Jorge M. del Campo

Calculation of exchange-correlation potentials with auxiliary function densities

The use of Hermite Gaussian auxiliary function densities from the variational fitting of the Coulomb potential for the calculation of exchange-correlation potentials is discussed. The basic working equations for the energy and gradient calculation are derived. The accuracy of this approximation for optimized structure parameters and bond energies are analyzed. It is shown that the quality of the approximation can be systematically improved by enlarging the auxiliary function set. Average errors of 0.5 kcal/mol are obtained with auxiliary function sets including f and g functions. The timings for a series of alkenes demonstrate a substantial performance improvement.

Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties

Imposition of the constraint that, for the hydrogen atom, the exchange energy cancels the Coulomb repulsion energy yields a non-empirical re-parameterization of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) exchange-correlation energy functional, and of the related PBE hybrid (PBE0). The re-parameterization, which leads to an increase of the gradient contribution to the exchange energy with respect to the original PBE functional, is tested through the calculation of heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies, for some well known test sets designed to validate energy functionals. The results for the re-parameterized PBE GGA, called PBEmol, give substantial improvement over the original PBE in the prediction of the heats of formation, while retaining the quality of the original PBE functional for description of all the other properties considered. The results for the hybrids indicate that, although the PBE0 functional provides a rather good description of these properties, the predictions of the re-parameterized functional, called PBEmolβ0, are, except in the case of the ionization potentials, modestly better. Also, the results for PBEmolβ0 are comparable to those of B3LYP. In particular, the mean absolute error for the bond distance test set is 17% lower than the corresponding error for B3LYP. The re-parameterization for the pure GGA (PBEmol) differs from that for the hybrid (PBEmolβ0), illustrating that improvement at the GGA level of complexity does not necessarily provide the best GGA for use in a hybrid.

A hierarchical transition state search algorithm

A hierarchical transition state search algorithm is developed and its implementation in the density functional theory program deMon2k is described. This search algorithm combines the double ended saddle interpolation method with local uphill trust region optimization. A new formalism for the incorporation of the distance constrain in the saddle interpolation method is derived. The similarities between the constrained optimizations in the local trust region method and the saddle interpolation are highlighted. The saddle interpolation and local uphill trust region optimizations are validated on a test set of 28 representative reactions. The hierarchical transition state search algorithm is applied to an intramolecular Diels-Alder reaction with several internal rotors, which makes automatic transition state search rather challenging. The obtained reaction mechanism is discussed in the context of the experimentally observed product distribution.

A MinMax self-consistent-field approach for auxiliary density functional theory

A MinMax self-consistent-field (SCF) approach is derived in the framework of auxiliary density functional theory. It is shown that the SCF convergence can be guided by the fitting coefficients that arise from the variational fitting of the Coulomb potential. An in-core direct inversion of the iterative subspace (DIIS) algorithm is presented. Due to its reduced memory demand this new in-core DIIS method can be applied without overhead to very large systems with tens of thousands of basis and auxiliary functions. Due to the new DIIS error definition systems with fractional occupation numbers can be treated, too.

Improved constraint satisfaction in a simple generalized gradient approximation exchange functional

Though there is fevered effort on orbital-dependent approximate exchange-correlation functionals, generalized gradient approximations, especially the Perdew-Burke-Ernzerhof (PBE) form, remain the overwhelming choice in calculations. A simple generalized gradient approximation (GGA) exchange functional [A. Vela, V. Medel, and S. B. Trickey, J. Chem. Phys. 130, 244103 (2009)] was developed that improves substantially over PBE in energetics (on a typical test set) while being almost as simple in form. The improvement came from constraining the exchange enhancement factor to be below the Lieb-Oxford bound for all but one value of the exchange dimensionless gradient, s, and to go to the uniform electron gas limit at both s = 0 and s → ∞. Here we discuss the issue of asymptotic constraints for GGAs and show that imposition of the large s constraint, lim(s→∞)s(1/2)F(xc)(n,s)<∞, where F(xc)(n, s) is the enhancement factor and n is the electron density, upon the Vela-Medel-Trickey (VMT) exchange functional yields modest further improvement. The resulting exchange functional, denoted VT{8,4}, is only slightly more complicated than VMT and easy to program. Additional improvement is obtained by combining VT{8,4} or VMT exchange with the Lee-Yang-Parr correlation functional. Extensive computational results on several datasets are provided as verification of the overall performance gains of both versions.

Self-assembly and recognition properties of a tetraanionic macrocyclic boronate ester in aqueous medium

A tetraanionic [2 + 2] boronate ester macrocycle is self-assembled from a dicatechol 3,3,3′,3′-tetramethyl-1,1′-spirobiindane-5,5′,6,6′-tetraol and 1,4-benzenediboronic acid in the presence of 2 equivalents of NaOH in water containing 0–5% vol DMSO. No templating by potential guest molecules is required for the self-assembly with close to quantitative yield of the macrocycle. The macrocycle is stable and binds efficiently various cationic guests at pH 9. For alkali and R4N+ cations the association constants KA are growing in the order Cs+ 105 M−1 for Pr4N+ The inclusion of R4N+ cations is confirmed by 1D and 2D 1H NMR and is further characterized by quantum mechanical calculations. The macrocycle binds efficiently some biologically important cationic guests (choline, acetylcholine, 1-methylnicotinamide) and discriminates Arg-OMe over Lys-OMe. It forms a highly fluorescent complex with an isoquinoline alkaloid berberine, which can be used for optical sensing of tetraalkylammonium guests by a displacement or ternary complex formation mechanism. These results extend previously limited to solid state or non-aqueous media applications of self-assembled boronate ester hosts for molecular recognition to practically more important aqueous solutions.

Substrate Specificity and Leaving Group Effect in Ester Cleavage by Metal Complexes of an Oximate Nucleophile

Deprotonated zinc(II) and cadmium(II) complexes of a tridentate oxime nucleophile (1, OxH) show a very high reactivity, breaking by 2-3 orders of magnitude the previously established limiting reactivity of oximate nucleophiles in the cleavage of substituted phenyl acetates and phosphate triesters, but are unreactive with p-nitrophenyl phosphate di- and monoesters. With reactive substrates, these complexes operate as true catalysts through an acylation-deacylation mechanism. Detailed speciation and kinetic studies in a wide pH interval allowed us to establish as catalytically active forms [Cd(Ox)]+, [Zn(Ox)(OH)], and [Zn(Ox)(OH)2]- complexes. The formation of an unusual and most reactive zinc(II) oximatodihydroxo complex was confirmed by electrospray ionization mass spectrometry data and supported by density functional theory calculations, which also supported the previously noticed fact that the coordinated water in [Zn(OxH)(H2O)2]2+ deprotonates before the oxime. Analysis of the leaving group effect on the cleavage of phenyl acetates shows that the rate-determining step in the reaction with the free oximate anion is the nucleophilic attack, while with both zinc(II) and cadmium(II) oximate complexes, it changes to the expulsion of the leaving phenolate anion. The major new features of these complexes are (1) a very high esterolytic activity surpassing that of enzyme hydrolysis of aryl acetate esters and (2) an increased reactivity of coordinated oxime compared to free oxime in phosphate triester cleavage, contrary to the previously observed inhibitory effect of oxime coordination with these substrates.