Automated Two Step Structure Prediction within GPAW

Transcription

1 Automated Two Step Structure Prediction within GPAW (a) c d e Lasse B. Vilhelmsen and Bjørk Hammer

2 Why We Need Automated Methods !E = "4.2 ev!e = "3.8 ev!e = "3.6 ev J. Wang and B. Hammer, Top. Catal. 44, 49 (2007) H. Häkkinen, S. Abbet, A. Sanchez, U. Heiz, and U. Landman, Angew. Chem. 42, 1297 (2003). A. Sanchez et al., J. Phys. Chem. A 103, 9573 (1999).

3 Genetic Algorithms! A method for finding global minima! Follows a Darwinian evolution scheme! Based on physical intuition and no formal convergence criteria # $&' $ %&' % %&' $ $&' #! " # $ % % $ $ # # " "!! $ # "!

4 Genetic Algorithms Generate random start population

5 Genetic Algorithms Generate random start population Select two parents for mating

6 Genetic Algorithms Generate random start population Select two parents for mating Mate the parents and perhaps mutate

7 Genetic Algorithms Generate random start population Select two parents for mating Mate the parents and perhaps mutate Relax to local minimum

8 Genetic Algorithms Generate random start population Select two parents for mating Mate the parents and perhaps mutate Relax to local minimum Adopt the structure in to the population

9 Encountered Au 8 structures

10 Au 8 Structures -4.50eV -4.00eV -3.50eV P1 P2 M1 L1 L2 L LB Vilhelmsen and Bjørk Hammer, PRL 108, (2012)

11 Two Step Optimization Technique Generate random start population Select two parents for mating Mate the parents and perhaps mutate Relax to local minimum Adopt the structure in to the population

12 Two Step Optimization Technique Relax with the LCAO basis Is the structure any good? Generate random start population Select two parents for mating Relax with the grid basis Yes No Mate the parents and perhaps mutate Adopt the structure in to the population

13 CPU Time Used A structural comparison removes 75% of the 63 structures steps before FD relaxation. 55 steps 44 CPU hours 572 CPU hours Net speedup of 7 Speedup of 3 17 steps 148 CPU hours

14 Au, Pd and Au/Pd in MOF-74

15 Parallelization Database (MySQL) Queuing System

16 Parallelization Frontend Generate population Check if Jobs need to be started Database (MySQL) Queuing System

17 Parallelization Frontend Generate population Check if Jobs need to be started Database (MySQL) Queuing System Generate new structures and submit them

18 Parallelization Frontend Generate population Check if Jobs need to be started Generate new structures and submit them Database (MySQL) Queuing System Job at Node Read Configuration

19 Parallelization Frontend Generate population Check if Jobs need to be started Generate new structures and submit them Database (MySQL) Queuing System Job at Node Read Configuration Relax while checking for uniqueness Mark configuration as relaxed

20 The Challenge of Testing A GA run includes many random factors Only multiple runs can test the performance

21 The System To Test With Density Functional Tight Binding calculations (DFTB) Ti 6 O 12 cluster random configurations only come within 0.66 ev of the best configuration

22 Distribution of Attempts

23 Importance of Population Size

24 Should We Use Mutations?

25 Conclucions! Energies and forces correlate well between the LCAO and FD bases! The GA is highly successful in predicting structures across many different system types! Using fast methods one can investigate the GA performance

26 Acknowledgements Thank you for your attention!

27 Successes cluster. reducing the lowest coordination of atoms in the cluster. The four added Pd atoms thus both increase the deformation of the UiO-66 framework and reduces the internal coordination of the Having established that Pd 28 is the largest cluster that can be confined to the A cage, we now consider clusters extending out of this cage. It is advantageous to exploit the periodicity of the UiO-66 structure to simulate a high Pd loading. A computational cell containing one unit cell of UiO-66 has two (a) A cages and one B cage. That means that four of the eight windows into the B cage are from the same A cage. Keeping one A cage in the cell filled with Pd 28 allows us to investigate the energetics of localized cluster size considered. connecting a network of A cages through B cages. e tested. The B cage is indicated Figure 6 shows the structure of the most stable Pd 12 and Pd 16 clusters in the B cage when one of the A cages in the cell is Vilhelmsen, L.B., et al., PRL (color online). Relevant structures and potential energies of Au 8 =F=MgOð100Þ as determined in two independent GA runs, elf-consistent PBE run (upper energy axis), and one self-consistent M06-L run (lower energy axis). In the PBE run, structures A gh D were found (upper solid red/gray arrows) while in the M06-L run, only structures B and C were found (lower solid red/gray s). The stability of A and D with M06-L is indicated for comparison (lower solid black arrows) as is the stability of structures E with either functional (dashed arrows). Structures D, E, and F are reported in [34], [9], and [6], respectively c d e Vilhelmsen, L.B. et al. JACS, 2012 Bechstein, R. et al., PRL 2012 Vilhelmsen, L.B. et al. JPCL, 2012 Figure 6. Pd 12 (left) and Pd 16 (right) adsorbed in the B type cage Martinez, U., et al., PRB 2011 together with Pd 28 adsorbed in the A type cage. The truncated Pd 28 cluster in the A-type cage is marked with bright semitransparent increasingly large Pd clusters in spheres. Figures 2, 3 and 6 and in the SI

28 Similiarity Criteria!E i = 0.7meV d max,i =1.026Å d rel,i = Energy criteria: d i = E j! E i > "E for all E j Structural criteria: d rel,i = " k D i (k)! D j (k) " k D i (k) < d rel and d max,i = max( D i! D j ) < d max