1. Lecture 6 Electronic Calculations
武晓君 江俊

2. The main thread underlying complex systems and complicated procedures: Electron Kinetics
Photon/
Electron
Energy
transfer
Material
Conversion
Photocatalysis
Catalysis
Mol-Photonics
Solar cell
Mol-Electronics
Optoelectronics
Photo-detector
Transition and evolution
Electronic/Excited state
generation and coupling

3. Charge Density Total charge Deformation charge ρ = ρ(total) - ρ(atoms)
Spin charge
ρ(spin)= ρ(up)- ρ(down)

4. Charge Density f + (r)= 1/(ΔN)(ρ N+Δ (r)- ρ N (r))
nucleophilic reaction (adding an electron)
f + (r)= 1/(ΔN)(ρ N+Δ (r)- ρ N (r))
electrophilic reaction (removing an electron)
f - (r)= 1/(ΔN)(ρ N (r)- ρ N-Δ (r))
Fukui Function:
A function that describes the electron density in a frontier orbital, as a result of a small change in the total number of electrons.
Prints the condensed Fukui functions for Hirshfeld, Mulliken, Voronoi, and if calculated, Bader charges.
Allows one to predict, using density functional theory, where the most electrophilic and nucleophilic sites of a molecule are.
Most chemical reaction in general involves a change in electron density. The Fukui function indicates this change in electron density of a molecule at a given position when the number of electrons have been changed.
The reaction will therefore then take place where f + or f - can be found to have a large value.

5. Angew. Chem. Int. Ed. 2015, 54,
Angew. Chem. Int. Ed. 2015, 54, 2980.

6. Charge Population Mulliken population
Cheap, Straightforward
Depending on the choice of basis set
Equal shared by two atoms
Löwdin population (transform atomic orbital basis functions into an orthonormal set of basis)
More stable, more expensive
NPA (Natural Bond Orbital scheme: transform occupied orbitals to an orthonormal set of natural orbital)
classifies and localizes orbitals into three distinct groups.
Mostly accurate, expensive
Density Matrix:
Number of electrons

7. Charge Population ESP charges
Generate Charge distribution which fit with the accurate electrostatic potential
Depends Strongly on molecular conformation (topological structure)
Core electrons contributes weakly

8. Charge Population Hirshfeld Analysis a density-based population scheme
weight function:

9. Charge Population Bader Analysis
The definition of an atom is based purely on the electronic charge density
According to the topological analysis of charge distribution, uses the zero flux surface to divide atoms
A zero flux surface is a 2-D surface on which the charge density is a minimum perpendicular to the surface. Typically in molecular systems, the charge density reaches a minimum between atoms and this is a natural place to separate atoms from each other.

10. Band structure & Density of State
dispersion relation
Energy .vs. Momentum (k)
Band gap
Electric Conductivity
channel
Direct bandgap
(strong photo-response)
Indirect bandgap
(weak photo-response)

11. Conjugated Polymer Increasing of size, Density of State(DOS) increases
Discrete molecular orbital to continuous band
HOMO-LUMO gap remains constant as 2.78eV
Energy structure analogous to inorganic Semiconductor

12. (5, 5) Metallic Single Walled Carbon Nanotube (SWCNT)
B3LYP/6-31G
Max: C atoms
G03 LUMO of 4.1 nm SWCNT
CIS LUMO of 4.1 nm SWCNT
CIS LUMO of 200 nm SWCNT

13. Band structure & Density of State
Doping
n-type doping
p-type doping
Defect state

14. nanoparticles
Doping energy level closed to conduction band of 3.4 nm
Computed with LSDA/STO-6G with G03

15. nanoparticles
Doping energy level closed to conduction band of 4.2 nm
Computed with LSDA/STO-6G with CIS
Doping energy level closed to conduction band of 3.4 nm
Computed with LSDA/STO-6G with G03

16. Occ.
Occ.
Doping P atom resulted in a energy level closed to the LUMO of pure Si nanoclusters P atom content fraction directly proportion to the free electron density of state
Unocc.
Unocc.
Occ.
Occ.
Doping P atom resulted in an occupied molecular orbital closed to the LUMO of pure Si nanoclusters
P atom content fraction directly proportion to the free electron density of state
We now can doping with P atom with concentration less than 5.0d-3 (For example: P atoms comparing
to Si atoms), which fits with most of the doping concentration in semiconductor technology field.

17. Band structure & Density of State
Band Folding
The choice of unit cell size would change k wave vector distribution, which might fold the band structure
One-atom unit
Two-atom unit
Band folding might lead the incorrect transforming from indirect bandgap to direct bandgap

18. IP (ionization potential ) AE (electron affinity) WF (work function)
Band structure & Density of State
IP (ionization potential )
AE (electron affinity)
WF (work function) EA IP WF
Strict in DFT theory,
but not strict in DFT computations.

19. Electron transport in molecular device
HOMO

20. WorkFunction CuO Ag Ag donate polarization charge to CuO
Lower down CO activation barrier
WorkFunction
CuO Ag Cu O
(100)
(111) Ef
Vac
Wf=
5.97 eV
4.45eV -e Ag
CuO
Y. Bai, et. al. W.X. Huang*, J. Jiang*, Y.J.Xiong* J. Am. Chem. Soc. 2014, 136, 14650
Semi1
Metal
Semi2 EF
e- e- e-
Semicond-Semicond nanoheterostructure
Type I interfacing with Metal
Vac.
Metal
e- e- e-
Semi1
Semi2 EF
Semicond-(Semicond/Metal)
Nanoheterostructure Type II
Vac. h+ e-
e e-
Semi1
Semi2 EF
Semicond-Semicond nanoheterostructure
Type I
e- e-
h+ h+ e- h+
T.T. Zhuang, et.al., J. Jiang*, S.H. Yu*, Angew. Chem. Int. Ed. 2015, 39, 11495
T.T. Zhuang, et.al., J. Jiang*, S.H. Yu*, Angew. Chem. Int. Ed. 2016, 55, 6396

21. Force Phonon Force & Vibration Frozen phonon Response function
Application:
Computing electron-phonon coupling, Superconductivity phase transition

23. Appl. Phys. Lett. 96 (2010)

24. electron-phonon coupling Excited states relaxation/Heat
Suppress energy relaxation
Y3+
electron-phonon coupling
Excited states relaxation/Heat
Na+ F-
Lanthanide doped
Crystal Matrix
NaYF4
Light induced smart phase transition—Enhance energy transferring by suppressing non-harmonic electron-phonon coupling

25. Laser induced
Temp. induced
Adv. Mater. 2015, 27, 5528

26. Instability
The surface system become very unstable when DOS at around Fermi level increases significantly
Perierls phase transition

27. magnetism n (mag) = n(up）- n(down) ρ(spin)= ρ(up)- ρ(down)
ferromagnetism
antiferromagnetism
ferrimagnetic
Spin Density Wave

28. Spin-density-functional theory

30.  projector augmented wave method

37. Thanks!

38. First Principle Based Simulations
for Electron Real-Space Time Evolution
Starting from the time-dependent Schrodinger equation:

39. Fock matrix:
Overlap matrix:

43. Stress
Force & Vibration
弹性系数

44. Instability
Stone铁磁理论