Curvy-steps approach to constraint-free extended-Lagrangian ab initio molecular dynamics, using atom-centered basis functions: convergence toward Born-Oppenheimer trajectories

A dynamical extension of the "curvy-steps" approach to linear-scaling self-consistent field calculations is presented, which yields an extended-Lagrangian formulation of ab initio molecular dynamics. An exponential parametrization of the one-electron density matrix, expressed in terms of atom-centered Gaussian basis functions, facilitates propagation along the manifold of density matrices in a geometrically correct fashion that automatically enforces idempotency constraints. The extended Lagrangian itself is constraint free, thus neither density matrix purification nor expensive, iterative solution for Lagrange multipliers is required. Propagation is highly efficient, and time steps compare favorably to those used in Car-Parrinello molecular dynamics simulations. The behavior of the method, especially with regard to the maintenance of adiabatic decoupling of nuclei and electrons, is examined for a sequence of diatomic molecules, and comparison is made to trajectories propagated on the converged Born-Oppenheimer surface. Certain claims to the contrary notwithstanding, our results demonstrate that vibrational frequencies may depend on the value of the fictitious mass parameter, even in an atom-centered basis. Light-atom stretching frequencies can be significantly redshifted, even when the nuclear and electronic energy scales are well separated. With a sufficiently small fictitious mass and a short time step, accurate frequencies can be obtained; we characterize appropriate values of these parameters for a wide range of vibrational frequencies.     

Structures and anion-binding properties of M4L6 tetrahedral cage complexes with large central cavities

Reaction of the bis-bidentate bridging ligand L(3), in which two bidentate chelating 3(2-pyridyl)pyrazole units are separated by a 3,3'-biphenyl spacer, with Co(II) salts affords tetranuclear cage complexes of composition [Co(4)(L(3))(6)]X(8)(X =[BF(4)](-), [ClO(4)](-), [PF(6)](-) or I(-)) in which four 6-coordinate Co(II) ions in an approximately tetrahedral array are connected by six bis-bidentate bridging ligands, one spanning each of the six edges of the Co(4) tetrahedron. In every case, X-ray crystallography reveals that the 'apical' Co(II) ion has a fac tris-chelate geometry, whereas the other three Co(II) ions have mer tris-chelate geometries, resulting in (non-crystallographic)C(3) symmetry for the cages; that this structure is retained in solution is confirmed by (1)H NMR spectroscopy of the paramagnetic cages. In every case one of the anions is located inside the central cavity of the cage, with the remaining seven outside. We found no clear evidence for an anion-based templating effect. The cage superstructure is sufficiently large to leave gaps in the centres of the faces through which the internal and external anions can exchange. Variable-temperature (19)F NMR spectroscopy was used to investigate the dynamic behaviour of the cages with X =[BF(4)](-) and [PF(6)](-) in MeCN solution: in both cases two separate signals, corresponding to external and internal anions, are clear at 233 K which have coalesced to a single signal at room temperature. Analysis of the linewidth of the minor signal (for the internal anion) at various temperatures below coalescence gave an activation energy for anion exchange of ca. 50 kJ mol(-1) in each case, a figure which suggests that anion exchange can occur via a conformational rearrangement of the cage superstructure in solution rather than opening of the cavity by cleavage of metal-ligand bonds.     

Thermal stereomutations and stereochemically elucidated [1,3]-carbon sigmatropic shifts of 1-(E)-propenyl-2-methylcyclobutanes giving 3,4-dimethylcyclohexenes

The thermal stereomutations and [1,3] carbon sigmatropic shifts shown by (+)-(1S,2S)-trans-1-(E)-propenyl-2-methylcyclobutane and by (-)-(1S,2R)-cis-1-(E)-propenyl-2-methylcyclobutane in the gas phase at 275 degrees C leading to 3,4-dimethylcyclohexenes have been followed. The reaction-time-dependent data for concentrations and enantiomeric excess values for substrates and [1,3] shift products have been deconvoluted to afford rate constants for the discrete isomerization processes. Both trans and cis substrates react through four stereochemically distinct [1,3] carbon shift paths. For one enantiomer of the trans reactant the relative rate constants are k(si) = 58%, k(ar) = 5%, k(sr) = 33%, and k(ai) = 4%. For a single enantiomer of the cis reactant, k'(si) = 18%, k'(ar) = 11%, k'(sr) = 51%, and k'(ai) = 20%. A trans starting material reacts through orbital symmetry allowed suprafacial,inversion and antarafacial,retention paths to give trans-3,4-dimethylcyclohexenes 63% of the time. A cis isomer reacts to give the more stable trans-3,4-dimethylcyclohexenes through orbital symmetry-forbidden suprafacial,retention and antarafacial,inversionpaths 71% of the time. The [1,3] carbon sigmatropic shifts are not controlled by orbital symmetry constraints. They seem more plausible rationalized as proceeding through diradical intermediates having some conformational flexibility after formation and before encountering an exit channel. The distribution of stereochemical outcomes may well be conditioned by dynamic effects. The thermal stereomutations of the 1-(E)-propenyl-2-methylcyclobutanes take place primarily through one-center epimerizations. For the trans substrate, the relative importance of the three distinction rate constants are k(2) = 48%, k(1) = 34%, and k(12) = 18%. For the cis isomer, k'(2) = 44%, k'(1) = 32%, and k'(12) = 24%. These patterns are reminiscent of ones determined for stereomutations in 1,2-disubstitued cyclopropanes.     

Beyond the Roger Brown rearrangement: long-range atom topomerization in conjugated polyynes

Long-range carbon atom topomerization in a 1,3-diyne has been demonstrated for the first time. 1-Phenyl-4-p-tolyl-1,3-butadiyne, (13)C-enriched at C-1, was synthesized and subjected to flash vacuum pyrolysis. At 800 degrees C and 0.01 Torr, this resulted in nearly complete (13)C label equilibration between C-1 and C-2, as seen by NMR analysis. Pyrolysis at 900 degrees C further led to ca. 35% of the label migrating about equally to C-3 and C-4. These results demonstrate that both intrabond and interbond atom exchange processes are operative, with the former having a lower activation barrier. DFT and Moller-Plesset calculations support a mechanism that passes through Brown rearrangement (1,2-shift), closure to trialene (bicyclo[1.1.0]-1,3-butadiene), bond-shift isomerization to exchange C-2 and C-3, and ring opening. The resulting vinylidene can rearrange to a butadiyne with the isotopic label at C-3 or C-4. Consistent with earlier calculations, trialene is predicted to have alternating peripheral bonds, with a weak central sigma bond and significant diradical character. Trialene is predicted [(B3LYP/6-311+G(2d,p)] to lie 64.6 kcal/mol above butadiyne, with barriers of 2.2 and 4.4 kcal/mol, respectively, for ring opening or bond-shift isomerization. Other potential rearrangement mechanisms which pass through tetrahedrene (E(rel) = 167.2 kcal/mol) or 1,2,3-cyclobutatriene (E(rel) = 161.1 kcal/mol) lie at much higher energies.     

Amino acid analysis by micellar electrokinetic chromatography with laser-induced fluorescence detection: application to nanolitre-volume biological samples from Arabidopsis thaliana and Myzus persicae

Amino acids were derivatised with 4-fluoro-7-nitrobenzo-2,1,3-oxadiazol (NBD-F), separated by micellar electrokinetic chromatography (MEKC), and detected by argon-ion (488 nm) laser-induced fluorescence. The optimised MEKC background electrolyte conditions were: 40 mM sodium cholate, 5 mM beta-cyclodextrin in 20 mM aqueous borate buffer, pH 9.1, with 7% v/v acetonitrile. Using these conditions, 19 amino acids were separated within 17 min. The limits of detection were in the range of 7.6-42.2 pmol/mL and limits of quantitation from 0.05-0.14 nmol/mL. The method was systematically validated for injection volume error, migration time variation, calibration linearity, accuracy, precision, and recovery. Nanolitre volume samples of phloem sap of individual sieve element cells from the plant Arabidopsis thaliana and honeydew from the aphid Myzus persicae were directly analysed with this method. Quantitative amino acid concentrations in these two biological matrices were profiled for the first time. This method is particularly important because it allows the complete profile of the amino acids obtained from individual phloem elements, allowing cell to cell and plant to plant variation to be quantified, which to date has not been possible with Arabidopsis thaliana.     

A formula for angular and hyperangular integration

A formula is derived which allows angular or hyperangular integration to be performed on any function of the coordinates of a D-dimensional space, provided that it is possible to expand the function as a polynomial in the coordinates x₁,x₂,...,x_d. The expansion need not be carried out for the formula to be applied. This revised version was published online in July 2006 with corrections to the Cover Date.     

Selective Transport of Lead(II) and Strontium(II) Through a Crown Ether-Based Polymer Inclusion Membrane Containing Dialkylnaphthalenesulfonic Acid

New polymer inclusion membranes (PIMs) containing 18-membered crownethers and dialkylnaphthalenesulfonic acid are proposed for Sr2+ and Pb2+removal from nitric acid solutions. The influence of source phasecomposition and stripping agents was characterized and permeabilitycoefficients were calculated. The PIMs are easy to prepare and may be usefulin separation and concentration procedures for these cations from complexmixtures such as nuclear waste. Long-term stability was obtained for atleast several weeks of constant use during which no significant change ofpermeability was observed.     

Formation of oxygen atoms in the reaction of chlorine atoms with ozone

Oxygen atoms are detected by NO + O + M chemiluminescence as a secondary product of the reaction between Cl and O₃. The mechanism Cl + O₃ → ClO + O₂(¹Σ⁺_g), O₂(¹Σ⁺_g) + O₃ → O₂ + O₂ + O is proposed to account for the oxygen atom formation. The branching ratio to the O₂(¹Σ⁺_g) product in the reaction of Cl with O₃ is estimated to be in the range (0.1–0.5) x 10^?2.     

Determination of standard pH values for sodium hydrogen diglycolate buffer (0.05m) from 5–65°C

Values of pa _H ^o for 0.05 mole-kg^?1 aqueous solutions of sodium hydrogen diglycolate in the temperature range 5–65°C have been obtained from cells without transport, and can be fitted to the equation $$\begin{gathered} pa^\circ _H = 3.5098 + 2.222 \times 10^{ - 3} ({T \mathord{\left/ {\vphantom {T {K - 298.15}}} \right. \kern-\nulldelimiterspace} {K - 298.15}}) \hfill \\ + 2.628 \times 10^{ - 5} ({T \mathord{\left/ {\vphantom {T {K - 298.15}}} \right. \kern-\nulldelimiterspace} {K - 298.15}})^2 \hfill \\ \end{gathered} $$ The analysis has been carried out by a multilinear regression procedure using a form of the Clarke and Glew equation. This buffer standard may be a useful alternative to the saturated potassium hydrogen tartrate buffer.