• Hamiltonian: Hartree-Fock, DFT
• Type of run
• Integrals file handling
• Coulomb and exchange infinite sums control.

The third input  section allows choice of Hamiltonian, of  truncation criteria of Coulomb and exchange infinite sums, and of the type of run. Default values are supplied  to guarantee reasonable accuracy for a large number of different crystalline systems.
All the choices of the third input block are optional. The END keyword must be inserted in the input stream to close the section.

Default values:

Hamiltonian - Hartree-Fock Theory (HF) methods

Within the HF theory two different theoretical methods are available in CRYSTAL:

Hartree-Fock Restricted Closed Shell is the default choice. When the choice is Unrestricted Open Shell, the initial guess for SCF must define the number of alpha and beta electrons. See input block 4, SCF, keyword SPINLOCK.

Hamiltonian - Density Functional Theory  (DFT) methods

The keyword DFT  selects a DFT Hamiltonian. Exchange-correlation functionals are separated in an exchange component  (keyword EXCHANGE) and a correlation component (keyword CORRELAT). If the correlation functional is not set, an exchange-only functional is used in the hamiltonian. If the exchange functional is not set, the Hartree-Fock potential is used.

The DFT input block must terminate with the keyword END[DFT].

Within DFT theory, a variety of functionals is defined:

• Local (-density approximation, LDA): functionals  of the electron density only;
• Gradient-corrected (GGA): functionals of the electron density and its gradient;
• Hybrid: the exchange functional is a linear combination of Hartree-Fock, local and gradient-corrected exchange term.

The  following functionals are available in CRYSTAL. See CRYSTAL03 User's Manual for complete documentation.

All functionals are formulated in terms of total density and spin density. Default is total density. To use functionals of spin density insert the keyword SPIN.

It is also possible to incorporate part of the exact Hartree-Fock exchange into the exchange functional through the keyword HYBRID, followed by the % of exact Hartree-Fock exchange. Any mixing (0-100) of exact Hartree-Fock and DFT exchange can be used.

NONLOCAL allows modifying the relative weight of the local and non-local part both in the exchange and the correlation potential, with respect to standard definition of GGA type potentials.

B3LYP and B3PW are global keywords, they define both exchange and correlation functionals.

Warning: In CRYSTAL the Becke's 3 parameter hybrid functionals adopt in their formula the VWN functional 5 (see the VWN original paper), and not the VWN functional 3, as in the most widely diffuse molecular codes.

The input to define a DFT B3LYP Hamiltonian is:

DFT
B3LYP
END

The global keywords correspond to the sequence:

   B3PW	        B3LYP    
   EXCHANGE	EXCHANGE
   BECKE	BECKE
   CORRELAT	CORRELAT
   PWGGA	LYP
   HYBRID	HYBRID
   20		20		% of Hartree-Fock exchange
   NONLOCAL	NONLOCAL
   0.9   0.81	0.9  0.81	weight of non local exchange and correlation

A numerical integration is used to compute the exchange-correlation energy. The exchange-correlation contribution to the Kohn-Sham matrix and to gradients is computed through the same quadrature. 
See CRYSTAL03 User's Manual, keyword DFT, for information on the integration grid and parameters.

Exercise: Re-define the MgO input to perform a DFT calculation with the BECKE-PWGGA/6-21G* theoretical model chemistry.

Type of run

Few possibilities are presented. See CRYSTAL03 User's Manual for complete list. No input data required.

The default choice is traditional SCF, with mono- and two-electron integrals stored on disk and read-in at each SCF iteration.

SCFDIR controls a  full direct SCF calculation, in which mono- and two-electron integrals are recomputed at each SCF cycle. In terms of elapsed  time, the ratio between a traditional SCF and a direct SCF strongly depends on the hardware. Check your installation.

TESTPDIM allows, at zero computational cost, check of the geometry through neighboring analysis.

A TESTRUN is recommended to evaluate the resources to allocate for your run, and decide the type of SCF, traditional or direct.

EIGS  is recommended when there is a suspect of numerical linear dependence, not yet catastrophic.

Integrals files handling

When the problem of integrals storage is not the disk space, but the size of the files, splitting of the integrals in several files is allowed by:

Coulomb and exchange infinite sums control.

Truncation criteria of Coulomb and Exchange infinite sums are based on the overlap between the functions involved into the integrals calculation. The meaning of the different tolerances (T1, T2, T3, T4, T5) is presented in Chapter 6 of CRYSTAL03 User's Manual and in the book:

C. Pisani, R. Dovesi, C. Roetti, "Hartree-Fock ab initio treatment of crystalline systems", 
Lecture Notes in Chemistry, Vol 48, Springer verlag, Heidelberg 1988.

The integral classification and the tecnique of calculation is very sofisticated, thus playing with the default settings of CRYSTAL is delicated and should be reserved to advanced-user only.  To modify the default values insert:

Information relative to Hamiltonian and computational parameters is printed in CRYSTAL output as follows:

****************************************************************************
 N. OF ATOMS PER CELL        2  COULOMB OVERLAP TOL         (T1) 10** -6
 NUMBER OF SHELLS            6  COULOMB PENETRATION TOL     (T2) 10** -6
 NUMBER OF AO               18  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
 ***************************************************************************
 TYPE OF CALCULATION :  RESTRICTED CLOSED SHELL
 HARTREE-FOCK HAMILTONIAN
 ***************************************************************************

Exercise: 

Run MgO, Silicon, Beryllium and Urea  in standard SCF mode and in SCF direct. Check the value of total energy, and compare the CPU and elapsed time. 

Insert the keyword TESTRUN, and run the same cases. Write in a table the size of reducible and irreducible density matrices, and the estimate of the upper bound of the number of integrals.
Repeat the calculation without symmetry (keyword SYMMREMO in geometry input). Compare the results.

 

symmops	number of symmetry operators
elapsed	elapsed time in seconds - machine dedicated
cpu	cpu time in seconds
biel	million of bielectronic integrals stored
mono	million of mono electronic integrals stored
pirr	size (words) of irreducible density matrix
pred	size (words) of reducible density matrix
K points	number of k points in IBZ - Pack-Monkhorst net shrinking factor (IS) 8
Energy	Total energy in hartree

Note the stability of total energy, computed with and without symmetry. 
The elapsed time increasing when symmetry is removed is due to the I/O of integrals during the SCF step.