在材料科學與凝態物理領域不斷演進中，第一原理模擬已經在方法上具有非常重要的地位。這些模擬由量子力學出發，不依靠經驗參數，為我們提供了在微觀尺度上研究材料原子組成和電子性質的方式。第一原理模擬不僅提供了實驗上無法觀測到的微觀現象，也在於它們具有普遍地提供預測能力。隨著人工智慧(AI)的出現，AI驅動的算法與基於第一原理的模擬之間的協同作用已帶來了加速材料發現和設計的新時代。這種融合不僅有助於了解複雜現象，並有助於促進新一代設備的設計。基於第一原理的模擬和AI的緊密結合不僅是互補的；它正在革命性地改變我們在21世紀如何接近、理解和利用材料的潛力。

第一部分 (I) 錫碘化物鈣鈦礦的介電性質分析
錫基鈣鈦礦是一種非常有潛力的材料，用以取代傳統具有毒性的鹵化鉛鈣鈦礦，但其不穩定性限制了其發光性能。然而，二維的錫基鈣鈦礦能夠提升激子束縛能進而提升光致發光量子產率(PLQY)。除此之外，二維錫基鈣鈦礦中的有機層與無機層之介電常數差異亦會影響機子束縛能。本篇將透過密度泛函理論探討以下二維錫基鈣鈦礦：(TEA)2SnI4, (PEA)2SnI4, (p-FPEA)2SnI4, (p-ClPEA)2SnI4 以及(p-BrPEA)2SnI4之介電常數，並探討其與PLQY之關係。其結果顯示改變陽離子組成，並不會大幅地影響陽離子層之介電常數，反而會誘導陰離子層的介電常數產生變化。

第二部分 (II) 電場於顯式溶劑之電化學模擬
本研究系統性評估了對Cu(111)表面上電化學CO二聚化的顯式溶劑模型。在存在吸附物和銅表面的情況下，對溶劑的組成在室溫下進行了分子動力學採樣。本研究通過考慮引入外加平板電場，對CO二聚化反應路徑上的能量和功函數進行探討。我們觀察到，即使在引入外加電場的情況下，使用定電位修正，CO二聚化過程的活化能和反應能仍然保持相近的數值，分別約為0.95電子伏特和0.35電子伏特。這一發現在顯式溶劑模擬下，再次確認了CO二聚化主要是一個由熱驅動的過程。此外，引入外加電場範圍從+0.2 V/Å到-0.2 V/Å，在pH = 7條件下，導致有效的電化學電位相對於標準氫電極從+1.766 V變化到-0.565 V。

第三部分 (III) 銅單原子催化劑在鈀表面上的動力學分析
本研究焦點是通過在Pd(111)表面上之單原子銅催化劑進行電化學CO和CHO耦合過程，探討C-C鍵形成進行計算。我們發現了過程中穩定的中間體，即[CuO2](CO)2，在暴露於CO氣體分子時被視為一種四牙和四面體的中間產物。在本篇電化學計算中，將CO團氫化為CHO的能量需求為0.87電子伏特，其低於常規Cu表面相應步驟的能量。本研究觀察到從頂層Pd原子到吸附物分子的電荷轉移效應，尤其是在過渡態處。這一現象導致了0.67電子伏特的C-C鍵形成能障。此外，C-C鍵形成的為放熱反應，為-0.21電子伏特，代表了利於生成C-C鍵的化學平衡條件。最後，由動力學建模分析討論氣體分子(CO、CO2、O2)的溫度和壓力影響，我們發現[CuO2]*(CO)2中間體在室溫下大量存在，並在乾燥的環境條件下表現出很好的化學耐受性。

In the evolving field of materials science and condensed matter physics, first-principles simulations have become an essential methodology. Rooted in quantum mechanics and without empirical parameters, these simulations offer insights into the behaviors of materials at atomic and electronic levels. Their strength not only comes from eliminating experimental input but also in delivering reliable predictions. With the rise of artificial intelligence (AI), the collaboration between AI-driven algorithms and first-principles simulations has initiated an era of rapid materials discovery and design. This combination aids in understanding complex phenomena and in designing advanced devices. The collaboration between first-principles simulations and AI is reshaping how we explore, comprehend, and utilize materials in the 21st century.

Part (I) Dielectric Profiles of Tin Iodide Perovskite
Tin-based perovskites hold great potential as a replacement for traditional toxic lead halide perovskites, but their instability has limited their luminescent performance. However, two-dimensional tin-based perovskites have the capability to enhance exciton binding energy and, consequently, improve photoluminescence quantum yield (PLQY). Additionally, the difference in dielectric constants between the organic and inorganic layers in two-dimensional tin-based perovskites also affects exciton binding energy. This study employs density functional theory to investigate the dielectric constants of the following two-dimensional tin-based perovskites: (TEA)2SnI4, (PEA)2SnI4, (p-FPEA)2SnI4, (p-ClPEA)2SnI4,and (p-BrPEA)2SnI4, and explores their relationship with PLQY. The results demonstrate that altering the cation composition does not significantly impact the dielectric constants of the cation layers but induces variations in the dielectric constants of the anion layers.

Part (II) Field-Dependent Explicit Electrochemical Simulations
This study presents a systematic assessment of the explicit modeling of electrochemical CO dimerization on the Cu(111) surface. Solvation configurations were sampled at room temperature in the presence of adsorbates and the Cu surface. The study characterizes the energetics and work functions along the CO dimerization pathway, considering plate-type electric force fields. It is observed that the activation barriers and reaction energies for the CO dimerization process remain relatively constant, around 0.95 eV and 0.35 eV, respectively, even when external electrostatic perturbations are introduced, using the constant-potential correction. This finding, supported by explicit simulations, reaffirms that CO dimerization is primarily a thermally-driven process. Furthermore, applying electric force fields ranging from +0.2 V/Å to -0.2 V/Å leads to effective electrochemical potential changes from +1.766 to -0.565 V vs. the standard hydrogen electrode under pH = 7 conditions.

Part (III) Kinetic Analysis of Single Cu Atom Catalyst on Pd surface
This study is primarily concerned with the computational characterization of the electrochemical formation of C-C bonds via the coupling process of CO and CHO, utilizing a dioxo-coordinated Cu single atom site ([CuO2]) supported on a Pd(111) surface. A stable intermediate, denoted as [CuO2](CO)2, was identified as a tetradentate and tetrahedral species that forms when exposed to CO gaseous molecules. Electrochemically, the hydrogenation of the carbonyl group to CHO was found to require only 0.87 eV of energy, which is conceivably lower than the corresponding step on conventional Cu surfaces. This study also observed a significant charge transfer effect from the top layer Pd atoms to the adsorbate moiety, particularly at the transition state (TS) structure. As a result, an accessible barrier for C-C bond formation at 0.67 eV was observed. Furthermore, the reaction energy for C-C bond formation was found to be exothermic at -0.21 eV, indicating a favorable chemical equilibrium condition. Taking into account the temperature and pressure effects of gaseous molecules (CO, CO2, O2), the [CuO2]*(CO)2 intermediate was found to be substantially populated at room temperature and exhibited chemical resilience under dry ambient conditions, as suggested by the results of kinetic modeling.

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