Energies of Atomization from Population Analysis on Hückel Wave Functions

1966 ◽  
pp. 39-47 ◽  
Author(s):  
FORREST S. MORTIMER
Keyword(s):  
Population Analysis ◽  
Wave Functions

The Interpretation of molecular wave functions: the development and application of Roby's method for electron population analysis

1982 ◽  
Vol 304 (1488) ◽  
pp. 533-565 ◽  
Keyword(s):  
Population Analysis ◽  
Chem Phys ◽  
Wave Functions ◽  
Multiple Bonds ◽  
Electron Population ◽  
Polarization Functions ◽  
Bond Strengths ◽  
Extended Basis ◽  
Two Hybrid ◽  
Single Bonds

An extensive investigation has been made of Roby’s (Molec. Phys. 27, 81 (1974)) projection-density method for electron population analysis, particularly as applied to extended basis molecular wave functions. In the developed method maximum possible populations are ascribed to atomic s.c.f. orbitals and minimum possible populations to polarization functions. Roby populations are reported for a range of diatomic and simple polyatomic molecules. For a given coordination number, the Roby atomic population n A reflects the electronegativities of an atom and its ligands. By equipartition of shared populations, atomic charges may also be defined. The two-centre shared populations s AB = n A + n B — are found to be coherent indicators of bond strengths. For conventional single bonds, s AB can often be roughly interpreted as S AB » 2 S ab ,where S ab is the overlap integral between the two hybrid atomic orbitals defined by a localized molecular orbital representing the A -B bond. Multiple bonds can be interpreted similarly. Multi-centre shared populations s ABC , s ABCD are helpful in descriptions o f the bonding in B 2 H 6 and P 4 . The Roby projector technique is particularly useful in determining the unique effects of polarization functions. Several wave functions for NF 3 and SO 3 are examined in detail, and the sulphur d functions are confirmed as the most important polarization functions. Various technical aspects of the Roby method are also explored, and the method is shown to have some significant advantages over the widely used Mulliken ( J. chem. Phys. 23, 1833 (1955)) method of population analysis.

Automated 3-D cell population analysis in thick tissue sections using laser-scanning confocal-microscopy data

1993 ◽  
Vol 51 ◽  
pp. 562-563
Author(s):  
Hakan Ancin
Keyword(s):  
Laser Scanning ◽  
Population Analysis ◽  
Three Dimensional ◽  
Large Data ◽  
Laser Scanning Confocal Microscopy ◽  
Tissue Slices ◽  
Scanning Confocal Microscopy ◽  
Tissue Sections ◽  
Spatially Adaptive ◽  
Microscopy Data

This paper presents methods for performing detailed quantitative automated three dimensional (3-D) analysis of cell populations in thick tissue sections while preserving the relative 3-D locations of cells. Specifically, the method disambiguates overlapping clusters of cells, and accurately measures the volume, 3-D location, and shape parameters for each cell. Finally, the entire population of cells is analyzed to detect patterns and groupings with respect to various combinations of cell properties. All of the above is accomplished with zero subjective bias.In this method, a laser-scanning confocal light microscope (LSCM) is used to collect optical sections through the entire thickness (100 - 500μm) of fluorescently-labelled tissue slices. The acquired stack of optical slices is first subjected to axial deblurring using the expectation maximization (EM) algorithm. The resulting isotropic 3-D image is segmented using a spatially-adaptive Poisson based image segmentation algorithm with region-dependent smoothing parameters. Extracting the voxels that were labelled as "foreground" into an active voxel data structure results in a large data reduction.

Magnetotunneling spectroscopy imaging of electron wave functions in self-assembled InAs quantum dots

2001 ◽  
Vol 171 (12) ◽  
pp. 1365
Author(s):  
E.E. Vdovin ◽  
Yu.N. Khanin ◽  
Yu.V. Dubrovskii ◽  
A. Veretennikov ◽  
A. Levin ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Wave Functions ◽  
Electron Wave ◽  
Inas Quantum Dots ◽  
Self Assembled
Sign in / Sign up

Export Citation Format

Share Document