我們根據第一原理密度泛函理論(DFT)分子動態模擬搭配虛位勢與LCAO基底函數來模擬分子吸附到半導體表面系統的分子動態軌跡；並且，為了探討乙烯和甲醇吸附到矽(001)表面的化學反應，我們分別利用短時間傅利葉轉換和小波轉換來觀察分子的振動模式隨著反應進行的變化。
分子動態模擬計算的結果顯示，乙烯吸附到Si(001)表面的非解離吸附反應路徑可分為間接吸附反應, 直接吸附反應,和repelling反應三種。首先，在間接吸附反應中，乙烯先利用π-bond與表面的buckled-down的矽原子作用，再透過π-bond的乙烯表面旋轉後在同一dimer上形成di-σ-bond的乙烯吸附結構。我們利用短時間傅立葉轉換(Short-time Fourier transform)分析隨著時間變化的C=C鍵振動模式，其時間解析光譜指出C=C雙鍵振動頻率在轉成di-σ-bond的吸附結構後變成C-C單鍵振動頻率，並與實驗光譜結果一致。另外，在直接吸附反應中，在48或150 K的模擬溫度下，乙烯可直接形成di-σ-bond的分子結構吸附在相同的dimer或兩個相鄰的dimer上。這可說明實驗上，在48及150 K溫度下，會有C-C單鍵振動頻率產生的原因。最後，repelling反應則是乙烯與表面產生無效碰撞，而導致分子離開表面。
甲醇吸附到Si(001)表面的模擬解離吸附反應路徑可分為解離吸附反應和repelling反應二種，其中解離吸附反應為主要的反應路徑。在解離吸附反應中，甲醇先利用氧原子上的未共用電子對與表面buckled-down矽原子上的空懸鍵鍵結，再經由解離甲醇上的O-H鍵後形成吸附在表面上的methoxy與氫原子。同時，我們透過模擬紅外光譜，可以量測與實驗相符合的Si-H鍵的振動訊號。接著，我們使用小波轉換(Wavelet transform) 量測隨著反應進行的O-H鍵振動模式，透過時頻光譜的分析顯示當甲醇分子吸附到表面時，其O-H鍵振動頻率位移到3000~3400 cm-1的頻譜範圍。這主要是由於這個氫原子與表面上buckled-up矽原子的空懸鍵之間的吸引力會促使O-H鍵的拉伸，進而造成O-H鍵的斷裂後形成methoxy和氫原子吸附在表面上。

Density functional theory (DFT)-based molecular dynamic simulation in combination with localized basis sets and pseudopotentails is used to investigate the dynamic behaviors of molecules adsorption onto Si(001) surface. In particular, both short time Fourier transform (STFT) and wavelet transform (WT) are implemented to study evolution of molecular vibrational modes along the molecular adsorption process in order to unravel the elementary steps leading to ethylene adsorption and methanol adsorption onto the Si(001) surface.

Based on the dynamic behaviors of ethylene adsorption onto Si(001) surface, three possible reaction pathways – the indirect adsorption, the direct adsorption, and the repelling reaction – have been found. Firstly, in the indirect adsorption, the ethylene (C2H4(ads)) forms the π-bonded C2H4(ads) with the buckled-down Si atom to adsorb on the Si(001) surface and then turns into the di-σ-bonded C2H4(ads). In addition, the time-resolved spectra constructed by STFT illustrates that the C=C stretching mode of the π-bonded C2H4(ads) shifts to the C-C stretching mode of di-σ-bonded C2H4(ads). Secondly, in the direct adsorption, the di-σ-bonded C2H4(ads) is formed directly with the Si intra-dimer or the Si inter-dimer. This reaction pathway leads to the C-C stretching mode and the C-H stretching mode of the di-σ-bonded C2H4(ads) appeared in the vibrational spectra at 48 K and 150 K, respectively. Finally, in the repelling reaction, the C2H4(g) first interacts with the Si dimer and then is repelled by Si atoms. Consequently, neither the π-bonded C2H4(ads) nor the di-σ-bonded C2H4(ads) is formed on the Si(001) surface.

Regarding the dynamics behavior of methanol adsorption, the methanol (CH3OH(g)) firstly approaches the Si(001) surface to bond with the buckled-down Si atom within the temperature range between 100 K and 300 K, and then the O-H bond of CH3OH(ads) breaks within 10 ps only at 300 K due to the elongation of the O-H bond. Furthermore, the time-resolved vibrational spectrum constructed by WT illustrates that the O-H stretching mode of CH3OH(ads) shifts to below 3400 cm-1 when the H atom of the O-H bond is close to the buckled-up Si atom of the adjacent dimer. This analysis points out that the noticeable attraction force between the H atom of the O-H bond and the dangling bond at the buckled-up Si atom of the adjacent dimer prompts the O-H bond to break causing both CH3O and H species to adsorb on the buckled-down and buckled-up Si atoms, respectively.

Chapter 1, Introduction	1
1.1 Ethylene adsorption onto Si(001) surface	3
1.2 Methanol dissociative adsorption onto Si(001) surface	6
References	8

Chapter 2, Theoretical background	12
2-1. Electronic structure calculation	12
 A. Born-Oppenheimer approximation	12
 B. Density functional theory	13
 C. Exchange-correlation functions	16
 D. Hellman-Feynman Theorem	17
 E. Pseudopotential	20
2-2. Molecular dynamics simulations	24
 A. Equations of motion	26
 B. Thermostats	27
2-3. SIESTA	34
 A. Electron Hamiltonian	34
 B. Overlap integral, kinetic energy, and potential energy	34
 C. Electron Density	35
 D. Brillouin zone sampling	36
 E. Total energy	37
References	38

Chapter 3, Simulated time-resolved vibrational spectra	40
3-1. Fermi-Golden rule	40
3-2. Absorption of radiation	46
 A. Anisotropic IR Spectra	51
 B. Quantum correction factor	52
3-3. Time-frequency analysis	53
3-4. Short-time Fourier transform (STFT)	55
 A. The formula of STFT	55
 B. Window function	56
 C. The resolutions in time domain and frequency domain	59
3-5. Wavelet transform (WT)	60
 A. The formula of WT	60
 B. Wavelet function	61
 C. The time-resolved spectrum constructed by wavelet transform	64
References	66

Chapter 4, Ab initio molecular dynamics study of ethylene adsorption onto Si(001) surface: Short-time Fourier transform analysis of structural coordinate autocorrelation function	68
4-1. Introduction	68
4-2. Computational method	70
4-3. Results and discussion	74
 A. Reaction pathways of ethylene adsorption onto Si(001) surface	74
 B. Calculated infrared spectra of C2H4(g), π–bonded and di-σ-bonded C2H4(ads) on Si(001)	82
 C. The spectrograms of the C-C stretching mode by STFT-SCAF	85
 D. The effect of temperature on the indirect adsorption	88
4-4. Conclusions	90
References	91

Chapter 5, Methanol dissociative adsorption unveiled by ab-initio molecular dynamics and wavelet transform analysis	94
5-1. Introduction	94
5-2 Computational method	96
5-3. Results and discussion	103
 A. Reaction pathways of methanol adsorption onto Si(001) surface	103
 B. Calculated infrared spectra of methanol dissociative adsorption onto Si(001) surface	107
 C. The time-resolved spectra of the O-H stretching mode by wavelet transform	110
 D. The effect of temperature for methanol dissociative adsorption	113
5-4. Conclusions	116
References	117

List of Figures
1-1 (a) The HREELS spectrum of C2H4 on Si(100)-c(4x2) at 48 K. (b) After exposing C2H4 on Si(100) at 48 K followed by heating at 150 K, the spectrum was measured at 48 K.  4
1-2 Infrared spectra of CH3OH(ads) on Si(001) at 100 K for increasing exposures and after heating to various temperatures are shown from (a) to (d) and (e) to (g),
respectively.  5
1-3 Infrared spectra of CH3OH(ads) on Si(001) at 100 K for increasing exposures and after heating to various temperatures are shown from (a) to (d) and (e) to (g),
respectively.  7
2-1 Comparison of a wavefunction in the Coulomb potential of the nucleus (blue) to the one in the pseudopotential (red). The real wavefunction, the pseudo
wavefunction, and corresponding potentials match above a certain cutoff radius 
.  21
2-2 The flow chart of the molecular dynamics simulation. 25
3-1 A plot of versus, showing how the central peak as
 and narrows as .  44
3-2 The power spectrum of the signal  transformed by Fourier transform. 53
3-3 The amplitude of the signal . 53
3-4 The rectangular function is shown at moving time   . The window length T is 360 time steps. Total time steps is 1080.  57
3-5 There are three sine functions of this signal, sin(16x), sin(40x), and sin(40x)+sin(80x), at different time.  57
3-6 There are three frequencies - 16, 40 and 80 (1/time) - in the spectrogram. It shows the variations of frequencies over time-evolution. Blue color is close to zero and red color is climax of peak. 58
3-7 Real part of the morlet wave   , window function   , and real part of basis function are shown in blue, green, and red lines. The moving time  is 180 time steps and the constant Nosc is 8.  61
3-8 Two wavelet functions show different window lengths which depends on the scale factor s.  62
3-9 Normalized Gaussian curves with expected value μ and variance 2. The corresponding parameters are.  63
3-10 According to the Eq. (3-72), the signal is composed of sine waves in 1.0 ps. 65
3-11 Three peaks, i.e. 2958, 3333, and 3708 cm-1, are shown in the power spectrum of sine waves by using Fourier transform.  65
3-12 The spectrogram of sine waves shows three peaks at different time and frequency.  65
4-1 The side view of the structural models of the initial position of the C2H4(g) above 10 Å of the Si(001) surface at the beginning of DFTMD simulation. The orange dash-line shows that the C2H4(g) is placed on the x-y plane. The red arrow indicates the direction of the motion of the C2H4(g) with a translational energy of 10-5 eV.  72
4-2 Three types (a) (b) and (c) of initial structures of the C2H4(g). In (d), there are 25 different initial positions of the C2H4(g) on the x-y plane of 5 x 5 grids 10 Å above of the Si(001)-p(2x2) surface. The red points represent repeated positions in the neighboring unit cell.  
72
4-3 The structural models illustrate that (a) the C2H4(g) translates to the surface, (b) one of two carbon atoms bonds with one Si dimer, and (c) the other carbon atom
attaches on another Si dimer to form the end-bridge type of the di--bonded C2H4(ads).  76
4-4 The structural models illustrate that (a) the C2H4(g) translates to the surface, (b) the C2H4(g) approaches to the Si dimer, and (c) both carbons of the C2H4(ads) bond with Si atoms on the same dimer to form di--bonds.  76
4-5 The time-evolutions of the Si-C bond lengths in the direct adsorption, indirect adsorption, and repelling reaction are shown. The circle points in red, green,
and green indicate the time at which the C2H4(g) attaches to the surface.  77
4-6 The trajectories of the C-C bond length in (a) the direct adsorption on the inter-dimer, (b) the direct adsorption on the intra-dimer, (c) the indirect
adsorption, and (d) the repelling reaction. The average C-C bond lengths at different time intervals are listed. The dash-lines indicate the time at which the C2H4(g) attaches to the surface or changes its bonding type.  78
4-7 The total energy trajectories subtracted by the total energy at the first step of DFTMD in (a) the direct adsorption on the inter-dimer, (b) the direct adsorption
on the intra-dimer, and (c) the indirect adsorption. The insets show structural models at different time.  79
4-8 The structural models illustrate that (a) the C2H4(g) translates to the surface, (b) the C2H4(g) reaches the surface and then forms the -bond, and (c) the C2H4(ads)
turns the -bond into the di-s-bonds.  81
4-9 Simulated IR spectra of (a) C2H4(g), (b) the -bonded C2H4(ads), (c) the di-s-bonded C2H4(ads) on Si intra-dimer, and (d) the di-s-bonded C2H4(ads) on Si inter-dimer at 150 K.  83
4-10 The spectrogram obtained by STFT-SCAF for the C-C bond length in the direct adsorption on the Si inter-dimer. The red dotted-dash line is the time at which the C2H4(g) attaches to the surface.  86
4-11 The spectrogram obtained by STFT-SCAF for the C-C bond length in the direct adsorption on the Si intra-dimer. The red dotted-dash line is the time at which the C2H4(g) attaches to the surface.  87
4-12 The spectrogram obtained by STFT-SCAF for the C-C bond length in the indirect adsorption. The red dotted-dash line is the time at which the C2H4(g) attaches to the surface.  88
4-13 Distributions of the C-C bond length at 48 K (green line), 150 K (blue line) and 300 K (red line). The average C-C bond length is approximately 1.398 Å. The inset (left) indicates that the standard deviations of the C-C bond length at 48 K, 150 K, and 300 K are 0.0070 Å, 0.0139 Å, and 0.0247 Å, respectively.  89
4-14 Distributions of the angle between the Si dimer row and the C-C bond at 48 K (green line), 150 K (blue line), and 300 K (red line).  90
5-1 The side view of the structural models of the initital position of CH3OH(g) above 10 Å of the Si(001) surface at the beginning of DFTMD simulations. The orange dash-line shows that CH3OH(g) is placed on the x-y plane. The red arrow indicates the direction of the motion of CH3OH(g) with a translational energy of 4x10-5 eV.  98
5-2 Three types (a), (b), and (c) of initial structures of CH3OH(g) above 10 Å of the Si(001) surface.  98
5-3 Two wavelet waves in blue line show different window lengths which depends on the scale factor s or frequency . The Gaussian window function is shown in green line.  101
5-4 According to the Eq. (5-7), the signal is composed of sine waves in 1.0 ps.   102
5-5 Three peaks, i.e. 2958, 3333, and 3708 cm-1, are shown in the power spectrum of sine waves by using Fourier transform.  102
5-6 The time-resolved spectrum of sine waves shows three peaks at different time. 102
5-7 The trajectories of the Si-O bond length along the dissociative adsorption and repelling reaction are shown. Both red and blue arrows indicate the time at which the CH3OH(g) is attached to the surface.  104
5-8 The structural models illustrate that (1) the CH3OH(ads) is translated toward the Si(001) surface at stage 1, (2) the O atom of the CH3OH(ads) bonds with the
buckled-down Si atom at stage 2, and (3) both CH3O(ads) and H(ads) species are adsorbed on the Si(001) surface subsequent to the O-H bond cleavage.  105
5-9 The total energy trajectory subtracted by that at the first step of the DFTMD simulation in the dissociative adsorption.  105
5-10 The calculated IR spectra at 3 stages, i.e. CH3OH(g), CH3OH(ads),and CH3O(ads)+H(ads) are shown, respectively. Based on the O-H dipole moment at stage 1 and stage 2, the IR peaks of the O-H stretching mode are shown in the both insets.  109
5-11 The trajectory of the O-H bond length along the dissociative adsorption from 0.0 ps to 6.0 ps is shown.  111
5-12 The distances between the HO atom and the buckled-up Si atoms are shown in top figure, and the time-resolved spectrum constructed by WT is shown in bottom figure.  112
5-13 The distributions of the angle between the Si dimer and the O-H bond at 100 K (green line), 200 K (blue line), and 300 K (red line) are shown. In the structural
figure, the black and blue arrows mean the vectors of the Si dimer and the O-H bond, respectively.  115
5-14 The distributions of the O-H bond length at 100 K (green line), 200 K (blue line), and 300 K (red line) are shown. The right inset indicates that the standard
deviations of the O-H bond length at these temperatures are 0.0152, 0.0160, and 0.0165 Å, respectively.  116

List of Tables
3-1 The total time and corresponding frequency resolution are listed. 60
4-1 Counts of reaction pathways in the DFTMD simulations at 48 K, 150 K, and 300 K. Total counts of reaction pathways are 75 at each temperature.  80
4-2 The simulated vibrational frequencies in cm-1 for ethylene adsorption on the Si(001) surface, in comparison with experimental results.  84
5-1 In the dissociative adsorption, the various bond lengths at three stages are listed, i.e. CH3OH(g), CH3OH(ads), and CH3O(ads)+H(ads).  105
5-2 The count of two reaction pathways and corresponding populations at 100, 200, and 300 K are listed. Total number of the DFTMD simulations at each temperature is 75.  106
5-3 Calculated IR spectra of methanol dissociative adsorption, corresponding experimental IR spectra, and normal modes calculations are listed.  110

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