Molecule specification (Z-matrix)
This input section specifies the nuclear positions and the number of electrons of α- and β-spin. There are several ways in which the nuclear configuration can be specified: as a Z-matrix, as Cartesian coordinates, or as a mixture of the two (note that Cartesian coordinates are just a special case of the Z-matrix).
The first line of the molecule specification section specifies the net electric charge (a signed integer) and the spin multiplicity (a positive integer). Thus, for a neutral molecule in a singlet state, the entry 0 1 is appropriate. For a radical anion, -1 2 would be used.
The remainder of the molecule specification gives the element type and nuclear position for each atom in the molecular system. The most general format for the line within it is the following:
Element-label[–Atom-type[–Charge]][(param=value[, ...])] Atom-position-parameters
Each line contains the element type, and possibly an optional molecular mechanics atom type and partial charge. Nuclear parameters for this atoms are specified in the parenthesized list. The remainder of the line contains information about the atom's location, either as Cartesian coordinates or as a Z-matrix definition. We'll begin by considering the initial and final items, and then go on to discuss the remaining items.
The following are the basic formats for specifying atoms within the molecule specification (omitting all of the optional items):
Element-label x y z
Element-label [n] atom1 bond-length atom2 bond-angle atom3 dihedral-angle [format-code]
Although these examples use spaces to separate items within a line, any valid separator may be used. The first form specifies the atom in Cartesian coordinates, while the second uses internal coordinates. Lines of both types may appear within the same molecular specification. The optional format-code parameter in the second line specifies the format of the Z-matrix input. For the syntax being described here, this code is always 0. It is needed only when additional parameters follow the normal data, as in an ONIOM calculation. n is an optional parameter related to freezing atoms during optimizations using ONIOM or (rarely) ones not performed using redundant internal coordinates.
Element-label is a character string consisting of either the chemical symbol for the atom or its atomic number. If the elemental symbol is used, it may be optionally followed by other alphanumeric characters to create an identifying label for that atom. A common practice is to follow the element name with a secondary identifying integer: C1, C2, C3, and so on; this technique is useful in following conventional chemical numbering.
In the first form, the remaining items on each line are Cartesian coordinates specifying the position of that nucleus. In the second form, atom1, atom2, atom3 are the labels for previously-specified atoms which will be used to define the current atoms' position (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).
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 (torsion) angle formed by the bond joining atom2 and atom3 with the plane containing the current atom, atom1 and atom2.
Here are two molecule specification sections for ethane:
0 1 0,1
C 0.00 0.00 0.00 C1
C 0.00 0.00 1.52 C2,C1,1.5
H 1.02 0.00 -0.39 H3,C1,1.1,C2,111.2
H -0.51 -0.88 -0.39 H4,C1,1.1,C2,111.2,H3,120.
H -0.51 0.88 -0.39 H5,C1,1.1,C2,111.2,H3,-120.
H -1.02 0.00 1.92 H6,C2,1.1,C1,111.2,H3,180.
H 0.51 -0.88 1.92 H7,C2,1.1,C1,111.2,H6,120.
H 0.51 0.88 1.92 H8,C2,1.1,C1,111.2,H6,-120.
The version on the left uses Cartesian coordinates while the one on the right represents a sample Z-matrix (illustrating element labels). Note that the first three atoms within the Z-matrix do not use the full number of parameters; only at the fourth atom are there enough previously-defined atoms for all of the parameters to be specified.
Here is another Z-matrix form for this same molecule:
0 1
C1
C2 C1 RCC
H3 C1 RCH C2 ACCH
H4 C1 RCH C2 ACCH H3 120.
H5 C1 RCH C2 ACCH H3 -120.
H6 C2 RCH C1 ACCH H3 180.
H7 C2 RCH C1 ACCH H6 120.
H8 C2 RCH C1 ACCH H6 -120.
Variables:
RCH = 1.5
RCC = 1.1
ACCH = 111.2
In this Z-matrix, the literal bond lengths and angle values have been replaced with variables. The values of the variables are given in a separate section following the specification of the final atom. Variable definitions are separated from the atom position definitions by a blank line or a line like the following:
Variables:
Symmetry constraints on the molecule are reflected in the internal coordinates. The C-H bond distances are all specified by the same variable, as are the C-C bond distances and the C-C-H bond angles.
This Z-matrix form may be used at any time, and it is required as the starting structure for a geometry optimization using internal coordinates (i.e., Opt=Z-matrix). In the latter case, the variables indicate the items to be optimized; see the examples for the Opt keyword for more details.