# Linear Transit¶

In a Linear Transit (LT) run you define a number of atomic coordinates (at least one) to be the LT parameters: these get an initial and a final value. The LT is defined as the simultaneous linear change of these parameters from their initial to their final values. This is carried out in a number of equidistant steps. In a non-linear transit calculation these may be not equidistant steps. The total number of LT points is specified on input. At each LT point the remaining atomic coordinates - those that are not LT parameters - may or may not be optimized: the (final) structure and energy at each LT point are computed. A Linear Transit (LT) run is therefore just a sequence of (related) constrained Geometry Optimizations.

The LT scan may be used for instance to sketch an approximate path over the transition states between reactants and products. From this a reasonable guess for the Transition State can be obtained which may serve as starting point for a true transition state search for instance.

Whenever a geometry subkey is applicable in a Geometry Optimization, it will apply in a Linear Transit run in each of the optimizations that are carried out at the distinct Linear Transit points, and the same default values apply.

## Linear Transit (new branch)¶

A transit calculation option has been added in the new optimization branch. This is capable of performing both linear transits, and non-linear transits, and is the default when the LINEARTRANSIT subkey is included in the GEOMETRY block key.

The new transit code works differently to the old: the transit is represented as a sequence of constrained optimizations. The CONSTRAINTS block key should be used to delineate the constraints applied at each stage of the transit.

To perform a linear transit, start and end values are supplied.

Constraints
angle 2 1 3 start=100.0 end=120.0
End

Geometry
LinearTransit 4
Optim Deloc
End


In the example above, 4 stages are required; ADF will interpolate the start and end values supplied for the angle between atoms 2, 1, and 3.

Non-linear transits are possible, and can even be combined with linear transits in other coordinates. To perform a non-linear transit in a particular coordinate, explicit values must be given.

Constraints
dist 1 2 0.8 0.9 1.1 1.15
angle 2 1 3 start=100.0 end=120.0
End

Geometry
LinearTransit 4
Optim Deloc
End


In the example above, 4 values are given for the distance between atoms 1 and 2. This distance constraint will be applied simultaneously with the linear transit constraints for the angle, with other degrees of freedom optimized at each stage of the transit.

It is worth noting that fixed constraints can also be used in a transit.

Constraints
dist 1 2 0.8 0.9 1.1 1.15
angle 2 1 3 100.0
End

Geometry
LinearTransit 4
Optim Deloc
End


In this example, the angle between atoms 2, 1, and 3 will be fixed at 100.0 degrees at all stages of the transit.

Finally, it should be pointed out that fully converged constraints are used by default in the transit calculations. They do not have to be fully met in the input, but if the input geometry is far from meeting the constraints, a large, erratic first geometry step may result.

You can avoid fully enforcing constraints, by adding a CONSTRAINTS subkey to the geometry block key:

Geometry
CONSTRAINTS partialconverge
End


In this case the constraints are not required to be fully met at each intermediate geometry, but are fully met at the converged geometries,

## Linear Transit (old branch)¶

The LINEARTRANSIT runtype has to be specified. Additional specifications are optional.

GEOMETRY
Branch Old
LinearTransit {NPoints}
end

NPoints
The number of LT points for which an optimization will be carried out If no value is supplied the default takes effect: 5.

There are a few obvious differences between a single optimization and a LT run. Most important is that the coordinate(s) that describe the LT path, the LT parameters, cannot be optimized: at each of the LT points they are frozen. This implies that technically speaking at each LT point a constrained optimization is carried out. One of the consequences is that the atoms coordinate type - Cartesian or Z-matrix - must also be the optimization coordinate type. The LT parameters themselves must be defined with the key GEOVAR, see below.

It is possible to freeze all coordinates so that the LT run is similar to a sequence of Single Point runs. However, energy gradients will be computed at each step, so that more CPU time is spent at each LT point than for just a Single Point calculation.

The number of LT points by which the path is traced is defined by the npoints argument to the subkey LinearTransit. It is possible to execute only a subset of these points, usually with the purpose to complete the calculation by using the restart facility of ADF. In this way you can break down a very large calculation into several smaller ones, or have the opportunity to check how things have been going for the first few LT points before deciding whether a continuation is useful. This may be achieved of course by simply defining different start- and end-values for the LT parameters in a related series of calculations, but it is more comfortable to specify the complete path once and just execute parts of it at a time. This is accomplished by giving a second value to the iterations subkey in the geometry block.

iterations Niter Niter2

Niter
The first argument of the subkey iterations in the GEOMETRY block, controlling the maximum number of iterations allowed to reach convergence, applies now for each LT point separately.
Niter2
The second argument specifies the maximum number of LT points to calculate in this run. If omitted (default) the whole LT scan is completed. Doing only part of the scan may be combined with the restart feature, so that the remainder can be done in a continuation run. See the restart key. A too large value of LT points is automatically adjusted: no more LT points are computed than required to complete the LT path as defined by the lineartransit subkey. A negative or zero value is not accepted and internally reset to one (1).

WARNING: if you use the QMMM functionality in combination with a Linear Transit, then only the coordinates of the true QM atoms can be used as LT parameters, no MM atoms must be involved in the LT parameter set.

## Symmetry in a Linear Transit¶

In a Linear Transit run it is imperative that the complete Linear Transit path as defined by the parameters conforms to the specified symmetry. If such is not the case, an error will occur or possibly the program will continue but not produce correct results. Note that when no symmetry is specified in input, the initial geometry defines the specified symmetry.