Binding energy of 2D materials using Quantum Monte Carlo

Ching-Ming Wei Institute of Atomic & Molecular Sciences,

Academia Sinica, TAIWAN

Quantum Monte Carlo in the Apuan Alps IX International Workshop, 26th July to 2nd August 2014

The Apuan Alps Centre for Physics @ TTI, Vallico Sotto, Tuscany, Italy

Support: MoST, Academia Sinica

Cheng-Rong Hsing (IAMS, 2002)

Quantum Monte Carlo Group at Taiwan

Cheng Ching (NCKU, 2007)

Chun-Ming Chang (NDHU, 2008) Ching-Ming Wei (IAMS, 2006)

Collaborators: Neil Drummond, Pablo Lopez Rıos, Richard Needs

魏金明 Wei, Ching-Ming 禾 standing grain

女 woman

鬼 ghost

金 gold

sun日 月moon

DFT + AIRSS will become one powerful tool to find structure minimums

Too many functionals!

DFT community does need a lot of benchmark results where QMC can contribute and help!

The CORRECT choice of Exchange-Correlation

Approximation is a “BIG” issue

in DFT !

QMC can provide help !

Good strategy for “poor” people (extremely CPU source limited) and “no interest” (actually no ability)

in the development of QMC method and theory is to tackle the subjects

related to material simulations with “big” difference when using

different ExC functionals.

VASP-PBE

Li, Na, K, Ca, Al, Ga, In, Sn, Ti, Fe, Pd, Au

IAMS

How about results from othe functional suchas LDA?

B C Si N O Al

adso

rptio

n en

ergy

(eV

)

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Sc Ti V Cr

Mn Fe Co Ni

Cu Zn Y Zr Nb

Mo Tc Ru

Rh

Pd

Ag

Cd La Hf

Ta W Re

Os Ir Pt

Au

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

LDA-V PBE-V PW91-V

Single atom @ graphene

LDA & GGA predict different adsorption energy at preferred adsorption site!

Except for Zn & Cd atom, the adsorption energy difference obtained by LDA and GGA is ranging from 0.4 ~ 1.8 eV.

QMC is needed to check the accuracy of exchange-correlation approximations !

IAMS

Single atom@graphene (DFT reults)

Need more accurate methods? QMC

CASINO code : QMC Methods R.J. Needs, M.D. Towler, N.D. Drummond and P. López Ríos, CASINO version 2.3 User Manual, University of Cambridge, Cambridge (2008).

http://www.tcm.phy.cam.ac.uk/~mdt26/casino2.html

*

3d8

4s2 3d10

4s

4d10

4d10

5s

5d9

6s 5d10

6s

Single atom @ graphene

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5Ni Pt Pd Cu Ag Au

adso

rptio

n en

ergy

(eV

)

LDA-CLDA-VPBE-VDMC

B T H B T H B T H B T H B T H B T H

CO adsorption on Pt(111) surface HCP FCC BRI TOP

Oxygen Carbon

Pt (1st layer)

Pt (2nd layer)

Pt (3rd layer)

If DFT will give a good description for the CO adsorption on late

transition metal (111) surfaces?

Experimental result : 88% top site 12% bridge site

[ref] Blackman, G. S. et al. Phys. Rev. Lett. 1988, 61, 2352

1. LDA & GGA results : FCC site 2. DFT w ith hybrid functionals:

TOP site is slightly favor than FCC site (∆Ε∼50 meV)

Times Cited: > 350

Experimental result : 88% top site 12% bridge site

[ref] Blackman, G. S. et al. Phys. Rev. Lett. 1988, 61, 2352

1. LDA & GGA results : FCC site 2. DFT with hybrid functionals : TOP site is slightly favor than FCC site (de~50 meV)

CO @ TM (1 1 1 ) surface – DFT- RPA

Except on Pd(111), CO adsorbs at Top

site, but LDA & PBE predict wrong sites!

CO @ Pt(1 1 1 ) – 400 electrons

DMC result : atop site Ead (fcc) = -0.73(6) eV Ead (bri) = -1.18(6) eV Ead (atop) = -1.57(6) eV

Exp. result : atop site ~ -1.5eV

CO @ Au(1 1 1 ) – 436 electrons

DMC result : atop site Ead (fcc) = -0.23(7) eV Ead (bri) = -0.36(7) eV Ead (atop) = -0.43(8) eV

Exp. result : atop site ~ -0.4eV

DMC input : 1. supercell : (θ(ML)=1/3) 2. time step = 0.01 3. number of moves = 30,000

3232 ×

Diffusion Monte Carlo can predict a correct adsorption site and adsorption energy.

But if there ex ists any simple reason for DFT to predict a w rong adsorption site?

CO @ Pt & Au (1 1 1 ) surface - DMC

Over-binding effect does not appear on Top-site, but showed on other sites, and led to wrong site prediction!

(In preparation)

http://www1.lsbu.ac.uk/water/phase.html

The phase diagram of water

One may ask: Why a“poor” guy like you jumping into so

expensive project which needs one meV/H2O accuracy? At that time, we are too stupid to know……

1kbar=100MPa

VASP-PBE result in 0 K

DFT calculation of Ice

Prof. J-L Kuo’s results

DMOL result

1. phase transition : Ih to III?? 2. transition pressure is 10 times larger

Structure of Ice

Ih II-112.82 hexagonal ice (P63/mmc, symmetry D6h)

rhombohedral crystals (R(-3)C, symmetry S6)

tetragonal crystals (Space group P 41 21 2)

III

VI tetragonal crystals (Space group P42/nmc)

II-113o

A6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0

C

5.4

5.6

5.8

6.0

6.2

6.4

6.6

6.8

7.0

7.2

-14.8 -14.7 -14.6 -14.5 -14.4

PES of Ice II

II-109o

A6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0

C

7.0

7.2

7.4

7.6

7.8

8.0

8.2

8.4

-14.82 -14.80 -14.78 -14.76 -14.74 -14.72 -14.70 -14.68 -14.66

relax volume

We are lucky enough to find one new phase, but can one find structural minimums in a more natural way?

AIRSS Application Bulk system : ICE II

AIRSS Process Random generation of O

atom positions and put constraints : specific symmetry Ice rule the distance between

oxygen atoms is sensible.

Random generation of H atom positions and put constraints : Ice rule the distance between O

and H atoms is sensible

DFT calculation

32

22

Totally 160 random structures

Exp. Structure II-112.82

rhombohedral crystals (R(-3)C, symmetry S6)

New BCC Structure

(bcc2)

New BCC Structure

(bcc1)

AIRSS Application Bulk system : ICE-II

~0.22eV

configurations

Tota

l ene

rgy

(eV

)

0 2 4 6 8 10 12 14 16 18-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.9

HSE06 LDA PBE0 PBE vdW86 DMC

ICE II to bcc phase transition barrier

reaction coordinate

eV

Finite size effect of QMC needs to be checked !

(In preparation)

van der Waals heterostructures

28

AK Geim & IV Grigorieva Nature 499, 419-425 (2013)

doi:10.1038/nature12385

The interaction energy of two BN films

More reliable method is needed: QMC

BN bilayer : supercell structure

c=30Å

d : bilayer distance

AA’ stacking Lateral : 3×3, 4x4

3×3 5Å

30

Interaction curve: DMC

31

σ < 2.5 meV/2BN (total E ~ -700 eV/2BN)

CPU > 5 million core-hours

2D systems

( )

( )

62 2 2

3 42 2

1

dxdy

x y d

rdrddr d

θ

+∞

−∞

+∞

−∞

+ +

= =+

∫

∫

33

66

44

for finite objects

for infinite parallel insulating shee

-

t- s

vdW

vdW

CErCEr

≈

≈

Long-Range behavior : D-4.5

34 3.5 4 4.5 5 5.5 6 6.5 7BN interlayer distance D ( )

1.5

3

10

20

3040506070

Mag

nitu

e of

inte

ract

ion

ener

gy (m

eV/2

BN

)

PBELDAvdW_DF2vdW_optPBEDMC(3x3)c30DMC(4x4)c30DMC(4x4)c30*

D-5.3

D-6

D- 4.5

D-10

D-5.3 vdW_optPBE D-4.5 DMC D-10 LDA D-6 vdW_DF2 D-10 PBE

The interaction energy of two BN films

Can Van der Waals functionals accounts for Binding Energy of 2D Layer Materials such

as graphene, BN flim, Silicene, MoS2?

The binding energy of silicene and graphene

Consider Morie Patterns w ith small lattice mismatch of hetero bilayer structures !

Silicene(√3x√3) / Graphene(√7x√7)

DFT-LDA optimized geometry is used in DMC calculation

1. DMC shows a little trend that LDA might have done a reasonable job !

2. Currently available Van der Waals functionals might not account for Binding Energy of 2D Layer Materials !

3. Doing a curve for each system is perhaps necessary !

After burning out more than one million core hours, the only thing that we learn

is we need at least ten million core hours to gain a little more understanding! It is too early to say…… !

Binding energy of 2D materials using Quantum Monte Carlo

Ching-Ming Wei Institute of Atomic & Molecular Sciences,

Academia Sinica, TAIWAN

Quantum Monte Carlo in the Apuan Alps XI International Workshop, 23th July to 30th July 2016

The Apuan Alps Centre for Physics @ TTI, Vallico Sotto, Tuscany, Italy

Support: MoST, Academia Sinica

See you in two years!