The CRYSTAL program
The CRYSTAL program has been jointly developed by The Theoretical Chemistry Group at the University of Torino (Italy) and the Computational Materials Science Group at Daresbury Laboratory (U.K.).
The CRYSTAL package performs ab initio calculations of the ground state energy, electronic wave function and properties of periodic systems.
Hartree-Fock or Kohn-Sham Hamiltonians (that adopt an Exchange-Correlation potential following the postulates of Density-Functional theory) can be used.
Systems periodic in 0 (molecules, 0D), 1 (polymers, 1D), 2 (slabs, 2D), and 3
dimensions (crystals, 3D) are treated on an equal footing.
In each case the
fundamental approximation made is the expansion of the single particle wave
functions ('Crystalline Orbital', CO) as a linear combination of Bloch functions
(BF) defined in terms of local functions (hereafter indicated as 'Atomic
Orbitals', AOs).
The local functions are, in turn, linear combinations of Gaussian type
functions (GTF), whose exponents and coefficients are defined by input. Functions
of s, p, and d symmetry can be used. Also available are sp shells (s and p
shells, sharing the same set of exponents). The use of sp shells can give rise
to considerable savings in CPU time.
The program can automatically handle space symmetry: 230 space groups, 80
layer groups, 99 rod groups, 45 point groups are available. In the case of
polymers it cannot treat helical structures (translation followed by a rotation
around the periodic axis). However, when commensurate rotations are involved, a
suitably large unit cell can be adopted.
Point symmetries compatible with translation symmetry are provided for
molecules.
Input tools allow the generation of slabs (2D system) or clusters (0D system)
from a 3D crystalline structure, the elastic distortion of the lattice, the
creation of a super cell with a defect and a large variety of structure editing.
Previous releases of the software in 1988 (CRYSTAL88), 1992 (CRYSTAL92), 1996 (CRYSTAL95)
and 1998 (CRYSTAL98) have been used in a wide variety of research with notable
applications in studies of stability of minerals, oxide surface chemistry, and
defects in ionic materials. See:
http://www.crystal.unito.it/compounds.html
Getting started with CRYSTAL
CRYSTAL performs two tasks:
| program | task |
| crystal | wave function calculation (geometry can be optimized) |
| properties | wave function analysis and one electron properties calculation. |
Wave function calculation
The input to CRYSTAL is strongly affected by the birthday date of the program (1978). A "continuity principle", "old input must work with the new program" was applied until CRYSTAL03.
The input deck for wave function calculation, an ASCII text file, is read by the program crystal.
The input to crystal includes a title and four sections (referred to as "blocks").
Every block of the input deck consists of keywords (cases insensitive, written left justified) and numerical parameters (free format).
Every block ends with the keyword END (mandatory: 3 characters only are interpreted, any ending is allowed, ENDgeom, ENDbas, etc etc) or STOP. The latter will cause immediate termination of execution.
Optional keywords can be
present in each section.
Extended information on input features are in "CRYSTAL03
User's Manual".
The input deck has the following structure (mandatory data)
| Title | |
| input block 1 | Geometry input (see tutorials: geometry
editing and geometry optimization) standard geometry input optional geometry optimization and editing keywords END |
| input block 2 | Basis set input (see tutorial: basis
set standard basis set input optional basis set related keywords END |
| input block 3 | Single particle Hamiltonian (default: RHF) (see
tutorial: Hamiltonian and
computational parameters optional general information keywords END |
| input block 4 | SCF control (see tutorial: SCF) sampling in reciprocal space (for 1D-2D-3D systems only) optional SCF related keyword END |
We consider MgO bulk as
a case study. MgO is for CRYSTAL what is water for molecular codes.
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.
Complete input for MgO wave function calculation follows, adopting the default values of all computational parameters. A minimal basis set, STO-3G, is adopted. Such a basis set is too poor to give a good wave function, but allows easy explanation of the input.
| Section | CRYSTAL input | Description | ||
| 0) Title | MgO bulk | Title | ||
|
1) Geometry Input
|
CRYSTAL
0 0 0 225 4.21 2 12 0. 0. 0. 8 0.5 0.5 0.5 |
Dimensionality of the system
Crystallographic information (3D only) Space Group number Lattice parameter(s) (Angstrom) Number of non equivalent atoms Conventional atomic number and fractional coordinates of the atoms |
||
| Optional keywords | ||||
| END | End of the geometry input section | |||
|
2) Basis set Input
|
12 3
1 0 3 2. 0. 1 1 3 8. 0. 1 1 3 2. 0. 8 2 1 0 3 2. 0. 1 1 3 6. 0. 99 0 |
Mg:atomic number and number of shells
Basis set input: code, type, nr. of primitives, formal charge and scale factor of the gaussian exponents in the shell Oxygen basis set: 2 shells 1:STO-nG; 0,s shell;3 primitives,2 elec; standard Pople scale factor 99: end of basis set definition |
||
| Optional keywords | ||||
| END | End of the basis set input section | |||
| 3) Hamiltonian and computational parameters | Optional keywords | Default choice: Restricted Hartree Fock | ||
| END | End of Hamiltonian section | |||
|
4) SCF Input
|
8 0 8 | Reciprocal space integration parameters | ||
| Optional keywords | ||||
| END | End of the SCF input section |
Few comments on the input data, fully explained in the related tutorials.
0. Title
The title section consists of one line (max 80 characters) of descriptive information about the job.
It is not processed, but printed in the output.
1. Geometry input
|
CRYSTAL |
Translational symmetry of the system: 3D |
|
0 0 0 |
crystallographic information (setting of the origin, space group code) |
|
225 |
space group number |
|
4.21 |
minimal set of cell parameters (a,b,c,alpha, beta, gamma): fcc cubic, 1 parameter, a |
|
2 |
number of non-equivalent atoms |
|
12 0. 0. 0. |
conventional atomic number and fractional coordinates of Mg |
|
8 0.5 0.5 0.5 |
conventional atomic number and fractional coordinates of O |
| END | No geometry editing - the geometry to compute the wave function is defined |
The translational symmetry of the system is defined by the keywords (written left justified):
CRYSTAL
3D
SLAB
2D
POLYMER 1D
MOLECULE 0D - no
translational symmetry
Keyword EXTERNAL reads geometry from an external file. See CRYSTAL03 User's Manual.
The symmetry operators are automatically generated according to the space group.
CRYSTAL refers to the primitive cell only (see geometry input). The two atoms in the primitive cell of bulk MgO are in a special crystallographic position, of multiplicity 1. If the multiplicity of the position is greater than 1, all atoms symmetry related are generated.
Subsequent edit of the structure (optional) is obtained by inserting keywords before the string END.
Geometry input examples for a number of structure are available in Chapter 4
of CRYSTAL03 User's
Manual and in the Geometry Input directory
The local functions of the crystalline basis set are of the same type of the
ones used in molecular codes.
For each centre, usually an atom, the associated basis set of contracted
gaussian functions is defined.
The basis set type "1" defines a STO-nG basis set
|
12 3
1 0 3 2. 0. 1 1 3 8. 0. 1 1 3 2. 0. 8 2 1 0 3 2. 0. 1 1 3 6. 0. 99 0 |
12 conventional atomic number (Mg) 3 number of shells 3; s (1AO), sp (4AO), sp(4AO) type, => 9 AO for MgO atom. Definition of the 3 shells follows. First shell: 1 BS input code (STO-nG); 0 shell type (s) 3 number of primitives 2. formal shell charge 0. scale factor - Pople value for STO-nG is used when the value is 0. 2nd shell - STO-3G, sp type (1), formal charge 8, standard scale factor 3rd shell - STO-3G, sp type (1), formal charge 2, standard scale factor 8 conventional atomic number (O)) 2 number of shells 3 (s, sp => 5AO) 1 BS input code (STO-nG) 0 shell type (s) 3 number of primitives 2. formal shell charge 0. scale factor - Pople value for STO-nG when the value is 0. 2nd shell - STO-3G, sp type (1), formal charge 6, standard scale factor 99 formal atomic number - end of BS definition |
|
| END | End of the basis set input section |
The "conventional atomic number" links the basis set to the atoms
entered in geometry input (see Basis Set
Input).
The electronic configuration of the atoms is used in the calculation of the
atomic wave function only (when the guess for SCF is a superposition of atomic
densities).
The number of electrons attributed to an atom is the sum of shell charges.
In this example,
12 electrons are attributed to Mg, and 8 to O; an ionic configuration (0 electrons
to the 3rd Mg shell, and 8 electrons to the second O shell) could lead to a better guess for a highly ionic
system like MgO.
Basis set input examples are available in Chapter 4 of CRYSTAL03
User's Manual .
Basis sets STO-3G for all atoms from Z=1 to Z=54 are given in sto-3g_basis
file.
3. Hamiltonian and computational parameters
| END | End of Hamiltonian section |
Default values are supplied for Hamiltonian (Restricted Hartree-Fock, RHF), truncation criteria of Coulomb and exchange sums, type of run (sequential, traditional SCF, integrals stored on disk).
A record with END is required to close the third input block.
4. SCF control parameters
| 8 0 8 |
8 shrinking factor -
Pack Monkhorst net 0 dummy variable - not used in CRYSTAL03 8 shrinking factor Gilat net |
|
| END | End of the SCF input section |
The only mandatory choice (for periodic systems) is the definition of the
sampling in reciprocal space (lattice vectors b1, b2,
b3) to compute Fermi energy. The input datum is the number of segments the first
reciprocal lattice vector (b1) is subdivided to generate a commensurate net of k points in the
first Irreducible Brillouin Zone (IBZ).
The Hamiltonian matrix computed in direct lattice, Fg, is Fourier
transformed at the given k points to obtain Fk. Eigenvalues Ek and eigenvectors Ak
are computed at each k point by solving the equation:
Hk Ak = Sk Ak Ek
All quantities referring to the k points of the "Gilat net" are computed by interpolation of the values calculated exactly at the k points of the Pack-Monkhorst net, and used to find the value of the Fermi energy by integration. When the system is an insulator, no bands are partially occupied, there are as many occupied bands as electrons. The Gilat shrinking factor can have the same value as Pack-Monkhorst.
Default values are chosen for convergence criteria, convergence tools as well as bands occupancy.
A test run to check the input and estimate the computational resources to be allocated is performed by inserting the following keywords:
|
keyword |
insert in block |
supply input blocks |
test |
|
TESTGEOM |
1 |
1 |
geometry |
|
TESTPDIM |
3 |
1-2-3-4 |
geometry, basis set, symmetry |
|
TESTRUN |
3 |
1-2-3-4 |
geometry, basis set, symmetry, disk space allocation |
A quick tour of CRYSTAL output
The following output is produced when running crystal with MgO input deck presented above..
|
Header of CRYSTAL. It reports the CRYSTAL version and the main authors of the code |
******************************************************************************* * * * CRYSTAL03 * * Release : 1.0 * * * * MAIN AUTHORS * * * * V.R. SAUNDERS(1), R. DOVESI(2), C. ROETTI(2), R. ORLANDO (2,3), * * C.M. ZICOVICH-WILSON(2,4), N.M. HARRISON(1,5), K. DOLL(1,6), * * B. CIVALLERI(2), I. J. BUSH(1), Ph. D'ARCO(2,7), M. LLUNELL(2,8) * * * * * * (1) COMPUTATIONAL SCIENCE & ENGINEERING DEPARTMENT - CLRC DARESBURY (UK) * * http://www.cse.dl.ac.uk/Activity/CRYSTAL * * (2) THEORETICAL CHEMISTRY GROUP - UNIVERSITA' DI TORINO - TORINO (ITALY) * * http://www.crystal.unito.it * * (3) UNIVERSITA' DEL PIEMONTE ORIENTALE - ALESSANDRIA (ITALY) * * (4) UNIVERSIDAD AUTONOMA DEL ESTADO DE MORELOS - 'CUERNAVACA (MEXICO) * * (5) IMPERIAL COLLEGE - LONDON (UK) * * (6) TU BRAUNSCHWEIG - BRAUNSCHWEIG (GERMANY) * * (7) UNIVERSITE' PIERRE ET MARIE CURIE - PARIS (FRANCE) * * (8) UNIVERSIDAD DE BARCELONA - BARCELONA (SPAIN)' * * ******************************************************************************* |
| Date and solar time |
EEEEEEEEEE STARTING DATE 02 09 2003 TIME 08:30:00.0 |
| Title section from input | MgO bulk |
|
3D system Summary of crystallographic information. Lattice parameters of the conventional cell 2 atoms in the asymmetric unit Atomic number and coordinates (fraction of lattice vectors) |
CRYSTAL CALCULATION
(INPUT ACCORDING TO THE INTERNATIONAL TABLES FOR X-RAY CRYSTALLOGRAPHY) CRYSTAL FAMILY : CUBIC CRYSTAL CLASS (GROTH - 1921) : CUBIC HEXAKISOCTAHEDRAL SPACE GROUP (CENTROSYMMETRIC) : F M 3 M LATTICE PARAMETERS (ANGSTROMS AND DEGREES) - CONVENTIONAL CELL A B C ALPHA BETA GAMMA 4.21000 4.21000 4.21000 90.00000 90.00000 90.00000 NUMBER OF IRREDUCIBLE ATOMS IN THE CONVENTIONAL CELL: 2 INPUT COORDINATES ATOM AT. N. COORDINATES 1 12 0.000000000000E+00 0.000000000000E+00 0.000000000000E+00 2 8 5.000000000000E-01 5.000000000000E-01 5.000000000000E-01 ******************************************************************************* << INFORMATION >>: FROM NOW ON, ALL COORDINATES REFER TO THE PRIMITIVE CELL ******************************************************************************* |
|
Lattice parameters of the primitive cell Coordinates of atoms in the primitive cell. Number of symmetry operators. |
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 |
| CRYSTAL output continues with the geometry editing section. In this case no geometry editing. |
*******************************************************************************
* GEOMETRY EDITING - INPUT COORDINATES ARE GIVEN IN ANGSTROM ******************************************************************************* GEOMETRY NOW FULLY CONSISTENT WITH THE GROUP |
| Symmetry operators in the lattice vector basis |
**** 48 SYMMOPS - TRANSLATORS IN FRACTIONARY UNITS V INV ROTATION MATRICES TRANSLATOR 1 1 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 2 2 0.00 1.00 -1.00 1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 0.00 0.00 3 3 -1.00 0.00 0.00 -1.00 0.00 1.00 -1.00 1.00 0.00 0.00 0.00 0.00 4 4 0.00 -1.00 1.00 0.00 -1.00 0.00 1.00 -1.00 0.00 0.00 0.00 0.00 5 6 0.00 1.00 0.00 0.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 6 5 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 7 8 1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 1.00 -1.00 0.00 0.00 0.00 8 7 1.00 -1.00 0.00 0.00 -1.00 1.00 0.00 -1.00 0.00 0.00 0.00 0.00 9 10 -1.00 0.00 1.00 -1.00 1.00 0.00 -1.00 0.00 0.00 0.00 0.00 0.00 10 9 0.00 0.00 -1.00 0.00 1.00 -1.00 1.00 0.00 -1.00 0.00 0.00 0.00 11 12 0.00 -1.00 0.00 1.00 -1.00 0.00 0.00 -1.00 1.00 0.00 0.00 0.00 12 11 -1.00 1.00 0.00 -1.00 0.00 0.00 -1.00 0.00 1.00 0.00 0.00 0.00 13 13 0.00 -1.00 0.00 -1.00 0.00 0.00 0.00 0.00 -1.00 0.00 0.00 0.00 14 14 -1.00 0.00 1.00 0.00 -1.00 1.00 0.00 0.00 1.00 0.00 0.00 0.00 15 16 0.00 1.00 0.00 0.00 1.00 -1.00 -1.00 1.00 0.00 0.00 0.00 0.00 16 15 1.00 0.00 -1.00 1.00 0.00 0.00 1.00 -1.00 0.00 0.00 0.00 0.00 17 17 -1.00 0.00 0.00 0.00 0.00 -1.00 0.00 -1.00 0.00 0.00 0.00 0.00 18 18 0.00 0.00 -1.00 0.00 -1.00 0.00 -1.00 0.00 0.00 0.00 0.00 0.00 19 21 0.00 -1.00 1.00 0.00 0.00 1.00 -1.00 0.00 1.00 0.00 0.00 0.00 20 22 1.00 -1.00 0.00 1.00 0.00 -1.00 1.00 0.00 0.00 0.00 0.00 0.00 21 19 0.00 1.00 -1.00 -1.00 1.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 22 20 0.00 0.00 1.00 -1.00 0.00 1.00 0.00 -1.00 1.00 0.00 0.00 0.00 23 23 1.00 0.00 0.00 1.00 -1.00 0.00 1.00 0.00 -1.00 0.00 0.00 0.00 24 24 -1.00 1.00 0.00 0.00 1.00 0.00 0.00 1.00 -1.00 0.00 0.00 0.00 25 25 -1.00 0.00 0.00 0.00 -1.00 0.00 0.00 0.00 -1.00 0.00 0.00 0.00 26 26 0.00 -1.00 1.00 -1.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 0.00 27 27 1.00 0.00 0.00 1.00 0.00 -1.00 1.00 -1.00 0.00 0.00 0.00 0.00 28 28 0.00 1.00 -1.00 0.00 1.00 0.00 -1.00 1.00 0.00 0.00 0.00 0.00 29 30 0.00 -1.00 0.00 0.00 0.00 -1.00 -1.00 0.00 0.00 0.00 0.00 0.00 30 29 0.00 0.00 -1.00 -1.00 0.00 0.00 0.00 -1.00 0.00 0.00 0.00 0.00 31 32 -1.00 0.00 1.00 0.00 0.00 1.00 0.00 -1.00 1.00 0.00 0.00 0.00 32 31 -1.00 1.00 0.00 0.00 1.00 -1.00 0.00 1.00 0.00 0.00 0.00 0.00 33 34 1.00 0.00 -1.00 1.00 -1.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 34 33 0.00 0.00 1.00 0.00 -1.00 1.00 -1.00 0.00 1.00 0.00 0.00 0.00 35 36 0.00 1.00 0.00 -1.00 1.00 0.00 0.00 1.00 -1.00 0.00 0.00 0.00 36 35 1.00 -1.00 0.00 1.00 0.00 0.00 1.00 0.00 -1.00 0.00 0.00 0.00 37 37 0.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 38 38 1.00 0.00 -1.00 0.00 1.00 -1.00 0.00 0.00 -1.00 0.00 0.00 0.00 39 40 0.00 -1.00 0.00 0.00 -1.00 1.00 1.00 -1.00 0.00 0.00 0.00 0.00 40 39 -1.00 0.00 1.00 -1.00 0.00 0.00 -1.00 1.00 0.00 0.00 0.00 0.00 41 41 1.00 0.00 0.00 0.00 0.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 42 42 0.00 0.00 1.00 0.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 43 45 0.00 1.00 -1.00 0.00 0.00 -1.00 1.00 0.00 -1.00 0.00 0.00 0.00 44 46 -1.00 1.00 0.00 -1.00 0.00 1.00 -1.00 0.00 0.00 0.00 0.00 0.00 45 43 0.00 -1.00 1.00 1.00 -1.00 0.00 0.00 -1.00 0.00 0.00 0.00 0.00 46 44 0.00 0.00 -1.00 1.00 0.00 -1.00 0.00 1.00 -1.00 0.00 0.00 0.00 47 47 -1.00 0.00 0.00 -1.00 1.00 0.00 -1.00 0.00 1.00 0.00 0.00 0.00 48 48 1.00 -1.00 0.00 0.00 -1.00 0.00 0.00 -1.00 1.00 0.00 0.00 0.00 |
| Size of direct lattice |
GCALCO - MAX INDICES DIRECT LATTICE VECTOR
10 10 10
NO.OF VECTORS CREATED 2999 STARS 59 RMAX (BOHR) 44.65152 |
|
The geometry used to compute the wave function is printed T asymmetric unit (F equivalent atom) |
GEOMETRY FOR WAVE FUNCTION - DIMENSIONALITY OF THE SYSTEM 3
(NON PERIODIC DIRECTION: LATTICE PARAMETER FORMALLY SET TO 500)
*******************************************************************************
LATTICE PARAMETERS (ANGSTROMS AND DEGREES) - BOHR = 0.5291772083 ANGSTROM
PRIMITIVE CELL - CENTRING CODE 5/0 (VOLUME= 18.65461525)
A B C ALPHA BETA GAMMA
2.97691955 2.97691955 2.97691955 60.000000 60.000000 60.000000
*******************************************************************************
ATOMS IN THE ASYMMETRIC UNIT 2 - ATOMS IN THE UNIT CELL: 2
ATOM X/A Y/B Z/C
*******************************************************************************
1 T 12 MG 0.000000000000E+00 0.000000000000E+00 0.000000000000E+00
2 T 8 O 5.000000000000E-01 -5.000000000000E-01 -5.000000000000E-01
|
|
Transformation matrix from primitive to
crystallographic cell (by columns) Lattice parameters crystallographic cell Coordinates of the atoms in the crystallographic cell |
TRANSFORMATION MATRIX PRIMITIVE-CRYSTALLOGRAPHIC CELL
-1.0000 1.0000 1.0000 1.0000 -1.0000 1.0000 1.0000 1.0000 -1.0000
*******************************************************************************
CRYSTALLOGRAPHIC CELL (VOLUME= 74.61846100)
A B C ALPHA BETA GAMMA
4.21000000 4.21000000 4.21000000 90.000000 90.000000 90.000000
COORDINATES IN THE CRYSTALLOGRAPHIC CELL
ATOM X/A Y/B Z/C
*******************************************************************************
1 T 12 MG 0.000000000000E+00 0.000000000000E+00 0.000000000000E+00
2 T 8 O -5.000000000000E-01 -5.000000000000E-01 -5.000000000000E-01
T = ATOM BELONGING TO THE ASYMMETRIC UNIT
|
|
Intracell Nuclear Repulsion (no physical
meaning)
Primitive cell lattice vectors and atomic coordinates in the cartesian frame |
INTRACELL NUCLEAR REPULSION (A.U.) 1.3933481212094E+01
CARTESIAN COORDINATES - PRIMITIVE CELL
DIRECT LATTICE VECTORS CARTESIAN COMPONENTS (ANGSTROM)
X Y Z
0.000000000000E+00 0.210500000000E+01 0.210500000000E+01
0.210500000000E+01 0.000000000000E+00 0.210500000000E+01
0.210500000000E+01 0.210500000000E+01 0.000000000000E+00
*******************************************************************************
* ATOM X(ANGSTROM) Y(ANGSTROM) Z(ANGSTROM)
*******************************************************************************
1 12 MG 0.000000000000E+00 0.000000000000E+00 0.000000000000E+00
2 8 O 2.105000000000E+00 2.105000000000E+00 2.105000000000E+00
|
|
Size of the system and computational parameters values |
*******************************************************************************
N. OF ATOMS PER CELL 2 COULOMB OVERLAP TOL (T1) 10** -6 NUMBER OF SHELLS 5 COULOMB PENETRATION TOL (T2) 10** -6 NUMBER OF AO 14 EXCHANGE OVERLAP TOL (T3) 10** -6 N. OF ELECTRONS PER CELL 20 EXCHANGE PSEUDO OVP (F(G)) (T4) 10** -6 CORE ELECTRONS PER CELL 12 EXCHANGE PSEUDO OVP (P(G)) (T5) 10**-12 N. OF SYMMETRY OPERATORS 48 POLE ORDER IN MONO ZONE 4 ******************************************************************************* |
| Hamiltonian |
TYPE OF CALCULATION : RESTRICTED CLOSED SHELL
HARTREE-FOCK HAMILTONIAN ******************************************************************************* |
|
SCF iteration procedure parameters (convergence criteria and shrinking factors); number and coordinates of the k-points used in the Pack-Monkhorst IBZ sampling (R real, C complex) |
NUMBER OF CYCLES 50 CONVERGENCE ON DELTAP 10**- 16
NO MIXING OF F MATRICES CONVERGENCE ON ENERGY 10**- 5 SHRINK. FACT.(MONKH.) 8 8 8 NUMBER OF K POINTS IN THE IBZ 29 SHRINKING FACTOR(GILAT NET) 8 NUMBER OF K POINTS(GILAT NET) 29 ******************************************************************************* *** K POINTS COORDINATES (OBLIQUE COORDINATES IN UNITS OF IS = 8) 1-R( 0 0 0) 2-C( 1 0 0) 3-C( 2 0 0) 4-C( 3 0 0) 5-R( 4 0 0) 6-C( 1 1 0) 7-C( 2 1 0) 8-C( 3 1 0) 9-C( 4 1 0) 10-C( 5 1 0) 11-C( 6 1 0) 12-C( 7 1 0) 13-C( 2 2 0) 14-C( 3 2 0) 15-C( 4 2 0) 16-C( 5 2 0) 17-C( 6 2 0) 18-C( 3 3 0) 19-C( 4 3 0) 20-C( 5 3 0) 21-R( 4 4 0) 22-C( 3 2 1) 23-C( 4 2 1) 24-C( 5 2 1) 25-C( 4 3 1) 26-C( 5 3 1) 27-C( 6 3 1) 28-C( 5 4 1) 29-C( 6 4 2) ******************************************************************************* |
| Cartesian components (in a.u.) of direct and reciprocal lattice vectors |
DIRECT LATTICE VECTORS COMPON. (A.U.) RECIP. LATTICE VECTORS COMPON. (A.U.)
X Y Z X Y Z
0.0000000 3.9778735 3.9778735 -0.7897669 0.7897669 0.7897669
3.9778735 0.0000000 3.9778735 0.7897669 -0.7897669 0.7897669
3.9778735 3.9778735 0.0000000 0.7897669 0.7897669 -0.7897669
|
|
Dimensions of density and hamiltonian matrix in direct space - note the effect of symmetry (666 irreducible matrix elements vs 13898 reducible) |
DISK SPACE FOR EIGENVECTORS (FTN 10) 10780 REALS SYMMETRY ADAPTION OF THE BLOCH FUNCTIONS ENABLED DIMENSIONS P(G)= 13898 F(G)= 2820 P(G),F(G) (IRR) 666 MAX G-VECTOR INDEX FOR 1- AND 2-ELECTRON INTEGRALS 319 INFORMATION **** GENBUF **** COULOMB BIPO BUFFER LENGTH (WORDS) = 66150 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT INPUT TELAPSE 0.01 TCPU 0.02 |
|
Geometry analysis. For all non equivalent atoms information on first n (6 default) neighbors is printed: number, type, distance, and position in terms of indices of the direct lattice cell. Mg has 6-12-8-6-24-24 equivalent neighbors in the first 6 shells. Oxygen has the same neighboring structure.
No internal degrees of freedom, the position of the atoms is fully defined by the symmetry. |
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 2 O -1 0 0 2 O 0-1 0 2 O 0 0-1
2 O -1-1 0 2 O -1 0-1 2 O 0-1-1
1 MG 12 2.9769 5.6256 1 MG -1 0 0 1 MG 1 0 0 1 MG -1 0 1
1 MG 1 0-1 1 MG -1 1 0 1 MG 1-1 0
1 MG 0-1 0 1 MG 0 1 0 1 MG 0-1 1
1 MG 0 1-1 1 MG 0 0-1 1 MG 0 0 1
1 MG 8 3.6460 6.8899 2 O 0 0 0 2 O -1-1 1 2 O -1 1-1
2 O 1-1-1 2 O -2 0 0 2 O 0-2 0
2 O 0 0-2 2 O -1-1-1
1 MG 6 4.2100 7.9557 1 MG -1-1 1 1 MG 1 1-1 1 MG -1 1-1
1 MG 1-1 1 1 MG -1 1 1 1 MG 1-1-1
1 MG 24 4.7069 8.8948 2 O 1 0-1 2 O -1 0 1 2 O 1-1 0
2 O -1 1 0 2 O 0 1-1 2 O 0-1 1
2 O -2 0 1 2 O -2 1 0 2 O 1 0-2
2 O 1-2 0 2 O 0-2 1 2 O 0 1-2
2 O -2-1 1 2 O -2 1-1 2 O -1-2 1
2 O -1 1-2 2 O 1-1-2 2 O 1-2-1
2 O -2-1 0 2 O -2 0-1 2 O -1-2 0
2 O -1 0-2 2 O 0-2-1 2 O 0-1-2
1 MG 24 5.1562 9.7438 1 MG -2 0 1 1 MG 2 0-1 1 MG -2 1 0
1 MG 2-1 0 1 MG -2 1 1 1 MG 2-1-1
1 MG -1-1 0 1 MG 1 1 0 1 MG -1-1 2
1 MG 1 1-2 1 MG -1 0-1 1 MG 1 0 1
1 MG -1 0 2 1 MG 1 0-2 1 MG -1 2-1
1 MG 1-2 1 1 MG -1 2 0 1 MG 1-2 0
1 MG 0-2 1 1 MG 0 2-1 1 MG 0-1-1
1 MG 0 1 1 1 MG 0-1 2 1 MG 0 1-2
2 O 6 2.1050 3.9779 1 MG 1 0 0 1 MG 0 1 0 1 MG 0 0 1
1 MG 1 1 0 1 MG 1 0 1 1 MG 0 1 1
2 O 12 2.9769 5.6256 2 O -1 0 0 2 O 1 0 0 2 O -1 0 1
2 O 1 0-1 2 O -1 1 0 2 O 1-1 0
2 O 0-1 0 2 O 0 1 0 2 O 0-1 1
2 O 0 1-1 2 O 0 0-1 2 O 0 0 1
2 O 8 3.6460 6.8899 1 MG 0 0 0 1 MG 1 1-1 1 MG 1-1 1
1 MG -1 1 1 1 MG 2 0 0 1 MG 0 2 0
1 MG 0 0 2 1 MG 1 1 1
2 O 6 4.2100 7.9557 2 O -1-1 1 2 O 1 1-1 2 O -1 1-1
2 O 1-1 1 2 O -1 1 1 2 O 1-1-1
2 O 24 4.7069 8.8948 1 MG -1 0 1 1 MG 1 0-1 1 MG -1 1 0
1 MG 1-1 0 1 MG 0-1 1 1 MG 0 1-1
1 MG 2 0-1 1 MG 2-1 0 1 MG -1 0 2
1 MG -1 2 0 1 MG 0 2-1 1 MG 0-1 2
1 MG 2 1-1 1 MG 2-1 1 1 MG 1 2-1
1 MG 1-1 2 1 MG -1 1 2 1 MG -1 2 1
1 MG 2 1 0 1 MG 2 0 1 1 MG 1 2 0
1 MG 1 0 2 1 MG 0 2 1 1 MG 0 1 2
2 O 24 5.1562 9.7438 2 O -2 0 1 2 O 2 0-1 2 O -2 1 0
2 O 2-1 0 2 O -2 1 1 2 O 2-1-1
2 O -1-1 0 2 O 1 1 0 2 O -1-1 2
2 O 1 1-2 2 O -1 0-1 2 O 1 0 1
2 O -1 0 2 2 O 1 0-2 2 O -1 2-1
2 O 1-2 1 2 O -1 2 0 2 O 1-2 0
2 O 0-2 1 2 O 0 2-1 2 O 0-1-1
2 O 0 1 1 2 O 0-1 2 2 O 0 1-2
THERE ARE NO SYMMETRY ALLOWED DIRECTIONS
TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT SYMM TELAPSE 0.01 TCPU 0.02
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Integrals calculation. Two-electron integrals computation time = SHLC - MONIRR; One-electron integrals computation time = MONMAD - SHLC |
INFORMATION **** EXCBUF **** EXCH. BIPO BUFFER: WORDS USED = 97362 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT MONIRR TELAPSE 0.06 TCPU 0.06 GAUSS70 FOR COULOMB GAUSS70 FOR EXCHANGE **SHELL_ORTHODOX** SPACE FOR BIEL. INTEGRALS 1 BUFFERS TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT SHLC TELAPSE 1.97 TCPU 1.91 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT MONMAD TELAPSE 2.05 TCPU 2.00 EEEEEEEEEE INT_CALC TERMINATION DATE 02 09 2003 TIME 15:51:49.6 |
| SCF iteration to compute the total energy starts. |
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MGO BULK CRYSTAL - SCF - TYPE OF CALCULATION : RESTRICTED CLOSED SHELL ******************************************************************************* TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT SDIK CPU 7.880 |
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Default initial guess for the wave function evaluation as superposition of atomic densities |
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ATOMIC WAVE FUNCTIONS ZNUC SCFIT TOTAL HF ENERGY KINETIC ENERGY VIRIAL THEOREM ACCURACY 12.0 5 -1.965119311E+02 1.917472779E+02 -2.024848609E+00 1.1E-06 8.0 1 -7.231180559E+01 7.850242955E+01 -1.921140989E+00 0.0E+00 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA |
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Information on the SCF
iteration. At each SCF cycle, total charge of the atoms (Mulliken scheme), total energy and values of the convergence criteria are printed; DETOT difference in total energy at cycle i and i-1; DP rms on density matrix; PX maximum difference between density matrix elements. It also indicates whether the system is an insulator or a conductor and the related Fermi level. FDIK-TOTENY time for Fourier transform and diagonalization TOTENY-PDIG time for the reconstruction of Hamiltonian matrix in direct space PDIG-FDIK time for calculation of Fermi energy |
CHARGE NORMALIZATION FACTOR 1.00000000; TOTAL ATOMIC CHARGES: 12.0000000 8.0000000 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT QGAM TELAPSE 2.06 TCPU 2.01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BIEL TELAPSE 2.07 TCPU 2.01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TOTENY TELAPSE 2.07 TCPU 2.01 CYC 0 ETOT(AU) -2.706738561044E+02 DETOT -2.71E+02 DP 1.00E+00 PX 0.00E+00 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT FDIK TELAPSE 2.07 TCPU 2.02 INSULATING STATE - TOP OF VALENCE BANDS (A.U.) -2.082E-01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT PDIG TELAPSE 2.08 TCPU 2.02 CHARGE NORMALIZATION FACTOR 1.00000000; TOTAL ATOMIC CHARGES: 10.9720201 9.0279799 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT QGAM TELAPSE 2.08 TCPU 2.02 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BIEL TELAPSE 2.09 TCPU 2.03 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TOTENY TELAPSE 2.09 TCPU 2.03 CYC 1 ETOT(AU) -2.711666415674E+02 DETOT -4.93E-01 DP 1.00E+00 PX 0.00E+00 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT FDIK TELAPSE 2.09 TCPU 2.04 INSULATING STATE - TOP OF VALENCE BANDS (A.U.) -6.167E-02 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT PDIG TELAPSE 2.09 TCPU 2.04 CHARGE NORMALIZATION FACTOR 1.00000000; TOTAL ATOMIC CHARGES: 11.3203964 8.6796036 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT QGAM TELAPSE 2.09 TCPU 2.04 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BIEL TELAPSE 2.10 TCPU 2.05 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TOTENY TELAPSE 2.10 TCPU 2.05 CYC 2 ETOT(AU) -2.712141249457E+02 DETOT -4.75E-02 DP 1.35E-02 PX 1.35E-01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT FDIK TELAPSE 2.10 TCPU 2.05 INSULATING STATE - TOP OF VALENCE BANDS (A.U.) -1.755E-01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT PDIG TELAPSE 2.11 TCPU 2.05 CHARGE NORMALIZATION FACTOR 1.00000000; TOTAL ATOMIC CHARGES: 11.1948077 8.8051923 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT QGAM TELAPSE 2.11 TCPU 2.05 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BIEL TELAPSE 2.11 TCPU 2.06 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TOTENY TELAPSE 2.11 TCPU 2.06 CYC 3 ETOT(AU) -2.712177270194E+02 DETOT -3.60E-03 DP 5.04E-03 PX 7.64E-02 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT FDIK TELAPSE 2.12 TCPU 2.06 INSULATING STATE - TOP OF VALENCE BANDS (A.U.) -1.386E-01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT PDIG TELAPSE 2.12 TCPU 2.07 CHARGE NORMALIZATION FACTOR 1.00000000; TOTAL ATOMIC CHARGES: 11.2327211 8.7672789 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT QGAM TELAPSE 2.12 TCPU 2.07 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BIEL TELAPSE 2.13 TCPU 2.07 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TOTENY TELAPSE 2.13 TCPU 2.07 CYC 4 ETOT(AU) -2.712180611061E+02 DETOT -3.34E-04 DP 1.37E-03 PX 1.36E-02 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT FDIK TELAPSE 2.13 TCPU 2.08 INSULATING STATE - TOP OF VALENCE BANDS (A.U.) -1.504E-01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT PDIG TELAPSE 2.14 TCPU 2.08 CHARGE NORMALIZATION FACTOR 1.00000000; TOTAL ATOMIC CHARGES: 11.2195509 8.7804491 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT QGAM TELAPSE 2.14 TCPU 2.08 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BIEL TELAPSE 2.14 TCPU 2.09 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TOTENY TELAPSE 2.14 TCPU 2.09 CYC 5 ETOT(AU) -2.712180950048E+02 DETOT -3.39E-05 DP 4.94E-04 PX 6.23E-03 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT FDIK TELAPSE 2.15 TCPU 2.09 INSULATING STATE - TOP OF VALENCE BANDS (A.U.) -1.465E-01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT PDIG TELAPSE 2.15 TCPU 2.10 CHARGE NORMALIZATION FACTOR 1.00000000; TOTAL ATOMIC CHARGES: 11.2237300 8.7762700 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT QGAM TELAPSE 2.15 TCPU 2.10 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BIEL TELAPSE 2.16 TCPU 2.10 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TOTENY TELAPSE 2.16 TCPU 2.10 CYC 6 ETOT(AU) -2.712180983825E+02 DETOT -3.38E-06 DP 1.49E-04 PX 1.48E-03 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT FDIK TELAPSE 2.16 TCPU 2.11 INSULATING STATE - TOP OF VALENCE BANDS (A.U.) -1.478E-01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT PDIG TELAPSE 2.17 TCPU 2.11 |
| At the end of SCF iterations each contribution to the total energy is displayed as well as the total energy and the virial coefficient |
CHARGE NORMALIZATION FACTOR 1.00000000; TOTAL ATOMIC CHARGES: 11.2223209 8.7776791 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT QGAM TELAPSE 2.17 TCPU 2.11 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BIEL TELAPSE 2.17 TCPU 2.12 +++ ENERGIES IN A.U. +++ ::: EXT EL-POLE : L = 0 -4.6907630069433E+02 ::: EXT EL-POLE : L = 1 -1.1466965027180E-21 ::: EXT EL-POLE : L = 2 -1.2944147700301E-19 ::: EXT EL-POLE : L = 3 -2.8401639980708E-22 ::: EXT EL-POLE : L = 4 -1.0955281290192E-04 ::: EXT EL-SPHEROPOLE 3.9641495581541E+00 ::: BIELET ZONE E-E 5.1160526532334E+02 ::: TOTAL E-E 4.6493004634353E+01 ::: TOTAL E-N + N-E -5.1175597833315E+02 ::: TOTAL N-N -7.3084276676762E+01 ::: KINETIC ENERGY 2.6712915158680E+02 ::: TOTAL ENERGY -2.7121809878875E+02 ::: VIRIAL COEFFICIENT 9.9240462879843E-01 TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT TOTENY TELAPSE 2.17 TCPU 2.12 CYC 7 ETOT(AU) -2.712180987888E+02 DETOT -4.06E-07 DP 1.49E-04 PX 1.48E-03 |
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Criteria satisfied to stop SCF iteration Final total energy, Hamiltonian (HF), unit of measure (hartree), number of cycles (7). |
=== SCF ENDED -CONVERGENCE ON ENERGY E(AU) -2.7121809878875E+02 CYCLES 7 TOTAL ENERGY(HF)(AU)( 7) -2.7121809878875E+02 DE-4.1E-07 DP 1.5E-04 PX 1.5E-03 EIGENVECTORS IN FORTRAN UNIT 10 |
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Total CPU and elapsed time Date |
TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT END TELAPSE 2.19 TCPU 2.13 EEEEEEEEEE TERMINATION DATE 02 09 2003 TIME 15:51:49.7 |
Complete input decks are available as example. All of these can run with the demo CRYSTAL03 version. Minimal basis set inputs run in few seconds.
| Minimal basis set | Extended basis set |
http://tutorials.crystalsolutions.eu/tutorials/others/quick.html.save
My name is Dr Abderrahmane Reggad. I'm a 54 year old and I am a researcher in materials' sciences.
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