[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
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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