Polygon method

Depositional areas for each core were approximated by both Theissen polygons and depth contours, although the reported fluxes are those only from the polygon method. In practice the two approaches gave virtually the same results. However, we favor the polygon method because proximity to the core site should be a better predictor of Hg accumulation in basins such as these, where sediment deposition is not correlated with lake depth. 

Use the Inscribed Polygon Method to Determine the Relative Energies of MOs for Cyclic, Completely Conjugated Compounds... 

Using the inscribed polygon method for five- and seven-membered rings... 

The inscribed polygon method is consistent with Huckel s 4n + 2 rule that is, there is always one lowest energy bonding MO that can hold two Jt electrons and the other bonding MOs come in degenerate pairs that can hold a total of four Jt electrons. For the compound to be aromatic, these MOs must be completely filled with electrons, so the magic numbers for aromaticity fit Huckel s 4n + 2 rule (Figure 17.11). 

Sample Problem 1 7.1 use the inscribed polygon method to show why cyclobutadiene is not aromatic. 

Use the inscribed polygon method to show the pattern of molecular orbitals in 1,3,5,7-cyclononatetraene and use it to label its cation, radical, and anion as aromatic, antiaromatic, or not aromatic. 

Inscribed polygon method (Section 17.10) A method to predict the relative energies of cyclic, completely conjugated compounds to determine which molecular orbitals are filled or empty. The inscribed polygon is also called a Frost circle. 

The spectra had the baseline corrected by the polygonal method [21], The used region was from 400 to 4,000 cm , and the spectra were normalized for the 1,510 cm (characteristic vibration of aromatics), originating 390 variables for both used lignins. Spectra were recorded in a Nicolet Avatar 320 FTIR spectrometer. Spectra were converted to text file files using OMNIC software (Nicolet). 

Besides polygonal approximation methods, higher order curve- and spline-fitting methods may be used where more precise approximations are required. These are more computationally expensive than most polygonalization methods, and they can be more difficult to apply. 

To predict the pattern of molecular orbitals found on a molecular orbital energy diagram, it is helpful to use the inscribed polygon method (Frost circles). 

Figure 25 Attaching a bridge using the open polygon method. The left-hand drawing is better.

In using the inscribed polygon method, always draw the vertex pointing down. 

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