隨著全球能源需求的增加，為了追求永續發展，如何逐漸擺脫對化石燃料的依賴和開發潔淨的再生能源成為了一門重要的課題。氫氣具有高能量密度，且其燃燒後的產物為無汙染的水，若能透過再生能源產生的電力進行電解水反應產氫，就不會對環境造成額外的汙染，使其成為一種十分具潛力的永續能源。然而，欲大規模以電化學方式產氫，尋找合適的催化劑替代鉑等貴金屬將是關鍵的問題。目前在理論計算領域，以2005年Nørskov提出的產氫反應火山圖，根據Brønsted−Evans−Polanyi (BEP) 關係認為熱力學計算的反應熱與動力學計算的活化能會呈現線性關係，因此主要透過熱力學計算，以氫原子吸附能作為描述符篩選材料。
　　本文透過恆定電壓下的密度泛函理論計算八種過渡金屬的(111)切面和(100)切面氫原子吸附能與活化能之間的關係，探討在電化學產氫反應中BEP 關係是否成立。計算結果顯示，氫原子吸附能確實會與活化能呈現線性關係。其中熱力學上最穩定的空心位點(hollow site)與較不穩定的頂部位點(top site)，兩種位點的氫原子吸附能皆與活化能有線性關係，而後者的線性關係較佳。
　　最後，根據上述以頂部位點所求得的線性關係式，將一系列以金為基底的單原子金屬合金的氫原子吸附能代入關係式中求得的活化能，與實際透過動力學計算所得到的活化能比較，其平均絕對誤差值小於0.08 eV，證實透過此線性關係式確實能良好的預測活化能。

In this modern world, the demand of energy has continued to increase rapidly. In order to achieve Sustainable Development, there is an urgency to develop a clean and renewable alternative to fossil fuels. Hydrogen has high energy density, and its only combustion byproduct is water, which is pollution-free. Therefore, hydrogen is one of the most attractive energy. Currently, most of the hydrogen is produced by fossil resources. It is not environmentally friendly. Using electricity from renewable energy to do the hydrogen evolution reaction (HER) is a promising pathway to achieve the efficient hydrogen production. However, the electrocatalysts for the HER is scarce and high price noble-metal like Pt. Therefore, it’s important to search for HER electrocatalysts that are composed of earth abundant and inexpensive materials. In 2005, Nørskov built the HER volcano plot, indicating that the hydrogen binding energy could be used as a descriptor. The hydrogen binding energy is connected to the activity of an electrocatalyst via the Sabatier principle and importantly the Brønsted−Evans−Polanyi (BEP) relationship. The latter one indicates that the reaction energy has a linear correlation to the kinetic barrier.
In this study, we investigated the HER on (111) and (100) index surfaces of eight face-centered cubic (fcc) transition metals, including Pt, Ir, Rh, Pd, Ni, Cu, Au, and Ag. Using DFT calculations combined with a constant electrode potential (const-U) model to examine the BEP relationship in the HER. We found that both of the hydrogen binding energy of the hollow site and the less favorable top site were indeed correlated to the kinetic barriers. However, the correlation of the latter was better. This led to a scheme for estimating the HER kinetic barriers with improved accuracy. Finally, this scheme was used to predict the HER barriers of Au based single-atom alloys. The results were similar to those calculated explicitly by const-U DFT.

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