Reflections on spontaneous asymmetric synthesis by amplifying autocatalysis

Spontaneous generation of chirality was observed in the course of studying the mechanism of asymmetric autocatalysis by NMR in ZnR2 alkylation of pyrimidin-5-aldehydes. A systematic study was carried out in order to discover its origins. Even in clean fresh non-glass reaction vessels spontaneous ee was clearly observed, and was not dependent on any single reaction parameter. For comparison it was demonstrated that enantiomerically pure Zn alkoxide catalyst could control the configuration of the reaction product even when present at below micromolar concentrations. The high propensity of the Soai reaction system to produce an enantiomerically enriched product without initial bias is suggested to result from stochastic effects. These are especially important in autocatalysis because all the final products can be derived by breeding from a small number of initial events. The statistical excess of one enantiomer in that set is sufficient to generate a measurable ee in the product. The process is aided by the requirement for dimerisation before the product is an active catalyst. An enumeration that rationalises these observations is provided.     

Evaluation of the Coulomb energy in relativistic self-consistent-field theory

 Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature. Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type functions. Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

Computational strategies for a four-component Dirac-Kohn-Sham program: implementation and first applications

An implementation of the generalized gradient approximation within the four-component formulation of relativistic density-functional theory using G-spinor basis sets is presented. This approach is based on the direct evaluation of the relativistic density and its gradient from the G-spinor amplitudes and gradients without explicit reference to the total density matrix. This proves to be a particularly efficient scheme, with an intrinsic computational cost that scales linearly with the number of G-spinor basis functions. In order to validate this new implementation, incorporated in the parallel version of the program BERTHA, a detailed study of the diatomic system CsAu is also reported. The spectroscopic constants D(e),r(e),omega(e), and x(e)omega(e) and the dipole moment mu have been calculated and compared with the best available theoretical and experimental data. The sensitivity of our results to the details of the numerical schemes used to evaluate the matrix elements is analyzed in detail. Also presented is a comparative study of molecular properties in the alkali auride series which have been obtained using several standard non-relativistic density functionals.     

Theoretical analysis of parity-violating energy differences between the enantiomers of chiral molecules

Fully relativistic four-component electronic structure ab initio calculations including neutral current corrections are reported for a number of small chiral molecules that are of interest in the experimental search for differences in the vibrational spectra of the two enantiomers of handed molecules. The largest vibrational energy differences, of the order 0.2 Hz, are found in chiral methane derivatives which include an iodine substituent. The vibrational energy differences in CHBrClF are 7 and 2 mHz for the carbon-chlorine and carbon-fluorine stretching modes, respectively, which are 3 to 4 orders of magnitude smaller than the precision reported in recent experiments.     

Nuclear quantum effects in calculated NMR shieldings of benzene; a Feynman path integral study

The Feynman path integral Monte Carlo approach has been coupled to the gauge including atomic orbital formalism in order to analyse the absolute magnetic shieldings of the benzene nuclei under the conditions of thermal equilibrium. The Hamiltonian employed in the derivation of ensemble averaged NMR quantities is of the Hartree-Fock type. The basis set used is of 6–31G quality. The spatial delocalization of the atoms leads to a deshielding of both types of benzene nuclei relative to the shieldings experienced at the minimum of the potential energy surface. This deshielding has to be traced back to bond length elongations in thermal equilibrium. The influence of the nuclear fluctuations on the NMR parameters of benzene is quantum driven up to temperatures of 400 K; classical fluctuations are of minor importance in this low-temperature window.     

Fresnel coherent diffractive imaging

We present an x-ray coherent diffractive imaging experiment utilizing a nonplanar incident wave and demonstrate success by reconstructing a nonperiodic gold sample at 24 nm resolution. Favorable effects of the curved beam illumination are identified.     

Nuclear electric quadrupole moment of gold

The nuclear quadrupole moment for (197)Au has been determined on the base of the state-of-art relativistic molecular calculations. The experimental shifts in the nuclear coupling constants in the series of molecules AuF, XeAuF, KrAuF, ArAuF, (OC)AuF, and AuH have been combined with highly accurate determinations of the electric field gradient (EFG) at the gold nucleus, obtained by molecular relativistic Dirac-Coulomb-Gaunt Hartree-Fock calculations. The electronic correlation contribution to the EFG is included with the CCSD(T) and CCSD-T approaches, also in the four-component framework, using a finite-difference method. In order to estimate the accuracy of their approach the authors have thoroughly investigated the convergence of the results with respect to the basis set employed and the size of the correlated orbital space. The effect of the full Breit electron-electron interaction on the nuclear quadrupole moment of gold has also been considered explicitly for the AuF molecule. They obtain for (197)Au a nuclear quadrupole moment of 510+/-15 mb, which deviates by about 7% from the currently accepted muonic value.     

Electron density fitting for the Coulomb problem in relativistic density-functional theory

A density fitting approach for the Coulomb matrix representation within the four-component formulation of relativistic density-functional theory is presented. Our implementation, which uses G-spinor basis sets, shares all the advantages of those found in nonrelativistic quantum chemistry. We show that very accurate Coulomb energies may be obtained using a modest number of scalar auxiliary basis functions for molecules containing heavy atoms. The efficiency of this new implementation is demonstrated in a detailed study of the spectroscopic properties of the gold dimer, and its scaling behavior has been tested by calculations of some closed-shell gold clusters (Au2, Au3+, Au4, Au5+). The algorithm is found to scale as O(N3), just as it does in the nonrelativistic case, and represents a dramatic improvement in efficiency over the conventional approach in the calculation of the Coulomb matrix, with computation times that are reduced to less than 3% for Au2 and up to 1% in the case of Au5+.