# Molecular Forcefield Methods for Describing Energetic Molecular Crystals: A Review

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Classic Forcefield Refitted for EMs and Their Applications

#### 2.1. Development of Refitted FFs

FFs | Valence Terms | van der Waals Interaction Term | Electrostatic Interaction Term | Applications |
---|---|---|---|---|

SRT [20] | \ | Buckingham 6-exp form | Coulomb function | RDX HMX CL-20 FOX-7 PETN (lattice parameter, density, mechanics) |

SAPT [38] | \ | Buckingham 6-exp form | Simplified Coulomb function | FOX-7 (thermal properties, pressure responses, isothermo) |

SRT-AMBER [32] | Harmonic bond stretching, harmonic angle bending, cosine torsion term | Buckingham 6-exp form | Coulomb function | RDX (lattice parameter, density, melting point, mechanics) TNAZ (lattice parameter, density, melting point) |

SB [27] | Harmonic bond term, angle term, dihedral term, anharmonic torsion term | Buckingham form | Coulomb function | RDX HMX CL-20 (shock compression, shear bands, elastic constants and modulus) |

Boyd’s [34] | Bond stretching described by Morse function, angle bending described by harmonic function | Buckingham LJ 6-12 form | Coulomb function | RDX (lattice parameter, density, thermodynamics, vibration spectra, thermal expansion, mechanics) |

NETMFF [40] | Bond term, angle term, dihedral (torsion angle) term, out-of-plane bending angle term, cross-coupling terms of bond–bond, bond–angle couplings | Damped Buckingham form | Coulomb function | RDX (lattice parameter, density, thermal expansion) |

GRBF [35] | Harmonic bond stretch term, bond-angle bend term, dihedral angle torsion term | Lennard–Jones 12-6 form | Coulomb function | TATB (lattice parameters, density, thermal expansion, isotherm) |

Bedrov’s [36] | Harmonic functions of covalent bonds, three-center bends, and improper dihedrals | Buckingham 6-exp form | Coulomb function | TATB (lattice parameter, thermal expansion, mechanics, vibration spectra, thermal conductivity) |

Neyertz’s [39] | Angle-bending deformations described by harmonic function, torsional motions around the dihedral angles τ, sp^{2} ring and NO_{2} structures kept planar described by harmonic function | Lenard-Jones 12-6 form | Coulomb function | TNT DNT (lattice parameter, density, tensile, bulk and shear modulus) |

Dreiding [41] | Bond stretching interaction term, angle bending interaction term, dihedral angle interaction term, inversion interaction term | Lennard–Jones 12-6 form | Coulomb function | TATB (geometries, crystal packing, thermal expansion) |

OPLS-AA [43] | Bond term, angle term, dihedral term | Lennard–Jones 12-6 form | Coulomb function | CL-20 (lattice parameter, density, polymorph prediction) |

#### 2.2. Functional Forms of the Refitted FFs

_{el}and a Lennard–Jones LJ 12-6 term [35]. Bedrov’s potential includes the harmonic functions of covalent bonds, three-center bends and improper dihedrals, and nonbonded interactions of Buckingham (exp-6) potential and Coulomb interactions [36]. In Neyertz’s potential, angle-bending deformations are described by harmonic function, and torsional motions around the dihedral angles τ are represented by a polynomial in cos τ, while sp

^{2}ring and NO

_{2}structures maintain planarity by using harmonic function [39]. Moreover, some general FFs were also refitted for energetic crystals, such as Dreiding for TATB [41] and OPLS-AA for CL-20 [43].

_{2}improper dihedral angles are not available in AMBER, and the parameters for O-NO

_{2}were used in SRT-AMBER, and there are some inaccuracies in the calculated orientations of the NO

_{2}groups; thus, modifications in the torsional parameters are needed. SB potential [27] with anharmonic torsions terms that display extrema at the torsion angles that correspond to stationary points on the conformational energy surface can effectively predict lattice parameters and elastic tensors for RDX and HMX. Furthermore, Boyd’s potential [34] managed to stabilize the RDX crystal lattice with flexible molecules in the correct conformation, with Morse bond stretching, harmonic angle bending, cosine torsions terms, and in which the torsion parameter C-N-N-O values were modified to adjust the N-NO

_{2}rotational barrier. Moreover, in NETMFF for RDX [40], many more parameters regarding functional groups were considered, including parameters c_4 for the carbon atom, n_3r for the nitrogen atom of the triazine ring, n_3o for the nitrogen atom of the NO

_{2}group, o_1 for the oxygen atom, and h_1 for the hydrogen atom; as well as torsion parameters for six RDX conformers. Consequently, the angles and torsions for the NO

_{2}group are well described, and the lattice parameters and thermal expansion are well predicted. In GRBF for TATB [35], the amino C-C-N-H and nitro C-C-N-O group rotational barriers were modified, and the nonbonded interactions for amino groups and nitro groups were also considered; similar parameters were considered in Neyertz’s potential for TNT and DNT [39], as well as in Bedrov’s [36] and Dreiding potentials for TATB [41]. The differences in the functional forms, including descriptions of functional groups for the FFs, bring differences in prediction precision and areas of application.

#### 2.3. Application of Prediction

#### 2.3.1. Cell Parameters and Density

#### 2.3.2. Polymorphism

#### 2.3.3. Vibration Spectra

_{2}stretch, nitro antisymmetric stretch plus amine scissor/rock, and ring stretch. The Boyd’s potential [34] has also been effectively applied to investigating the vibration spectra for RDX, in which special attention has been paid to the vibrational states between 200 and 700 cm

^{−1}described as “doorway modes” for the transfer of energy from lattice phonons to the molecular vibrations involved in bond breaking [46,47].

#### 2.3.4. Thermal Property

#### 2.3.5. Mechanical Property

#### 2.3.6. Shock Responses

## 3. Consistent Forcefields and Their Applications for EMs

#### 3.1. Theory

_{b}, K

_{a}, K

_{t}, K

_{χ}, K

_{bb}, K

_{ba}, K

_{aa}, K

_{bt}, K

_{at}, k are the fitting parameters for bond, angle, dihedral, OOPA, and mixing terms, respectively; r

_{ij}is the distance between two valence-bonded atoms i and j, q

_{i}and q

_{j}are their electronic charges, and ε

_{ij}and r

_{0}are the LJ-9-6 parameters. It can be noticed that, in the non-bond interactions, the van der Waals (vdW) interaction term is in the form of Lennard–Jones (LJ) 9-6, for which the mixing rule is shown as Equations (2) and (3), where ε

_{i}and ε

_{j}are the fitting parameters.

#### 3.2. Applications

#### 3.2.1. Morphology

#### 3.2.2. Polymorphism

_{21/c}, P-1, P

_{212121}, P

_{21}, P

_{bca}, C

_{2/c}, and P

_{na21}were investigated. The polymorphs of a series of compounds of polynitrohexaazaadmantanes were predicted, including 2,4,6,8-tetranitrohexaazaadmantane, 2,4,6,8,10-pentanitrohexaazaadmantane, and 2,4,6,8,9,10-hexanitrohexaazaadmantane, with results close to the experimental observations [84].

#### 3.2.3. Properties

## 4. Reactive Forcefields and the Applications for EMs

#### 4.1. Theory

_{Reax}) includes bond dissociation energy term (E

_{bond}), lone pair energy penalty term (E

_{lp}), energy penalty for over-coordinated atoms (E

_{over}), energy contribution for the resonance of the n-electron between attached under-coordinated atomic centers (E

_{under}), angle bending energy term (E

_{val}), energy penalty needed to reproduce the stability of systems with double bonds sharing an atom in a valency angle (E

_{pen}), three-body conjugation term to describe the stability of -NO

_{2}groups (E

_{coa}), torsion angle energy term (E

_{tors}), contribution of conjugation effects to the molecular energy (E

_{conj}), H-bond energy term (E

_{H-bond}), van der Waals interaction term (E

_{vdW}), and Coulomb interaction term (E

_{Coulomb}). In addition, long-range London dispersion (E

_{lg}) correction was added in the total energy terms of ReaxFF-lg (E

_{Reax-lg}) [115], where r

_{ij}is the distance between atom i and atom j, R

_{eij}is the equilibrium vdW distance between atoms i and j, and C

_{lg,ij}is the dispersion energy correction parameter (Equations (5) and (6)).

_{ij}), which can be derived from the calculations of σ-bonds (BO

_{ij}

^{σ}), π-bonds (BO

_{ij}

^{π}), and π-π bonds (BO

_{ij}

^{π-π}) as Equation (7).

_{o}is the equilibrium distance; r

_{ij}

^{σ}, r

_{ij}

^{π}, and r

_{ij}

^{ππ}are the interatomic distance for σ-bonds, π-bonds, and π-π bonds, respectively; and p

_{bo}

_{,1}, p

_{bo}

_{,2}, p

_{bo}

_{,3}, p

_{bo}

_{,4}, p

_{bo}

_{,5}, and p

_{bo}

_{,6}are the fitting parameters. Then, the energy terms can be derived from bond order values; for example, the bond dissociation term E

_{bond}can be described as Equation (8).

_{e}

^{σ}, D

_{e}

^{π}, and D

_{e}

^{ππ}are the bond parameters for σ-bonds, π-bonds, and π-π bonds, respectively; p

_{be}

_{1}and p

_{be}

_{2}are the fitting parameters. ReaxFF [98,99,100] was initially developed for simulating combustion of hydrocarbon and reactions of energetic compounds, and the functional groups such as nitro group are well-parameterized, thus various energetic compounds such as RDX, HMX, CL-20, PETN, NM, TNT, TATB, and TATP were applied [115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136]. The ReaxFF-based MD simulations provide an efficient way to investigate the chemical reactions and other properties of various molecular crystals under particular conditions.

#### 4.2. Applications

#### 4.2.1. Structural Optimization

#### 4.2.2. Vibration Spectra

#### 4.2.3. Shock-Induced Chemistry

#### 4.2.4. Thermal Decomposition

#### 4.2.5. NN-Trained ReaxFF (NNRF)

## 5. Conclusions and Outlooks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BTF: | benzotrifuroxan |

CL-20: | 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane |

DATNBI: | 4,4′,5,5′-tetranitro-1H,1′H-[2,2′-bi-imidazole]-1,1′-diamine |

DNAN: | 2,4-dinitroanisole |

DNP: | 3,4-dinitro-1H-pyrazole |

DNT: | 2,4-dinitrotoluene |

FOX-7: | 1,1-diamino-2,2-dinitroethene |

HMX: | octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine |

MATNB: | 1-methyl-amino-2,4,6-trinitrobenzene |

MTNP: | 1-methyl-3,4,5-trinitro-1H-pyrazole |

MTO: | 2,4,6-triamino-1,3,5-triazine-1,3,5-trioxide |

MTO3N: | 2,4,6-trinitro-1,3,5-triazine-1,3,5-trioxide |

NM: | nitromethane |

PETN: | 2,2-bis[(nitrooxy)methyl]propane-1,3-diyldinitrate |

RDX: | 1,3,5-trinitro-1,3,5-triazinane |

TATB: | 1,3,5-triamino-2,4,6-trinitrobenzene |

TATP: | triacetone triperoxide |

TNA: | 2,4,6-trinitroaniline |

TNAZ: | 1,3,3-trinitroazetidine |

TNB: | 1,3,5-trinitrobenzene |

TNT: | 1,3,5-trinitrotoluene |

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**Figure 3.**Shock-induced shear bands (

**a**) and the intermolecular and intramolecular temperatures (

**b**) in RDX crystal calculated using SB potential. Reprinted by permission from [28]; copyright 2008 American Physical Society. Permission conveyed through the American Physical Society and SciPris.

**Figure 4.**Calculated THZ spectra of RDX and TATP (in blue) vs. experimental (in dashed red) (

**a**) and calculated 2D THz spectra of time domain dipole response for different excitation frequencies (

**b**). Reprinted by permission from [116]; copyright 2014 American Chemical Society. Permission conveyed through Copyright Clearance Center, Inc.

**Figure 5.**Diagram of CS-RD model for PETN (

**a**) shock along (1 0 0) and slip along {1 1 0}<1 −1 1>, represented as (1 0 0)/{1 1 0}<1 −1 1>; (

**b**) (1 1 0)/{1 0 0}<0 1 1>; (

**c**) (1 0 1)/{1 0 0}<0 0 1>; (

**d**) (0 0 1)/{1 0 1}<−1 0 1>; (

**e**) (0 0 1)/{1 0 1}<−1 1 1>.

**Figure 6.**Fitting procedure of NNRF (

**a**) and the predicted infrared spectra of RDX using NNRF (

**b**). Reprinted by permission from [143]; copyright 2021 Springer Nature Limited. Permission conveyed through Copyright Clearance Center, Inc.

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**MDPI and ACS Style**

Qian, W.; Xue, X.; Liu, J.; Zhang, C.
Molecular Forcefield Methods for Describing Energetic Molecular Crystals: A Review. *Molecules* **2022**, *27*, 1611.
https://doi.org/10.3390/molecules27051611

**AMA Style**

Qian W, Xue X, Liu J, Zhang C.
Molecular Forcefield Methods for Describing Energetic Molecular Crystals: A Review. *Molecules*. 2022; 27(5):1611.
https://doi.org/10.3390/molecules27051611

**Chicago/Turabian Style**

Qian, Wen, Xianggui Xue, Jian Liu, and Chaoyang Zhang.
2022. "Molecular Forcefield Methods for Describing Energetic Molecular Crystals: A Review" *Molecules* 27, no. 5: 1611.
https://doi.org/10.3390/molecules27051611