Title

Cell Parameters

Symmetry

Atom Parameters

Positional Parameters
Temperature Factors

The first card in the ORTEP input is a title card with FORMAT (18A4), consisting of up to 72 characters of alphanumeric identification information. This will appear periodically in the output file.

The second input card contains the cell parameters with FORMAT (I1,F8.6,5F9.6). Any one of the following four input alternatives may be used. [No indicator is needed to specify which type. The routine that reads the cell parameters assumes a 1.0 Å, a* < 1.0 Å^-1, (or *) 1.0^o, and |cos | (or |cos *|) < 1.0.]

Columns	Type A	Type B	Type C	Type D
1	Symmetry format indicator	Symmetry format indicator	Symmetry format indicator	Symmetry format indicator
2-9	a (Å)	a (Å)	a* (Å-1)	a* (Å-1)
10-18	b (Å)	b (Å)	b* (Å-1)	b* (Å-1)
19-27	c (Å)	c (Å)	c* (Å-1)	c* (Å-1)
28-36	(o)	cos	* (o)	cos *
37-45	(o)	cos	* (o)	cos *
46-54	(o)	cos	* (o)	cos *

The parameters a*, etc., refer to the reciprocal unit cell such that a· a* = 1. All four types will be printed out regardless of which type was used for input.

An integer value in column 1 of the cell parameter card indicates the format used for the crystal symmetry cards that follow.

Crystal symmetry in ORTEP-III may be supplied in either of two styles. The first of these is identical to that of OR TEP-II and is triggered by having a "0" or blank in column 1 of the cell parameter card. A "1" in that position indicates the symmetry operators are provided in a free format using the xyz coordinate triplet notation found in the International Tables for Crystallography. These two styles are referred to as Type 0 and Type 1.

The number of symmetry cards (NSYM) may not exceed 96. At least one (the identity operator) is required. The reason for the maximum of 96 is that the symmetry operator number (SN) occupies only two places in the ADC. If it is not possible to supply all the symmetry operators for the space group (or if the user chooses not to supply all of them), atoms in the ORTEP input file will require multiple entries with those lattice centering translations added which are not provided in the symmetry cards.

A Type 0 symmetry card has FORMAT (I1,F14.10,3F3.0,2(F15.10,3F3.0)) and will be interpreted in one of two ways, depending on the value of the number in columns 70-72. If that number is < 5.0, the card is interpreted as a crystallographic symmetry operation; but if the number is 5.0, the card is interpreted as a general helix-screw symmetry operation along the c* crystal axis (third axis of the standard Cartesian system). The two symmetry types can be intermixed if desired.

Columns	(a) Crystallographic symmetry (value in columns 70-72 < 5)	(b) Helix symmetry (value in columns 70-72 5)
1	0 last card only	0 last card only
2-15	T1	T1
16-18	S11	-
19-21	S12	-
22-24	S13	-
25-39	T2	T2
40-42	S21	-
43-45	S22	-
46-48	S23	-
49-63	T3	T3
64-66	S31	L
67-69	S32	M
70-72	S33	N

(a) Crystallographic symmetry: Transformed triclinic coordinates (X₁, Y₁, Z₁) are obtained from input triclinic coordinates (X, Y, Z) by

or in matrix notation

where T = (T₁, T₂, T₃) as fractions of cell edges.

Only symmetry cards for general symmetry equivalent positions are permitted. Symmetry cards that explicitly designate special positions such as X,X,X; X,X,Z; X,Y,0; 1/4,Y,0; 1/4,1/4,1/4 are not allowed.

(b) Helix screw symmetry:

where T = (T₁, T₂, T₃ + L/N) as fractions of cell edges and S is a counterclockwise rotation of L· M/N cycles about the c* axis.

Example: The Pauling and Corey right-handed alpha helix of poly-L-alanine repeats after 13 turns and 47 residues and can be represented by 47 symmetry cards with N = 47; M = 13; L = 0, 1, ..., 46; T₁, T₂, T₃ = 0. In the ORTEP input file of poly-L-alanine provided here, the input atom list contains the contents of one residue. There are 48 symmetry cards with operator 1 and operator 48 related by a translation along c for simplicity.

Type 1 symmetry cards do not have a specific format with the following two exceptions: (1) the symmetry information on each card must not go beyond column 72, and (2) column 1 must be "0" (or blank) on all symmetry cards other than the last one in the set, which must be non-zero. Below is an example set of Type 1 symmetry cards to illustrate the flexibility of this style.

                    X,Y,Z
                    X    -Y   Z+1/2
                      X+0.5,   Y+.5,  Z
                   1x+1/2,-y+1/2,1/2+z

As shown, letters may be either upper or lower case. Commas or blanks may be used to separate the components of the triplet. The three components may not have blanks within them. Decimal fractions may be used with or without an initial "0". Fractions may precede or follow the letters.

Regardless of how the symmetry information is provided, the last card of the set must have a non-zero value in column 1 to signal the end of the symmetry cards. If the value is "1", the atom parameter information immediately follows in the ORTEP input file. If the value is "2", the atom parameter information is read from a different file, and the ORTEP instructions follow the symmetry cards.

Two cards are required for each input atom. The first contains the chemical symbol and positional parameters, and the second contains temperature factor information or other information that specifies how the atom is to be represented on the drawing. Several alternate inputs are possible for each of the two cards, and the number in column 63 denotes the type used on that particular card. The number of atoms (variable NATOM) may range from 1 to 500.

The positional parameter cards have FORMAT(A6,3X,6F9.0).

Columns	Type 0	Type 1	Type 2	Type 3
1-6	Up to 6 alphanumeric characters centered in the 6-place field
7-9	-
10-18	Feature #1 or other	Feature #1 or other	Feature #1 or other	x0 (Å, Cartesian)
19-27	Feature #2 or other	Feature #2 or other	Feature #2 or other	y0 (Å, Cartesian)
28-36	x (fractional, crystal)	x (Å, crystal)	x (Å, Cartesian)	r (Å, cylindrical)
37-45	y (fractional, crystal)	y (Å, crystal)	y (Å, Cartesian)	(o, cylindrical)
46-54	z (fractional, crystal)	z (Å, crystal)	z (Å, Cartesian)	z (Å, cylindrical)
63	0	1	2	3

Type 0 is the normal input based on triclinic coordinates. Coordinates in Angstroms along the unit cell vector may be entered with Type 1. Type 2 may be used to place a model described in Cartesian coordinates onto a general triclinic lattice. The orientation of the Cartesian system xyz in the general lattice abc is the standard Cartesian system type with x along a and z along c*. Type 3 is similar to Type 2 except that cylindrical coordinates r, , z are used and the axis of the system can be displaced from zero in the xy Cartesian plane by the displacement x₀, y₀. Cylindrical coordinates are often used to describe helical structures. The x₀, y₀ translation should be zero if helical symmetry operators are used. This translation feature is meant to be used for explicitly describing the contents of a multiple helix cell.

Column fields 10-18 and 19-27 on Type 0, 1, and 2 positional parameter cards may be used in ORTEP-III to enter feature information about the atoms. Normally, these fields are ignored by ORTEP so any numeric values may be here or the fields may be blank. The information in these fields will be interpreted as atom features only if instructions are invoked that specifically look at atom features. Features can not be entered on Type 3 positional parameter cards.

Temperature factor cards have FORMAT(I1,F8.0,5F9.0,7X,F2.0).

Columns	Types 0,1,2,3,10	Types 4,5,8,9	Type 6		Type 7
1	A sentinel 0 for last atom only
2-9	b11	U11	B	B	R	R
10-18	b22	U22	0	0	0	0
19-27	b33	U33	0	VDC1 (from)	0	VDC1 (from)
28-36	b12	U12	0	VDC1 (to)	0	VDC1 (to)
37-45	b13	U13	0	[VDC2 (from)]	0	[VDC2 (from)]
46-54	b23	U23	0	[VDC2 (to)]	0	[VDC2 (to)]
62-63	0, 1, 2, 3, or 10	4, 5, 8, or 9	6 (or 0)	6 (or 0)	7	7

Anisotropic temperature factor Types 0, 1, 2, 3, and 10 use the following formula for the complete temperature factor.

-D(b₁₁h² + b₂₂k² + b₃₃² + cb₁₂hk + cb₁₃h + cb₂₃k)

The coefficients b_ij (i,j = 1,2,3) of the various types are defined with the following constant settings.

type 0:	Base = e, c = 2, D = 1
type 1:	Base = e, c = 1, D = 1
type 2:	Base = 2, c = 2, D = 1
type 3:	Base = 2, c = 1, D = 1
type 10:	Base = e, c = 2, D = 22

Anisotropic temperature factor Types 4, 5, 8, and 9 use the following formula for the complete temperature factor, in which a₁*, a₂*, and a₃* are reciprocal cell dimensions.

exp[-D(a₁*²U₁₁h² + a₂*²U₂₂k² + a₃*²U₃₃² + Ca₁*a₂*U₁₂hk + Ca₁*a₃*U₁₃h + Ca₂*a₃*U₂₃k)]

The coefficients U_ij (i,j = 1,2,3) of the various types are defined with the following constant settings.

type 4:	C = 2, D = 1/4
type 5:	C = 1, D = 1/4
type 8:	C = 2, D = 22
type 9:	C = 1, D = 22

Type 6 allows the input of the Debye-Waller isotropic temperature factor B, which is used as follows:

exp (-B sin² / ²),

where is the wavelength and is the Bragg angle. The parameter B is related to mean-square displacement of the atom from its mean position by the relation

.

When the isotropic temperature factor is used, the atom is represented as an isotropic ellipsoid (sphere) with equal principal axes of length µ. When the field in columns 19-27 is "0" or blank, the directions of the principal axes are along the standard Cartesian system axes. However, these arbitrary orthogonal vectors can be reoriented by using the two vector designator codes VDC₁ and VDC₂; then the three new principal-axis vectors will be VDC₁, (VDC₁ VDC₂), and VDC₁ (VDC₁ VDC₂). This is strictly an artistic feature of no physical significance.

Type 7 allows the input of arbitrary spheres of radius R in Angstroms. The vector triplet orientation is specified as with type 6. An additional feature allows a completely blank card (except perhaps column 1) to be used for a temperature factor card. In this case the program assumes type 7 with an R = 0.1 Å.

If VDC₂ is omitted on Type 6 or Type 7 temperature factor cards, the program will choose one of the three lattice vectors for VDC₂.

A type 10 temperature-factor input card may be used to load Cartesian temperature factors having components in the standard Cartesian system. This feature complements the Type 3 Cartesian positional parameter input system and is useful for plotting mean-square displacements caused by internal molecular motions as calculated from spectroscopic normal-coordinate analyses.

New in ORTEP-III is the method for specifying the orientations and sizes of the pass (cigar-shaped) and pale (pancake-shaped) ellipsoids used in critical net illustrations without giving their quadratic form coefficients. The temperature factor card following the atom parameter card for a pass or pale has the format shown below.

Columns
1	A sentinel 0 if last atom
2-9	Unique axis length (Å)
10-18	Second (and third) axis length (Å)
19-27	VDC1 (from)
28-36	VDC1 (to)
37-45	(optional) VDC2 (from)
46-54	(optional) VDC2 (to)
63	7

VDC₁ is a vector parallel with the unique axis of the cigar-shaped pass or pancake-shaped pale and VDC₂ is a second vector not parallel with VDC₁ such that VDC₁ VDC₂ is a second principal axis of that ellipsoid. If VDC₁ and VDC₂ are parallel, VDC₂ is replaced by a suitable lattice translation vector. VDC₂ may be omitted from the input if desired, and the program will choose one of the three lattice vectors for VDC₂.

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Page last revised: July 11, 1997