The paper presents a reaction path Hamiltonian for polyatomic molecules, which describes the dynamics along the steepest descent path on the potential energy surface. The Hamiltonian is derived using a set of internal coordinates that include the arc length along the reaction path and normal coordinates orthogonal to it. This approach allows for the description of both the reaction path and vibrational modes. The Hamiltonian is expressed in terms of these coordinates and their conjugate momenta, enabling the study of molecular dynamics, such as chemical reactions. The paper shows how the effects of reaction path curvature can be incorporated into the vibrationally adiabatic approximation, improving tunneling probabilities in reactions like H + H₂ → H₂ + H. The Hamiltonian is derived for a general N-atom system in 3D space with non-zero total angular momentum. The reaction path Hamiltonian is shown to be useful for describing intramolecular dynamics and tunneling corrections in transition state theories. The paper also discusses the derivation of the Hamiltonian for a generic cartesian system and provides examples of its application to collinear and three-dimensional reactions. The results demonstrate the effectiveness of the reaction path Hamiltonian in accurately describing molecular dynamics, particularly in cases involving tunneling.The paper presents a reaction path Hamiltonian for polyatomic molecules, which describes the dynamics along the steepest descent path on the potential energy surface. The Hamiltonian is derived using a set of internal coordinates that include the arc length along the reaction path and normal coordinates orthogonal to it. This approach allows for the description of both the reaction path and vibrational modes. The Hamiltonian is expressed in terms of these coordinates and their conjugate momenta, enabling the study of molecular dynamics, such as chemical reactions. The paper shows how the effects of reaction path curvature can be incorporated into the vibrationally adiabatic approximation, improving tunneling probabilities in reactions like H + H₂ → H₂ + H. The Hamiltonian is derived for a general N-atom system in 3D space with non-zero total angular momentum. The reaction path Hamiltonian is shown to be useful for describing intramolecular dynamics and tunneling corrections in transition state theories. The paper also discusses the derivation of the Hamiltonian for a generic cartesian system and provides examples of its application to collinear and three-dimensional reactions. The results demonstrate the effectiveness of the reaction path Hamiltonian in accurately describing molecular dynamics, particularly in cases involving tunneling.