Dear all, We have done some calculations using the option:
WriteMullikenPop 3 I would like to know what is precisely the meaning of the off-diagonal terms that are printed in the output (see example with relevant input and output below). I understand that the diagonal terms give the Mulliken charges on the atoms from the diagonal terms of the rho*S, where rho = density matrix and S is the overlap of basis orbitals. If that is not correct, I would appreciate if somebody could enlighten me. But how about the off-diagonal? I considered the possibility that they would give the off-diagonal terms of the rho(k)*S(k) matrix, i.e., in the basis of Bloch sums, but they are not printed per k-point, so this does not seem right. To put it another way, since atom i and j can be neighbors more than once, considering the periodic images, what would the off-diagonal terms in the matrix below represent? Thanks a lot in advance for any help on this. Ricardo Nunes Departamento de Fisica - UFMG ================ Input: ================ WriteMullikenPop 3 # Species and atoms NumberOfSpecies 1 NumberOfAtoms 2 %block ChemicalSpeciesLabel 1 79 Au %endblock ChemicalSpeciesLabel LatticeConstant 2.673694 Ang %block LatticeVectors 9.350359 0.000000 0.000000 0.000000 9.350359 0.000000 0.000000 0.000000 1.000000 %endblock LatticeVectors # Atomic coordinates AtomicCoordinatesFormat Ang %block AtomicCoordinatesAndAtomicSpecies 0.04618072 0.04352611 -0.00000014 1 Au 1 0.04608645 2.47934396 1.33684744 1 Au 2 %endblock AtomicCoordinatesAndAtomicSpecies ================ Output: ================ mulliken: Overlap Populations between Atoms 1 2 1 10.488 0.100 2 0.100 10.489 mulliken: Overlap Populations between Orbitals 1 2 3 4 5 6 7 8 6s 6s 5dxy 5dyz 5dz2 5dxz 5dx2-y2 5dxy 1 6s 0.780 -0.018 0.000 0.000 0.000 0.000 0.000 0.000 2 6s -0.018 0.138 0.000 0.000 0.000 0.000 0.000 0.000 3 5dxy 0.000 0.000 1.954 0.000 0.000 0.000 0.000 0.008 4 5dyz 0.000 0.000 0.000 1.853 0.000 0.000 0.000 0.000 5 5dz2 0.000 0.000 0.000 0.000 1.795 0.000 0.000 0.000 6 5dxz 0.000 0.000 0.000 0.000 0.000 1.923 0.000 0.000 7 5dx2-y2 0.000 0.000 0.000 0.000 0.000 0.000 1.898 0.000 8 5dxy 0.000 0.000 0.008 0.000 0.000 0.000 0.000 0.003 9 5dyz 0.000 0.000 0.000 0.014 0.000 0.000 0.000 0.000 10 5dz2 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 11 5dxz 0.000 0.000 0.000 0.000 0.000 0.010 0.000 0.000 12 5dx2-y2 0.000 0.000 0.000 0.000 0.000 0.000 0.014 0.000 13 6Ppy 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 14 6Ppz 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 15 6Ppx 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 16 6s -0.024 0.012 0.000 0.003 0.000 0.000 0.000 0.000 17 6s 0.012 0.008 0.000 0.003 0.000 0.000 0.004 0.000 18 5dxy 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 19 5dyz 0.003 0.003 0.000 -0.002 -0.001 0.000 -0.002 0.000 20 5dz2 0.000 0.000 0.000 -0.001 -0.001 0.000 0.000 0.000 21 5dxz 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 22 5dx2-y2 0.000 0.004 0.000 -0.002 0.000 0.000 0.000 0.000 23 5dxy 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 24 5dyz 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 25 5dz2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 26 5dxz 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 27 5dx2-y2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 28 6Ppy 0.007 0.005 0.000 0.008 0.000 0.000 0.003 0.000 29 6Ppz 0.005 0.002 0.000 0.000 0.002 0.000 0.004 0.000 30 6Ppx 0.000 0.000 0.005 0.000 0.000 0.001 0.000 0.000