Example: TS search using partial Hessian: C2H6 internal rotation¶

Download TS_C2H6.run

Frequently when searching for a transition state, one needs an accurate second derivatives matrix, a Hessian. An exact Hessian may be obtained analytically but this may be very expensive for large molecules. In such cases it may be beneficial to calculate Hessian matrix elements only for atoms directly involved in the reaction for which a transition state is sought for. The rest of the Hessian can then be approximated using a cheaper method.

In this example, a saddle point of the ethane internal rotation around C-C bond is found. In principle, only hydrogen atoms contribute to the normal mode we are interested in. Therefore we calculate a partial Hessian matrix including hydrogen atoms only. For this purpose, the AnalyticalFreq block key is used. In this block, a NUC keyword is added specifying that the second derivatives are calculated for atom 3 (and its symmetry-equivalents) only. Note that the Hessian matrix elements between symmetry-equivalent atoms, for example between 3,H and 4.H are also calculated. The rest of the matrix is estimated using the default method.

$ADFBIN/adf <<eor
TITLE Ethane transition state search using partial Hessian

ATOMS
1 C       0.000000000000       0.000000000000       0.767685465031
2 C       0.000000000000       0.000000000000      -0.767685465031
3 H       0.964354016767       0.347635559279       1.177128271450
4 H      -0.181115782790      -1.008972856410       1.177128271450
5 H      -0.783238233981       0.661337297125       1.177128271450
6 H      -0.500471876676       0.894626767091      -1.177128271450
7 H      -0.524533568868      -0.880734742626      -1.177128271450
8 H       1.025005445540      -0.013892024465      -1.177128271450
END

BASIS
type DZ
core Large
END

AnalyticalFreq
 NUC 3
End

BeckeGrid
 quality good
End
eor

After the Hessian is calculated, the resulting TAPE21 file is used for a subsequent transition state search:

mv TAPE21 ethane-frq.t21

$ADFBIN/adf <<eor
TITLE Ethane transition state search using partial Hessian

ATOMS
1 C       0.000000000000       0.000000000000       0.767685465031
2 C       0.000000000000       0.000000000000      -0.767685465031
3 H       0.964354016767       0.347635559279       1.177128271450
4 H      -0.181115782790      -1.008972856410       1.177128271450
5 H      -0.783238233981       0.661337297125       1.177128271450
6 H      -0.500471876676       0.894626767091      -1.177128271450
7 H      -0.524533568868      -0.880734742626      -1.177128271450
8 H       1.025005445540      -0.013892024465      -1.177128271450
END

Fragments
  H t21.H
  C t21.C
END

GEOMETRY
    smooth conservepoints
    TransitionState mode=1
    optim All Cartesian
    iterations 30
    step rad=0.15
    hessupd BOFILL
    converge e=1.0e-4 grad=1.0e-3 rad=1.0e-3
END

RESTART ethane-frq.t21

BeckeGrid
 quality good
End
eor

Important note: care should be taken to specify correct mode in the TransitionState keyword. Because a significant part of the Hessian will not be calculated exactly, it is possible that it will have more than one negative eigenvalue, in which case the one we are interested in may not be the first one. In such a case, one needs to specify the correct mode number in the TransitionState keyword.