Concise Physical Chemistry

c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

334 QUANTUM MOLECULAR MODELING

Z-MATRIX (ANGSTROMS AND DEGREES)

CD Cent Atom N1 Length/X N2 Alpha/Y N3 Beta/Z J

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11C

2 2 O 1 1.439156( 1)

3 3 H 1 1.066156( 2) 2 109.116( 6)

4 4 H 1 1.066156( 3) 2 109.116( 7) 3 -120.422( 10) 0

5 5 H 1 1.066156( 4) 2 109.116( 8) 3 119.800( 11) 0

6 6 H 2 1.066156( 5) 1 109.116( 9) 3 60.253( 12) 0

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Z-Matrix orientation:

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Center Atomic Atomic Coordinates (Angstroms)

Number Number Type X Y Z

---------------------------------------------------- ---------

1 6 0 0.000000 0.000000 0.000000

2 8 0 0.000000 0.000000 1.439156

3 1 0 1.007363 0.000000 -0.349152

4 1 0 -0.510100 0.868665 -0.349152

5 1 0 -0.500630 -0.874157 -0.349152

6 1 0 0.499824 0.874618 1.788308

FILE 20.10 Optimized Geometry from a GAUSSIAN©CSTO-3G Calculation on Methanol

(internal and Cartesian coordinates).

Even this simple molecule would be a discouraging prospect for hand calculation

as seen from the printout of the number of basis functions and primitive Gaussians:

14 basis functions, 42 primitive gaussians, 14 cartesian

basis functions

9 alpha electrons 9 beta electrons

The approximate input geometry is optimized during the program run. Output files

can be obtained in either internal or Cartesian (external) coordinates. Bond distances

and angles have been corrected in small amounts by the program.

The expected distinction between the C H bond lengths and the O H length in the

optimized geometry (1.439 vs. 1.066A) is found in lines 2 and 3 of the ̊ z-matrix. Also,

all simple angles and dihedral angles have been shifted from their original inputs.

The presence of an oxygen atom in the molecule distorts the tetrahedral geometry of

the CH 3 group slightly. The calculated energy is

TOTAL ENERGY= -113.5386327

20.13 FINDING (^) fH^298 OF METHANOL
Either the GAUSSIAN or GAMESS calculation gives the STO-3G molecular energy
as−113.538633 hartrees. This energy is relative to the separated nuclei and electrons.