Theory- Si an exploration of what is a bond via charge density. Electron poor materials research group Group meeting Nov 11, 2010 Theory- Si an exploration of what is a bond via charge density. volume of

Procedure Static Calculations of the 4 FCC structures were computed from accurate relaxation (see previous weeks precentation) Calculations were done on a Gamma 11X11X11 grid USED NG(X,Y,Z)F of 6XNG(X,Y,Z) for accurate charge density grid. An extra flag was used in the INCAR file: LAECHG = .TRUE. Turns on All Electron CHGCAR file outputs and outputs 3 files AECCAR0: core charge density AECCAR1: atomic AE charge density (overlapping atomic charge density) AECCAR2: AE charge density The files AECCAR0 and AECCAR2 are added together for bader analysis per instructions: http://theory.cm.utexas.edu/bader/vasp.php chgsum.sh AECCAR0 AECCAR2, chsum is a shellscript Outputs CHGCAR_sum Bader analysis is done on the vasp CHGCAR from the static run bader.x -p atom_index -p bader_index CHGCAR -ref CHGCAR_sum atom_index: Write the atomic volume index to a charge density file bader_index: Write the Bader volume index to a charge density file

Si - Atom location and charge Bader analysis ACF.dat : # X Y Z CHARGE MIN DIST ATOMIC VOL -------------------------------------------------------------------------------- 1 0.0000 0.0000 0.0000 3.9681 1.1316 20.2891 2 1.3672 1.3672 1.3672 4.0319 1.1051 20.6007 VACUUM CHARGE: 0.0000 VACUUM VOLUME: 0.0000 NUMBER OF ELECTRONS: 8.0000 Bader charge shift = 0.0319

Si atomic bounding box according to Bader

Charge density Isosurfaces High charge density of valence electrons. 0.24 electrons/Å3 (I think :P) Vesta claims 0.08 volume of cubic cell is 40.8898 angs^3 8 valence electrons in cell. 8/40.8898 = 0.1956

Subtracted Charge density Calculate charge density of crystal. CHGCAR Now calculate the charge density of each of the atoms within the crystal individually using the same lattice constants and same input parameters. Subtract the charge density of individual (CHGCAR-1, CHGCAR-2 …) atoms from the charge density of the crystal. Giving a resultant charge denstiy ρf.

Subtracted charge density. ρf > 0 Here the isosurface lies in line directly between bonded Si Atoms

Subtracted charge density. ρf < 0 Here the isosurface lies in a line with the Si-Si bonds but on the opposite side of the nearest bonding atom.

Subtracted charge density. ρf > 0 is yellow, ρf < 0 is blue

Subtracted charge density. Slice of charge density.

Subtracted charge density. Slices of charge density.