Anharmonic Effect on Unimolecular Reactions with Application to the Photodissociation of Ethylene

Abstract

The importance of anharmonic effect on dissociation of molecular systems, especially clusters, has been noted. In this paper, we shall present a theoretical approach that can carry out the first principle calculations of anharmonic canonical and microcanonical rate constants of unimolecular reactions within the framework of transition state theory. In the canonical case, it is essential to calculate the partition function of anharmonic oscillators; for convenience, the Morse oscillator potential will be used for demonstration in this paper. In the microcanical case, which involves the calculation of the total number of states for the activated complex and the density of states for the reactant, we make use of the fact that both the total number of states and the density of states can be expressed in the inverse Laplace transformation of the partition functions and that the inverse Laplace transformation can in turn be carried out by using the saddle-point method. We shall also show that using the theoretical approach presented in this paper the total number of states and density of states can be determined from thermodynamic properties and the difference between the method used in this paper and the thermodynamic model used by Krems and Nordholm will be given. To demonstrate the application of our theoretical approach, we chose the photodissociation of ethylene at 157 and 193 nm as an example.

Anharmonic Effect of N‐Propyl Peroxy Dissociation

“…calculated the rate constant of the reaction n ‐C 3 H 7 O 2 → CH 3 CHCH 2 + HO 2 using the master equation simulation model at low temperatures (296–700 K), and compared the theoretical calculation results with those of experiments . The rate constants obtained with the RRKM (Rice–Ramsperger–Kassel– Marcus) method were reasonably consistent with DeSain's results. At 300 and 700 K, the results of the present study were 3.44 × 10 −10 and 2.90 × 10 2 s −1 , while Desain's results were 3.02 × 10 −11 and 7.12 × 10 2 s −1 .…”

Anharmonic effect of the unimolecular dissociation of CH3COOH

“…For this reason, using experimental thermodynamic data, Troe presented a simple empirical method for generating anharmonic vibrational densities of states [21]. Recently, a method proposed by Yao and Lin (YL) [22] could carry out the first principle calculations about the rate constants of molecular reactions within the framework of the transition state theory proposed. With this method, the anharmonic effect that was on the dissociation of molecular reaction had been examined.…”

“…We can find lots of examples in our previous papers [22]. The increasing ratio of total number of states W (E) and density of state ρ (E) are different.…”

The anharmonic effect study of coupled Morse oscillators for the unimolecular reaction

“…The total amount of state and density of state can be obtained from the inverse Laplace transformations of canonical partition function and its related function. The inverse Laplace transformation can be performed by using the saddle-point method or method of steepest descent [21] . According to the above method, the central point is to calculate the partition function.…”

“…In our previous papers [21,22] , we performed ab initio calculations of the potential energy surface (PES) for photodissociation of some molecules and obtained rate constant of the dissociation by using RRKM theory in the harmonic oscillator (HO) approximation, and the importance of anharmonic effect was also discussed in a previous paper by using different potential models. In this paper, the anharmonic effect of SBFMO will be considered for some model systems and a real molecule.…”