  We study the Chern-Simons partition function of orthogonal quantum group
invariants, and propose a new orthogonal Labastida-Mari\~{n}o-Ooguri-Vafa
conjecture as well as degree conjecture for free energy associated to the
orthogonal Chern-Simons partition function. We prove the degree conjecture and
some interesting cases of orthogonal LMOV conjecture. In particular, We provide
a formula of colored Kauffman polynomials for torus knots and links, and
applied this formula to verify certain case of the conjecture at roots of unity
except $1$. We also derive formulas of Lickorish-Millett type for Kauffman
polynomials and relate all these to the orthogonal LMOV conjecture.
