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

[Amit Sharma]

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


     QUAD_POL_XX    QUAD_POL_ZZ      QUAD_POL_XZ

    -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.


Thanks in advance

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

! not sure about this

! 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

! QUAD,xxfield,yyfield,zzfield,xyfield,xzfield,yzfield;

! XX field

QUAD,0,0,0,0,0,0; hf; e_0=energy

QUAD,0.005,0,0,0,0,0; hf;  e_r=energy

QUAD,-0.005,0,0,0,0,0; hf;  e_l=energy

! XX quandrupole polarizability using finite diff

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


! ZZ

QUAD,0,0,0,0,0,0; hf; e_0=energy

QUAD,0,0,0.005,0,0,0; hf;  e_r=energy

QUAD,0.0,0,-0.005,0,0,0; hf;  e_l=energy

! quandrupole polarizability

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

table, quad_pol_xx, pol_xx

table, quad_pol_zz, pol_zz


! cross term xx_zz

symmetry,nosym

QUAD,0,0,0,0,0,0; hf; e_0=energy

QUAD,0,0,0,0,0.005,0; hf;  e_r=energy

QUAD,0.0,0,0,0,-0.005,0; hf;  e_l=energy

! quandrupole polarizability

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

table, quad_pol_xz

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