Cracking of n-heptane in HZSM-5 zeolite

Abstract

Cracking of n-heptane in HZSM-5 zeolite is studied through generalized gradient approximation mediated single point calculations at the BLYP-DZVP level on the extremal points of a corresponding quantum molecular dynamics simulation carried out at 800 K using the same level of theory. The global reactivity descriptors like electronegativity, hardness and electrophilicity are important in understanding the reaction mechanism in terms of the stabilities and reactivities of various species involved. Different centers become reactive towards electrophilic and nucleophilic attacks during the process of hydrocarbon cleavage and local reactivity descriptors adequately take care of that.

Introduction

In the present day, petroleum refineries crude oils are converted to various useful products like fuels [1] with little or no pollution by using sophisticated and efficient techniques. Owing to the large dimensionality of the problem the related research [2], [3] becomes expensive [4] and empirical in nature and forces researchers to understand the underlying principles using quantum chemical methodologies [5], [6], [7], [8] of involved catalysis and the transformation of hydrocarbons. The cracking of hydrocarbons takes place when they diffuse through the microporous cavities of aluminosilicate crystals popularly known as zeolites inside which the actual reactions take place [9], [10]. For the conversion of crude oil the HZSM-5 sieve-based catalyst is frequently used as an additive because of its high selectivity though a thorough knowledge of the activity, reactivity and selectivity of this catalyst is yet to come [11], [12], [13].

Density functional theory (DFT) [14] has been found to be successful in providing insights into the chemical reactivity and selectivity, respectively, in terms of global reactivity parameters like electronegativity [15] (χ) and hardness [16] (η) and local ones like Fukui function $(f(\overrightarrow{r}))$ [17] and local softness $(s(\overrightarrow{r}))$ [18]. A hardness-based principle is the maximum hardness principle (MHP) [19], which states that, ‘there seems to be a rule of nature that molecules arrange themselves so as to be as hard as possible’.

For an N-electron system with total energy (E) and external potential $(v(\overrightarrow{r}))$, electronegativity χ and hardness η are, respectively, defined as the following first-order [20] and second-order [21] derivatives, viz.

$$\chi =-\mu =-{\left(\frac{\partial E}{\partial N}\right)}_{v(\overrightarrow{r})}$$

and

$$\eta =\frac{1}{2}{\left(\frac{{\partial }^{2}E}{\partial N^2}\right)}_{v(\overrightarrow{r})}$$

where μ is the chemical potential.

Recently, Parr et al [22] have introduced an electrophilicity index (ω) defined as

$$\omega =\frac{{\mu }^2}{2\eta }$$

which is proposed to be a measure of the electrophilic power of a molecule. The maximum amount of charge an electrophile may accept is given as [21]

$$\mathrm{\Delta }{N}_{\text{max}}=-\frac{\mu }{\eta }$$

Local quantities like Fukui function $(f(\overrightarrow{r}))$ and local softness $(s(\overrightarrow{r}))$ are necessary in understanding the site selectivity. Fukui function is defined as [17]

$$f(\overrightarrow{r})={\left(\frac{\delta \mu }{\delta v(\overrightarrow{r})}\right)}_N={\left(\frac{\partial \rho }{\partial N}\right)}_{v(\overrightarrow{r})}$$

Three different types of Fukui function $(f(\overrightarrow{r}))$ [17] have been defined on the basis of the discontinuity in chemical potential at integer N, viz.

$$f^{+}(\overrightarrow{r})={\left(\frac{\partial \rho }{\partial N}\right)}_{v(\overrightarrow{r})}^{+}\approx \rho {(\overrightarrow{r})}_{\text{LUMO}}$$

$$f^{-}(\overrightarrow{r})={\left(\frac{\partial \rho }{\partial N}\right)}_{v(\overrightarrow{r})}^{-}\approx \rho {(\overrightarrow{r})}_{\text{HOMO}}$$

$$f^0(\overrightarrow{r})=\frac{1}{2}(f{(\overrightarrow{r})}^{+}+f{(\overrightarrow{r})}^{-})$$

A local version of ω is also available [23], [24].

In the present work we study the variations of various descriptors of reactivity and selectivity as given above, along the reaction path of the cracking of a hydrocarbon in HZSM-5 zeolite.

Our starting point is the results of a quantum molecular dynamics study by Martinez-Magadán et al. [13] on cracking of n-heptane inside HZSM-5 zeolite catalyst modeled as a single ring of 10 silanol units where bridging and capping oxygen atoms are connected to silicons and hydrogens, respectively.