Automated PES Exploration¶

Overview¶

While many details of a PES exploration calculation depend on the specific job selected, some aspects are common to all PES explorations jobs. Here we give a brief overview of a typical PES exploration, using a Process Search job as example.

A PES exploration calculation generally consists of multiple expeditions, each with several explorers.

Explorers are given an initial structure, and their goal is to find a nearby critical point (a local minimum, a saddle point or both). The explorer moves around the PES by modifying the atomic positions of the system and by using the specified Engine to compute energy and gradients.

An expedition is a collection of explorers all starting from the same point on the PES.

Before setting off for the first expedition, the input structure is optimized and added to the Energy Landscape, which is the database of all interesting points found during the exploration (see the section Results: the “Energy Landscape” for more details).

Starting from this initial structure, a number of PES explorers (3 in the diagram below) will set off in random directions exploring the potential energy surface and looking for nearby critical points.

Explorers have “stop conditions” (e.g. a maximum number of steps or a maximum energy above the starting point) so in general not all explorers will successfully find a critical point. In this case, only one of the explorers found relevant critical points: a saddle point and a local minimum. These newly found critical points are added to the Energy Landscape.

After the first expedition is over, the program will start with the second expedition. The starting point for the next expedition will be a randomly chosen local minimum from the list of minima present in the Energy Landscape (the possible starting points for an exploration are called seed states. See also the DynamicSeedStates option).

In this example, the starting point of the second expedition is the new local minimum found during the first expedition. A new set of explorers will set off in random directions from this point.

In the diagram above, one of the explorer found a saddle point that was already found in a previous exploration. This structure will not be added to Energy Landscape since it was already seen before (see the Structure comparison section for more details). The newly found critical points are added to the Energy Landscape.

Usually, many expeditions and/or many explorers are needed to map the PES, but you should keep in mind that the computation time of the calculation will roughly be proportional to the product NumExpeditions x NumExplorers.

By having many explorers you will have a higher chance of comprehensively mapping the PES near the starting point of each expedition. By having many expeditions, you will have a higher chance of traveling further away from the initial structure.

It should be emphasized that the PES exploration task is stochastic in nature, as it uses random numbers to perform initial-displacements. This means that if you run the same calculation twice you might find different critical points.

Job selection and main options¶

To use one of the PES Exploration procedures you should set the Task to PESExploration and specify one of the jobs in the PESExploration%Job key:

Task PESExploration

PESExploration
   Job [ProcessSearch | BasinHopping | SaddleSearch | LandscapeRefinement | BindingSites]
End

The input options for the various jobs are described in the corresponding sections: Process Search, Basin Hopping, Saddle Search, Landscape Refinement, Binding Sites.

It is then important pick an appropriate number of expeditions and explorers. Having many expeditions and explorers will result in a more comprehensive PES exploration, but since the computation time will roughly be proportional to the product NumExpeditions x NumExplorers you’ll need to find an appropriate balance.

PESExploration
   NumExpeditions integer
   NumExplorers integer
   DynamicSeedStates Yes/No
End

PESExploration

Type:	Block
Description:	Configures details of the automated PES exploration methods.

NumExpeditions

Type:	Integer
Default value:	1
Description:	Sets the number of subsequent expeditions our job will consist of. Larger values result in a more comprehensive exploration of the potential energy surface, but will take more computational time.

NumExplorers

Type:	Integer
Default value:	1
Description:	Sets the number of independent PES explorers dispatched as part of each expedition. Larger values will result in a more comprehensive exploration of the potential energy surface, but will take more computational time. By default an appropriate number of explorers are executed in parallel.

DynamicSeedStates

Type:	Bool
Default value:	Yes
Description:	Whether subsequent expeditions may start from states discovered by previous expeditions. This should lead to a more comprehensive exploration of the potential energy surface. Disabling this will focus the PES exploration around the initial seed states.

The following miscellaneous input option generally apply to most PES exploration calculations:

PESExploration
   WriteHistory [None | Converged | All]
   Temperature float
   FiniteDifference float
End

PESExploration

Type:	Block
Description:	Configures details of the automated PES exploration methods.

WriteHistory

Type:	Multiple Choice
Default value:	Converged
Options:	[None, Converged, All]
Description:	When to write the molecular geometry (and possibly other properties) to the history on the ams.rkf file. The default is to only write the converged geometries to the history. Can be changed to write no frames at all to the history, or write all frames (should only be used when testing because of the performance impact). Note that for parallel calculations, only the first group of processes writes to ams.rkf.

Temperature

Type:	Float
Default value:	300.0
Unit:	Kelvin
Description:	The temperature that the job will run at. This may be used in different ways depending on the job, e.g. acceptance probabilities for Monte-Carlo based jobs, thermostatting for dynamics based jobs, kinetic prefactors for jobs that find transition states. Some jobs may not use this temperature at all.

FiniteDifference

Type:	Float
Default value:	0.01
Unit:	Angstrom
Description:	The finite difference distance to use for Dimer, Hessian, Lanczos, and optimization methods.

Results: the “Energy Landscape”¶

The results of a PES Exploration are the structures and energies of the critical points found. There are multiple ways for you to inspect the results:

• The energy landscape can be visualized using the AMSMovie GUI module (In AMSMovie: File → Open and select the ams.rkf file of your calculation). See the GUI tutorials (e.g. Automated reaction pathway discovery for hydrohalogenation) for more details.
• The results are printed to the text output under the header Final Energy Landscape, see below.
• The results are stored on the ams.rkf binary results file in the section EnergyLandscape
• In PLAMS, you can use the get_energy_landscape method of the AMSResults object to conveniently extract the results.

----------------------
Final Energy Landscape
----------------------

      Id        Energy(a.u.)         RE(eV)   RE(kcal/mol)    Counts    Crit. point
   --------------------------------------------------------------------------------
       1           -5.782789        0.00000         0.0000         4            Min
       2           -5.748792        0.92510        21.3334         4            Min
       3           -5.689025        2.55143        58.8375         4             TS  1 <--> 2

Number of configurations                             3
Number of local minima                               2
Number of transition states                          1
Energy range (a.u.)                           0.093763
Energy range (eV)                              2.55143
Energy range (kcal/mol)                        58.8375

Configurations
--------------
3
Id 1 Energy(hartree)     -5.78278852 isTS=False
H       -5.05604362312999       1.04394551246415       0.36836337958238
C       -4.06812264817497       0.95005534859126      -0.01533183100739
N       -3.00601476684712       0.84907755770632      -0.42810754191928
3
Id 2 Energy(hartree)     -5.74879169 isTS=False
H       -4.01886309319822       1.09046314142766       1.01610923624838
C       -4.06910389782095       0.79751242545583      -1.12016730790896
N       -4.04221404713293       0.95510285187825       0.02898207831626
3
Id 3 Energy(hartree)     -5.68902502 isTS=True
H       -4.51488871821561       1.04261603660424       0.52096081259126
C       -4.32990923520194       0.88203060069718      -0.58636688911847
N       -3.28538308473452       0.91843178146029      -0.00966991681712

Continue a PES exploration from a previous calculation¶

You can load an Energy Landscape obtained from PES exploration calculation and use it as starting point for a new PES exploration. In this way you can extend your Energy Landscape, and potentially use different PES exploration algorithms.

To load a previously computed energy landscape, use the PESExploration%LoadEnergyLandscape%Path option (note: you should still provide an input system in the System block even if you are loading a previous Energy Landscape. The input system will be optimized and added to the energy landscape as a minimum).

It is often convenient to load only some of the states from a previous calculation; this can be done via the Remove or KeepOnly input options. Specify the seed states with the SeedStates option.

These are all the input options related to the loading an Energy Landscape:

PESExploration
   LoadEnergyLandscape
      KeepOnly integer_list
      Path string
      Remove integer_list
      SeedStates integer_list
   End
End

PESExploration

LoadEnergyLandscape

Type:	Block
Description:	Options related to the loading of an Energy Landscape from a previous calculation.

KeepOnly

Type:	Integer List
GUI name:	List of states to keep
Description:	Upon loading the Energy Landscape, only keep the states specified here. The states should be specified via a list of integers referring to the indices of the states you want to keep.

Path

Type:	String
GUI name:	Load energy landscape from
Description:	The path to load an energy landscape from. Accepts either AMS result folders, or .con files in the native EON format (only available through the text input file).

Remove

Type:	Integer List
GUI name:	List of states to remove
Description:	Upon loading the Energy Landscape, remove (i.e. do not load) the states specified here. The states should be specified via a list of integers referring to the indices of the states you want to remove (i.e. the states you don’t want to load).

SeedStates

Type:	Integer List
GUI name:	List of seed states
Description:	By default when you start a new PES Exploration from a loaded Energy Landscape, expeditions can start from any of the loaded minima. By using this input option, you can instruct the program to only use some of the states as ‘expedition starting point’. The states that serve as ‘expedition starting points’ should be specified via a list of integers referring to the indices of the states.

Troubleshooting¶

The PES exploration in AMS is quite sensitive to noise on the potential energy surface. A too noisy PES may result in bad convergence of the individual explorers, or states being rejected because their PES point character is not the expected one.

In case of problems we therefore advise to set engine options that result in a smoother PES. Often this can be accomplished by setting the NumericalQuality keyword in the engine input.

Especially the ReaxFF engine has a rather noisy PES by default, which may cause problems in a PES exploration job. Please refer to the ReaxFF manual for advice on how to smoothen the ReaxFF potential energy surface:

• ReaxFF manual: Smoothened potential energy surface
• ReaxFF manual: Geometry optimization issues

Structure comparison¶

During a PES exploration some critical points will most likely be encountered more than once.

Whenever a critical point is found, the program will ask itself: is this a new structure, or have I already encountered this before? If the structure was not seen before (i.e. it’s a novel configuration), it will be added to the list of structures found during the exploration. If the structure was already found before, the program will simply increase a counter keeping track of how many times a specific structure was found during the PES exploration.

When deciding if two structures are the same or not, the program will compare both the geometry and the energy of the two configurations. Several parameters and thresholds can be tweaked in the PESExploration%StructureComparison block to tell AMS under which conditions two systems should be considered equal.

PESExploration
   StructureComparison
      CheckRotation Yes/No
      CheckSymmetry Yes/No
      DistanceDifference float
      EnergyDifference float
      IndistinguishableAtoms Yes/No
      NeighborCutoff float
      RemoveTranslation Yes/No
   End
End

PESExploration

StructureComparison

Type:	Block
Description:	Settings for structure comparison.

CheckRotation

Type:	Bool
Description:	Rotates the system optimally before comparing structures. The default is to do this only for molecular systems when there are no fixed atom constraints.

CheckSymmetry

Type:	Bool
Default value:	No
Description:	Considers that two systems are equal if they are equivalent by symmetry.

DistanceDifference

Type:	Float
Default value:	0.1
Unit:	Angstrom
Description:	If the distance between two mapped atoms is larger than this threshold, the two configurations are considered different structures.

EnergyDifference

Type:	Float
Default value:	0.01
Unit:	eV
Description:	If the energy difference between two configurations is larger than this threshold, the two configurations are considered to be different structures.

IndistinguishableAtoms

Type:	Bool
Default value:	Yes
Description:	If yes, the order of the atoms does not affect the structural comparison. Atoms of the same element are then indistinguishable.

NeighborCutoff

Type:	Float
Default value:	3.3
Unit:	Angstrom
Description:	Atoms within this distance of each other are considered neighbors.

RemoveTranslation

Type:	Bool
Description:	Translates the system optimally before comparing structures. The default is to do this only when there are no fixed atom constraints.

Process Search job¶

Task PESExploration

PESExploration
   Job ProcessSearch

   ProcessSearch
      # Options for the Process Search procedure. See description below.
   End

   SaddleSearch
      # Options for the Saddle Search part of the Process Search procedure.
   End
End

PESExploration
   ProcessSearch
      MinimizationOffset float
   End
End

Saddle Search job¶

Task PESExploration

PESExploration
   Job SaddleSearch

   SaddleSearch
      # Options for the Saddle Search procedure. See description below.
   End
End

PESExploration
   SaddleSearch
      ConvergedForce float
      DisplaceAtomsInRegion string
      DisplaceMagnitude float
      MaxEnergy float
      MaxIterations integer
      MinEnergyBarrier float
      MinModeMethod [dimer | lanczos]
   End
End

Basin Hopping job¶

Task PESExploration

PESExploration
   Job BasinHopping

   Temperature float

   BasinHopping
      # Options for the Basin Hopping procedure. See description below.
   End
End

PESExploration
   BasinHopping
      DisplaceAtomsInRegion string
      Displacement float
      PushApartDistance float
      Steps integer
   End
End

Fragmented states¶

When studying adsorption processes, it is required to review those situations where a transition state (TS) does not mediate the adsorption process. They are formally known as non-activated exothermic adsorption processes. These processes are not discovered naturally in the PES exploration. Since the AMS2022 release, there is a systematic way of including those processes. To this aim, we defined the fragmented states, where the adsorbate and adsorbent are infinitely far away from each other.

The fragmented states can be included in the Energy Landscape through the use of the CalculateFragments keyword:

PESExploration
   CalculateFragments Yes/No
End

PESExploration

CalculateFragments

Type:	Bool
Default value:	No
Description:	Must be used together with an adsorbent set as the StatesAlignment%ReferenceRegion. Runs a final calculation of the adsorbate and adsorbent (marked by the ReferenceRegion) individually. The fragmented state is included in the energy landscape.

The keyword has to be used together with a reference region set via the StatesAlignment%ReferenceRegion keyword. The calculation of the fragmented states will happen at the very end of a PES exploration. For every minimum in the energy landscape, two geometry optimizations will be performed: one with only the atoms belonging to the reference region (the adsorbent), the other with only the atoms outside of the reference region (the adsorbate). This relaxes the structure of the adsorbent in the absence of the adsorbate, and vice versa.

The total energy of the fragmented state is then simply taken as the sum of the energies of both fragments, and the adsorption energy is the difference between the adsorbed and fragmented state.

You will find fragmented states and the fragments in the text output following the Final Energy Landscape section. The example shown above would look like this:

----------------------
Final Energy Landscape
----------------------

        Id        Energy(a.u.)         RE(eV)   RE(kcal/mol)    Counts    Crit. point
     --------------------------------------------------------------------------------
         1           -7.651642        0.00000         0.0000         1            Min
         2           -7.651572        0.00191         0.0441         1            Min
         3           -7.623820        0.75709        17.4589         1            Min
         4           -7.622548        0.79170        18.2571         7             TS 2<-->3
         5           -7.622430        0.79491        18.3310         5             TS 3<-->1

Number of configurations                             5
Number of local minima                               3
Number of transition states                          2
Energy range (a.u.)                           0.029212
Energy range (eV)                              0.79491
Energy range (kcal/mol)                        18.3310

Fragments
---------

Number of fragments                                  2

        Id             Formula        Energy(a.u.)              Region
     -----------------------------------------------------------------
         1                  CO           -0.424454              active
         2                Pt36           -7.154286             surface

Fragmented States
-----------------

Number of fragmented states                          1

        Id           Fragments        Energy(a.u.)         RE(eV)   RE(kcal/mol)
     ---------------------------------------------------------------------------
         1                 1,2           -7.578740        1.98377        45.7467 -->1
                                                                                 -->2
                                                                                 -->3

Notice the following: 1) one fragment may be included in multiple fragmented states, and 2) multiple states may be connected to the same fragmented state. The latter happens when the individual optimizations of adsorbate and adsorbent yield the same results for multiple states. By definition, these states are considered connected if the difference in energy is lower than PESExproration%SaddleSearch%MaxEnergy, which by default is 20.0 eV. Interestingly, you may find, for example, that an adsorbed fragment is in multiple fragmented states together with different surface defects. In other words: the adsorbed fragment is always the same when you remove it from the surface, but the surface may look different, depending on the geometry from which the adsorbent is removed.

The following figure shows a graphical representation of the energy landscape of the example above (made with amsmovie). The blue line represents the fragmented state.

Landscape Refinement¶

The LandscapeRefinement Job can be used to re-optimize the critical points (local minima and saddle points) found in a previous PES exploration calculation using a different engine or different engine settings.

Since PES exploration calculations can be computationally demanding, a possible strategy is to first perform a PES exploration using either a fast engine or computationally cheap settings for the engine of choice, and then to refine the energy landscape obtained using a more accurate (and computationally more expensive) method.

The LandscapeRefinement job needs a previously computed Energy Landscape. See the section Continue a PES exploration from a previous calculation for more details.

To perform a Landscape Refinement calculation you should specify:

Task LandscapeRefinement

PESExploration
   Job LandscapeRefinement

   LoadEnergyLandscape
     Path path/to/previous/calculation/ams.results
   End
End

Optimizer¶

Geometry optimizations are performed for most PES Explorations job types. In the PESExploration%Optimizer block you may configure some of the parameters for these geometry optimizations:

PESExploration
   Optimizer
      ConvergedForce float
      MaxIterations integer
      Method [CG | QM | LBFGS | FIRE | SD]
   End
End

PESExploration

Optimizer

Type:	Block
Description:	Configures the details of the geometry optimizers used by the PES explorers.

ConvergedForce

Type:	Float
Default value:	0.005
Unit:	eV/Angstrom
Description:	Convergence threshold for nuclear gradients.

MaxIterations

Type:	Integer
Default value:	400
Description:	Maximum number of iterations allowed for optimizations.

Method

Type:	Multiple Choice
Default value:	CG
Options:	[CG, QM, LBFGS, FIRE, SD]
Description:	Select the method for geometry optimizations.

Binding Sites¶

Binding sites can be determined from an Energy Landscape.

When computing binding sites you will first need to define a reference region, which typically will be a surface or a cluster (regions can be specified in the system input block, or via the “Model → Regions” panel in AMSinput). AMS will then go though all the local minima of Energy Landscape and mark as ‘binding sites’ the positions where an atom of an adsorbed molecule is neighboring atoms in the reference region.

For instance, in Example: PES Exploration, Binding Sites for O on Pt 111, the platinum surface is the reference region, while the oxygen atom is the adsorbate. In the picture below, you can see the oxygen binding sites on the platinum 111 surface (the two different types of binding sites are marked by a blue square and a red triangle respectively).

Lines connecting the the binding sites will be drawn if 1) there is a transition state connecting two local minima associated to these binding-sites (notice that may there are multiple local minima associated with the same binding site), and 2) there is at least an atom (from the adsorbate region) that changes its position from the first binding site to the second one mediated by the same transition state described above. In this process, AMS will align as much as possible all local minima and transition states to the input’s file structure but ignoring the atoms in the region adsorbate trying to establish a common reference frame (see also the StatesAlignment input block below).

PESEXploration
  Job [ProcessSearch | BasinHopping | LandscapeRefinement]

  BindingSites
    Calculate Yes
  End

  StatesAlignment
    ReferenceRegion reference_region_name
  End
End

PESEXploration
  Job BindingSites

  LoadEnergyLandscape
    Path path/to/previous/calculation/ams.results
  End

  StatesAlignment
    ReferenceRegion reference_region_name
  End
End

PESExploration
   BindingSites
      AllowDisconnected Yes/No
      Calculate Yes/No
      DistanceDifference float
      NeighborCutoff float
   End
End

PESExploration
   StatesAlignment
      DistanceDifference float
      ReferenceRegion string
   End
End

References¶