University of Northern Iowa UNI ScholarWorks Faculty Publications Faculty Work 2016 Calculating Heat of Formation Values of Energetic Compounds: A Comparative Study Michael S. Elioff Millersville University of Pennsylvania Jordon Hoy University of Northern Iowa See next page for additional authors Let us know how access to this document benefits ouy Copyright ©2016 Michael S. Elioff, Jordan Hoy, and John A. Bumpus. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This work is licensed under a Creative Commons Attribution 4.0 License. Follow this and additional works at: https://scholarworks.uni.edu/che_facpub Part of the Chemistry Commons Recommended Citation Elioff, Michael S.; Hoy, Jordon; and Bumpus, John A., "Calculating Heat of Formation Values of Energetic Compounds: A Comparative Study" (2016). Faculty Publications. 1. https://scholarworks.uni.edu/che_facpub/1 This Article is brought to you for free and open access by the Faculty Work at UNI ScholarWorks. It has been accepted for inclusion in Faculty Publications by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. Authors Michael S. Elioff, Jordon Hoy, and John A. Bumpus This article is available at UNI ScholarWorks: https://scholarworks.uni.edu/che_facpub/1 Hindawi Publishing Corporation Advances in Physical Chemistry Volume 2016, Article ID 5082084, 11 pages http://dx.doi.org/10.1155/2016/5082084 Research Article Calculating Heat of Formation Values of Energetic Compounds: A Comparative Study Michael S. Elioff,1 Jordan Hoy,2 and John A. Bumpus2 1 Department of Chemistry, Millersville University of Pennsylvania, Millersville, PA 17551, USA 2Department of Chemistry and Biochemistry, University of Northern Iowa, Cedar Falls, IA 50614, USA Correspondence should be addressed to John A. Bumpus; [email protected] Received 9 October 2015; Revised 26 December 2015; Accepted 27 December 2015 Academic Editor: Dennis Salahub Copyright © 2016 Michael S. Elioff et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Heat of formation is one of several important parameters used to assess the performance of energetic compounds. We evaluated Δ the ability of six different methods to accurately calculate gas-phase heat of formation ( 298,g) values for a test set of 45 nitrogen- containing energetic compounds. Density functional theory coupled with the use of isodesmic or other balanced equations yielded Δ ± calculated results in which 82% (37 of 45) of the 298,g values were within 2.0 kcal/mol of the most recently recommended experimental/reference values available. This was compared to a procedure using density functional theory (DFT) coupled with an Δ ± atom and group contribution method in which 51% (23 of 45) of the 298,g values were within 2.0 kcal/mol of these values. The Δ T1 procedure and Benson’s group additivity method yielded results in which 51% (23 of 45) and 64% (23 of 36) of the 298,g values, respectively, were within ±2.0 kcal/mol of these values. We also compared two relatively new semiempirical approaches (PM7 and Δ RM1) with regard to their ability to accurately calculate 298,g. Although semiempirical methods continue to improve, they were found to be less accurate than the other approaches for the test set used in this investigation. 1. Introduction assess the performance of energetic materials [5]. In prac- tice, most theoretical approaches calculate gas-phase heat There is substantial interest in the discovery and development Δ of formation ( 298,g) values. Solid- or liquid-phase val- of new energetic compounds which include high explosives ues are then calculated by subtracting heat of sublimation and propellants and there is special interest in the discovery (Δ 298, )orheatofvaporization(Δ 298, )values, and development of high energy density materials (HEDMs). sub vap respectively, from the gas-phase value. Collectively, compounds that have densities greater than or 3 Our interest concerns the use of relatively rapid methods equal to 1.9 g/cm , detonation velocities greater than or equal for the calculation/prediction of accurate gas-phase heat of to 9.0 km/s, and detonation pressures greater than or equal formation values. During the past several years two relatively to 40.0 GPa are known as HEDMs [1]. The usefulness of rapid computational procedures have been described for use HEDMs in a variety of processes has been understood for in determining Δ 298, values [6–8]. One procedure, devel- at least a century [2]. Two important considerations with g oped by Byrd and Rice [6, 7], uses density functional theory regard to HEDMs are that they can be dangerous and costly to (DFT) coupled with an atom and group contribution method synthesize. Moreover, increasing environmental concerns call to determine Δ 298, for energetic compounds. Another formoreeffectivewaysofpredictingperformanceofHEDMs g procedure, developed by Ohlinger et al. [8], was designed to [3]. Manufacturers must be able to determine the amount of be applicable to a broader range of compounds. The latter energy that can be stored in a molecule while maintaining an relies on a novel multilevel computational approach known acceptable level of stability [4]. as T1 that approaches the accuracy of the G3MP2 method [9] Δ The condensed-phase heat of formation ( 298,s or while simultaneously reducing the computation time by 2-3 Δ 298,l) is one of several important parameters used to orders of magnitude [8]. In the investigations reported here, 2 Advances in Physical Chemistry we have compared the effectiveness of these two procedures group value is not among those included in the database Δ with regard to their ability to accurately calculate 298,g for the NIST WebBook applet. To address this problem values of nitrogen-containing energetic compounds. Oper- we first calculated an enthalpy group value for an azido Δ ating under the assumption that newer procedures are not group attached to a carbon atom. The 298,g of methyl necessarily more reliable than more established methods, we azide has been determined experimentally and by high also assessed and compared the ability of two other well- level computation. We used the value of 71.2 kcal/mol Δ ± establishedproceduresusedtocalculate 298,g. Specif- ( 1.0 kcal/mol) recommended by Dorofeeva et al. [21]. ically,weassessedandcomparedresultsusingthegroup Subtracting the methyl group value (−10.2 kcal/mol) from additivity method developed by Benson and his colleagues the heat of formation of methyl azide gives a value of [10, 11] as well as density functional theory coupled with the 81.4 kcal/mol for the azido group. The group additivity Δ use of isodesmic, isogyric, or other balanced equations [12]. approachwasthenusedtocalculate 298,g values of We also used and compared two relatively new semiempirical azido-containing compounds as follows. First the NIST Δ Δ models (PM7 and RM1) [13, 14] to calculate 298,g. applet was used to calculate the 298,g valuefortheamino analog of the azido compound. Then, the azido group value 2. Methods of 81.4 kcal/mol was used in the calculation instead of the amino group value. Using this simple modification of the Δ The test set used in this investigation consisted of the gas- group additivity approach 298,g values were calculated Δ phase heat of formation ( 298,g) values for forty-five for six of the eight compounds in our test set that contained Δ nitrogen-containing energetic compounds studied by Byrd an azido group. Calculation of 298,g for the remaining Δ and Rice [6, 7]. 298,g values were calculated using the compounds that contained an azido group is described below. T1 procedure which is based on the G3MP2 [9] multilevel The ASTM CHETAH 8.0 software program [25] was used Δ ab initio model chemistry as implemented in the Spartan’10 to calculate 298,g values for a few other compounds in our and 14 suite of programs. Semiempirical theory using the test set whose Δ 298, values could not be calculated using RM1 and PM7 model chemistries [13, 14] were used to cal- g the NIST applet. culate Δ as implemented in Spartan 14 (Wavefunction 298,g The group additivity difference method as described by Inc., Irvine, CA) and MOPAC2012 (http://openmopac.net/), Cohen and Benson [26] was used to calculate the Δ respectively. 298,g value for nitromethane. For nitromethane, it should be men- Gas-phaseheatofformationvalueswerealsocalculated tioned that experimental values of −17.8 and −19.3 kcal/mol using density functional theory as implemented in Spartan 10 have been reported and used extensively. Interestingly, there and14coupledwiththeuseofisodesmic,isogyricandother is considerable theoretical as well as experimental support for balanced equations. An informative account of the details both values [20, 22–24, 27–29]. In the present investigation, concerning the calculation of Δ using this approach 298,g the group additivity value for nitromethane (−18.0 kcal/mol) has been presented by Cramer [12]. Most of the equations was calculated by subtracting the group value (−6.6 kcal/mol) used were isodesmic equations. For the studies reported for a methylene (–CH2–) group bound to a nitrogen atom herein total electronic energies ( Tot ), zero point energies Δ − from the calculated 298,g value of 24.6 kcal/mol for (ZPE), and thermal correction ()valuesforcompounds nitroethane. We note that this value is 1.5 kcal/mol greater in all of the equations were calculated using the M06 2X ∗ ∗ than that previously reported by Bumpus and Willoughby functional [15, 16] and the 6-31G basis set. The 6-31G basis [27]. It should also be noted that recent experimental set is a medium size basis set.