state energy, subject to a fixed number of elements in the finite-element mesh. To this end, we first develop an estimate for the finite-element discretization error in the Kohn-Sham ground-state energy as a function of the characteristic mesh-size distribution, h(r), and the exact ground-state electronic fields comprising of wavefunctions and electrostatic potential. We subsequently determine the optimal mesh distribution for the chosen representative solution by determining the h(r) that minimizes the discretization error. The resulting expressions for the optimal mesh distribution are in terms of the degree of the interpolating polynomial and the exact solution fields of the Kohn-Sham DFT problem. Since the exact solution fields are a priori unknown, we use the asymptotic behavior of the atomic wavefunctions [38] away from the nuclei to determine the coarse-graining rates for the finite-element meshes used in our numerical study. Though the resulting finite-element meshes are not necessarily optimal near the vicinity of the nuclei, the mesh coarsening rate away from the nuclei provides an efficient way of resolving the vacuum in non-periodic calculations.We next implement an efficient solution strategy for solving the finite-element discretized eigenvalue problem, which is crucial before assessing the computational efficiency of the basis. We note that the non-orthogonality of the finite-element basis results in a discrete generalized eigenvalue problem, which is computationally more expensive than the standard eigenvalue problem that results from using an orthogonal basis like planewaves. We address this issue by employing a spectral finite-element discretization and Gauss-Lobatto quadrature rules to evaluate the integrals which results in a diagonal overlap matrix, and allows for a trivial transformation to a standard eigenvalue problem. Further, we use the Chebyshev acceleration technique for standard eigenvalue problems to efficiently compute the occupied eigenspace (cf. e.g. [39] in the context of electronic structure calculations). Our investigations suggest that the use of spectral finite-elements and Gauss-Lobatto rules in conjunction with Chebyshev acceleration techniques to compute the eigenspace gives a 10 − 20 fold computational advantage, even for modest materials system sizes, in comparison to traditional methods of solving the standard eigenvalue problem where the eigenvectors are computed explicitly. Further, the proposed approach has been observed to provide a staggering 100 − 200 fold computational advantage over the solution of a generalized eigenvalue problem that does not take advantage of the spectral finite-element discretization and Gauss-Lobatto quadrature rules. In our implementation, we use a self-consistent field (SCF) iteration with Anderson mixing [40], and employ the finite-temperature Fermi-Dirac smearing [3] to suppress the charge sloshing associated with degenerate or close to degenerate eigenstates around the Fermi energy.We next study various numerical aspects of the finite-...

Emerging technologies have made high-speed GC practical and useful for an increasing range of applications.C and GC/MS are the most frequently used methods for the speciation and quantification of volatile and semivolatile organic compounds. The total cost for these analyses is enormous. Protracted sample turnaround times, which are common for contract laboratories, cause expensive bottlenecks. Dramatic reductions in analysis time could lead to significant economic advantages for applications involving environmental and chemical process monitoring. This Report considers several emerging technologies that have made high-speed GC (HSGC) practical and useful for a rapidly increasing range of applications Slow road to high speedThe potential for a favorable trade of resolution for speed was recognized soon after the development of the open-tubular separation column by Golay in 1957 (1). In 1962 Desty and co-workers (2) used a gas-tight syringe, which was struck by a mallet, to introduce a 10-ms vapor plug into a 2-m long, 0.07-mm i.d. wall-coated metal capillary column. The result was the separation of all nine heptane isomers in about 5 s. A mirror galvanometer array and photographic paper recorded the chromatograms.Wall-coated open-tubular (capillary) GC columns were slow to win acceptance; high-speed capillary column GC, even slower. In part, this resistance was caused by the extraordinary resolving power of long capillary columns, which focused research attention on the separation of increasingly complex mixtures. As a result, analysis time and selectivity became less frequent topics for research. The number of widely used stationary phases dwindled, and the one-size-fits-all approach to methods development became common Often, the column length and the temperature-programming profile are ad-

A novel gas valve inlet system for gas chromatography is described. The device incorporates a capillary sample gas delivery tube containing a small orifice in its side from which sample vapor continuously flows. A precision micro stepper motor is used to translate the sample delivery tube parallel to its axis so that the orifice passes by the end of the fused silica separation column. The inlet end of the column and the sample delivery tube are housed in a pressurized injection port which also contains purge flows to vent sample between injections. Two operating modes are described. In the sweep mode, the orifice sweeps past the column end at a constant, adjustable velocity. In the park mode, the orifice is parked in front of the column end for a software selectable time. Injection sample size and bandwidth are adjustable. Bandwidths (σ) as small as a few milliseconds make the inlet suitable for high-speed gas chromatography as well as conventional GC.

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