以機器學習方法訓練二維凡德瓦異質結構之分子勢場

Abstract

銻烯是一種類似於石墨烯的翹曲六方晶格排列的結構，伴隨著原子上下交錯排列，其優異的半導體電學性質甚至優於其他二維材料，且在大氣中也不易與空氣產生氧化降解。但是其製備過程與其他二維材料相比非常不易，科學家思考利用異質結構方式獲得大面積高品質的銻烯，表面化學穩定的過渡金屬二硫屬化合物便成為異質結構作為基板的最佳選擇。本研究嘗試以分子模擬研究銻烯在二硫化鉬基板上的結構性質，探討二硫化鉬是否適合作為銻烯生長的基板。 對於分子模擬而言，第一原理計算能夠提供最精確的原子間作用力。然而，第一原理計算十分耗費計算與時間資源，而凡得瓦異質結構因為要考慮misfit strain乃至扭曲角，使得模擬系統大小往往遠超其所能處理的範圍。古典分子動力模擬能考慮更大的系統，然而對古典分子模擬而言，分子勢場是不可或缺的。對於複雜的系統來說，由於複雜化學組成以及原子間交互作用，使得建立分子勢場十分具有挑戰性。本研究採用機器學習-類神經網路方法訓練異質結構分子勢能，稱之為神經網路勢能，既有著經驗勢的速度且精準度也直逼第一原理的計算。異質結構分子勢場訓練過程系將上萬筆銻、二硫化鉬，以及異質結構及相對應的以第一原理計算之系統能量輸入訓練集並進行訓練。經過訓練的神經網路模型其驗證及預測的結果均與相對應的第一原理計算結果吻合，證明此一分子勢能具有高度精確性。 我們以訓練完成的神經網路勢能場進行分子模擬測試兩個約一千顆原子異質結構在室溫300K下的系統穩定性，我們的模擬結果顯示兩個系統溫度和能量皆穩定，更重要的是，與第一原理分子動力學相比，利用神經網路勢能進行分子動力學計算有著更高的計算效率。接著，我們利用神經網路勢能對異質結構進行結構優化，採取的優化演算法為BFGS和共軛梯度法，我們藉由比較兩種優化算法最終結構演示了神經網路勢能的侷限。最後，我們發現銻烯因二硫化鉬基板引入的壓縮應變，導致其六角環結構產生扭曲現象。本論文顯示了神經網路模型能夠快速精確的估算化學複雜系統，如凡得瓦異質結構之系統能量，從而能夠進行更大尺度的分子模擬以探索其結構性質。

Antimonene is a structure similar to graphene with twisted hexagonal rings and staggered antimony atoms with superior electronic properties over other two-dimensional materials as well as stability under ambient condition. However, fabrication of high-quality antimonene is difficult relative to other two-dimensional materials. One promising solution is to make use of layered transition-metal-dichalcogenide (TMD) material as growing template, and grow antimonene nanosheets atop, forming van der Waals heterostuctures. In this study, we explored the possibilities of utilizing molybdenum disulfide (MoS2) as the growing template of the vdW heterostructure by performing molecular simulations to examine the structural properties of antimonene grown on MoS2. The most accurate measure of molecular simulation of antimonene/MoS2 heterostructures is ab initio molecular simulations. However, ab initio calculations are extremely computationally expensive, making them literally unusable for vdW heterostructures, which misfit strains or even twist angles must be taken into account. Classical molecular simulations can overcome system size issues. However, interatomic potential is the key component of classical molecular simulations, and it is extremely difficult to parameterize an interatomic potential for vdW heterostructures due to complex compositions and interactions. In this study, we harnessed the power of machine learning and constructed an artificial neural network (ANN) model to evaluate system energies with high fidelity to respective ab initio calculation for given structures. We anticipate that ANN model can have both of the computation efficiency of classical interatomic potential and the accuracy of the ab initio calculations. The ANN model was obtained by extensive training processes. In the training processes tens of thousands of structures of bulk antimonene, MoS2, and Sb/MoS2 heterostructures along with their energies from ab initio calculations were fed into the training sets. The trained ANN model can successfully evaluate energy of structures from both the training sets and validation sets with excellent agreements with those from ab initio calculations, suggesting that this trained ANN potential is robust and can be utilized for molecular simulations. We then performed classical molecular simulations of two different sb/MoS2 heterostructures with system size around one thousand atoms - a system size almost beyond the reach of ab initio calculations - using the trained ANN potential. Both systems were stable during the classical molecular simulations, and we also demonstrate that molecular simulations using the ANN potential yields much higher computation efficiency relative to ab initio molecular simulations. Next, we tested the ANN potential by performing structural optimization of Sb/MoS2 heterostructure by using both BFGS conjugate gradient minimizer, and we reveal the limitations of ANN potential model. Finally, we examined the optimized monolayer Sb/MoS2 heterostructure, and we observed distorted hexagonal rings in antimonene due to compressive misfit strains imposed on monolayer antimonene. The present study demonstrated that ANN model is a powerful tool in evaluating energies/forces of chemically complex systems such as vdW heterostructures with high accuracy, thereby allowing large scale molecular simulations for exploration of structural properties of vdW heterostructures.