화합물의 비선형광학 및 분자동력학적 성질 연구를 위한 계산화학

전승준고려대학교 화학과

연구 목적

• 유기 화합물의 비선형광학 성질의 계산화학적 연구 -

양자역학적 또는 모형이론의 계산

• 분자동역학모의실험 (MD) 과 Instantaneous Normal

Mode(INM) 분석에 의한 응축상의 화학반응동역학

연구

분자의 대칭성에 따른 Optical Polarization(P)

Linear

Centrosymmetric

Noncentrosymmetric

Push-Pull type Polyenes 유기분자의 광학적 비선형성

Stark Energy and Dipole Moment

Nonlinear Optical Research in Push-Pull Polyenes

Experimental Method for Hyperpolarizability

• Hyper -Rayleigh Scattering(HRS)

• Electric Field Induced Second Harmonic Generation

(EFISH)

Quantum Mechanical Calculation

Bond-Length Alternation(BLA)

or Bond-Order Alternation(BOA)

Push-Pull Polyene

HE t

t Et

t VVB

CT

0

Theoretical Background on Valence-bond Charge-Transfer(VB-CT) Model

• Hamiltonian

• The Energy of VB state and CT state

E k Q Q

E V k Q Q

V Q V k Q Q k Q Q

VB VB

CT CT

CT VB

12

1212

12

0 2

00 2

00 2 0 2

( )

( )

( ) ( ) ( )

g VB CT

e VB CT

f f

f f

( )

( )

/ /

/ /

1

1

1 2 1 2

1 2 1 2

Eigenfunctions and Eigenvalues

• The Electronic groung and excited eigenfunctions

• The eigenvalues of the ground and excited states

E Q V k Q Q k Q Q V t

E Q V k Q Q k Q Q V t

g VB CT

e VB CT

( ) ( ) ( )

( ) ( ) ( )

/

/

12

12

12

12

4

12

12

12

12

4

00 2 0 2 2 2 1 2

00 2 0 2 2 2 1 2

HE t

t EVB

CT CT

Push-Pull Polyene in an Electric Field

• The induced dipole moment of the electronic ground state

P

dE

dV Q

V Q tz

g CT

CT

CT( )( )

( )/

12

2 42 2

1 2

• Two-state model Hamiltonian

zz zCT

zzzz CT

zzzzz CT

e g

dP dt

d Pd

t V

d Pd

t V t

E E V t

( )/ |

( )

!( )

( ) ( ) ( ) /

0

2 2

3

2

20

2 3

5

3

30

2 4 2 2

7

2 1 2

2

12

3

13

4

0 0 4

Push-Pull Polyene in an Electric Field

• Polarizability and Hyperpolarizabilities

Vibrational hyperpolarizability

Eletric field 가존재하면 평형의 구조가 달라짐

Electric field 가 가해졌을때 구조가 달라짐에 따른 dipole 의 변화를 harmonic 으로 가정

Electronic

Vibrational

zzzkk

g z

k

zz

k

zzzv

zzze

CT VB

c

M

Q Q

t k Q Q

32 4

1

6

2 2 20 0

2 0 0 2

3

!

( )

,

Vibrational Contributions to Hyperpolarizabilities

• Vibrational first-hyperpolarizability

zzzzkk

g z

k

zzz

k

zz

k

zzzzv

zzzze

CT VB

c

M

Q Q Q

VV t

t k Q Q

13 4

14 3

19

8

4

2 2 20 0

2

2

2 2

2 0 0 2

3

!

( )

( )

,

Vibrational Contributions to Hyperpolarizabilities

• Vibrational second-hyperpolarizability

zz zm g mg mg

zzz z z zm gl g

mg mg mg

g m

g l l m m g

( ; ) | |

( ; , ) | | | | | |

( )( ) ( )( ) ( )( )lg lg lg

1 1 1

21

12

1 12

2

2

Sum-over-State Expressions for Molecular Polarizability and Hyperpolarizabilities

zzzz z z z zq gn gm g

mg ng qg mg ng qg

mg ng qg mg ng

g m m n n q q g( ; , , ) | | | | | | | |

( )( )( ) ( )( )( )

( )( )( ) ( )(

3

1

13 2

12

12

1

3

2 3

1

13

1

13

13

3

)( )

| | | | | | | |

( )( )( ) ( )( )( )

( )( )( ) ( )( )(

qg

z zn gm g

z z

mg ng ng mg ng ng

mg ng ng mg ng ng

g m m g g n n g

)

Sum-over-State Expressions for Molecular Polarizability and Hyperpolarizabilities

zzzz zzzzD

zzzzN

zzzzD CT

eg

zzzzN CT

eg

t VD

t VN

( ; , , ) ( ; , , ) ( ; , , )

( ; , , ) ( )

( ; , , ) ( )

3 3 3

3

3

2 2 2

4

4 4 2

4

Dynamic Second Hyperpolarizability

zzeg

eg

zzzeg e g

eg

zzzzeg e g

eg

eg

eg

eg e g

M

M M M

M M M M

E E V t

2

3

4 4

0 0 4

2

2

2

2 2

3

4

3

2 1 2

| |

| | ( )

| | ( ) | |

( ) ( ) ( ) /

Polarizability and Hyerpolarizabilities at Zero-Frequency Limit

• Polarizability and Hyperpolarizabilities

Vibrational Contributions to the Molecular First and Second Hyperpolarizabilities of a Push-Pull Polyene

·김현수 ·조민행 전승준고려대학교 화학과

The vibrational contributions to the first and second hyperpolarizabilitiesof a push-pull polyene are theoretically studied by using the valence-bondcharge-transfer model. The formal relationships between the vibrationaland electronic contributions to the hyperpolarizabilities are derived. It isfound that there exist strong correlations between the vibrationalcontributions and bond length alternation of a push-pull polyene. Bycalculating these contributions numerically, it is proven that the vibratinalcontributions, estimated from the IR, Raman, and hyper-Ramanmeasurements, to the hyperpolarizabilities can also provide a measure ofthe nonlinear optical property.

Applications of the Valence-Bond Charge-Transfer Model to Sum-over-State Expressions for the Molecular

First and Second Hyperpolarizabilities

·김현수 ·조민행 전승준고려대학교 화학과

The sum-over-state expressions for the first and secondhyperpolarizabilities of a push-pull polyene are calculated by using thevalence-bond charge-transfer model and invoking two-stateapproximations. Extensions of the static results obtained previously. (Lu,Chen, Perry, and Goddard III, J. Am. Chem. Soc. 116 (1994) 10679) tothe dynamic first and second hyperpolarizabilities are presented. Byseparately calculating various dipole moments and transition energy gap,the origins of the molecular hyperpolarizabilities and their dependenceson the bond length alternation are discussed.

INM 연구

분자동역학 모의실험 (MD)

순간적 액체구조를 이용하여 Hessian Matrix 계산

얻어진 Matrix 의 diagonalization

위의 과정을 이용하여 구한 INM 의 주파수분포를 조사하여INM 을 이용하여 상관함수를 계산

Chemical Reaction Dynamics, Liquid Dynamics, Spectroscopic Analysis