When such a Z-matrix is used for a geometry optimization in internal coordinates ( Opt=Z-matrix), the values of the variables will be optimized to locate the lowest energy structure. The two H-O distances are specified by the same variable, as are the two H-O-O bond angles. Symmetry constraints on the molecule are reflected in the internal coordinates. Here is another version of the previous Z-matrix: Variables may be used to specify some or all of the values within the Z-matrix. 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. The fourth and final line is the only one for which all three internal coordinates need be given. 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 next line lists an oxygen atom and specifies the internuclear distance between it and the hydrogen as 0.9 Angstroms. The first line of the Z-matrix simply specifies a hydrogen. This code is needed only when additional parameters follow the normal Z-matrix specification data, as in an ONIOM calculation.Īs an initial example, consider hydrogen peroxide. For the syntax being described here, this code is always 0. The optional format-code parameter specifies the format of the Z-matrix input. Note that bond angles must be in the range 0° < angle < 180°. The position of the current atom is then specified by giving the length of the bond joining it to atom1, the angle formed by this bond and the bond joining atom1 and atom2, and the dihedral angle formed by the plane containing atom1, atom2 and atom3 with the plane containing the current atom, atom1 and atom2. Alternatively, the other atoms' line numbers within the molecule specification section may be used for the values of variables, where the charge and spin multiplicity line is line 0. A common practice is to follow the element name with a secondary identifying integer: C1, C2, etc.Ītom1, atom2, atom3 are the labels for previously-specified atoms and are used to define the current atoms' position. If the elemental symbol is used, it may be optionally followed by other alphanumeric characters to create an identifying label for that atom. Element-label is a character string consisting of either the chemical symbol for the atom or its atomic number. The most-used Z-matrix format uses the following syntax:Įlement-label, atom 1, bond-length, atom 2, bond-angle, atom 3, dihedral-angle Īlthough these examples use commas to separate items within a line, any valid separator may be used. These are set consistently for a maximum of 250,000 real atoms (including ghost but not dummy atoms), and a maximum of 250,000 Z-matrix centers (atoms, ghost atoms, and dummy atoms).Įach line of a Z-matrix gives the internal coordinates for one of the atoms within the molecule. There are restrictions on the size of a Z-matrix: the maximum number of variables and the maximum number of atoms within a calculation. This section presents a brief overview of traditional Z-matrix descriptions of molecular systems.
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