臺灣博碩士論文加值系統

這篇論文的主要工作在於研究甲醛分子線性寡聚合物的非線性光學性質的研究，並對該結果和梯形寡聚合物的結果做個比較。我們選用有現場方法(finite field approach)來估算靜態非線性光學係數(static hyperpolarizablity)並且使用Nakano 等人所提出的hyperpolarizabilty density analsis(HDA) 來觀察空間中電子對於β和γ值的貢獻情形。
在決定最佳化結構的部份，我們使用DFT(密度泛涵理論) 搭配數種基底函數(basis set)來與甲醛實驗值比較。得到的結果是B3LYP/6-31+G(d,p)此種組合與實驗值最接近並且利用此組合來得到 -(-H2CO-)n-,n=2~7的最佳化結構，該結構做為接下來的研究之用。
計算靜態非線性光學係數時，將C=O方向定為x方向，此方向βxxx and γxxx的貢獻為其主要。線性寡聚合物βxxx and γxxx 的趨勢表現則是隨著甲醛單體的增加而隨之增加和梯形寡聚合物γxxx 的趨勢相同，但是與梯形寡聚合物 βxxx呈現振盪的表現則有些不同。HDA中則用圖形來說明空間中電子對於非線性光學性質的貢獻情形。在比較非線性光學係數與甲醛單體數目的比值時，線性寡聚合物的值都比梯形寡聚合物的值來的大。

We investigate nonlinear optical properties of linear formaldehyde oligomers -(-H2CO-)n-,n=1~7 by using density functional theory calculation in comparison with those of the ladder formaldehyde oligomers . The geometries of the formaldehyde and its linear oligomers are optimized by the B3LYP using the 6-31+G(d,p) basis set. The finite-field approach(FF) could be used to calculate the static first and second hyperpolarizablitityβxxx and γxxx. The hyperpolarizability density analysis (HDA) provides pictorial and intuitive understanding of the spatial contribution to the static hyperpolarzability. The βxxx and γxxx values increase with number of formaldehyde (n) for the linear connection, but only γxxx value increase with n for the ladder connection. The NLO properties/n of the linear oligomers are greater than those of the ladder oligomers.

Abstract………….…………………………………....................I
中文摘要……………….………………………………………II
Contents………....…………………………………………….III
List of Tables………….……………………………………... IV
List of Figures…………..……………………………………VII

Chapter 1 Introduction………………………………………….1
1.1 Formaldehyde………………………………………………………...2
1.2 The NLO studies for the organic oligomers NLO……………..2
1.3 NLO…………………………………………………………………..3

Chapter 2 Methodology and Computation…………………….10
2.1 Density functional theory…………………………………………...11
2.2 Calculatin of hyperpolarizability……………………………………13
2.2-1 Derivative method……………………………………………...13
2.2-2 Finite-field approach…………………………………………...14
2.2-3 Hyperpolarizability density analysis…………………………...15

Chapter 3 Result and Discussion……………………………...19
3.1 Optimized Geometries of formaldehyde oligomers………………..20
3.2 Formaldehyde dimers…………………………………………........24
3.3 Linear formaldehyde oligomers (H2CO)n, n=3~7…...........………..31
3.4 NLO properties……………………………………………………...37
3.4.1 Field strength…………………………………………………...37
3.4.2 Finite-field approach…………………………………………....43
3.4.3 Basis set dependence of βxxx and γxxxx for (H2CO)2………….....43
3.4.4 Electron correlation dependence of βxxx andγxxxx for (H2CO)2…..
……………………………………………………………..45
3.5 Hyperpolarizability density analysis………………………….…...47
3.5.1 Spatial contributions to βzzz and γzzzz for (CH2O)n n=2-7…….49
3.2.4 Variations of the nonlinear optical properties and chain-length dependencies of linear oligomers and ladder oligomers Variations of the βzzz and γzzzz of formaldehyde oligomers for FF and HDA approaches………………………….........................................60

Chapter 4 Conclusion………….………………………………65

References………….………………………………………….68`

List of Tables

Table 2-1 General Schemes for Calculations of Optical Nonlinearity of Microscopic molecule……………………………………………..……11
Table 3-1 Selected optimization parameter and energy of formaldehyde monomer…………………………………….………………………….22
Table 3-2 Computed wave numbers (cm-1) for the C=O
stretching vibration and dipole moment (debye) of
CH2O…………………………….……………………………………...23
Table 3-3 Computed geometries of linear formaldehyde dimers………………………………………………………..……….....28
Table 3-4 Computed geometries of ladder formaldehyde dimer…………………………………………………………….………29
Table 3-5 Computed geometries of formaldehyde oligomers by B3LYP/
6-31+G(d,p)………………………………………..…………………...33





















List of Figures

Figure 1.2-1 Applications of nonlinear optical device………………4
Figure 1.2-2Scheme of second-harmonic generation in NLO material
(a) Description of SHG (b) Photon description of SHG………………….5
Figure 2.3-1 Schematic diagram of the first hyperpolarizability density
……………………………………………………………17
Figure 2.3-2 Schematic diagram of the second hyperpolarizability density
……………………………………………………………18
Figure 3.1-1 Molecular geometry of H2CO optimized by B3LYP using a 6-31+G(d,p) basis set.………………………………..…… ……………21
Figure 3.2-2 Molecular geometry of linear and ladder formaldehyde dimmers optimized by B3LYP using a 6-31+G(d,p) basis set………………………………………………………..27
Figure 3.3-1 Molecular geometry of linear formaldehyde oligomers optimized by B3LYP using a 6-31+G(d,p) basis set………………………………………………………..33
Figure 3.4.1.1 Variation of βzzz with field strength for formaldehyde oligomers by FF using B3LYP/6-31+G(d,p)…………………………………….38
Figure 3.4.1.2 Variation of βzzz with field strength for formaldehyde oligomers by HDA using B3LYP/6-31+G(d,p).…………………………………....39
Figure 3.4.1.3 Variation of γzxzz with field strength for formaldehyde oligomers by FF using B3LYP/6-31+G(d,p)…………………………………….40
Figure 3.4.1.4 Variation of γzxzz with field strength for formaldehyde oligomers by HDA using B3LYP/6-31+G(d,p)….
…………………………………………………………41
Figure 3.4.3.1 Variations in the βxxx of (H2CO)2 for various basis sets and electron correlation methods using field strength of 0.0025 au………...........................................................................47
Figure 3.4.3.2 Variations in the γxxxx of (H2CO)2 for various basis sets and electron correlation methods using field strength of 0.0025 au
………..............................................................................48
Figure 3.5-1 Contour plots of βxxx and γxxxx densities on the xy plane of (CH2O)2……………………………………………………………..53
Figure 3.5-2 Contour plots of βxxx and γxxxx densities on the xy plane of (CH2O)3……………………………………………………………...54

Figure 3.5-3 Contour plots of βxxx and γxxxx densities on the xy plane of (CH2O)4……………………………………………………………...55
Figure 3.5-4 Contour plots of βxxx and γxxxx densities on the xy plane of (CH2O)5……………………………………………………………...56
Figure 3.5-5 Contour plots of βxxx and γxxxx densities on the xy plane of (CH2O)6……………………………………………………………...57
Figure 3.5-6 Contour plots of βxxx and γxxxx densities on the xy plane of (CH2O)7……………………………………………………………...58
Figure 3.6-1 The static longitudinal first hyperpolarizability ,β, of linear and ladder oligomers -(CH2O)n- by B3LYP………………….….61
Figure 3.6-1 The static longitudinal second hyperpolarizability ,γ,
of linear and ladder oligomers -(CH2O)n- by B3LYP……………………………………………………………….….62
Figure 3.6-3 Chain-length dependency of longitudinal β /n (n: the number of formaldehyde units) for linear and ladder form by B3LYP…63
Figure 3.6-4 Chain-length dependency of longitudinal γ /n (n: the number of formaldehyde units) for linear and ladder form by B3LYP…………64

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