! EXAM25.
!   Illustration of coordinate systems for geometry searches.
!   Arbitrary molecule, chosen to illustrate ring, methyl on
!   ring, methine H10, imino in ring, methylene in ring.
!
!      H8 H9
!        \|
!      H7-C6  O1---O5   H13
!          \ /       \ /
!           C2       C4
!          /  \     /  \
!         H10    N3     H12
!                |
!                H11
!                       
!   The initial AM1 energy is -48.6594935, RMS=0.0200113
!                      final E    final RMS  #steps
!   Cartesians       -48.7022572  0.0000259    44
!   dangling Z-mat   the OO bond crashes on 1st step
!   good Z-matrix    -48.7022550  0.0000137    27
!   deloc. coords.   -48.7022538  0.0000249    23
!   nat. internals   -48.7022570  0.0000207    15
!
!   Note that the delocalized coordinates have very easy
!   input compared to the natural internals, and take many
!   fewer steps to converge than Cartesian coordinates.
!
 $contrl scftyp=rhf runtyp=optimize coord=zmt $end
 $system timlim=1 $end
 $statpt hess=guess nstep=100 nprt=-1 npun=-2 $end
 $basis  gbasis=am1 $end
 $guess  guess=huckel $end
 $data
Illustration of coordinate systems
C1
O
C 1 rCOa
N 2 rCNa 1 aNCO
C 3 rCNb 2 aCNC  1 wCNCO
O 4 rCOb 3 aOCN  2 wOCNC
C 2 rCC  1 aCCO  5 wCCOO
H 6 rCH1 2 aHCC1 1 wHCCO1
H 6 rCH2 2 aHCC2 1 wHCCO2
H 6 rCH3 2 aHCC3 1 wHCCO3
H 2 rCHa 1 aHCOa 5 wHCOOa
H 3 rNH  2 aHNC  1 wHNCO
H 4 rCHb 5 aHCOb 1 wHCOOb
H 4 rCHc 5 aHCOc 1 wHCOOc

rCOa=1.43
rCNa=1.47
rCNb=1.47
rCOb=1.43
aNCO=106.0
aCNC=104.0
aOCN=106.0
wCNCO=30.0
wOCNC=-30.0
rCC=1.54
aCCO=110.0
wCCOO=-150.0
rCH1=1.09
rCH2=1.09
rCH3=1.09
aHCC1=109.0
aHCC2=109.0
aHCC3=109.0
wHCCO1=60.0
wHCCO2=-60.0
wHCCO3=180.0
rCHa=1.09
aHCOa=110.0
wHCOOa=100.0
rNH=1.01
aHNC=110.0
wHNCO=170.0
rCHb=1.09
rCHc=1.09
aHCOb=110.0
aHCOc=110.0
wHCOOb=150.0
wHCOOc=-100.0
 $end

To use Cartesian coordinates:
--- $contrl nzvar=0 $end

To use conventional Z-matrix, with a dangling O-O bond:
--- $contrl nzvar=33 $end

To use well chosen internals, with all 5 ring bonds defined:
--- $contrl nzvar=33 $end
--- $zmat   izmat(1)=1,1,2,  1,2,3,  1,3,4,  1,4,5,  1,5,1,
     2,1,2,3,  2,5,4,3,  3,5,1,2,3,  3,1,5,4,3,
     1,6,2,  2,6,2,1,  3,6,2,1,5,  
     1,6,7,  1,6,8,  1,6,9,  2,7,6,2,  2,8,6,2,  2,9,6,2,  
     3,7,6,2,1,  3,8,6,2,1,  3,9,6,2,1,
     1,10,2,  2,10,2,1,  3,10,2,1,5,
     1,11,3,  2,11,3,2,  3,11,3,2,1,
     1,12,4,  2,12,4,5,  3,12,4,5,1,  
     1,13,4,  2,13,4,5,  3,13,4,5,1 $end

To use delocalized coordinates:
--- $contrl nzvar=33 $end
--- $zmat   dlc=.true. auto=.true. $end

To use natural internal coordinates:
 $contrl nzvar=44 $end
 $zmat   izmat(1)=1,1,2, 1,2,3, 1,3,4, 1,4,5, 1,5,1, ! ring !
     2,5,1,2,   2,1,2,3,   2,2,3,4,   2,3,4,5,   2,4,5,1,
     3,5,1,2,3, 3,1,2,3,4, 3,2,3,4,5, 3,3,4,5,1, 3,4,5,1,2,
        1,2,6,  2,6,2,1,  2,6,2,3,  4,6,2,1,3,  ! methyl C !
     1,6,7,  1,6,8,  1,6,9,                    ! methyl Hs !
     2,7,6,8,  2,8,6,9,  2,9,6,7,  2,9,6,2,  2,7,6,2,
     2,8,6,2,  3,7,6,2,1,
        1,10,2,  2,10,2,1,  2,10,2,3,  2,10,2,6, ! methine !
        1,11,3,  2,11,3,2,  2,11,3,4,  4,11,3,2,4, ! imino !
    1,12,4,  1,13,4,                           ! methylene !
     2,12,4,13,  2,12,4,3,  2,13,4,3,  2,12,4,5,  2,13,4,5

        ijS(1)=1,1,  2,2,  3,3,  4,4,  5,5,         ! ring !
          6,6, 7,6, 8,6, 9,6,10,6,
               7,7, 8,7, 9,7,10,7,
         11,8,12,8,13,8,14,8,15,8,
         11,9,12,9,     14,9,15,9,
               16,10,   17,11,18,11,   19,12,   ! methyl C !
         20,13,  21,14,  22,15,                ! methyl Hs !
         23,16, 24,16, 25,16, 26,16, 27,16, 28,16,
         23,17, 24,17, 25,17,
                24,18, 25,18,
                              26,19, 27,19, 28,19,
                                     27,20, 28,20,
         29,21,
            30,22,    31,23,32,23,33,23,
              32,24,33,24,                       ! methine !
            34,25,  35,26,36,26,  37,27,           ! imino !
         38,28,  39,29,                        ! methylene !
         40,30, 41,30, 42,30, 43,30, 44,30,
                41,31, 42,31, 43,31, 44,31,
                41,32, 42,32, 43,32, 44,32,
                41,33, 42,33, 43,33, 44,33

        Sij(1)=1.0, 1.0, 1.0, 1.0, 1.0,             ! ring !
            1.0, -0.8090, 0.3090,  0.3090, -0.8090,
                 -1.1180, 1.8090, -1.8090, 1.1180,
            0.3090, -0.8090, 1.0, -0.8090, 0.3090,
            -1.8090, 1.1180,      -1.1180, 1.8090,
                    1.0,   1.0,-1.0,   1.0,     ! methyl C !
         1.0,   1.0,   1.0,                    ! methyl Hs !
         1.0, 1.0, 1.0,-1.0,-1.0,-1.0,
         2.0,-1.0,-1.0,
              1.0,-1.0,
                        2.0,-1.0,-1.0,
                             1.0,-1.0,
         1.0,
            1.0,     2.0,-1.0,-1.0,   1.0,-1.0,  ! methine !
            1.0,   1.0,-1.0,    1.0,               ! imino !
         1.0,  1.0,                            ! methylene !
         4.0, 1.0, 1.0, 1.0, 1.0,
              1.0,-1.0, 1.0,-1.0,
              1.0, 1.0,-1.0,-1.0,
              1.0,-1.0,-1.0, 1.0    $end