Contour maps

We confine ourselves here to scanning probe microscopies (see Section VIII-2B) scanning tunneling microscopy (STM) and atomic force microscopy (AFM), in which successive profiles of a surface (see Fig. VIII-1) are combined to provide a contour map of a surface. It is conventional to display a map in terms of dark to light areas, in order of increasing height above the surface ordinary contour maps would be confusing to the eye. 

In a crossed-beam experiment the angular and velocity distributions are measured in the laboratory coordinate system, while scattering events are most conveniently described in a reference frame moving with the velocity of the centre-of-mass of the system. It is thus necessary to transfonn the measured velocity flux contour maps into the center-of-mass coordmate (CM) system [13]. Figure B2.3.2 illustrates the reagent and product velocities in the laboratory and CM coordinate systems. The CM coordinate system is travelling at the velocity c of the centre of mass... 

View the contour map m several planes to see the general Torm of the distiibiiiioii. As long as you don t alter the molecular coordinates, you don t need to repeat th e wave function calculation. Use the left mouse button and the IlyperChem Rotation or Translation tools (or Tool icons ) to change the view of amolecnle without changing its atomic coordinates. 

When a molecule rotates, IlypcrChem abandons the current contour map because it is no longer valid and you must explicitly request a new contour map via the Graph check box. 

If a iTioleciile is rotated by chan gin g th c position of the viewer (left mouse btiLlon rotation) ih en the moleetile s position in ihetnolee-ular eoorditi ale system h as not ch an ged and anolb er con lour plot can be requested without recotn pu tin g the wave ftinetion. fb at is, m any orbitals can he plotted after a sin gle poin t ah initio or setn i-einpirical calculation,. iti y contour map is available without recotn putation of the wave function. 

Sketch the probability of finding an electron in the 2s orbital of hydrogen at distance r from a hydrogen nucleus as a function of r as a contour map with heavy lines at high probability and light lines at low probability. How does this distribution differ from the Is orbital ... 

If a molecule is rotated by changing the position of the viewer (left mouse button rotation) then the molecule s position in the molecular coordinate system has not changed and another contour plot can be requested without recomputing the wave function. That is, many orbitals can be plotted after a single point ab initio or semi-empirical calculation. Any contour map is available without recomputation of the wave function. 

The results of electrostatic potential calculations can be used to predict initial attack positions of protons (or other ions) during a reaction. You can use the Contour Plot dialog box to request a plot of the contour map of the electrostatic potential of a molecular system after you done a semi-empirical or ab initio calculation. By definition, the electrostatic potential is calculated using the following expression ... 

If we use a contour map to represent a three-dimensional surface, with each contour line representing constant potential energy, two vibrational coordinates can be illustrated. Figure 6.35 shows such a map for the linear molecule CO2. The coordinates used here are not normal coordinates but the two CO bond lengths rj and r2 shown in Figure 6.36(a). It is assumed that the molecule does not bend. 

Local Site Condition Evaluation. In addition to visiting the site, drawing up a contour map and geology reports, acquiring sod-bearing information, and a knowledge of boundaries, setbacks, local requirements, utdity tie-in locations, sewer connections, access to roadways, pipelines, radroads, etc, may be needed to make a fliU assessment. 

Comparison of Alignment Charts and Cartesian Graphs. There are typically fewer lines on an alignment chart as compared to Cartesian plots. This reduces error introduced by interpolation and inconsistency between scales. For example, to find a point (x,j) on a Cartesian graph one draws two lines, one perpendicular to each axis, and these reference lines intersect at the point x,j). This point (x,j) may correspond to some finite value found by rea ding a contour map represented by a family of curves corresponding to different values of the function. 

An alignment chart is used by drawing one reference line through the two axes. This reference line, which need not be perpendicular to either axis, crosses a result axis at a unique finite value. This result axis represents the contour map on a Cartesian graph. Thus each line on an alignment chart represents a point on a Cartesian graph. 

Fig. 10-9. The evolution and transport of a large hazy air mass. Contour maps of noon visibility for June 25-July 5, 1975. Source Lyons, W. A., and Husar, R. B., Mon. Weather Rev. 104, 1623-1626 (1976).

To evaluate the wind speed at height H it is necessary to know the value of for the required location. This may be obtained either from a local weather station or from wind contour maps of the country. Normally, represents the hourly mean wind speed that is exceeded 50% of the time at a particular site. 

Figure 13 shows contour maps at an instant in time when 75% of the fuel is left in the calculation domain. Each contour plot shows contour values for the following percentages of the maximum in the plane in question 0.95, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05. In the plots the highest value is denoted... 

Figure 13. Velocity vectors and contour maps. Case 3.

The spirit of this kind of calculation is to give a rough and ready visualization to the potential reactivity of a molecule. For example, Figure 16.3 is a contour map for aspirin. These maps look much better in colour, and it is often possible to spot the route that an approaching charged reagent would take. 

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