16.3.1 Z-matrix input

The general form of an atom specification line is

[group[,]]atom, $p_1$, $r$, $p_2$, $\alpha$, $p_3$, $\beta$, $J$

or, alternatively,

[group[,]]atom, $p_1$, $x$, $y$, $z$

where

group

atomic group number (optional). Can be used if different basis sets are used for different atoms of the same kind. The basis set is then referred to by this group number and not by the atomic symbol.

atom

chemical symbol of the new atom placed at position $p_0$. This may optionally be appended (without blank) by an integer, which can act as sequence number, e.g., C1, H2, etc. Dummy centres with no charge and basis functions are denoted either Q or X, optionally appended by a number, e.g, Q1; note that the first atom in the z-matrix must not be called X, since this may be confused with a symmetry specification (use Q instead).

$p_1$

atom to which the present atom is connected. This may be either a number n, where $n$ refers to the $n$'th line of the Z-matrix, or an alphanumeric string as specified in the atom field of a previous card, e.g., C1, H2 etc. The latter form works only if the atoms are numbered in a unique way.

$r$

Distance of new atom from $p_1$. This value is given in bohr, unless ANG has been specified directly before or after the symmetry specification.

$p_2$

A second atom needed to define the angle $\alpha(p_0,p_1,p_2)$. The same rules hold for the specification as for $p_1$.

$\alpha$

Internuclear angle $\alpha(p_0,p_1,p_2)$. This angle is given in degrees and must be in the range $0 \lt \alpha \lt 180^{0}$.

$p_3$

A third atom needed to define the dihedral angle $\beta(p_0,p_1,p_2,p_3)$. Only applies if $J=0$, see below.

$\beta$

Dihedral angle $\beta(p_0,p_1,p_2,p_3)$ in degree. This angle is defined as the angle between the planes defined by $(p_0,p_1,p_2)$ and $(p_1,p_2,p_3)$ ( $-180^{0} \le \beta \le 180^{o}$). Only applies if $J=0$, see below.

$J$

If this is specified and nonzero, the new position is specified by two bond angles rather than a bond angle and a dihedral angle. If $J=\pm 1$, $\beta$ is the angle $\beta(p_0,p_1,p_3)$. If $J=1$, the triple vector product $({\bf p}_1-{\bf p}_0) \cdot [({\bf p}_1-{\bf p}_2) \times ({\bf p}_1-{\bf p}_3)]$ is positive, while this quantity is negative if $J=-1$.

x,y,z

Cartesian coordinates of the new atom. This form is assumed if $p_1\le0$; if $p_1\lt 0$, the coordinates are frozen in geometry optimizations.

All atoms, including those related by symmetry transformations, should be specified in the Z-matrix. Note that for the first atom, no coordinates need be given, for the second atom only $p_1,r$ are needed, whilst for the third atom $p_3,\beta,J$ may be omitted. The 6 missing coordinates are obtained automatically by the program, which translates and re-orients the molecule such that the origin is at the centre of mass, and the axes correspond to the eigenvectors of the inertia tensor (see also CHARGE option above).

Once the reorientation has been done, the program then looks for symmetry ($D_{2h}$ and subgroups), unless the NOSYM option has been given. It is possible to request that reduced symmetry be used by using appropriate combinations of the options X,Y,Z,XY,XZ,YZ,XYZ. These specify symmetry operations, the symbol defining which coordinate axes change sign under the operation. The point group is constructed by taking all combinations of specified elements. If symmetry is explicitly specified in this way, the program checks to see that the group requested can be used, swapping the coordinate axes if necessary. This provides a mechanism for ensuring that the same point group is used, for example, at all points in the complete generation of a potential energy surface, allowing the safe re-utilization of neighbouring geometry molecular orbitals as starting guesses, etc..