Sciencemadness Discussion Board

Thermocalculations in Energetic Materials

DubaiAmateurRocketry - 20-8-2018 at 23:08

Introduction and Method

Recently, I visited almost every thermochemical calculation methods out there. Most of them are quantum mechanics - quantum chemistry based, while some involves emprical fitting while anothers are group add:

CBS-X such as CBS-4M, CBS-QBS. G3, G3MP2, and G2. The W1 theory:W1U. B3LYP at 6-21, 6-31, 6-31g(d), 6-311g+(2d,p), and B3PW91 at 6-31g(d,p). PM3, PM6, PM7 from MOPAC. Group adding from EMDB1.0 trial version, Keshavarz et al.

Equations that I have tried:

Ochterski 2000. [1]
Rice et al, 1999. [2]
Bryd & Rice 2006. [3]
Poltizer et al, 1997, 2001, and 2005. [4,5,6]
Klapotke, 2017 [7]

Here are some advantages and disadvantages of each that I have to give.

PM3, PM6, PM7 are fast and empirical-based methods. By fast I mean extremely fast, they're all almost below 1 minute. This is a method I want to talk about a lot since it fits amateurs the most. Since they're fitted to empirical data, it gives rather far-off deviations toward novel structures. TTTO's W1U (the absurdly accurate 0.3kcal deviation method) is 230.7 kcal, and all PM methods give off extremely far deviations toward this number (>20kcal). The heat of formation of PM methods on furoxans, 1,2,4,5-tetrazines, 1,2,3,4-tetrazines, 1,2,3,4-tetrazine-2,4-dioxides, and other similar N→O structures gives off high deviation. Their performance on nitro groups vary. PM7's usual deviation on energetic materials is around 6-12 kcal/mol.

B3LYP 6-31g(d) is the most computationally affordable method with relatively acceptable errors.

B3LYP 6-311g+(2d,p) is more accurate on tetrazine dioxides.

W1U method is affordable only on <20 atoms on a super-computer, but its result is probably more accurate than experimental ones.

CBS-QB3 and CBS-4M are relatively accurate but crash on large molecules.

equation.png - 69kB

For most of the below, I use the above equation unless otherwise stated:


PM3, PM6, PM7
Here is a list of PM3, PM6, PM7 results and their deviation:
PM367.png - 58kB

Here is a long list of PM7 results against various compounds, some of the nitrogen compound's gaseous HOF are calculated using ESP method against their experimental data.
PM7.png - 44kB

W1U method is the one of the most computationally expensive method. It is far out of reach for my computer to run anything bigger than methane, I tried ethane and after half a day, it worked, but it will not run 1-H-tetrazole or triazoles. W1U.png - 34kB

B3LYP 6-31g(d)
B3LYP-6-31g(d), Rather accurate average deviation here.
6-31g(d).png - 40kB

B3LYP 6-31g(d) 1999 Rice Correction
The same as above, however using a new equation fitted for energetic materials by Rice et al 1999.
Rice 1999.png - 62kB

B3LYP 6-311g+(d2,p)
B3LYP-6-311g+(2d,p) Its suppose to give better results than the one above, however did not, although I have not yet ran the entire test set that I personally prefer yet. Some promising improves in tetrazine dioxides results are seen here.
6-311g+(2d,p).png - 78kB

CBS-X method, I deleted a lot of data, so it looks unfinished, however the average error for solid state heat of formation was about 6kcal/mol for CBS-4M, only 2 compounds were performed on CBS-QBS and CBS-APNO. For me at least, CBS-X methods run into errors on any compound bigger than TNT and RDX. (12 hours of HMX and 20 hour CL-20 runs provides weird errors reports).
CBS-X.png - 61kB

Sugestions and guide:

PM methods are available on the free program MOPAC, the installation procedure is difficult and is almost like an IQ test - I failed few times!

Carefully read citation [1]'s last few pages, they have literally all the numbers you need. EZPE is 0 for B3LYP based methods. All the results you will obtain using these are gaseous heat of formation. For solid, use equations from either [2] or [6].

Multiwfn is a free software to obtain surface area and average electrostatic potential of a molecular surface. This is required for calculation of ESP-method of enthalpy of sublimation, which is required for the solid phase heat of formation.

Gaussian 09 has all the basis set above. Potentially ORCA, PSI4, GAMESS, Spartan, and a few others have these too. ORCA and GAMESS is free. I have personally also use ORCA for other calculations, however through cmd, and it took me a while to get used to it.

I never took chemistry and had to drop out of calculus II in college, there is some readings to do, but I believe anyone can do it :) Obtaining Gaussian is hard, try asking forum members is the best legal tip I can provide.

Reference and Extra Reading:

[1] Ochterski, Joseph W. "Thermochemistry in gaussian." Gaussian Inc (2000): 1-19.

[1] Rice, Betsy M., Sharmila V. Pai, and Jennifer Hare. "Predicting heats of formation of energetic materials using quantum mechanical calculations." Combustion and flame 118.3 (1999): 445-458.

[2] Byrd, Edward FC, and Betsy M. Rice. "Improved prediction of heats of formation of energetic materials using quantum mechanical calculations." The Journal of Physical Chemistry A 110.3 (2006): 1005-1013.


-Politzer, Peter, et al. "Calculation of heats of sublimation and solid phase heats of formation." Molecular Physics 91.5 (1997): 923-928.

-Politzer, Peter, et al. "Computational characterization of energetic materials." Journal of Molecular Structure: THEOCHEM 573.1-3 (2001): 1-10.

-Politzer, Peter, et al. "Computational prediction of standard gas, liquid, and solid‐phase heats of formation and heats of vaporization and sublimation." International journal of quantum chemistry 105.4 (2005): 341-347.

[7] Klapötke, Thomas M. Chemistry of high-energy materials. Walter de Gruyter GmbH & Co KG, 2017.

Simmie, John M. "A database of formation enthalpies of nitrogen species by compound methods (CBS-QB3, CBS-APNO, G3, G4)." The Journal of Physical Chemistry A 119.42 (2015): 10511-10526.

and its supplementary files:

Simmie, John M., and Kieran P. Somers. "Benchmarking compound methods (CBS-QB3, CBS-APNO, G3, G4, W1BD) against the active thermochemical tables: A litmus test for cost-effective molecular formation enthalpies." The Journal of Physical Chemistry A 119.28 (2015): 7235-7246.

and its supplementary files:


And Yes, I can calculate the theoretical heat of formation of novel compounds for you upon request under this post.

[Edited on 21-8-2018 by DubaiAmateurRocketry]

simply RED - 21-8-2018 at 06:29

Really good work! Congratulations! Many thanks for sharing the results.

One thing to note, the energetic materials community works in MJ/kg. For example TNT E(detonation) is ~ 4 MJ/kg and that of RDX is ~ 5.5 MJ/kg. So it could be nice the enthalpies of formation to be presented in MJ/kg also, much more intuitive.
Also, you may try to calculate some energies of detonation or combustion.
E(detonation) = E(molecule) - E(products)

Another one: ZPE = 0 is impossible! By 0 you mean you did not calculate it. Quantum oscillators have zero point energy even at 0 K, ZPE is never 0.
You calculate enthalpy of formation at 0 K and 298 K, do you know how the program does it? First it calculates the vibrational /and optionally rotational/ states energies and then populates these energies to the point of 298 K. As you can imagine, this calculation is by itself ZPE corrected.

[Edited on 21-8-2018 by simply RED]

DubaiAmateurRocketry - 21-8-2018 at 11:02

red, yes, it seems on B3LYP that the eZPE is already corrected, for some reason.

edit, otherwise, the equation would not work, this weird eZPE issue is same for B3LYP and CBS-x methods for anyone who need to calculate enthalpy.

[Edited on 21-8-2018 by DubaiAmateurRocketry]

simply RED - 23-8-2018 at 05:29

If you perform vibrational analysis, the program may automatically correct ZPE. Whether or not, it should be written in the manual of the software.

DubaiAmateurRocketry - 24-9-2018 at 22:20

So recently after a lot of effort to do computational chemistry for energetic materials, I can help anyone here to compute enthalpies to relatively high accuracy.

I have access to both extremely high-end workstation computers as well as cluster computers. I am running Linux WebMO interface with Gaussian, NWChem, ORCA, and MOPAC.

I also have a GTX1080Ti graphics card currently doing nothing on my shelf which i am looking forward to in GPU accelerating Gaus/NWChem calculations.

Methods such as CBS-4M, CBS-QBS, W1U (up to 10 atoms), G3MP2B3 can obtain results to extremely high accuracy (average deviation for G3MP2B3 is 2.5kcal/mol).

Currently, I'm working on crystal structure prediction, which seems to be an extremely hard task, I am looking at the software USPEX at the moment.