# [molpro-user] dipole-quadrupole molecular polarizability tensors

Elking, Denny (NIH/NIEHS) [G] ElkingD at niehs.nih.gov
Tue Jan 4 19:26:40 GMT 2011

Dear Molpro Users/Developers Community,

My question involves calculating dipole-dipole, dipole-quadrupole, quadrupole-quadrupole (and possibly higher order) molecular polarizability tensors.
As an example, I want to calculate the HF/6-31G* polarizability tensors for water in a Cartesian basis set with its geometry given at the end.

1) I can get the dipole-dipole polarizability tensor for water using the "polarizability,DM" keyword
DMX             DMY             DMZ
DMX               3.800512        0.953377        0.000000
DMY               0.953377        3.677339        0.000000
DMZ               0.000000        0.000000        6.630503
This result agrees with Cadpac.
X                         Y                         Z
X         3.80051678        0.95338204        0.00000000
Y         0.95338204        3.67734383        0.00000000
Z         0.00000000        0.00000000        6.63050501

2) I can also get the quadrupole-quadrupole polarizability tensor using the "polarizability,SM" keyword
XX                       YY                 ZZ                   XY                  XZ             YZ
XX                6.272522       2.751293        4.254370       0.548811        0.000000  0.000000
YY                2.751293        6.138914        3.993306        0.485337        0.000000 0.000000
ZZ               4.254371        3.993308      15.545155        2.020682       0.000000 0.000000
XY                0.548811        0.485337        2.020682        2.216464        0.000000 0.000000
XZ                0.000000        0.000000        0.000000        0.000000        4.512145 2.372242
YZ                0.000000        0.000000        0.000000        0.000000        2.372242  4.205661
I realize this is not in traceless Cartesian form, but that's ok.  It can be converted to the traceless Buckingham convention later.
For reference, Cadpac gives the traceless quadrupole-quadrupole polarizability tensor as
XX                    YY            ZZ                XY                 XZ          YZ
XX     2.228177   -0.314077   -1.914100   -0.352099    0.000000    0.000000
YY   -0.314077    2.325307   -2.011230   -0.399705    0.000000    0.000000
ZZ   -1.914100   -2.011230    3.925330    0.751804    0.000000    0.000000
XY   -0.352099   -0.399705    0.751804    1.662349    0.000000    0.000000
XZ    0.000000    0.000000    0.000000    0.000000    3.384112    1.779185
YZ    0.000000    0.000000    0.000000    0.000000    1.779185    3.154249

3) However, if I try to calculate the dipole-quadrupole polarizability tensor using the "polarizability,DM,SM" keyword, I get something which is not correct.
DMX              DMY               DMZ              XY                     XZ                YZ
DMX               3.800512        0.953377        0.000000        0.000000        0.000000        0.000000        0.000000        0.000000        0.000000
DMY               0.953377        3.677339        0.000000        0.000000        0.000000        0.000000        0.000000        0.000000        0.000000
DMZ               0.000000        0.000000        6.630503        0.000000        0.000000        0.000000        0.000000        0.000000        0.000000
XX                       YY               ZZ                 XY                      XZ           YZ                XX
XX                3.800512        0.953377        0.000000        0.000000        0.000000   0.000000        0.000000        0.000000        0.000000
YY                0.953377        3.677339        0.000000        0.000000        0.000000   0.000000        0.000000        0.000000        0.000000
ZZ                0.000000        0.000000        6.630503        0.000000        0.000000   0.000000        0.000000        0.000000        0.000000
XY                0.000000        0.000000        0.000000        6.272522        2.751293   4.254370        0.548811        0.000000        0.000000
XZ                0.000000        0.000000        0.000000        2.751293        6.138914   3.993306        0.485337        0.000000        0.000000
YZ                0.000000        0.000000        0.000000        4.254371        3.993308  15.545155        2.020682        0.000000        0.000000
It appears the order of the the tensor components is mixed up in the output file and/or some components may be missing, i.e. all the dipole-quadrupole components are 0.0.
For comparison, the dipole-quadrupole polarizability from Cadpac is
XX                    YY            ZZ                XY                 XZ          YZ
X     1.222188    1.345750   -2.567938   -1.061641    0.000000    0.000000
Y     1.132216    1.275191   -2.407407   -0.994397    0.000000    0.000000
Z    0.000000    0.000000    0.000000    0.000000   -4.803013   -4.502759

The keyword "polarizability,DM,SM" may be the wrong syntax for calculating the dipole-quadrupole tensors.  On the other hand, if "polarizability,DM,SM"  is the correct, syntax, then
I suspect Molpro calculates the polarizability tensors correctly, but there seems to be a problem in how the values get printed out.

Any help or suggestions is greatly appreciated.  Many thanks in advance.

Best regards,
Dennis Elking

***, water cartesian coordinates (XYZ format)
memory,1,m
basis=6-31G*
CARTESIAN
geomtyp=xyz
geometry={
3
WATER CARTESIAN COORDINATES
O   0.04575896   0.04289840   0.00000000
H  -0.36311204  -0.34041260   0.75865000
H  -0.36311204  -0.34041260  -0.75865000
}

hf
polarizability,DM

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