Stability and equilibrium structure
Adsorption at crystalline surfaces
One-electron Properties
⌘ ⌘ ⌘ CRYSCOR09: Examples of application ⌘ ⌘ ⌘
a
L. Maschio, D. Usvyat, M. Schütz, B. Civalleri,
Periodic LMP2 method applied to molecular crystals: Study of solid NH3 and CO2 using extended basis sets.
J. Chem. Phys. 132, 134706 (2010)
M. Halo, S. Casassa, L. Maschio, C. Pisani, R. Dovesi, D.Ehinon, I. Baraille, M. Rérat, D. Usvyat,
Periodic ab initio estimates of the dispersive interaction between molecular nitrogen and a monolayer of hexagonal BN.
Phys.Chem.Chem.Phys. 13, 4434 (2011)
C.Pisani, M.Itou, Y.Sakurai, R.Yamaki, M.Ito, A.Erba,L.Maschio,
Beyond a single-determinantal description of the density matrix of periodic systems: Experimental versus theoretical Compton profiles of crystalline silicon. Phys.Rev. B 83, 125208 (2011)
The comparison of directional CPs of Si measured at SPring8 with calculated ones reveals definite inadequacies of the most popular theoretical models for the description of the EMD in crystals. LMP2 results are instead in good agreement with the experiment.
R. Martinez-Casado, G. Mallia, D. Usvyat, L. Maschio, S. Casassa, M. Schütz, N.M. Harrison,
Periodic quantum mechanical simulation of the He-MgO(100) interaction potential. J. Chem. Phys. 134, 014708 (2011).
Using a slab supercell 2x2 model, He/(MgO adsorption is well described by LMP2 while DFT performs unsatisfactorily
S, Casassa, R. Dovesi et al.,
Relative stability of aluminium hydroxides: a DFT vs LMP2 study.
(In preparation, 2011).
CO
2NH
3Due to its accurate account of both short-range and long-range (dispersive) interactions, LMP2 is particularly well suited for describing molecular crystals
Compton Profile Anisotropy in Silicon: J[110](p) – J[100](p) (All data in a.u.)
(1) (2) (3) (4)
Results obtained either from the polarizabilities of the two systems (C6, C6+C8) or by means of LMP2 (HF+MP2) closely agree at long range.
With respect to the zoo of DFT functionals, LMP2 gives reference, usually correct indications of the relative stability of crystalline allotropes
… one step into
electron correlation in
crystals
C R Y S C O R 0 9
A computational tool for the ab-initio study
of electron correlation in crystals
Web site: www.cryscor.unito.it
Contacts: cryscor@unito.it
C.Pisani, S.Casassa, L.Maschio Department of Chemistry IFM
University of Torino (I)
M.Schütz, D.Usvyat
Inst. Physical Theoretical Chem. University of Regensburg (D)
CRYSCOR09 performs LMP2 calculations for non conducting systems periodic in 0,1,2 and 3 D.
LMP2 means that standard Møller-Plesset theory at order 2 is adopted, in a local formulation similar to that used in the molecular MOLPRO package. Part of the integral package is taken from that code, on the basis of a joint agreement.
LMP2 is a well-assessed, parameter-free method:
it provides a high-quality reference description
of the energetics and electronic structure
of covalent, ionic, molecular crystals.
The Hartree-Fock (HF) zero-order solution plus all basic information concerning the system is provided by the periodic code CRYSTAL09(
see scheme below).
AO-GTF basis setCRYSTAL and CRYSCOR use a basis set of Atomic Orbitals (AO), contractions of Gaussian Type Functions (GTF). Comparison with results from standard molecular codes is thus straightforward.
Dual Basis set option
The description of the virtual manifold can be improved by adding AO-GTFs on top of those suitable for HF/DFT calculations for crystals (given at the CRYSTAL site: www.crystal.unito.it).1,5
Simple input
Using standard input (geometry, basis set), CRYSTAL09 performs full symmetry analysis, solves the HF problem and transmits all required information to CRYSCOR09 via disc. Some tolerances can be set to adjust accuracy vs cost of the LMP2 calculation.
Symmetry adapted Wannier Functions (SAWF)
CRYSTAL09 prepares and transmits to CRYSCOR09 the SAWFs: these are local, orthonormal functions, equivalent to each other wrt crystal group operations, which span altogether the occupied Fock manifold.2 Their role in the LMP2 calculation is essential;
they also permit a “chemical” analysis of the correlation energy.
Fast calculation of integrals
Effective algorithms are used for calculating 2-electron integrals, based on a periodic extension of Density Fitting techniques3 and
on the use of multipolar expansion methods.
Quasi-linear scaling of computational times
Symmetry exploitation, efficient integration techniques, clever use of the locality Ansatz, allow LMP2 times to scale about linearly with N (compared to standard N5 of canonical MP2).
LMP2 energy
The LMP2 energy per crystal cell is the main result of the calculation; its contribution to cohesive energies must be corrected for the Basis Set Superposition Error.1
Fix-index option
Serves to reduce numerical noise in geometry optimizations.
Lennard-Jones extrapolation
Allows the estimate of dispersive interactions up to infinite distance.
LMP2 Correction to Density Matrix (DM)
The LMP2 correction to the HF DM is evaluated via a Lagrangian technique.4 The corrected DM can be fed back to CRYSTAL09 for
calculating and plotting Electron Charge Density (ECD), Electron Momentum Density (EMD), Compton Profiles, X-ray factors.
M a i n f e a t u r e s
[1] C. Pisani, L. Maschio, S. Casassa, M. Halo, M. Schütz and D. Usvyat, Periodic Local MP2 Method for the Study of Electronic Correlation in Crystals: Theory and Preliminary Applications,
J. Comput. Chem., 29, 2113 (2008).
[2] S. Casassa, C. Zicovich-Wilson and C. Pisani, Symmetry-adapted Localized Wannier Functions suitable for periodic local correlation methods, Theor. Chem. Acc., 116, 726 (2006).
[3] L. Maschio and D. Usvyat, Fitting of local densities in periodic systems, Phys. Rev. B, 78, 073102 (2008).
[4] D. Usvyat and M. Schütz, Orbital-unrelaxed Lagrangian density matrices for periodic systems at the local MP2 level,
J. Phys.: Conf. Ser., 117, 012027 (2008).
[5] A. Erba, C. Pisani, S. Casassa, L. Maschio, M. Schütz, and D. Usvyat , MP2 versus DFT study of the Compton profiles of crystalline urea, Phys. Rev. B, 81, 165108 (2010).
E s s e n t i a l b i b l i o g r a p h y
Symmetry-independent SAWFs of Boron Nitride
Hexagonal BN wh1 wh2 wh3 Cubic BN wc Quasi-linear scaling of computational times HF (CRYSTAL09) and LMP2 (CRYSCOR09) supercell calculations for a 3-L MgO slab
(VTZ aug basis set)
User’s Manual, Demo version, Tutorials
At the CRYSCOR web site (webmaster: M. Lorenz), you can get free of charge:• The User’s manual (by A. Erba and M. Halo); • A DEMO version of CRYSCOR09
(all functionalities, maximum 3 irreducible atoms); • Examples of input and output;
• A collection of tutorials
