Question about output of the full dipole moment matrix

[lyzhao]

Dear all,
Based on the manual p.60 (section 4.8.3 *DIPOLEMOMENTMATRIX),
the u_ii denotes the permanent dipole moment for the i'th excited state, that is, <i|u|i>
However, the source code or comments of output shows that
u_ii comes from the transition dipole moments between state X and Y : <X | A - <A> | Y>,
when X=Y, <X | A - <A> | Y> = <X|A|Y> - <X|Y><A> = <X|A|Y> - Detla_XY *<G|A|G> = <X|A|X> - <G|A|G>, G means ground state
that is, u_ii seems to be the difference between the dipole moments of excited state X and gound state G.
So, I want to make sure what the u_ii means.

Any help will be appreciated.
Best regards.
Lan

[nhl]

Dear Lan,

The u_ii is the difference between the expectation values of the position operator of the excited state and the ground state (the minus in the dipole operator is not included). I.e.

- u_ii = <X|A|X> - <G|A|G>, where A is the dipole operator.

To compute the dipole moment of the excited states, you therefore also need the ground state dipole moment from a .RUN PROPERTIES calculation. (Alternatively, if you use .RUN RESPONSE, only the electronic part of the dipole moment to the ground state will be computed and you will need to add the nuclear contribution by hand).

Best regards,
Nanna

[lyzhao]

Dear Nanna,
Thanks for your reply. I am sorry for not enough information in the orginal post.
I am now using LSDalton 2015 which can provide the full dipole moment matrix.
As an example, in the following output of H2O molecule with the first four excited states:
full output please see attachment

Code: Select all

DipoleMomentMatrix: Transition moments between the groundstate and the excited states
   STATE  Freq(au)  Freq(eV)         X           Y           Z
    1    0.290634    7.908566  -0.0000000  -0.0000000  -0.1601016
    2    0.362426    9.862112  -0.3135477  -0.4436653  -0.0000000
    3    0.371324   10.104248   0.0000000   0.0000000  -0.0000023
    4    0.457017   12.436052   0.4411302  -0.3117509  -0.0000000
 
The transition dipole moments between state X and Y for operator XDIPLEN: <X | A - <A> | Y>
               Column   1     Column   2     Column   3     Column   4
       1      -0.50302310    -0.00000000    -1.15779947     0.00000000
       2      -0.00000000    -0.55086143     0.00000000     1.13501285
       3      -1.15779947     0.00000000    -0.42914374    -0.00000000
       4       0.00000000     1.13501285    -0.00000000    -0.51353763
 
The transition dipole moments between state X and Y for operator YDIPLEN: <X | A - <A> | Y>
 ....................... 
The transition dipole moments between state X and Y for operator ZDIPLEN: <X | A - <A> | Y>
  ...................... 
The Full Dipole Moment Matrix
 
Column 0 indicate the Ground State. Element (0,0) is therefore the ground state dipole moment
Elements (0,X) is therefore the transition state dipole moment of the X. excited state
Elements (X,Y) is the transition dipole moment between state X and Y
Dipole Moment Matrix for X coordinate
 
               Column   0 |   Column   1     Column   2     Column   3
       0       0.49700610 |  -0.00000000    -0.31354766     0.00000000
       ---------------------------------------------------------------
       1      -0.00000000 |  -0.50302310    -0.00000000    -1.15779947
       2      -0.31354766 |  -0.00000000    -0.55086143     0.00000000
       3       0.00000000 |  -1.15779947     0.00000000    -0.42914374
       4       0.44113018 |   0.00000000     1.13501285    -0.00000000
 
               Column   4
       0       0.44113018
       ------------------
       1       0.00000000
       2       1.13501285
       3      -0.00000000
       4      -0.51353763
 
Dipole Moment Matrix for Y coordinate
  .............
Dipole Moment Matrix for Z coordinate
 .................. 

HERE, I want to know what diagonal elements (X,X) X!=0 is in this Full Dipole Moment Matrix.
Are they the dipole moments of excited states or the differences between dipole moments i.e., <X|A|X> - <G|A|G>, as shown in the preceding output
for example: (1,1)_x =-0.50302310 in the full dipole moment matrix
and in the preceding output
The transition dipole moments between state X and Y for operator XDIPLEN: <X | A - <A> | Y>
Column 1 Column 2 Column 3 Column 4
1 -0.50302310 -0.00000000 -1.15779947 0.00000000
2 -0.00000000 -0.55086143 0.00000000 1.13501285

Best regards.
Lan

[tkjaer]

They are the differences between dipole moments i.e., <X|A|X> - <G|A|G>, as shown in the preceding output

The only thing I did was collecting these informations. Naturally I could have subtracted the groundstate dipole moment but I did not. I did not think about it. Would you prefer if I change this?

TK

[lyzhao]

Dear tkjaer,
Thanks for your reply.

Would you prefer if I change this?

I can deal with it if I know its meaning.
I recommend to add a line comment: (X,X) X!=0, denotes <X|A|X> - <G|A|G>
in the following comments for the full dipole moment matrix

Code: Select all

Column 0 indicate the Ground State. Element (0,0) is therefore the ground state dipole moment
Elements (0,X) is therefore the transition state dipole moment of the X. excited state
Elements (X,Y) is the transition dipole moment between state X and Y

Because the Element (0,0) would be zero, if all the diagonal elements are understood to be <X|A|X> - <G|A|G>

Best regards.
Lan

[tkjaer]

Comment have been added, and will be included in the next tarball/patch

[tlovell]

I would like to clarify how to read the output of the full dipole moment matrix. I would like to know the change in permanent dipole moment between my ground and 1st excited state and ground and 2nd excited state (ie ∣Δµ01∣ and ∣Δµ02∣). To find this, do I figure out the square root of the sum of squares of my X, Y, and Z component for [1,1] in the transition dipole moment matrices (which would be µ11). Then the absolute value of µ11 minus the permanent dipole moment for the ground state (which is already given) would be the ∣Δµ01∣ I’m looking for? I’ve attached my output file and spread sheet to see if I’m doing things correctly.

Thank you!