# [molpro-user] finite field polarizability off-diagonal terms

Amit Sharma greifsw at gmail.com
Sat Apr 9 14:28:46 CEST 2016

```Hi all,
I would like to obtain polarizability for open-shell systems but first I am
testing the finite field approach with DIP and QUAD field and comparing the
results obtained with "polarizability" command.  Testing for closed-shell
Ar-He system  (input at the end)
Dipole-polarizability obtained is:

-4.22965863 - by taking derivative of dipole

-4.22965857 - by 2nd order derivative of energy

DMX             DMY             DMZ

DMX        4.200905        0.000000        0.000000

DMY        0.000000        4.200905        0.000000

DMZ        0.000000        0.000000        4.229658

-23.93578551   -65.64281257      -38.73100109

QMXX            QMYY            QMZZ            QMXZ
QMYZ           QMXY

QMXX             23.935795        8.885450      -32.821244
0.000000        0.000000         0.000000

QMYY              8.885450       23.935795      -32.821244
0.000000        0.000000         0.000000

QMZZ            -32.821244      -32.821244       65.642488
0.000000        0.000000         0.000000

QMXZ              0.000000        0.000000        0.000000
38.732249        0.000000         0.000000

QMYZ              0.000000        0.000000        0.000000
0.000000       38.732249         0.000000

QMXY              0.000000        0.000000        0.000000
0.000000        0.000000         7.525173

Up to this point it all seems good except for the sign (which I know how to
correct).

My question is about obtaining terms line  DMX-QMXX or DMX-QMXY type terms
using finite difference and also how to obtain hyperpolarizability using
finite difference, obtaining terms like  z,zz. I tried this but not sure if
its right.

!First dipole hyperpolarizability

! z,zz ???

! third derivative of energy

dip,0.0,0.0,0.005; hf;  e_r = energy

dip,0.0,0.0,-0.005; hf;  e_l = energy

dip,0.0,0.0,2*0.005; hf;  e_2r = energy

dip,0.0,0.0,-2*0.005; hf;  e_2l = energy

hyperpol = (e_2r-2*e_r+2*e_l-e_2l)/(2*0.005*0.005*0.005)

text, Hyperpolarizability

table, hyperpol

2nd-question: how do we obtain DMX-QMXY type terms. which field should be
applied and what is the finite difference expression for this.

Amit

-- complete input here.

***,Trial calculation for Ar + He long range potential

geometry={angstrom

Ar

He 1 R

}

! some distance

R=3.67473242

basis=vdz

hf

polarizability,dm

!! this does not work

pol_xx = POLXX

pol_zz = POLZZ

! save dipole moment in AU and Debye

dip_mom_z=dmz

dip_mom_z_debye=dip_mom_z*2.541765

! test finite field approach

dip,0.0,0.0,0.0;   hf;  e_0 = energy  ! e_center

dipz_0=dmz

dip,0.0,0.0,0.005;  hf;  e_r = energy ! e_right

dipz_r=dmz

dip,0.0,0.0,-0.005; hf;  e_l = energy ! e_left

dipz_l=dmz

! dipole moment along z as finite difference

d_zz = (e_r - e_l)/(2*0.005)

d_zz_debye = d_zz*2.541765

! dipole polaribzability as finite difference of dipole

dip_pol_zz = (dipz_r - dipz_l)/(2*0.005)

! dipole polarizability as 2nd order derivative of energy

pol = (e_r+e_l-2.0*e_0)/(0.005*0.005)

table, dip_mom_z, d_zz, dip_pol_zz

table, dip_mom_z_debye, d_zz_debye

table, pol

!First dipole hyperpolarizability

! z,zz ???

! third derivative of energy

dip,0.0,0.0,0.005; hf;  e_r = energy

dip,0.0,0.0,-0.005; hf;  e_l = energy

dip,0.0,0.0,2*0.005; hf;  e_2r = energy

dip,0.0,0.0,-2*0.005; hf;  e_2l = energy

hyperpol = (e_2r-2*e_r+2*e_l-e_2l)/(2*0.005*0.005*0.005)

text, Hyperpolarizability

table, hyperpol

!!! apply quandrupole field

! XX field

! XX quandrupole polarizability using finite diff

! ZZ

! quandrupole polarizability

! cross term xx_zz

symmetry,nosym

! quandrupole polarizability