Evangelos Miliordos

Benchmark Theoretical Study of the π–π Binding Energy in the Benzene Dimer

We establish a new estimate for the binding energy between two benzene molecules in the parallel-displaced (PD) conformation by systematically converging (i) the intra- and intermolecular geometry at the minimum, (ii) the expansion of the orbital basis set, and (iii) the level of electron correlation. The calculations were performed at the second-order Møller-Plesset perturbation (MP2) and the coupled cluster including singles, doubles, and a perturbative estimate of triples replacement [CCSD(T)] levels of electronic structure theory. At both levels of theory, by including results corrected for basis set superposition error (BSSE), we have estimated the complete basis set (CBS) limit by employing the family of Dunnings correlation-consistent polarized valence basis sets. The largest MP2 calculation was performed with the cc-pV6Z basis set (2772 basis functions), whereas the largest CCSD(T) calculation was with the cc-pV5Z basis set (1752 basis functions). The cluster geometries were optimized with basis sets up to quadruple-ζ quality, observing that both its intra- and intermolecular parts have practically converged with the triple-ζ quality sets. The use of converged geometries was found to play an important role for obtaining accurate estimates for the CBS limits. Our results demonstrate that the binding energies with the families of the plain (cc-pVnZ) and augmented (aug-cc-pVnZ) sets converge [within <0.01 kcal/mol for MP2 and <0.15 kcal/mol for CCSD(T)] to the same CBS limit. In addition, the average of the uncorrected and BSSE-corrected binding energies was found to converge to the same CBS limit much faster than either of the two constituents (uncorrected or BSSE-corrected binding energies). Due to the fact that the family of augmented basis sets (especially for the larger sets) causes serious linear dependency problems, the plain basis sets (for which no linear dependencies were found) are deemed as a more efficient and straightforward path for obtaining an accurate CBS limit. We considered extrapolations of the uncorrected (ΔE) and BSSE-corrected (ΔEcp) binding energies, their average value (ΔEave), as well as the average of the latter over the plain and augmented sets (ΔẼave) with the cardinal number of the basis set n. Our best estimate of the CCSD(T)/CBS limit for the π-π binding energy in the PD benzene dimer is De = -2.65 ± 0.02 kcal/mol. The best CCSD(T)/cc-pV5Z calculated value is -2.62 kcal/mol, just 0.03 kcal/mol away from the CBS limit. For comparison, the MP2/CBS limit estimate is -5.00 ± 0.01 kcal/mol, demonstrating a 90% overbinding with respect to CCSD(T). The spin-component-scaled (SCS) MP2 variant was found to closely reproduce the CCSD(T) results for each basis set, while scaled opposite spin (SOS) MP2 yielded results that are too low when compared to CCSD(T).

The Origin of the Reactivity of the Criegee Intermediate: Implications for Atmospheric Particle Growth

The electronic structure of the simplest Criegee intermediate, H2COO, is practically that of a closed shell. On the biradical scale (β), where 0 corresponds to the pure closed shell and 1 to a pure biradical, its β value is only 0.10, suggesting that its ground electronic state is best described as a H2C=O(δ+)-O(δ-) zwitterion. However, this picture of a nearly inert closed shell contradicts its rich reactivity in the atmosphere. It is shown that the mixing of its ground state with the first triplet excited state, which is a pure biradical state of the type H2C˙-O-O˙, is responsible for the formation of strongly bound products during reactions inducing atmospheric particle growth.

On the validity of the basis set superposition error and complete basis set limit extrapolations for the binding energy of the formic acid dimer

We report the variation of the binding energy of the Formic Acid Dimer with the size of the basis set at the Coupled Cluster with iterative Singles, Doubles and perturbatively connected Triple replacements [CCSD(T)] level of theory, estimate the Complete Basis Set (CBS) limit, and examine the validity of the Basis Set Superposition Error (BSSE)-correction for this quantity that was previously challenged by Kalescky, Kraka, and Cremer (KKC) [J. Chem. Phys. 140, 084315 (2014)]. Our results indicate that the BSSE correction, including terms that account for the substantial geometry change of the monomers due to the formation of two strong hydrogen bonds in the dimer, is indeed valid for obtaining accurate estimates for the binding energy of this system as it exhibits the expected decrease with increasing basis set size. We attribute the discrepancy between our current results and those of KKC to their use of a valence basis set in conjunction with the correlation of all electrons (i.e., including the 1s of C and O). We further show that the use of a core-valence set in conjunction with all electron correlation converges faster to the CBS limit as the BSSE correction is less than half than the valence electron/valence basis set case. The uncorrected and BSSE-corrected binding energies were found to produce the same (within 0.1 kcal/mol) CBS limits. We obtain CCSD(T)/CBS best estimates for De = - 16.1 ± 0.1 kcal/mol and for D0 = - 14.3 ± 0.1 kcal/mol, the later in excellent agreement with the experimental value of -14.22 ± 0.12 kcal/mol.

Low energy isomers of (H2O)25 from a hierarchical method based on Monte Carlo temperature basin paving and molecular tailoring approaches benchmarked by MP2 calculations

We report new global minimum candidate structures for the (H2O)25 cluster that are lower in energy than the ones reported previously and correspond to hydrogen bonded networks with 42 hydrogen bonds and an interior, fully coordinated water molecule. These were obtained as a result of a hierarchical approach based on initial Monte Carlo Temperature Basin Paving sampling of the clusters Potential Energy Surface with the Effective Fragment Potential, subsequent geometry optimization using the Molecular Tailoring Approach with the fragments treated at the second order Møller-Plesset (MP2) perturbation (MTA-MP2) and final refinement of the entire cluster at the MP2 level of theory. The MTA-MP2 optimized cluster geometries, constructed from the fragments, were found to be within <0.5 kcal/mol from the minimum geometries obtained from the MP2 optimization of the entire (H2O)25 cluster. In addition, the grafting of the MTA-MP2 energies yields electronic energies that are within <0.3 kcal/mol from the MP2 energies of the entire cluster while preserving their energy rank order. Finally, the MTA-MP2 approach was found to reproduce the MP2 harmonic vibrational frequencies, constructed from the fragments, quite accurately when compared to the MP2 ones of the entire cluster in both the HOH bending and the OH stretching regions of the spectra.

Isotopomer-selective spectra of a single intact H2O molecule in the Cs+(D2O)5H2O isotopologue: Going beyond pattern recognition to harvest the structural information encoded in vibrational spectra

We report the vibrational signatures of a single H2O molecule occupying distinct sites of the hydration network in the Cs(+)(H2O)6 cluster. This is accomplished using isotopomer-selective IR-IR hole-burning on the Cs(+)(D2O)5(H2O) clusters formed by gas-phase exchange of a single, intact H2O molecule for D2O in the Cs(+)(D2O)6 ion. The OH stretching pattern of the Cs(+)(H2O)6 isotopologue is accurately recovered by superposition of the isotopomer spectra, thus establishing that the H2O incorporation is random and that the OH stretching manifold is largely due to contributions from decoupled water molecules. This behavior enables a powerful new way to extract structural information from vibrational spectra of size-selected clusters by explicitly identifying the local environments responsible for specific infrared features. The Cs(+)(H2O)6 structure was unambiguously assigned to the 4.1.1 isomer (a homodromic water tetramer with two additional flanking water molecules) from the fact that its computed IR spectrum matches the observed overall pattern and recovers the embedded correlations in the two OH stretching bands of the water molecule in the Cs(+)(D2O)5(H2O) isotopomers. The 4.1.1 isomer is the lowest in energy among other candidate networks at advanced (e.g., CCSD(T)) levels of theoretical treatment after corrections for (anharmonic) zero-point energy. With the structure in hand, we then explore the mechanical origin of the various band locations using a local electric field formalism. This approach promises to provide a transferrable scheme for the prediction of the OH stretching fundamentals displayed by water networks in close proximity to solute ions.

Efficient procedure for the numerical calculation of harmonic vibrational frequencies based on internal coordinates.

We propose a general procedure for the numerical calculation of the harmonic vibrational frequencies that is based on internal coordinates and Wilsons GF methodology via double differentiation of the energy. The internal coordinates are defined as the geometrical parameters of a Z-matrix structure, thus avoiding issues related to their redundancy. Linear arrangements of atoms are described using a dummy atom of infinite mass. The procedure has been automated in FORTRAN90 and its main advantage lies in the nontrivial reduction of the number of single-point energy calculations needed for the construction of the Hessian matrix when compared to the corresponding number using double differentiation in Cartesian coordinates. For molecules of C1 symmetry the computational savings in the energy calculations amount to 36N - 30, where N is the number of atoms, with additional savings when symmetry is present. Typical applications for small and medium size molecules in their minimum and transition state geometries as well as hydrogen bonded clusters (water dimer and trimer) are presented. In all cases the frequencies based on internal coordinates differ on average by <1 cm(-1) from those obtained from Cartesian coordinates.

Ground and Excited States of the [Fe(H2O)6]2+ and [Fe(H2O)6]3+ Clusters: Insight into the Electronic Structure of the [Fe(H2O)6]2+–[Fe(H2O)6]3+ Complex

We report the ground and low-lying electronically excited states of the [Fe(H2O)6](2+) and [Fe(H2O)6](3+) clusters using multiconfiguration electronic structure theory. In particular, we have constructed the potential energy curves (PECs) with respect to the iron-oxygen distance when removing all water ligands at the same time from the cluster minima and established their correlation to the long-range dissociation channels. Due to the fact that both the second and third ionization potentials of iron are larger than the one for water, the ground-state products asymptotically correlate with dissociation channels that are repulsive in nature at large separations, as they contain at least one H2O(+) fragment and a singly positively charged metal center (Fe(+)). The most stable equilibrium structures emanate, via intersections and/or avoided crossings, from the channels consisting of the lowest electronic states of Fe(2+)((5)D, 3d(6)) or Fe(3+)((6)S, 3d(5)) and six neutral water molecules. Upon hydration, the ground state of Fe(2+)(H2O)6 is a triply ((5)Tg) degenerate one, with the doubly ((5)Eg) degenerate state lying ∼20 kcal/mol higher in energy. Similarly, the Fe(3+)(H2O)6 cluster has a ground state of (6)Ag symmetry under Th symmetry, which is well-separated from the first excited state. We also examine a multitude of electronically excited states of many possible spin multiplicities and report the optimized geometries for several selected states. The PECs of those states exhibit a high density of states. Focusing on the ground and the first few excited states of the [Fe(H2O)6](2+) and [Fe(H2O)6](3+) clusters, we studied their mutual interaction in the gas phase. We obtained the optimal geometries of the Fe(2+)(H2O)6-Fe(3+)(H2O)6 gas-phase complex for different Fe-Fe distances. For distances shorter than 6.0 Å, the water molecules in the respective first solvation shells located between the two metal centers were found to interact via weak hydrogen bonds. We examined a total of 10 electronic states for this complex, including those corresponding to the electron transfer (ET) from the ferrous to the ferric ion. The ET process is discussed and a possible path via a quasi-symmetric transition state is suggested.

Hückel versus Möbius aromaticity: The particle in a cylinder versus a Möbius strip

The one-particle-constrained-to-a-Moebius-strip model is studied quantum mechanically. The results are used to account for the chemical concept of Moebius aromaticity. In addition, the one-particle-in-a-cylinder model is used to explain the Hueckel aromaticity. Using the principles of quantum mechanics and applying the appropriate boundary conditions, the 4N + 2 and 4N electrons aromaticity rules are confirmed for these two types of aromaticity. A numerical technique for obtaining an exact solution of the Schroedinger equation of the Moebius model is also suggested.

Enantioselective Syntheses of Homopropargylic Alcohols via Asymmetric Allenylboration

A chiral phosphoric acid catalyzed allenylboration reaction is reported. Homopropargyl alcohols with an internal alkyne unit were obtained in good yields with high enantioselectivities under the developed conditions.

Aufbau Rules for Solvated Electron Precursors: Be(NH3)40,± Complexes and Beyond

Tetra-amino beryllium complexes and ions, Be(NH3)40,±, have a tetrahedral Be(NH3)42+ core with one, two, or three outer electrons orbiting its periphery. Our calculations reveal a new class of molecular entities, solvated electron precursors, with Aufbau rules (1s, 1p, 1d, 2s, 1f, 2p, 2d) that differ from their familiar hydrogenic counterparts and resemble those of jellium or nuclear-shell models. The cores radial electrostatic potential suffices to reproduce the chief features of the ab initio results. Wave function and electron-propagator methods combined with diffuse basis sets are employed to calculate accurate geometries, ionization energies, electron affinities, and excitation energies.