- Running CRYSCOR
- General input comments
- Exercises proposed
Migen Halo, 2010-10-13
1. BasicsBriefly summarizing the main concepts:
- dynamic electron correlation energy is the energy due to the instantaneous correlation of electron motions
- it represents only a small part of the total energy of a system, BUT
- it is essential to explain phenomena involving dispersive forces
- it contributes a large fraction of the cohesive energy in ionic crystals
- it provides a substantial part of the strength of covalent chemical bonds in molecules and solids.
- the Hartree-Fock (HF) solution does not take into account electron correlation;
- Density Functional Theory (DFT) considers only local electron correlation in its standard formulations or introduces empirical parameters,
- the MP2 (Møller-Plesset at the second-order) perturbative correction currently implemented uses the HF solution as an uperturbed reference state; this solution is provided by the CRYSTAL program
- local functions (called "Wannier functions, WF'') are adopted instead of delocalized Bloch functions; this permits the exploitation of the short-range nature (E ∝ R-6) of electron correlation. The main advantage of the local approach is the achievement of a scaling which is much lower (nearly linear - N or N2) than that of "classical'' MPn methods, whose scaling is typically ≥ N5. The scaling is the quantity of computational resources, in terms of time and memory, as a function of the irreducible number of atoms N of the system.
- the localization procedure and the MP2 method itself are not suitable for conducting systems;
- periodic structures have peculiar features, such as translational symmetry, thus their treatment is rather different from that of molecules.
As far as concerns the theoretical background, refer to the publications and to the supporting material to be found in the CRYSCOR webpage; the more significant among them are listed here below:
- CRYSCOR code general presentation:
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).
- Symmetry Adapted Wannier functions:
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).
- MP2 correction to the density matrix:
C. Pisani, S. Casassa and L. Maschio, On the Prospective Use of the One-Electron Density Matrix as a Test of the Quality of Post-Hartree-Fock Schemes for Crystals, Z. Phys. Chem., 220, 913 (2006)
D. Usvyat and M. Schütz, Orbital-unrelaxed Lagrangian density matrices for periodic systems at the local MP2 level, J. Phys.: Conf. Ser., Honorary issue Pisani, 117, 012027 (2008).
2. Running CRYSCORAs just said, CRYSCOR can be considered the post-HF option of the CRYSTAL program, since all the information at the HF level is provided by CRYSTAL. Therefore, to execute a CRYSCOR job, you first have to run a CRYSTAL calculation.
Actually, the CRYSTAL calculations to be run are two:
- The first one (crystal executable) performs a wave function calculation. Geometry and symmetry information, Fock and density matrix, canonical eigenvalues and eigenvectors are stored on fortran unit fort.9.
- The second one (properties executable)
calculates on request a number of quantities of interest.
By means of the
LOCALIkeyword, localized Wannier functions (WF) are calculated from the subset of occupied (delocalized) crystalline orbitals and symmetrized (keyword
SYMMWF). The related information is stored on fortran unit fort.80.
For the use of CRYSTAL please refer to the related Tutorials on the CRYSTAL website;
here only the script usage is reported along with the CRYSCOR one.
The crystal and properties executables are to be run according to the following syntax (input file names to be used without extension):
runprop09 crystal_input_file crystal_f9_unitThe script for running CRYSCOR calculations is runcryscor09; it needs 3 arguments:
- the name of the cryscor input file,
- the name of the fortran file .f9 produced in a preliminary crystal calculation,
- the name of the fortran file .f80 produced in a preliminary properties calculation, all to be given without extension.
runcryscor09 cryscor_input_file crystal_f9_unit properties_f80_unit
The extensions of the input and the output files needed/produced are summarized in table 1.
|executable||input file||output file|
4. General input comments
a. Basic inputThe CRYSCOR input consists of a series of keywords (KW) followed by the respective arguments, to be written in free format. The order of KWs is pratically free.
A minimal CRYSCOR input file looks as follows (table 2):
|KNET||CRYSTAL eigenvalue calculation|
|MEMORY||Memory required (megabytes)|
|DOMDEF||Definition of the virtual space|
|1 2 3|
|PAIR||Definition of the occupied space|
MEMORYare the only mandatory cards to run a CRYSCOR calculation.
- the MP2 technique involves biexcitations of electron pairs from the occupied to the virtual space;
- these spaces are described in terms of localized functions, which are the Wannier functions (WF) for the occupied manifold and the PAOs - Projected Atomic Orbitals - for the virtual one,
PAIRindicates the distance (in Å) between two Wannier functions; if the WF-WF pair distance results within the chosen value, then corresponding product distributions are calculated, otherwise they are neglected.
PAIRkeyword acts then by "reducing'' the occupied space, which is a basic requirement of the local approach.
DOMDEFdefines the number of stars to be included in the domain:
- a star is the set of atoms at the same distance from a reference atom;
let's focus for instance on LiH:
the H- ion in the reference cell represents the first star, its 6 Li+
first neighbours the second star and its 12 second H-- neighbours
the third star (in the whole 3 stars with a total of 19 atoms),
DOMDEF(1) is not the only way of defining WFs' domains; for molecular crystals, the KW
MOLDOMselects all the atoms belonging to a given molecule.
- the domain is the set of PAOs associated to each atom belonging to the selected stars.
These keywords concerning the virtual space act again in the sense of reducing it, which is fundamental to achieve the low-scaling typical of local methods.
TOBJis the tolerance that affects the tails of the localized functions WFs and PAOs. A 10-3 value provides reliable results.
b. When approximations are activated...The computation of bielectronic integrals represents the most expensive part of the calculation, that is why in CRYSCOR are implemented two very efficient approximated techniques for their estimation, namely Density Fitting (DF) and the Multipolar (MP) technique. The two approximations are complementary, since DF is particularly suited for close-by WF-WF pairs, whereas MP can be safely used only for large distances.
- To activate DF the following KWs are to be added in the input:
DFITTINGkeyword is followed by:
- the type of DF activated
DIRECT(see reference M. Schütz, D. Usvyat, M. Lorenz, C. Pisani, L. Maschio, S. Casassa, M. Halo, Density fitting for correlated calculations in periodic systems, Accurate Condensed-Phase Quantum Chemistry, Series: Computation in Chemistry, 27 (2010).)
- the density fitting basis set (type of basis Valence-Triple-Zeta in this case).
- the type of DF activated
- To activate MP you have to add to the input the keyword
MULTIPO, followed by the multipoles order value, which is usually 4. The multipolar computation is activated automatically for distant pairs, that is, referring to the just showed input file, for pairs between 6 and 10 Å, and it is here always explicitly inserted for didactic purposes.
4. Exercises proposed
In the following exercises are proposed on different types of systems, i.e. LiH as a representative of ionic crystals, H2O polymer to check the relation molecular-periodic, NH3 as a representative of molecular crystals, and Argon adsorbed on MgO to show the treatment of adsorption phenomena. The different tutorial sections can be chosen from the menu on the left at the top of this page.
LiH and NH3 tutorial sessions are specially designed to teach the user to prepare the input and read the CRYSCOR output.
Furthermore, in NH3 are proposed:
- an extensive analysis of the localized and symmetrized Wannier functions as provided by CRYSTAL and
- exercises on the MP2 correction to the HF one-electron density matrix.