<div dir="ltr">Hi all,<div>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)</div><div>Dipole-polarizability obtained is:</div><div><br></div><div><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> -4.22965863 - by taking derivative of dipole </p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> -4.22965857 - by 2nd order derivative of energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">       DMX       DMY       DMZ</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> DMX    4.200905    0.000000    0.000000</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> DMY    0.000000    4.200905    0.000000</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">
</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Â DMZÂ Â Â Â 0.000000Â Â Â Â 0.000000Â Â Â Â 4.229658</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Â Â Â QUAD_POL_XXÂ Â QUAD_POL_ZZ Â Â Â QUAD_POL_XZ</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Â Â -23.93578551 Â -65.64281257 Â Â Â -38.73100109</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px">Â Â Â Â Â Â Â Â Â Â Â QMXXÂ Â Â Â Â Â QMYYÂ Â Â Â Â Â QMZZÂ Â Â Â Â Â QMXZÂ Â Â Â Â Â QMYZ Â Â Â Â Â QMXY<br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Â QMXX Â Â Â Â Â Â 23.935795Â Â Â Â 8.885450Â Â Â -32.821244Â Â Â Â 0.000000Â Â Â Â 0.000000 Â Â Â Â 0.000000</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Â QMYYÂ Â Â Â Â Â Â 8.885450 Â Â Â 23.935795Â Â Â -32.821244Â Â Â Â 0.000000Â Â Â Â 0.000000 Â Â Â Â 0.000000</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Â QMZZÂ Â Â Â Â Â -32.821244Â Â Â -32.821244 Â Â Â 65.642488Â Â Â Â 0.000000Â Â Â Â 0.000000 Â Â Â Â 0.000000</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Â QMXZÂ Â Â Â Â Â Â 0.000000Â Â Â Â 0.000000Â Â Â Â 0.000000 Â Â Â 38.732249Â Â Â Â 0.000000 Â Â Â Â 0.000000</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Â QMYZÂ Â Â Â Â Â Â 0.000000Â Â Â Â 0.000000Â Â Â Â 0.000000Â Â Â Â 0.000000 Â Â Â 38.732249 Â Â Â Â 0.000000</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">
</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"> QMXY       0.000000    0.000000    0.000000    0.000000    0.000000     7.525173</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Up to this point it all seems good except for the sign (which I know how to correct).</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">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.</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">!First dipole hyperpolarizability</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! z,zz ???</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! third derivative of energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_r <span style="color:rgb(206,121,36)">=</span> energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,-<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_l <span style="color:rgb(206,121,36)">=</span> energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_2r <span style="color:rgb(206,121,36)">=</span> energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,-<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_2l <span style="color:rgb(206,121,36)">=</span> energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">hyperpol <span style="color:rgb(206,121,36)">=</span> <span style="color:rgb(213,59,211)">(</span>e_2r-<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span>e_r<span style="color:rgb(206,121,36)">+</span><span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span>e_l-e_2l<span style="color:rgb(213,59,211)">)</span><span style="color:rgb(206,121,36)">/</span><span style="color:rgb(213,59,211)">(</span><span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">)</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">text, Hyperpolarizability</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">
</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">table, hyperpol</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">2nd-question: how do we obtain DMX-QMXY type terms. which field should be applied and what is the finite difference expression for this.</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Thanks in advance</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Amit</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">-- complete input here.</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><span style="color:rgb(206,121,36)">***</span>,Trial calculation <span style="color:rgb(206,121,36)">for</span> Ar <span style="color:rgb(206,121,36)">+</span> He long range potential</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">geometry<span style="color:rgb(206,121,36)">=</span>{angstrom</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">Ar</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">He <span style="color:rgb(195,55,32)">1</span> R</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">}</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! some distance</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(195,55,32)"><span style="color:rgb(0,0,0)">R</span><span style="color:rgb(206,121,36)">=</span>3<span style="color:rgb(213,59,211)">.</span>67473242</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">basis<span style="color:rgb(206,121,36)">=</span>vdz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">hf</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">polarizability,dm</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">!! this does not work</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">pol_xx <span style="color:rgb(206,121,36)">=</span> POLXX</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">pol_zz <span style="color:rgb(206,121,36)">=</span> POLZZ</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! save dipole moment in AU and Debye</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip_mom_z<span style="color:rgb(206,121,36)">=</span>dmz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip_mom_z_debye<span style="color:rgb(206,121,36)">=</span>dip_mom_z<span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">2</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">541765</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! test finite field approach</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span>  hf<span style="color:rgb(213,59,211)">;</span> e_0 <span style="color:rgb(206,121,36)">=</span> energy ! e_center</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dipz_0<span style="color:rgb(206,121,36)">=</span>dmz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_r <span style="color:rgb(206,121,36)">=</span> energy ! e_right</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dipz_r<span style="color:rgb(206,121,36)">=</span>dmz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,-<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_l <span style="color:rgb(206,121,36)">=</span> energy ! e_left</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dipz_l<span style="color:rgb(206,121,36)">=</span>dmz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! dipole moment along z as finite <span style="color:rgb(206,121,36)">difference</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">d_zz <span style="color:rgb(206,121,36)">=</span> <span style="color:rgb(213,59,211)">(</span>e_r - e_l<span style="color:rgb(213,59,211)">)</span><span style="color:rgb(206,121,36)">/</span><span style="color:rgb(213,59,211)">(</span><span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">)</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">d_zz_debye <span style="color:rgb(206,121,36)">=</span> d_zz<span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">2</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">541765</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! dipole polaribzability as finite <span style="color:rgb(206,121,36)">difference</span> of dipole</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip_pol_zz <span style="color:rgb(206,121,36)">=</span> <span style="color:rgb(213,59,211)">(</span>dipz_r - dipz_l<span style="color:rgb(213,59,211)">)</span><span style="color:rgb(206,121,36)">/</span><span style="color:rgb(213,59,211)">(</span><span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">)</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! dipole polarizability as <span style="color:rgb(195,55,32)">2</span>nd order derivative of energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">pol <span style="color:rgb(206,121,36)">=</span> <span style="color:rgb(213,59,211)">(</span>e_r<span style="color:rgb(206,121,36)">+</span>e_l-<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(206,121,36)">*</span>e_0<span style="color:rgb(213,59,211)">)</span><span style="color:rgb(206,121,36)">/</span><span style="color:rgb(213,59,211)">(</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">)</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">table, dip_mom_z, d_zz, dip_pol_zz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">table, dip_mom_z_debye, d_zz_debye</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">table, pol</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">!First dipole hyperpolarizability</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! not sure about this</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! z,zz ???</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! third derivative of energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_r <span style="color:rgb(206,121,36)">=</span> energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,-<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_l <span style="color:rgb(206,121,36)">=</span> energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_2r <span style="color:rgb(206,121,36)">=</span> energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">dip,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,-<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_2l <span style="color:rgb(206,121,36)">=</span> energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">hyperpol <span style="color:rgb(206,121,36)">=</span> <span style="color:rgb(213,59,211)">(</span>e_2r-<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span>e_r<span style="color:rgb(206,121,36)">+</span><span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span>e_l-e_2l<span style="color:rgb(213,59,211)">)</span><span style="color:rgb(206,121,36)">/</span><span style="color:rgb(213,59,211)">(</span><span style="color:rgb(195,55,32)">2</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">)</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">text, Hyperpolarizability</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">table, hyperpol</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">!!! apply quandrupole field</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! QUAD,xxfield,yyfield,zzfield,xyfield,xzfield,yzfield<span style="color:rgb(213,59,211)">;</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo"><span style="color:rgb(213,59,211)">! XX field</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_0<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_r<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,-<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_l<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! XX quandrupole polarizability using finite <span style="color:rgb(206,121,36)">diff</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">quad_pol_xx <span style="color:rgb(206,121,36)">=</span> <span style="color:rgb(213,59,211)">(</span>e_r<span style="color:rgb(206,121,36)">+</span>e_l-<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(206,121,36)">*</span>e_0<span style="color:rgb(213,59,211)">)</span><span style="color:rgb(206,121,36)">/</span><span style="color:rgb(213,59,211)">(</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">)</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! ZZ</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_0<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_r<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,-<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_l<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! quandrupole polarizability</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">quad_pol_zz <span style="color:rgb(206,121,36)">=</span> <span style="color:rgb(213,59,211)">(</span>e_r<span style="color:rgb(206,121,36)">+</span>e_l-<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(206,121,36)">*</span>e_0<span style="color:rgb(213,59,211)">)</span><span style="color:rgb(206,121,36)">/</span><span style="color:rgb(213,59,211)">(</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">)</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">table, quad_pol_xx, pol_xx</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">table, quad_pol_zz, pol_zz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;min-height:13px"><br></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! cross term xx_zz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">symmetry,nosym</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_0<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_r<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">QUAD,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,<span style="color:rgb(195,55,32)">0</span>,-<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span>,<span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">;</span> hf<span style="color:rgb(213,59,211)">;</span> e_l<span style="color:rgb(206,121,36)">=</span>energy</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">! quandrupole polarizability</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">quad_pol_xz <span style="color:rgb(206,121,36)">=</span> <span style="color:rgb(213,59,211)">(</span>e_r<span style="color:rgb(206,121,36)">+</span>e_l-<span style="color:rgb(195,55,32)">2</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(206,121,36)">*</span>e_0<span style="color:rgb(213,59,211)">)</span><span style="color:rgb(206,121,36)">/</span><span style="color:rgb(213,59,211)">(</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(206,121,36)">*</span><span style="color:rgb(195,55,32)">0</span><span style="color:rgb(213,59,211)">.</span><span style="color:rgb(195,55,32)">005</span><span style="color:rgb(213,59,211)">)</span></p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">table, quad_pol_xz</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo">
</p><p style="margin:0px;font-size:11px;line-height:normal;font-family:Menlo;color:rgb(206,121,36)">---</p></div><div><br></div></div>