1. Structure and excited-state dynamics of the S1 B3u‐S0 Ag states of pyrene through high-resolution laser spectroscopy
Yasuyuki Kowaka
We study the vibrational,rotational structure,
and the excited-state dynamics of molecules.
PAHs ,including pyrene, are a good target for studying the excited-state dynamics.
Kyoto University

2. Excited-state Dynamics
Predissociation S2 IC
ISC
IVR S1 T1
abs.
fluo.
phos.
This diagram shows the various relaxation processes, which is called the excited-state dynamics.
There are fluorescence and phosphorescence as radiative processes, and IC to the S0 state, ISC to the triplet state , IVR, and predissociation as radiationless processes.
The bond energies are significantly higher than the excitation energy of the S1-S0 transition
so that predissociation would not occur at the zero-vibrational level in the S1 state of pyrene.
In this presentation, I will talk about IC,ISC, and IVR processes. S0

3. This Work IC ISC IVR Ultrahigh-resolution spectrum
Electronic structure of S1
Accurate molecular constants
Theoretical calculation
Molecular structure
ISC
IVR
I speak about the flow of this presentation.
First, I talk about the results of the vibrational analysis and then I talk about the excited-state dynamics.
In order to consider IC, I determined the accurate molecular constants through ultrahigh-resolution of 0-0 transition
and molecular structures combining its constants with theoretical calculation.
I elucidated IC considering the molecular structures and vibrational structures.
In order to consider ISC and IVR, I observed the change of the spectrum in the strong magnetic field and dispersed fluorescence spectra respectively.
Ultrahigh-resolution spectrum in magnetic field of 1.2 Tesla
Dispersed fluorescence spectrum

4. Pyrene (C16H10) i σxy σyz σzx E C2(z) C2(x) C2(y) Ag 1 B1g -1 R(z) B2g
R(x)
B3g
R(y) Au
B1u z
B2u x
B3u y
I designate molecular axis as this figure.
If pyrene is a planar molecule, it belongs to D2h and I go on speaking on this assumption.
Accurate molecular structures in the S0 and S1 states have not been determined.
Yet, no reliable theoretical calculation which sufficiently includes configuration interaction have not been done.

5. Vibrational Spectra Dispersed fluorescence spectrum
fluorescence excitation spectrum
First, I would like to speak on the results of vibrational analysis.
This spectrum shows dispersed fluorescence spectrum, the other shows fluorescence excitation spectrum.
The vibrational assignments are based on the theorical calculation and the analysis of rotational envelopes.

6. Results of Vibronic Transition of Pyrene
ag vibronic transition (B-type)
← Franck-condon Factor
b1g vibronic bands (A-type) seen in the spectrum
← S1-S2 Vibronic Coupling
Fluorescence lifetime in the S1 state is long (1400 ns).
Vibrational structures in the S0 and S1 states are similar.
As a result of vibrational analysis, totally-symmetric ag vibrations are active.
Strong b1g vibronic transitions in the spectrum are observed by S1-S2 Vibronic Coupling
and Intensity borrowing from the S2 state. Fluorescence lifetime in the S1 state is very long, 1.4 μs.
Vibrational structure in the S0 state is similar to that in the S1 state.

7. Observation of Ultrahigh-Resolution Spectrum
Etalon Marker
Ref:I2 absorption
Nd YVO4 Laser
Ring Ti:S Laser
skimmer, φ2 mm
Pulse nozzle
Magnet
Ar +
sample
Computer
This is the illustration of the experimental device for ultrahigh-resolution spectrum.
150 ℃
Photon counter
slit, width 2 mm UV PM

8. Ultrahigh-Resolution Spectrum of Pyrene
This is 0-0 transition ultrahigh-resolution spectrum of pyrene.
Each rotational line is sufficiently resolved and I assigned about 1500 lines.

9. Assignment of Pyrene Here is the results of assigned spectrum.
This is a part of the Q branch of observed spectrum,
the upper is that of the simulated spectrum using the obtained rotational constants from the analysis of the observed spectrum.
The simulated spectrum is in agreement with the observed one.

10. Band of Pyrene Calculated Observed Cm
This is true of the whole spectrum. -1 Cm

11. Rotational Constants Calc. Expt. A B C S0 （10-2 cm-1）a) 3.38922
S1 （10-2 cm-1）b)
cisd/4-31g
TDDFT/cam-b3lyp/6-31g（d,p）
Expt. A B C
S0 （10-2 cm-1）
S1 （10-2 cm-1）
This table shows the rotational constants by the analysis of the spectrum and by theoretical calculation.
I performed theoretical calculation on the assumption that pyrene is planar and D2h symmetry.
The differences between the experimental values and the calculated ones are less than 0.03% in the S0 state and 0.2% in the S1 state respectively ,
and both values are very close,
so I conclude that the molecular structures in both states by theoretical calculation are actual molecular structures and that pyrene in both states belong to D2h.
The inertial defects in both states are nearly 0, so I also conclude in this point that pyrene is a planar molecule.
The difference between experimental values in the S0 and S1 states is very small, so pyrene's structures don't change greatly on the electronic excitation.
｜Ic－Ia－Ib｜ ≪ Ic
Both in the S0 and S1 states
Moment of inertia defect

12. Ab initio Calculation of Excited State
Ground State
Excited State
ΔSCF
TDDFT
When a molecule is in the ground state, its electrons fill the lowest orbitals.
When a molecule in the excited state is calculated,　different calculation methods describe different electronic states of the excited state.
.In this study, I use CIS approach, TDDFT approach, and SAC-CI approach calculating molecular structure in the S1 state.

13. Results of Theoretical Calculation in the S1 stateB C
Expt.
TDDFT CAM-B3LYP/
6-31G(d.p)
TDDFT WB97XD/
TDDFT B2PLYPD/
cc－pvdz
TDDFT B3LYP/
6-31G
CIS/6-31G （d.p）
CIS/cc-pvtz
SAC-CI/6-31g(d,p)
This table shows the results of theoretical calculation of the S1 state.
CIS and SAC-CI approaches don't introduce configuration interaction and electron-correlation sufficiently,
However, if the effect of CI is considered further in the SAC-CI approach, the calculation values may be close to the experimental ones.
As for TDDFT, when I use these functions, the rotational constants tend to be like those by CIS.
However, when I use long range corrected functions, the constants are very close to those by the experiment. In the calculation of the S0 state,
The calculation approach and the basis which introduce electron-correlation tend to be very close to the rotational constants by the experiment.
It's important to consider electron-correlation in the calculation of pyrene.
In the unit of 10-2 cm-1

14. Internal Conversion Rate
Fermi’s golden rule
Non-adiabatic
Franck-Condon Overlap
adiabatic
Franck-Condon Overlap
The transition probability of IC is described as this equation.
This equation shows that the cause of IC is the interaction between the vibrations in the S0 and S1 states.
That is, the transition probability depends on the overlaps between a vibrational wavefunction in both states.
WIC depends on these vibrational overlaps.

15. Contribution to Internal Conversion
In pyrene, molecular and vibrational structure in the S0 state are very close to those in the S1 state.
The potential curves of pyrene in both states are like this and the overlap-integral is very small.
Therefore, the IC rate is considered to be very small at the few vibrational level in the S1 state. Actually, the lifetime is 1.4 μs, very long.
IC is very slow in the S1 state of pyrene

16. Ultrahigh Resolution Spectrum in Magnetic Field
H= 1.2T
H= 0
Next, I talk about ISC and IC processes.
In order to certain whether ISC occurs or not, We measured Zeeman broadenings of individual rotational lines by applying the external magnetic field.
The observed Zeeman broadening was very small, indicating that the triplet mixing is very small.
This small mixing is met by El-Sayed rule,which state that π-π transition is forbidden.
As a result, ISC is considered to be very slow.
Relative Energy

17. Remarkable Radiationless Transition in the Vibronic Levels
I continue to present what makes a slight radiationless transition occur.
ISC doesn't occur, because the spectum in the strong magnetic field doesn't change, so I conclude that the radiationless transition is IC.
This graph shows that the fluorescence lifetime is remarkably short in a specific vibrational levels of the S1 state, suggesting that IC is fast in a specific vibrational mode.
We are now trying to assign these bands by higher level ab initio calculation
Graph of fluorescence lifetime (ns) vs. energy relative to the S1 origin at cm-1. The circles represent the lifetime after excitation into a distinct line of the spectrum, while the squares designate values measured after excitation into the surrounding background.
J. Phys. Chem., 1986, 90 (5), Elisa A. Mangle and Michael R. Topp

18. Dispersed Fluorescence Spectra
Finally, I speak on IVR.
This figures show dispersed fluorescence spectra.
As excited-energy is higher, the whole spectrum and line-width are broaden.
When excited-energy is above 1000cm-1, the intensity of spectrum on the higher energy region is weaker and the baseline on the lower energy region is up.
This is the definite evidence of IVR. IVR generally occurs in large PAH molecules.
It is noteworthy that the threshold energy is remarkably small in pyrene. It may be due to its long lifetime.
The IVR probability becomes larger during the long lifetime in the excited level.
indicates IVR

19. Conclusions ISC to T state is very slow IC to S0 state is very slow
Predissociation doesn’t occur
Florescence lifetime is very long
in the S1 state
IVR occurs above 730 cm-1
In conclusion, radiationless processes are very slow, so fluorescence lifetime is very long,1.4 μs,
but IC may be a little fast in the other slow radiationless processes.
IVR occurs above 730cm-1.
Let me end with a presentation above.

20. Results of Theoretical Calculation in the S0 stateB C
Expt.
CISD/4-31G
CISD/6-31G
MP2/cc-pvtz
MP2/6-31G(d,p)
HF/cc-pvtz
HF/6-31G(d,p)
DFT/cc-pvtz
DFT/6-31G(d,p)
こちらがS１の理論計算の結果をまとめた表です。
CISでは軌道間相互作用を考慮していますが、電子相関をとりいれていないため、実験値と満足のいく一致が見られませんでした。
CISでは基底にかかわらず、Aが大きく、Bが小さな値が出る傾向がありました。SAC-CIに関しても同じ傾向がみられましたが、defaultでの計算しか行っていないため、CIの効果をさらに考慮していけば、
実験値との一致が見られる可能性があると思います
またTDDFTでは
一般的に用いられているb3lypのHybrid型、摂動項を加えたDouble-hybrid型の汎関数ではCISと同じ傾向が得られましたが、
長距離補正を取り込んだ汎関数cam-b3lyp,wb97xdはA,B,Cにおいて非常に良い値が得ることができました。
この汎関数は電子相関を考慮しており、
また、S0に関して良い値を与えた基底であるcc-pvxz型は一電子および二電子励起配置を含めた相関作用を取り込んでいる基底です。
最も良い値を与えたcisd法は、一電子励起および二電子励起を持つ電子配置を持つ電子配置状態関数を取り込んでいます。
そのため、ピレンの理論計算に関しては電子相関が非常に重要で考えることができます。
In the unit of 10-2 cm-1

21. The Change of the Molecular Structure upon Electronic Excitation
1.4448
1.4233
1.3478
1.3730
+0.12
1.4015
1.3883
Angle (°)
+0.59
the S0 state
the S1 state
1.4169
1.4498
1.3960
1.4037
+0.53
in the unite of Bond length (Å)
+0.63
1.4319
1.3857

22. Observation of LIF Excitation Spectrum
laser ray
photon
counter
carrier
gas
chamber PM
dye
laser
computer
i) To identify electric structure of S1
molecular beam
それでは振電スペクトルの話に入ります。これはLIF励起スペクトルの実験の概略図です。サンプルとアルゴンを高真空中に噴出することによりよく冷却された分子線を形成することができます。
pump
laser
fluorescence
laser intensity plot

23. Observation of Dispersed Fluorescence Spectrum
Laser ray
carrier
gas
photon
counter
fluorescence
chamber
dye
laser PM
computer
i) To identify electric structure of S1
molecular beam
分散蛍光スペクトルは先ほどの実験装置に分光器を入れて観測しました。
両者の違いは励起光の波長を掃引しているか、輻射光を波長ごとに観測しているか
pump
laser
monochromator
laser intensity plot

24. Excitation Fluorescence Spectra
まず蛍光励起スペクトルに関してですが、フランクコンドンの原理を受け入れるならば、
スペクトル中にはag振動のみが観測され、そのスペクトルはB-Typeのみになるはずですが、スペクトル中のピークを拡大してみるとA-typeのピークが確認することができました。
これは、B3uの帰属表現に属しているS2がS0S2遷移からのintennsity borrowingがおこり、
B1g対称振動への遷移が大きな強度を持ってA-typeのピークとしてスペクトル中に現れたと考えることができます。
これをもとに帰属を行っていきました。

25. Configuration Interaction(CI)
LUMO+1
LUMO CI
1La
HOMO S2
HOMO-1 S1
1Lb
La,Lbが逆転します。
このことは0－0バンドのピークがB-typeであることからも確認できます。
このため、蛍光励起スペクトルにおいてb1g対称性振動の強度が強く出ています。
一般的に、HOMO-LUMO遷移は遷移強度が大きく、それと比べるとHOMO-1-LUMO,HOMO-LUMO+1遷移は弱いため、
ピレンはS0－S1遷移がHOMO-1－LUMO、HOMO-LUMO+1であるため、遷移強度が小さいと考えることができ、実際に観測したスペクトルの強度が小さく、蛍光寿命も長いことが確かめることができた。
B1g振動の強度を小さく見積もるとS0とS1の振動のエネルギーと強度は似ているため振動構造は類似していると考えらる。
今回の実験から観測された蛍光の強度は小さくその寿命は1.4μsと長いことから実際の遷移強度が小さいことが確かめられた。
1Lb has much smaller Transition Intensity than 1La.
S1:long fluorescenece lifetime(about 1.4 μs)

26. A part of Assignment of Vibration
Scaling factor 　　　　 　

27. Rotational Envelopes Useful to distinguish between
ag bands and b1g bands
A-type
B-type
B-type
A-type
000

28. Direction of the Transition Moment
A type
ΔKa = 0, ±2, ・・・
ΔKc = ±1, ±3, ・・・
KaKc = ee-eo , oo-oe
B type
ΔKa = ±1,±3, ・・・
ΔKc = ±1, ±3, ・・・
KaKc = ee-oo , eo-oe
C type
ΔKa = ±1, ±3,・・・
ΔKc = 0, ±2,・・・
KaKc = ee-oe , oo-eo

29. Rotational Envelopes

30. Excitation spectra of Pyrene-h10 and Pyrene-d10