# First Principle Electronic Structure Calculation Prof Kim Jai Sam 279 2077 Students Lee Geun Sik Yun So Jeong Lab 공학4 125 279 5523 http ctcp pos

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```					First Principle Electronic
Structure Calculation

Prof. Kim Jai Sam (279-2077)

Students : Lee Geun Sik,
Yun So Jeong

Lab. 공학4-125 (279-5523)

http://ctcp.postech.ac.kr
Our Research Area

• Optical property of nanocrystal (Yun)
 optoelectronics, biology

• Structural phase transition of crystal (Lee)
 most accurate calculation in phase transition

• Surface problem (Lee)

 All require electronic structure calculation of crystal!
Electronic structure
calculation of crystal
It was impossible to solve many body problem quantum mechanically.

H ({R},{r})  E({R},{r})
2               2
H          i2        2
I
i   2m      I 2M I
1            e2             Z I e2   1         Z I Z J e2
                                  
2 i , j | ri  rj | I ,i | RI  ri | 2 I , J | RI  RJ |

and Density Functional Theory
(Hohenberg and Kohn 1964, Kohn and Sham 1965),
it became possible.
Density Functional theory
Thomas-Fermi-Dirac (1929)
Model expression of total energy in
terms of electron density

E()
Fermi

Kohn-Hohenberg-Sham
(1964)
Exact relationship between electron
density and molecular energy ..
..but, form of relationship not known
W. Kohn                   E()
Kohn-Sham total-energy functional
Kinetic energy of electron
     2    2
E { i }  2   i       i d 3r                 Coulomb interaction
i        2m                             between ion and electron
  Vion (r )n(r )d 3r                                   Coulomb interaction
between electrons
e 2 n(r )n(r ') 3 3
                 d rd r '
2     | r r '|                                      exchange-correlation
energy of electrons
 E XC [n(r )]                                          static Coulomb interaction
 Eion ({RI })                                          between ions

DFT says that total energy is a unique functional of the electron density!
Minimum energy is the ground state energy!
Many electrons problem

Variational method

Self-consistent one-electron equation
(Kohn-Sham equation)
Kohn-Sham equation

 2 2              
     Veff (r )   i (r )  Ei  i (r )
 2m               

Veff (r )  Vion (r )  VH (r )  VXC ( r )

ion Coulomb        classical electronic    exchange-correlation potential
potential          Coulomb potential       of electron gas (LDA,GGA)

Minimize total energy functional self-consistently!
Approximations to the exchange-correlation
functional: LDA and GGA
Collection of functionals
Self-consistent
computational procedure
Currently using simulation
packages in our lab

VASP : Pseudopotential, Ultra-soft, PAW, parallel execution in supercomputer.
 studying CdSe quantum dot system

SIESTA : localized orbital basis and pseudopotential, parallel execution,
very small basis, handle very large system (nano system).
 studying now

WIEN97 : LAPW method, parallel execution in supercomputer.
 9 publications since 2001, mainly TiFe, TiFeH, TiFe(001) system.
Surface electronic structure

TiFe (001)

Physical Review B, 65, 085410 (2002)
Density of States

TiFe (001)

Physical Review B, 65, 085410 (2002)
Surface band structure

TiFe (001)

Physical Review B, 65, 085410 (2002)
electron density of H/TiFe (001)

Int. J. Hydrogen Energy, 27, 403-412 (2002)
Angular momentum projected
density of states

H/TiFe (001)

Int. J. Hydrogen Energy, 27, 403-412 (2002)
Topology of electronic band I

Ag2Se (SG19, P212121)

CMo2 (SG60, Pbcn)

J. Phys. Cond. 15, 2005-2016 (2003)
Topology of electronic band II

PdSe2 (SG61, Pbca)

BFe (SG62, Pnma)

J. Phys. Cond. 15, 2005-2016 (2003)
Parallelization of WIEN97
with MPI and SCALAPACK I

smaller memory
usage with parallel
execution!
Parallelization of WIEN97
with MPI and SCALAPACK II

shorter cpu time
with parallel
execution!
Energy spectrum of nano structure
Luminescent Materials I
Quantum Dots (optical property)

CdSe quantum dot
Diameter ~ 4 nm
TEM image
CdS nanoparticles

HRTEM image of
single CdS nanoparticle
Photoluminescence of bare CdSe
and coated CdSe dots

Synthetic Metals, 139, 649-652 (2003)
Applications in biology
of optical quantum dots

10 distinguishable colors
of ZnS coated CdSe QDs

Optical coding and tag
based on emission
wavelength of ZnS
coated CdS QDs
Structural phase transition
by ab initio method
Find the phase which minimize Gibbs free energy,
G = E – TS + PV on (P,T) plane.
Pressure ↔ volume
Temperature ↔ entropy of phonon, harmonic approximation

Helmholtz free energy requires phonon density of states, g(ω).
Phonon band structure
and density of states

MgO

Solid curve: theoretical calculation   J. Chem. Phys. 118, 10174 (2003)
Open circle: experimental result
Pressure and Temperature
phase diagram
J. Chem. Phys. 118, 10174 (2003)

MgO                                                        B1:NaCl structure
B2:CsCl structure

Theoretical results agree with experiments quite well!
Future Plan

• Quantum computing
 quantum dot is one of candidates for qubit.
 optical properties of quantum dot

• TDDFT (Time Dependent DFT)
 calculate electronic structure for excited states.

• Surface physics : catalysis, hydrogen storage

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