CRYSTAL 981.0

February 26, 1999

V.R Saunder, R. Dovesi, C. Roetti, M. Causa, N.M. Harrison, R. Orlando, C. M. Zicovish-Wilson

Oleg Sychev

Crystal 98 2

Properties of interest&Methods

Properties of interest

Equilibrium structurePhononsRelaxation around defects

Energy dispersionDensity of statesSpatial charge densityChemical bondingMagnetic interactions

Dinamical simulationsPhase boundaries

Methods

All-electronsTotal-energy methods (DFT):FLAPW, FP-LMTO, Gaussian

pseudopotencial

Methods using simplifying assumptions for the crystal potencial:

LMTO-ASA, ASW

Semiempirical methodsClassical molecular dynamics;

model Hamiltonians

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Theory Stationary Shrodinger equation:

1em,unitsatomic:followingthefor

existmustdr)r(:)r(ofopertiesPr

densityeargch),r()r(e:electronanfor

,densityprobality)r(

functionwave)r(,energypotencial)r(U),r(Um2

H

)r(E)r(H

2

2

2

22

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TheoryHartree-Fock method

LLiLi

N

1i

*i

N

1i

*i

2

)r(fa)r(

:functionsbasiseappropriatoveransionexpanbydrepresentetypicalareforsearched

orbitalsparticleonethe;yconvergencsufficienttilliterate:solutionacticalPr

\)r(rd)r(rr

)r()r(

)r(rdrr

)r()r(

)r(U2

1

Crystal 98 5

TheoryDensity functional theory

.)etcionapproximatgradient

dgeneralizeGGA,ionapproximatdensitylocalLDA(

energyncorrelatioexchangetheofFunctional:E

Edr)r(E

rdrdrr

)r()r(

2

1E

xc

xc

N

1i

xci

Crystal 98 6

Installation

Installation size is 173Mb on CD WWW Sites:

http://www.chimifm.unito.it/teorica/crystal/crystal.html

http://www.cse.clrc.ac.uk/cmg/CRYSTAL/

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Installation

CRYSTAL98 use: Unix Linux systems(all versions) Windows NT

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Introduction

The CRYSTAL package performs ab initio calculations of the ground state energy, elec-tronic 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).

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Structure

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(in the order 2z2-x2-y2; xz; yz; x2-y2; xy) 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.

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Structure The program can automatically handle space

symmetry: 230 space groups, 80 layer groups, 99 rod groups, 45 point groups are available (Appendix A). 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 supercell with a defect and a large variety of structure editing.

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FunctionalityThe basic functionality of the code is

outlined below. The single particle potential

Restricted Hartree Fock Theory Unrestricted and Restricted Open

Shell Hartree Fock Theory Density Functional Theory for

Exchange and Correlation Effective Core Pseudopotentials

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Functionality

Algorithms Parallel processing (replicated data) Traditional SCF Direct SCF

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Functionality

Structural Editing Use of space, layer, rod and point group

symmetry Removal, insertion deletion and substitution

of atoms Displacement of atoms Rotation of groups of atoms Extraction of surface models from 3D crystal

structure Cluster generation from 3D crystals Cluster of molecules from molecular crystals

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Functionality Properties

Band structure Density of states Electronic charge density maps Electronic charge density on a 3D grid Mulliken population analysis Spherical harmonic atom and shell multipoles X-ray structure factors Electron momentum distributions Compton profiles Electrostatic potential, field and field gradients Spin polarised generalisation of properties Hyperfine electron-nuclear spin tensor A posteriori Density Functional correlation energy

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Wave function analysis and properties

Total energy Hartree-Fock wave function Hartree-Fock wave-function+DF a posteriori

correction for correlation DF SCF wave function

Band structure Density of states

Band projected DOSS AO projected DOSS

All Electron Charge Density - Spin Density Density maps Mulliken population analysis Density analytical derivatives

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Wave function analysis and properties

Atomic multipoles Electrostatic potential

Electrostatic potential maps Point charge electrostatic potential maps

Electric field Electric field gradient Structure factors Compton profiles Electron Momentum Density Fermi contact

ADEQUATE DESCRIPTION OF COPPER BAND STRUCTUREADEQUATE DESCRIPTION OF COPPER BAND STRUCTURE

Figure 3 Figure 4

M

k Z

X

K

K WL

U

Xk y

M

k X

a

our

data

b

data

from

Ref.

ADEQUATE DESCRIPTION OF MgO BAND STRUCTUREADEQUATE DESCRIPTION OF MgO BAND STRUCTURE

Figure 3 Figure 4

M

k Z

X

K

K WL

U

Xk y

M

k X

a

our

data

b

data

from

Ref.

Crystal 98 19

The functionality of the various programs and their links are as follows:

integrals

definition of geometry and BS calculation of symmetry information classification,

selection, computation of one-and two-electron integrals

fortran files: geometry,BS, symmetry information one- and two-electron integrals

scfiterative solution of SCF

equations

ground state wave function

unformatted

propertiesground state properties

scfdirdefinition of geometry and BS

calculation of symmetry information classification, selection of one- and two-electron integrals computation of one-electron integrals iterative solution of SCF equation and calculation of two-

electron integrals

formatted

convertconversion ascii/binary

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Compilation

Crystal98 is written in FORTRAN 77 and is therefore easily compiled on architectures for which executibles are not provided. You may also wish to compile the code to alter the dimensions of internal arrays or to select compilation and linkage options to increase the performance of the code.

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Testing the Installation

It is very important that the installation of the code is checked by running the validation suite which is contained on the CD

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The parallel Implementation CRISTAL98 supports parallel execution on

modestly parallel hardware on computers (nodes) linked by relatively low perfomance networks (eg: Ethenet).CPU and DISK resources are shared efficiently while the memory usage is replicated on each node.

One node is chosen as the master.The master spawns the program onto other nodes (slaves) and operates dynamical load balancing of the task execution via a shared atomic counter.

During integral generation a task is defined as the calculation of a block of integrals.Thus each node computes a number of integrals which are stored to its local disk.

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Basic problems of CRYSTAL98

Optimization basis for concrete physical tasks

Value Energy Fermi is either overestimated(DFT method) or underestimated(HF-method)

Time of calculation depends from computer sizes memory (as HDD size, so Extended memory size)

Crystal 98 24

CRYSTAL 981.0

February 26, 1999

V.R Saunder, R. Dovesi, C. Roetti, M. Causa, N.M. Harrison, R. Orlando, C. M. Zicovish-Wilson

http://www.chimifm.unito.it/teorica/crystal/crystal.html

http://www.cse.clrc.ac.uk/cmg/CRYSTAL/