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Table of Contents

Table of ContentsAdvanced device relaxation - manual workflow

IntroductionPreparationsElectrode relaxationCentral region relaxation1DMIN optimization of the interface using 2-probe calculationsInfographics

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Advanced device relaxat ion - manual workf lowAdvanced device relaxat ion - manual workf low

In this tutorial you will learn how to use a combinat ion of “Rigid” const raints and a simple opt imizat ionrout ine to perform eff icient and reliable relaxat ion of the internal coordinates in a device configurat ion.

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In the O-2018.6 release, we int roduced a so-called Study Object to automate the workflows describedin this tutorial. That is now the recommended way of performing device geometry opt imizat ions inQuantumATK, and if you have access to O-2018.06 or newer, you should go to the correspondingtutorial Relaxat ion of devices using the Opt imizeDeviceConfigurat ion study object . Users of previousversions can st ill perform the calculat ions using the more complex workflow, that is described here.

In t roduct ionIn t roduct ion

Relaxat ion of the internal coordinates of device configurat ions can be a tedious and t ime consuming task.There are two main reasons for this:

The 2-probe configurat ion consists of three dist inct regions: Two elect rodes and a cent ral regionconsist ing of elect rode extensions and a scat tering region. The geometry of each region should beseparately opt imized in a f irst -principles manner, but both elect rode extensions in the cent ral region mustalways match the corresponding elect rode.

St ep 1:St ep 1: Opt imize the elect rodes. After opt imizat ion of the elect rodes, it is important to make sure thatthe elect rode extensions in the cent ral region match the opt imized elect rodes.

St ep 2:St ep 2: Opt imize the cent ral region. The opt imum length of the cent ral region is usually not known a priori.

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In the case of a periodic bulk, one would minimize the st ress tensor. However, the st ress f ield is notuniquely defined for a device configurat ion, so another approach is needed.

In the second step, we must rely on minimizing the device total energy while explicit ly preserving theinternal coordinates of the elect rode extensions. There are at least two different ways to do this usingQuantumATK.

BRR met hodBRR met hod

After building the 2-probe configurat ion from fully relaxed elect rodes, you ext ract the cent ral region bulkand relax it with “Rigid” const raints on the atoms belonging to the elect rode extensions. The device orinterface is then reassembled from the relaxed bulk. This is a computat ionally eff icient approach and willusually capture a large fract ion of the required geometry relaxat ion. We shall refer to this method as BulkRigid Relaxat ion (BRR).

The BBR method does not calculate the total energy using a full device geometry, so the reassembleddevice may not be exact ly in the global minimum-energy geometry. Some types of elect ronic st ructurecalculat ions may be sensit ive to this difference, others may not .

1D minimiz at ion1D minimiz at ion

A somewhat more brute-force approach is to explicit ly minimize the device total energy wrt . internalcoordinates and the cent ral region length, i.e., do the full 2-probe calculat ions and vary the cent ral regionlength. This is a 1D minimizat ion problem with relaxat ion of the atomic posit ions at each step, so we shallrefer to this method as 1DMIN. We have developed a procedure for doing this as eff icient ly as possiblewith QuantumATK, but the computat ions are in general more demanding than with BRR. It is thereforerecommended to use 1DMIN only after pre-relaxing the cent ral region with the BRR method.

This tutorial int roduces the elect rode relaxat ion and the cent ral region relaxat ion using BRR and 1DMINmethods. The methods are illust rated for relaxing a silver-gold interface using a classical potent ial. Theclassical potent ial is selected for computat ional convenience, and the same procedure could be used foranother relaxat ion method like DFT. In general we recommend to check ATK-ForceField calculat ions withDFT calculat ions.

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We have prepared a graphical explanat ion of the steps out lined above. You can see and download theinfographic of the present tutorial at the Infographics paragraph.

Preparat ionsPreparat ions

First make a new project called ‘device_relaxat ion’. Our start ing point is an unrelaxed 2-probe deviceconfigurat ion. It was created using the QuantumATK Interface Builder follow the tutorial at this link:Building an interface between Ag(100) and Au(111). The geometry can also be downloaded as this f ile: Ag_Au_ interface.py.

Save the py-f ile in your project folder, locate the device configurat ion on the LabFloor, and drag-and-dropthe configurat ion to the BuilderBuilder.

The 2-probe configurat ion should look like the one illust rated below. It consists of a left elect rode,Ag(100), the cent ral region, and a right elect rode Au(111). Use the plugin to split the device into a leftelect rode, right elect rode and central region.

Elect rode relaxat ionElect rode relaxat ion

The device geometry was constructed using the interface builder (Building an interface between Ag(100)and Au(111)). Prior to building the interface the left and right crystal st ructures were set up using theirexperimental geometries. We will assume that the experimental geometry is also the lowest energyst ructure of the theoret ical method we will use for relaxing the device geometry.

In the interface builder we choose “St rain second surface” upon select ing the surface cell. This meansthat the Ag(100) surface was kept in its experimental geometry, while the Au(111) surface was st rained inthe x,y direct ions upon forming the interface. When the crystal is st rained in the x,y direct ions, it will relaxin the z-direct ion according to the Poisson rat io of the material.

In the following we will apply this relaxat ion to the Au(111) crystal, by relaxing the st ress in the z-direct ionwhile keeping the x, y direct ions f ixed. The obtained relaxat ion of Au(111) will be t ransferred to the goldatoms in the cent ral region.

Open the builder and change the name of the right elect rode to Au111. Double click the geometry to makeit act ive and send it to the Script erScript er. Add the following objects:

New Calculator Opt imizeGeometry

Now open the New Calculator object and select the AT K- ForceFieldAT K- ForceField “EAM_Zhou_2004” potent ial. ClickOK.

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For QuantumATK-versions older than 2017, the AT K- ForceFieldAT K- ForceField calculator can be found under thename AT K- ClassicalAT K- Classical.

Next open the Opt imize Geometry object :

1. Set the force tolerance to 0.012. Set the st ress tolerance to 0.0013. Uncheck z in the “Constrain cell” checkboxes

Send the script to the Job Manager and run the relaxat ion. It should take less than a minute toexecute. When f inished inspect the log f ile.

You should now see a new object on the LabFloorLabFloor called “Au111.hdf5”. It contains two configurat ions,corresponding to the geometry before and after the relaxat ion. Select the two geometries and drop themonto the ViewerViewer. In the viewer you can hoover the mouse over the unit cell of each configurat ion andyou will not ice that the length of the C vector is 7.064 Å before the relaxat ion and 7.011 after therelaxat ion. This informat ion could also be obtained from the log f ile, “Au111.log”.

The relaxat ion results in a small compressive st rain of 0.75%. To apply this to the cent ral region, open theBuilder and double click the cent ral region configurat ion.

1. Rename the stash item to “cent ral”.2. Select all the gold atoms by drawing a rectangle around them.3. Open the Bulk Tools ‣ St retch Cell plugin.4. Enter 0.9925 along the C axis.5. Use “Selected atoms are” st retched.6. Click Apply.

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The st rain is so t iny that it is not possible to see any visual change in the st ructure. However, you mayopen the “Lat t ice Parameters..” plugin and click the and but tons to see how the C cell vectorchanges when you undo and redo the st retch. Similarly, you can inspect the Coordinate List .

Cent ral reg ion relaxat ionCent ral reg ion relaxat ion

You are now going to relax the cent ral region only. We want the elect rode extensions to be able to movefreely (but rigidly) during geometry relaxat ion. We therefore add vacuum on both ends:

Make sure that no atoms are selected, by clicking the background of the plot t ing window. In Bulk Tools ‣Stretch Cell use the C-vector slider to increase the cell length by 30% or simply type in a mult iplicat ionfactor of 1.3. The cell is st retched once you click Apply.

Move to Coordinate Tools ‣ Center and uncheck A and B. Center the cent ral region by clicking Apply.

We want to f ix the atoms in the elect rode extensions by including an addit ional layer of the cent ral region.The addit ional layer will help the Device from Bulk tool in QuantumATK to ident ify the length of theelect rode. For this purpose select the 5 outermost silver atoms. Open Select ion Tools ‣ Tags. Enter Lef tLef tin the box named “Click here to write a new tag...”. Press Return.

Next select the 4 outermost gold atoms, and tag them RightRight .

Send the configurat ion to the Script Generat orScript Generat or and set up the calculat ion:

Add a New Calculator and an Opt imizeGeometry object .

Choose the ATK-ForceField engine and the “EAM_Zhou_2004” potent ial for these calculat ions.

Make the following changes to the Opt imizeGeometry object :

1. Set the force tolerance to 0.01 eV/Å.2. Check “Save t rajectory” and set the f ilename to central.hdf5 .3. Click “Add Constraints” to set up the Rigid constraints on the elect rode extensions.4. Check that the Left and Right tags are assigned to the correct atoms in the configurat ion. Do this by

clicking the tags. Choose “Rigid” const raints for both tags.5. Click OK and return to the Scripter.

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Choosing instead a “Fixed” const raint for one of the tagged regions while keeping the other one “Rigid”,may save BFGS relaxat ion steps and thereby computat ional t ime.

Send the script to the Job ManagerJob Manager and run the calculat ion. It should be very fast . Once f inished, thecentral.hdf5 output f ile appears on the LabFloorLabFloor.

You can use the ViewerViewer plugin to see the t rajectory of the relaxat ion as illust rated in the animat ionbelow.

The relaxed central region is saved in central.hdf5 as the bulk configurat ion with id “glD002”. This is yourinit ial guess for the cent ral region geometry. Drag-and-dro it on to the BuilderBuilder.

Click Device Tools ‣ Device From Bulk to turn the central.hdf5 bulk into a device configurat ion. You canleave the set t ings for elect rode and central region lengths at default values.

The interface configurat ion should now look like illust rated below. Rename the configurat ion to “device” byusing F2 or with a right mouse-click.

1DMIN opt im izat ion of t he in t er face using 2- probe1DMIN opt im izat ion of t he in t er face using 2- probecalcu lat ionscalcu lat ions

We are now ready to search for the global minimum-energy geometry of the Ag(100)-Au(111) interface.Save the device configurat ion as a HDF5 f ile named device_in.hdf5 by choosing “Save as” after right -clicking the device Stash item.

You are now going to apply a simple SciPy minimiz at ionSciPy minimiz at ion procedure in search for the cent ral region lengththat minimizes the interface total energy. The device configurat ion you just saved in device_in.hdf5 isthe start ing point for this.

Two scripts are needed. You can download them here: device.py and opt imize.py. Save both scriptsin the folder where device_in.hdf5 was saved. The f irst script ( device.py ) reads in the deviceconfigurat ion and sets up and runs the calculat ion, while the second script ( optimize.py ) containsfunct ions and classes used by device.py .

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To use the script device.py for other systems you need to edit the script and change the definit ion ofthe potent ial to an appropriate potent ial for your new system.

Both scripts should now be available in the QuantumATK “Project Files” list . Drag-and-drop device.py ontoJobsJobs. The Job Manager will open. Click to run the script .

Once f inished (it ’s fast !), a window with the f igure below will pop up. The blue points are total energies ofrelaxed interface configurat ions. The init ial cell length is 28.51 Å and the other blue points are t rial guessesmade by the algorithm. The red point indicates the opt imum central region length which is 28.58 Å. Theopt imizat ion rout ine simply maps out the illust rated potent ial-energy surface and f inds its minimum!

The job will f inish when you close the pop-up window.

The relaxed configurat ions are saved in the output f ile device_out.hdf5 along with the total energies. Theconfigurat ion corresponding to the red point (the f inal device or interface geometry) is the latest deviceconfigurat ion (the one with largest id number).

Using the ViewerViewer plugin, the minimum-energy interface configurat ion looks like this:

In this case the change to the st ructure after the 1DMIN relaxat ion is minute compared to the BRRrelaxat ion. Often the BRR will be suff icient ly accurate and there is no need for the 1DMIN step. The 1DMINapproach is only needed for ext reme accuracy.

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