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Spin constraints for SF-DFT optimization and FSM pathways

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Member
Registered: May 2018
Posts: 3
When running a minimum energy crossing point (MECP) optimization with SF-TDDFT, the state is specified by spin as well as state index with the keywords mecp_state1 and mecp_state2. By default, singlets are considered states with <S**2> < 1.2 (set by the keyword cis_s2_thresh).

However, only the state index is specified when running an optimization (i.e. set_state_deriv) or a FSM minimum energy path (i.e. set_state_reactant, set_state_product). This can be a problem when, for example, trying to find a path where the S1 and T1 states can cross such as the path from the Franck-Condon point to a conical intersection. Including cis_s2_thresh doesn't appear to have an effect.

Is there a way to specify spin when running optimizations or paths?

Here is a minimum working example for ethylene where state 3 is S1.

$w:/*f`J\!nmolecule
0 3
C 0.6651727179 0.0000000000 0.0000000000
C -0.6651727179 0.0000000000 0.0000000000
H 1.2333346678 0.9240428128 0.0000000000
H 1.2333346678 -0.9240428128 0.0000000000
H -1.2333346678 0.9240428128 0.0000000000
H -1.2333346678 -0.9240428128 0.0000000000
****
C 0.7253107457 0.2383892336 -0.2142528223
C -0.6211506000 -0.0254768222 -0.0024600132
H 1.2165367040 -0.5345034691 -0.8395482690
H 1.0214469092 -0.3171924481 0.7427335054
H -1.0537039461 -1.0236766735 0.1900453499
H -1.3734531866 0.7670207830 0.0897971196
$w:/*f`J\!nend

$w:/*f`J\!nrem
jobtype fsm
fsm_nnode 10
fsm_ngrad 4
fsm_mode 2
fsm_opt_mode 2
max_cis_cycles 200
method bhhlyp
spin_flip true
basis cc-pVDZ
cis_n_roots 4
set_state_reactant 3
set_state_product 3
$w:/*f`J\!nend

Ideally there should be a way to specify the 2nd singlet state rather than relying on the spin not changing.
Administrator
Registered: Oct 2017
Posts: 15
This usage is not correct - FSM works for transition states. MECP has a different topology: it is a minimum energy point in the seam, and its search requires different algorithms. Q-Chem manual has examples on how to make inputs for MECP optimization. For your case, it would look like this:


$w:/*f`J\!nmolecule
0 3
C 0.6651727179 0.0000000000 0.0000000000
C -0.6651727179 0.0000000000 0.0000000000
H 1.2333346678 0.9240428128 0.0000000000
H 1.2333346678 -0.9240428128 0.0000000000
H -1.2333346678 0.9240428128 0.0000000000
H -1.2333346678 -0.9240428128 0.0000000000
$w:/*f`J\!nend

$w:/*f`J\!nrem
jobtype opt
max_cis_cycles 200
method bhhlyp
spin_flip true
mecp_opt = true
mecp_state1 [1,0]
mecp_state2 [0,1]
basis cc-pVDZ
cis_n_roots 4
$w:/*f`J\!nend


The job with this input successfully found MECP between the triplet and first singlet.
Member
Registered: May 2018
Posts: 3
You misunderstood my question. I optimized the 2nd geometry in my input with MECP between S0 and S1, which I was able to do because I can specify spin. Now imagine I want to optimize a minimum (on S1, for example) that is far from my starting geometry. If a triplet state crosses S1 during the optimization, the state indices will change and I may end up optimizing a triplet state minimum instead.

In the example I gave, I would like to find the minimum energy path from the Franck-Condon region to the conical intersection geometry. This is exactly what methods such as the nudged elastic band method or FSM do. They optimize the path rather than explicitly searching for a transition state.

Despite the code existing for MECP optimizations, there seems to be no way of activating spin selection for a FSM calculation or a geometry optimization. The closest keyword I can find is state_follow but that doesn't have spin criteria. I have been looking for a "follow" keyword for spin but there doesn't appear to be anything in the documentation.
Administrator
Registered: Oct 2017
Posts: 15
Since the formalism is not spin-adapted, there is no good solution over it --- if spin contamination is severe, triplets and singlets are not distinguishable. This is a common situation in spin-flip methods if the dominant excitation is out of the active space. I recommend to use conventional gradient methods to locate MECP between states of interest, and run 2 geometry optimizations, starting from this point - they will give the corresponding paths. STATE_FOLLOW is a useful option to recognize the state by its density. If you experience a complicated situation of multiple crossings, you need to check each point during the optimization. I do not think that usage of FSM is a good idea just because of math behind MECP. The code for MECP optimization uses gradient-based algorithms.

Do not mix MECP and TS - although there is some similarity in kinetic theories between them, they are quite different in therms of maths and algorithms of optimization.
Member
Registered: May 2018
Posts: 3
Quote
Since the formalism is not spin-adapted, there is no good solution over it --- if spin contamination is severe, triplets and singlets are not distinguishable.


Could you not say exactly the same thing about MECP optimization? There exists a (crude) approximation of the multiplicity of state based on the criteria <S**2> < 1.2, but it is only enabled for MECP optimizations. I'm curious if there is a reason this feature isn't available for other optimizations.

The fact that one of my geometries is at a crossing point is irrelevant. In ethylene, the MECP is also the S1 minimum. The path taken by a geometry optimization is not guaranteed to be the minimum energy path. Unless I misunderstand the FSM formalism, it should find a minimum energy path connecting two geometries regardless of whether a transition state is present. That is all I am looking for: The minimum energy path between two arbitrary geometries with spin criteria.

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