Energetics and spin- and Λ-doublet selectivity in the infrared multiphoton dissociation HN3(X̃ 1A′)→N2(X 1Σ+g)+NH(X 3Σ−,a 1Δ): Theory

Abstract

An investigation of the energetics and mechanism of the dissociation of ground state HN₃(X̃ ¹A’) into ground state N₂(X ¹∑⁺_g)+NH(X ³∑⁻) products is presented. This process, which can be induced by multiphoton infrared pumping, occurs through a crossing between the lowest‐energy singlet potential energy, which correlates asymptotically with electronically excited NH products (a ¹Δ), and the lowest triplet surface. By means of ab initio CASSCF and MCSCF‐CI calculations we have determined that the geometry at the minimum singlet–triplet crossing corresponds to an approximately linear N₃ backbone with a perpendicular NH bond. The interior N–N distance is ∼3.6 bohr. This transition state lies ∼12 500 cm⁻¹ above the energy of X̃ ¹A’ state of HN₃ at the experimental equilibrium geometry. Since the N–N and N–H bonds are perpendicular at this transition state, there will be no torques tending to twist the system out of a planar geometry. The crucial singlet–triplet coupling occurs because the HN₃ wave function in the region of this transition state can be considered an equal admixture of N₂(X)⋅NH(a ¹Δ) and N₂(X)⋅NH(b ¹∑⁺). Since the ground state HN₃ wave function as well as the relevant spin–orbit Hamiltonian are symmetric with respect to reflection of the spatial and spin components of all the electrons in the plane of the molecule, and since the NH fragment must rotate in the plane of the initital HN₃ molecule if the dissociation is planar, NH products can be formed only in states in which the wave function (electronic+rotational) is also symmetric with respect to this operation. For a molecule in a ³∑⁻ electronic state the wave functions in only the F₁ and F₃ multiplets will be symmetric so that one would expect population in only the F₁ and F₃ levels. A similar symmetry argument implies that the NH products formed in the lowest spin‐allowed channel [N₂(X ¹∑⁺_g)+NH(a ¹Δ)] will be found predominantly in the Δ(A’) Λ‐doublet state, which is symmetric with respect to reflection of the spatial coordinates of the electrons in the plane of rotation. This spin‐ and Λ‐doublet selectivity has been found experimentally by Stephenson, Casassa, and King (accompanying article). The implications of similar spin selectivity in other photodissociation processes leading to molecules in ³∑⁻ states, e.g., SO(X ³∑⁻) and O₂(X ³∑⁻_g), are also considered.