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$ZMAT

$ZMAT group (required if NZVAR is nonzero in $CONTRL)

This group lets you define the internal coordinates in which the gradient geometry search is carried out. These need not be the same as the internal coordinates used in $DATA. The coordinates may be simple Z-matrix types, delocalized coordinates, or natural internal coordinates.
You must input a total of M=3N-6 internal coordinates (M=3N-5 for linear molecules).
NZVAR in $CONTRL can be less than M IF AND ONLY IF you are using linear bends. It is also possible to input more than M coordinates if they are used to form exactly M linear combinations for new internals. These may be symmetry coordinates or natural internal coordinates. If NZVAR > M, you must input IJS and SIJ below to form M new coordinates. See DECOMP in $FORCE for the only circumstance in which you may enter a larger NZVAR without giving SIJ and IJS.

**** IZMAT defines simple internal coordinates ****

IZMAT is an array of integers defining each coordinate.
The general form for each internal coordinate is code number,I,J,K,L,M,N
IZMAT =1 followed by two atom numbers. (I-J bond length)
=2 followed by three numbers. (I-J-K bond angle)
=3 followed by four numbers. (dihedral angle) Torsion angle between planes I-J-K and J-K-L.
=4 followed by four atom numbers. (atom-plane) Out-of-plane angle from bond I-J to plane J-K-L.
=5 followed by three numbers. (I-J-K linear bend) Counts as 2 coordinates
     for the degenerate bend, normally J is the center atom. See $LIBE.
=6 followed by five atom numbers. (dihedral angle) Dihedral angle between planes I-J-K and K-L-M.
=7 followed by six atom numbers. (ghost torsion) Let A be the midpoint between atoms I and J, and B be the midpoint between atoms M and N. This coordinate is the dihedral angle A-K-L-B. The atoms I,J and/or M,N may
be the same atom number. (If I=J AND M=N, this is a conventional torsion).
Examples: N2H4, or, with one common pair, H2POH.
Example - a nonlinear triatomic, atom 2 in the middle:
$ZMAT IZMAT(1)=1,1,2, 2,1,2,3, 1,2,3 $END
This sets up two bonds and the angle between them. The blanks between each coordinate definition are not necessary, but improve readability mightily.

**** the next define delocalized coordinates ****
DLC is a flag to request delocalized coordinates. (default is .FALSE.)
AUTO is a flag to generate all redundant coordinates, automatically. The DLC space will consist of all non-redundant combinations of these which can be found.
The list of redundant coordinates will consist of bonds, angles, and torsions only. (default is .FALSE.)
NONVDW is an array of atom pairs which are to be joined by a bond, but might be skipped by the routine that automatically includes all distances shorter than the sum of van der Waals radii. Any angles and torsions associated with the new bond(s) are also automatically included.
The format for IXZMAT, IRZMAT, IFZMAT is that of IZMAT:
IXZMAT is an extra array of simple internal coordinates which you want to have added to the list generated by AUTO. Unlike NONVDW, IXZMAT will add only the coordinate(s) you specify.
IRZMAT is an array of simple internal coordinates which you would like to remove from the AUTO list of redundant coordinates. It is sometimes necessary to remove a torsion if other torsions around a bond are being frozen, to obtain a nonsingular G matrix.
IFZMAT is an array of simple internal coordinates which you would like to freeze. See also FVALUE below. Note that IFZMAT/FVALUE work only with DLC, see the IFREEZ option in $STATPT to freeze coordinates if you wish to freeze simple or natural coordinates.
FVALUE is an array of values to which the internal coordinates should be constrained.
It is not necessary to input $DATA such that the initial values match these desired final values, but it is helpful if the initial values are not too far away.

**** SIJ,IJS define natural internal coordinates ****

SIJ is a transformation matrix of dimension NZVAR x M, used to transform the NZVAR internal coordinates in IZMAT into M new internal coordinates.
SIJ is a sparse matrix, so only the non-zero elements are given, by using the IJS array described below. The columns of SIJ will be normalized by GAMESS. (Default: SIJ = I, unit matrix)
IJS is an array of pairs of indices, giving the row and column index of the entries in SIJ.
example - if the above triatomic is water, using
IJS(1) = 1,1, 3,1, 1,2, 3,2, 2,3
SIJ(1) = 1.0, 1.0, 1.0,-1.0, 1.0
gives the matrix S=   1.0   1.0 0.0
                0.0   0.0 1.0
                1.0 -1.0 0.0
which defines the symmetric stretch, asymmetric stretch, and bend of water.
references for natural internal coordinates:
P.Pulay, G.Fogarasi, F.Pang, J.E.Boggs J.Am.Chem.Soc. 101, 2550-2560(1979 )
G.Fogarasi, X.Zhou, P.W.Taylor, P.Pulay J.Am.Chem.Soc. 114, 8191-8201(1992 )
reference for delocalized coordinates:
J.Baker, A. Kessi, B.Delley J.Chem.Phys. 105, 192-212(1996 )

Beispiel: N₂O₄

Input

!
! N2O4-Molekuel
!
$CONTRL SCFTYP=RHF MULT=1 RUNTYP=OPTIMIZE NZVAR=12 COORD=ZMT $END
$SYSTEM TIMLIM=1000 MEMORY=5000000 $END
$ZMAT IZMAT(1)=1,2,1 1,3,1 1,4,1 1,5,2 1,6,2 2,3,1,2 2,4,1,2
                2,5,2,1 2,6,2,1 3,4,1,2,3 3,5,2,1,3 3,6,2,1,4 $END
$BASIS GBASIS=STO NGAUSS=6 $END
$GUESS GUESS=HUCKEL $END
$DATA
N2O4-Molekuel
DNH 2

N1
N2 1 1.800
O3 1 1.200 2 112.0
O4 1 1.200 2 112.0 3 180.0
O5 2 1.200 1 112.0 3   0.0
O6 2 1.200 1 112.0 4   0.0
$END
Die Z-Matrix wurde nach der unten stehenden Skizze konstruiert.
                           z
                           |
                       O3 | O4
                           |
                           N1
                           |
           ----------------|---------------> x
                           |
                           N2
                           |
                       O5 | O6

Entsprechend wurde IZMAT(1) gebildet.

Output

ATOM ATOMIC               COORDINATES (BOHR)
     CHARGE        X              Y             Z
N1   7.0    0.0000000000   0.0000000000   1.7007533889
N1   7.0    0.0000000000   0.0000000000 -1.7007533889
O3   8.0   -2.1025481104   0.0000000000 -2.5502379666
O3   8.0    2.1025481104   0.0000000000   2.5502379666
O3   8.0   -2.1025481104   0.0000000000   2.5502379666
O3   8.0    2.1025481104   0.0000000000 -2.5502379666

Jetzt kommt eine andere Nummerierung heraus

                           z
                           |
                       O5 | O4
                           |
                           N1
                           |
           ----------------|---------------> x
                           |
                           N2
                           |
                       O3 | O6

Gestaltet man die Z-Matrix so, dass sie den Output-Koordinaten entspricht (Variante 2):

!
! N2O4-Molekuel
!
$CONTRL SCFTYP=RHF MULT=1 RUNTYP=OPTIMIZE NZVAR=12 COORD=ZMT $END
$SYSTEM TIMLIM=1000 MEMORY=5000000 $END
$ZMAT IZMAT(1)=1,2,1 1,3,2 1,4,1 1,5,1 1,6,2 2,3,2,1 2,4,1,2
2,5,1,2 2,6,2,1 3,4,1,2,3 3,5,1,2,3 3,6,2,1,4 $END
$BASIS GBASIS=STO NGAUSS=6 $END
$GUESS GUESS=HUCKEL $END
$DATA
N2O4-Molekuel
DNH 2

N1
N2 1 1.800
O3 2 1.200 1 112.0
O4 1 1.200 2 112.0 3 180.0
O5 1 1.200 2 112.0 3 0.0
O6 2 1.200 1 112.0 4 0.0
$END

werden die Koordinaten aber wieder geändert!!!

ATOM ATOMIC            COORDINATES (BOHR)
     CHARGE      X              Y             Z
N1    7.0   0.0000000000   0.0000000000 1.7007533889
N1    7.0   0.0000000000   0.0000000000 -1.7007533889
O3    8.0 -2.1025481104   0.0000000000 2.5502379666
O3    8.0   2.1025481104   0.0000000000 -2.5502379666
O3    8.0 -2.1025481104   0.0000000000 -2.5502379666
O3    8.0   2.1025481104   0.0000000000 2.5502379666

                           z
                           |
                       O3 | O6
                           |
                           N1
                           |
           ----------------|---------------> x
                           |
                           N2
                           |
                       O5 | O4

Ändert man nur die kodierte Z-Matrix:

erhält man die korrekte Kodierung:

--------------------
INTERNAL COORDINATES
--------------------

- - ATOMS - - COORDINATE COORDINATE
NO. TYPE      I J K L M N (BOHR,RAD)    (ANG,DEG)
----------------------------------------------------------------
1 STRETCH   2 1        3.4015068      1.8000000
2 STRETCH   3 2        2.2676712      1.2000000
3 STRETCH   4 1        2.2676712      1.2000000
4 STRETCH   5 1        2.2676712      1.2000000
5 STRETCH   6 2        2.2676712      1.2000000
6 BEND      3 2 1      1.9547688    112.0000000
7 BEND      4 1 2      1.9547688    112.0000000
8 BEND      5 1 2      1.9547688    112.0000000
9 BEND      6 2 1      1.9547688    112.0000000
10 TORSION   4 1 2 3    3.1415927    180.0000000
11 TORSION   5 1 2 3    0.0000000      0.0000000
12 TORSION   6 2 1 4    0.0000000      0.0000000

So sollte man vorgehen. Also, Z-Matrix aufstellen, Rechnen, Kodierung entsprechend dem Output ändern.

MAXIMUM GRADIENT = 0.0000077 RMS GRADIENT = 0.0000026
1 ***** EQUILIBRIUM GEOMETRY LOCATED *****

N2O4-Molekuel
              COORDINATES OF SYMMETRY UNIQUE ATOMS (ANGS)
ATOM CHARGE      X               Y               Z
------------------------------------------------------------
N1 7.0    0.0000000000    0.0000000000   -0.8098918283
O3 8.0    1.1484791572    0.0000000000   -1.3201862562

              COORDINATES OF ALL ATOMS ARE (ANGS)
ATOM CHARGE      X              Y             Z
------------------------------------------------------------
N1   7.0   0.0000000000   0.0000000000   0.8098918283
N1   7.0   0.0000000000   0.0000000000 -0.8098918283
O3   8.0 -1.1484791572   0.0000000000 -1.3201862562
O3   8.0   1.1484791572   0.0000000000   1.3201862562
O3   8.0 -1.1484791572   0.0000000000   1.3201862562
O3   8.0   1.1484791572   0.0000000000 -1.3201862562

--------------------
INTERNAL COORDINATES
--------------------

- - ATOMS - - COORDINATE COORDINATE
NO. TYPE       I J K L M N (BOHR,RAD) (ANG,DEG)
----------------------------------------------------------------
1 STRETCH    2 1        3.0609473        1.6197837
2 STRETCH    3 2        2.3749013        1.2567437
3 STRETCH    4 1        2.3749013        1.2567437
4 STRETCH    5 1        2.3749013        1.2567437
5 STRETCH    6 2        2.3749013        1.2567437
6 BEND       3 2 1      1.9889183      113.9566250
7 BEND       4 1 2      1.9889183      113.9566250
8 BEND       5 1 2      1.9889183      113.9566250
9 BEND       6 2 1      1.9889183      113.9566250
10 TORSION    4 1 2 3    3.1415927      180.0000000
11 TORSION    5 1 2 3    0.0000000        0.0000000
12 TORSION    6 2 1 4    0.0000000        0.0000000

INTERNUCLEAR DISTANCES (ANGS.)
------------------------------

            N1            N1           O3            O3

1 N1   0.0000000     1.6197837 *   2.4199663 *   1.2567437 *
2 N1   1.6197837 *   0.0000000     1.2567437 *   2.4199663 *
3 O3   2.4199663 *   1.2567437 *   0.0000000     3.4996549
4 O3   1.2567437 *   2.4199663 *   3.4996549     0.0000000
5 O3   1.2567437 *   2.4199663 *   2.6403725 *   2.2969583 *
6 O3   2.4199663 *   1.2567437 *   2.2969583 *   2.6403725 *

             O3            O3

1 N1   1.2567437 *   2.4199663 *
2 N1   2.4199663 *   1.2567437 *
3 O3   2.6403725 *   2.2969583 *
4 O3   2.2969583 *   2.6403725 *
5 O3   0.0000000     3.4996549
6 O3   3.4996549     0.0000000

* ... LESS THAN 3.000

NUCLEAR ENERGY = 233.8072019488
ELECTRONIC ENERGY = -640.2158501469
TOTAL ENERGY = -406.4086481981

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