Gaussian 03 Online ManualLast update: 2 October 2006 | |

This page presents a brief overview of traditional Z-matrix
descriptions of molecular systems. ## Using Internal CoordinatesEach line of a Z-matrix gives the internal coordinates for one of the atoms within the molecule. The most-used Z-matrix format uses the following syntax:
Although these examples use
commas to separate items within a line, any valid separator may be used.
The position of the current atom is then specified by giving
the length of the bond joining it to The optional format-code parameter
specifies the format of the Z-matrix input. For the syntax being described here,
this code is always As an initial example, consider hydrogen peroxide. A Z-matrix for this structure would be: H O 1 0.9 O 2 1.4 1 105.0 H 3 0.9 2 105.0 1 120.0 The first line of the Z-matrix simply specifies a hydrogen. The next line lists an oxygen atom and specifies the internuclear distance between it and the hydrogen as 0.9 Angstroms. The third line defines another oxygen with an O-O distance of 1.4 Angstroms (i.e., from atom 2, the other oxygen) and having an O-O-H angle (with atoms 2 and 1) of 105 degrees. The fourth and final line is the only one for which all three internal coordinates need be given. It defines the other hydrogen as bonded to the second oxygen with an H-O distance of 0.9 Angstroms, an H-O-O angle of 105 degrees and a H-O-O-H dihedral angle of 120 degrees. Variables may be used to specify some or all of the values within the Z-matrix. Here is another version of the previous Z-matrix: H O 1 Symmetry constraints on the molecule are reflected in the internal
coordinates. The two H-O distances are specified by the same variable, as are
the two H-O-O bond angles. When such a Z-matrix is used for a geometry optimization
in internal coordinates ( Variables: R1 0.9 R2 1.4 A 105.0 Constants: D 120.0 See the examples
in the discussion of the ## Mixing Internal and Cartesian CoordinatesCartesian coordinates are actually a special case of the Z-matrix, as in this example: C 0.00 0.00 0.00 C 0.00 0.00 1.52 H 1.02 0.00 -0.39 H -0.51 -0.88 -0.39 H -0.51 0.88 -0.39 H -1.02 0.00 1.92 H 0.51 -0.88 1.92 H 0.51 0.88 1.92 It is also possible to use both internal and Cartesian coordinates within the same Z-matrix, as in this example: O 0 xo 0. zo C 0 0. yc 0. C 0 0. -yc 0. N 0 xn 0. 0. H 2 r1 3 a1 1 b1 H 2 r2 3 a2 1 b2 H 3 r1 2 a1 1 -b1 H 3 r2 2 a2 1 -b2 H 4 r3 2 a3 3 d3 Variables: xo -1. zo 0. yc 1. xn 1. r1 1.08 r2 1.08 r3 1.02 a1 125. a2 125. d3 160. b1 90. b2 -90. This Z-matrix has several features worth noting: The variable names for the Cartesian coordinates are given symbolically in the same manner as for internal coordinate variables. The integer 0 after the atomic symbol indicates symbolic Cartesian coordinates to follow. Cartesian coordinates can be related by a sign change just as dihedral angles can.
## Alternate Z-matrix FormatAn alternative Z-matrix format allows nuclear positions to be specified
using two bond angles rather than a bond angle and a dihedral angle. This is indicated
by a C4 O1 0.9 C2 120.3 O2 180.0 0 C5 O1 1.0 C2 110.4 C4 105.4 1 C6 O1 R C2 A1 C3 A2 1 The first line uses a dihedral angle while the latter two use a second bond angle. ## Using Dummy AtomsThis section will illustrate the use
of dummy atoms within Z-matrices, which are represented by the pseudo atomic symbol
N X 1 1. H 1 nh 2 hnx H 1 nh 2 hnx 3 120.0 H 1 nh 2 hnx 3 -120.0 nh 1.0 hnx 70.0 The position of the dummy on the axis is irrelevant, and the distance
1.0 used could have been replaced by any other positive number. Here is a Z-matrix for oxirane: X C1 X halfcc O X ox C1 90. C2 X halfcc O 90. C1 180.0 H1 C1 ch X hcc O hcco H2 C1 ch X hcc O -hcco H3 C2 ch X hcc O hcco H4 C2 ch X hcc O -hcco halfcc 0.75 ox 1.0 ch 1.08 hcc 130.0 hcco 130.0 This example illustrates two points. First, a dummy atom is placed
at the center of the C-C bond to help constrain the cco triangle to be isosceles.
The following examples
illustrate the use of dummy atoms for specifying linear bonds. Geometry optimizations
in internal coordinates are unable to handle bond angles of l80 degrees which
occur in linear molecular fragments, such as acetylene or the C N C 1 cn X 2 1. 1 90. H 2 ch 3 90. 1 180. cn 1.20 ch 1.06 Similarly, in this Z-matrix intended for a geometry optimization, N C 1 cn X 2 1. 1 half O 2 co 3 half 1 180.0 H 4 oh 2 coh 3 0.0 cn 1.20 co 1.3 oh 1.0 half 80.0 coh 105. ## Model Builder Geometry SpecificationsThe
model builder is another facility within The
basic input to the model builder is called a The short formula matrix also implicitly
defines the rotational geometry about each bond in the following manner. Suppose
atoms X and Y are explicitly specified. Then X will appear in row Y and Y will
appear in row X. Let
The model builder can only build structures with atoms in their normal valencies. If a radical is desired, its extra valence can be "tied down" using dummy atoms, which are specified by a minus sign before the atomic symbol (e.g., -H). Only terminal atoms can be dummy atoms. The two available models (A and B) differ in that model A takes into account the type (single, double, triple, etc.) of a bond in assigning bond lengths, while model B bond lengths depend only on the types of the atoms involved. Model B is available for all atoms from H to Cl except He and Ne. If Model A is requested and an atom is used for which no Model A bond length is defined, the appropriate Model B bond length is used instead. |