Fact 1: The cause of a sunset is from the angle of the sunlight, because the amount of scattering increases as the light passes through more and more of the atmosphere.
Fact 2: Higher frequency / lower wavelength light (towards the blue and violet side of the spectrum) scatters more than lower frequency / higher wavelength light (towards the orange and red side of the spectrum)
Fact 3: During a sunset, you can frequently still see blue skies, sometimes not even very observably far from where the sunset is occurring.
Combining all of these facts together, I wonder if it is possible to have a "black" sunset, where the light passes through so much atmosphere that light itself scatters too much to reach the observer directly. This would give the impression of an interesting blackness coming from the sunset, and the sun might even be visible without needing to use special glasses.
Would this kind of sunset be possible? Assume that the hypothetical planet in question can be changed however necessary to make this work - including size, atmosphere, axial tilt, distance to star, etc.
I'm talking about the possibility of a lack of light occurring only at the horizon due to atmospheric scattering.
Further clarification: Assume my question involves a clear sky, because cloud cover does not address the aspect of the most light scattering only at the horizon. Also, I'm not talking about a light that is black, I'm talking about a lack of light that is black.
Good answers will tell me yes or no, and will explain why or why not based on science.