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Introduction 5,Functionality 6,Typographical Conventions 7. Acknowledgements 8,Getting Started Installation and testing 8. Program errors 8,1 Wave function calculation Basic input route 9. 1 1 Geometry and symmetry information 9,Geometry input for crystalline compounds 10. Geometry input for molecules polymers and slabs 10. Geometry input from external geometry editor 11,Comments on geometry input 11.

1 2 Basis set 14, 1 3 Computational parameters hamiltonian SCF control 18. 2 Wave function calculation Advanced input route 21. 2 1 Geometry editing 21,Electric field perturbation 32. 2 2 Basis set input 46,Effective core pseudo potentials 50. Pseudopotential libraries 51, 2 3 Computational parameters hamiltonian SCF control 54. DFT Hamiltonian 58,3 Geometry optimization 82,4 Frequency calculations at point 98.

Harmonic frequency calculation at 98,Anharmonic calculation for X H stretching 106. 5 Properties 108,5 1 Preliminary calculations 108,5 2 Properties keywords 109. 5 3 Spontaneous polarization and piezoelectricity 142. 6 Input examples 147,6 1 Standard geometry input 147. CRYSTAL 147,POLYMER 153,MOLECULE 154,6 2 Basis set input 154. Valence only basis set input 155,6 3 SCF options SPINEDIT 157.

6 4 Geometry optimization OPTGEOM 159,7 Basis set 168. 7 1 Molecular BSs performance in periodic systems 168. 7 2 Core functions 169,7 3 Valence functions 169,Molecular crystals 169. Covalent crystals 169,Ionic crystals 170,From covalent to ionics 171. Metals 171, 7 4 Hints on crystalline basis set optimization 171. 7 5 Check on basis set quasi linear dependence 172. 8 Theoretical framework 174,8 1 Basic equations 174.

8 2 Remarks on the evaluation of the integrals 175. 8 3 Treatment of the Coulomb series 176,8 4 The exchange series 177. 8 5 Bipolar expansion approximation of Coulomb and exchange integrals 178. 8 6 Exploitation of symmetry 178,Symmetry adapted Crystalline Orbitals 179. 8 7 Reciprocal space integration 180, 8 8 Electron momentum density and related quantities 180. 8 9 Elastic Moduli of Periodic Systems 182,Examples of matrices for cubic systems 183. Bulk modulus 185, 8 10 Spontaneous polarization through the Berry phase approach 186.

Spontaneous polarization through the localized crystalline orbitals approach 186. 8 11 Piezoelectricity through the Berry phase approach 187. Piezoelectricity through the localized crystalline orbitals approach 187. A Symmetry groups 189,A 1 Labels and symbols of the space groups 189. A 2 Labels of the layer groups slabs 192,A 3 Labels of the rod groups polymers 193. A 4 Labels of the point groups molecules 196, A 5 From conventional to primitive cells transforming matrices 197. B Summary of input keywords 198,C Reciprocal lattice sampling 206. D Printing options 207,E External format 211,F Normalization coefficients 221.

G Incompatibility 230,H CRYSTAL06 versus CRYSTAL03 231. I Relevant strings 234,J Acronyms 235,Bibliography 236. Subject index 244,Introduction, The CRYSTAL package performs ab initio calculations of the ground state energy energy. gradient 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 See Chapter 8. The local functions are in turn linear combinations of Gaussian type functions GTF whose. exponents and coefficients are defined by input section 1 2 Functions of symmetry s p d. and f can be used see page 16 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 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 super cell with a. defect and a large variety of structure editing See Section 2 1. Previous releases of the software in 1988 CRYSTAL88 1 1992 CRYSTAL92 2 1996. CRYSTAL95 3 1998 CRYSTAL98 4 and 2003 CRYSTAL03 5 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 Applications in. http www crystal unito it, The CRYSTAL package has been developed over a number of years For basic theory and. algorithms see Theory in,http www crystal unito it theory html.

The required citation for this work is, R Dovesi V R Saunders C Roetti R Orlando C M Zicovich Wilson F Pascale. B Civalleri K Doll N M Harrison I J Bush Ph D Arco M Llunell. CRYSTAL06 User s Manual University of Torino Torino 2006. CRYSTAL06 output will display the references relevant to the property computed when. Updated information on the CRYSTAL code as well as tutorials to learn basic and advanced. CRYSTAL usage are in,http www crystal unito it,Functionality. The basic functionality of the code is outlined below. The single particle potential,Restricted Hartree Fock Theory 2 3. Unrestricted Open Shell Hartree Fock Theory 2 3, Density Functional Theory for Exchange and Correlation 2 3. Spin Density Functional Theory 2 3,Hybrids HF DFT B3LYP B3PW 2 3.

Effective Core Pseudo potentials 2 2, Finite field perturbation added to the Hamiltonian 2 1. Algorithms, Parallel processing replicated data See http www crystal unito it Manuals crystal03 P pdf. Massive Parallel Processing distributed data,Traditional SCF. Full Direct SCF 2 3,Structural Editing,Use of space layer rod and point group symmetry. Deformation of the crystallographic cell 2 1, Removal 2 1 insertion 2 1 substitution 2 1 of atoms.

Displacement of atoms 2 1,Rotation of groups of atoms 2 1. Extraction of surface models from a 3D crystal structure 2 1. Cluster generation from a 3D crystal 2 1,Cluster of molecules from molecular crystal 2 1. Properties,Band structure 5 2 Density of states 5 2. Electronic charge density maps 2D 3D grid 5 2 5 2,Mulliken population analysis 2 3. Spherical harmonic atom and shell multipoles 5 2,X ray structure factors 5 2.

Electron momentum distributions 5 2 5 2,Compton profiles 8 27. First order density matrix,Reciprocal form factors. Electrostatic potential field and field gradients 5 2 5 2. Spin polarized generalization of properties,Hyperfine electron nuclear spin tensor 5 2. A posteriori Density Functional correlation energy 5 2. Localization of Crystalline Orbitals 5 2, Spontaneous polarization through Berry phase approach 5 3. Spontaneous polarization through localized orbitals approach 5 3. Piezoelectricity through Berry phase approach 5 3, Piezoelectricity through localized orbitals approach 5 3.

Optical dielectric constant 5 2, Analytic nuclear coordinates and cell parameters gradient of the energy. Harmonic frequencies at point 4, Geometry optimizer in cartesian and redundant internal coordinates 3. Conventions, In the description of the input data which follows the following notation is adopted. new record,free format record, An alphanumeric datum first n characters meaningful. atom label sequence number of a given atom in the primitive cell as. printed in the output file after reading of the geometry input. symmops symmetry operators,default values,italic optional input.

optional input records follow II,additional input records follow II. Part of the code is written in fortran 77 The name of the variables is associated with the type. of data following the fortran 77 convention if the first letter of the name is I J K L M or. N the type is integer Otherwise the type is real, Arrays are read in with a simplified implied DO loop instruction of Fortran 77. dslist i m1 m2, where dslist is an input list i is the name of an integer variable whose value ranges from m1. Example page 27 LB L L 1 NL, NL integer data are read in and stored in the first NL position of the array LB. All the keywords are entered with an A format case insensitive the keywords must be typed. left justified with no leading blanks, conventional atomic number usually called NAT is used to associate a given basis set.

with an atom The real atomic number is the remainder of the division NAT 100. Output files may have a name assigned by the OPEN instruction or the default name as. signed to a fortran unit by the system Mosts of the operating system assign the name. fort fortran unit number,Acknowledgements, Embodied in the present code are elements of programs distributed by other groups. In particular the atomic SCF package of Roos et al 6 the GAUSS70 gaussian integral. package and STO nG basis set due to Hehre et al 7 the code of Burzlaff and Hountas for. space group analysis 8 and Saunders ATMOL gaussian integral package 9. We take this opportunity to thank these authors Our modifications of their programs have. sometimes been considerable Responsibility for any erroneous use of these programs therefore. remains with the present authors, It is our pleasure to thank Piero Ugliengo for continuous help useful suggestions rigorous. We acknowledge Furio Cora careful testing of the development versions of CRYSTAL. Michele Catti significantly contributed to the implementation of the geometry optimizer with. discussion suggestions contributions to the coding. We are also in debt with Cesare Pisani for his constant support of and interest in the devel. opment of the new version of the CRYSTAL program, Financial support for this research has been provided by the italian MURST Ministero della. Universita e della Ricerca Scientifica e Tecnologica and the United Kingdom CCLRC Council. for the Central Laboratories of the Research Council. Getting Started, Instructions to download install and run the code are available in the web site. http www crystal unito it documentation README,Program errors.

A very large number of tests have been performed by researchers of a few laboratories that. had access to a test copy of CRYSTAL06 We tried to check as many options as possible but. not all the possible combinations of options have been checked We have no doubts that errors. The authors would greatly appreciate comments suggestions and criticisms by the users of. CRYSTAL in case of errors the user is kindly requested to contact the authors sending a. copy of both input and output by E mail to the Torino group crystal unito it. Wave function calculation Basic,input route,1 1 Geometry and symmetry information. The first record of the geometry definition must contain one of the keywords. CRYSTAL 3D system,SLAB 2D system,POLYMER 1D system. MOLECULE 0D system,EXTERNAL geometry from external file. DLVINPUT geometry from DLV 10 Graphical User Interface. Three input schemes are used The first is for crystalline systems and is specified by the. keyword CRYSTAL The second is for slabs polymers and molecules as specified by the key. words SLAB POLYMER or MOLECULE respectively In the third scheme with keyword. EXTERNAL or DLVINPUT the unit cell atomic positions and symmetry operators may. be provided directly from an external file see Appendix E page 217 Such an input file can. be prepared by the keyword EXTPRT crystal input block 1 page 32 properties Sample. input decks for a number of structures are provided in section 6 1 page 147. Geometry input for crystalline compounds,rec variable value meaning. IFLAG convention for space group identification Appendix A 1 page 189. 0 space group sequential number 1 230,1 Hermann Mauguin alphanumeric code.

IFHR type of cell for rhombohedral groups meaningless for non. rhombohedral crystals,0 hexagonal cell,1 rhombohedral cell. IFSO setting for the origin of the crystal reference frame. 0 origin derived from the symbol of the space group where there. are two settings the second setting of the International Tables is. 1 standard shift of the origin when two settings are allowed the first. setting is chosen, 1 non standard shift of the origin given as input see test22. space group identification code following IFLAG value. IGR space group sequence number IFLAG 0,A AGR space group alphanumeric symbol IFLAG 1. if IFSO 1 insert II, IX IY IZ non standard shift of the origin coordinates x y z in fractions of. the crystallographic cell lattice vectors times 24 to obtain integer. a b c minimal set of crystallographic cell parameters. translation vector s length A ngstrom,crystallographic angle s degrees.

C M Zicovich Wilson 1 4 F Pascale5 B Civalleri1 K Doll6 N M Harrison 2 7 I J Bush Ph D Arco8 M Llunell9 1 Theoretical Chemistry Group University of Turin Dipartimento di Chimica IFM Via Giuria 5 I 10125 Torino Italy 2 Computational Science amp Engineering Department CCLRC Daresbury Daresbury Warrington Cheshire UK WA4 4AD 3 Universit a del Piemonte Orientale

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