根據第一原理分子動態模擬搭配極化率自動相關函數(polarizability autocorrelation function)與其傅利葉轉換(Fourier transform)建立表面增強拉曼光譜(surface enhanced Raman scattering，SERS)，探討(1)吡啶吸附於銀團簇表面增強拉曼光譜的靜態化學增強機制及(2)4,4’-聯吡啶分子接面在不同導電態的SERS光譜。

第一部份中模擬了吡啶吸附於銀團簇於室溫的SERS光譜，並透過我們所開發的單頻濾波器(single-frequency-pass filter，SFPF)成功解析光譜上五個增強的拉曼訊號，包括υ6a、υ1、υ12、υ9a及υ8a。根據分析結果，分子吸附後部份電荷轉移至金屬，造成吡啶環上的鍵軟化(bond softening)，進而導致分子振動振幅增加。此外，吸附後所生成之氮-銀鍵的振動會與此五個分子振動模式耦合。最後，振動所促成的分子與金屬間電荷轉移，使吡啶在振動時伴隨著本身電荷密度的變化。這些因素使得吡啶振動時的極化率改變量有顯著的增加，因而導致拉曼訊號的增強。

第二部分中，4,4’-聯吡啶分子接面的模擬SERS光譜顯示導電態的光譜訊號比非導電態的增強效應高10~102倍。而訊號的相對強度方面，由於同時來自振動結構、振動耦合及電荷轉移因素的貢獻，在非導電態SERS光譜上的吡啶環呼吸運動的訊號有最大的增強效應。在導電態的SERS光譜上，由於振動結構及電荷轉移因素的貢獻，C-H 彎曲運動有最強的增強效應。此外，我們模擬了直立與傾斜的導電態4,4’-聯吡啶分子接面，並嘗試探討電荷在金屬間透過分子振動的傳遞機制。根據分析結果，我們觀察到了三種機制，包括(1)金屬之間一步電荷轉移、(2)金屬之間兩步電荷轉移、(3)金屬與分子之間的電荷交換。

The simulated surface enhanced Raman scattering (SERS) spectra are calculated by using ab initio molecular dynamics (AIMD) simulations in connection with a Fourier transform of the polarizability autocorrelation function to investigate (1) the static chemical enhancement behind the SERS spectrum of pyridine adsorbed on Ag20 cluster and (2) the SERS spectra of 4,4’-bipyridine molecular junction in different conductance states. 

The simulated SERS spectrum of pyridine adsorbed on Ag20 cluster (pyridine-Ag20) at room temperature reproduces all five enhanced vibrational modes, υ6a, υ1, υ12, υ9a, and υ8a, of pyridine, which can be assigned and identified by using the new analytical scheme, namely, single-frequency-pass filter (SFPF) based on the Fourier transform filtering technique. The calculated results indicate that the vibrational amplitudes of adsorbed pyridine are enhanced due to the electron transfer from pyridine to Ag¬20 cluster and the softening of pyridine bond. Furthermore, the N-Ag stretching of pyridine-Ag20 will couple with these five vibrational modes of adsorbed pyridine. Consequently, the charge transfer between pyridine and Ag20 cluster induced by different molecular vibrational modes prompts the redistribution of electron density of pyridine. These factors collectively cause the noticeable change in polarizability during the molecular vibrations and result in the enhancement of Raman peaks.

The simulated SERS spectra of 4,4’-bipyridine/gold single molecule junction in different conductance states show that the Raman peaks of ON state are enhanced by an additional one or two order of magnitude in comparison with OFF state. Considering the relative intensities of SERS spectra, the largest enhanced peak for OFF state is ring breathing mode due to the simultaneous contribution from structural change, vibrational coupling, and charge transfer. For ON state, the C-H bending mode has the largest enhancement due to structural change and charge transfer effects. In addition, 4,4’-bipyridine junction in the ON state with perpendicular and tilted orientations are examined for understanding the electron transport across the junction induced by different molecular vibrations. As a result, three types of mechanisms for charge transfer can be observed including (1) one-step and (2) two-step charge transfer from one Au4 cluster to another and (3) charge exchange between 4,4’-bipyridine and two Au4 clusters.

Chapter 1 Introduction 1

Chapter 2 Theoretical background 6
 2-1 Electronic calculation 6
  2-1-1 Density functional theory 6
  2-1-2 Exchange-correlation energy 9
  2-1-3 Pseudopotentails 11
 2-2 Molecular dynamics simulation 13
  2-2-1 Ab initio molecular dynamics 14
  2-2-2 Connection to thermodynamic variables 17
  2-2-3 Ensemble 18
 2-3 Normal mode analysis 21
 2-4 SIESTA method 24
  2-4-1 Pseudopotential 24
  2-4-2 Basis set 25
  2-4-3 Electron Hamiltonian 26
  2-4-4 Total energy 27
  2-4-5 External electric field 28

Chapter 3 Simulation of Raman Spectrum 29
 3-1 Raman differential scattering cross section 29
 3-2 Convolution and correlation function 35
 3-3 Simulated Raman spectrum 38
  3-3-1 Computing Raman spectrum from molecular dynamics simulation 38
  3-3-2 Vibrational modes assignment 41
  3-3-3 Fourier transforms of structural coordinate and charge autocorrelation functions 44

Chapter 4 Chemical mechanism of surface-enhanced Raman spectrum of pyridine adsorbed on silver cluster 46
 4-1 Introduction 46
 4-2 Computational details 51
 4-3 Results and discussion 52
  4-3-1 Calculated ground state properties 52
  4-3-2 Calculated Raman and SERS spectra 54
  4-3-3 Enhanced mechanism behind the SERS spectra 58
 4-4 Conclusion 67

Chapter 5 Surface-enhanced Raman spectra of 4,4'-bipyridine molecular junction in different conductance states 69
 5-1 Introduction 69
 5-2 Computational details 73
 5-3 Results and discussion 75
  5-3-1 Calculated ground state properties 75
  5-3-2 Calculated Raman and SERS spectra and vibrational modes assignment 76
  5-3-3 SERS spectra of the junctions in different states 81
  5-3-4 Electron transport properties of molecular junction with perpendicular and tilted orientations 88
 5-4 Conclusion 96

Reference 98

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