Subject: ESR anisotropic coupling constants

From: <[email-masked]>
Date: Wed, 19 Mar 1997 10:53:45 +0100 (CET)

I have received several requests about the computation of ESR anisotropic
coupling constants by Gaussian94. Since this seems a general question I
directly post this message for the whole CCL community.
These constants are nothing else than field gradients computed with the
spin rather than the total electronic density and not including the nuclear
contribution. Furthermore the resulting tensor must be put in the zero-trace
form. In gaussian94 it is possible to force these options by setting in the
keyword list the following items:
PROP IOP(6/17=2,6/26=4)
Here follows an input and the relevant part of the output for a STO-3G
computation of H2NO
----------------------------------------------------------------------------
#UHF/PROP IOP(6/17=2) IOP(6/26=4) 

H2NO  

 0 2
 X
 X 1 1.0
 N 2 1.0  1 90.0
 H 3 NH   2 90.0  1   THETA
 H 3 NH   2 90.0  1  -THETA
 O 3 NO   2 ALPHA 1  180.0

 NH=1.0179
 NO=1.2778
 THETA=58.9235   
 ALPHA=110.0
-----------------------------------------------------------------------------

Fermi contact analysis (atomic units).
              1
  1  N     .042923
  2  H    -.005038
  3  H    -.005038
  4  O     .098025

 **********************************************************************

            Electrostatic Properties Using The SCF Density

 **********************************************************************

 Warning!  Using spin rather than total density!

 --- Only the electronic contributions will be computed ---

 -----------------------------------------------------
    Center         ---- Electric Field Gradient ----
                     XX            YY            ZZ
 -----------------------------------------------------
    1 Atom         .119043      -.295145      -.363285
    2 Atom         .002506       .031422       .029384
    3 Atom         .002506       .031422       .029384
    4 Atom        2.130337     -1.663300     -1.698867
 -----------------------------------------------------
-----------------------------------------------------
    Center         ---- Electric Field Gradient ----
                       ( tensor representation )
                   3XX-RR        3YY-RR        3ZZ-RR
 -----------------------------------------------------
    1 Atom         .298838      -.115349      -.183489
    2 Atom        -.018598       .010318       .008280
    3 Atom        -.018598       .010318       .008280
    4 Atom        2.540947     -1.252690     -1.288257
 -----------------------------------------------------

these are the principal values of anisotropic coupling constants

-------------------------------------------------------------------------------

Since the directions of principal moments are often significant and transforma-
tion to more conventional units can be performed once for ever, I have modified
the links 601 and 602 of gaussian to obtain the following output for the same
input

-------------------------------------------------------------------------------

 ------------------------------------------------------------------------------
                       Isotropic Fermi Contact Couplings
 ------------------------------------------------------------------------------

     Atom                 a.u.       MegaHertz       Gauss       10(-4) cm-1

   1  N(14)               .04292      13.86856       4.94865       4.62605
   2  H                  -.00504     -22.51979      -8.03562      -7.51179
   3  H                  -.00504     -22.51979      -8.03562      -7.51179
   4  O(17)               .09802     -59.42481     -21.20426     -19.82198

 ------------------------------------------------------------------------------

 **********************************************************************

            Electrostatic Properties Using The SCF Density

 **********************************************************************

 Warning!  Using spin rather than total density!

 --- Only the electronic contributions will be computed ---
       Atomic Center    1 is at   -.021142   .543231   .000000
       Atomic Center    2 is at    .158563  1.036966   .871810
       Atomic Center    3 is at    .158563  1.036966  -.871810
       Atomic Center    4 is at   -.021142  -.734569   .000000
 -----------------------------------------------------
    Center         ----  Spin Dipole Couplings  ----
                   3XX-RR        3YY-RR        3ZZ-RR
 -----------------------------------------------------
    1 Atom         .298838      -.115349      -.183489
    2 Atom        -.018598       .010318       .008280
    3 Atom        -.018598       .010318       .008280
    4 Atom        2.540947     -1.252690     -1.288257
 -----------------------------------------------------
    Center         ----  Spin Dipole Couplings  ----
                     XY            XZ            YZ
 -----------------------------------------------------
    1 Atom        -.074772       .000000       .000000
    2 Atom         .004800       .007098       .035617
    3 Atom         .004800      -.007098      -.035617
    4 Atom        -.099769       .000000       .000000

 ------------------------------------------------------------------------------
           Anisotropic Spin Dipole Couplings in Principal Axis System
 ------------------------------------------------------------------------------

     Atom            a.u.   MegaHertz   Gauss  10(-4) cm-1        Axes

            Baa     -.1835    -7.077    -2.525    -2.361   .0000   .0000  1.0000
   1 N(14)  Bbb     -.1284    -4.953    -1.767    -1.652   .1724   .9850   .0000
            Bcc      .3119    12.030     4.293     4.013   .9850  -.1724   .0000
           1/R**3   -.5394   -20.803    -7.423    -6.939
 
            Baa     -.0268   -14.276    -5.094    -4.762  -.2361  -.6571   .7158
   2 H      Bbb     -.0193   -10.278    -3.667    -3.428   .9631  -.2560   .0828
            Bcc      .0460    24.554     8.762     8.190   .1288   .7090   .6933
           1/R**3    .0633    33.780    12.053    11.268
 
            Baa     -.0268   -14.276    -5.094    -4.762   .2361   .6571   .7158
   3 H      Bbb     -.0193   -10.278    -3.667    -3.428   .9631  -.2560  -.0828
            Bcc      .0460    24.554     8.762     8.190   .1288   .7090  -.6933
           1/R**3    .0633    33.780    12.053    11.268
 
            Baa    -1.2883    93.221    33.264    31.095   .0000   .0000  1.0000
   4 O(17)  Bbb    -1.2553    90.837    32.413    30.300   .0263   .9997   .0000
            Bcc     2.5436  -184.059   -65.677   -61.395   .9997  -.0263   .0000
           1/R**3  -1.2318    89.138    31.807    29.733

 ------------------------------------------------------------------------------

-------------------------------------------------------------------------------
  Vincenzo Barone                          | 
  Professor of Theoretical Chemistry       |
  Dipartimento di Chimica                  | tel. +39-81-5476503
  Universita' Federico II                  | fax  +39-81-5527771
  via Mezzocannone 4                       | e-mail [email-masked]
  I-80134 Napoli                           |
  Italy                                    |
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