本論文藉由修改開源pseudopotential產生器OPIUM，使其可以產生鍊金師贗勢。鍊金師贗勢方法由李明憲老師提出，將兩元素之贗化波函數漸變，隨著波函數漸變也將本徵值線性漸變，如此可以做到將兩元素原子大小漸變。原子大小漸變鍊金師贗勢測試結果良好，可以做到晶胞大小線性漸變。獲得良好的測試結果後便使用鍊金師贗勢方法討論為何矽沒有平面結構的議題。鍊金師贗勢方法很好的模擬大小漸變的過程(符合超晶胞的晶胞邊長)，對於矽比碳大因此沒有平面結構的這個論點，給予支持的證據。並在此議題的測試中，有較VCA方法更好的超晶胞模擬的表現。鍊金師贗勢方法可以應用在物性研究中認為是大小效應造成物性變化的論點，給予證明或予以反證。鍊金師贗勢方法沒有VCA方法在模擬原子比例接近時，有巨大誤差的缺點，在未來的發展，具有取代VCA成為更好的晶體近似方法的潛力。

We modify the open source of pseudopotential generator which is called OPIUM.We made the code which can produce alchemist pseudopotential in this thesis。Alchemist pseudopotential method is proposed by my advisor professor Ming-Hsien Lee.It is a way to vary in size from one atom to another by changing pseudo wave function and mixing eigenvalue linearly.Atomic-size-varying type alchemist pseudopotential can linearly vary the lattice constant in our test.We use alchemist pseudopotential to discuss the reason why silicon can not have plane structure after we have excellent result of test.Alchemist pseudopotential method simulate the process of size varing(lattice constant are correspond with super cell),so alchemist pseudopotential can support the argument that the silicon can not construct the plane structure because the size of silicon is larger than that of carbon.In this case Alchemist pseudopotential have better simulation of super cell than VCA.Alchemist pseudopotential can apply to recognize the size whether it causes physical properties changing.Alchemist pseudopotential have potential to replace VCA because it doesn’t make huge misteak in half mixing like VCA does.

第一章 簡介......................................................................................................... 1
1.1動機 ............................................................................................................... 1
1.2 贗勢 .............................................................................................................. 2
1.2.1 OPW贗勢 ................................................................................................... 2
1.2.2 Norm-Conserving贗勢 ............................................................................... 3
1.2.3 Optimized pseudopotential .......................................................................... 5
1.2.4 Kleinman Bylander form ............................................................................... 6
1.2.5 Ultrasoft pseudopotential ............................................................................ 7
1.3 虛擬晶體近似法 ........................................................................................... 8
1.3.1虛擬晶體近似簡介 ..................................................................................... 8
1.3.2 Ramer & Rappe的VC Pseudopotential方法 ............................................. 8
第二章鍊金師贗勢(Alchemist Pseudopotential)之程式功能擴增與試用 ....... 12
2.1模型 .............................................................................................................. 12
2.2做法 .............................................................................................................. 16
2.2.1切入程式 ................................................................................................... 17
2.2.2重新贗化波函數 ....................................................................................... 17
2.2.3植入rc之外位勢........................................................................................ 19
2.2.4 重新贗化波函數遇到的問題 ................................................................... 30
2.3小結 ............................................................................................................... 33
第三章碳矽原子大小漸變測試 ......................................................................... 34
3.1鑽石結構測試 ............................................................................................... 34
3.2大小效應對平面結構的影響 ........................................................................ 37
3.2.1碳矽大小漸變石墨烯結構測試 ................................................................. 37
3.2.2碳鍺大小漸變石墨烯結構測試 ................................................................. 43
3.3 VCA測試 ........................................................................................................ 47
3.4超晶胞測試 .................................................................................................... 54
3.4.1超晶胞幾何結構最佳化，並比較鍊金師贗勢方法與VCA方法 ............. 54
3.4.2 Supper cell 計算時，同一比例下，幾何結構多樣性的問題 .................. 61
3.5小結 ................................................................................................................ 63
第四章結論與未來工作 ....................................................................................... 65
4.1結論 ................................................................................................................. 65
4.2未來工作 .......................................................................................................... 65
參考文獻 ................................................................................................................ 67

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