摘要：Aiming at the specific cases existing in spatial angles calculation the paper investigates five types of them： lines in specific orientations, planes in specific orientations, two lines defining a plane and angles between them, orientations and relevant parameters of a line lying on a plane, and orientations and relevant parameters of a plane passing through a line. The results are presented. The strategy presented provides a firm theoretic basis for the application of the new method of spatial angles calculations.

摘要：Heterostructure engineering holds exceptional promise for the development of high-performance electrocatalysts for overall water ***,production of inexpensive and high-efficiency bifunctional electrocatalysts remains a ***,we demonstrate a simple method to synthesize a paper-mulberry(Broussonetia papyrifera)-inspired Co_(9)S_(8)@CoNi_(2)S_(4)/nickel foam(Co_(9)S_(8)@CoNi_(2)S_(4)/NF)heterojunction with high catalytic activity and *** process involves in situ growth of NiCo layered double hydroxide and in situ derivatization of ZIF-67,followed by the S heteroatom *** Co_(9)S_(8)@CoNi_(2)S_(4)/NF benefits from the heterostructure and functional advantages of multidimensional building blocks including one-dimensional(1D)nanowires,2D nanosheets and *** optimized Co_(9)S_(8)@CoNi_(2)S_(4)/NF heterojunction with 10% sulphur content reveals excellent electrocatalytic activity with the lower overpotentials of 68 mV for hydrogen evolution reaction(HER)and 170 mV for oxygen evolution reaction(OER)at 10 mA cm^(-2) in the 1.0 mol L^(-1) KOH solution,which is superior to the recently reported transition metal based *** outstanding performance is attributed to the strong interface coupling between CoNi_(2)S_(4) and Co_(9)S_(8),the advantage of multidimensional structure and the customized electronic *** density functional theory suggests that the interface between Co_(9)S_(8) and CoNi_(2)S_(4) optimizes the adsorption of the multiple intermediates and further facilitates water splitting *** work offers a generic approach for heterostructure engineering design of highperformance catalytic system applications.