Spin-state splittings, highest-occupied-molecular-orbital and lowest-unoccupied-molecular-orbital energies, and chemical hardness.

It is known that the exact density functional must give ground-state energies that are piecewise linear as a function of electron number. In this work we prove that this is also true for the lowest-energy excited states of different spin or spatial symmetry. This has three important consequences for chemical applications: the ground state of a molecule must correspond to the state with the maximum highest-occupied-molecular-orbital energy, minimum lowest-unoccupied-molecular-orbital energy, and maximum chemical hardness. The beryllium, carbon, and vanadium atoms, as well as the CH(2) and C(3)H(3) molecules are considered as illustrative examples. Our result also directly and rigorously connects the ionization potential and electron affinity to the stability of spin states.

Chemical and biological applications of digital-microfluidic devices

The advent of digital microfluidic lab-on-a-chip (LoC) technology offers a platform for developing diagnostic applications with the advantages of portability, reduction of the volumes of the sample and reagents, faster analysis times, increased automation, low power consumption, compatibility with mass manufacturing, and high throughput. Moreover, digital microfluidics is being applied in other areas such as airborne chemical detection, DNA sequencing by synthesis, and tissue engineering. In most diagnostic and chemical-detection applications, a key challenge is the preparation of the analyte for presentation to the on-chip detection system. Thus, in diagnostics, raw physiological samples must be introduced onto the chip and then further processed by lysing blood cells and extracting DNA. For massively parallel DNA sequencing, sample preparation can be performed off chip, but the synthesis steps must be performed in a sequential on-chip format by automated control of buffers and nucleotides to extend the read lengths of DNA fragments. In airborne particulate-sampling applications, the sample collection from an air stream must be integrated into the LoC analytical component, which requires a collection droplet to scan an exposed impacted surface after its introduction into a closed analytical section. Finally, in tissue-engineering applications, the challenge for LoC technology is to build high-resolution (less than 10 microns) 3D tissue constructs with embedded cells and growth factors by manipulating and maintaining live cells in the chip platform. This article discusses these applications and their implementation in digital-microfluidic LoC platforms. © 2007 IEEE.