Z‑Matrix Format for Jaguar Geometry Input

Like Cartesian geometries, Z‑matrix-format geometries also specify atoms by atom labels that begin with the one- or two-letter element symbol. The atom label is case-insensitive. The element symbol may be followed by additional characters, as long as the atom label has eight or fewer characters and the element symbol is still clear.

The first line of the Z‑matrix should contain only one item: the atom label for the first atom. For example,

N1

This atom is placed at the origin. The second line contains the atom label for atom 2, the identifier of atom 1, and the distance between atoms 1 and 2. Identifiers can either be atom labels or atom numbers (the position in the list: 1 for the first atom, 5 for the fifth atom listed, and so on). In this example, the identifier for the first atom could be either “N1” or “1.” The second atom is placed along the positive z‑axis. For example,

N1
C2   N1  1.4589

places the carbon atom (C2) at (0.0, 0.0, 1.4589) in Cartesian coordinates. Distances between atoms must be positive.

The third line is made up of five items: the atom label for atom 3, the identifier of one of the previous atoms, the distance between this atom and atom 3, the identifier of the other previous atom, and the angle defined by the three atoms. In this example,

N1
C2   N1  1.4589
C3   C2  1.5203   N1  115.32

the final line states that atoms C3 and C2 are separated by 1.5203 Å and that the C3–C2–N1 bond angle is 115.32°. The bond angle must be between 0° and 180°, inclusive. The third atom (C3 in this case) is placed in the xz plane (positive x).

The fourth line contains seven items: the atom label for atom 4, an atom identifier, the distance between this atom and atom 4, a second atom identifier, the angle defined by these three atoms, a third atom identifier, and a torsional angle. In this example,

N1
C2   N1  1.4589
C3   C2  1.5203   N1  115.32
O4   C3  1.2036   C2  126.28   N1  150.0

the last line states that atoms O4 and C3 are 1.2036 units apart, that the O4–C3–C2 bond angle is 126.28°, and that the torsional angle defined by O4–C3–C2–N1 is 150.0°. This information is sufficient to uniquely determine a position for O4. If the first three atoms in the torsional angle definition were collinear or very nearly collinear, O4’s position would be poorly defined. You should avoid defining torsional angles relative to three collinear (or nearly collinear) angles. In such a case you should use dummy atoms to define the torsional angle (see Variables and Dummy Atoms in Jaguar Z‑Matrix Input).

The torsional angle is the angle between the plane formed by the first three atoms (in this case N1–C2–C3) and the plane formed by the last three atoms (in this case C2–C3–O4). Looking from the second to the third atom (C2 to C3), the sign of the angle is positive if the angle is traced in a clockwise direction from the first plane to the second plane, and negative if the angle is traced counterclockwise.

An alternative for specifying the fourth atom’s position is to use a second bond angle instead of a torsional angle. To specify another bond angle, add 1 or −1 to the end of the line. The second bond angle is the angle between the first, second, and fourth atoms (in the example above, the O4–C3–N1 angle). Since there are two possible positions for the atom which meet the angle specifications, the position is defined by the scalar triple product r₁₂× (r₂₃ × r₂₄), where r_ij = r_i − r_j is the vector pointing from atom j to atom i. If this product is positive, the value at the end of the line should be 1. If it is negative, the value should be ‑1. You should use torsional angles instead of second bond angles if you want to perform a constrained geometry optimization, however, since Jaguar cannot interpret any constraints on bond lengths or angles for geometries containing second bond angles.

All additional lines of the Z‑matrix should have the same form as the fourth line. The complete Z‑matrix for the example molecule (the 150° conformation of glycine) is

N1
C2   N1  1.4589
C3   C2  1.5203   N1  115.32
O4   C3  1.2036   C2  126.28   N1  150.0
O5   C3  1.3669   C2  111.39   N1  -31.8
H6   N1  1.0008   C2  113.55   C3  -69.7
H7   N1  1.0004   C2  112.77   C3   57.9
H8   C2  1.0833   N1  108.89   H6  170.0
H9   C2  1.0782   N1  110.41   H6   52.3
H10  O5  0.9656   C3  111.63   C2 -178.2