Conformational and state-specific effects in reactions of 2,3-dibromobutadiene with Coulomb-crystallized calcium ions.

Recent advances in experimental methodology enabled studies of the quantum-state- and conformational dependence of chemical reactions under precisely controlled conditions in the gas phase. Here, we generated samples of selected gauche and s-trans 2,3-dibromobutadiene (DBB) by electrostatic deflection in a molecular beam and studied their reaction with Coulomb crystals of laser-cooled Ca+ ions in an ion trap. The rate coefficients for the total reaction were found to strongly depend on both the conformation of DBB and the electronic state of Ca+. In the (4p)2P1/2 and (3d)2D3/2 excited states of Ca+, the reaction is capture-limited and faster for the gauche conformer due to long-range ion-dipole interactions. In the (4s)2S1/2 ground state of Ca+, the reaction rate for s-trans DBB still conforms with the capture limit, while that for gauche DBB is strongly suppressed. The experimental observations were analysed with the help of adiabatic capture theory, ab initio calculations and reactive molecular dynamics simulations on a machine-learned full-dimensional potential energy surface of the system. The theory yields near-quantitative agreement for s-trans-DBB, but overestimates the reactivity of the gauche-conformer compared to the experiment. The present study points to the important role of molecular geometry even in strongly reactive exothermic systems and illustrates striking differences in the reactivity of individual conformers in gas-phase ion-molecule reactions.

The C(3P) + O2(3Σg-) → CO2 ↔ CO(1Σ+) + O(1D)/O(3P) reaction: thermal and vibrational relaxation rates from 15 K to 20 000 K.

Thermal rates for the C(3P) + O2(3Σg-) ↔ CO(1Σ+)+ O(1D)/O(3P) reaction are investigated over a wide temperature range based on quasi classical trajectory (QCT) simulations on 3-dimensional, reactive potential energy surfaces (PESs) for the 1A', (2)1A', 1A'', 3A' and 3A'' states. These five states are the energetically low-lying states of CO2 and their PESs are computed at the MRCISD+Q/aug-cc-pVTZ level of theory using a state-average CASSCF reference wave function. Analysis of the different electronic states for the CO2 → CO + O dissociation channel rationalizes the topography of this region of the PESs. The forward rates from QCT simulations match measurements between 15 K and 295 K whereas the equilibrium constant determined from the forward and reverse rates is consistent with that derived from statistical mechanics at high temperature. Vibrational relaxation, O + CO(ν = 1,2) → O + CO(ν = 0), is found to involve both, non-reactive and reactive processes. The contact time required for vibrational relaxation to take place is τ ≥ 150 fs for non-reacting and τ ≥ 330 fs for reacting (oxygen atom exchange) trajectories and the two processes are shown to probe different parts of the global potential energy surface. In agreement with experiments, low collision energy reactions for the C(3P) + O2(3Σg-, ν = 0) → CO(1Σ+) + O(1D) lead to CO(1Σ+, ν' = 17) with an onset at Ec ∼ 0.15 eV, dominated by the 1A' surface with contributions from the 3A' surface. Finally, the barrier for the COA(1Σ+) + OB(3P) → COB(1Σ+) + OA(3P) atom exchange reaction on the 3A' PES yields a barrier of ∼7 kcal mol-1 (0.300 eV), consistent with an experimentally reported value of 6.9 kcal mol-1 (0.299 eV).

The N(4S) + O2(X3Σ) ↔ O(3P) + NO(X2Π) reaction: thermal and vibrational relaxation rates for the 2A', 4A' and 2A'' states.

The kinetics and vibrational relaxation of the N(4S) + O2(X3Σ-g) ↔ O(3P) + NO(X2Π) reaction is investigated over a wide temperature range based on quasiclassical trajectory simulations on 3-dimensional potential energy surfaces (PESs) for the lowest three electronic states. Reference energies at the multi reference configuration interaction level are represented as a reproducing kernel and the topology of the PESs is rationalized by analyzing the CASSCF wavefunction of the relevant states. The forward rate matches one measurement at 1575 K and is somewhat lower than the high-temperature measurement at 2880 K whereas for the reverse rate the computations are in good agreement for temperatures between 3000 and 4100 K. The temperature-dependent equilibrium rates are consistent with results from JANAF and CEA results. Vibrational relaxation rates for O + NO(ν = 1) → O + NO(ν = 0) are consistent with a wide range of experiments. This process is dominated by the dynamics on the 2A' and 4A' surfaces which both contribute similarly up to temperatures T ∼ 3000 K, and it is found that vibrationally relaxing and non-relaxing trajectories probe different parts of the potential energy surface. The total cross section depending on the final vibrational state monotonically decreases which is consistent with early experiments and previous simulations but at variance with other recent experiments which reported an oscillatory cross section.

N3 +: Full-dimensional ground state potential energy surface, vibrational energy levels, and dynamics.

The fundamental vibrational frequencies and higher vibrationally excited states for the N3 + ion in its electronic ground state have been determined from quantum bound state calculations on three-dimensional potential energy surfaces (PESs) computed at the coupled-cluster singles and doubles with perturbative triples [CCSD(T)]-F12b/aug-cc-pVTZ-f12 and multireference configuration interaction singles and doubles with quadruples (MRCISD+Q)/aug-cc-pVTZ levels of theory. The vibrational fundamental frequencies are 1130 cm-1 (ν1, symmetric stretch), 807 cm-1 (ν3, asymmetric stretch), and 406 cm-1 (ν2, bend) on the higher-quality CCSD(T)-F12b surface. Bound state calculations based on even higher level PESs [CCSD(T)-F12b/aug-cc-pVQZ-f12 and MRCISD+Q-F12b/aug-cc-pVTZ-f12] confirm the symmetric stretch fundamental frequency as ∼1130 cm-1. This compares with an estimated frequency from experiment at 1170 cm-1 and previous calculations [Chambaud et al., Chem. Phys. Lett. 231, 9-12 (1994)] at 1190 cm-1. The remaining disagreement with the experimental frequency is attributed to uncertainties associated with the widths and positions of the experimental photoelectron peaks. Analysis of the reference complete active space self-consistent field wave function for the MRCISD+Q calculations provides deeper insight into the shape of the PES and lends support for the reliability of the Hartree-Fock reference wave function for the coupled cluster calculations. According to this, N3 + has a mainly single reference character in all low-energy regions of its electronic ground state (3A″) PES.

Assessment of DFT for endohedral complexes' dipole moment: PNO-LCCSD-F12 as a reference method.

We present a systematic evaluation of the performance of a wide range of exchange-correlation functionals and related dispersion correction schemes for the computation of dipole moments of endohedral complexes, formed through the encapsulation of an AB molecule (AB = LiF, HCl) inside carbon nanotubes (CNTs) of different diameter. The consistency and accuracy of (i) generalized gradient approximation, (ii) meta GGA, (iii) global hybrid, and (iv) range-separated hybrid density functionals are assessed. In total, 37 density functionals are tested. The results obtained using the highly accurate pair natural orbitals based explicitly correlated local coupled cluster singles doubles (PNO-LCCSD-F12) method of Werner and co-workers [Schwilk et al., J. Chem. Theory Comput., 2017, 13, 3650; Ma et al., J. Chem. Theory Comput., 2017, 13, 4871] with the aug-cc-pVTZ basis set serve as a reference. The static electric dipole moment is computed via the finite field response or, when possible, as the expectation value of the dipole operator. Among others, it is shown that functionals belonging to the class of range-separated hybrids, provide results closest to the coupled cluster reference data. In particular, the ωB97X as well as the M11 functional may be considered as a promising choice for computing electric properties of noncovalent endohedral complexes. On the other hand, the worst performance was found for the functionals which do not include the Hartree-Fock exchange. The analysis of both the coupled cluster and the DFT results indicates a strong coupling of dispersion and polarization that may also explain why lower level DFT methods, as well as Hartree-Fock and MP2, cannot yield dipole moments beyond a qualitative agreement with the higher order reference data. Interestingly, the much smaller and less systematically constructed basis sets of Pople of moderate size provide results of accuracy at least comparable with the extended Dunning's aug-cc-pVTZ basis set.

Organometallic Fe-Fe Interactions: Beyond Common Metal-Metal Bonds and Inverse Mixed-Valent Charge Transfer.

The compounds [Fe(CO)3 (dRpf)]n+ , n=0, 1, 2 and dRpf=1,1'-bis(dicyclohexylphosphino)ferrocene ([1]n+ ) or 1,1'-bis(diisopropylphosphino)ferrocene ([2]n+ ), were obtained as two-step reversible redox systems by photolytic and redox reactions. The iron-iron distance decreases from about 4 Što about 3 Šon oxidation, which takes place primarily at the tricarbonyliron moiety. Whereas ferrocene oxidation is calculated to occur only in excited states, the near infrared absorptions of the mixed-valent monocations are due to an unprecedented "inverse" inter-valence charge transfer from the electron-rich iron(II) in the ferrocene backbone to the electron-deficient tricarbonyliron(I). Protonation of complex 1 results in the formation of the structurally characterized hydride [1H]BF4 , which reacts with acetone to form the dication, 12+ , and isopropanol. While the hydride [2H]BF4 was found to be unstable, protonation of 2 in acetone resulted in the clean formation of 22+, formally a hydrogen transfer.

Communication: Improved pair approximations in local coupled-cluster methods.

In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Møller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger.

Conformer-specific polar cycloaddition of dibromobutadiene with trapped propene ions.

Diels-Alder cycloadditions are efficient routes for the synthesis of cyclic organic compounds. There has been a long-standing discussion whether these reactions proceed via stepwise or concerted mechanisms. Here, we adopt an experimental approach to explore the mechanism of the model polar cycloaddition of 2,3-dibromo-1,3-butadiene with propene ions by probing its conformational specificities in the entrance channel under single-collision conditions in the gas phase. Combining a conformationally controlled molecular beam with trapped ions, we find that both conformers of the diene, gauche and s-trans, are reactive with capture-limited reaction rates. Aided by quantum-chemical and quantum-capture calculations, this finding is rationalised by a simultaneous competition of concerted and stepwise reaction pathways, revealing an interesting mechanistic borderline case.

Scalable Electron Correlation Methods. 4. Parallel Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD-F12).

We present an efficient explicitly correlated pair natural orbital local coupled cluster (PNO-LCCSD-F12) method. The method is an extension of our previously reported PNO-LCCSD approach ( Schwilk et al., J. Chem. Theory Comput. 2017 , 13 , 3650 - 3675 ). Near linear scaling with the molecular size is achieved by using pair, domain, and projection approximations, local density fitting and local resolution of the identity, and by exploiting the sparsity of the local molecular orbitals as well as of the projected atomic orbitals. The effect of the various domain approximations is tested for a wide range of chemical reactions and intermolecular interactions. In accordance with previous findings, it is demonstrated that the F12 terms significantly reduce the domain errors. The convergence of the reaction and interaction energies with respect to the parameters that determine the domain sizes and pair approximations is extensively tested. The results obtained with our default thresholds agree within a few tenths of a kcal mol-1 with the ones computed with very tight options. For cases where canonical calculations are still feasible, the relative energies of local and canonical calculations agree within similar error bounds. The PNO-LCCSD-F12 method needs only 25-40% more computer time than a corresponding PNO-LCCSD calculation while greatly improving the accuracy. Our program is well parallelized and capable of computing accurate correlation energies for molecules with more than 150 atoms using augmented triple-ζ basis sets and more than 5000 basis functions. Using several nodes of a small computer cluster, such calculations can be carried out within a few hours.

Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD).

A well-parallelized local singles and doubles coupled-cluster (LCCSD) method using pair natural virtual orbitals (PNOs) is presented. The PNOs are constructed using large domains of projected atomic orbitals (PAOs) and orbital specific virtual orbitals (OSVs). We introduce a hierarchy of close, weak, and distant pairs, based on pair energies evaluated by local Møller-Plesset perturbation theory (LMP2). In contrast to most previous implementations of LCCSD methods, the close and weak pairs are not approximated by LMP2 but treated by higher-order methods. This leads to greatly improved accuracy for large systems, in particular when long-range dispersion interactions are important. Close pair amplitudes are optimized using approximate LCCSD equations, in which slowly decaying terms that mutually cancel at long-range are neglected. For weak pairs, the same approximations are used, but in addition, the nonlinear terms are neglected (coupled electron pair approximation). Distant pairs are treated by spin-component scaled (SCS)-LMP2 using multipole approximations. For efficiency reasons, various projection approximations are also introduced. The impact of these approximations on absolute and relative energies depends on the PNO domain sizes. The errors are found to be negligible, provided that sufficiently large PNO domains are used for close and weak pairs. For the selection of these domains the usual natural orbital occupation number criterion is found to be insufficient, and an additional energy criterion is used. For extended one-dimensional systems, the computational effort of the method scales nearly linearly with the number of correlated electrons, but the linear scaling regime is usually not reached in real-life applications for three-dimensional systems. Nevertheless, due to the parallelization that is efficient up to about 100-200 CPU cores (dependent on the molecular size), accurate calculations for three-dimensional molecules with about 100 atoms and augmented triple-ζ basis sets (e.g., cc-pVTZ-F12) can be carried out in 1-3 h of elapsed time (depending on the molecular structure and the number of CPU cores, excluding the time for Hartree-Fock). The convergence of the results with respect to the thresholds and options that control the domain, pair, and projection approximations is extensively tested. Benchmark examples for several difficult and large cases are presented, which demonstrate that the errors of relative energies (e.g., reaction energies, barrier heights) caused by the pair and projection approximations can be reduced to below 1 kJ mol-1. The remaining errors are mainly caused by the finite PAO domains. The larger these are made, the more intramolecular or intermolecular basis set superposition errors are introduced, and the canonical results are approached only very slowly. This problem is eliminated in the explicitly correlated variant of our method (PNO-LCCSD-F12), which will be described in a separate paper, along with a larger set of benchmark calculations.

Scalable electron correlation methods I.: PNO-LMP2 with linear scaling in the molecular size and near-inverse-linear scaling in the number of processors.

We propose to construct electron correlation methods that are scalable in both molecule size and aggregated parallel computational power, in the sense that the total elapsed time of a calculation becomes nearly independent of the molecular size when the number of processors grows linearly with the molecular size. This is shown to be possible by exploiting a combination of local approximations and parallel algorithms. The concept is demonstrated with a linear scaling pair natural orbital local second-order Møller-Plesset perturbation theory (PNO-LMP2) method. In this method, both the wave function manifold and the integrals are transformed incrementally from projected atomic orbitals (PAOs) first to orbital-specific virtuals (OSVs) and finally to pair natural orbitals (PNOs), which allow for minimum domain sizes and fine-grained accuracy control using very few parameters. A parallel algorithm design is discussed, which is efficient for both small and large molecules, and numbers of processors, although true inverse-linear scaling with compute power is not yet reached in all cases. Initial applications to reactions involving large molecules reveal surprisingly large effects of dispersion energy contributions as well as large intramolecular basis set superposition errors in canonical MP2 calculations. In order to account for the dispersion effects, the usual selection of PNOs on the basis of natural occupation numbers turns out to be insufficient, and a new energy-based criterion is proposed. If explicitly correlated (F12) terms are included, fast convergence to the MP2 complete basis set (CBS) limit is achieved. For the studied reactions, the PNO-LMP2-F12 results deviate from the canonical MP2/CBS and MP2-F12 values by <1 kJ mol(-1), using triple-ζ (VTZ-F12) basis sets.

Dinuclear planar chiral ferrocenyl gold(I) & gold(II) complexes.

Oxidation of Au(I) in the presence of Fe(II) allowed for the synthesis of unique dinuclear ferrocenyl Au(II) complexes via the first reported enantiopure planar chiral ferrocenyl Au(I) complex. (Spectro)electrochemical studies show that oxidation at Fe(II) is favoured, but DFT studies suggest that the energy differences for oxidation of one or the other metal should be quite small.