Thermochemistry and Group Additivity Values for Fused Two Ring

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Thermochemistry and Group Additivity Values for Fused Two Ring Species and Radicals Lawrence Lai, Sarah Khanniche, and William H. Green J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b01065 • Publication Date (Web): 22 Mar 2019 Downloaded from http://pubs.acs.org on April 5, 2019

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The Journal of Physical Chemistry

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Thermochemistry and Group Additivity Values for

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Fused Two Ring Species and Radicals

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Lawrence Lai, Sarah Khanniche, William H. Green*

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Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139

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Abstract

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Motivated by the lack of understanding in the chemical mechanisms of alkylaromatic pyrolysis, the

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thermochemistry of fused two ring aromatic molecules and radicals were calculated in this work using the

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CBS-QB3 level of theory. The enthalpies of formation of some fused ring species differ by as much as 13

10

kcal/mol from previous estimates. New group values were defined to facilitate better thermochemistry

11

estimates in the future, and were found to match the CBS-QB3 calculated values with an average deviation

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of 0.4 kcal/mol and a standard deviation of 0.9 kcal/mol, a substantial improvement from previous

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estimation methods. We discuss the thermochemical characteristics of the various polycyclic and radical

14

groups developed in this work.

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Introduction

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The accurate evaluation of thermochemical properties is extremely important for the purposes of

17

constructing kinetic models for alkylaromatic pyrolysis systems, an extensively studied area of high

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relevance to crude oil upgrading1-3 and production of chemicals4,5. One particular tool for constructing

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kinetic models is the Reaction Mechanism Generator (RMG)6 which requires reliable fast estimates of

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thermochemical properties in order to generate useful chemical mechanisms. Previous work has shown

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the effects of thermochemistry on product distribution1, where changes as small as 2 kcal/mol in the Gibbs

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free energy of a few key species could significantly alter the yield of relevant products.

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This work is motivated by attempts to accurately model formation of fused two ring aromatic species,

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likely precursors of coke formation in alkylaromatic pyrolysis. While the thermochemical databases carry

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a high volume of information, the information specifically describing the thermochemistry of fused two

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ring species at the industrially relevant pyrolysis temperature of 450°C is sparse, and scattered throughout

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different sources, with many different methods of estimation or levels of theory. These thermochemical

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databases include the NIST thermochemical tables7, the Third Millennium Ideal Gas and Condensed Phase

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Thermochemical Database8, Active Thermochemical Tables9, Pedley et al.10, and Goldsmith et al.11. Table

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1 summarizes the thermochemical databases and their characteristics

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Table 1 Summary of thermochemical databases and their various characteristics

Database NIST Thermochemical Tables7 Third Millennium Ideal Gas and Condensed Phase Thermochemical Database8 Active Thermochemical 9 Tables Pedley et al.10 Goldsmith et al.11

Source Experimental theoretical Experimental theoretical

Type of species and Enthalpy, entropy, and tabulated heat capacities for stable species, radicals, and ions and Full NASA polynomials for stable species and radicals

Experimental theoretical Experimental theoretical Theoretical only

and Enthalpy only for stable species, radicals, and ions and Enthalpy only for organic species Enthalpy, entropy, and tabulated heat capacities for small carbon containing species and radicals only

14 15

This work calculates the thermochemistry of relevant reaction intermediates starting from long chain

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alkylaromatic radicals leading up to fused two ring aromatics (naphthalene and indene) and spiro

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compounds (phenyl migration intermediates). The energies were calculated using the CBS-QB3 level of 2 ACS Paragon Plus Environment

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theory. Group additivity values (GAVs) were developed to aid the future estimation of thermochemistry

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for similar compounds at high accuracy to avoid repeatedly running costly quantum calculations.

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The group additivity value (GAV) method was developed by Benson12,13 and further refined by Ritter and

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Bozzelli14; this method is a simple and convenient means to estimate the thermochemical properties of

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molecules, including the enthalpy of formation, entropy, and heat capacities given the known group values

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that constitute molecules of interest. This GAV method was further developed by Lay et al.15 to describe

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the energy of radical species through hydrogen bond increments (HBI) under the following scheme:

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∆𝐻°𝑓298 𝐾(𝑅 ∙ ) = ∆𝐻°𝑓298 𝐾(𝑅𝐻) + 𝐻𝐻𝐵𝐼 ― ∆𝐻°𝑓298 𝐾(𝐻)

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Where HHBI is the hydrogen bond increment of a radical type

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∆𝐻°𝑓298 𝐾(𝑅 ∙ ) is the enthalpy of formation of the radical

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∆𝐻°𝑓298 𝐾(𝑅𝐻) is the enthalpy of formation of the corresponding hydrogenated stable species

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and ∆𝐻°𝑓298 𝐾(𝐻) is the enthalpy of formation of the hydrogen atom, 52.1 kcal/mol.

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HBI values have also been described for entropy and heat capacity:

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∆𝑆°𝑓298 𝐾(𝑅 ∙ ) = ∆𝑆°𝑓298 𝐾(𝑅𝐻) + 𝑆𝐻𝐵𝐼

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𝐶𝑃,𝑇(𝑅 ∙ ) = 𝐶𝑃,𝑇(𝑅𝐻) + 𝐶𝑃,𝑇𝐻𝐵𝐼

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This method is currently used by THERM14 and RMG6 to estimate the thermochemistry of unknown

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radicals.

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Existing GAVs for polycyclic groups were described in Benson et al.12, Yu et al.16, and Han et al.17, citing

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data from calorimetry experiments and computational calculations using various levels of theory (such as

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B3LYP//6-31G(d) or M06-2X//cc-pVTZ). Some previous GAVs were developed under different 3 ACS Paragon Plus Environment


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schemes; for example, Benson describes polycyclic aromatics using atom centered groups, Yu et al. used

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bond-centered groups, and Han et al. treats an entire 2-ring structure as a group to better account for ring

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strain effects. These different methods give different estimates of the molecule’s thermochemistry, and it

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is often hard to know which of the estimates are accurate.

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Lay et al.15 and Li and Curran18 reported HBI values for many radical groups such as secondary and

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tertiary benzyl radicals, allyl radicals, and super allylic radicals, but these group structures may not be

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sufficiently specific to describe aromatic related radicals described in this work. Some of Lay et al.’s HBI

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values are derived from experimental data and are likely accurate, but other values are derived from semi-

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empirical calculations and are more doubtful.

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In response to the aforementioned shortcomings, this work updates polycyclic and radical groups

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encountered in our mechanisms of interest using the CBS-QB3 level of theory, Han’s17 method for

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estimating polycyclics, and retains the HBI format of Lay for radicals to maintain internal consistency

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with RMG’s database.

16 17

Another method of rapid estimation for thermochemistry of unknown species is through machine learning

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algorithms, suggested by Li et al.19, where a molecular graph convolutional neural network is used with a

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dropout training strategy to achieve the extrapolation of thermochemistry from a large database of training

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species. There are currently advantages and disadvantages for using Li et al.’s method; some of the

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advantages include (1) the lack of user interference in designing new group values, (2) the incorporation

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of features that may not be possible in the GAV method, and (3), the ease of retraining an estimation

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model. However, these advantages are met by drawbacks such as (1) the lack of user transparency, since


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users will no longer know the contributions towards a thermochemistry estimate, and (2) a large quantity

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of data is required for this method of estimation to be effective. Considering the potential benefits of both

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methods, these two methods should be developed in parallel until the available training data for Li et al.

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allows its benefits to outweigh its disadvantages.

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Computational Details

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In this work, quantum mechanical calculations are performed using Gaussian 0320, followed by the

8

calculation of partition functions and fitting to NASA polynomials using the Cantherm software package

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that is part of RMG. Finally, group additivity estimates are derived through least-squares, solving the

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associated system of linear algebra equations using Python’s numpy module.

11 12

Gaussian 03 Calculations

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Thermochemical and kinetic data were calculated using the Gaussian 03 quantum chemistry package20.

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Geometry, energy, and harmonic frequency, calculations were performed at the CBS-QB3 level of theory;

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hindered rotor calculations were performed in the B3LYP/CBSB7 level of theory. Hindered rotor

16

calculations were made for each rotatable bond; these scans were stepped in 10° increments for the full

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360° rotation with constrained optimizations at each step. The treatment of hindered rotors including the

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method of separating the large-amplitude and small-amplitude (harmonic oscillation) degrees of freedom

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is described in detail in Sharma et al.21.

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RMG – Cantherm

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Partition functions were calculated using the rigid-rotor-harmonic-oscillator approximation with 1-D

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hindered rotor corrections. We assumed the 1-D rotors were separable (independent rotors 5 ACS Paragon Plus Environment


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approximation). The rotor moments of inertia were taken as I(2,3) at the equilibrium geometry. Eigenvalues

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for each rotor were computed in a basis set of 12 pairs of sine and cosine terms. The resulting

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thermodynamic parameters were fitted to NASA polynomials using the Cantherm package of RMG22.

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This work uses a scaling factor of 0.99 for the harmonic frequency analysis, and the recommended bond

5

additivity corrections23. For cases where there are optical isomers and/or internally symmetric hindered

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rotors, R*ln(Symmetry number) is subtracted from the entropy of the molecule, where R is the gas

7

constant. This subtraction assumes the species of interest is a homogenous mixture of all different optical

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isomers in all conformations. The SGAV and SHBI values reported here do not include the symmetry

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correction, it is assumed the user will apply the symmetry number correction for their particular molecule

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of interest.

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RMG is an active open-source software project; as a result, the methods are constantly being improved.

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To facilitate replication of this work, the exact version of Cantherm used in this work can be found in the

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GitHub version commit string found in the supporting information. Cantherm has been renamed to

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Arkane as of the publication of this article; but due to the version of RMG used, this article will continue

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to refer to the software package as Cantherm.

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Group Additivity Estimates

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A script was written utilizing python’s numpy module to convert thermochemistry values to hydrogen

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bond increments or group additivity values that minimize the error in the following linear system of

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equations:

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(𝐴)(𝐵) + (𝐶)(𝐷) = (𝐸)


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Matrix operations were carried out to solve for the unknown matrix B, each row of which carries the

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unknown GAV and HBI values (including enthalpy, entropy, and heat capacity at various temperatures).

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Each row of matrix A carries the number of occurrences of each unknown group in one of the compounds

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in the training set.

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Each row of matrix C carries the number of occurrences of each known group in one of the molecules in

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the training set.

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Each row of matrix D carries the known group values for one of the groups found in matrix C. Same

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format as matrix B.

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Matrix E is a matrix of thermochemistry data for the compounds in our training set. Same format as

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Matrix B.

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The weighted least-squares equation for B is

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𝐵 = 𝑊𝑧 Where

𝑊 = (𝑄𝑇𝑄)

―1 𝑇

𝑄

𝑄𝑖𝑗 = 𝐴𝑖𝑗/𝜎𝑖 𝜎𝑖 = 𝜎2𝐸𝑖 +

∑𝐶 𝜎

2 2 𝑖𝑗 𝐷𝑗

𝑗

𝑧𝑖 =

𝐸𝑖 ― ∑𝑗𝐶𝑖𝑗𝐷𝑗 𝜎𝑖

𝜎𝐸𝑖 denotes the uncertainty for thermochemistry data of species i 𝜎𝐷𝑗 denotes the uncertainty for the thermochemistry data of the known group j 14

The sensitivities of the inferred group values Bi to errors in E or D is given by ∂𝐵𝑗

15

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∂𝐸𝑖 ∂𝐵𝑗 ∂𝐷𝑙

=―

= 𝑊𝑖𝑗

∑𝑊 𝐶

𝑖𝑗 𝑗𝑙

𝑙



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In the development of group additivity values, Matrix E does not contain any entropy modifications due

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to symmetry, since symmetry is not an inherent part of the group additivity estimation method. Instead,

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RMG’s group additivity evaluation method evaluates external rotational symmetry, internal symmetry due

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to hindered rotors, and optical isomers of a molecule and accounts for entropy changes due to symmetry

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after all group additivity contributions are made.

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Uncertainty Analysis The uncertainty associated to each GAV developed in this work was derived through uncertainty propagation24, which uses the following equation:

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𝑠𝐺𝐴𝑉 =

𝑑 𝐺𝐴𝑉 2 2 𝑠𝑖 𝑑𝑖

∑( 𝑖

)

12 Where sGAV is the standard deviation of a group additivity value i is a component that contributes to the development of the GAV, including the CBS-QB3 method25, and the uncertainty of other GAVs that belong to the model species si is the uncertainty associated to component i 13 14

The standard deviation of the group additivity value sGAV is divided by the square root of number of points

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used to generate the value to give the standard error, documented in the supporting information. This

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work finds the uncertainty of the enthalpy of published GAVs to be 0.5-5.3 kcal/mol, and uncertainty of

17

entropy to be 0.2-2.5 cal/mol K.

18


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This work presents reliable GAV for many functional groups that will be helpful in kinetic modeling. In

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particular, further work on spiro radicals will be helpful to reduce the uncertainty in the associated group

3

values, and so more accurate estimates of other molecules containing those groups.

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More details for the computation of uncertainties, and the uncertainties of all GAVs are published in the

6

supporting information.

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Results and Discussion Fused Two Ring Aromatic Formation Mechanism

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The selection of fused two ring species investigated in this work is motivated by our observation of

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ethyltetralin and propylindane products of hexylbenzene pyrolysis1. This work further investigates the

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thermochemistry of the formation of these compounds, and proposes the reaction mechanisms in Figure

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1 and Figure 2 for the formation of fused two ring aromatic compounds in hexylbenzene pyrolysis:

14

H

15 16

Figure 1 Proposed formation mechanism for propylindene from the third hexylbenzene radical



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H

1 2

Figure 2 Proposed formation mechanism of ethylnaphthalene from the fourth hexylbenzene radical

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In the two proposed mechanisms, a hexylbenzene radical on the third/fourth carbon off the alkyl chain

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undergoes intramolecular addition to form a fused two ring structure, forming a radical precursor of

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propylindane/ethyltetralin. This precursor loses a hydrogen either through hydrogen beta-scission or

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disproportionation to form the stable species propylindane and ethyltetralin. Throughout the pathway,

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stable species may further lose hydrogen in allylic/benzylic positions through hydrogen abstraction, and

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radical species may lose hydrogen adjacent to radical carbons to through hydrogen beta-scission and

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disproportionation until the fused species becomes fully aromatized into propylindene and

11

ethylnaphthalene. This work calculates the thermochemistry of all the polycyclic compounds in Figure 1

12

and Figure 2 (for thermochemistry of hexylbenzene radicals see Lai et al.1).

13 14

In addition, this work also investigates the thermochemistry of the competing phenyl migration pathways,

15

a competing class of intramolecular addition pathways with only one shared carbon atom. Figure 3 shows

16

the phenyl migration pathways of interest.


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1 2

Figure 3. Proposed phenyl migration pathways from hexylbenzene to x-phenyl-1-hexyl radicals.

3 4

Here we focus on the thermochemistry of the fused ring radical. Due to the confounding unknowns of the

5

polycyclic correction and the radical correction in this class of compound, the thermochemistry of both

6

the radicals and their stable species counterparts were calculated. The thermochemistry of the x-phenyl-

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1-hexyl radicals are reported in the supporting information. Note the spiro radical intermediates have

8

different resonance forms which of course have the same energy. However, in the GAV/HBI method, one

9

needs to supply different HBI values for each resonance form, since each 𝑅 ∙ is derived from a different

10

RH.

11



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This work is primarily focused on the thermochemistry of the aforementioned reaction pathways,

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and derivation of GAV’s so that other similar pathways could be accurately estimated. A detailed

3

study of the transion states of the same reactions was recently reported by Khanniche et al.26

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Thermochemistry of Fused Two Ring Aromatic Species

5

As found in previous work1, accurate thermochemistry is needed to make correct predictions for product

6

yield. The thermochemistry of all polycyclic species shown in Figure 1-Figure 3. In Figure 3,

7

hydrogenated counterparts of the calculated species in the 1,3 and 1,4-cyclohexadiene resonance

8

structures were also calculated to determine the unknown radical and polycyclic thermochemical groups.

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In addition, all variants of species in the three figures with varying chain lengths up to 12 carbons were

10

also calculated; for example, indene, methylindene, and ethylindene were calculated alongside

11

propylindene. This resulted in the calculation of 83 species at the CBS-QB3 level of theory.

12

Thermochemical data calculated are gathered in Table 2. Full NASA Polynomials can be found in the

13

supporting information. A few of these species have been studied previous, and comparisons to prior

14

works for those species are listed in Table 3.

15 16

Table 2 Thermochemical data of species calculated in this work.

SMILES String Aromatic Pi Radicals of Indane C1=CC=C2CCCC2[CH]1 CC1CCC2=CC=C[CH]C21 CCC1CCC2=CC=C[CH]C21 CCCC1CCC2=CC=C[CH]C21 Alkylated Indanes C1=CC=C2CCCC2=C1 CC1CCC2=CC=CC=C21 CCC1CCC2=CC=CC=C21 CCCC1CCC2=CC=CC=C21 Benzylic Radicals of Indane C1=CC=C2CC[CH]C2=C1 CC1C[CH]C2=CC=CC=C21

Enthalpy of formation (298 K) (kcal/mol)

Entropy (298 K) (cal/mol K)

44.7 36.7 31.7 26.8

87.7 96.0 104.1 112.4

13.2 5.6 0.6 -4.5

82.1 90.5 98.3 107.0

49.5 42.2

84.7 93.4


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C[C]1CCC2=CC=CC=C21 39.4 CCC1C[CH]C2=CC=CC=C21 37.0 CC[C]1CCC2=CC=CC=C21 34.6 CCCC1C[CH]C2=CC=CC=C21 32.0 CCC[C]1CCC2=CC=CC=C21 29.2 Alkylated Indenes C1=CC=C2CC=CC2=C1 38.0 CC1C=CC2=CC=CC=C21 31.3 CC1=CCC2=CC=CC=C21 28.3 CCC1C=CC2=CC=CC=C21 26.3 CCC1=CCC2=CC=CC=C21 23.3 CCCC1C=CC2=CC=CC=C21 21.2 CCCC1=CCC2=CC=CC=C21 18.1 Aromatic Pi Radicals of Tetralin C1=CC=C2CCCCC2[CH]1 32.3 CC1CCCC2=CC=C[CH]C21 25.1 CCC1CCCC2=CC=C[CH]C21 21.2 Alkylated Tetralins C1=CC=C2CCCCC2=C1 4.6 CC1CCCC2=CC=CC=C21 -2.1 CCC1CCCC2=CC=CC=C21 -6.8 Benzylic Radicals of Tetraln C1=CC=C2CCC[CH]C2=C1 39.2 C[C]1CCCC2=CC=CC=C21 30.8 CC1CC[CH]C2=CC=CC=C21 32.8 CC[C]1CCCC2=CC=CC=C21 25.7 CCC1CC[CH]C2=CC=CC=C21 28.3 Alkylated Dihydronaphthalenes C1=CC=C2CCC=CC2=C1 29.4 CC1=CCCC2=CC=CC=C21 21.0 CC1CC=CC2=CC=CC=C21 22.8 CCC1=CCCC2=CC=CC=C21 16.0 CCC1CC=CC2=CC=CC=C21 16.9 Allylic and Benzylic Radicals of Dihydronaphthalene C1=CC=C2C=C[CH]CC2=C1 57.4 C1=CC=C2C=CC[CH]C2=C1 62.0 CC1[CH]C=CC2=CC=CC=C12 50.8 C[C]1CC=CC2=CC=CC=C12 53.7 CC1=C[CH]CC2=CC=CC=C12 49.2 CC1=CC[CH]C2=CC=CC=C12 53.6 CCC1[CH]C=CC2=CC=CC=C12 44.2 CC[C]1CC=CC2=CC=CC=C12 49.3 CCC1=C[CH]CC2=CC=CC=C12 44.7 CCC1=CC[CH]C2=CC=CC=C12 48.7 Naphthalenes C1=CC=C2C=CC=CC2=C1 35.1 CC1=CC=CC2=CC=CC=C12 27.0 CCC1=CC=CC2=CC=CC=C12 22.1 Phenyl Migration Radicals

93.7 100.7 101.2 109.5 108.7 79.8 88.5 87.9 96.9 96.3 105.9 106.0 89.8 98.2 106.5 97.4 95.3 103.0 88.2 96.8 96.3 102.5 102.9 85.2 92.3 93.2 98.9 102.1 87.1 86.5 93.6 93.5 96.3 95.1 101.9 102.8 103.5 102.9 82.3 89.9 96.6



CCCCC1CC12C=CC=CC2 CCCC1CCC12C=CC=CC2 CCC1CCCC12C=CC=CC2 CC1CCCCC12C=CC=CC2 Rad 2 Phenyl Migration 1_4 CCCCC1CC12C=CCC=C2 CCCC1CC12C=CCC=C2 CCC1CC12C=CCC=C2 CC1CC12C=CCC=C2 C1CC12C=CCC=C2 Rad 2 Phenyl Migration 1_3 CCCCC1CC12C=CC=CC2 CCCC1CC12C=CC=CC2 CCC1CC12C=CC=CC2 CC1CC12C=CC=CC2 C1CC12C=CC=CC2 Rad 3 Phenyl Migration 1_4 CCCC1CCC12C=CCC=C2 CCC1CCC12C=CCC=C2 CC1CCC12C=CCC=C2 C1CCC12C=CCC=C2 Rad 3 Phenyl Migration 1_3 CCCC1CCC12C=CC=CC2 CCC1CCC12C=CC=CC2 CC1CCC12C=CC=CC2 C1CCC12C=CC=CC2 Rad 4 Phenyl Migration 1_4 CCC1CCCC12C=CCC=C2 CC1CCCC12C=CCC=C2 C1CCCC12C=CCC=C2 Rad 4 Phenyl Migration 1_3 CCC1CCCC12C=CC=CC2 CC1CCCC12C=CC=CC2 C1CCCC12C=CC=CC2 Rad 5 Phenyl Migration 1_4 CC1CCCCC12C=CCC=C2 C1CCCCC12C=CCC=C2 Rad 5 Phenyl Migration 1_3 CC1CCCCC12C=CC=CC2 C1CCCCC12C=CC=CC2

43.3 43.0 25.8 21.5

118.6 118.4 108.1 103.4

24.5 29.3 34.3 40.2 46.8

117.2 106.3 97.5 89.4 81.6

25.2 30.1 35.2 41.3 47.8

117.5 107.2 98.3 90.5 82.7

21.3 26.6 32.5 40.9

110.5 101.8 93.7 87.2

21.8 27.0 32.6 40.9

111.3 102.6 95.0 87.9

3.7 9.0 17.2

106.2 98.8 92.3

5.9 9.6 16.8

108.3 98.6 92.6

-0.8 6.9

101.6 95.4

0.0 6.2

106.3 95.6

Page 14 of 31

1 2

Table 3 Thermochemical data comparison between this work and other literature sources (all data available).

Molecular Structure

Enthalpy of formation (298 K) (kcal/mol)

Entropy (298 K) (cal/mol K)

This Work

This Work

Literature


Literature

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13.2

14.510

82.1

38.0

39.28 39.110

79.8

4.6

6.410

97.4

29.4

28.08

85.2

85.98

62.0

54.98

86.5

86.98

35.1

28.28 35.910

82.3

80.216

27.0

28.327

89.9

89.827

80.38

1 2

Fewer experimental entropy values were reported than enthalpy values. For example, entropy values are

3

missing for two of the molecules in Table 3. While we believe the computational methods employed here

4

to compute entropies are fairly reliable, they are certainly not perfect, and caution is recommended when

5

using values without suitable benchmarking. This matter is particularly prominent since ring puckering

6

effects that may exist in this work’s species calculations might not be treatable using the 1-D hindered

7

rotor harmonic oscillator approximation.

8 9

A comparison of these calculated values were made with RMG’s estimates. Figure 4 shows the

10

distribution of Gibbs free energy difference between RMG’s estimates and this work’s calculations at 298

11

K. On average, RMG overestimates the Gibbs free energy of the fused polycyclic species by 7.3 kcal/mol,

12

with a standard deviation of 4.1 kcal/mol. The deviations range from -3 to +13 kcal/mol. 15 ACS Paragon Plus Environment


45 40 35

Frequency

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 31

30 25 20 15 10 5 0 -4

-3

1 2 3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

Gibbs Free Energy Deviation (GAV - CBS-QB3) (298K)

11

12

13

14

15

Figure 4 Distribution of Gibbs free energy deviation (kcal/mol) for 83 calculated fused two ring species up to 12 carbon atoms. Distribution for previous RMG estimates (white) and with updated group values (black) are shown.

4 5

As demonstrated in our previous work1, this difference in Gibbs free energy is significant to adversely

6

affect product distribution predictions. To facilitate better estimations of similar molecules and radicals in

7

the future, we have updated RMG’s group values used to describe the polycyclic species of interest.

8 9

Figure 4 shows the updated energy deviations from the new group values derived from our

10

thermochemistry calculations. The average deviation of Gibbs free energy has been dropped to 0.4

11

kcal/mol, with a standard deviation of 0.9 kcal/mol; it can also be seen that the deviations follow a more

12

normal distribution. The specific differences that led to this decrease are discussed in the following

13

sections.

14 15

Derived Group Values

16

RMG’s thermochemistry estimation is based off Benson’s thermochemical group additivity28, Lay et al.’s

17

radical hydrogen bond increments15, and Han et al.’s calculations for polycyclic compounds17. These

18

values were evaluated from various calorimetry experiments, literature sources, and calculations at various

19

levels of theory. 16 ACS Paragon Plus Environment

Page 17 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 2

The thermochemistry groups in question for this work are polycyclic groups which were derived using

3

limited training data by Han et al.17, and hydrogen bond increments where the radical descriptors from

4

Lay et al. (derived for simple radicals) were not specific enough to describe the resonance behavior of the

5

more complicated radicals considered here. The groups that were in question in this work are summarized

6

in Table 4 and Table 5.

7 8

1.1.1. Polycyclic Group Values

9

The thirteen polycyclic groups involve structures of indane, indene, tetralin, dihydronaphthalene,

10

naphthalene, and several spiro compounds. Table 4 shows the original and updated values for enthalpy

11

and entropy, as well as the sources of the original values. Group values for CP can be found in the

12

supporting information.

13 14

Table 4. Original and updated values of polycyclic groups and the sources of RMG’s original group values.

Polycyclic Group

H(298K) Kcal/mol

S(298K) cal/mol K

Original

Updated

Original

Updated

3.7

2.7

23.2

22.3

2.1

2.2

33.1

28.7

-0.2

-0.2

15.0

18.6

Source of Original RMG Value

CBS-QB3 calculation for indane

Verevkin (2011), experimental H,


PM7 level of theory S and Cp29

CBS-QB3 calculation for tetralin


Page 18 of 31

Han et al. (2018) M06-2X/cc-pVTZ 4.3

-1.1

20.9

20.5

0

-1.0

-2.8

-2.0

calculations for shown species17 Long et al. (2018), CBS-QB3 calculations for Naphthalene30 Han et al. (2018) M06-2X/cc-pVTZ

26.7

24.8

53.7

55.6

calculations for shown species17 Han et al. (2018) M06-2X/cc-pVTZ

32.1

30.4

58.5

58.8


30.0

22.6

51.0

50.9


34.4

27.0

53.3

54.0


14.2

4.5

47.8

46.6


17.4

9.2

48.9

49.4


9.4

-0.4

40.5

39.6


12.7

3.6

42.7

45.3

calculations for shown species17

1 2

Indane, tetralin, and naphthalene previously had group values based off the same level of theory, albeit a

3

narrower selection of model compounds. As a result, the thermochemistry corrections of these groups are

4

relatively small. The original and updated group values differ by < 1 kcal/mol for enthalpy of formation,


Page 19 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

and < 6 cal/mol K for entropy. These differences account for less than 2 kcal/mol difference in the Gibbs

2

free energy at 298 K.

3 4

The original RMG values for the indene polycyclic group were taken from work by Verevkin et al.29,

5

where the enthalpy of formation of indene was experimentally determined, and the entropy and heat

6

capacity values were calculated using the PM7 level of theory. Based on our assessment, it is inconclusive

7

whether Verevkin’s estimation is more accurate than our work’s results. Our CBS-QB3 calculations finds

8

the same enthalpy of formation as Verevkin’s experimental work, which is reassuring. For the entropy of

9

this polycyclic group, a 6 cal/mol K difference was observed due to the difference in calculation method

10

and the smaller set of model compounds used in the old estimation. The PM7 method has a 1.86 kcal/mol

11

root mean square error in enthalpy of stable molecules32 and 5 cal/mol K in entropy33; this can be compared

12

to the accuracy of CBS-QB3 documented by Somers and Simmie34, with a mean signed error of -2.78

13

kcal/mol in ΔHf298K for closed shell species. Unfortunately, the accuracy of CBS-QB3 entropies for a

14

broad range of molecules has not been documented in the literature, but previous calculation examples

15

from our work have been in close agreement with the literature1,16. Between this work (Table 3) and Lai

16

et al.1, entropy values calculated by CBS-QB3 differ by no more than 2 cal/mol K to found literature

17

sources.

18 19

The dihydronaphthalene polycyclic correction has a 5 kcal/mol difference in enthalpy, a relatively stark

20

disagreement with our previous source of thermochemistry estimation. This difference brings ~5 kcal/mol

21

difference in the Gibbs free energy of a species at 298K, and is an important correction to RMG’s

22

thermochemistry group values. The original source of this polycyclic correction came from the M06-

23

2X/cc-pVTZ level of theory. Differences larger than 5 kcal/mol in enthalpy of formation between this



Page 20 of 31

1

level of theory and CBS-QB3 has been observed in the past in our group’s work for calculations on

2

hexylbenzene1, and this change is an important correction to the polycyclic group value of

3

dihydronaphthalene.

4 5

The polycyclic groups for spiro compounds differ from previous estimates by up to 13 kcal/mol in

6

enthalpy of formation, and up to 2 cal/mol K in entropy. The large discrepancies in the enthalpy of

7

formation are due to the differences between M06-2X/cc-pVTZ and the more accurate CBS-QB3 (with

8

BAC) method used here. Consistent with common chemical intuition, polycyclic groups featuring three

9

or four membered rings exhibit a much higher enthalpy correction than groups with five or sixed

10

membered secondary rings, as small rings exhibit ring strain. It can be seen that 1,4-cyclohexadienes have

11

a lower enthalpy of formation than 1,3-cyclohexadiene isomers.

12 13

1.1.2. Hydrogen Bond Increments for Radicals

14

Four HBI values were originally used by RMG to estimate the thermochemistry of our fused polycylic

15

species. These groups lacked sufficient specificity towards our radicals of interest; therefore Table 5

16

shows our newly developed HBI groups (13 total), their hydrogen bond increment values, as well as the

17

sources of the original HBI values. Group values for CP can be found in the supporting information.

18 19 20

Table 5. Original and updated HBI groups for radicals, with their respective enthalpy/entropy values and the source of RMG’s original value. Enthalpy values in kcal/mol, and entropy values in cal/mol K.

Old Group

H 298K 75.0

S Structure New Group 298K Label 1.3

A

H 298K 73.7


S Source of Original RMG Value 298K 0.8

CBS-QB3 calculations for methylcylohexadienyl and hexylcyclohexadienyl radicals

Page 21 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


85.6

88.1

83.8

-3.8

-4.9

-5.3

B

74.5

0.4

C

70.7

-1.8

D

72.5

2.7

E

73.5

-3.3

F

74.0

-1.2

G

80.1

1.9

H

86.4

1.3

I

88.5

3.1

J

83.7

1.4

K

84.7


1.7

Roth et al.35 experimental enthalpy, Lay et al.15 MNDO/PM3 calculations for entropy. Model compound is 1-buten-3-yl radical

Lai et al.1 CBS-QB3 calculations Model compounds include benzyl, ethylbenzyl, propylbenzyl, butylbenzyl, pentylbenzyl, and hexylbenzyl radicals

Robaugh et al.36 and Hippler et al.37 experimental enthalpy, Lay et al.15 MNDO/PM3 calculations


L

85.4

4.4

M

83.3

2.1

Page 22 of 31

for entropy. Model compound is 2-Phenyl-2propyl radical

1 2

Several HBI groups can be found in the Handbook of Bond Dissociation Energies in Organic Compounds

3

by Luo38. The cited groups are shown in Table 6 for comparison. It was found that the CBS-QB3 fitted

4

values are typically > 2 kcal/mol higher than the various literature sources found with the exception of the

5

dihydronaphthalene radical. The methods of determining BDE’s cited in Table 6 include correlation

6

between BDEs and rate constants/activation energies39-41, photoacoustic calorimetry42, and pyrolysis

7

kinetics43; it is reasonable to believe that the CBS-QB3 method can generate more accurate

8

thermochemistry results than the methods used.

9 10 11

Table 6 All available comparisons between this work’s hydrogen bond increments compared to Handbook of Bond Dissociation Energies in Organic Compounds38. Figures shown in kcal/mol.

This Work

Luo38

88.5

85.939

86.4

82.942 83.639 82.640

84.7

79.341

80.1

86.043 80.440

12


Page 23 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

The four spiro radicals (C through F) differ noticeably from the original source, with a < 5 kcal/mol

2

difference in enthalpy and < 4 cal/mol K difference in entropy. This indicates that these fused

3

cyclohexadienyl radicals differ modestly in energy from analogous radicals which don’t have fused rings.

4

The only exception is the enthalpy correction of group C, where this difference originates from the high

5

ring strain geometry of this species, and the introduction of a radical greatly alters this ring strain.

6 7

The addition of a fused ring to secondary and tertiary benzylic radicals does not cause the enthalpy HBI

8

correction for the radical to change very much in the case of H and I structures (within 2 kcal/mol), but

9

causes a large difference in entropy correction up to 8.5 cal/mol K. This difference in entropy is due to

10

hindered rotor difference between a free benzyl radical and a fused benzyl radical; particularly, non-fused

11

benzyl radicals lose a hindered rotor with the introduction of the radical (due to resonance with the

12

aromatic pi bonds), whereas fused benzyl radicals do not experience changes in hindered rotors with the

13

introduction of a radical.

14 15

The enthalpy and entropy of formation of G and J differ from its original source by 5 kcal/mol and 5

16

cal/mol K respectively, missing the extra stabilization due to resonance with the aromatic ring as well as

17

the difference in entropy associated with rotor loss. This resonance stabilization is not fully reflected in

18

the HBI group, since part of it is attached to the polycyclic group value.

19 20

This work finds that there is little difference in enthalpy correction between radicals found on five

21

membered secondary ring structures (e.g. indane) versus radicals found on six membered secondary ring

22

structures (e.g. tetralin), with enthalpy differences lower than 2 kcal/mol. The same is found for entropy,

23

where this difference is found to be less than 3 cal/mol K.



Page 24 of 31

1 2

Conclusions

3

This study was motivated by the lack of data on thermochemistry of fused two ring aromatics relevant to

4

intramolecular addition and phenyl migration reactions, classes of reactions that are of great interest in

5

understanding the chemistry of alkylaromatics. This work provides thermochemistry values for 83

6

alkylated fused two ring species. Group additivity values are derived from the aforementioned

7

thermochemistry values; these groups include polycyclics for fused two ring aromatics, and hydrogen

8

bond increment values for radicals that were previously lacked sufficient specificity. These new group

9

values agree with the Gibbs free energy found from CBS-QB3 calculations within 0.4 kcal/mol, with a

10

standard deviation of 0.9 kcal/mol. Discussion was provided, highlighting differences between old sources

11

and our current work, and rationalizing differences based on the molecular features such as hindered rotor

12

effects and resonance stabilization. The newly developed groups can be used in the future to estimate the

13

thermochemistry of species that carry similar structures, and will aid the prediction of the formation of

14

fused two ring aromatics.

15 16

Acknowledgements

17

The authors gratefully acknowledge the support of Saudi Aramco for funding this study under Contract

18

Number 6600023444, and Dr. Ki-Hyouk Choi, Mohnnad Alabsi, and Massad S. Alanzi for their input.

19 20

The authors thank Mengjie Max Liu, Allen Mark Payne, and Matthew Johnson for their intuition towards

21

the chemistry of alkylaromatics as a contribution to this article. We thank all RMG developers, including

22

Ryan Gillis, Mark Goldman, and Richard West, for the development and maintenance of the RMG

23

software that facilitated this investigation. 24 ACS Paragon Plus Environment

Page 25 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Associated Content

2

Supporting Information

3

GitHub version commit strings for RMG-Py and RMG- databased used in this project (section S1),

4

CHEMKIN formatted NASA polynomials of x-Phenyl-1-hexyl radicals calculated using CBS-QB3

5

(section S2), NASA polynomials for all species calculated in this work (section S3), heat capacity GAVs

6

for groups in Tables 4 and 5 (section S4), and uncertainty of GAVs for groups in Tables 4 and 5 (section

7

S5).

8 9 10

Author Information Corresponding Author

11

William H. Green

12

Phone: 617-253-4580

13

Fax: 617-324-3127

14

E-mail: [email protected]

15

References

16

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Fuels, 2018, 32, 5489-5500.

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(2) Carr A. G.; Class C. A.; Lai L.; Kida Y.; Monrose T.; Green W. H. Supercritical Water Treatment of

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Crude Oil and Hexylbenzene: An Experimental and Mechanistic Study on Alkylbenzene

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Decomposition. Energy Fuels, 2015, 29, 5290-5302.

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(3) Freund H.; Olmstead W. N. Detailed Chemical Kinetic Modeling of Butylbenzene Pyrolysis. Int. J.

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Chem. Kinet., 1989, 21, 561-574.



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Formation in Hexylbenzene Radicals. J. Phys. Chem. A., 2018, 122, 9778-9791.

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TOC Graphic

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Thermochemistry and Group Additivity Values for Fused Two Ring

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