A new measure of orthogonality for multi-dimensional chromatography

Multi-dimensional chromatographic techniques, such as (comprehensive) two-dimensional liquid chromatography and (comprehensive) two-dimensional gas chromatography, are increasingly popular for the analysis of complex samples, such as protein digests or mineral oils. The reason behind the popularity of these techniques is the superior performance, in terms of peak-production rate (peak capacity per unit time), that multi-dimensional separations offer compared to their one-dimensional counterparts. However, to fully utilize the potential of multi-dimensional chromatography it is essential that the separation mechanisms used in each dimension be independent of each other. In other words, the two separation mechanisms need to be orthogonal. A number of algorithms have been proposed in the literature for measuring chromatographic orthogonality. However, these methods have their limitations, such as reliance on the division of the separation space into bins, need for specialist software or requirement of advanced programming skills. In addition, some of the existing methods for measuring orthogonality include regions of the separation space that do not feature peaks. In this paper we introduce a number of equations which provides information on the spread of the peaks within the separation space in addition to measuring orthogonality, without the need for complex computations or division of the separation space into bins.     

Pseudopotential calculations including core-valence correlation: Alkali and noble-metal compounds

A summary is given of our recently developed semiempirical pseudopotentials and their applications, and new results are presented on the K₂ molecule.     

Multielectron coincidence spectroscopy for core-valence doubly ionized states of CO

Double photoionization into states which have holes in one core and one valence orbitals has been observed in CO using a state-of-the-art multielectron coincidence method. The core-valence CO2+ structures exhibited on the electron coincidence spectra are assigned by comparison with the available calculation [H. Schulte et al., J. Chem. Phys. 105, 11108 (1996)]. Features of the spectrum confirm that the properties of the CO2+ states are characterized by the interaction between the localized valence holes and the core holes.     

A note on atomic density

In atomic systems, electron density has a simple finite expansion in spherical harmonics times radial factors. The difficulties in the calculation of some radial factors are illustrated in the low‐lying states of the carbon atom. Single‐particle methods such as Hartree–Fock and approximate density functional theory cannot ensure the correct expansion of the density in spherical harmonics. Wave‐function methods are appropriate but, as some expansion terms are entirely due to correlation, these methods only will give correct results for high‐quality variational functions. Using full‐configuration integration (CI), all the terms predicted by the theory appear and are not negligible but the convergence of the term due to correlation toward its correct value is uncertain even for very large CI spaces. © 2012 Wiley Periodicals, Inc.     

A note on electro-optic effects

Tinoco's second-order electro-optic effect in isotropic fluids is discussed for the case of very high electric fields. The possibility of observing a linear electro-optic effect in oriented molecules of certain symmetry types is also analyzed.     

A note on generalised time-lags

Derivations of an expression for the generalised outgoing ‘adsorption’ time-lag pertaining to transport through a slab membrane made by [Rutherford and Do, Review of time lag permeation technique as a method for characterisation of porous media and membranes, Adsorption 3 (1997) 283] and by [Ash et al., Sorption and surface flow in graphitized carbon membranes. II. Time-lag and blind pore character, Proc. Roy. Soc. London, Ser. A, 304 (1968) 407] are not in agreement. Causes for the discrepancy are identified. Two extensions of the generalised procedure are given with particular attention being paid to ΔL, the time-lag difference.     

Solvent influence on the orthogonality of noncovalently functionalized terpolymers

Poly(norbornene) terpolymers containing palladated sulfur‐carbon‐sulfur (SCS) pincer complexes, cyanuric acid, and thymine moieties in their side‐chains were synthesized by ring‐opening metathesis polymerization. Functionalization of the terpolymers was achieved by self‐assembling (i) the Hamilton wedge to the cyanuric acid receptor, (ii) diaminopyridine to the thymine receptor, and (iii) pyridine to the palladated pincer complexes. While all three noncovalent interactions are fully orthogonal to each other in dichloromethane, the employment of a dioxane/chloroform solvent mixture results in the quantitative disassembly of one of the hydrogen bonding recognition units (the Hamilton wedge:cyanuric acid pair) during the metal‐coordination event. This disassembly is completely independent from the diaminopyridine: thymine hydrogen‐bonding pair and allows for the selective removal of one of the side‐chain functionalities. This removal occurs with a switch‐type mechanism: as one functionality is put on (the pyridine), another one (the Hamilton‐wedge receptor) is taken off quantitatively. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1936–1944, 2008     

A note on sorption measuring instruments

Gas sorption phenomena can be used to characterise porous solids and dispersed materials. Usually isotherms of nitrogen and noble gases like He, Ar, Kr are measured at low temperatures (77–90 K). Other gases and vapours like water, CO₂ and benzene are used at near ambient conditions of pressure and temperature. From the amount of gas adsorbed on the (external or internal) surface characteristic quantities like the specific surface area, specific pore volume and pore spectrum of the material are derived by standardised methods. Experimental techniques most often used are the carrier gas, the volumetric/manometric and the gravimetric method. A comprehensible overview of today's available instruments, their advantages and drawbacks is given.This revised version was published online in November 2005 with corrections to the Cover Date.     

A note on equivariant Euler characteristic

We give a new equivariant cohomological characterization of the equivariant Euler characteristic of aG-simplicial set as defined by Brown. This implies in particular that the equivariant Euler characteristic is aG-homotopy invariant.     

A note on the partitioning technique

A new derivation of the wave operator of the partitioning technique is given. Furthermore this approach is applied to derive wave operators for the inverse hamiltonian and in general for functions of the hamiltonian.     

A note on generalized Green functions

A partial-wave expansion in terms of Jost function is obtained for the sngle-particle generalized Green function. Each partial-wave generalized Green function so obtained is in closed form. The results apply at least to Jost function treatable potentials.     

A note on time-dependent variattonal principles

It is demonstrated that the least action time-dependent variational principle suggested by Kerman and Koonin is equivalent to Frenkel's variational principle. A set of equations suitable for the variational treatment of a number of time-dependent problems has been derived in the course of this analysis.     

Direct energy functional minimization under orthogonality constraints

The direct energy functional minimization problem in electronic structure theory, where the single-particle orbitals are optimized under the constraint of orthogonality, is explored. We present an orbital transformation based on an efficient expansion of the inverse factorization of the overlap matrix that keeps orbitals orthonormal. The orbital transformation maps the orthogonality constrained energy functional to an approximate unconstrained functional, which is correct to some order in a neighborhood of an orthogonal but approximate solution. A conjugate gradient scheme can then be used to find the ground state orbitals from the minimization of a sequence of transformed unconstrained electronic energy functionals. The technique provides an efficient, robust, and numerically stable approach to direct total energy minimization in first principles electronic structure theory based on tight-binding, Hartree-Fock, or density functional theory. For sparse problems, where both the orbitals and the effective single-particle Hamiltonians have sparse matrix representations, the effort scales linearly with the number of basis functions N in each iteration. For problems where only the overlap and Hamiltonian matrices are sparse the computational cost scales as O(M2N), where M is the number of occupied orbitals. We report a single point density functional energy calculation of a DNA decamer hydrated with 4003 water molecules under periodic boundary conditions. The DNA fragment containing a cis-syn thymine dimer is composed of 634 atoms and the whole system contains a total of 12,661 atoms and 103,333 spherical Gaussian basis functions.