Canonical pairing and Hirzebruch-Riemann-Roch formula for matrix factorizations

We formulate a realization of the canonical pairing in the negative cyclic homology of the category of local matrix factorizations and for global matrix factorizations, by introducing a twisted de Rham valued Todd class we establish a formula of the Hirzebruch-Riemann-Roch theorem in the case of periodic cyclic homology.