# [molpro-user] one question about calculating polarizability

Tatiana Korona tania at tiger.chem.uw.edu.pl
Wed Sep 5 09:30:32 BST 2012

```Hi,

A dipole polarizability is defined as minus one times polarization propagator,
i.e.

alpha_yy= - << Y;Y>>

This minus in included in the example you cited (see the second part of the
denominator: field(3)=-0.005):

dpolz(m)=(e(k+n)+e(k+2*n)-2*e(k))/((field(2)-field(1))*(field(3)-field(1)))
/ 0.005              * (-0.005)

Best wishes,

Tatiana

On Tue, 4 Sep 2012, CC XX wrote:

> Dear Ms/Mr,
>         Now, I am obsessed by one question, can you help me solve the
> problem? Thank you very much!
>         It is about calculating the polarizability of one molecule by
> differential method. Based on a case (H2O molecule) in Molpro manual, the
> input file is displayed as following:
> "
>
> ***,H2O finite field calculations
>
> r=1.85,theta=104                   !set geometry parameters
> geometry={O;                       !z-matrix input
>          H1,O,r;
>          H2,O,r,H1,theta}
> basis=avtz                         !define default basis
> field=[0,0.005,-0.005]             !define finite field strengths
> \$method=[hf,mp4,ccsd(t),casscf,mrci]
>
> k=0
> do i=1,#field                      !loop over fields
>  dip,,,field(i)                   !add finite field to H
>  do m=1,#method                   !loop over methods
>    k=k+1
>    \$method(m)                     !calculate energy
>    e(k)=energy                    !save energy  enddo
> enddo
>
> k=0
> n=#method
> do m=1,#method
>  k=k+1
>  energ(m)=e(k)
>  dipmz(m)=(e(k+n)-e(k+2*n))/(field(2)-field(3))   !dipole moment as
> first energy derivative
>  dpolz(m)=(e(k+n)+e(k+2*n)-2*e(k))/((field(2)-field(1))*(field(3)-field(1)))
> !polarizability as second der.enddo
>
> table,method,energ,dipmz,dpolz
> title,results for H2O, r=\$R, theta=\$theta, basis=\$basis
> ---
>
> "
>
> The result is as following:
> "
> METHOD        ENERG        DIPMZ        DPOLZ
> HF        -76.05828804   0.79028512   8.66914177
> MP4       -76.34319951   0.72435361   9.84241227
> CCSD(T)   -76.34178065   0.72957181   9.67032932
> CASSCF    -76.11356760   0.72500885   8.89662369
> MRCI      -76.32839170   0.70823783   9.20622885
> "
> As showing above, the value of polarizability in z direction is positive.
> But when I calculate the z direction component of the polarizability by
> adding a finite electronic field in z direction, and then compute the
> derivative of dipole with respect to the field, the value of this
> derivative is found be negative but have the same magnitude by and large.
> The input file of normal calculation is:
> "
> ***,H2O finite field calculations
> r=1.85,theta=104               !-->set geometry parameters
> geometry={O;                   !-->z-matrix input
> H1,O,r;
> H2,O,r,H1,theta}
> basis=avtz                     !-->define default basis
> {hf}
> {mrci;dm;
> natorb,2140.2}
> "
> The result is:
> "
> !RHF STATE 1.1 Dipole moment           0.00000000     0.00000000
> 0.79032209
> !CI(SD) STATE 1.1 Dipole moment        0.00000000     0.00000000
> 0.74610325
> "
> Add the field (0.001):
> "
> ***,H2O finite field calculations
> r=1.85,theta=104                   !-->set geometry parameters
> geometry={O;                       !-->z-matrix input
> H1,O,r;
> H2,O,r,H1,theta}
> basis=avtz                         !-->define default basis
> field=0.001                        !-->define finite field strengths
> dip,,,field
> {hf}
> {mrci;dm;
> natorb,2140.2
> "
> The result is:
> "
> !RHF STATE 1.1 Dipole moment           0.00000000 0.00000000 0.78165042
> !CI(SD) STATE 1.1 Dipole moment        0.00000000 0.00000000 0.73678704
>
> "
> So, for the HF method, polzz=(0.78165042-0.79032209)/0.001=-8.67167
> and, for the CD(SD),    polzz=(0.73678704-0.74610325)/0.001=-9.31621
> Actually, this derivative is also the value of polarizability [I also found
> this definition in some references pol_zz=d(dip_z)/d(E_z) ]. So why the
> result of this method is negative? Or there're some details in Molpro
> calculations which I neglected? Thanks a lot!
>
> Best regards,
> Changjian
>

Dr. Tatiana Korona http://tiger.chem.uw.edu.pl/staff/tania/index.html
Quantum Chemistry Laboratory
University of Warsaw
Pasteura 1, PL-02-093 Warsaw, POLAND

`The man who makes no mistakes does not usually make anything.'
Edward John Phelps (1822-1900)

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