Clustering and deformation are important for dynamics of nuclear structure, and cluster structures couple to deformed states.

However, its mechanism is unclear.

Cluster structures that couple to each deformed state and the mechanism are investigated in $^{35}$Cl.

The antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM) are used.

An AMD function is a Slater determinant of Gaussian wave packets.

By energy variational calculations with constraints for deformation and clustering, wave functions that have deformed and $\alpha$-$^{31}$P and $t$-$^{32}$S cluster structures are obtained.

Adopting those wave functions as GCM basis, wave functions of ground and excited states are calculated.

Various cluster deformed bands are obtained and predicted.

The $K^\pi = \frac{1}{2}^-$ deformed bands contains large amount of $\alpha$-$^{31}$P and $t$-$^{32}$S cluster structure components.

Particle-hole configurations of both cluster structures are same as dominant components of the $K^\pi = \frac{1}{2}^-$ bands in small intercluster distance.

Particle-hole configurations of cluster structure in small intercluster distance are important for coupling of cluster structure to deformed states.