Ferrocenium Boronic Acid Catalyzed Deoxygenative Coupling of Alcohols with Carbon- and Nitrogen-Based Borate and Silane Nucleophiles.

A boronic acid catalyzed carbon-carbon and carbon-nitrogen bond-forming reaction for the functionalization of various π-activated alcohols has been developed. Ferrocenium boronic acid hexafluoroantimonate salt was identified as an effective catalyst in the direct deoxygenative coupling of alcohols with a variety of potassium trifluoroborate and organosilane nucleophiles. In a comparison between these two classes of nucleophiles, the use of organosilanes leads to higher reaction yields, increased diversity of the alcohol substrate scope, and high E/Z selectivity. Furthermore, the reaction proceeds under mild conditions and yields up to 98%. Computational studies provide a rationalization for a mechanistic pathway for the retention of E/Z stereochemistry when E or Z alkenyl silanes are used as nucleophiles. This methodology is complementary to existing methodologies for deoxygenative coupling reactions involving organosilanes, and it is effective with a variety of organosilane nucleophile sub-types, including allylic, vinylic, and propargylic trimethylsilanes.

ΔNO and the complexities of electron correlation in simple hydrogen clusters.

The Δ natural orbital (ΔNO) two-electron density matrix (2-RDM) and energy expression are derived from a multideterminantal wave function. The approximate ΔNO 2-RDM is combined with an on-top density functional and a double-counting correction to capture electron correlation. A trust-region Newton's method optimization algorithm for the simultaneous optimization of ΔNO orbitals and occupancies is introduced and compared to the previous iterative diagonalization algorithm. The combination of ΔNO and two different on-top density functionals, Colle-Salvetti (CS) and Opposite-spin exponential cusp and Fermi-hole correction (OF), is assessed on small hydrogen clusters and compared to density functional, single-reference coupled-cluster, and multireference perturbation theory (MRMP2) methods. The ΔNO-CS and ΔNO-OF methods outperform the single-reference methods and are comparable to MRMP2. However, there is a distinct qualitative error in the ΔNO potential energy surface for H4 compared to the exact. This discrepancy is explained through analysis of the ΔNO orbitals, occupancies, and the two-electron density.

Measuring correlated electron motion in atoms with the momentum-balance density.

Three new measures of relative electron motion are introduced: equimomentum, antimomentum, and momentum-balance. The equimomentum is the probability that two electrons have the exact same momentum, whereas the antimomentum is the probability that their momenta are the exact opposite. Momentum-balance (MB) is the difference between the equimomentum and antimomentum and, therefore, indicates if equal or opposite momentum is more probable in a system of electrons. The equimomentum, antimomentum, and MB densities are also introduced, which are the local contribution to each quantity. The MB and MB density of the extrapolated-full configuration interaction wave functions of atoms of the first three rows of the periodic table are analyzed, with a particular focus on contrasting the correlated motion of electrons with opposite-spin and parallel-spin. Coulomb correlation between opposite-spin electrons leads to a higher probability of equimomentum, whereas Fermi correlation between parallel-spin electrons leads to a higher probability of antimomentum. The local contribution to MB, given an electron is present, is a minimum at the nucleus and generally increases as the distance from the nucleus increases. There are also interesting similarities between the effects of Fermi correlation and Coulomb correlation (of opposite-spin electrons) on MB.

Capturing static and dynamic correlation with ΔNO-MP2 and ΔNO-CCSD.

The ΔNO method for static correlation is combined with second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions are adapted from finite-temperature CCSD, which includes orbital occupancies and vacancies, and expanded orbital summations. Correlation is partitioned with the aid of damping factors incorporated into the MP2 and CCSD residual equations. Potential energy curves for a selection of diatomics are in good agreement with extrapolated full configuration interaction results and on par with conventional multireference approaches.

On-top density functionals for the short-range dynamic correlation between electrons of opposite and parallel spin.

Separate, one-parameter, on-top density functionals are derived for the short-range dynamic correlation between opposite and parallel-spin electrons, in which the electron-electron cusp is represented by an exponential function. The combination of both functionals is referred to as the Opposite-spin exponential-cusp and Fermi-hole correction (OF) functional. The two parameters of the OF functional are set by fitting the ionization energies and electron affinities, of the atoms He to Ar, predicted by ROHF in combination with the OF functional to the experimental values. For ionization energies, the overall performance of ROHF-OF is better than completely renormalized coupled-cluster [CR-CC(2,3)] and better than, or as good as, conventional density functional methods. For electron affinities, the overall performance of ROHF-OF is less impressive. However, for both ionization energies and electron affinities of third row atoms, the mean absolute error of ROHF-OF is only 3 kJ mol-1.

The Relative Alignment of Electron Momenta in Atoms and Molecules and the Effect of a Static Electric Field.

The relative momentum of electron pairs in atoms and small molecules is examined through calculation of the p1 · p2 probability distribution. The likelihood of aligned or antialigned momenta between paired electrons is determined from the calculated distributions. Coulomb correlation aligns the momenta of electron pairs, and the amount of alignment varies when considering momenta in specific directions in three-dimensional space. A static electric field is found to have competing effects on momentum alignment parallel and perpendicular to the electric field. However, the net effect of the electric field on alignment is significantly smaller than the effect of Coulomb correlation. Recent experimental advances suggest that such a correlation of electron momenta can now be measured directly using attosecond spectroscopic tools.

Determination of the inhibitor dissociation constant of an individual unmodified enzyme molecule in free solution.

Single enzyme molecule assays on E. coli ß-galactosidase were performed using a capillary electrophoresis-based method. Three types of assays were performed. The catalytic rate of 20 individual molecules was assayed in duplicate in the presence of 50 µM substrate. The ratio of rates for the second incubation relative to the first was 0.96 ± 0.03, showing the reproducibility of the method. In the second assay, the rates were determined in the absence and presence of 210 µM L-ribose, a competitive inhibitor. The ratio of the rate in the presence of inhibitor to that in its absence for 19 individual molecules was 0.44 ± 0.23. This large relative standard deviation suggests that each individual enzyme molecule was affected to a different extent by the presence of the inhibitor, which is consistent with KI being heterogeneous. To estimate KI for individual molecules, a third assay was performed. Each molecule was incubated in the presence of 30 and 50 µM substrate and then in the presence of 50 µM substrate plus 210 µM inhibitor. Comparison of the rates in the two substrate concentrations allowed for the determination of the individual Km of each molecule. From this value and the difference in rates in the presence and absence of inhibitor, the individual molecule KI values were determined. This value was found to differ between individual molecules and was found to increase with an increase in Km . Modeling showed that a heterogeneity in KI results in an alteration in the Michaelis-Menten curve for a population of enzymes in the presence of a competitive inhibitor.

A cumulant functional for static and dynamic correlation.

A functional for the cumulant energy is introduced. The functional is composed of a pair-correction and static and dynamic correlation energy components. The pair-correction and static correlation energies are functionals of the natural orbitals and the occupancy transferred between near-degenerate orbital pairs, rather than the orbital occupancies themselves. The dynamic correlation energy is a functional of the statically correlated on-top two-electron density. The on-top density functional used in this study is the well-known Colle-Salvetti functional. Using the cc-pVTZ basis set, the functional effectively models the bond dissociation of H2, LiH, and N2 with equilibrium bond lengths and dissociation energies comparable to those provided by multireference second-order perturbation theory. The performance of the cumulant functional is less impressive for HF and F2, mainly due to an underestimation of the dynamic correlation energy by the Colle-Salvetti functional.

Transition-metal-free access to primary anilines from boronic acids and a common (+)NH2 equivalent.

Diversely substituted anilines are prepared by treatment of functionalized arylboronic acids with a common, inexpensive source of electrophilic nitrogen (H2N-OSO3H, HSA) under basic aqueous conditions. Electron-rich substrates are found to be the most reactive by this method. However, even moderately electron-poor substrates are well tolerated under the room temperature conditions. Sterically hindered substrates appear to be equally effective compared to unhindered ones. Highly electron-deficient substrates afford product in very low yields at room temperature, but moderate to good yields are obtained at refluxing temperatures. Our method is also amenable to electrophilic amination of several common boronic acid derivatives (e.g., pinacol esters). We demonstrate that it can be combined with metal-halogen exchange reactions or a variety of directed ortho metalation protocols in a "one-pot" sequence for the synthesis of aromatic amines with unique substitution patterns. DFT studies, in combination with experimental results, suggest that the reaction occurs via base-mediated activation of HSA, followed by 1,2 aryl B-N migration. This mode of activation appears to be critical for the success of the reaction and allows, for the first time, a general, electrophilic amination of boronic acids at ambient temperature.

Highly enantioselective (-)-sparteine-mediated lateral metalation-functionalization of remote silyl protected ortho-ethyl N,N-dialkyl aryl O-carbamates.

We report the enantioselective, lateral deprotonation of ortho-protected or functionalized tertiary N,N-dialkyl aryl O-carbamates 5-7 (Scheme 2 ) and meta-protected carbamates 14, 15, and 20 (Schemes 5 and 7 ) by s-BuLi/(-)-sparteine and subsequent quench with a variety of electrophiles to give products 11-13 and 16, 17, and 21 in yields up to 96% and enantiomeric ratios up to 99:1. The influence of organolithium reagents, ratio of organolithium/(-)-sparteine pair versus N,N-dialkyl aryl O-carbamate starting materials, temperature, solvents, electrophiles, substituents located ortho or meta to the O-carbamate moiety, and O-carbamate N-substituents was investigated. The identical absolute configuration of the stereogenic center of the major enantiomers of the products, as established by single-crystal X-ray analysis for substrates (S)-11c, (S)-19, and (S)-21a, provides evidence for a consistent stereochemical course in the enantioselective deprotonation. Mechanistic investigations, including an estimate of the configurational stability of the benzyllithium species 9 (starting from 12e; Scheme 8 ) and 23 (starting from 17e; Scheme 9 ), both derived by tin-lithium exchange, and 24 (starting from 20; Scheme 9 ) are reported. The experimental results, together with semiempirical molecular orbital calculations (PM3/SMD), are consistent with a process in which enantioinduction occurs in the deprotonation step (Scheme 11 ).

Non-pairwise additivity of the leading-order dispersion energy.

The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained in terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is -0.11 kJ mol(-1) well(-1), which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.

Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals.

We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb operator [T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Theory Comput. 7, 830 (2011)] and the long-range Ewald operator [T. Limpanuparb and P. M. W. Gill, J. Chem. Theory Comput. 7, 2353 (2011)]) are employed in quantum chemical calculations. We derive a recurrence relation that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and propose a near-optimal algorithm for its use.

Intracule functional models. V. Recurrence relations for two-electron integrals in position and momentum space.

The approach used by Ahlrichs [Phys. Chem. Chem. Phys., 2006, 8, 3072] to derive the Obara-Saika recurrence relation (RR) for two-electron integrals over Gaussian basis functions, is used to derive an 18-term RR for six-dimensional integrals in phase space and 8-term RRs for three-dimensional integrals in position or momentum space. The 18-term RR reduces to a 5-term RR in the special cases of Dot and Posmom intracule integrals in Fourier space. We use these RRs to show explicitly how to construct Position, Momentum, Omega, Dot and Posmom intracule integrals recursively.

The two faces of static correlation.

Restricted Hartree-Fock (RHF) and UHF wavefunctions for beryllium-like ions with nuclear charge 3 ≤ Z ≤ 5 are found using a near-complete Slater basis set. The triplet (RHF → UHF) instability and correlation energy are investigated as a function of Z and we find that the instability vanishes for Z > 4.5. We reproduce this surprising behavior using a minimal-basis model and, by comparing with the stretched H(2) molecule, conclude that "static" (also known as nondynamical, near-degeneracy, first-order, or strong) correlation comes in two flavors: one that can be captured by UHF and another that cannot. In the former (Type A), there is an "absolute near-degeneracy"; in the latter (Type B), there is a "relative near-degeneracy." This dichotomy clarifies discussions of static correlation effects.

The nature of electron correlation in a dissociating bond.

We have constructed the unrestricted Hartree-Fock (UHF), restricted Hartree-Fock (RHF), and full configuration interaction (FCI) position and momentum intracules and holes for H···H at bond lengths R from 1 to 10 bohrs. We trace the recently discovered inversion of the UHF position hole at intermediate R to over-localization of the spin-orbitals, and support this by a correlation energy component analysis. The RHF and UHF momentum holes are found to be more complicated; however their features are explained through decomposition of electron correlation effects. The UHF momentum hole is also found to invert and exhibits interesting behavior at large R. The RHF (but not UHF) and FCI momentum intracules exhibit Young-type interference patterns related to recent double photoionization experiments. Our analyses yield the most comprehensive picture to date of the behavior of the electrons during homolytic bond fission.

Crystal structure and computational study of an oxo-bridged bis-titanium(III) complex.

The solid-state structure of the new compound µ-oxido-bis[dichloridotris(tetrahydrofuran-κO)titanium(III)], [Ti2Cl4O(C4H8O)6], at 150 K has been determined. The crystal has monoclinic (C2/c) symmetry and the complex features C2 symmetry about the bridging O atom. Positional disorder is evident in one of the three tetrahydrofuran environments. A post-Hartree-Fock computational analysis indicates that the complex has nearly degenerate triplet and singlet spin states, with the former favoured slightly by ca 2 kJ mol-1.

Hydration and Secondary Ozonide of the Criegee Intermediate of Sabinene.

A computational study of the formation of secondary ozonide (SOZ) from the Criegee intermediates (CIs) of sabinene, including hydration reactions with H2O and 2H2O, was performed. All of the geometries were optimized at the B3LYP and M06-2X with several basis sets. Further single-point energy calculation at the CCSD(T) was performed. Two major pathways of SOZ formation suggest that it is mainly formed from the sabinene CI and formaldehyde rather than sabina ketone and formaldehyde-oxide. However, in both pathways, the activation energies are within a range of ±5 kJ mol-1. Furthermore, the hydration reactions of the anti-CI with H2O and 2H2O showed that the role of the second water molecule is a mediator (catalyst) in this reaction. The dimer hydration reaction has lower activation energies than the monomer by 60 and 69 kJ mol-1, at the M06-2X/6-31G(d) and CCSD(T)+CF levels of the theory, respectively. A novel water-mediated vinyl hydroperoxide (VHP) channel from both the monomer and dimer has been investigated. The results indicate that the direct nonmediated VHP formation and dissociation is interestingly more possible than the water-mediated VHP. The density functional theory calculations show that the monomer is faster than the dimer by roughly 22 kJ mol-1. Further, the infrared spectrum of sabina ketone was calculated at B3LYP/6-311+G(2d,p); the calculated carbonyl stretching of 1727 cm-1 is in agreement with the experimental range of 1700-1800 cm-1.

Distributions of r1·r2 and p1·p2 in Atoms.

We consider the two-electron position and momentum dot products, α = r1·r2 and ß = p1·p2, and present a method for extracting their distributions, A(α) and B(ß), from molecular wave functions built on Gaussian basis functions. The characteristics of the Hartree-Fock AHF(α) and BHF(ß) for He and the first-row atoms are investigated, with particular attention to the effects of Pauli exchange. The effects of electron correlation are studied via the holes, ΔA(α) ≡ A(α) - AHF(α) and ΔB(ß) ≡ B(ß) - BHF(ß), and the hole structures are rationalized in terms of radial and angular correlation effects. Correlation effects are also examined through an analysis of the first moments of A(α), AHF(α), B(ß), and BHF(ß).

SEST: Simulated Electronic Structure Theory.

A novel approach to empirically modeling the electronic structure of molecules is introduced. The theory is based on relationships between molecular orbital energy components and the average distance between electrons and electrons and nuclei. The electron-electron and electron-nucleus distances are subsequently related to interatomic distances which provides a means for modeling the electronic structure of molecules. The general energy expression for a simulated electronic structure theory is defined, along with the functional form of the interatomic distance dependent energy functions. The theory is used to model the hydrogen molecule, the first-row hydrides, and ethane. The models, which have the correct RHF/6-31G(d) optimized geometries, also fit the RHF/6-31G(d) energy at equilibrium and the UHF/6-31G(d) energy at the bond dissociation limit as well as some vibrational frequencies.

Computational study of the reactions of SiH3X (X=H, Cl, Br, I) with HCN.

Ab initio calculations were carried out for the reactions of silane and halosilanes (SiH3X, X=H, Cl, Br, I) with HCN. Geometries of the reactants, transition states, intermediates and products were optimized at HF, MP2, and B3LYP levels of theory using the 6-31G(d) and 6-31G(d,p) basis sets. Energies were also obtained using G3MP2 and G3B3 levels of theory. Intrinsic reaction coordinate (IRC) calculations were performed to characterize the transition states on the potential energy surface. It was found that HCN can react with silane and halosilanes via three different mechanisms. One involves HX elimination by a one-step pathway producing SiH3CN. The second mechanism consists of H2 elimination, producing SiH2XCN via a one-step pathway or three multiple-step pathways. The third mechanism involves dissociation of SiH3X to various products, which can then react with HCN. Activation energies, enthalpies, and free energies of activation along with the thermodynamic properties (DeltaE, DeltaH, and DeltaG) of each reaction pathway were calculated. The reaction of SiH3X with HCN produce different products depending on substituent X. We have found that the standard 6-31G(d) bromine basis set gave results which were in better agreement with the G3MP2 results than for the Binning-Curtiss basis set. Computed heats of formation (DeltaHf) for SiH3CN, SiH3NC, SiH2ClCN, SiH2BrCN, SiH2ICN, SiHCl, SiHBr, and SiHI were found to be 133.5, 150.8, -34.4, 23.6, 102.4, 48.7, 127.1, and 179.8 kJ mol-1, respectively. From enthalpies calculated at G3MP2, we predict that the DeltaHf for SiH2 to be 262.8 kJ mol-1 compared to the experimental value of 273.8+/-4.2 kJ mol-1.