Single particle method

Zuleta, M., Bjornbom, P., and Lundblad, A. Characterization of the electrochemical and ion-transport properties of a nanoporous carbon at negative polarization by the single-particle method../. Electrochem. Soc. 153, 2006 A48-A57. 

In prindple, the energy functional can be represented by any single-particle method, including all DFT functionals, or other formalisms like Hartree-Fock (HF) or semiempirical methods. In modem AIMD, the electronic stmcture method most commonly used is the KS formulation of DFT, which seeks to determine the exact ground-state energy and electron density directly, without computing a many-electron wave function. 

Effect of Heat Generation on Adsorption Rate Measurement by a Single Particle Method... 

The importance of the particle levitation methods is that they allow the study of how a single particle responds to changes in environment. The infrared molecular spectroscopy of single particles is possible [253], as are photophysical studies using adsorbed or dissolved dyes. 

Equations 3 to 7 indicate the method by which terminal velocity may be calculated. Erom a hydrodynamic force balance that considers gravity, buoyancy, and drag, but neglects interparticle forces, the single particle terminal velocity is... 

The results for the chemical potential determination are collected in Table 1 [172]. The nonreactive parts of the system contain a single-component hard-sphere fluid and the excess chemical potential is evaluated by using the test particle method. Evidently, the quantity should agree well with the value from the Carnahan-Starling equation of state [113]... 

Our work demonstrates that EELS and in particular the combination of this technique with first principles electronic structure calculations are very powerful methods to study the bonding character in intermetallic alloys and study the alloying effects of ternary elements on the electronic structure. Our success in modelling spectra indicates the validity of our methodology of calculating spectra using the local density approximation and the single particle approach. 

To measure the strength of the forces exerted on particles, various analytical techniques have been developed [6, 7]. Unfortunately, since most of these techniques are based on hydrodynamics, assumption of the potential profiles is required and the viscosities of the fiuid and the particle sizes must be precisely determined in separate experiments, for example, using the viscous flow technique [8,9] and power spectrum analysis of position fluctuation [10]. Furthermore, these methods provide information on ensemble averages for a mass of many particles. The sizes, shapes, and physical and chemical properties of individual particles may be different from each other, which will result in a variety of force strengths. Thus, single-particle... 

In his pioneering work Baetzold used the Hartree-Fock (HF) method for quantum mechanical calculations for the cluster structure (the details are summarized in Reference 33). The value of the HF procedure is that it yields the best possible single-determinant wave function, which in turn should give correct values for expectation values of single-particle operators such as electric moments and... 

Unlike the simulations which only consider particle-cluster interactions discussed earlier, hierarchical cluster-cluster aggregation (HCCA) allows for the formation of clusters from two clusters of the same size. Clusters formed by this method are not as dense as clusters formed by particle-cluster simulations, because a cluster cannot penetrate into another cluster as far as a single particle can (Fig. 37). The fractal dimension of HCCA clusters varies from 2.0 to 2.3 depending on the model used to generate the structure DLA, RLA, or LTA. For additional details, the reader may consult Meakin (1988). 

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