Subject: Summary: C60 coordinates

From: [email-masked]
Date: Thu, 7 Dec 2000 10:36:25 -0600 (CST)

Hi,

it turned out that many people are interested in getting the replies
to my ccl quesiton

> Hi,

> I wonder if someone could provide me with a Z-matrix input
> for buckminster-fullerene C60. I need my program to recognize
> as much of the icosahedral symmetry as possible.
>
>                           Thank you,
>                                 Marketa Munzarova

So, here are the replies: 

Gert von Helden's sent me a very elegant Z-matrix input, based on building
the pentagons and hexagons on C60 surface:
****************************************************************************
Hi,

G98 should recognize the full symmetry of C60 with the following 
z-matrix (note that
two angles, instead of one dihedral, is used for atom 6):

Hope that helps,   Gert
-----------------------
# AM1 opt

C60

    0   1
c
c   1 r5
c   2 r5  1 108.0
c   3 r5  2 108.0  1 0.00
c   4 r5  3 108.0  2 0.00
c   5 r6  4 120.0  1 120.0 1
c   6 r5  5 120.0  4 0.00
c   7 r6  6 120.0  5 0.00
c   8 r5  7 120.0  6 0.00
c   9 r5  4 120.0  3 0.00
c  10 r6  9 120.0  4 0.00
c 11 r5 10 120.0  9 0.00
c 12 r5  3 120.0  2 0.00
c 13 r6 12 120.0  3 0.00
c 14 r5 13 120.0  2 0.00
c 15 r5  2 120.0  1 0.00
c 16 r5 15 108.0 14 0.00
c 17 r5 16 108.0 15 0.00
c 18 r6 14 120.0 13 0.00
c 19 r5 18 120.0 14 0.00
c 20 r6 19 120.0 13 0.00
c 21 r5 13 108.0 12 0.00
c 22 r6 11 120.0 10 0.00
c 23 r5 22 120.0 11 0.00
c 10 r5 11 120.0 22 0.00
c 11 r5 10 120.0  9 0.00
c 12 r5  3 120.0  2 0.00
c 13 r6 12 120.0  3 0.00
c 14 r5 13 120.0  2 0.00
c 15 r5  2 120.0  1 0.00
c 16 r5 15 108.0 14 0.00
c 17 r5 16 108.0 15 0.00
c 18 r6 14 120.0 13 0.00
c 19 r5 18 120.0 14 0.00
c 20 r6 19 120.0 13 0.00
c 21 r5 13 108.0 12 0.00
c 22 r6 11 120.0 10 0.00
c 23 r5 22 120.0 11 0.00
c 10 r5 11 120.0 22 0.00
c 8 r5  9 108.0  10 0.00
c 26 r6  8 120.0  7 0.00
c 27 r5 26 120.0  8 0.00
c 28 r6 27 120.0 26 0.00
c 29 r5  7 108.0  6 0.00
c 30 r6 29 120.0 28 0.00
c 31 r5 30 120.0 29 0.00
c 32 r6 31 120.0 30 0.00
c 33 r5 28 108.0 27 0.00
c 34 r5 33 108.0 28 0.00
c 35 r6 27 120.0 26 0.00
c 36 r5 24 108.0 23 0.00
c 37 r5 36 108.0 24 0.00
c 38 r6 23 120.0 22 0.00
c 39 r5 38 120.0 37 0.00
c 40 r5 39 108.0 20 0.00
c 41 r6 19 120.0 18 0.00
c 42 r5 41 120.0 19 0.00
c 43 r5 17 120.0 16 0.00
c 44 r5 43 108.0 42 0.00
c 45 r5 44 108.0 43 0.00
c 46 r6 42 120.0 41 0.00
c 47 r5 46 120.0 42 0.00
c 48 r5 40 120.0 39 0.00
c 49 r5 48 108.0 47 0.00
c 50 r5 49 108.0 48 0.00
c 51 r6 47 120.0 46 0.00
c 52 r5 51 120.0 47 0.00
c 53 r5 52 108.0 32 0.00
c 54 r6 53 120.0 45 0.00
c 55 r5 54 120.0 53 0.00
c 56 r5 44 120.0 43 0.00
c 57 r5 56 108.0 55 0.00
c 58 r5 57 108.0 56 0.00
c 59 r6 55 120.0 54 0.00

r5 1.474
r6 1.420

***********************************************************************************

Another very nice Z-matrix input, definig the carbons with respect to the C60
centre and a number of dummies, has been sent by Roy Jensen
-----------------------------------------------------------------------------------
Gaussian test jobs 322 and 333 have C60 in z-matrix format.
I have copied 322 below if you do not have it.

Roy Jensen

-------------------
%chk=test322
%mem=2000000,4000000
#p RHF/STO-3G test opt freq

Gaussian Test Job 322 (Part 1):
C60 Icosahedral

0 1
X
X 1 1.
X 1 1. 2 90.
X 1 1. 2 90. 3 180.
X 1 1. 3 C1  2   0.
X 1 1. 3 C1  5  C2
X 1 1. 3 C1  5  C3
X 1 1. 3 C1  5 -C2
X 1 1. 3 C1  5 -C3
X 1 1. 4 C1  2 180.
X 1 1. 4 C1 10  C2
X 1 1. 4 C1 10  C3
X 1 1. 4 C1 10 -C2
X 1 1. 4 C1 10 -C3
C 1 R 3 A 5 0.
C 1 R 3 A 6 0.
C 1 R 3 A 7 0.
C 1 R 3 A 8 0.
C 1 R 3 A 9 0.
C 1 R 5 A 3 0.
C 1 R 5 A 3 C2
C 1 R 5 A 3 C3
C 1 R 5 A 3 -C2
C 1 R 5 A 3 -C3
C 1 R 6 A 3 0.
C 1 R 6 A 3 C2
C 1 R 6 A 3 C3
C 1 R 6 A 3 -C2
C 1 R 6 A 3 -C3
C 1 R 7 A 3 0.
C 1 R 7 A 3 C2
C 1 R 7 A 3 C3
C 1 R 7 A 3 -C2
C 1 R 7 A 3 -C3
C 1 R 8 A 3 0.
C 1 R 8 A 3 C2
C 1 R 8 A 3 C3
C 1 R 8 A 3 -C2
C 1 R 8 A 3 -C3
C 1 R 9 A 3 0.
C 1 R 9 A 3 C2
C 1 R 9 A 3 C3
C 1 R 9 A 3 -C2
C 1 R 9 A 3 -C3
C 1 R 4 A 10 0.
C 1 R 4 A 11 0.
C 1 R 4 A 12 0.
C 1 R 4 A 13 0.
C 1 R 4 A 14 0.
C 1 R 10 A 4 0.
C 1 R 10 A 4 C2
C 1 R 10 A 4 C3
C 1 R 10 A 4 -C2
C 1 R 10 A 4 -C3
C 1 R 11 A 4 0.
C 1 R 11 A 4 C2
C 1 R 11 A 4 C3
C 1 R 11 A 4 -C2
C 1 R 11 A 4 -C3
C 1 R 12 A 4 0.
C 1 R 12 A 4 C2
C 1 R 12 A 4 C3
C 1 R 12 A 4 -C2
C 1 R 12 A 4 -C3
C 1 R 13 A 4 0.
C 1 R 13 A 4 C2
C 1 R 13 A 4 C3
C 1 R 13 A 4 -C2
C 1 R 13 A 4 -C3
C 1 R 14 A 4 0.
C 1 R 14 A 4 C2
C 1 R 14 A 4 C3
C 1 R 14 A 4 -C2
C 1 R 14 A 4 -C3
     Variables:
R 3.52429
A 20.5346
     Constants:
C1 63.434948823
C2 72.0
C3 144.0

********************************************************************************

Several people sent me cartesian coordinates inputs, which can be converted
to full Z-matrixes.

Here are the cartesian coordinates from N. Dragoe, in G98 format:
********************************************************************************
Hi,

These are the coordinates for C60. I am not sure but I think you could
transfer them into Z-matrix with Gaussian.
--------
                        Standard orientation:
 ---------------------------------------------------------------------
 Center     Atomic     Atomic              Coordinates (Angstroms)
 Number     Number      Type              X           Y           Z
 ---------------------------------------------------------------------
    1          6             0        0.726656   -1.000157    3.300459
    2          6             0        1.175755    0.382026    3.300459
    3          6             0        1.410183   -1.940951    2.581756
    4          6             0        2.281725    0.741377    2.581756
    5          6             0        2.281725    1.977639    1.817704
    6          6             0        0.000000    1.236262    3.300459
    7          6             0        0.000000    2.399147    2.581756
    8          6             0        1.175755    2.781173    1.817704
    9          6             0       -0.683527   -2.941108    1.817704
   10          6             0       -1.410183   -1.940951    2.581756
   11          6             0        0.683527   -2.941108    1.817704
   12          6             0       -0.726656   -1.000157    3.300459
   13          6             0       -1.175755    0.382026    3.300459
   14          6             0       -2.585938   -1.558925    1.817704
   15          6             0       -3.008381   -0.258779    1.817704
   16          6             0       -2.281725    0.741377    2.581756
   17          6             0        0.726656   -3.399304   -0.581443
   18          6             0       -0.726656   -3.399304   -0.581443
   19          6             0        1.410183   -3.177213    0.581443
   20          6             0       -1.410183   -3.177213    0.581443
   21          6             0       -2.585938   -2.322977    0.581443
   22          6             0       -1.175755   -2.781173   -1.817704
   23          6             0       -2.281725   -1.977639   -1.817704
   24          6             0       -3.008381   -1.741534   -0.581443
   25          6             0        3.008381   -1.741534   -0.581443
   26          6             0        2.281725   -1.977639   -1.817704
   27          6             0        2.585938   -2.322977    0.581443
   28          6             0        1.175755   -2.781173   -1.817704
   29          6             0        0.000000   -2.399147   -2.581756
   30          6             0        2.281725   -0.741377   -2.581756
   31          6             0        1.175755   -0.382026   -3.300459
   32          6             0        0.000000   -1.236262   -3.300459
   33          6             0        3.008381   -0.258779    1.817704
   34          6             0        3.457479    0.359351    0.581443
   35          6             0        2.585938   -1.558925    1.817704
   36          6             0        3.457479   -0.359351   -0.581443
   37          6             0        3.008381    0.258779   -1.817704
   38          6             0        3.008381    1.741534    0.581443
   39          6             0        2.585938    2.322977   -0.581443
   40          6             0        2.585938    1.558925   -1.817704
   41          6             0       -0.726656    1.000157   -3.300459
   42          6             0        0.726656    1.000157   -3.300459
   43          6             0        1.410183    1.940951   -2.581756
   44          6             0       -1.410183    1.940951   -2.581756
   45          6             0       -3.008381    0.258779   -1.817704
   46          6             0       -2.281725   -0.741377   -2.581756
   47          6             0       -1.175755   -0.382026   -3.300459
   48          6             0       -2.585938    1.558925   -1.817704
   49          6             0       -3.008381    1.741534    0.581443
   50          6             0       -3.457479    0.359351    0.581443
   51          6             0       -3.457479   -0.359351   -0.581443
   52          6             0       -2.585938    2.322977   -0.581443
   53          6             0       -0.726656    3.399304    0.581443
   54          6             0       -1.175755    2.781173    1.817704
   55          6             0       -2.281725    1.977639    1.817704
   56          6             0       -1.410183    3.177213   -0.581443
   57          6             0        0.683527    2.941108   -1.817704
   58          6             0        1.410183    3.177213   -0.581443
   59          6             0        0.726656    3.399304    0.581443
   60          6             0       -0.683527    2.941108   -1.817704

******************************************************************************************

James Stewart provided  me with cartesian coordinates in MOPAC format:

------------------------------------------------------------------------
c60.MOP
                                                                                
  C    0.000000  0    0.000000  0    0.000000  0    0   0   0
  C    1.457458  1    0.000000  0    0.000000  0    1   0   0
  C    1.457489  1  107.999603  1    0.000000  0    2   1   0
  C    1.457474  1  107.999603  1    0.000000  1    3   2   1
  C    1.457443  1  108.001343  1    0.000000  1    1   2   3
  C    5.199631  1   90.000244  1   31.718307  1    1   2   3
  C    1.457489  1   35.998703  1  238.281448  1    6   1   2
  C    1.383911  1  119.999756  1  217.376038  1    4   3   2
  C    1.457474  1  120.001495  1    0.000000  1    8   4   3
  C    1.457458  1  108.001343  1    0.000000  1    6   7   8
  C    2.841415  1   59.999008  1  142.622208  1    1   2   3
  C    1.457474  1  144.000046  1  280.812653  1   11   1   2
  C    1.457458  1  107.999603  1   63.433105  1   12  11   1
  C    1.457489  1  107.999603  1    0.000000  1   13  12  11
  C    1.383926  1  120.001495  1  217.379532  1    2   1   5
  C    6.651367  1   77.666138  1   52.436615  1    1   2   3
  C    1.383926  1  120.001495  1  142.622208  1   10   6   7
  C    1.457489  1  120.001495  1  221.812057  1   17  10   6
  C    1.457489  1  107.999603  1  142.622208  1   18  17  10
  C    1.457474  1  107.999603  1  217.376038  1   16  17  10
  C    1.383926  1  119.999756  1  359.683517  1   16  17  10
  C    1.457474  1  119.999756  1  221.810303  1   21  16  17
  C    1.457489  1  107.999603  1  142.622208  1   22  21  16
  C    1.457504  1  107.999603  1    0.000000  1   23  22  21
  C    1.383926  1  119.999756  1  142.622208  1    6   7   8
  C    1.383942  1  119.998000  1  142.623962  1    1   2   3
  C    1.457489  1  119.999756  1  221.810303  1   26   1   2
  C    1.457489  1  107.999603  1  142.623962  1   27  26   1
  C    1.457504  1  107.999603  1    0.000000  1   28  27  26
  C    1.383926  1  119.999756  1  142.622208  1   11  12  13
  C    1.383911  1  119.999756  1  217.376038  1    3   2   1
  C    1.383896  1  119.999756  1  217.376038  1   14  13  12
  C    1.457489  1  119.998000  1    0.000000  1   32  14  13
  C    1.383911  1  119.999756  1    0.000000  1   18  17  10
  C    1.383926  1  119.998000  1    0.000000  1    9   8   4
  C    1.383926  1  119.999756  1  142.623962  1    5   1   2
  C    1.383926  1  119.999756  1  217.377792  1    7   6  10
  C    1.383911  1  119.999756  1  217.376038  1   24  23  22
  C    1.457489  1  119.999756  1    0.000000  1   38  24  23
  C    1.383881  1  119.999756  1    0.000000  1   27  26   1
  C    1.383926  1  120.001495  1  217.379532  1   23  22  21
  C    1.457474  1  119.999756  1    0.000000  1   41  23  22
  C    1.457474  1  107.999603  1  142.623962  1   42  41  23
  C    1.383865  1  119.999756  1  217.376038  1   28  27  26
  C    1.383881  1  120.001495  1    0.000000  1   39  38  24
  C    1.457474  1  119.999756  1    0.000000  1   41  23  22
  C    1.457474  1  107.999603  1  142.623962  1   42  41  23
  C    1.383865  1  119.999756  1  217.376038  1   28  27  26
  C    1.383881  1  120.001495  1    0.000000  1   39  38  24
  C    6.054962  1   60.000748  1  100.813156  1    1   2   3
  C    1.457474  1  107.999603  1  259.186844  1   46   1   2
  C    1.383896  1  119.999756  1  217.377792  1   19  18  17
  C    1.383881  1  120.001495  1    0.000000  1   33  32  14
  C    1.383896  1  120.001495  1  217.376038  1   13  12  11
  C    1.383911  1  119.999756  1  217.376038  1   43  42  41
  C    1.457489  1  119.998000  1    0.000000  1   51  43  42
  C    1.383926  1  119.999756  1  142.623962  1   46  47  48
  C    1.383911  1  120.001495  1  217.376038  1   12  11  15
  C    1.383911  1  120.001495  1  217.377792  1   29  28  27
  C    1.383926  1  119.999756  1  142.622208  1   20  16  17
  C    1.383911  1  119.998000  1  217.376038  1   47  46  50
  C    1.383896  1  120.001495  1    0.000000  1   52  51  43
  C    1.383926  1  119.999756  1    0.000000  1   42  41  23
  C    1.383911  1  119.999756  1    0.000000  1   22  21  16

***********************************************************************************

Pascal Bonnet sent me both cartesian coordinates and their conversion to the
full Z-matrix. Either can be obtained at the web page of prof. Yoshida:

    http://shachi.cochem2.tutkie.tut.ac.jp/Fuller/Fuller.html

***********************************************************************************

Geoff Hutchison's reply included a full Z-matrix input:
***********************************************************************************
As it happens, I had a BuckyBall Molfile, so I converted it to Gaussian
Z-matrix for you. See the attached file.

Cheers,
-Geoff Hutchison
Northwestern Chemistry
------------------------
 C 
  C    1 r2 
  C    2 r3    1 a3
  C    3 r4    2 a4    1 d4
  C    4 r5    3 a5    2 d5
  C    1 r6    2 a6    3 d6
  C    4 r7    3 a7    2 d7
  C    7 r8    4 a8    3 d8
  C    8 r9    7 a9    4 d9
  C    7 r10    4 a10    3 d10
  C    10 r11    7 a11    4 d11
  C    11 r12    10 a12    7 d12
  C    12 r13    11 a13    10 d13
  C    10 r14    7 a14    4 d14
  C    3 r15    2 a15    1 d15
  C    13 r16    12 a16    11 d16
  C    16 r17    13 a17    12 d17
  C    17 r18    16 a18    13 d18
  C    18 r19    17 a19    16 d19
  C    6 r20    1 a20    2 d20
  C    1 r21    2 a21    3 d21
  C    21 r22    1 a22    2 d22
  C    19 r23    18 a23    17 d23
  C    23 r24    19 a24    18 d24
  C    16 r25    13 a25    12 d25
  C    12 r26    11 a26    10 d26
  C    11 r27    10 a27    7 d27
  C    27 r28    11 a28    10 d28
  C    15 r29    3 a29    2 d29
  C    29 r30    15 a30    3 d30
  C    30 r31    29 a31    15 d31
  C    31 r32    30 a32    29 d32
  C    22 r33    21 a33    1 d33
  C    33 r34    22 a34    21 d34
  C    24 r35    23 a35    19 d35
  C    35 r36    24 a36    23 d36
  C    26 r37    12 a37    11 d37
  C    37 r38    26 a38    12 d38
  C    28 r39    27 a39    11 d39
  C    39 r40    28 a40    27 d40
  C    40 r41    39 a41    28 d41
  C    31 r42    30 a42    29 d42
  C    32 r43    31 a43    30 d43
  C    33 r44    22 a44    21 d44
  C    34 r45    33 a45    22 d45
  C    35 r46    24 a46    23 d46
  C    36 r47    35 a47    24 d47
  C    37 r48    26 a48    12 d48
  C    38 r49    37 a49    26 d49
  C    39 r50    28 a50    27 d50
  C    41 r51    40 a51    39 d51
  C    42 r52    31 a52    30 d52
  C    44 r53    33 a53    22 d53
  C    46 r54    35 a54    24 d54
  C    49 r55    38 a55    37 d55
  C    55 r56    49 a56    38 d56
  C    56 r57    55 a57    49 d57
  C    57 r58    56 a58    55 d58
  C    58 r59    57 a59    56 d59
  C    59 r60    58 a60    57 d60
Variables:
r2= 1.3802
r3= 1.3706
a3= 120.01
r4= 1.3802
a4= 120.00
d4= 359.97
r5= 1.3706
a5= 119.99
d5=   0.03
r6= 1.3705
a6= 119.99
d6=   0.03
r7= 1.3704
a7= 119.96
d7= 138.15
r8= 1.3704
a8= 107.98
d8= 217.44
r9= 1.3703
a9= 108.02
d9= 359.97
r10= 1.3804
a10= 120.07
d10= 359.97
r11= 1.3715
a11= 120.11
d11= 221.69
r12= 1.3799
a12= 119.87
d12=   0.15
r13= 1.3698
a13= 120.05
d13=   0.03
r14= 1.3704
a14= 119.97
d14=   0.03
r15= 1.3702
a15= 108.01
d15= 142.57
r16= 1.3696
a16= 108.08
d16= 142.73
r17= 1.3799
a17= 120.04
d17= 217.29
r18= 1.3716
a18= 119.89
d18= 359.97
r19= 1.3705
a19= 108.04
d19= 142.58
r20= 1.3703
a20= 107.99
d20= 217.44
r21= 1.3704
a21= 119.97
d21= 221.85
r22= 1.3702
a22= 107.97
d22= 142.56
r23= 1.3715
a23= 108.02
d23= 359.97
r24= 1.3693
a24= 107.83
d24=   0.03
r25= 1.3736
a25= 108.08
d25=   0.20
r26= 1.3729
a26= 120.09
d26= 138.56
r27= 1.3694
a27= 107.85
d27= 142.75
r28= 1.3693
a28= 108.26
d28= 359.97
r29= 1.3703
a29= 107.97
d29= 359.97
r30= 1.3702
a30= 108.04
d30=   0.03
r31= 1.3804
a31= 119.93
d31= 217.36
r32= 1.3704
a32= 119.98
d32= 138.16
r33= 1.3804
a33= 120.00
d33= 217.33
r34= 1.3695
a34= 120.01
d34= 138.37
r35= 1.3848
a35= 120.01
d35= 216.94
r36= 1.3739
a36= 119.83
d36= 139.17
r37= 1.3852
a37= 119.80
d37=   0.46
r38= 1.3746
a38= 120.08
d38= 358.59
r39= 1.3800
a39= 120.21
d39= 217.58
r40= 1.3696
a40= 120.04
d40= 137.97
r41= 1.3696
a41= 108.10
d41= 217.28
r42= 1.3715
a42= 120.10
d42= 359.81
r43= 1.3716
a43= 108.03
d43= 217.19
r44= 1.3697
a44= 120.08
d44= 359.89
r45= 1.3731
a45= 108.06
d45= 216.90
r46= 1.3746
a46= 119.80
d46= 359.63
r47= 1.3426
a47= 108.01
d47= 217.28
r48= 1.3426
a48= 119.25
d48= 221.15
r49= 1.3740
a49= 108.98
d49= 217.92
r50= 1.3735
a50= 120.08
d50= 359.46
r51= 1.3728
a51= 108.06
d51= 359.79
r52= 1.3693
a52= 107.86
d52= 142.77
r53= 1.3735
a53= 108.09
d53= 143.06
r54= 1.3425
a54= 108.13
d54= 142.98
r55= 1.3425
a55= 108.04
d55=   0.71
r56= 1.4358
a56= 120.29
d56= 141.94
r57= 1.3426
a57= 120.10
d57= 359.48
r58= 1.3747
a58= 108.15
d58= 218.50
r59= 1.3741
a59= 108.98
d59= 359.54
r60= 1.3427
a60= 108.02
d60=   0.71

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Finally, here is Marcel Swart's advice:

-------------
Try building it, save it in Cartesian coordinates and afterwards use 
Babel to do the conversion to Z-matrix.

Marcel Swart

********************************************************************************************

Many thanks to everybody who replied!

                                                    Marketa

******************************************************************
Marketa L. Munzarova            e-mail:  [email-masked]
220 Baker Lab                    phone:   1-607-255-0597
Cornell University
Ithaca, New York, 14850-1301
******************************************************************