Electron Transfer Rules in Nature Regulated by Element Electronegativity and Mineral Work Function


Research groups from Peking University and Beihang University revealed the electron transfer rules in nature regulated by element electronegativity and mineral work function


On March 31st, 2023, Nature Communications online published a paper titled “Electron transfer rules of minerals under pressure informed by machine learning” (URL: https://www.nature.com/articles/s41467-023-37384-1), which was cooperatively completed by the research groups of Anhuai Lu / Yan Li from the School of Earth and Space Sciences, Peking University and Xiangzhi Bai from the School of Astronautics, Beihang University.


Element electronegativity is the tendency of an atom to attract electrons when forming a chemical bond, and mineral work function is the minimum thermodynamic energy needed to remove an electron from a solid to a point in the vacuum outside the solid surface. Element electronegativity and mineral work function, which are significantly affected by external conditions, especially pressure, are important indicators to evaluate the electron transfer behaviors of minerals. Unfortunately, it is almost impossible to measure the electronegativity of elements and the work function of minerals under extreme conditions with currently existing experimental techniques. High-throughput calculations based on density functional theory are extremely time-consuming when dealing with natural minerals with complex compositions because of the exponential increase in the computation with the increasing number of electrons and dimensions (known as curse of dimensionality). Until now, the behavior and mechanism of electron transfer in complex Earth system have not been revealed and predicted.


The joint research team of Yan Li, Xiangzhi Bai and Anhuai Lu applied big-data and deep-learning methods to construct a densely connected attention network, using the electronegativity values ​​of 96 elements from H to Cm in the periodic table at 50, 100, 200 and 500 GPa as dataset. They obtained the mapping relationship between element electronegativity and electronic configuration, pressure, and realized the quantitative prediction of element electronegativity under arbitrary pressure from 0 to 500 GPa. The correlation coefficient (R2) between the predicted values and ground-truth is 0.987, and the mean absolute error (MAE) is low as 0.283 eV. Based on this, a functional analytical expression to describe the quantitative dependence of element electronegativity on electronic configuration (atomic number, principal quantum number, valence electron number) and pressure, was established by using the symbolic regression algorithm, thus revealing the periodic changes of element electronegativity under different pressures (Figure 1).

Fig. 1 Deep learning predicted the electronegativity of 96 elements under arbitrary pressure from 0 to 500 GPa, and a functional analytic expression regarding its relationship with pressure and electron configuration was established based on the symbolic regression algorithm.


Based on the quantitative relationship between element electronegativity and mineral work function, the concept of pressure-modulated relative work function of minerals was further proposed. It was calculated as the arithmetic mean value of electronegativity of all constituent atoms of minerals under a certain pressure, so as to evaluate the electron transfer activity at mineral phase interface in the complex Earth’s system. The relative work function values ​​of all known minerals in nature at arbitrary pressure from 0 to 500 GPa were calculated (for example, those values at 0 and 100 GPa are shown in Fig. 2a). Under pressure, the delocalization of valence electrons in all elements is enhanced and shows diversity for different elements, leading to a pressure-dependent interfacial work function difference between mineral phases with different compositions. It can explain the general increasing trend in the electrical conductivity of minerals from the crust to the core, and interpret high conductivity anomalies at the discontinuities between deep minerals (Fig. 2b). In addition, the valence electrons of metals have stronger delocalization and weaker binding energy than those of nonmetal elements, resulting in electron transfer driven by the increasing interface work function difference between metal-bearing and nonmetal-bearing minerals with pressure. This research also quantitatively predicts the order of electron transfer activity at the interface of Fe(II)-containing minerals and water under different pressures (Fig. 2c), and points out that reducing hydrocarbon species would be definitely formed due to the pressure-induced electron transfer between Fe(II)-containing minerals and inorganic carbon (such as carbonate minerals or carbon dioxide). So, it can be deemed as an intrinsic mechanism of hydrogen and methane production by minerals during the cold subduction processes.


Fig. 2 Based on the pressure-modulated relative work function of minerals, the quantitative law of the valence electron transfer at the interface regulated by the chemical composition and electronic configuration characteristics of minerals is revealed. (a) Mineral work function changes with chemical composition and pressure. (b) Using mineral work function to explain the increase in electrical conductivity of deep minerals with depth and the abnormal phenomenon of high conductivity of discontinuous boundaries. (c) Using mineral work function to predict the activity order of electron transfer between Fe(II)-bearing minerals and H2O at different pressures.


Electron transfer is the most basic process in nature, and plays important roles in energy conduction, element cycling and life activities. Through deep learning and symbolic regression methods, this research expresses the complex variables, that are closely related to mineral electron transfer but difficult to detect or analyze, into a predictable and interpretable analytical formula. The quantitative rules of electron transfer activity of minerals determined by the difference of interfacial work function is revealed. It deepens the theoretical understanding of the Earth’s substance cycling driven by electron transfer, and realizes the theoretical predictions that pressure-induced electron transfer of minerals from the surface to the deep. In addition, the obtained electronegativity values ​​of elements under different pressures are also of great value in understanding the basic physical and chemical properties of elements and their compounds, such as polarizability and ionization energy.


Yanzhang Li, Boya postdoctoral fellow in the School of Earth and Space Sciences, Peking University, and Hongyu Wang, master degree candidate in the School of Astronautics, Beihang University, and Yan Li, associate professor in the School of Earth and Space Sciences, Peking University are the co-first authors of this paper. Yan Li, Xiangzhi Bai and Anhuai Lu are the co-corresponding authors. This study was supported by the National Natural Science Foundation of China and the Deep-time Digital Earth (DDE) Big Science Program.