CRYSTAL geometry input B. Civalleri

Summary

• Overview and goals
• Example 1. A simple case: MgO
• From ICSD data to the CRYSTAL geometry input
• The bulk structure (conventional cell, primitive cell)
• Creating a super cell
• Symmetry and geometry editing
• Removal, addition, substitution, displacement of atoms
• 2D input; the slab model
• Example 2. Molecular crystals: urea
• From crystallographic data to the CRYSTAL geometry input
• The bulk structure
• From bulk to molecules
• Other useful keywords
• Summary of the CRYSTAL geometry input keywords

List of CRYSTAL geometry input examples

References

Description of the geometry input section and the main optional keywords to edit the crystalline structure is presented. We primarily focus on systems with 3D periodicity: for 2D, 1D and 0D geometry refer to the CRYSTAL User's Manual. Note, however, that most of the 3D structures editing facilities  can be applied to systems with lower periodicity.

Special attention will be given on how you can extract structural information from crystallographic databases and literature papers.
Refer to CRYSTAL User's Manual for complete description of the geometry input section and related keywords.

For this tutorial we assume that you know the basic concepts of crystallography. 
See: P.Ugliengo, CRYSTALLOGRAPHIC STRUCTURAL DATA.

This tutorial consists of two parts:

Example 1. A simple case: MgO, introduces the main features of the geometry input for a very simple inorganic system. Standard input and geometry editing keywords will be discussed.

Example 2. Molecular crystals: urea, discusses the case of a molecular crystal. CRYSTAL allows special  editing of the geometry for molecular crystals.

A small collection of CRYSTAL geometry input examples is supplied.

Geometry input is read and processed by the program crystal. 

The keyword TESTGEOM stops the run after reading the geometry input block and processing the data. It is inserted in all geometry input examples. It is useful to check crystal structures.

MgO crystallizes in a cubic cell with a rock-salt structure. The crystal structure can be described as a fcc lattice of Mg ions with O ions occupying all the octahedral holes or vice versa. The rock-salt structure is the most common for MX compounds.

MgO is an important oxidic system in minerals, in defective systems as well as in adsorption phenomena. Therefore, despite its simplicity, MgO has been the subject of many research studies. Thus, it represents a good example to show how geometry editing  options can be used with CRYSTAL.

Let us start from the crystallographic information you find on the ICSD database.
Here is the output from an entry for MgO in the ICSD database.

The information you need to define the crystal structure is highlighted. Basically, the crystal structure is determined by the space group, by the shape and size of the unit cell and by the relative position of the atoms in the asymmetric unit.

MgO geometry input, derived from ICSD data, will be prepared and discussed, line by line.

1. Title section

MgO bulk: crystal structure from ICSD

The first line contains the title section. It can be useful to indicate the system in study and other relevant information about the job. The title section is printed in the output file, but it is not otherwise used by CRYSTAL.

2. Dimensionality of the system

CRYSTAL

The first record of the geometry definition must specify the dimensionality of the system.
CRYSTAL adopts four keywords: CRYSTAL, SLAB, POLYMER and MOLECULE, for 3D, 2D, 1D and 0D systems, respectively. In this case the keyword to specify is CRYSTAL.

The keyword EXTERNAL allows geometry input from external file (see CRYSTAL User's Manual for further details).

3. Crystallographic information (for 3D systems only)

0 0 0

three integer numbers:
- convention for the space group identification: sequential number (0) or alphanumeric code (1).
- type of cell for rhombohedral groups: hexagonal (0) or rhombohedral (1).
- setting of the origin (see CRYSTAL User's Manual for further details).

4. Space group

225

It can be indicated either with its sequential number (0), as in this case, or by the Hermann-Mauguin alphanumeric code (1). In the ICSD file you can find both of them.

So, till now, the input file would look something like this:

according to the sequential number (on the left) or the alphanumeric code (on the right).
Note: CRYSTAL adopts F M 3 M instead of F M -3 M for compatibility with a previous edition of the International Tables for Crystallography (see CRYSTAL User's Manual for further details).

5. Lattice parameters

4.21

The minimal set of crystallographic cell parameters is indicated (in Angstrom and degrees). For MgO, cubic system, the length of the edge of the cell fully defines shape and size of the conventional unit cell (note, however, that CRYSTAL works on the primitive cell).

6. Atomic position specification

2
12    0.0   0.0   0.0
8     0.5   0.5   0.5

The first line gives the number of atoms in the asymmetric unit. One line per atom in the asymmetric unit follows, to specify the conventional atomic number and the coordinates in fractional units of the crystallographic lattice vectors. These atoms are usually indicated as non-equivalent atoms, i.e. atoms not symmetry related. The whole structure of MgO is defined by 2 atoms. 

7. Closing the geometry input section

END

This keyword ends the geometry input section. Before ending the section, you may specify optional keywords to modify the structure.

The completed input file looks like:

Exercise:
Create a file mgo.d12 and type the geometry input above. Visualize the structure following the instructions reported in the How to run CRYSTAL section.

Exercise:
Here is reported an entry for \(\alpha\)-alumina from the ICSD database. Use the crystallographic information to prepare the corresponding CRYSTAL geometry input file and visualize the structure.

CONVENTIONAL CELL	PRIMITIVE CELL

Solution

When running CRYSTAL with the previous input for MgO you will get the following output.

 *******************************************************************************
 *                                                                             *
 *                               CRYSTAL14                                     *
 *                      public : 1.0.2 - Feb 23rd, 2013                        *
 *                       HTTP://WWW.CRYSTAL.UNITO.IT                           *
 *                                                                             *
 *                              MAIN AUTHORS                                   *
 *                                                                             *
 *  R. DOVESI(1,11), V.R. SAUNDERS(2), C. ROETTI(1,11), R. ORLANDO(1,11),      *
 *  C.M. ZICOVICH-WILSON(1,3), F. PASCALE(4), B. CIVALLERI(1,11),              *
 *  K. DOLL(5), N.M. HARRISON(2,6), I. J. BUSH(7), Ph. D'ARCO(8),              *
 *  M. LLUNELL(9), M. CAUSA'(10), Y. NOEL(8)                                   *
 *                                                                             *
 *        CONTRIBUTIONS TO THE CURRENT RELEASE HAVE BEEN GIVEN BY              *
 *                                                                             *
 *  L. MASCHIO(1,11), S. CASASSA(1,11), A. ERBA(1,11), M. FERRABONE(1,11),     *
 *  M. DE LA PIERRE(1,11), M. FERRERO(1,11), V. LACIVITA(1,11),                *
 *  J. BAIMA(1,11), E. ALBANESE(1,11), M.F. PEINTINGER(12), R. BAST(13),       *
 *  M. RERAT(14), B. KIRTMAN(15), R. DEMICHELIS(1,16)                          *
 *                                                                             *
 * (1) THEORETICAL CHEMISTRY GROUP - UNIVERSITA' DI TORINO - TORINO (ITALY)    *
 *     http://www.crystal.unito.it                                             *
 * (2) COMPUTATIONAL SCIENCE & ENGINEERING DEPARTMENT - STFC DARESBURY (UK)    *
 *     http://www.stfc.ac.uk/CSE/randd/cmg/CRYSTAL/25806.aspx                  *
 * (3) UNIVERSIDAD AUTONOMA DEL ESTADO DE MORELOS - CUERNAVACA (MEXICO)        *
 * (4) UNIVERSITE' DE LORRAINE - NANCY (FRANCE)                                *
 * (5) UNIVERSITAET ULM - ULM (GERMANY); (6) IMPERIAL COLLEGE - LONDON (UK)    *
 * (7) NAG - OXFORD (UK); (8) UPMC - SORBONNE UNIVERSITES - PARIS (FRANCE)     *
 * (9) UNIVERSIDAD DE BARCELONA - BARCELONA (SPAIN)                            *
 *(10) UNIVERSITA' DI NAPOLI "FEDERICO II" - NAPOLI (ITALY)                    *
 *(11) NIS - NANOSTRUCTURED INTERFACES AND SURFACES - TORINO (ITALY)           *
 *(12) MPI FUER CHEMISCHE ENERGIEKONVERSION - MUELHEIM AN DER RUHR (GERMANY)   *
 *(13) UNIVERSITY OF STOCKHOLM - STOCKHOLM (SWEDEN)                            *
 *(14) UNIVERSITE' DE PAU ET DES PAYS DE L'ADOUR - PAU (FRANCE)                *
 *(15) UNIVERSITY OF CALIFORNIA SANTA BARBARA - SANTA BARBARA (USA)            *
 *(16) CURTIN UNIVERSITY - PERTH (AUSTRALIA)                                   *
 *                                                                             *
 ********************************************************************************
 EEEEEEEEEE STARTING  DATE 21 11 2014 TIME 12:07:07.7

The header of CRYSTAL reports the CRYSTAL version and the main authors of the code. 
The title section from the input file follows.

Summary of the crystallographic information. The periodicity of the system is indicated.

The lattice parameters of the conventional cell and the atomic position of the atoms in the asymmetric unit, as given in input, are reported.

 *******************************************************************************

 << INFORMATION >>: FROM NOW ON, ALL COORDINATES REFER TO THE PRIMITIVE CELL

 *******************************************************************************

 LATTICE PARAMETERS  (ANGSTROMS AND DEGREES) - PRIMITIVE CELL
       A          B          C         ALPHA      BETA     GAMMA        VOLUME
    2.97692    2.97692    2.97692     60.0000   60.0000   60.0000      18.65462

 COORDINATES OF THE EQUIVALENT ATOMS (FRACTIONARY UNITS)

 N. ATOM EQUIV AT. N.          X                  Y                  Z

   1   1   1   12 MG    0.00000000000E+00  0.00000000000E+00  0.00000000000E+00

   2   2   1    8 O    -5.00000000000E-01 -5.00000000000E-01 -5.00000000000E-01

 NUMBER OF SYMMETRY OPERATORS         :   48

The crystallographic or conventional cell is used as standard option in input. It may be non-primitive, which means that it may not coincide with the cell of minimum volume (primitive cell) which contains just one lattice point. Note that, for maximum calculation efficiency, CRYSTAL works on the primitive cell. Hence, the conventional cell is transformed into the primitive cell (1/4 of the conventional cell), all the following structural information are referred to the primitive cell.

The transformation matrices conventional \(\Leftrightarrow \) primitive cell are given in Appendix A.5 of CRYSTAL User's Manual.

In the output file, the lattice parameters of the primitive cell and the corresponding atomic positions (in fractionary units) are reported. In this section, all the atoms in the primitive cell are displayed and indicated as equivalent atoms. For each non-equivalent atom the corresponding block of equivalent atoms is reported. For MgO two atoms only build up the primitive cell, as they are in special positions.

In figure, the conventional cell and the primitive cell, enclosed in the conventional cell, of MgO are shown:

CONVENTIONAL CELL	PRIMITIVE CELL

With the following banner ends the standard CRYSTAL geometry output. After that, the output file continues with the geometry output section relative to the optional keywords.

*******************************************************************************
* GEOMETRY EDITING - INPUT COORDINATES ARE GIVEN IN ANGSTROM
*******************************************************************************

Exercise:
Compute the volume for the conventional cell and compare it with the primitive cell. Which is the ratio between the two cell volumes? Check the result on the printout.

Exercise:
Have a look at the output file for \(\alpha\)-alumina and examine the sections we have described above.

So far, we have considered the standard CRYSTAL geometry input.
In the following section optional geometry keywords, allowing structural editing, are presented.
Each keyword will be presented by a specific example. So, for each example, you can edit the input, run CRYSTAL and visualize the resulting structure.

The keyword SUPERCEL allows generation of a super cell by transformation of the lattice vectors of the primitive cell.

A super cell is obtained by defining the new unit cell vectors as linear combination of the primitive cell unit vectors. The new translation vectors b₁', b₂', b₃' are defined in terms of the old vectors b₁, b₂, b₃ and of the transformation matrix, E, read in input by rows, as follows:

b₁' = e₁₁ b₁ + e₁₂b₂ + e₁₃ b₃
b₂' = e₂₁ b₁ + e₂₂b₂ + e₂₃ b₃
b₃' = e₃₁ b₁ + e₃₂b₂ + e₃₃ b₃

The symmetry is automatically reduced to the point symmetry operators without translational components and a further reduction of the symmetry is also possible. A shift of the origin to minimize the number of symmetry operators with translational component is automatically performed by crystal.
More information on the expansion matrix in "Defects"
Note: super cells can be generated for 2D and 1D systems as well. In that case, the number of matrix elements decrease from 9 to 4 and to 1, respectively.

For instance, the MgO primitive cell can be transformed in the crystallographic one by the following matrix:

This corresponds to defining a quadruple cell.

Here is reported the corresponding CRYSTAL geometry input:

Insert the highlighted lines in your MgO input file and run CRYSTAL.
Looking at the output file you will find the following section:

 *******************************************************************************
 * SUPERCELL OPTION
 *******************************************************************************


        EXPANSION MATRIX OF PRIMITIVE CELL
 E1    -1.000     1.000     1.000
 E2     1.000    -1.000     1.000
 E3     1.000     1.000    -1.000

 NUMBER OF ATOMS PER SUPERCELL   8

        DIRECT LATTICE VECTORS COMPONENTS (ANGSTROM)
 B1     4.210     0.000     0.000
 B2     0.000     4.210     0.000
 B3     0.000     0.000     4.210

 LATTICE PARAMETERS  (ANGSTROM AND DEGREES)
       A          B          C         ALPHA      BETA     GAMMA        VOLUME
    4.21000    4.21000    4.21000     90.0000   90.0000   90.0000      74.61846


 **** ATOMS BELONGING TO THE SUPERCELL
 LABEL AT.NO.      COORDINATES (ANGSTROM AND FRACTIONARY)
     1    12     0.0000     0.0000     0.0000     0.0000     0.0000     0.0000
     2    12     2.1050     2.1050     0.0000     0.5000     0.5000     0.0000
     3    12     2.1050     0.0000     2.1050     0.5000     0.0000     0.5000
     4    12     0.0000     2.1050     2.1050     0.0000     0.5000     0.5000
     5     8     0.0000     0.0000     2.1050     0.0000     0.0000     0.5000
     6     8     2.1050     2.1050     2.1050     0.5000     0.5000     0.5000
     7     8     2.1050     0.0000     0.0000     0.5000     0.0000     0.0000
     8     8     0.0000     2.1050     0.0000     0.0000     0.5000     0.0000

 **************************** SUPERCELL GENERATED ****************************

The expansion matrix, given in input, the new lattice vectors components and lattice parameters, and the labels, atomic number, coordinates of the 8 atoms in the supercell are reported.

Atom LABEL is the sequence number of the atom in the cell. In any geometry editing atoms are identified by their "label";.

The new cell parameters correspond to the crystallographic lattice parameters. The new cell contains four MgO formula units.

Exercise:
Try to define larger super cells from the MgO primitive cell, e.g. with 16 atoms, 32 atoms and so on. Hints in "Defects".

Exercise: \(\alpha\)-alumina has a hexagonal unit cell but its primitive cell is rhombohedral, with volume 1/3 of the conventional cell. Starting from the rhombohedral cell, define the expansion matrix to generate the crystallographic cell.

Hint for a better visualization:
The SUPERCEL keyword can be used for visualizing larger fragments of the crystal structure when a molecular visualizer is used. 

The SUPERCEL option is a useful starting point for interesting applications in materials science.  For instance, such a keyword can be combined with other options to define defective systems.

 When a geometry editing (removal, insertion, substitution, displacement of atoms) modifies a site of the structure,  the program can maintain or modify (reduce) the number of symmetry operators. Two keywords control the symmetry:

KEEPSYMM: In any subsequent editing of the geometry, the program will endeavor to maintain the number of symmetry operators. The symmetry operators are applied to the "perturbation", and if the multiplicity of the site is greater than 1, the perturbation will be multiplied by application of the symmetry operators.

BREAKSYMM [default]: subsequent modification of the geometry are allowed to alter (reduce: the number of symmetry operators can not be reduced) the point group symmetry. The new group is a subgroup of the original group and it is automatically obtained by crystal

The keyword SYMMREMO removes all point symmetry operators.

See keyword MODISYMM (input block 2, "Basis set", CRYSTAL User's Manual) for removal of selected symmetry operators.

The keyword ATOMSYMM prints the point group associated with each atomic position and the set of symmetry related atoms.

The keyword SYMMDIR prints the symmetry allowed directions, corresponding to the internal degrees of freedom (to obtain printing full crystal input must be submitted, block 1 2 3 4, with keyword TESTPDIM in block 3 - See CRYSTAL User's Manual)

MgO primitive cell - 48 symmetry operators:

ATOM 1 ATOMIC NUMBER 12 - NUMBER OF SYMMOPS WHICH DO NOT MOVE THE ATOM 48 NO EQUIVALENT ATOMS ATOM 2 ATOMIC NUMBER 8 - NUMBER OF SYMMOPS WHICH DO NOT MOVE THE ATOM 48 NO EQUIVALENT ATOMS THERE ARE NO SYMMETRY ALLOWED DIRECTIONS

MgO 16 atoms super cell - 48 symmetry operators.
Translational symmetry is not recognized within the super cell.

******************************************************************************* ATOMS IN THE ASYMMETRIC UNIT 5 - ATOMS IN THE UNIT CELL: 16 ATOM X/A Y/B Z/C ******************************************************************************* 1 T 12 MG 0.000000000000E+00 0.000000000000E+00 0.000000000000E+00 2 T 12 MG -1.704907916233E-17 1.704907916233E-17 -5.000000000000E-01 3 F 12 MG -1.704907916233E-17 -5.000000000000E-01 1.704907916233E-17 4 F 12 MG 7.692414413785E-17 -5.000000000000E-01 -5.000000000000E-01 5 F 12 MG -5.000000000000E-01 -1.704907916233E-17 1.704907916233E-17 6 F 12 MG -5.000000000000E-01 7.272286071947E-17 -5.000000000000E-01 7 F 12 MG -5.000000000000E-01 -5.000000000000E-01 -1.085557425201E-17 8 T 12 MG 5.000000000000E-01 -5.000000000000E-01 -5.000000000000E-01 9 T 8 O -2.500000000000E-01 -2.500000000000E-01 2.500000000000E-01 10 T 8 O -2.500000000000E-01 -2.500000000000E-01 -2.500000000000E-01 11 F 8 O -2.500000000000E-01 2.500000000000E-01 2.500000000000E-01 12 F 8 O -2.500000000000E-01 2.500000000000E-01 -2.500000000000E-01 13 F 8 O 2.500000000000E-01 -2.500000000000E-01 2.500000000000E-01 14 F 8 O 2.500000000000E-01 -2.500000000000E-01 -2.500000000000E-01 15 F 8 O 2.500000000000E-01 2.500000000000E-01 2.500000000000E-01 16 F 8 O 2.500000000000E-01 2.500000000000E-01 -2.500000000000E-01 T = ATOM BELONGING TO THE ASYMMETRIC UNIT ATOM 1 ATOMIC NUMBER 12 - NUMBER OF SYMMOPS WHICH DO NOT MOVE THE ATOM 48 NO EQUIVALENT ATOMS ATOM 2 ATOMIC NUMBER 12 - NUMBER OF SYMMOPS WHICH DO NOT MOVE THE ATOM 8 NUMBER OF ATOMS EQUIVALENT BY SYMMETRY 5 SEQUENCE NUMBERS OF THESE ATOMS 7 5 3 4 6 ATOM 3 ATOMIC NUMBER 12 - NUMBER OF SYMMOPS WHICH DO NOT MOVE THE ATOM 8 NUMBER OF ATOMS EQUIVALENT BY SYMMETRY 5 SEQUENCE NUMBERS OF THESE ATOMS 6 2 5 4 7 . . . . . . . . . . . . . . ATOM 8 ATOMIC NUMBER 12 - NUMBER OF SYMMOPS WHICH DO NOT MOVE THE ATOM 48 NO EQUIVALENT ATOMS ATOM 9 ATOMIC NUMBER 8 - NUMBER OF SYMMOPS WHICH DO NOT MOVE THE ATOM 8 NUMBER OF ATOMS EQUIVALENT BY SYMMETRY 5 SEQUENCE NUMBERS OF THESE ATOMS 16 14 12 11 13 ATOM 10 ATOMIC NUMBER 8 - NUMBER OF SYMMOPS WHICH DO NOT MOVE THE ATOM 24 NUMBER OF ATOMS EQUIVALENT BY SYMMETRY 1 SEQUENCE NUMBERS OF THESE ATOMS 15 . . . . . . . . . . . . . SYMMETRY ALLOWED INTERNAL DEGREE(S) OF FREEDOM: 1 SYMMETRY ALLOWED DIRECTION 1 ATOM 9 (Z= 8) 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4082483 0.0000000 0.0000000 0.0000000 -0.4082483 0.0000000 0.0000000 0.0000000 0.4082483 0.0000000 0.0000000 -0.4082483 0.0000000 0.4082483 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.4082483

dx,dy,dz corresponding the the degree of freedom analyzed, for all the atoms

NEIGHBORS OF THE NON-EQUIVALENT ATOMS N = NUMBER OF NEIGHBORS AT DISTANCE R ATOM N R/ANG R/AU NEIGHBORS (ATOM LABELS AND CELL INDICES) 1 MG 6 2.1050 3.9779 9 O 0 0 0 11 O 0 0 0 12 O 0 0 0 13 O 0 0 0 14 O 0 0 0 16 O 0 0 0

The unique degree of freedom corresponds to the displacement of the first neighbors Oxygens. 

After geometry editing, the symmetry is recognized through the symmetry operators, but the space group is not known. The program findsym (Harold T. Stokes and Dorian M. Hatch, package ISOTROPY ) identifies the space group of a crystal 3D, given the positions of the atoms in a unit cell. Input data are written by keyword FINDSYM in file FINDSYM.DAT, and saved as inpfilename.FINDSYM by the script runcry.

Substitution of atoms

A simple example of a defective systems are substitutional defects. For instance, CRYSTAL has been used to study the energy of formation of a Ca defect in MgO: C. Freyria-Fava, R. Dovesi, V.R. Saunders, M. Leslie and C. Roetti, ``Ca and Be substitution in bulk MgO: ab initio Hartree-Fock and ionic model supercell calculation'', J. Phys.: Cond. Matter 5, 4793-4804 (1993).

For this purpose a 16 atoms super cell of MgO was adopted. Here is reported the corresponding geometry input section:

The keyword ATOMSUBS allows substitution of selected atoms in the cell, as defined when the keyword is entered. The total number of atoms to be substituted and, for each atom, the corresponding label and the new atomic number must be indicated.

Insert the lines shown above in your MgO input file and run CRYSTAL.

 *******************************************************************************
 * SUBSTITUTION OF   1 ATOM(S)
 *******************************************************************************
 ATOM N.   1 MG (Z= 12) SUBSTITUTED WITH CA (Z= 20)

In the output file the section above is displayed. Note: ATOM N. stands for atom number.

So, the procedure to define a substitutional defect is:

• define the super cell and run CRYSTAL;
• identify in the output file the atom to be substituted, the corresponding label in the cell and the site symmetry;
• modify the input file adding the ATOMSUBS input section.

Exercise:
Starting from the silicon CRYSTAL geometry input, generate a super cell and create a carbon substitutional defect. (Si data: cubic system, space group 227, a=5.42; one atom in the asymmetric unit in 1/8, 1/8, 1/8, standard origin setting).

Another example of defective systems are vacancies. One of them is the so-called trapped-electron-hole centre. In such centres there are very often charge compensating impurities, e.g. a H atom. In MgO, this kind of defects are denoted as MgO:[H]⁰. The H atom formally substitutes a Mg atom at its lattice position and migrates towards one of the neighboring O atoms, forming a strong covalent bond with it. The hole localizes at the opposite O atom completely. This defective system has been the subject of a recent paper.

In order to create the final defective structure the initial MgO primitive cell have to be modified with a series of geometry keywords. The new part of the input file looks something like:

Insert the new lines in the MgO bulk input and run CRYSTAL.

******************************************************************************* * SUBSTITUTION OF 1 ATOM(S) ******************************************************************************* ATOM N. 1 MG (Z= 12) SUBSTITUTED WITH H (Z= 1) ******************************************************************************* * DISPLACEMENT OF 3 ATOMS ******************************************************************************* ATOM N. 1 AT. N. 1 DISPLACED BY (A) 0.00000 0.00000 1.13100 ATOM N. 19 AT. N. 8 DISPLACED BY (A) 0.00000 0.00000 -0.00500 ATOM N. 17 AT. N. 8 DISPLACED BY (A) 0.00000 0.00000 -0.10000 THE NUMBER OF SYMMETRY OPERATORS HAS BEEN REDUCED FROM 48 TO 8 *******************************************************************************

Note that, in this example, the first atomic displacement has been done allowing a symmetry reduction. Indeed, the number of symmetry operators changes from 16 to 8 (see above). Whereas, after KEEPSYMM, in the second displacement, the current symmetry is maintained and all the atoms related by symmetry are moved (see below).

 *******************************************************************************
 * DISPLACEMENT OF    1 ATOMS
 *******************************************************************************

 ATOM N.   21 AT. N.   8 DISPLACED BY (A)   0.11000   0.00000   0.00400

 SYMMETRY MAINTAINED - 21 ATOM(S) SYMMETRY-RELATED : SEQUENCE NUMBER OF ATOM(S)
  31  24  32
 OLD COORDINATES (FRAC. UNITS)   0.00000   0.25000   0.25000
 NEW COORDINATES (FRAC. UNITS)   0.00048   0.26354   0.26306

A 32 atoms super cell has been used as starting perfect cell and the defective center has been created substituting a Mg atom by a H atom. Atoms 17 and 19, Oxygens, are 2 of the six equivalent first neighbors of the atom at the origin. When H is at the origin, H moves towards Oxygen 19, to form an OH group.
ATOMDISP allows displacement of selected atoms in the cell as defined when the keyword is entered. The point symmetry of the system is reduced.

In summary, for this example, a 32 atoms super cell of MgO has been adopted. The Mg atom at the origin is substituted with a hydrogen atom. Some atomic positions are changed in two steps. First, the position of the three atoms involved in the defect center (O-H...O) are displaced, allowing a reduction of the symmetry, then, preserving the symmetry (keyword KEEPSYMM), the neighbor oxygen atoms are relaxed. ATOMDISP is used to relax the atoms of the defect  zone, keeping the maximum symmetry compatible with the model of the defect.

Exercise:
Instead of a hydrogen atom, the trapped-hole may contain other cations. Define a defect structure with Li instead of H.

Another useful keyword related to ATOMINSE is ATOMREMO, which removes selected atoms from the primitive cell.

• 2D input, referring to one of the 80 layer groups, subset of the 230 space groups. Atom coordinates are expressed in different units: fractionary (directions with translational symmetry) and Angstrom,(non periodic direction). See section 1.1 and Appendix A.2 of "CRYSTAL User's Manual".
  
  
• 3D input, followed by the specification of the Miller indices of the surface of interest

The keyword SLABCUT allows generation of a slab of given thickness, parallel to a plane of the 3D lattice specified by  the h ,k , l crystallographic Miller indices.

Not all crystalline surfaces are physically stable or worthy of investigation. This is specially true for ionic or semi-ionic crystals. As an example, you may create a polar surface. It consists of charged layers alternating in such a way that the repeat unit has a net dipole per unit area, normal to the surface. Such surfaces are unstable and can only be prepared with substantial reconstruction or with the adsorption of charged species. See, for instance, the MgO (111) surface.

A section is dedicated to "Surfaces and adsorption". This section describes how to simulate a crystalline surface with CRYSTAL.

CRYSTAL test cases 04-24, 05-25, 06-26, 07-27 show how to obtain the same 2D structure with 2D input (04,05,06,07) and 3D input + cutting of a slab (24, 25, 26, 27)

For molecular crystals special optional geometry keywords are available. As an example the urea crystalline structure will be used to illustrate such keywords.

The crystal structure of urea has a tetragonal cell with four molecules in the unit cell (see figure below, on the left). The molecules are linked to each other through hydrogen bonds, so as to form infinite planar tapes. The arrangement of tapes is depicted in the figure below on the right. They are mutually orthogonal, the cohesion among them is provided by hydrogen bonds. Hence, each oxygen is involved in four nearly equivalent hydrogen bonds, two within the tape and two with neighbouring tapes. Notice that the molecules within adjoining tapes are oppositely oriented with respect to the crystallographic c axis; this provides a further source of tape binding through dipole-dipole forces.

As for MgO, let us start from crystallographic data. Structural data on carbon-containing crystals can be find either on specific databases such as the Cambridge Structure Database (CSD) or directly from research articles and books. In the following, urea crystallographic data are reported from both of resources.

CSD entry:

Crystal data from a resource book of crystal structure:

CSD crystal data corresponds to the urea structure determined at 12 K. As noticed in the discussion on the reliability of crystallographic structural data, structures which have been solved at low temperature are to be preferred over those determined at room temperature.
In the table above you can assess the dependence of the crystal data upon the temperature.
Hence, by using the structural data obtained at 12K the CRYSTAL geometry input for urea can be prepared:

All of the previously reported keywords may be used to modify the crystal structure of molecular crystals (e.g. SUPERCEL, ATOMDISP, ATOMINSE, SLABCUT, ...).

Exercise:
Try to use the SUPERCEL keyword to visualize a large portion of the urea crystal structure.

However, few other keywords are specific for molecular crystals.
This is the case of the MOLEXP keyword. It allows to modify the cell parameters according to increments given in input. However, although the volume of the cell is modified, the symmetry and the internal geometry of the molecules in the cell are kept.
The urea input with MOLEXP is reported below:

Here the lattice parameters of the urea primitive cell are expanded by 0.5 Angstrom. The corresponding output is shown below:

After a classification of the molecular fragments in the primitive cell, the old lattice vectors are changed according to the increment given in input, and the new cell parameters are shown.

Exercise:
Insert the MOLEXP input section in your urea geometry input, run CRYSTAL and visualize the modified crystal structure. Notice how the internal molecular geometry is preserved by changing the volume.

For molecular crystals an important geometry manipulation is the extraction of molecular fragments from the bulk structure. In CRYSTAL this task is accomplished by the MOLECULE keyword. This option allows to extract one (or more) molecules from a molecular crystal on the basis of chemical connectivity, defined by the sum of covalent radii.
Note: For a proper identification of the molecules it may be necessary a modification of the atomic radii (e.g. when there are very short H-bonds linking the molecules in the lattice). This can be done by using the RAYCOV option (see the CRYSTAL User's Manual for further details)

In order to use the MOLECULE option two separate runs are necessary:

Step 1. Identification of molecular fragments in the cell
The first step consists in a search of the molecular fragments in the primitive cell, based on the chemical connectivity. Accordingly, the atoms are reordered on the basis of the new classification. In order to do that, the ATOMORDE keyword must be used. No input data are required.
The urea input file looks something like:

UREA BULK CRYSTAL 0 0 0 113 5.565  4.684 5 6  0.0000  0.5000  0.3260 8  0.0000  0.5000  0.5953 7  0.1459  0.6459  0.1766 1  0.2575  0.7575  0.2827 1  0.1441  0.6441 -0.0380	Standard geometry input for urea bulk
ATOMORDE	Keyword to classify molecular fragments in the cell
TESTGEOM END	Stop execution after geometry step End of the geometry input section

Here the ATOMORDE output section is reported:

 *******************************************************************************
 *  SEARCHING THE MOLECULES OF THE CRYSTAL
 *******************************************************************************

 MOLECULAR FRAGMENT N.    1
 REFERENCE ATOM:    1 IN CELL  0 0 0  COORDINATES    0.000  -2.783   1.527
 FRAGMENT COMPOSITION:
  SEQ.  NO.
  NEW   OLD    CELL   AT. NO.             COORD.(A)
   1     1    0  0  0    6       0.0000   -2.7825    1.5270
   2     3    0  0  1    8       0.0000   -2.7825    2.7884
   3     5    0  0  0    7       0.8119   -1.9706    0.8272
   4     6    0 -1  0    7      -0.8119   -3.5944    0.8272
   5    13    0  0  0    1       0.8019   -1.9806   -0.1780
   6     9    0  0  0    1       1.4330   -1.3495    1.3242
   7    14    0 -1  0    1      -0.8019   -3.5844   -0.1780
   8    10    0 -1  0    1      -1.4330   -4.2155    1.3242

 MOLECULAR FRAGMENT N.    2
 REFERENCE ATOM:    2 IN CELL  0 0 0  COORDINATES   -2.783   0.000  -1.527
 FRAGMENT COMPOSITION:
  SEQ.  NO.
  NEW   OLD    CELL   AT. NO.             COORD.(A)
   9     2    0  0  0    6      -2.7825    0.0000   -1.5270
  10     4    0  0 -1    8      -2.7825    0.0000   -2.7884
  11     7    0  0  0    7      -1.9706   -0.8119   -0.8272
  12     8   -1  0  0    7      -3.5944    0.8119   -0.8272
  13    15    0  0  0    1      -1.9806   -0.8019    0.1780
  14    11    0  0  0    1      -1.3495   -1.4330   -1.3242
  15    16   -1  0  0    1      -3.5844    0.8019    0.1780
  16    12   -1  0  0    1      -4.2155    1.4330   -1.3242

 *******************************************************************************

Each molecular fragment is identified and the atoms are reordered fragment by fragment. Notice that further manipulations will refer to the new atomic numbering.

Step 2. Definition of the molecular fragment
The second step concerns the definition of the molecular fragment by means of the MOLECULE keyword. Now we know the necessary information to run MOLECULE. In input, the number of molecules to be extracted must be specified as well as a label of an atom for each molecule and the integer coordinates of the cell where that atom is positioned.
As an example, the geometry input for the definition of an isolated urea molecule and the corresponding output section are reported:

 *******************************************************************************
 * MOLECULAR CALCULATION
 *******************************************************************************

 MOLECULAR FRAGMENT N.    1
 REFERENCE ATOM:    1 IN CELL  0 0 0  COORDINATES    0.000  -2.783   1.527
 FRAGMENT COMPOSITION:
  SEQ.  NO.
  NEW   OLD    CELL   AT. NO.             COORD.(A)
   1     1    0  0  0    6       0.0000   -2.7825    1.5270
   2     3    0  0  1    8       0.0000   -2.7825    2.7884
   3     5    0  0  0    7       0.8119   -1.9706    0.8272
   4     6    0 -1  0    7      -0.8119   -3.5944    0.8272
   5    13    0  0  0    1       0.8019   -1.9806   -0.1780
   6     9    0  0  0    1       1.4330   -1.3495    1.3242
   7    14    0 -1  0    1      -0.8019   -3.5844   -0.1780
   8    10    0 -1  0    1      -1.4330   -4.2155    1.3242

 *******************************************************************************

On the basis of the previous re-ordering, the molecular structure is defined and then a molecular calculation begins.
Edit the input reported above, run CRYSTAL and visualize the isolated molecule.

When dealing with more than one molecule, it may be difficult to identify the proper molecular fragments to be extracted. A useful tool is to print a full neighboring analysis of the non-equivalent atoms. By default, every full run, CRYSTAL prints up to 6 stars of neighbors. The default value may be changed by means of the NEIGHBOR keyword.
Note: In order to use NEIGHBOR you need a complete CRYSTAL input (Geometry + Basis Set + Hamiltonian).
As an example, for urea bulk, the following section is printed in the output file:

 NEIGHBORS OF THE NON-EQUIVALENT ATOMS
                                                                                          
 N = NUMBER OF NEIGHBORS AT DISTANCE R
    ATOM  N     R/ANG      R/AU   NEIGHBORS (ATOM LABELS AND CELL INDICES)
   1 C    1     1.2614     2.3837   2 O    0 0 0
   1 C    2     1.3447     2.5411   3 N    0 1 0   4 N    0 1 0
   1 C    2     2.0367     3.8488   6 H    0 1 0   8 H    0 1 0
   1 C    2     2.0477     3.8696   5 H    0 1 0   7 H    0 1 0
   1 C    2     2.6461     5.0004  14 H    0 1 1  16 H    1 0 1
   1 C    2     3.1089     5.8750  13 H    0 1 0  15 H    1 0 0
                                                                                          
   2 O    1     1.2614     2.3837   1 C    0 0 0
   2 O    2     1.9922     3.7647  14 H    0 1 1  16 H    1 0 1
   2 O    2     2.0582     3.8895   5 H    0 1 1   7 H    0 1 1
   2 O    2     2.2726     4.2946   3 N    0 1 0   4 N    0 1 0
   2 O    2     2.5002     4.7246   6 H    0 1 0   8 H    0 1 0
   2 O    2     2.9550     5.5842   3 N    0 1 1   4 N    0 1 1
                                                                                          
   3 N    1     1.0053     1.8997   5 H    0 0 0
   3 N    1     1.0092     1.9070   6 H    0 0 0
   3 N    1     1.3447     2.5411   1 C    0-1 0
   3 N    1     2.2726     4.2946   2 O    0-1 0
   3 N    1     2.2965     4.3397   4 N    0 0 0
   3 N    1     2.4939     4.7127   7 H    0 0 0
                                                                                          
   5 H    1     1.0053     1.8997   3 N    0 0 0
   5 H    1     1.7473     3.3019   6 H    0 0 0
   5 H    1     2.0477     3.8696   1 C    0-1 0
   5 H    1     2.0582     3.8895   2 O    0-1-1
   5 H    1     2.2682     4.2862   7 H    0 0 0
   5 H    1     2.4939     4.7127   4 N    0 0 0
                                                                                          
   6 H    1     1.0092     1.9070   3 N    0 0 0
   6 H    1     1.7473     3.3019   5 H    0 0 0
   6 H    1     1.9922     3.7647  10 O    0 0 1
   6 H    1     2.0367     3.8488   1 C    0-1 0
   6 H    2     2.4984     4.7214  13 H    1 0 0  15 H    1 0 0
   6 H    1     2.5002     4.7246   2 O    0-1 0

For each non-equivalent atom information on the first six (default) neighbors is printed: number, type, distance, position (indices of the cell). For instance C1 is linked to O2 in the same cell at 1.2614 Angstrom. Whereas, O2 is linked to H14, which is in the next cell, by an H-bond.

Exercise:
In the urea crystal structure, each oxygen is involved in four nearly equivalent hydrogen bonds. Use the previous neighboring analysis to isolate a molecular fragment that contains the four H-bonds.

When dealing with molecular crystals an important observable is the interaction energy. For a H-bonded molecular crystal as urea, the interaction energy is usually referred to the number of H-bonds. Basically, it coincides with the formation energy of the crystal per hydrogen bond with respect to the molecule in gas-phase.

Two optional keywords may help in computing the interaction energy: MOLSPLIT and MOLEBSSE. Even if they are involved in the total energy calculation they must be specified in the geometry input section.
The keyword MOLSPLIT performs an expansion of the lattice, in such a way that the molecules of the crystal are at an infinite distance from each other. No input data are required.

MOLEBSSE computes the BSSE in molecular crystals via the counterpoise method. A molecular calculation is performed with a basis set including the basis functions of the selected molecules and the neighboring atoms. The corresponding input section is reported below:

Note: Before running MOLEBSSE use ATOMORDE to identify the molecular fragments in the primitive cell.

Here is a summary of the CRYSTAL geometry input keywords. For each keyword a brief explanation is reported as well as whether the keyword requires any specific additional data (Input).
Refer to CRYSTAL User's Manual for full documentation.

Note: the NEIGHBOR option requires the full CRYSTAL input (Geometry + Basis Set + Hamiltonian)

References

T. Hahn,
International Tables for Crystallography,
Reidel Publishing Company, 1987

T.C.W Mak, G.-D. Zhou,
Crystallography in Modern Chemistry - A Resource Book of Crystal Structures,
Wiley, 1992

Research papers

R. Dovesi and R. Orlando
Convergence properties of the super cell approach in the study of local defects in solids
Phase Trans. 52, 151-167 (1994)

R. Orlando, R. Dovesi, P. Azavant, N.M. Harrison and V.R. Saunders
A super-cell approach for the study of localized defects in solids: carbon substitution in bulk silicon
J. Phys.: Cond. Matter 6, 8573-8583 (1994).

R. Orlando, P. Azavant, M.D. Towler, R. Dovesi and C. Roetti
Cluster and super cell calculations for carbon-doped silicon
J. Phys.: Cond. Matter 8, 1123-1133 (1996).

A. Lichanot, R. Orlando, G. Mallia, M. Merawa, R. Dovesi
V_OH center in magnesium oxide: an ab initio super cell study
Chem. Phys. Lett. 318, 240 (2000)

R. Dovesi, R. Orlando, F. Ricca and C. Roetti
CO adsorption on MgO crystals: Hartree-Fock calculations for regular ad layers on a (001) lattice plane
Surface Sci. 186, 267-278 (1987).

R. Dovesi, M. Causa', R. Orlando, C. Roetti, and V.R. Saunders
Ab initio approach to molecular crystals: A periodic Hartree-Fock study of crystalline urea
J. Chem. Phys. 92, 7402 (1990).

C. Gatti, V.R. Saunders, C. Roetti
Crystal field effects on the topological properties of the electronic density in molecular crystals: The case of urea
J. Chem. Phys. 101, 10686 (1994)