Transition state search¶

A transition state (TS) search is very much like a geometry optimization: the purpose is to find a stationary point on the potential energy surface, primarily by monitoring the energy gradients, which should vanish. The difference between a transition state and a minimum is that at the transition state the Hessian has a negative eigenvalue: We are at a saddle point, not a minimum, with the “negative” mode connecting the two basins on the potential energy surface.

A transition state search in AMS is performed by selecting the corresponding task:

Task TransitionStateSearch

Due to the similarities between energy minimization and transition state search, the TransitionStateSearch task in AMS is actually implemented as a special kind of geometry optimization using the quasi-Newton optimizer. As such all the settings and keywords described on the geometry optimization manual page also apply to transition state searches.

In a geometry optimization with a quasi-Newton based optimizer the Hessian is used to make a reasonably sized step in the “downhill” direction on the potential energy surface, as the goal is simply to minimize the energy. A transition state search is a bit different: In the first step a normal mode is picked along which the energy is to be maximized, while it is minimized along all other directions. Normally the mode with the lowest eigenvalue is picked, since we know that there should be exactly one negative eigenvalue at the TS geometry, but one can also choose an approximate reaction coordinate, either by setting the ReactionCoordinate or by adding another System block named final, similar to how it’s done for NEB. If the initial geometry is sufficiently close to the transition state, i.e. we are close to the saddle, the lowest mode is normally the correct one to follow in order to get to the ridge of the saddle. Alternatively a different mode can also be selected manually.

TransitionStateSearch
   ModeToFollow integer
   ReactionCoordinate
      Angle string
      Coordinate string
      Dihedral string
      Distance string
   End
End

TransitionStateSearch

Type

Block

Description

Configures some details of the transition state search.

ModeToFollow

Type

Integer

Default value

1

Description

In case of Transition State Search, here you can specify the index of the normal mode to follow (1 is the mode with the lowest frequency).

ReactionCoordinate

Type

Block

Description

Specify components of the transition state reaction coordinate (TSRC) as a linear combination of internal coordinates (distances or angles).

Angle

Type

String

Recurring

True

Description

The TSRC contains the valence angle between the given atoms. Three atom indices followed by the weight.

Coordinate

Type

String

Recurring

True

Description

The TSRC contains Cartesian displacement of an atom: atom index followed by [x|y|z] and the weight.

Dihedral

Type

String

Recurring

True

Description

The TSRC contains the dihedral angle between the given atoms. Four atom indices followed by the weight.

Distance

Type

String

Recurring

True

Description

The TSRC contains the distance between the given atoms. Two atom indices followed by the weight.

This selection happens only in the first step. Subsequent steps will attempt to maximize along the mode that resembles most (by overlap) the previous maximization direction.

Practice shows that a transition state are much harder to find than a minimum. For a large part this is due to the much stronger anharmonicities that usually occur near the TS, which threaten to invalidate the quasi-Newton methods to find the stationary point. For this reason it is good advice to be more cautious in the optimization strategy when approaching a transition state:

• We recommend starting the transition state search with an intial geometry that is already close to the transition state. One can use a potential energy surface scan along something resembling the reaction coordinate to get a rough idea where the transition state is. This geometry can then be used as an initial geometry for the transitions state search.

• It is strongly recommended to provide a good initial Hessian for the transition state search. Otherwise the first step of the search may not be taken in the correct direction and subsequent steps may keep steering in the wrong direction. In AMS this is easily possible by loading a Hessian from a previous calculation, see the initial Hessian section of this manual. A good way to obtain a reasonable Hessian is to compute it explicitly with one of the fast engines (i.e. at a lower lever of theory) and read that Hessian as the initial Hessian for the transition state search at a higher level of theory.

• When no accurate initial Hessian is available, it may be a good idea to specify an approximate normal mode vector using the ReactionCoordinate input block. A reaction coordinate (RC) is a linear combination of distances and/or valence and dihedral angles:

  TransitionStateSearch
    ReactionCoordinate
      Distance  i j     fac
      Distance  i j     fac
      Angle     i j k   fac
      Dihedral  i j k l fac
    End
  End
  

  Here, i, j, k, and l are atom indices, and the fac is the factor with which the internal coordinate enters the linear combination.

  One should be careful when specifying more than one bond or angle as the reaction coordinate. For example, suppose atom 2 is located between atoms 1 and 3. Then the following ReactionCoordinate block:

  TransitionStateSearch
    ReactionCoordinate
      Distance 1 2  1.0
      Distance 2 3 -1.0
    End
  End
  

  means that the RC consists of two distances: R(1-2) and R(2-3). The positive direction of the RC is defined as an increase of the R(1-2) and a decrease of the R(2-3). In other words, this RC corresponds to atom 2 moving along the R(1-3) axis.

• As an alternative to ReactionCoordinate one can add a second System to the input and call it final. The difference between the initial and the final geometry will be used as the reaction coordinate. For non-periodic systems, the difference is computed in the internal coordinates and only coordinates that differ significantly (by more than about 0.1 Bohr or radian) are included. For this reason, the final geometry should not be too close to the initial. For periodic systems, the difference in the Cartesian coordinates is used. In this case, only coordinates that differ by more than 0.5 Bohr are included.

• When the method converges it is usually a good idea to verify that the found geometry is indeed a transition state. This can be done by performing a frequency analysis and checking whether the Hessian has exactly one negative eigenvalue (represented by a mode with a negative frequency). Doing so is expensive however. Since we are really only interested in the lowest two normal modes calculating the full Hessian is however not necessary and one can use the faster PES point characterization instead. This uses a Davidson-type algorithm to obtain the lowest few normal modes without constructing the full Hessian. The user is referred to the PES point characterization documentation page for further details.