Twisted de Rham Cohomology

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Let $M$ be a smooth manifold and $H$ a closed odd-degree form. Then $(\Omega^{\bullet}(M), d_H)$ defines a complex where $d_H := d + H\wedge$. The cohomology of this complex is called twisted de Rham cohomology.

I am looking for some references which explicitly calculate the twisted de Rham cohomology for some simple examples such as $\mathbb{R}^n$.

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