluster single point energies are used to benchmark the DFT results. Independent of the selected quantum-chemical method, a large set of clusters is required for an accurate thermodynamic description of the binary mixture. The liquid phase of neat NMF is found to be dominated by the cyclic trans-NMF pentamer, which can be interpreted as a linear trimer that is stabilized by explicit solvation of two further NMF molecules. This cluster reflects the known hydrogen bond network preferences of neat NMF.

First UHF Implementation of the Incremental Scheme for Open-Shell Systems.

The incremental scheme makes it possible to compute CCSD(T) correlation energies to high accuracy for large systems. We present the first extension of this fully automated black-box approach to open-shell systems using an Unrestricted Hartree-Fock (UHF) wave function, extending the efficient domain-specific basis set approach to handle open-shell references. We test our approach on a set of organic and metal organic structures and molecular clusters and demonstrate standard deviations from canonical CCSD(T) values of only 1.35 kJ/mol using a triple ζ basis set. We find that the incremental scheme is significantly more cost-effective than the canonical implementation even for relatively small systems and that the ease of parallelization makes it possible to perform high-level calculations on large systems in a few hours on inexpensive computers. We show that the approximations that make our approach widely applicable are significantly smaller than both the basis set incompleteness error and the intrinsic error of the CCSD(T) method, and we further demonstrate that incremental energies can be reliably used in extrapolation schemes to obtain near complete basis set limit CCSD(T) reaction energies for large systems.

Non-covalent Interactions of CO2 with Functional Groups of Metal-Organic Frameworks from a CCSD(T) Scheme Applicable to Large Systems.

The strength of interactions between CO2 and 23 building blocks of metal-organic frameworks are reported in this paper. This theoretical study is based on an incremental, explicitly correlated coupled-cluster scheme with interference effects. This scheme allows the accurate calculation of molecular complexes such as zinc acetate (32 non-hydrogen atoms) at the CCSD(T) level, close to the basis set limit. Higher CO2 affinity for complexes with nitrogen-containing heterocycles is predicted from the calculated interaction energies. The good agreement between the interaction energies obtained from the CCSD(T) scheme and DFT-D3 is discussed.

Efficient Calculation of Accurate Reaction Energies-Assessment of Different Models in Electronic Structure Theory.

In this work we analyze the accuracy and the efficiency of different schemes to obtain the complete basis set limit for CCSD(T). It is found that composite schemes using an MP2 increment to reach the basis set limit provide high accuracy combined with high efficiency. In these composite schemes the MP2-F12/cc-pVTZ-F12 method is suitable to compute the MP2 contribution at the basis set limit. We propose to use the def2-TZVP or the TZVPP basis sets at the coupled cluster level in combination with the cc-pVTZ-F12 basis set at the MP2 level to compute reaction energies close to the basis set limit, if high accuracy methods like CCSD(T)(F12*) or 56-extrapolations are no longer feasible due to the computational effort. The standard deviation of CCSD(T)+ΔMP2/cc-pVTZ-F12/def2-TZVP and CCSD(T)+ΔMP2/cc-pVTZ-F12/TZVPP is found to be only 0.93 and 0.65 kJ/mol for a test set of 51 closed shell reactions. Furthermore, we provide a comprehensive list of different computational strategies to obtain CCSD(T) reaction energies with an efficiency and accuracy measure. Finally we analyze how different choices of the exponent in the correlation factor (γ) change the results when using explicitly correlated methods. The statistical results in this study are based on a set of 51 reaction energies in the range of 0.7 to 631.5 kJ/mol.

Rearrangement Reactions of Tritylcarbenes: Surprising Ring Expansion and Computational Investigation.

As a rule, acetylides and sulfonyl azides do not undergo electrophilic azide transfer because 1,2,3-triazoles are usually formed. We show now that treatment of tritylethyne with butyllithium followed by exposure to 2,4,6-triisopropylbenzenesulfonyl azide leads to products that are easily explained through the generation of short-lived tritylethynyl azide and its secondary product cyanotritylcarbene. Furthermore, it is demonstrated that tritylcarbenes generally do not produce triphenylethenes exclusively, as was stated in the literature. Instead, these carbenes always yielded also (diphenylmethylidene)cycloheptatrienes (heptafulvenes) as side products. This result is supported by static DFT, coupled cluster, and ab initio molecular dynamics calculations. From these investigations, the fused bicyclobutane intermediate was found to be essential for heptafulvene formation. Although the bicyclobutane is also capable of rearranging to the triphenylethene product, only the heptafulvene pathway is reasonable from the energetics. The ethene is formed straight from cyanotritylcarbene.

4,5-Dihydro-1,2,3-oxadiazole: A Very Elusive Key Intermediate in Various Important Chemical Transformations.

4,5-Dihydro-1,2,3-oxadiazoles are postulated to be key intermediates in the industrial synthesis of ketones from alkenes, in the alkylation of DNA in vivo, and in the decomposition of N-nitrosoureas; they are also a subject of great interest for theoretical chemists. In the presented report, the formation of 4,5-dihydro-1,2,3-oxadiazole and the subsequent decay into secondary products have been studied by NMR monitoring analysis. The elusive properties evading characterization have now been confirmed by (1) H, (13) C, and (15) N NMR spectroscopy, and relevant 2D experiments at very low temperatures. Our experiments with suitably substituted N-nitrosoureas using thallium(I) alkoxides as bases under apolar conditions answer important questions on the existence and the secondary products of 4,5-dihydro-1,2,3-oxadiazole.

Incremental evaluation of coupled cluster dipole polarizabilities.

In this work we present the first implementation of the incremental scheme for coupled cluster linear-response frequency-dependent dipole polarizabilities. The implementation is fully automated and makes use of the domain-specific basis set approach. The accuracy of the approach is determined on the basis of a test suite of 47 molecules and small clusters. The local approximation in the coupled cluster singles and doubles polarizability exhibits a mean error of 0.02% and a standard deviation of 0.32% when using a third-order incremental expansion. With the proposed approach, it is possible to compute polarizabilities with larger basis sets compared to the canonical implementation and thus it is possible to obtain higher total accuracy. The incremental scheme yields the smallest errors for weakly-bound and quasi-linear systems, while two- and three-dimensional (cage-like) structures exhibit somewhat larger errors as compared to the full test set.

New accurate benchmark energies for large water clusters: DFT is better than expected.

In this work, we use MP2 and coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] as well as their corresponding explicitly correlated (F12) counterparts to compute the interaction energies of water icosamers. The incremental scheme is used to compute benchmark energies at the CCSD(T)/CBS(45) and CCSD(T)(F12*)/cc-pVQZ-F12 level of theory. The four structures, dodecahedron, edge sharing, face sharing, and fused cubes, are part of the WATER27 test set and therefore, highly accurate interaction energies are required. All methods applied in this work lead to new benchmark energies for these four systems. To obtain these values, we carefully analyze the convergence of the interaction energies with respect to the basis set. Furthermore, we investigate the influence of the basis set superposition error and the core-valence correlation. The interaction energies are: dodecahedron -198.6 kcal/mol, edge sharing -209.7 kcal/mol, face sharing -208.0 kcal/mol, and fused cubes -208.0 kcal/mol. For water clusters, we recommend to use the PW6B95 density functional of Truhlar in combination with Grimme's dispersion correction (D3), as the mean absolute error is 0.9 and the root mean-squared deviation is only 1.4 kcal/mol.

Water 26-mers Drawn from Bulk Simulations: Benchmark Binding Energies for Unprecedentedly Large Water Clusters and Assessment of the Electrostatically Embedded Three-Body and Pairwise Additive Approximations.

It is important to test methods for simulating water, but small water clusters for which benchmarks are available are not very representative of the bulk. Here we present benchmark calculations, in particular CCSD(T) calculations at the complete basis set limit, for water 26-mers drawn from Monte Carlo simulations of bulk water. These clusters are large enough that each water molecule participates in 2.5 hydrogen bonds on average. The electrostatically embedded three-body approximation with CCSD(T) embedded dimers and trimers reproduces the relative binding energies of eight clusters with a mean unsigned error (MUE, kcal per mole of water molecules) of only 0.009 and 0.015 kcal for relative and absolute binding energies, respectively. Using only embedded dimers (electrostatically embedded pairwise approximation) raises these MUEs to 0.038 and 0.070 kcal, and computing the energies with the M11 exchange-correlation functional, which is very economical, yields errors of only 0.029 and 0.042 kcal.

Nitrogen and Sulfur Compounds in Atmospheric Aerosols: A New Parametrization of Polarized Molecular Orbital Model Chemistry and Its Validation against Converged CCSD(T) Calculations for Large Clusters.

The parametrization of the polarized molecular orbital (PMO) method, which is a neglect-of-diatomic-differential-overlap (NDDO) semiempirical method that includes polarization functions on hydrogens, is extended to include the constituents that dominate the nucleation of atmospheric aerosols, including ammonia, sulfuric acid, and water. The parametrization and validation are based mainly on CCSD(T)/CBS results for atmospheric clusters composed of sulfuric acid, dimethylamine, and ammonia and on M06-2X exchange-correlation functional calculations for other constituents of the atmospheric aerosols. The resulting model, called PMO2a, is parametrized for molecules containing any type of H, C, or O, amino or ammonium N, and S atoms bonded to O. The new method gives greatly improved electric polarization compared to any other member of the family of NDDO methods. In addition, PMO2a is shown to outperform previous NDDO methods for atomization energies and atmospheric aerosol reaction energies; therefore, its use can be recommended for realistic simulations.

Metal-metal interaction in Fischer carbene complexes: a study of ferrocenyl and biferrocenyl tungsten alkylidene complexes.

A series of ferrocenyl (Fc = ferrocenyl; fc = ferrocen-1,1'-diyl) and biferrocenyl (Bfc = 1',1″-biferrocenyl; bfc = 1',1″-biferrocen-1,1‴-diyl) mono- and biscarbene tungsten(0) complexes of the type [(CO)5W═C(OMe)R] (1, R = Fc; 3, R = Bfc) and [(CO)5W═C(OMe)-R'-(OMe)C═W(CO)5] (2, R' = fc; 4, R' = bfc) were synthesized according to the classical synthetic methodology by reacting W(CO)6 with LiR (R = Fc, fc, bfc), followed by a subsequent alkylation using methyl trifluoromethanesulfonate. Electrochemical investigations were carried out on these complexes to get a closer insight into the electronic properties of 1-4. The ferrocenyl and biferrocenyl moieties in 1-4 show reversible one-electron redox events. It was further found that the Fischer carbene unit is reducible in an electrochemical one-electron transfer process. For the tungsten carbonyl moieties, irreversible oxidation processes were found. In addition, charge transfer studies were performed on 1-4 using in situ UV-vis-NIR and infrared spectroelectrochemical techniques. During the UV-vis-NIR investigations, typical low energy transitions for the mixed-valent biferrocenyl unit were found. A further observed high energy NIR absorption is attributed to a metal-metal charge transfer transition between the tungsten carbonyl fragment and the ferrocenyl/biferrocenyl group in the corresponding oxidized states, which can be described as class II systems according to Robin and Day. This assignment was verified by infrared spectroelectrochemical studies. The electrochemical investigations are supported by density functional theory calculations. The structural properties of 1-4 in the solid state were investigated by single-crystal X-ray diffraction studies showing no substituent effects on bond lengths and angles. The biferrocenyl derivatives exhibit syn-conformation of the ferrocenyl and carbene building blocks.

Carbene formation in ionic liquids: spontaneous, induced, or prohibited?

We present a theoretical study of carbene formation from the 1-ethyl-3-methylimidazolium acetate ionic liquid in the absence and presence of CO2 in gas and liquid phase. Although CO2 physisorption constitutes a precursory step of chemisorption (the CO2's reaction with carbenes, which forms from cations via proton abstraction by anions), it also enables a very stable CO2-anion associate. However, this counteracts the chemical absorption by reducing the basicity of the anion and the electrophilicity of the CO2, which is reflected by charge transfer. Accordingly, the observable carbene formation in the gas phase is hindered in the presence of CO2. In the neat liquid, the carbene formation is also suppressed by the charge screening compared to the case of the gas phase; nevertheless, indications for carbene incidents appear. Interestingly, in the CO2-containing liquid we detect more carbene-like incidents than in the neat one, which is caused by the way CO2 is solvated. Despite the weakness of the CO2-cation interaction, the CO2-anion associate is distorted by cations, which can be seen in longer associate distances and reduced "binding" energies. While the single solvating anion is shifted away from CO2, many more solvating cations approach it compared to the case of the gas phase. This leads to the conclusion that while the ionic liquid effect stabilizes charged species, introducing neutral species such as CO2 provides an opposite trend, leading to an inverse ionic liquid effect with the facilitation of carbene formation and thus of chemical absorption.

Incremental CCSD(T)(F12)|MP2-F12-A Method to Obtain Highly Accurate CCSD(T) Energies for Large Molecules.

In this work, we apply the recently proposed MP2 correction to incremental energies within the domain-specific basis set approach to incrementally expanded CCSD(T)(F12) energies. The approach is tested for a set of 27 molecules with different electronic structures including water clusters, aqua complexes, aliphatic hydrocarbons, alkenes, alkynes, aromatic systems, and amino acids. The root mean squared deviation of the absolute energies with respect to the standard calculation is 1.7 kJ/mol, the mean absolute deviation is 1.2 kJ/mol, and the range is 4.7 kJ/mol. The wall time of the computations is reduced due to the application of a doubly parallel strategy-the independent coupled cluster calculations are performed on up to 70 nodes in parallel, and in addition the computations on one node are performed with the SMP-parallelized coupled cluster code in TURBOMOLE. Using this strategy, we can perform computations in minutes or hours, instead of days or months. Applying the proposed scheme enables us to routinely treat systems with 50 atoms at the CCSD(T)(F12) level in combination with appropriate basis sets to obtain nearly CBS accuracy. Also, larger systems are still feasible on a standard cluster as demonstrated for H3O(+)(H2O)25Cl(-) with 80 atoms.

Incremental CCSD(T)(F12*)|MP2: A Black Box Method To Obtain Highly Accurate Reaction Energies.

In this work we present a new partitioning scheme for the incremental approach in combination with the efficient (F12*) approximation for explicitly correlated coupled cluster (J. Chem. Phys. 2010, 132, 231102). Furthermore we establish a black-box truncation scheme which provides chemical accuracy for the absolute energies of 81 molecules and 51 reaction energies. The errors in the absolute CCSD(T)/cc-pVTZ-F12 energies due to the local approximations are characterized by mean = -0.24 kJ/mol, σ = 0.49 kJ/mol, mae = 0.37 kJ/mol, rmsd = 0.54 kJ/mol, and range = 3.63 kJ/mol. For the reaction energies we find mean = 0.07 kJ/mol, σ = 0.49 kJ/mol, mae = 0.33 kJ/mol, rmsd = 0.49 kJ/mol, and range = 2.40 kJ/mol. On the basis of these findings it is evident that the incremental scheme provides highly accurate CCSD(T) energies of benchmark quality.