行政院國家科學委員會專題研究計畫 期中進度報告
光解過程電子極化之理論及離子成像實驗研究(1/3)
計畫類別： 個別型計畫 計畫編號： NSC91-2113-M-110-012- 執行期間： 91 年 08 月 01 日至 92 年 07 月 31 日 執行單位： 國立中山大學化學系(所) 計畫主持人： 陳國美 報告類型： 精簡報告 報告附件： 出席國際會議研究心得報告及發表論文 處理方式： 本計畫可公開查詢 中 華 民 國 92 年 5 月 19 日行政院國家科學委員會補助專題研究計畫
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光解過程電子極化之理論及離子成像實驗研究(1/3)
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計畫編號：NSC 92－2113－M－110－012－
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執行單位：國立中山大學化學系
中 華 民 國 92 年 5 月 15 日
(二)中英文摘要及關鍵詞
關鍵詞：對應定律，電子角動量極化，離子成像
本研究計畫利用離子成像技巧研究分子光解過程的動態學及對應定律。研 究重點包括光碎片之電子角動量極化及理論探討光解之對應定律。
Keywords：correlation rule, electronic angular momentum polarization, ion imaging
Ion imaging techniques will be employed to study molecular photodissociation dynamics and correlation rules. The present project focuses on the experimental studies of the electronic angular momentum polarizations of photofragments and the theoretical framework development of photodissociation correlation rules
(三)報告內容 I. 前言 自 1992 年以來，申請人在螢光成像實驗及理論研究領域，已發表 15 篇學 術論文，其中刊登於國際一流期刊的原創性論文共 11 篇。在分子光解動力學 上，我們發展了獨創的實驗方法，理論分析架構，產物向量對應的偵測技術與 分子動力行為之間的關係，緊密結合理論與實驗，是自成一家之言的研究工作。 最近我們已完成一套離子成像實驗裝置，將產物偵測的適用範圍及靈敏度大幅 提高，針對成對光解對應關係，包括動量對應，角動量對應，角動量極化及多 重向量對應的問題展開持續的研究。 II.研究目的 分子光解過程是眾多化學反應中最單純的，但是多原子分子的光解仍然極 為複雜而難以完整敘述其動力過程[1]。自從 70 年代採用調頻雷射偵測產物的能 態佈居，角動量極化，角分佈，速度分佈，多重解離通道分支比例等特性以來， 在實驗技術上有極大進展，包括雷射引發螢光(LIF)[2,3]，共振增強多光子電離 (REMPI)[2,3]，飛秒技巧[4]，飛行時間光碎片平移光譜學 (TOFPTS)[5]，Rydberg 標 示 技 巧[6,7](Rydbergtaggng) 及 成 像 技 術[8,9](ion-imaging and fluorescence imaging)等有力研究工具，獲得大量極有意義的動力學資料，對促進了解控制化 學反應進行的勢能面，角動量耦合及其動力學具深遠影響。
成像技術是一種能同時提供多重動力資料的研究方法，在採用速度投射 (velocity mapping)技巧[10]將飛散的產物離子(經由 REMPI 產生)重新聚焦於多通 道平板偵測器(multichannal plate detector, MCP)而大幅降低了成像的散光，從而 提昇其速度解析能力， 離子成像已成 為研究 基本化學反應的一種重 要實驗技 術。本計畫就是利用我們自行建造的一套離子成像裝置進行實驗研究，詳情請 見第三節。
[參考資料]
[1] R. Schinke, Photodissociation Dynamics (Cambridge Univ. Press, Cambridge, 1993).
[2] Atomic and Molecular Beam Methods , ed. G. Scoles (Oxford Univ. Press,
New York, 1998), Vol. I.
[3] The Chemical Dynamics and Kinetics of Small Radicals , eds. K. Liu
and A. Wagner (World Scientific, Singapore, 1995).
[4] L. R. Khundkar and A. H. Zewail, Annu. Rev. Phys. Chem. 41, 15 (1990). [5]A. M. Wodtke and Y. T. Lee, in Molecular Photodissociation Dynamics, eds. M.
N. R. Ashfold and J. E. Baggott (The Royal Society of Chemistry, London, 1987).
Chem. Phys. 92, 7027 (1990).
[7] L. Schnieder, K. Seekamp-Rahn, J. Borkowski; E. Wrede, and K. H. Welge, Science, 269, 207 (1995).
[8] A. J. R. Heck and D. W. Chandler, Annu. Rev. Phys. Chem. 46, 335 (1995). [9] K. Chen, Chem. Phys. Lett. 198, 288 (1992).
[10] A. T. J. B. Eppink and D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1997).
III. 研究方法 － 實驗部份
我們採用 Parker 的 photofragment velocity mapping 設計觀念，如下圖所示 [Buijsse, et. Al. JCP 108, 7229 (1998)]:
組裝完成的離子影像實驗裝置機械設計圖如附。已完成真空測試並能達成設計目 標。目前 (92 年 5 月)繼續特性測試，諸如加速電場的電壓控制獲取清晰成像，影 像尺度與反彈速度關係的校準以及 MCP 脈衝電壓的最佳控制，影像平均等問 題。整套裝置除分子束真空室外，還包括脈衝束閥，MCP 偵測器，CCD 相機， 各式脈衝高壓電源及雷射光源，是我們累積多年儀器設備始能執行此一前沿實 驗。 理論架構發展部分： a. 重要雙原子分子各基態激發態與其原子漸進態之間的變換關係。(包括 O2, NO, OH, CN 等) b. 利用密度矩陣方法計算在 2 + 1 REMPI 偵測方法下產物成對對應的狀態解析 角分佈(包括 I, O, Cl, NO, N2等) CCD TOF laser PC PS MCP PV SK R
source ionization detection E G
c. 推展 Hund 耦合方式(a)至(c)變換關係至線性三原子分子，如 ICN。
d. 發展三原子分子親態(parental state)與成對產物態之間的對應定律，如 H2O, NO2, N2O 等。
IV. 結果與討論 1. 儀器採購
本年度獲得貴會支援 850,000 元(配合本校重點支援款 150,000 元)先行採購全 套 Roper Scientific/Princeton Instrument數 位 相 機 系 統7361-0001 P I-MAX 1024RB，預計 92 年 7 月可送達。唯尚缺 400,000 元購置一套控制器及數位器 (7438-0009 PTG & Controller with 16 bit 100 kltz digitizer)，擬請同意於下年度計 畫研究設備費 800,000 元內勻支(採購基本型倍頻裝置)。
2. 發表Electronic angular momentum polarization of atomic fragments in diatomic
photodissociat ions: Correlat ion between states in the mo lecular and the asymptotic regions, JCCS 49, 723 (2002)。如附錄 I。
3. 撰寫初稿Identification of structural symmetries of CH3 and CD3 by their nuclear spin statistical weights and line strength of transitions。如附錄 II。
附錄 II
Identification of structural
symmetries of
CH
3and
CD
3by their nuclear spin statistical weights and line strengths of
transitions
Kuo-mei Chena)
Department of Chemistry, National Sun Yat-sen University, Kaohsiung,
a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
Planar structures of CH and 3 CD with a 3 D3h ground state symmetry
were first inferred from the intensity alternations of the K 0 sub-band in the 2144 Å transitions of CD . Nuclear spin statist3 ical weights of various rovibronic levels of CH and 3 CD are reexamined under the symmetry 3 operations of C3υ and D3h point groups. The line strength formulas for
either a planar or a pyramidal structure are inconsistent with the experimentally observed transitions. Only a quasiplanar structure with a small potential barrier (less than the zero-point energy) along the inversion normal mode for the methyl radical agrees well with the spectroscopic results. For future analyses of
spectroscopic transitions o f CH3 and CD3, symmetry-adapted
rovibronic-nuclear spin wave functions and rotational line strengths reported in this work should be utilized.
I. INTRODUCTION
In his classical work, Herzberg1 inferred the planar structure of CD 3
from the intensity alternations of the 0K sub-band in the B~ X~
transition around 2144 Å. The physical reasoning which ascertained the even-odd alternation of nuclear spin statistical weights for 0K rotational energy levels of an XY molecule with a 3 D3h symmetry has long been
established by the scheme of Wilson,2,3 where the irreducible representations of the rotational subgroups of the full molecular point group were employed to classify the energy states. Since then, several researchers have extended the classification scheme of molecular energy levels to those labeled by irreducible representations of the full point group. Notably, Hougen4 has derived the transformation relationships of rotational wave functions of a symmetric top under rotational and reflection symmetry operations. When the transformation properties of the complete wave functions are examined under all the possible
symmetry operations, Hougen’s results will play a pivotal role.
Although early electron spin resonance studies5 on the methyl radical did not reach a definite conclusion on its planarity, Hirota and co-workers6 elucidated unequivocally the D3h structure of CH3 b a s e d o n t h e i r high-resolution infrared diode laser absorption spectroscopy of the v band. 2
Additional infrared absorption studies on CD and the 3 v band by Hirota, 3
Sears and their co-workers followed.7-11 High-resolution coherent Raman spectra of the v band of 1 CH3, which have been obtained by Nibler and
co-workers,12,13 were analyzed according to a planar equilibrium geometry. In recent years, rotationally-resolved, resonance-enhanced multiphoton ionization spectroscopy (REMPI) of the methyl radical14-16 has been employed to study the photodissociation dynamics of its precursors.17-20 To extract
information on the population distribution of methyl radicals in various rotational states, the two-photon absorption line strength formula of symmetric
tops21 was invariably utilized in the analysis of the REMPI spectra. Because the symmetry-adapted wave functions are linear combinations of symmetric top rotational state vectors when nuclear spin statistical weights are taken into account,22 we decide to reexamine the problem of allowed rovibronic states of
3
quasiplanar (with a potential barrier along the inversion normal mode) and pyramidal molecular geometries. It turns out unexpectedly that the quantum number K (the projection of the rotational angular momentum N onto the
molecular z-axis) should be constrained more stringently than those stated in previous literatures2, 3 for a planar D3h geometry. It is the purpose of this
work to report the explicit rovibronic-nuclear spin wave functions of allowed energy levels and their statistical weights under the three assumed geometries. Comparisons of the present results with spectroscopic transitions of CH and 3
3
CD in the infrared and ultraviolet spectral regions were implemented to infer their correct structure. The line strength formula for a two-photon absorption process21 h a s b e e n e x t e n d e d t o t r e a t v i b r o n i c t r a n s i t i o n s ,w h e r e symmetry-adapted rovibronic-nuclear spin wave functions in the present treatment were utilized.
II. SYMMETRY-ADAPTED ROVIBRONIC STATES OF CH AND 3
3
CD
When the influence of an inversion barrier on the geometry of an XY 3 molecule is considered, there are three possible structures: 1) a planar D3h
barrier, and 3) a pyramidal C3υ geometry with a large barrier. A schematic
diagram is depicted in Fig. 1 to illustrate the dependence of the potential energy curve on the inversion vibration mode (v ). For the two structures with a 2 C3υ
symmetry, the Q2 is an umbrella mode (a ). For the geometric structure with a 1
h
D3 symmetry, the Q2 is an out-of-plane bending mode (a ). The reflection 2 symmetry properties of the vibrational levels (v mode) with respect to 2 υ
in the case of a quasiplanar structure are marked by a “+” or a “” superscript, for levels with eigenvalue +1 or 1, respectively.
We follow closely the scheme of Townes and Schawlow22 to construct the explicit rovibronic-nuclear spin wave functions of CH and 3 CD in a few 3
relevant vibronic states. Because the spin-rotation interaction of the methyl radical is quite small (coupling constant 0.012 cm1
),6 one can ignore the role of the electron spin in the discussion of its symmetry properties.23 Our results are listed in Tables I to VI. Nuclear spin basis functions for CH and 3 CD 3
are presented in Tables I and V, respectively, including their transformation properties under various symmetry operations. The rotational wave function of a symmetric top molecule NKM is a normalized Wigner rotation matrix,24 where N denotes the total rotational angular momentum quantum number, and K is its projection onto the molecular z-axis. Its transformation
properties have been thoroughly discussed by Hougen4 and are given by NKM K i NKM C3 exp( 2 /3) , (1a) KM N NKM N K υ (1) , (1b) and NKM NKM K h (1) . (1c)
When CH and 3 CD are in a planar configuration, the symm3 etry operation )
(
2 x
C in a D3h point group is equivalent to υ . The original treatment of the nuclear spin statistical weight by Wilson2 has not considered the symmetry operation h. From Eq. (1c), it is clear that NKM is symmetric under h when K is even, and is antisymmetric under h when K is odd.
III. IDENTIFICATION OF THE GROUND STATE GEOMETRY OF
3
CH AND CD 3
From Tables II and III, it is evident that the constraint on the allowed K
observations. If the methyl radical adopts a D3h geometry, then all the even
K levels will be missing when it is in a 2A vibronic state, and all the odd 2 K and even N , K 0 levels will be absent when it is in a 2A vibronic 1
state. On the contrary, the even-odd alternations in the optical and infrared transitions1, 6 were observed only in those K 0 levels. Thus, one can safely rule out the possibility of a planar methyl radical.
If the methyl radical adopts a pyramidal C3υ structure with a high
inversion barrier such that the vibrational wave function of the umbrella mode cannot tunnel through the potential hump, then the v vibrations will always 2
display an a symmetry no matter if the vibrational quantum number 1 2 is chosen to be even or odd. It infers that the statistical weight should be those without considering the contribution of the v vibrations. On the other hand, 2
Hirota and co-workers6 have found that the even-odd alternation of the K 0 rotational levels in the ground electronic state of methyl radicals is reversed when infrared transitions from even and odd 2 levels are examined. In light of these experimental evidences, a quasiplanar C3υ geometry is the remaining
candidate to be considered. Since no inversion doubling of K 0 rotational levels of methyl radicals has been observed in the high-resolution infrared absorption experiment,6 the height of the inversion barrier must be less than the
zero-point energy of the v mode (303 cm2 1).6 The potential energy curve of a quasiplanar C3υ structure in Fig. 1b is depicted according to this scenario. Townes and Schawlow22 have elucidated that the v vibrational wave 2
functions in a quasiplanar structure undergo a Q2 Q2 inversion when two protons or deuterons are permuted. Because this permutation of two nuclei is equivalent to υ , the eigenvalue of the umbrella mode under υ is +1 when
2 is even, and 1 when 2 is odd.
Combining all these facts, we can establish that the methyl radical should adopt a quasiplanar C3υ structure with a 2A2 ground electronic state. Its vibronic symmetry depends on whether 2 i s even (2A ) o r o d d (2 2A ). 1
Referring to Table IV, we list the explicit rovibronic-nuclear spin wave functions and their corresponding statistical weights when CH is in a 3 2A2
vibronic state. For the case of a 2A vibronic state, one just interchange the 1
wave functions and the statistical weights of even N entries with those of odd
N entries, as listed in Table IV. For brevity, we only consider the case of
3
CD i n a q u a s i p l a n a r C3υ s t r u c t u r e . T h e s y m me t r y-adapted rovibronic-nuclear spin wave functions and their statistical weights of CD in 3 a 2A2 vibronic state are listed in Table VI. Similarly, interchange of the even and odd N entries of Table VI should be executed when CD is in a 3
1 2
A vibronic state.
IV. ROTATIONAL LINE STRENGTH S
To facilitate the spectroscopic analysis of the methyl radical, especially the
REMPI detection of reaction products, we calculate the rotational line strengths24 o f o n e- a n d t w o-photon parallel transitions (K 0) o f a
quasiplanar C3υ symmetry top. For perpendicular transitions (K 1) to degenerate vibronic states (E one should consult Hougen), ’s scheme4 to construct the symmetry-adapted wave functions.
For the infrared transitions of CH from an even 3 υ to a 2 υ +1 2 vibrational state and K0 (K 0), the rotational line strength S(N,N) is given by24 2 0 0 0 1 ) 1 2 )( 1 2 ( ) , ( N g N N N N N S , (2)
where N must be an even integer, the statistical weight g is 4, and ( ) is a 3-j symbol.24 From the properties of 3-j symbols, N can only be N1. Transitions from odd N rotational levels are missing because their statistical
weights are null (see Table IV). For the infrared transitions of CH from an 3 odd υ to a 2 υ +1 vibrational state an2 d K0, S(N,N) is identical to
Eq. (2), except that N is an odd integer. For the Q branch of K0 transitions, one can prove easily that
2 1 2 2 0 1 ) ) 1 ( 1 ( 2 1 ) 1 2 ( ) ( K K N N N g N S N 2 2 0 1 ) 1 2 ( K K N N N g . (3)
Similarly, the rotational line strength for the R and P branch (N N 1) of 0 K transition is given by 2 1 0 1 ) ) 1 ( 1 ( 2 1 ) 1 2 )( 1 2 ( ) , ( K K N N N N g N N S N N 2 0 1 ) 1 2 )( 1 2 ( K K N N N N g . (4)
In Eqs. (3) and (4), g is 4 when K is a multiplier of 3, and is 2 when K is not a multiplier of 3 (see Table IV). These infrared rotational line strength formulas of CH are in total conformity wi3 th the experimental results by Hirota et al.6 When the infrared transitions of the v mode of 2 CD are 3
considered, appropriate statistical weights (see Table VI) should be utilized in the above rotational line strength formulas.
For the 2+1 REMPI detection of CH and 3 CD through resonant 3
Rydberg states (np 2A2 X~ 2A2 , K 0 parallel transitions21), the rotational line strength formula for the two-photon absorption process can be obtained by substituting the symmetry-adapted rovibronic-nuclear spin wave functions into the theoretical expressions of Chen and Yeung.21 F o r a commonly employed detection scheme, we consider the case of two-photon absorption of identical photons in polarization, where “ ” denotes that the probe laser is plane-polarized. Our results on the two-photon absorption rotational line strengths of CH and 3 CD are summarized in Tables VII and 3
VIII, respectively. It is assumed that the assignment of excited Rydberg states is
2
2A in a quasiplanar
υ
C3 geometry. Both experimentally observed 0 , 00 2 , 02
0 2
2 , 2 , 22 2 , 11 2 vibronic bands13 17 and the feasible 2 , 10 2 transitions are 10 treated in detail. The electronic-vibronic integrals E and F in the line strength expressions have been defined in Ref. 21. Although symmetry-adapted rovibronic-nuclear spin wave functions are employed in the derivation, the original formula of two-photon absorption rotational line strengths by Chen and Yeung21 is retained just by introducing appropriate statistical weights. It is
known that the Franck-Condon factors for displaced oscillators with unequal vibrational frequencies are in general non-null for υ2= odd transitions.25 Because the v mode frequencies of the excited 32 p Rydberg state are 1342
cm-1 for CH and 1034 cm3 -1 for CD317 in comparison with 606 cm-1 for
3
CH 6 and 458 cm-1 for CD38 in the ground electronic state, it is reasonable to speculate that their equilibrium positions for the double-minimum potentials are not the same. On the other hand, the rotational line strengths for the 2 , 10
0 1
2 vibronic bands are identically zero (see Tables VII and VIII). Thus, the absence of the 2 , 10 2 vibronic transitions in the 2+1 REMPI spectra of 10
3
CH and CD317 supports that the excited Rydberg states are also in a quasiplanar 2A electronic levels. 2
Different spectral profiles of the REMPI spectra of the 0 (00 2 , 02 2 , 02 2 ) 22 and 2 (11 2 ) vibronic bands have been identified.13 17 These spectroscopic characteristics are attributed to their differences in 0K rotational line strength expressions (see Tables VII and VIII) and the preferentially populated
0
K l e ve l s i n t h e p h o t o l y t i c ge n e r a t i o n o f me t h y l r a d i c a l s . I f rotationally-resolved REMPI spectra of the 2 vibronic bands of 11 CD are 3
available in the future, in which the effect of predissociation on the linewidths is less than those in the case of CH ,3 15 then the line strength expressions listed
in Table VIII are indispensable in spectral analyses.
From the above analysis on rotational line strengths and comparisons with spectroscopic transitions, we infer that both ground and excited Rydberg states of CH and 3 CD h a ve a 3 2A symmetry (2 υ =0) in a quasi2 planar
υ
C3 structure. Because their electronic wave functions are antisymmetric with respect to υ, it is interesting to note the spatial orientation of the unpaired
electron of the methyl radical. An instantaneous configuration of the methyl radical at the minima of the double-minimum potential (see Fig. 1b) is depicted in Fig. 2a. For comparison, the commonly-accepted model of the methyl radical is depicted in Fig. 2b.
V. CONCLUSIONS
Combining theoretical reasonings and experiment al evidences, we
conclude that the methyl radical has a quasiplanar C3υ structure, and that the barrier heights of the double-minimum potential with respect to the v mode 2
should be less than their zero-point energies of CH and 3 CD3,respectively.
A state-of-the-art quantum chemical calculation is urgently needed to confirm that the electronic ground state of the methyl radical is 2A and that the 2
rotational line strength expressions for 2+1 REMPI processes of various vibronic bands of the methyl radical are useful to extract information on their rotational state population and alignment.
ACKNOWLEDGMENT
This research was supported by the National Science Council of the Republic of China.
