Transition state optimization
Qcore supports transition state (TS) optimization using the eigenvectorfollowing algorithm. This is done by setting the option ts = true
within the optimize()
command. The minimal input for a TS optimization is:
optimize(
structure( xyz =
[[C, 1.7750, 0.5026, 0.0000],
[C, 0.4916, 0.1859, 0.0000],
[C, 0.6671, 0.5360, 0.0000],
[H, 0.4532, 1.2741, 0.0000],
[H, 1.6489, 0.0536, 0.0000],
[H, 2.6886, 0.1279, 0.0000],
[O, 0.7308, 1.8618, 0.0000],
[O, 1.8897, 1.7305, 0.0000],
[H, 0.5902, 2.2396, 0.0000]] )
ts = true
xyz_output = 'malondialdehyde_ts.xyz'
xtb()
)
In this example, we seek the protontransfer TS structure of Malondialdehyde using GFNxTB. We start with an initial structure that is reasonably close to the true TS structure.
Searching for a TS is usually more difficult than geometry optimization. The model Hessian used in downhill minimization is not adequate for TS optimization. Therefore, the optimize()
command will compute the exact Hessian using the energy method provided. This must contain at least one imaginary frequency. To increase the chance of finding the desired TS structure we also recommend first performing a constrained optimization. By fixing bonds/angles/dihedrals that are close to the TS, the Hessian is more likely to possess the desired imaginary frequency. Here is an example input:
! first perform constrained optimization
constrained_opt := optimize(
structure(xyz =
[[C, 1.7750, 0.5026, 0.0000],
[C, 0.4916, 0.1859, 0.0000],
[C, 0.6671, 0.5360, 0.0000],
[H, 0.4532, 1.2741, 0.0000],
[H, 1.6489, 0.0536, 0.0000],
[H, 2.6886, 0.1279, 0.0000],
[O, 0.7308, 1.8618, 0.0000],
[O, 1.8897, 1.7305, 0.0000],
[H, 0.5902, 2.2396, 0.0000]]
)
bond(atoms = [7, 9] value = 1.38 angstrom)
bond(atoms = [8, 9] value = 1.38 angstrom)
xtb()
)
! perform TS search by loading constrained structure
ts_opt := optimize(
structure(load = constrained_opt)
ts = true
xtb()
)
! compute Hessian and normal modes for the optimized TS structure
final_hess := hessian(
structure(load = ts_opt)
save_normal_modes = 'final.Molden'
xtb()
)
In this example, we also demonstrate how to perform linked calculations:

First, a constrained geometry optimization is performed, with the two OH bond lengths set to 1.38 Å and the remaining degrees of freedom relaxed. The results are stored in the userdefined variable
constrained_opt
using the:=
operator. 
The resulting geometry is used to launch a transition state optimization by loading
constrained_opt
into thestructure()
subcommand.
The results are stored in the userdefined variablets_opt
. 
To confirm the transitionstate nature of the structure, the TSoptimized geometry is used to perform a vibrational frequency calculation by loading
ts_opt
in to thestructure()
subcommand. The resulting frequencies and normal modes are output to the userdefined file'final.Molden'
.
Qcore also allows the Hessian to be computed at a lowerlevel of theory. This scheme requires care, but it can massively accelerate the process of TS optimization. In the final example below, we demonstrate calculating the Hessian using GFNxTB to find the HartreeFock TS structure. The Hessian is saved to guess_hessian
and loaded in to the optimize()
command with load = guess_hessian
. Here is an example input:
! first perform constrained optimization
constrained_opt := optimize(
structure( xyz =
[[C, 1.7750, 0.5026, 0.0000],
[C, 0.4916, 0.1859, 0.0000],
[C, 0.6671, 0.5360, 0.0000],
[H, 0.4532, 1.2741, 0.0000],
[H, 1.6489, 0.0536, 0.0000],
[H, 2.6886, 0.1279, 0.0000],
[O, 0.7308, 1.8618, 0.0000],
[O, 1.8897, 1.7305, 0.0000],
[H, 0.5902, 2.2396, 0.0000]]
)
bond( atoms = [7, 9] value = 1.38 angstrom )
bond( atoms = [8, 9] value = 1.38 angstrom )
xtb()
)
! perform a cheap hessian calculation
guess_hessian := hessian(
structure( load = constrained_opt )
xtb()
)
! perform TS search by loading constrained structure and initial guess hessian
ts_opt := optimize(
structure( load = constrained_opt )
load = guess_hessian
ts = true
dft( xc = pbe ao = '631G*' )
)
! compute Hessian and normal modes for the optimized TS structure
final_hess := hessian(
structure( load = ts_opt )
save_normal_modes = 'final.Molden'
dft( xc = pbe ao = '631G*' )
)