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This article is cited by 34 publications. We further draw an analogy with the appearance of imaginary terms in simple models of barrier scattering, which may help understanding the unusually effective long-range electron transfer in biological systems. Our symmetry analysis helps to identify essential constraints in the theoretical description of the CISS effect. Hence, they are not related to the breaking of time-reversal symmetry resulting from the fact that molecules are open systems in a junction. These imaginary terms originate from the spin–orbit coupling, and they preserve the Hermitian nature of the Hamiltonian. On the basis of first-principles calculations and analytical considerations, we perform a symmetry analysis of the key quantities determining transport probabilities of electrons of different spin orientations. We are taking an essential step into this direction by analyzing the importance of imaginary terms in the Hamiltonian as a necessary condition for nonvanishing spin polarization in helical structures. The CISS effect is attributed to spin–orbit coupling, but a sound theoretical understanding of the surprising magnitude of this effect in molecules without heavy atoms is currently lacking. Also, CISS-induced spin polarization has a considerable promise for new spintronic devices and the design of quantum materials. x 2 + y = 3 a 2 + b = 3 b 2 - a = 3 No, these are not equivalent equations, so it is not symmetric with respect to the line y = -x.The chiral-induced spin selectivity (CISS) effect, which describes the spin-filtering ability of diamagnetic structures like DNA or peptides having chiral symmetry, has emerged in the past years as the central mechanism behind a number of important phenomena, like long-range biological electron transfer, enantiospecific electrocatalysis, and molecular recognition. y = -x (a, b) and (-b, -a) should produce equivalent equations. x 2 + y = 3 a 2 + b = 3 b 2 + a = 3 No, these are not equivalent equations, so it is not symmetric with respect to the line y = x. y = x (a, b) and (b, a) should produce equivalent equations. x 2 + y = 3 a 2 + b = 3 Yes, these are equivalent equations, so it is symmetric with respect to the y-axis. y-axis (a, b) and (-a, b) should produce equivalent equations. x 2 + y = 3 a 2 + b = 3 a 2 - b = 3 No, these are not equivalent equations, so it is not symmetric with respect to the x-axis. Here is how: Symmetry with respect to the line: Test Results x-axis (a, b) and (a, -b) should produce equivalent equations. You can figure this out without actually graphing the equation. Ex 2: Determine whether the graph of x 2 + y = 3 is symmetric with respect to the x-axis, y-axis, the line y = x, the line y = -x, or none of Answer: y-axis these.

Origin symmetry