First Principle Study of Magnetic and Electronic Properties

8/8/2019 First Principle Study of Magnetic and Electronic Properties

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First principles study of anion doped perovskites

related SrMnO 3

Abdallah Abdelrahman M.

Ph.D. student


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Outline

W hat are the first principles calculation?How an ab initio calculation works

Hartree fock approximationdensity functional theory

W hat are perovskite

Ab initio modeling in solid state physics(CRYSTAL code)Result and discussion


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W hat are the first principlescalculation?

The world around us is made of condensed matter.

The prediction of the behaviour of systems(empirical or semi-empirical models)

Due to the complexity of condensed matter systems,and the difficulty in building accurate models, the

predictive power of such an approach can beseverely limited.


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the first principles(ab initio) calculation are

A method of calculating atomic and molecular structure directly from the first principles of quantum mechanics , without using quantitiesderived from experiment (such as ionization

energies found by spectroscopy) as parameters.


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How an ab initio calculationworks

Ab-initio calculations require a largeamount of numerical computation.the amount of computing time requiredincreases rapidly as the size of theatom or molecule increases.The development of computing power

has enabled the properties of bothsmall and large systems to becalculated accurately, so that this formof calculation can now replace semi-empirical calculations.


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Computational Methodology abinitio electronic structuremethods

The Schrdinger equation for manyelectrons

H is containing kinetic energy, externalpotential and electron-electron coulomb

interactions +kinetic energy and ions-ions interaction .

_ a _ a i I i I r R E r R H ;; =!=


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{

{

!

J I J I

J I I

I I

j i j i I i I i

I r

i e

e Z Z

M

r r

er

e Z m i

22

2

2

,

22

2

2

1

2

2

1

2

J

J

{{!

J I J I

J I

j i j i I i I i

I r

i e

e Z Z

r r

e

r

e Z

mi

22

,

22

2

2

1

2

1

2

J

T

And H can be written as

t ex V intV


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The Hartree ApproximationFor a legal wavefunction (antisymmetric,normalised)

- the total energy is

- and the single particle Hartree

{ d

!

==!

i i j j i j i i ex t

e

r i

H H H

r r e

r V m

H E

J J J J J J 1

22

222J

_ a N N i H r r r r J J J .......2211!=

r r r r

er V m i i i i j

j j ex t

e

r J I J J J !

-

d{

1

22

22J


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Hartree Fock Theory

An on set for the structure of wavefunction

_ a ? A N N i HF r r r N

r J J J .......de t!

12211!=

r r r r

e

r r r

er V m

i i

i j j i j

i

i j j j ex t

e

r

J I J J J

J J J

!d

-

d

{

{

1

1

2

2

222J


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Th e Hartree Fock Equations

{

{

dd!d

!

!

!

- d

ddd

dd

i j i i

j j i i ex i

j j

j j

i i i i j

ex i j ex t

e

r

r r

r r r r r r

r r

r r

r r r d r r

r r er d r r r er V

m

J J

J J J J V

V V

J V

J I J V V

,

,2

2

2222J

Non-interacting electrons under th e influence of mean field

potential consisting of classicalcoulomb potential and non-local

exch

ange potential


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Density functional theory

DFT the theoremsDFT theory is a theoreticalframework for treading thecomplicated interactions in an N-electron system leading to effectiveone-electron equations.

To find the exact ground stateenergy knowledge of the chargedensity (r) is enough !


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W hat are perovskites

The perovskite unit cell ABX 3 where the larger A cation isdepicted in green, the B cations are shown in white andthe X anions are shown in red.

CaTiO3


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A n expanded view of t h eperovskite structure


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A b initio Modeling in Solid StateP h ysics wit h

CRY S T AL C ode

The CRYSTAL package consists of two

executables: crystalperforms integrals calculation and SCF partcomputes total energy and wavefunction

performs geometry optimizationcalculates vibrational frequencies at G pointproperties

performs the wavefunction analysis (e.g. one-

electron properties)


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CRY S T AL input sc h eme

CRYSTAL input is given by keywords Itconsists of three sections:

0. Title1. Geometry input section2. Basis set input section

3. Method & SCF input section


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B asis set input section8 40 0 8 2. 0 1. 080 20 .0 0 .00 10 81338. 0 0 .00 80 4255.4 0 .0 532469.22 0 .168123.9 0 0 .35819.264 0 .38553.851 0 .14681.212 0 .7 28

0 1 4 6. 0 1. 049.43 - 0 .00 883 0 .00 95810 .4 7 -0 .0 915 0 .0 6963.235 - 0 .0 40 2 0 .2 0 651.21 7 0 .3 7 9 0 .34 7

0 1 1 0 .0 1. 00 .4 7 64 1. 0 1. 0

0 1 1 0 .0 1. 00 .18 0 2 1. 0 1. 0

99 0

1-Atomic number andnumber of shells

2-Basis set input:

2.1- code,

2.2-type, nr. of primitive,

2. 3-formal charge and

2.4-scale factor of theshell.


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CRY S T AL input D FT inputblock

D FTS P INB 3L Y PENDSH R INK6 6

S C FD IRMAX CYC L E12 0S P INL OC K0 12 0L EVSHIF T6 1FMIX IN G

30A T OMS P IN89 1 1 0 -1 11 1 12 -1 13 1 14 -1 15 1 16 -1PPAN

END

1-DFT input block

2- the system is spin-polarizedsystems

3-correlation and exchange

functionalEnd of the DFT input block

4-Reciprocal space integrationparameters

5- convergence utility

End of the Method input section


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CRY S T AL outputEEEEEEEEEE S T A RT IN G DA T E 18 07 20 10 T IME 1 0 :33:14.9SrMnO3 194 antferromagnetic ud

CRY S T AL C AL C ULA T ION(INP UT A CC OR D IN G T O T HE I N T ER NA T IONAL T A B L ES FO R X -R A Y

CRY S T ALL OGR AP H Y )CRY S T AL FA MIL Y : HE XA G ONALCRY S T AL C LA SS ( GR OT H - 1921) : D IHE XA G ONAL D IP YR A MIDAL

S PA C E GR OU P (C EN TR OS Y MME TR IC ) : P 63/M M C

LA TT IC E PA R A MET ER S ( AN G S TR OMS AND D EGR EES) - C ON VEN T IONAL C ELL

A B C ALP HA B ET A G A MMA5.4434 0 5.4434 0 9. 070 40 90 .00000 90 .00000 12 0 .00000

N UMB ER OF I RR ED UC IB L E A T OMS I N T HE C ON VEN T IONAL C ELL : 5

INP UT C OO R D INA T ES

A T OM A T . N . C OO R D INA T ES1 238 0 .000000000000 E+ 00 0 .000000000000 E+ 00 0 .000000000000 E+ 002 238 3.33333 0000000 E- 0 1 6.6666 70000000 E- 0 1 2.5 00000000000 E- 0 13 225 3.33333 0000000 E- 0 1 6.6666 70000000 E- 0 1 6.122 000000000 E- 0 14 8 5. 000000000000 E- 0 1 0 .000000000000 E+ 00 0 .000000000000 E+ 005 8 -1.8 07000000000 E- 0 1 -3.614 000000000 E- 0 1 2.5 00000000000 E- 0 1


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TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT MOQGAD TELAPSE 6567.71TCPU 6555.49TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT SHELLX TELAPSE 6650.92

TCPU 6638.60+++ ENERGIES IN A.U. +++

::: EXT EL-POLE -3.8645620245026E+03::: EXT EL-SPHEROPOLE 4.5938172844779E+01::: BIELET ZONE E-E 4.1965071955803E+03::: TOTAL E-E 3.7788334392249E+02::: TOTAL E-N + N-E -2.1603424670753E+03::: TOTAL N-N -5.9233952856580E+02::: KINETIC ENERGY 1.0698788970100E+03

::: PSEUDO TOTAL ENERGY -1.3049197547086E+03::: VIRIAL COEFFICIENT 9.0102703758549E-01TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT MONMO3 TELAPSE 6655.50

TCPU 6643.18NUMERICALLY INTEGRATED DENSITY 98.0349663745 98.0346135635TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT NUMDFT TELAPSE 6670.33

TCPU 6657.99

CYC 42 E T OT (A U) -1.43 77 17 84328 7 E+ 0 3 D ET OT -6. 0 6E- 0 8tst 9.51E- 0 9 PX 4.22E- 0 5

== S C F E ND ED - C ON VERG EN C E O N EN ERGY E( A U) -1.43 77 17 843286 7 E+ 0 3 CYC L ES 42


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GR AD IEN T N OR M 0 .000 86 7 GR AD IEN T T HR ESHO LD 0 .5 00000

P R ED ICT ED EN ERGY C HAN G E - 0 .459E- 0 6

MAX GR AD IEN T 0 .000 445 T HR ESHO LD 0 .000 45 0 C ON VERG ED Y ESR MS GR AD IEN T 0 .000 21 0 T HR ESHO LD

0 .000 300 C ON VERG ED Y ESMAX D IS PLA C . 0 .00 1365 T HR ESHO LD

0 .00 18 00 C ON VERG ED Y ESR MS D IS PLA C . 0 .000 413 T HR ESHO LD

0 .00 12 00 C ON VERG ED Y ES

C ON VERG EN C E T ES T S S A T ISFIE D A FT ER 17 EN ERGY AND GR AD IEN T C AL C ULA T ION S

******************************************************************* OP T END - C ON VERG ED * E(A U): -

1.43 77 19141 0 45E+ 0 3 P OIN T S 1 7 *


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OVE R LAP P OP ULA T ION C OND EN SE D T O A T OMS FO R

FIR S T 6 N EIG HB OR S4 S R ( 0 0 0 ) 6.352 3.361 0 .000A T OM A 9 O A T OM B C ELL R (A B )/A U R (A B )/AN G

OVP OP (A B )8 M N ( 1 0 0 ) 3.555 1.881 0 .0 236 M N ( 1 1 0 ) 3.555 1.881 0 .0 23

11 O ( 0 -1 0 ) 5.13 0 2. 7 15 - 0 .00 11 S R ( 0 0 0 ) 5.13 0 2. 7 15 0 .000

11 O ( 10

0

) 5.130

2.7

15 -0

.00

117 O ( 0 0 0 ) 5.153 2. 7 27 -0 .00 1


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R esults and discussion


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THANK FOR YOUR ATTENTION

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First Principle Study of Magnetic and Electronic Properties