Definitions

Number Run (NR) and Number Run Type

Prime Parameters and Primer Constants

Reference, Working, and Standard Cartesian Coordinate Systems

An addressable point in the crystal is any point for which an atom designator code exists. In general, the addressable region is a 9 9 9 block of unit cells.

In order to specify a particular atom in the crystal within a reasonable distance from the crystallographically defined origin, the following five-component atom designator code (ADC) is used.

where

AN = atom number (0 AN NATOM 500) - the numerical position of the atom in the input list of atoms, which contains NATOM atoms. Atom 0 is not in the input list but refers to the crystal origin point (0., 0., 0.).

TA,TB,TC = crystal lattice translation digits - cell translations along
cell edges **a**, **b**, and **c**, respectively. Each digit in an ADC can range
from 1 to 9; consequently, it is possible to move up to 4 cells in any
direction from the origin cell 555.

SN = symmetry operator number (0 SN NSYM 96) - the numerical position of the symmetry operator in the input list of symmetry operators, which contains NSYM entries. Symmetry operator 0 is not in the input list but refers to an identity operator. However, the identity operation (corresponding to position x,y,z) generally must be somewhere in the input symmetry operator list and is usually the first operator.

*Example*: An atom designator code of 347502 refers to atom 3 moved
through symmetry operation 2, then translated -1 cell translation along
**a**, +2 cell translations along **b**, and 0 cell translations along **c**.

A straight run sequence of atoms can be defined using two
atom designator codes
with a "-" preceding the second of the two. The run
hierarchy is: first, atom number AN; second, symmetry operator number
SN; third, **a** translation TA; fourth, **b** translation TB; and last, **c**
translation TC.

*Example*: ADR (145502-245603) will generate the 8-atom run 145502, 245502,
145503, 245503, 145602, 245602, 145603, 245603.

Exceptions allowed in the "origin" ADRs of
instructions 101, 102, 402/412, 403/413, and 404/414 **only**:

- The minus sign may be eliminated.
- If the second atom in the atom designator run has the same symmetry and translation components as the first atom, the second atom may be represented by its atom number component alone.
- If the symmetry and translation components of both atoms are 55501,
both atoms may be represented by their atom number components alone.
*Example*: ADR (345502-745502) may also be represented as (345502 745502) or (345502 7). ADR (355501-755501) may also be represented as (355501 755501) or (355501 7) or (3 7).

An atom feature is a user-defined characteristic of a group of atoms that may be assigned to the atoms in the ORTEP input as needed for a given task. For example, the atomic number may be provided with each atom to make selecting atoms of the same element easier. Up to two features may be assigned to each atom. These are referred to as Feature #1 and Feature #2.

An atom number run is a subset of the atom designator run. In this case, only the atom number AN changes. Normally, an ANR is entered by using only the atom number values for the first and last members of the sequence without a "-".

*Example*: (1 4) will designate atoms 1, 2, 3, and 4 of the input list.

A box of enclosure is a parallelepiped that can be centered about any
addressable point
and assigned arbitrary dimensions.
The orientation depends upon either the unit cell axes (triclinic box of
enclosure) or the reference axes (rectangular box of enclosure).
The box of enclosure can have
a **complete population**, a **partial population**,
or a **vector screened population**
as described for the
sphere of enclosure.

A feature number run is used to identify those atoms having a particular atom feature within a specified value range.

A number run is a generic term that refers to both atom number runs (ANR) and feature number runs (FNR). The number run type identifies the number run. Number run type 0 refers to an ANR, type 1 refers to an FNR on Feature #1, and type 2 refers to an FNR on Feature #2.

The more basic among the many settable parameters in ORTEP are the prime parameters. The default values assigned to these prime parameters are often similar or identical from one problem to the next. Among the first things ORTEP does is a call to subroutine PRIME, which sets as many prime parameters as possible to reasonable default primer constant values. For example, the maximum plot dimensions (instruction 301) are set to 10.5 in. for X and 8.0 in. for Y, and the overall scale for plotting (instruction 600 series) is set to 1.0 in./Å. If the value assigned to a particular constant by the PRIME subroutine is satisfactory, the user does not have to reset this constant with ORTEP instructions.

Many of the ORTEP calculations use fractional coordinates based
on the crystal axes **a**, **b**, and **c** (triclinic coordinate system);
but other steps necessitate the introduction of orthonormal base vector
triplets (Cartesian coordinate systems). Two Cartesian systems, reference
and working, are utilized. The reference (major) system is used for all
operations except plotting, where the working (minor) system is used.
For a right-eye or left-eye stereo view, the working system is moved
from the reference system by rotation about an axis of the reference
system. However, certain decisions made while plotting must still be
referred to the reference system to maintain accurate stereopsis. The
user can define and orient the two Cartesian systems through the series
500 instructions. Until a 500-series instruction is given, a "standard
Cartesian system" is utilized for both the reference and working
systems. The orthonormal base vectors of the standard system are
oriented as follows:

x axis alonga,y axis along (

ab)a,z axis along (

ab) =c*,

where **a**, **b**, and **c** are crystal axes and
denotes the outer vector
product (cross product). The symbol **c*** refers to a reciprocal axis.

A sphere of enclosure specifies some or all of the atoms lying within a
sphere of radius D_{max}
about a given "origin" atom without the necessity
of delineating each atom individually. The sphere of enclosure is said
to contain a **complete population** if all addressable atoms within the
D_{max} radius are included. If
the sphere of enclosure contains only
certain types of atoms that are derived from a group of sequential
atoms in the input list or atoms having particular
features, then the sphere is said to have a **partial
population**. Finally, the population (complete or partial) of the
sphere of enclosure can be screened as selectively as desired through
the use of
vector search codes,
and the resulting content is
called a **vector screened population**.

A sphere of enclosure can be centered on any addressable atom, but the
origin atom should not be chosen in the outermost cells because of the
possibility of having nonaddressable points within the

D_{max} radius.

A vector direction is specified by two atom designator codes. The vector direction is from the first to the second.

*Example*: 253704 263704 is a vector along the positive **a** direction of
the crystal lattice.

A vector search code consists of two number runs and a distance range. It is used for finding interatomic distances that have a particular chemical significance, such as covalent and coordination bonds.

*Example*: Suppose that metal atoms are numbers 1 and 2 in the atom list,
oxygen atoms are 6-12, and the interatomic distance range between
metals and oxygens is 1.9 Å to 2.4 Å. The metal-to-oxygen vectors can be
specified by the vector search code (1 2) (6 12) (1.9 2.4). Several
variations of this basic code are used in the program.

The vector searches in ORTEP-III for the 100 instructions and 400 instructions have been generalized to allow both atom number runs and feature number runs with the number run type specified in column 24. In addition, it is no longer necessary to specify all three screening ranges found on this card (i.e., origin, target, and distance range). Any ranges not specified (i.e., zero or blank in the maximum value entry) are omitted from the screening. If there is more than one vector search card, the parameter LOGC controls the logic of the screening. If the value is "0" (the default), an atom satisfying the screening conditions on any one of the No. 2 trailer cards will be retained (i.e., it is a logical union of the results). If the value is "1", an atom must satisfy the screening conditions on all the cards to be retained (i.e., it is an intersection of the results). If a value of "1" is needed for LOGC, a "1" is placed in column 27 of a Format No. 1 trailer card that goes between the main instruction card and the Format No. 2 VSC cards. If the value for LOGC is "0", the Format No. 1 card is not needed.

Online Documentation Table of Contents ORTEP-III Home Page

*Page last revised: Wednesday, 25-Mar-1998 12:52:31 EST*