Pseudo potential exercises

Transcription

1 Pseudo potential exercises Johan M. Carlsson Fritz-Haber-Institut der Max-Planck-Gesellschaft D Berlin Introduction Castep contains an "on the fly" OTF-pseudo potential generator that can be used to give a pseudo potential for the individual run, but it can also be used as a pseudo potential generator such that you can save and use the pseudo potential also in later calculations. The on the fly generator is invoked by replacing the link to the pseudo potential file in the %Block Species_pot by a pseudo potential string. C A r_loc r_cut_wf r_inner E1 E2 E3 P1:P2:P3(qc=6)[] A=angular momentum channel that is going to be used for the local potential. r_local=cut-off radius for the local potential. r_cut_wf=cut-off radius for the wave functions that determine the range of the beta projectors. r_inner=the cut-off radius for the pseudoization of the augmentation charge. E1,E2 and E3 are the recommendations for the cut-off energy in Hartree units. P1,P2... are the definitions for the Beta projectors in terms of n and l quantum numbers. An example for Carbon: C :21(qc=3)[] Exercises 1. Generate a pseudo potential for Carbon using the OTF. Create a cell file for Diamond and enter the pseudo potential string in the BLOCK SPECIES_POT: %BLOCK LATTICE_CART! In Angstroms %ENDBLOCK LATTICE_CART %BLOCK POSITIONS_FRAC C C %ENDBLOCK POSITIONS_FRAC Kpoints_MP_grid SYMMETRY_GENERATE C :21(qc=3)[]

2 And a parameters file: # Inputfile for Castep # What is to be done? task : singlepoint # Calculation parameters xc_functional : PBE cut_off_energy : 350 Run the Diamond calculation. The Castep file is going to contain a pseudo potential documentation: Pseudopotential Report - Date of generation Element: C Ionic charge: 4.00 Level of theory: PBE Reference Electronic Structure Orbital Occupation Energy 2s p Pseudopotential Definition Beta l e Rc scheme norm qc qc qc qc 0 loc pn 0 Augmentation charge Rinner = Partial core correction Rc = " :21(qc=3)[]" <- Here is the pseudo potential documentation string. Author: Chris J. Pickard, Cambridge University Doing a self consistent calculation for the test configuration Atomic calculation performed for C: 1s2 2s2 2p2 Converged in 54 iterations to an ae energy of ev AE eigenvalue nl 10 = AE eigenvalue nl 20 = AE eigenvalue nl 21 = PS eigenvalue nl 20 = PS eigenvalue nl 21 =

3 2. Check the wave functions and pseudo potential with xmgrace. The OTF generator generates three analysis files that you can visualize with xmgrace: C_OTF.pwave The all-electron and pseudo wave functions.

4 C_OTF.beta. The Beta-projector functions and the local potential V loc (in this case the local potential is located in the d channel). C_OTF.econv. The estimate of convergence with respect to the plane wave cut-off for the generated pseudo potential.

5 3. Do a convergence test with Castep for your pseudo potential Save your pseudo potential. Make a copy of the Diamond cell file and exchange the pseudo potential string to the name of the generated pseudo potential. C C_OTF.usp Does the convergence test give the same result as the estimate from the OTF-generator? 4. Calculate the Murnaghan equation of state for diamond. The Murnaghan equation of state gives the relationship between the Cohesive energy E(V) and volume V, the bulk modulus B and the first derivative of the bulk modulus B. E(V ) = E 0 + B 0 V B (1 V 0 B ( B 1) V ) 1+ V 0 V Determine the equation of state for diamond: Generate a number of cell files where the lattice parameter vary by 0.1 A. Calculate the total energy and make a curve fit to the Murnaghan equation of state. Some reference values from the literature are: Lattice parameter Cohesive Energy Bulk Modulus All-electron* 3.57 Å 433 GPa Experiment Å 7.37 ev/atom 442 GPa B *Kunc et al., Hi. Pres. Res. 24, 101 (2004). +C. Kittel, Introduction to Solid State Physics. Is the curve looking smooth? Does is agree with experiments? Why not?

6 5. Compare the test pseudo potential to the default OTF pseudo potential for Carbon. Return to your Diamond cell and remove the completely. Running Castep without any pseudo potential definition activates the default OTF pseudo potential for Carbon. Pseudopotential Report - Date of generation Element: C Ionic charge: 4.00 Level of theory: PBE Reference Electronic Structure Orbital Occupation Energy 2s p Pseudopotential Definition Beta l e Rc scheme norm qc qc qc qc 0 loc pn 0 Augmentation charge Rinner = Partial core correction Rc = " :21(qc=6)#[]" Author: Chris J. Pickard, Cambridge University Compare this pseudo potential settings to the first test settings. Have a look at the three analysis files. Do they look the same? Which one looks better? 6. Try to optimize the pseudo potential. Return to your Diamond cell with the OTF string. By changing the numbers in the string you can change the pseudo potential. Try to vary the parameters one at a time, run Castep to generate the OTF analysis plots and check the effects of the: a) Wave functions: Find a cut-off radius for the wave functions. What is the bond length in diamond? b) Local potential: Select the appropriate angular momentum channel for the local potential and find a cutoff radius for the local potential. Which is the electronic configuration of carbon? c) Is core correction necessary? Where should I set the radius for the core correction. d) Smooth out the potential: Select the qc-optimization Experiment with qc to see how the predicted cut-off energy varies. 7. Do a Convergence test for your new pseudo potential. 8. Do the Murnaghan calculations for diamond using your new pseudo potential. Has it improved the values for lattice parameter, cohesive energy and bulk modulus?