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1 ab-initio calculation of structural properties of cubic ice Hadi Arabi Maryam Vahedi Physics Department Birjand University, Birjand, Iran Ali mokhtari Department of physics Isfahan University of Technology Isfahan Iran

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Page 1: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

ab-initio calculation of structural properties

of cubic ice

Hadi Arabi

Maryam VahediPhysics Department

Birjand University, Birjand, Iran

Ali mokhtariDepartment of physics Isfahan University of Technology

Isfahan Iran

Page 2: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Page 3: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Outline

1-Different phases of ice

2-Theoretical aspect of the work

3- Data analysis

4- Conclusions

Page 4: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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The most important matter in the world is water. 15% of the weight of Earth is water , and in the North and South ocean most of them is in the form of ice. Therefore physical and chemical properties, of different phases of ice are great important.

Page 5: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Diagram of various phases of ice

Page 6: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Table of different phases of ice with their relative parameters

Page 7: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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General ice with hexagonal structure (IceIh) between -80 up to 0 centigrade and general pressure

Page 8: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Structure of cubic ice between -130 up to -80 centigrade which is unstable . This phasecan be produced from phases II ,III ,VI,VII in liquid nitrogen temperature. In -100the cubic ice changes to Ih phase of ice.

Page 9: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Unit cell of cubic ice which shows only oxygen atoms . O-H-O bands are represented with orange lines

Page 10: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Relation between unit cell and layer structure in closed-packed of cubic ice

Page 11: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1Ice- II phase with rhombohedral structure

Page 12: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Cubic III-phase structure, oxygen atoms shows with blue circle which closer oxygen with bigger circle and O-H-O bands represented as red lines

Page 13: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Cubic V-phase with monoclinic structure. The unit cells are represented as cubic

Page 14: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Cubic VII phase composes of two structures of cubic Ice which represented one with red lines and the other with orange lines.

The conventional cell has 8 bcc cubic.

Page 15: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Cubic Ice

In this structure eight molecules of water are in the conventional cell.Number of configurations are 2**16.Bernell-Fowler rules are restricted the number of states.1) The distance between each oxygen and hydrogen atoms in a molecule is about 0.95 angstrom.2) Water molecule in unite cell stay in a position where only one hydrogen of each molecule is located between two oxygen atoms.3) Each molecule of water has surrounded by for other oxygen atoms. It is located somehow that always two hydrogen atoms pointed to two oxygen atoms.

Page 16: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Page 17: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Total dipole moments of each configurations of cubic ice structures which are 8,4√√√√2,4 and 0 respectively.

Page 18: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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The important of computational physics in solid state physics

1- Analysis of physical phenomena which are not possible to happen or if they happen, it is not possible to repeat them.2-Variation of parameters in a physical process in the direction and size of variation which are not normal.

Classic3-Many body system

Quantum

Page 19: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Born-Oppenhimer approximation

Nucleus in atoms are stable regarding to the motion of electrons

),...,,,,...,,(),...,,,,...,,( 21212121 αα ψψ RRRrrrERRRrrrH NN

������ =

nnetot EEE +=

NNeeNeNk

ek HHHHHH −−− ++++=

)()()( ieiee

eek rErHHH ψψ =++ −

)()()( αα ψψ RERHHH totalNN

eNk =++ −

Page 20: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Solution of Schrodinger equation for system of electrons

First we have to change equation of system of electrons to a sum of separate equations for each electron. There are two approaches for it:

1- Wave function is accepted as a variable parameter: Hartree and Hartree-Fock methods.

2- Density is considered as a variable parameter : Tomas Fermi and density functional theory

Page 21: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Hartree and Hartlee-Fock method:In this method the wave function of the system is considered as a multiplication of wave functions of single particles. Also we consider that each electron see an effective potential from nucleus and other electrons

)()...()(),...,,( 21321 Nrrrrrr������ ψψψψ =

)()()2

( 22

iiiiiext rrVm

��� ψεψ =+∇−

� � ′−′′

+−

−=α α

α

rr

rnrde

rr

ZerV

iext ��

��)(

)( 22

)()( �=i

ii rrn�� ψ

Page 22: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Density functional theory

This theory in 1964 presented by Kohn and Hohonberg.We can deduced all properties of a system in ground state using density of ground state.

Kohn and Sham in 1965 replace the equation of the system by groups of equations of single particles in the system.

� �� +−

′++= )]([)()(

2)()()]([)]([

2

rnErr

rnrnrdrd

edrrVrnrnTrnE XC

���

�������

Page 23: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Problems with single particle equationsVery large number of electrons in system:

Using Bloch theorem and choosing appropriate K in reciprocal lattice.

Wave function of a particle in level n with wave vector of K

)().exp()(,,

rurKirKnKn

������ =ψ )()(

,,Rruru

KnKn

����� +=

).exp()()(,

rGiGKcru

G

nKn

�����

� �′

+=

)]).(exp[)()(, rGKiGKcr

G

nkn

������

++=�′

ψ

Page 24: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Pseudo potential approximation

Area around the nucleus is divided to core and valance regions

Wave function of core electrons are localized in the region and play no role in ionic bonds.

Valance electrons in core region have high kinetic energy and their wave function has a lot of vibrations in the core which need a huge number of plane wave for their construction.

In summation plane wave those with low kinetic energy has more important. Therefore we can continue the extension of plane waves up to a certain value called cut off energy.

Page 25: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Wave function,pseudo wave function, real potential and pseudo potential are illustrated qualitatively

Page 26: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Properties of ad-initio pseudo potentials

Wave function and pseudo wave function of conduction valance band must coincide to each other out of core. Also potential andpseudo potential functions have the same properties.

Pseudo potential function is not localized outside core, which means it relates to L quantum number. We have to consider the charge conservation for both potential

and pseudo potentials inside the core.

�� =cc r

psl

r

l drrrdrrr

0

22

0

22)(4)(4�� ψπψπ

Page 27: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Wave scattering form core for potential and pseudo potential should be the same. This condition leads to continues of logarithmic derivative of wave function and pseudo wave function at r = rc

Page 28: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Kerker method

Pseudo wave function in the core region explained as:

)()()( 1 rfrrRrrF ll

l

���� ===

)()( rPrf ll

�� =)()( rP

llerf�� =

lllll rrrrP δγβα +++= 234)(�

Page 29: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

0))r(Pexp(r]E)r(Vr

)1l(l

dr

d[ l

1ll

psl22

2

=−+++− + ��

ccrrlrrl

1l )r())r(Pexp(r ==+ ψ=

��

])(

[)( 1+= lc

clcl

r

rLnrP

�� ψ

ccrrlrrl

ll

l rrPrrPrl==

+ ′=′++ )()(exp(])()1[( 1 ��� ψ

ccrrlrrl

lll

ll

l rrPrPrprrPlrl==

++− ′′=′+′′+′+++ )())(exp(])()1(2)1([ 1211 ��� ψ

Page 30: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Qc-tuning method This method is an extended of optimum procedure for producing pseudo potential.

Rap and his co-worker,1990,presented a method called RRKJ. They choose the pseudo wave function of valence electrons as a linear combination of Bessel equation. First we produce the pseudo wave function and then by using reciprocal schrodinger equation, we calculate the pseudo potential.

�=

=n

i

ilipsl rqjr

1

)()(�� αψ

crr <

)()( rr lpsl

�� ψψ = crr ≥

Page 31: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Wave function and pseudo wave function of S,P and D orbital of oxygen atom produced by Kerker method.

0 1 2 3 4 5 6 7 8 9 10

rΨΨ ΨΨ

(r)

-1.0-0.8-0.6-0.4

-0.20.00.20.40.60.81.0

Oxygen Atom

0 1 2 3 4 5 6 7 8 9 10

r ΨΨ ΨΨ(r

)

-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

R(Ao)

0 1 2 3 4 5 6 7 8 9 10

r ΨΨ ΨΨ(r

)

-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Kerker Pseudopotential

s

p

d

Page 32: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1Potential and pseudo potential of S,P and D orbitals of oxygen atom produced by Kerker method.

Kerker pseudopotential

0 1 2 3 4 5 6 7 8 9 10

Pse

udop

oten

tial

-30

-25

-20

-15

-10

-5

0

R(Ao)

Oxygen Atom

d

p

s

Page 33: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Logarithmic derivative of real potential and pseudo potential ofS,P and D orbitals of oxygen perused

..........PS------- ACTUAL

Kerker Pseudopotential

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-5-4-3-2-1012345

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-5

-4

-3-2

-101

23

45

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-5

-4

-3

-2

-1

0

1

2

3

4

5

Energy (ev)

Oxygen Atom

s

p

d

Page 34: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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(Left)-Wave function and pseudo wave function of S,P orbitals of hydrogen atom.

(right)- Potential and pseudo potential of S and P orbitals of hydrogen atom.

0 1 2 3 4 5 6 7 8 9 10

rΨΨ ΨΨ

(r)

-1.0

-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Hydrogen Atom

0 1 2 3 4 5 6 7 8 9 10

r ΨΨ ΨΨ(r

)

-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Kerker pseudopotential

s

p

R(Ao)

Page 35: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Logarithmic derivative of real potential and pseudo potential of S and P orbitals of hydrogen

..........PS------- ACTUAL

Kerker Pseudopotential

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-10

-5

0

5

10

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-10

-5

0

5

10

Energy (ev)

Hydrogen Atom

s

p

Page 36: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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(Left)-Wave function and pseudo wave function of S,D orbitals of hydrogen atom. (right)- Potential and pseudo potential of S and D orbitals of hydrogen atom.

Kerker Pseudopotential

0 1 2 3 4 5

Pse

udop

oten

tial

-12

-10

-8

-6

-4

-2

0

_____s

........... d

R(Ao)

Hydrogen Atom

s

d

0 1 2 3 4 5 6 7 8 9 10

rΨΨ ΨΨ

(r)

-1.0-0.8

-0.6-0.4-0.20.00.20.40.6

0.81.0

Hydrogen Atom

R(Ao)

0 1 2 3 4 5 6 7 8 9 10

r ΨΨ ΨΨ(r

)

-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Kerker Pseudopotential

s

d

Page 37: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

Logarithmic derivative of real potential and pseudo potential of S and P orbitals of hydrogen.

.� .� .� .� .� .� .� .� .� .�P� S�-� -� -� -� -� -� -� �A� C� T� U� A� L� K� e� r� k� e� r� �P� s� e� u� d� o� p� o� t� e� n� t� i� a� l�

-�4� -�3� -�2� -� 1� 0� 1� 2� 3� 4�

L�o�g�a�r�i�t�h�m�i�c� � �D�e�r�i�v�a�t�i�v�e�

-�1� 0�

-� 5�

0�

5�

1� 0�

-� 4� -�3� -�2� -�1� 0� 1� 2� 3� 4�

L�o�g�a�r�i�t�h�m�i�c� � �D�e�r�i�v�a�t�i�v�e�

-�1� 0�

-�5�

0�

5�

1� 0�

E� n� e� r� g� y� �(� e� v� )�

H� y� d� r� o� g� e� n� �A� t� o� m�

s�

d�

Page 38: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

(Left)-Wave function and pseudo wave function of S,P orbitals of oxygen atom.

(right)- Potential and pseudo potential of S and d orbitals of hydrogen atom.

Qc-Tuning Pseudopotential

0 1 2 3 4 5

PSE

UD

OP

OT

EN

TIA

L

-7

-6

-5

-4

-3

-2

-1

0

_____s

---------p

.........d

R(A0)

Hydrogen Atom

s

d

0 1 2 3 4 5 6 7 8 9 10

-1.0

-0.8-0.6

-0.4-0.20.0

0.20.4

0.60.81.0

Oxygen Atom

0 1 2 3 4 5 6 7 8 9 10

r ΨΨ ΨΨ (r

)

-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

R (Ao)

0 1 2 3 4 5 6 7 8 9 10

r ΨΨ ΨΨ (r

)

-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Qc-Tuning Pseudopotential

S

p

d

r ψψ ψψ(( ((r

)

Page 39: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

Logarithmic derivative of real potential and pseudo potential of S and P orbitals of oxygen perused by Qc-tuning method

..........PS

------- ACTUALQc-Tuning Pseudopotential

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-5-4-3-2-1012345

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-5

-4

-3

-2-1

0

1

2

3

4

5

-4 -3 -2 -1 0 1 2 3 4L

ogar

ithm

ic D

eriv

ativ

e

-5

-4

-3

-2

-1

0

1

2

3

4

5

Energy (ev)

Oxygen Atom

Page 40: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

(Left)-Wave function and pseudo wave function of S,P orbitals of hydrogen atom.(right)- Potential and pseudo potential of S and d orbitals of hydrogen atom.

Qc-Tuning Pseudopotential

0 1 2 3 4 5

Pse

udop

oten

tial

-6

-5

-4

-3

-2

-1

0

_____s

---------p

R (Ao)

Hydrogen Atom

s

p0 1 2 3 4 5 6 7 8 9 10

rΨΨ ΨΨ

(r)

-1.0-0.8-0.6-0.4-0.20.00.20.40.6

0.81.0

Hydrogen Atom

0 1 2 3 4 5 6 7 8 9 10

r ΨΨ ΨΨ(r

)

-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Qc-Tuning Pseudopotential

s

p

R(Ao)

Page 41: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

Logarithmic derivative of real potential and pseudo potential of S and P orbitals of hydrogen.

..........PS------- ACTUAL

Qc-Tuning Pseudopotential

-4 -3 -2 -1 0 1 2 3 4

Log

arith

mic

Der

ivat

ive

-5-4-3-2-1012345

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-5

-4

-3

-2

-1

0

1

2

3

4

5

Energy (ev)

Hydrogen Atom

s

p

Page 42: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

(Left)-Wave function and pseudo wave function of S,d orbitals of hydrogen atom.(right)- Potential and pseudo potential of S and d orbitals of hydrogen atom.

Qc-Tuning Pseudopotential

0 1 2 3 4 5

PS

EU

DO

PO

TE

NT

IAL

-7

-6

-5

-4

-3

-2

-1

0

_____s

---------p

.........d

R(A0)

Hydrogen Atom

s

d

0� 1� 2� 3� 4� 5� 6� 7� 8� 9� 1� 0�

�r�ΨΨΨΨ�(�r�)�

-� 1� .� 0�-� 0� .� 8�-� 0� .� 6�-� 0� .� 4�-� 0� .� 2�0� .� 0�0� .� 2�0� .� 4�0� .� 6�0� .� 8�1� .� 0�

H� y� d� r� o� g� e� n� �A� t� o� m�

R� (� A� 0� )�

0� 1� 2� 3� 4� 5� 6� 7� 8� 9� 1� 0�

r�ΨΨΨΨ�(�r�)�

0� .� 0�

0� .� 2�

0� .� 4�

0� .� 6�

Q� c� -� T� u� n� i� n� g� �P� s� e� u� d� o� p� o� t� e� n� t� i� a� l�

s�

d�

Page 43: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

Logarithmic derivative of real potential and pseudo potential of S and D orbitals of hydrogen.

..........PS------- ACTUAL

Qc-Tuning Pseudopotential

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-10

-5

0

5

10

-4 -3 -2 -1 0 1 2 3 4

Log

arit

hmic

Der

ivat

ive

-10

-5

0

5

10

Energy (ev)

Hydrogen Atom

s

d

Page 44: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

For minimizing the energy of each configuration and structural parameter identification, we do need to determine the positions of atoms and use them as an input for calculation

Page 45: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

0.29160 0.29160 0.308270.95832 0.95832 0.308270.04168 0.20840 0.058350.20840 0.04168 0.058350.45832 0.45832 0.308270.79160 0.79160 0.308270.70840 0.54168 0.058350.54168 0.70840 0.058350.54168 0.20840 0.558350.70840 0.04168 0.558350.79160 0.29160 0.808270.45832 0.95832 0.808270.20840 0.54168 0.558350.04168 0.70840 0.558350.95832 0.45832 0.808270.29160 0.79160 0.808270.12504 0.12504 0.141710.62504 0.62504 0.141710.62504 0.12504 0.641710.12504 0.62504 0.641710.37496 0.37496 0.391630.87496 0.87496 0.391630.87496 0.37496 0.891630.37496 0.87496 0.89163

0.29160 0.29160 0.308270.95832 0.95832 0.308270.04168 0.20840 0.058350.20840 0.04168 0.058350.45832 0.45832 0.308270.70839 0.70839 0.225060.79160 0.45831 0.974990.54168 0.70840 0.058350.54168 0.20840 0.558350.79160 0.95831 0.474980.70839 0.20839 0.725060.45832 0.95832 0.808270.20840 0.54168 0.558350.04168 0.70840 0.558350.95832 0.45832 0.808270.29160 0.79160 0.808270.12504 0.12504 0.141710.62504 0.62504 0.141710.62504 0.12504 0.641710.12504 0.62504 0.641710.37496 0.37496 0.391630.87496 0.87496 0.391630.87496 0.37496 0.891630.37496 0.87496 0.89163

0.29160 0.29160 0.308270.04168 0.04168 0.225060.95831 0.29160 0.974980.20840 0.04168 0.058350.45831 0.45832 0.308270.79160 0.79160 0.308270.7084 0.5417 0.058350.5417 0.7084 0.058350.5417 0.2084 0.558350.79160 0.95831 0.474980.70839 0.20839 0.725060.45832 0.9583 0.80830.20840 0.54168 0.558350.04168 0.70840 0.558350.95832 0.45832 0.808270.29160 0.79160 0.808270.12504 0.12504 0.141710.62504 0.62504 0.141710.62504 0.12504 0.641710.12504 0.62504 0.641710.37496 0.37496 0.391630.87496 0.87496 0.391630.87496 0.37496 0.891630.37496 0.87496 0.89163

0.29160 0.29160 0.308270.95832 0.95832 0.308270.04168 0.20840 0.058350.20840 0.04168 0.058350.54168 0.54168 0.225060.70839 0.70839 0.225060.79160 0.45831 0.974980.4583 0.79160 0.974980.4583 0.29160 0.474980.79160 0.95831 0.474980.70839 0.20839 0.725060.5417 0.04168 0.725060.20840 0.54168 0.558350.04168 0.70840 0.558350.95832 0.45832 0.808270.29160 0.79160 0.808270.12504 0.12504 0.141710.62504 0.62504 0.141710.62504 0.12504 0.641710.12504 0.62504 0.641710.37496 0.37496 0.391630.87496 0.87496 0.391630.87496 0.37496 0.891630.37496 0.87496 0.89163

1 2 3 4

Positions of atoms in four different configurations of cubic ice

Page 46: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Total energy versus cut off energy with Qc-tuning method and GGA approximation

Total energy versus cut of energy obtained by Qc-tuning and GGA approximation

(unit cell) (conventional cell)

Ecut(ev)200 400 600 800 1000 1200 1400

Tota

l Ener

gy(

ev)

-940

-930

-920

-910

-900

-890

-880

GGAQc

Ecut(ev)0 200 400 600 800 1000 1200 1400

Tota

l ener

gy

(ev)

-3680

-3660

-3640

-3620

-3600

-3580

-3560

-3540

-3520

-3500

-3480

GGA

-3728.1091-3728.1420Convectional cell

-922.0743-922.0355Unit cell(ev)

Ecut=1200evEcut=900evEcut(ev)

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Total energy versus cut off energy with Kerker method and GGA approximation

Total energy versus cut off energy obtained by Kerker methodunit cell conventional cell

-3726.7754-3726.7590Convectional cell(ev)

-928.1509-928.165250unit cell energy(ev)

Ecut=1300�Ecut=1200cut of energy (ev)

GGA

Ecut(ev)200 400 600 800 1000 1200 1400

Tot

al E

ner

gy(

ev)

-925

-920

-915

-910

-905

-900

-895

-890

-885

Qc

Ecut(ev)0 200 400 600 800 1000 1200 1400

Tota

l ener

gy

(ev)

-3750

-3700

-3650

-3600

-3550

-3500

-3450

-3400

GGA

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Page 49: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Comparison of total energy of four different configurations of cubic ice phases

-3745.733617-3745.74040-3745.74815-3745.761838Energy (ev)

(by other)

-3685.9369-3685.9413-3685.9682-3686.7968Calculated energy(ev)

4 3 2 1Configuration

Page 50: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Total energy (ev) for unit cell and conventional cell:

-3750.03-3741.032-935.258Total energy by Kerker [Ecut=1200]

-3686.81-3676.2-919.050Total energy by Qc-method [Ecut=900]

Convectional cell energy

Unit cell energy*4Unit cell energy

Cut of energy

Page 51: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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The total energy versus volume for unit cell calculation and Qc-tuning method

V(A0)3

20 40 60 80 100 120

To

tal e

ner

gy

-920

-918

-916

-914

-912

-910

-908

GGA

LDA

Page 52: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Parameters obtained by Qc-tuning for unit cell without motion of Ion

Parameters obtained by Qc-tuning for unit cell with motion of Ion

5.1286.68476274.6789-914.5774.82010.1291GGA

9.626.970484.6671-908.6274.25670.08614LDA

errora(Å) Vo Eo Bop Bo approach

0.226.336762.6117-919.0501.03980.2152GGA

0.226.226762.6117-912.2061.01020.2208LDA

errora(A)VoEoBopBoapproach

Page 53: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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The effect of D and P orbitals of hydrogen atom on structure parameterStructural parameters obtained by using unite cell and d orbital of hydrogen atom in

pseudo potential in Qc-tuning method…

Total energy versus volume for unite cell using d orbital of H atom and Qc-tuning method

0.336.336763.6117-912.2901.52320.21256LDA

0.336.336762.6117-918.9890.9935480.2261GGA

errora(A)VoEoBopBoapproach

V(A0)3

20 40 60 80 100 120

To

tal e

ner

gy

-920

-918

-916

-914

-912

-910

-908

GGA

LDA

Page 54: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Effect of various of Rc in structural properties of cubic ice

Variation of structural parameters versus cut off radius for GGA approximation and Qc-tuning method in calculation of unit cell

0.336.336763.6117-919.0010.65170.3189Rc(s,p)H=1.228(a.u)

Rc(d)H=1.25(a.u)

Rc(s,p,d)O=1.8(a.u)

0.336.33763.6117-918.1321.392050.271728 RcH=1.15(a.u)

RcO=1.8(a.u)

19.597.6040109.921-927.2192.688760.10228Rc(s,p,d)H=1.228(a.u)

Rc(s,p,d)O=1.5(a.u)

errora (Å) Vo Eo Bop Bo

Page 55: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Length of O-H band 0.97 Angstrom 0.92 Angstrom 0.95 Angstrom

The curves of total energy versus volume of conventional cell computed from pseudo potential obtained by Qc-tuning method

GGA

V(Ao)3

100 150 200 250 300 350 400 450 500

To

tal E

nerg

y(ev

)

-3690

-3680

-3670

-3660

-3650

-3640

GGA

LDA

GGA

V(Ao)3

100 150 200 250 300 350 400 450 500

Tot

al E

ner

gy(

ev)

-3690

-3685

-3680

-3675

-3670

-3665

-3660

-3655

-3650

-3645

GGA

LDA

GGA

V(Ao)3

100 150 200 250 300 350 400 450 500

To

tal E

ner

gy(

ev)

-3690

-3685

-3680

-3675

-3670

-3665

-3660

-3655

-3650

-3645

GGA

LDA

Page 56: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Calculated length of O-H band for cubic ice Different values for it has been reported

The length of O-H band is 0.97 Å

6.5190 277.047-3685.932.98810.16650.93

6.4107 263.466-3686.622.287050.2036540.95

6.3562256.798-3686.812.121720.2224810.97

a(Å) Vo Eo Bop Bo O-H(Å)

Page 57: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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The Band Structure of cubic ice obtained by Wien2k soft wear. The gap energy is 5.4 ev

Page 58: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Conclusion:A)- We find the right configuration for Cubic Ice. B)-To compute exchange correlation energy, GGA and LDA approximations reach to the same value, but cell parameter which obtained by GGA method is slightly closer to the experimental value. C)-In pseudo potential calculation there will be no different in the outcome results if we consider p or d for exited state of hydrogen atom.D)- Structural determination for unit cell and conventional cell gives the same results which indicated that the positions of atoms have been calculated correctly. E)- We deduce the length of O-H band in cubic Ice which is 0.97 angstrom.

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Page 60: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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Minimizing the functional energy:

1- Solution to single equations of Kohn-Shem for single particle2- Conjugate gradient procedure

)()(21

)()()()(2

οοοο xxxx

FxxxFxxxFxF

ji

T −∂∂

∂−+∇−+=

Page 61: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

1

.

:

Vxc

:

[ ]{ [ ]})()()()( rnVrnVrVrV xcHps

l

Unscreenpsl

���� +−=

))(())(())()(( rnVrnVrnrnV valHcoreHvalcoreH

���� +=+

[ ]{ [ ]})()()()( rnVrnVrVrV valxcvalHps

l

Unscreenpsl

���� +−=

Page 62: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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rc .

Page 63: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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)(...)()(

...

)(...)()(

)(...)()(

!

1),...,,(

21

22212

11111

321

rrr

rrr

rrr

Nrrr

NNN

N

N

���

���

���

���

ψψψ

ψψψ

ψψψ

ψ =

)()()( σχϕψ iiiii rr�� =

One of the problems in Hearty approximation is that with changing the positions of electrons in the system,the total wave function is not

ant symmetry,and the Pouli rule is not valid.To solve this problem fock:

Page 64: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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(Ab initio)

.1-

BHS

.2-

Page 65: Physics Department Birjand University, Birjand, Irancophen04/Talks/Arabi.pdf · The important of computational physics in solid state physics 1- Analysis of physical phenomena which

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For structural determination we have to put pressure on the crystal. We increase and decrease the cell parameter and using Mornagon equation of state.

cteBVV

B

BVvE

B

++−′

=

]11

)([][

ο

ο ο