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The meaning of overlap matrix position/momentum operator
Date: 2024/04/11 18:16
Name: Liang Liu   <liangliu@mail.sdu.edu.cn>

Hello! I have obtained the outputs from analysis_example and *.scfout from the calculations on H2 molecular. Each hydrogen has one s-PAO. I'm puzzled by the following sections:

Overlap matrix with position operator x
global index=1  local index=0 (global=1, Rn=0 [0 0 0])
-1.580512401E-06
global index=1  local index=1 (global=2, Rn=0 [0 0 0])
  5.181934010E-01
global index=2  local index=0 (global=2, Rn=0 [0 0 0])
  1.580512401E-06
global index=2  local index=1 (global=1, Rn=0 [0 0 0])
-5.181934010E-01

I guess "Overlap matrix with position operator x" is: <s1| x |s2>, where s1, s2 are the s-PAOs, and the diagonal element should correspond to the atom coordinate. However, the diagonals from outputs = +/-1.58E-06 are not like any type of coordinate since the bond length of H2 is 0.74 angstrom and the molecular is placed in a box with size of 10 angstrom.
Am I missing somethings?

On the other hand, the "Overlap matrix with momentum operator px" also bothers me:

Overlap matrix with momentum operator px
global index=1  local index=0 (global=1, Rn=0 [0 0 0])
  9.051099278E-06
global index=1  local index=1 (global=2, Rn=0 [0 0 0])
-2.891951944E-01
global index=2  local index=0 (global=2, Rn=0 [0 0 0])
-9.051099278E-06
global index=2  local index=1 (global=1, Rn=0 [0 0 0])
  2.891951944E-01

It shows that the diagonals of <s1| px |s2> are not zero but how can the localized PAOs display finite expectations of momentum. Or all of my thinking are wrong?
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