Shape Calculations

2/29/11:
Using the program "Shape", the 'octahedrality' of Te is examined. The resulting number can be interpreted on a scale from 0 to 100, where 0 would represent perfect geometrical alignment and 100 would represent perfect distortion. Here is the input file:

$ V Te Compounds, Te coordination    
! Oxygens  Metal    
     6       7     
! Octahedron, Pentagonal Pyramid, Johnson Pentagonal Pyramid    
     3     2     5
mz84
   O    -14.30071     9.34143     8.74273
   O    -12.34116     7.94082     8.29434
   O    -13.76719    11.92894     8.87485
   O    -12.74553    10.37025     6.70175
   O    -13.20813    11.09876    11.31230
   O    -11.41923    12.33730     7.58173
  Te   -12.71052    10.35175     8.58565
mz133
   O    8.06696     4.52295     2.35615
   O    8.79474     6.89596     3.09586
   O    9.20725     5.19837     6.82254
   O    7.76981     2.85714     4.55979
   O    10.12859     2.14839     3.88286
   O    7.29509     5.48599     4.95659
  Te   8.67855     4.44958     4.13778
laqnib
   O    5.30096     1.47566     1.26613
   O    3.98255     1.97700    -1.00423
   O    3.85649    -0.72801    -0.84988
   O    5.67896    -1.92696    -2.11809
   O    4.67924     0.50731    -3.30069
   O    6.04483     2.64792    -2.75689
  Te   5.13450     0.51442    -1.47989
laqnoh
   O    4.30989    -3.47190    -1.03298
   O    4.10406    -4.06801    -5.69872
   O    5.28783    -6.61245    -4.14422
   O    5.15849    -1.89103    -4.87357
   O    3.15913    -2.76888    -3.32744
   O    3.15718    -5.45315    -3.45488
  Te   4.43022    -4.10919    -3.84309
ajiqeq
   O    4.23397     3.54831    -7.07768
   O    2.97171     2.45607    -3.16288
   O    1.96222     3.02084    -5.56270
   O    1.61736     0.32434    -5.45618
   O    2.80912     1.49640    -7.78692
   O    3.47875    -1.02988    -6.47456
  Te   3.04161     1.47825    -5.92562

The '6' is the number of vertices, the '7' indicates that the central metal is the 7th atom listed in each data set. '3', '2', and '5' indicate a calculation on each data set with respect to octahedral, pentagonal pyramidal, and johnson pentagonal pyramidal geometries respectively. These numerical codes can be found in the shape manual under the list or reference shapes with six vertices. Output:

V Te Compounds, Te coordination     

OC-6            3 Oh    Octahedron                                         
JPPY-6          5 C5v   Johnson pentagonal pyramid J2                      
PPY-6           2 C5v   Pentagonal pyramid                                 

Structure [ML6 ]         OC-6       JPPY-6        PPY-6
 mz84           ,      11.810,      21.862,      21.765
 mz133          ,      11.671,      22.061,      21.532
 laqnib         ,      12.391,      20.038,      20.845
 laqnoh         ,      11.887,      22.048,      22.079
 ajiqeq         ,      12.617,      20.109,      20.995

Therefore clearly we are much closer to octahedral geometry than either of the pentagonal pyramidal geometries, as expected. Ordering the first column:

mz133 , 11.671
mz84 , 11.810
laqnoh , 11.887
laqnib , 12.391
ajiqeq , 12.617

So what do these results mean? From Alex:

"The hypothesis was that the orientation of the [VO5] in mz10-133 resulted in a more octahedral coordination environment on the Te center. The data seem to scale nicely with the sixth Te … O distance."

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