SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become a popular symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a description of its features, and a discussion of select submodules. The supplementary material provide additional examples and further outline details of the architecture and features of SymPy.Subjects Scientific

Gas phase hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) is a relatively stable molecule which releases a large amount of energy upon decomposition. Although gas-phase unimolecular decomposition experiments suggest at least two major pathways, there is no mechanistic understanding of the reactions involving RDX or other energetic molecules (such as HMX and TATB), used in applications ranging from automobile air bags to rocket propellants. For the unimolecular decomposition of RDX, we find three pathways: (i) concerted decomposition of the ring to form three CH 2 NNO 2 (M ) 74) molecules, and (ii) homolytic cleaVage of an NN bond to form NO 2 (M ) 46) plus RDR (M ) 176), which subsequently decomposes to form various products. Experimental studies suggest that the concerted pathway is dominant while theoretical calculations have suggested that the homolytic pathway might require significantly less energy. We report here a third pathway: (iii) successive HONO elimination to form 3 HONO (M ) 47) plus stable 1,3,5-triazine (TAZ) (M ) 81) with subsequent decomposition of HONO to HO (M ) 17) and NO (M ) 30) and at higher energies of TAZ into three HCN (M ) 27). We examined all three pathways using first principles quantum mechanics (B3LYP, density functional theory), including the barriers for all low-lying products. We find: A threshold at ∼40 kcal/mol for which HONO elimination leads to TAZ plus 3 HONO, while NN homolytic cleavage leads to RDR plus NO 2 , and the concerted pathway is not allowed; above ∼52 kcal/mol the TAZ of the HONO elimination pathway can decompose into 3 HCN while the HONO can decompose into HO + NO; above ∼60 kcal/mol the concerted pathway opens to form CH 2 NNO 2 ; at a threshold of ∼65 kcal/mol the RDR of the NN homolytic pathway can decompose into other products. These predictions are roughly consistent with previous experimental results and should be testable with new experiments. This should aid the development of a kinetic scheme to understand combustion and decomposition of solid-phase RDX and related energetic compounds (e.g., HMX).

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An effective approach for ab initio calculations of activation free energies of enzymatic reactions is developed and examined. This approach uses an empirical valence bond (EVB) potential surface as a reference potential for evaluating the free energies of a hybrid ab initio quantum mechanics/molecular mechanics (QM(ai)/MM) potential surface. This procedure involves an automated calibration of the EVB potential using gas-phase ab initio calculations. In addition, strategies for treating the contact region of QM and MM atoms as well as enzyme and solvent environments are developed. Two levels of ab initio calculations are used in studying the QM atoms:  the HF/4-31G method, which allows calculations on a large number of points while still giving accurate results, and the MP2/6-31+G* approach. The QM(ai)/MM method is implemented and examined by simulating the nucleophilic attack step in the catalytic reaction of subtilisin. It is found that the use of the EVB potential as a reference allows one to obtain the actual ab initio activation free energies of enzymatic reactions. Possible powerful simplifications such as the use of the ab initio intermolecular electrostatic energy are discussed, and the advantage of focusing on the difference between the reaction in protein and solution is demonstrated.