• 沒有找到結果。

本研究利用密度泛函理論的 B3LYP 和 B3PW91 泛函數,配合不同基底函數 6-311++G(d,p)、6-311++G(2d,p)及aug-cc-pVTZ計算出HFCS分子、HFCS+(X)離子基態、

與HFCS+(A)離子第一激發態的平衡結構,得到其鍵長與鍵角,也計算了兩者的諧和振動 頻率,雖然分子與離子計算結果無實驗值做對照,但發現六種基組數值已十分貼近,也 與Baker等人[43]的理論計算結果相近,顯示 B3LYP 和 B3PW91 泛函數對於本研究的 計算具有可行性。

在絕熱游離能的計算上,本研究利用CCSD(T)為計算方法,採用B3LYP/aug-cc-pVTZ 基組計算下的平衡結構,求出其能量ECBS,並進行零點能(zero-point energy, ZPE)修正,

求得絕熱游離能與實驗值極為相近,離子基態及第一激發態的計算值為10.16和11.46 eV,

與實驗值的差距分別為0.01和0.03 eV。

最後我們利用量子化學計算所得到的平衡結構和振動模式,再用張嘉麟教授於2013 年開發的FCI計算公式計算出法蘭克-康登因子,並模擬HFCS電離成HFCS+(X)離子基態、

HFCS+(A)離子第一激發態之光電子光譜,再與實驗光電子光譜相比對,結果發現兩者的 光譜型態與實驗光譜極為相似,且在訊號強度分布和相對能量都有極高度類似。

在光譜模擬過程中,我們可從計算出的法蘭克-康登因子明確的辨認 HFCS 分子每 一個躍遷訊號是來自於哪一個振動模式的躍遷、或哪些振動模式組合成的躍遷,並明 確標定之。這相對於實驗光譜來說,要清楚分辨每一個躍遷訊號是十分困難的,但透 過模擬光譜中計算所得的激發能與光譜強度分佈,便能明確的進行實驗光譜的分析與 標定。

總結而言,本研究是第一次對於解析HFCS的光電子光譜提供理論計算的佐證依據,

模擬光譜與實驗光譜吻合,絕熱激發能的計算也與實驗值相當接近,故我們支持Baker 等人觀察到的分子,應是HFCS無誤。本研究顯示,結合理論與實驗的光電子光譜,可 做為鑑定分子的工具之一,未來可進行更多的相關研究,以探究其可行性。

參考文獻

[1] 蘇世剛,牟中原, Chemistry (The Chin. Chem. Soc., Taiwan) 47 (1989) 308.

[2] I. N. Levine, Quantum chemistry, Pearson, Boston, (2014).

[3] L. H. Thomas, The calculation of atomic fields, Proc. Camb. Phil. Soc. 23 (1927) 542.

[4] E. K. U. Gross, R. M. Dreizler, Density Functional Theory, Plenum, New York, (1994).

[5] J. L. Chang , C. H. Huang , S. C. Chen, T. H. Yin, Y. T. Chen , An analytical approach for computing Franck-Condon integrals of harmonic oscillators with arbitrary dimensions, J. Comput. Chem. 34 (2013) 757.

[6] J. Franck, Elementary processes of photochemical reactions , Trans. Faraday Soc. 21 (1926) 536.

[7] E. Condon , A Theory of Intensity Distribution in Band Systems, Phys. Rev. 28 (1926) 1182.

[8] E. U. Condon, Nuclear Motions Associated with Electron Transitions in Diatomic Molecules, Phys. Rev. 32 (1928) 858.

[9] A. S. Coolidge, H. M. James, R. D. Present, A Study of the Franck‐Condon Principle, J.

Chem. Phys. 4 (1936) 193.

[10] J. L. Chang, Y. T. Chen, Ab initio calculations of low-lying electronic states of vinyl chloride, J. Chem. Phys. 116 (2002) 7518.

[11] J. L. Chang , A new formula to calculate Franck-Condon factors for displaced and distorted harmonic oscillators, J. Mol. Spectrosc. 232 (2005) 102.

[12] J. L. Chang, C. W. Tsao, Ab initio calculations of excited states of vinyl bromide, Chem. Phys. Lett. 428 (2006) 23.

[13] J. L. Chang, A new method to calculate Franck–Condon factors of multidimensional harmonic oscillators including the Duschinsky effect, J. Chem. Phys. 128 (2008) 174111.

[14] R. S. Mulliken, Electronic Structures of Polyatomic Molecules and Valence. II.

Quantum Theory of the Double Bond, Phys. Rev. 41 (1932) 751.

[15] C. Manneback, Computation of the intensities of vibrational spectra of electronic bands in diatomic molecules, Phys. 17 (1951) 1001

[16] F. Duschinsky, On the interpretation of electronic spectra of polyatomic molecules I.

The Franck-Condon principle, Acta Phys., URSS 7 (1937) 551.

[17] T. E. Sharp, H.M. Rosenstock, Franck-Condon Factors for Polyatomic Molecules, J.

Chem. Phys. 41 (1964) 3453.

[18] P. M. Hunt,M. S. ChildInterference structure in franck—condon overlap functions, Chem. Phys. Lett. 58(1978)202

[19] C. Manneback, Computation of the intensities of vibrational spectra of electronic bands in diatomic molecules, Phys. 17 (1951) 1001.

[20] A. M. Mebel, M. Hayashi, K. K. Liang, S.H. Lin, Ab Initio Calculations of Vibronic Spectra and Dynamics for Small Polyatomic Molecules:  Role of Duschinsky Effect, J.

Phys. Chem. A 103 (1999) 10674.

[21] R. Islampour, M. Dehestani, S. H. Lin, A New Expression for Multidimensional Franck–Condon Integrals, J. Mol. Spectrosc. 194 (1999) 179.

[22] B. Hajgató, D. Szieberth, P. Geerlings, F. DeProft, M. S. Deleuze, A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes, J. Chem. Phys. 131 (2009) 224321.

[23] S. Rayne , K. Forest, Singlet–triplet excitation energies of naphthyl cations: High level composite method calculations suggest a singlet ground state, J. Comput. Chem. 983 (2012) 69.

[24] E. Hutchisson, Band Spectra Intensities for Symmetrical Diatomic Molecules, Phys.

Rev. 36 (1930) 410.

[25] C. Manneback, Computation of the intensities of vibrational spectra of electronic bands in diatomic molecules, Phys. 17 (1951) 1001.

[26] M. Wagner, Exakte Berechnung von Franck-Condon-Integralen, Z. Naturforsch Teil A 14 (1959) 81.

[27] F. Ansbacher, A note on the overlap integral of two harmonic oscillator wave functions , Z. Naturforsch Teil A 14 (1959) 889.

[28] S. Koide, Ü ber die Berechnung von Franck-Condon-Integralen, Z. Naturforsch Teil A 15 (1960) 123.

[29] E. V. Doktorov, I. A. Malkin, V. I. Man'ko, Dynamical symmetry of vibronic transitions in polyatomic molecules and the Franck-Condon principle, J. Mol.

Spectrosc. 56 (1975) 1.

[30] E. V. Doktorov, I. A. Malkin, V. I. Man'ko, Dynamical symmetry of vibronic transitions in polyatomic molecules and the Franck-Condon principle, J. Mol.

Spectrosc. 64 (1977) 302.

[31] L. S. Cederbaum, W. Domcke, A many‐body approach to the vibrational structure in molecular electronic spectra. I. Theory, J. Chem. Phys. 64 (1976) 603.

[32] D. Gruner, P. Brumer, Efficient evaluation of harmonic polyatomic Franck-Condon factors, Chem. Phys. Lett. 138 (1987) 310.

[33] J. Lermé, Multidimensional Franck-Condon integrals in the case of strong normal coordinate mixing, Chem. Phys. 145 (1990) 67.

[34] P. T. Ruhoff, Recursion relations for multi-dimensional Franck-Condon overlap integrals, Chem. Phys. 186 (1994) 355.

[35] A. Toniolo, M. Persico, Efficient calculation of Franck–Condon factors and vibronic couplings in polyatomics, J. Comput. Chem. 22 (2001) 968.

[36] A. Hazra, M. Nooijen, Derivation and efficient implementation of a recursion formula to calculate harmonic Franck–Condon factors for polyatomic molecules, Int. J.

Quantum Chem. 95 (2003) 643.

[37] M. Dierksen, S. Grimme, An efficient approach for the calculation of Franck–Condon integrals of large molecules, J. Chem. Phys. 122 (2005) 244101.

[38] P. Å . Malmqvist, N. Forsberg. Franck-Condon factors for multidimensional harmonic oscillators, Chem. Phys. 228 (1998) 227.

[39] R. Islampour, M. Dehestani, S. H. Lin, A New Expression for Multidimensional Franck–Condon Integrals, J. Mol. Spectrosc. 194 (1999) 179.

[40] H. Kikuchi, M. Kubo, N. Watanabe, H. Suzuki, H. Suzuki, Computational method for calculating multidimensional Franck–Condon factors: Based on Sharp-Rosenstock’s method, J. Chem. Phys. 119 (2003) 729.

[41] C. L. Lee, S. H. Yang, S. Y. Kuo, J. L. Chang, A general formula of two-dimensional Franck–Condon integral and the photoelectron spectroscopy of sulfur dioxide, J. Mol.

Spectrosc. 256 (2009) 279.

[42] J. L. Chang, S. T. Huang, C. C. Chen, T. T. Yang, C. C. Hsiao, H. Y. Lu, C. L. Lee, Theoretical calculations of C2v excited states of SO2+, Chem. Phys. Lett. 486 (2010) 12.

[43] J. Baker, V. A. Butcher, J. M. Dyke, E. P. F. Lee, A Study of the Reactions of Molecular Fluorine with CH3SCH3 and CH3SSCH3 with UV Photoelectron Spectroscopy: First Observation of the HFCS Molecule, J. Phys. Chem. 99 (1995) 10147.

[44] E. Schrödinger, Quantisierung als Eigenwertproblem, Ann. Phys. (Leipzig) 79 (1926) 489.

[45] E. Schrödinger, An Undulatory Theory of the Mechanics of Atoms and Molecules, Phys. Rev. 28 (1926) 1049.

[46] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas, Phys. Rev. B136 (1964) 864.

[47] W. Kohn, L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. A 140 (1965) 1133.

[48] A. D. Becke, Density‐functional thermochemistry. I. The effect of the exchange‐only gradient correction, J. Chem. Phys. 96 (1992) 2155.

[49] A. D. Becke, Density‐functional thermochemistry. II. The effect of the Perdew-Wang generalized-gradient correlation correction, J. Chem. Phys. 97 (1992) 9173.

[50] S. M. Blinder, Basic Concepts of Self-Consistent-Field Theory, Am. J. Phys. 33 (1965) 431.

[51] B. G. Johnson, M. J. Frisch, Analytic second derivatives of the gradient-corrected density functional energy. Effect of quadrature weight derivatives, Chem. Phys. Lett.

216 (1993) 133.

[52] B. Miehlich, A. Savin, H. Stoll, H. Preuss, Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr, Chem. Phys. Lett. 157 (1989) 200.

[53] A. D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A38 (1988) 3098.

[54] J. C. Slater, Quantum Theory of Molecular and Solids, Vol. 4, McGraw-Hill, NewYork, (1974).

[55] M. J. Frisch, J. A. Pople, J. S. Binkley, Self‐consistent molecular orbital methods 25.

Supplementary functions for Gaussian basis sets, J. Chem. Phys. 80 (1984) 3265.

[56] T. H. Dunning Jr., Gaussian basis sets for use in correlated molecular calculations. I.

The atoms boron through neon and hydrogen, J. Chem. Phys. 90 (1989) 1007.

[57] R. A. Kendall, T. H. Dunning Jr., R. J. Harrison, Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions, J. Chem. phys. 96 (1992) 6796.

[58] D. E. Woon, T. H. Dunning Jr., Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon, J. Chem. Phys. 98 (1993) 1358.

[59] K. A. Peterson, D. E.Woon, T. H. Dunning Jr., Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H + H2 → H2 + H reaction, J. Chem. Phys. 100 (1994) 7410.

相關文件