Spreadsheet Activity #7:  Plotting d(x2-y2) Orgital model in Two Dimensions

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One-dimensional graphs of molecular orbitals are simple using spreadsheets.  For example, a planar  representation of the (dx2-y2) orbital may be constructed using the equation: 
                R = sqrt(15/(16*pi))*cos(2*angle)
Try out your skills at evaluating this equation between 0 and 360 degrees and plot your results in both (pseudo)-Polar and Cartesian Coordinates.  This is most easily accomplished by converting numerical data from polar coordinates (r,theta) to Cartesian (x,y) coordinates.  To assist you, and to show the slight differences between formulas in various spreadsheets, the formulas for this exercise are listed below:

Formulas for columns:

    A2:Theta (deg):     Fill data in 2-degree steps from 0 to 360 degrees         
    B2:Theta (rad):      Lotus & Quatro: +A2*@PI/180
                                 Excel:                  =A2*PI()/180                                    
    C2: Radius             Lotus & Quatro: +@SQRT(15/16*@PI))*COS(2*B2)
                                 Excel:                  =SQRT(15/(16*PI()))*COS(2*B2)   
    D2: x-coord:         Lotus & Quatro: +C2*@COS(B2)
                                 Excel:                  =C2*COS(B2)                                  
    E2: Y-coord:         Lotus & Quatro: +C2*@SIN(B2)
                                 Excel:                  =C2*SIN(B2)                                    

	A	B	C	D	E
1	(deg)	(rad)	Radius	x-coord	y-coord
2	0	0.0000	0.5463	0.5463	0.0000
3	2	0.0349	0.5449	0.5446	0.0190
4	4	0.0698	0.5410	0.5396	0.0377
5	6	0.1047	0.5343	0.5314	0.0559
6	8	0.1396	0.5251	0.5200	0.0731
...	...	...	...	...	...
181	360	6.2832	0.5463	0.5463	0.0000

 

 

Excel Programming Tips

Most spreadsheets have utilities to help fill data into a column or row.  For example, you can let Excel fill in the numbers 0,2,4,6,…..,180 down column A.  There are a variety of ways to do this:

1 – Type in the first few numbers in the series (0,2,4..).  Then highlight the cells where you have typed these numbers;  then click and hold your mouse arrow on the lower right corner of the lowest cell and drag downwards to fill the remaining cells.

2 – Calculate the numbers by building formulas in a neighboring cell and copying it throughout the range.  In this case, you could select cell A3 and enter the formula “=A2+2.”  This will display the value 2 in this cell.  Copying this formula downwards throughout the range will display the numbers you want.  Note:  If the initial value in cell A2 is changed, all the numbers based upon this formula will also change.  To lock them, copy the entire range and then paste as values (not formulas).  e.g. click on Edit > Paste Special > Values.