Finite temperature string by K-means clustering sampling with order parameters as collective variables for molecular crystals: application to polymorphic transformation between ß-CL-20 and ε-CL-20.

Polymorphic transformation of molecular crystals is a fundamental phase transition process, and it is important practically in the chemical, material, biopharmaceutical, and energy storage industries. However, understanding of the transformation mechanism at the molecular level is poor due to the extreme simulating challenges in enhanced sampling and formulating order parameters (OPs) as the collective variables that can distinguish polymorphs with quite similar and complicated structures so as to describe the reaction coordinate. In this work, two kinds of OPs for CL-20 were constructed by the bond distances, bond orientations and relative orientations. A K-means clustering algorithm based on the Euclidean distance and sample weight was used to smooth the initial finite temperature string (FTS), and the minimum free energy path connecting ß-CL-20 and ε-CL-20 was sketched by the string method in collective variables, and the free energy profile along the path and the nucleation kinetics were obtained by Markovian milestoning with Voronoi tessellations. In comparison with the average-based sampling, the K-means clustering algorithm provided an improved convergence rate of FTS. The simulation of transformation was independent of OP types but was affected greatly by finite-size effects. A surface-mediated local nucleation mechanism was confirmed and the configuration located at the shoulder of potential of mean force, rather than overall maximum, was confirmed to be the critical nucleus formed by the cooperative effect of the intermolecular interactions. This work provides an effective way to explore the polymorphic transformation of caged molecular crystals at the molecular level.

Experimental and theoretical investigation into the response to shock wave for booster explosives JO9C, JH14, JH6, and insensitive RDX.

In order to reduce the vulnerability, the responses to shock waves for booster explosives JO9C, JH14, JH6, and insensitive RDX were evaluated using shock wave partition loading test. To explain the experimental results, molecular dynamics simulation, intermolecular interaction and bond dissociation energy (BDE), and shock initiation pressures were evaluated using the B3LYP, MP2 (full), and M06-2X methods with the 6-311 + + G(2df,2p) basis set. The order of the responsivity is JO9C > JH14 > JH6 > insensitive RDX. The binding energies follow the order of JH14* ≈ JO9C* < insensitive RDX* < JH6*. The interaction energies and BDEs are in RDX∙∙∙(CH3COOCa)+ > RDX∙∙∙CH3COOH > RDX∙∙∙CH2FCH2F. Thus, it can be inferred that for the RDX-based explosives, the stronger the binding energy, intermolecular interaction, and BDE are, the more insensitive the booster is, and thus, the larger energy has to be consumed to overcome the above three kinds of energies during the initiation process, leading to the smaller energy output and weaker response. However, it should be noted that it is mainly the density and the type of explosive that influence the depth of the dent produced on the steel witness block. The essence of the responses to shock waves is revealed by the reduced density gradient, atoms in molecules, and surface electrostatic potentials. HIGHLIGHTS: • Response of booster to shock wave was evaluated by shock wave partition loading test. • Responsivity to shock wave is explained by binding energy, intermolecular interaction, and BDE. • Shock initiation pressures were evaluated. • Essence of responses to shock wave is revealed by RDG, AIM and ESP.

A theoretical investigation into the cooperativity effect on the TNT melting point under external electric field.

External electric field has been regarded as an effective tool to induce the variation of melting points of molecular crystals. The melting point of 2,4,6-trinitrotoluene (TNT) was calculated by molecular dynamics simulations under external electric field, and the electric field effects on the cooperativity effects of the ternary (TNT)3 were investigated at the M06-2X/6-311+G(d) and ωB97X-D/6-311++G(2d,p) levels. The results show that the melting points are decreased while the intermolecular interactions are strengthened under the external electric fields, suggesting that the intermolecular interactions cannot be used to explain the decreased melting points. A deduction based on the cooperativity effect is put forward: the enhanced cooperativity effects create the more serious defects in the melting process of the molecular crystal under the external electric fields, and simultaneously the local order parameters are decreased, leading to the decreased melting point. Thus, the cooperativity effect stemmed from the intermolecular C-H∙∙∙O H-bonding interactions controls the change of TNT melting point under the external electric field. Employing the information-theoretic approach (ITA), the origin of the cooperativity effects on the melting points of molecular crystal is revealed. This study opens a new way to challenge the problems involving the melting points for the molecular crystal under the external electric fields. However, note that above deduction needs to be improved; after all, the simple (TNT)3 model cannot replace the crystal structure.

External electric field reduces the explosive sensitivity: a theoretical investigation into the hydrogen transference kinetics of the NH2NO2∙∙∙H2O complex.

Controlling the selectivity of detonation initiation reaction to reduce the explosive sensitivity has been a Holy Grail in the field of energetic materials. The effects of the external electric fields on the homolysis of the N-NO2 bond and initiation reaction dynamics of NH2NO2∙∙∙H2O (i.e., intermolecular and 1,3-intramolecular hydrogen transfers) were investigated at the MP2/6-311++G(2d,p) and CCSD/6-311++G(2d,p)//MP2/6-311++G(2d,p) levels. The results show that the N-NO2 bond is not the "trigger linkage." The notable transiliences of the activation energy of the intermolecular hydrogen transfer are found with the field strength of - 0.012 a.u. along the -x-direction, leading to the conversion of the main reaction between the intermolecular and 1,3-intramolecular hydrogen transference. The activation energies of two kinds of the hydrogen transferences are increased under the external electric fields along the -y-direction. In particular, due to the conversion of the main reaction, the activation energies of the overall reaction are increased significantly along the -x-direction, leading to the significant reduced explosive sensitivities. Therefore, by controlling the field strengths and orientations between the "reaction axis" and external electric field along the y- and x-directions, the selectivity of the initiation reaction could be controlled and the explosive sensitivity could be reduced. Employing AIM (atoms in molecules) and surface electrostatic potentials, the origin of the control of reaction selectivity and the reduction of sensitivity is revealed. This work is of great significance to the improvement of the technology that the external electric fields are added safely into the energetic material system to enhance the explosive performance. Graphical abstract.

Hydration and swelling: a theoretical investigation on the cooperativity effect of H-bonding interactions between p-hydroxy hydroxymethyl calix[4]/[5]arene and H2O by many-body interaction and density functional reactivity theory.

In order to explore the nature of the hydration and swelling of superabsorbent resin, a theoretical investigation into the cooperativity effect of the H-bonding interactions in the hydrates of four model compounds that can be regarded as the units of hydroquinone formaldehyde resin (HFR) (i.e., O-hydroxymethyl-1,4-dihydroxybenzene, methylene di-O-hydroxymethyl-1,4-dihydroxybenzene, p-hydroxy hydroxymethyl calix[4]arene and p-hydroxy hydroxymethyl calix[5]arene) was carried out by many-body interaction and density functional reactivity theory. The HFR···H2O···H2O complexes, in which the H2O···H2O moieties are bound with both the hydroxyl groups of HFR, are the most stable. For the HFR(H2O)n clusters, the interaction energy per building block is increased as the number of the size n increases, indicating the cooperativity effect. Therefore, a deduction is given that the cooperativity effects of the H-bonding interactions play an important role in the process of the hydration and swelling of HFR, and the swelling behavior is mainly attributed to the cooperativity effects which arised from the interactions between the H2O molecules. The origin of the cooperativity effect was examined employing several information-theoretic quantities in the density functional reactivity theory. The degree of swelling of HFR was quantitated using a measure of volume. Graphical abstract.

A dynamic and electrostatic potential prediction of the prototropic tautomerism between imidazole 3-oxide and 1-hydroxyimidazole in external electric field.

In order to obtain an optimum scheme for separating the proton-transfer tautomer, a dynamic investigation into the effect of the external electric field on the proton-transfer tautomeric conversion in imidazole 3-oxide and 1-hydroxyimidazole was carried out at the M06-2X/6-311++G** and CCSD(T)/6-311++G(2d,p) level, accompanied by the analysis of the surface electrostatic potentials. The results show that, for both the forward reaction "imidazole 3-oxide → N-hydroxyimidazole free radical → 1-hydroxyimidazole" and its reverse reaction processes, the fields parallel to the N→O or N-OH bond axis affect the barrier heights and rate constants considerably more than those parallel to the other orientations. As the field strength is increased along the orientation from the O to N atom, the chemical equilibrium moves toward the direction for the formation of 1-hydroxyimidazole, while the amount of imidazole 3-oxide is increased with the increased field strength along the opposite orientation. In the fields along the orientation consistent with the dipole moment, the electrostatic potentials and their variances "abnormally" increase for the transition states with the N→O bond in comparison with those in no field (they decrease generally), which enhances the nucleophilicity of the coordination O atom and the electrophilicity of the activated H atom. The analyses of the AIM (atoms in molecules) and NICS (nucleus-independent chemical shift) were used to explain the above anomaly. Graphical Abstract Electrostatic potentials and their variances "abnormally" increase in the external electric field, which greatly affects tautomeric conversion.

Theoretical investigation into the cooperativity effect between the intermolecular π∙π and H-bonding interactions in the curcumin∙cytosine∙H2O system.

In order to reveal the mechanism of drug action and design of DNA/RNA-targeted drugs containing aromatic rings, the cooperativity effects between the intermolecular π∙∙∙π and H-bonding interactions in curcumin(drug)∙∙∙cytosine(DNA/RNA base)∙∙∙H2O were investigated by the B3LYP-D3 and MP2(full) methods with the 6-311++G(2d,p) basis set. The π∙∙∙π interaction plays an important role in stabilizing the linear ternary complexes with the cooperativity effects, and the cyclic structures suffer the anticooperativity effects. The cooperativity or anticooperativity effects are notable, which could lead to a possible significant change in drug activity. The hydration is essentially the cooperativity or anticooperativity effect. These results were confirmed by the atoms in molecules (AIM), reduced density gradient (RDG), and surface electrostatic potentials analyses. The cyclic complexes are more stable, from which it can be deduced that the drug always links with the DNA/RNA base and H2O by the π∙∙∙π or H-bonding interactions, and only in this way can the drug activity be shown. Therefore, the designed DNA/RNA-targeted drugs should possess a certain number of hydrophilic groups in contact with the DNA/RNA base and H2O to reconcile drug activity by the cooperativity effect between the π∙∙∙π and H-bonding interactions, as is in agreement with many of the drugs in use. Graphical abstract RDG isosurface of ternary complex.

A dynamics prediction of nitromethane → methyl nitrite isomerization in external electric field.

As a follow-up to our investigation into the effect of external electric field on the chemical bond strength, the effects of external electric field on the CH3NO2 → CH3ONO isomerization dynamics were investigated using the MP2/6-311++G(2d,p) and CCSD/6-311++G(2d,p) methods. The rate constants in the absence and presence of various field strengths were calculated. The results show that, when the field strength is larger than +0.0060 a.u. along the C-NO2 bond axis, the barriers of the isomerization are lower than the C-NO2 bond dissociation energies, leading to the preferences of the isomerization over the C-NO2 bond dissociation. In this case, the sensitivities are higher than that in no field. However, in the other fields, the C-NO2 bond scission is favored and the sensitivities are almost equal to that in no field. Several good linear correlations are found between the field strengths and the changes of the bond lengths or corresponding electron densities.

A theoretical prediction of the relationships between the impact sensitivity and electrostatic potential in strained cyclic explosive and application to H-bonded complex of nitrocyclohydrocarbon.

Seven models that related the features of molecular surface electrostatic potentials (ESPs) above the bond midpoints and rings, statistical parameters of ESPs to the experimental impact sensitivities h 50 of eight strained cyclic explosives with the C-NO2 bonds were theoretically predicted at the DFT-B3LYP/6-311++G** level. One of the models was used to investigate the changes of h 50 for the nitrocyclohydrocarbon frameworks in the H-bonded complexes of HF with nitrocyclopropane, nitrocyclobutane, nitrocyclopentane, and nitrocyclohexane. The results show that the correlation coefficients of the obtained models are small. When adding the effect of ring strain, the value of correlation coefficient is increased. According to the calculated h 50, the sensitivities in the frameworks are increased after hydrogen bonding. As a global feature of molecules, surface electrostatic potential is more available to judge the sensitivity change than the trigger bond dissociation energy or ring strain energy in H-bonded complex.

A theoretical prediction of the possible trigger linkage of CH3NO2 and NH2NO2 in an external electric field.

The effects of an external electric field on the C/N-NO2 bond with C/N-H and N-O bonds in CH3NO2 or NH2NO2 were compared using the DFT-B3LYP and MP2 methods with the 6-311++G(2d,p) and aug-cc-pVTZ basis sets. The results show that such fields have a minor effect on the C-N or C-H bond but a major effect on the N-O bond in CH3NO2, while in NH2NO2 electric fields affect the N-N bond greatly but the N-O or N-H bond only slightly. Thus, in CH3NO2, oxygen transfer or unimolecular isomerization to methyl nitrite might precede breaking of the C-N bond in the initial stages of decomposition, and the N-O bond could be the trigger bond in electric fields. In NH2NO2, however, N-N bond rupture may be preferential in an electric field and, consequently, the N-N bond might always be the real trigger bond. Atoms in molecules and natural bond orbital delocalization analyses, together with examination of shifts in electron density and frequencies support the above viewpoints. Forty-eight good linear correlations were found along the different field orientations at different levels of theory, including those between field strength (E) and changes in N-O/N-N bond length (ΔR N-O/N-N), ρ (N-O/N-N) values [Δρ (N-O/N-N), or stretching frequencies of the N-O/N-N bond (ΔυN-O/N-N). Graphical Abstract External electric fields have a major effect on the N-O or N-N bond inCH3NO2 or NH2NO2 , leading to a possible N-O trigger bond inCH3NO2 or a real N-N trigger bond in NH2NO2 in an electric field.

A B3LYP and MP2(full) theoretical investigation into the cooperativity effect between dihydrogen-bonding and H-M∙∙∙π (M = Li, Na, K) interactions among HF, MH with the π-electron donor C2H2, C2H4 or C6H6.

The DFT-B3LYP/6-311++G(3df,2p) and MP2(full)/6-311++G(3df,2p) calculations were carried out on the binary complex formed by HM (M = Li, Na, K) and HF or the π-electron donor (C2H2, C2H4, C6H6), as well as the ternary system FH∙∙∙HM∙∙∙C2H2/C2H4/C6H6. The cooperativity effect between the dihydrogen-bonding and H-M∙∙∙π interactions was investigated. The result shows that the equilibrium distances R(H∙∙∙H) and R(M∙∙∙π) in the ternary complex decrease and both the H∙∙∙H and H-M∙∙∙π interactions are strengthened when compared to the corresponding binary complex. The cooperativity effect of the dihydrogen bond on the H-M∙∙∙π interaction is more pronounced than that of the M∙∙∙π bond on the H∙∙∙H interaction. Furthermore, the values of cooperativity effect follow the order of FH∙∙∙HNa∙∙∙π > FH∙∙∙HLi∙∙∙π > FH∙∙∙HK∙∙∙π and FH∙∙∙HM∙∙∙C6H6 > FH∙∙∙HM∙∙∙C2H4 > FH∙∙∙HM∙∙∙C2H2. The nature of the cooperativity effect was revealed by the analyses of the charge of the hydrogen atoms in H∙∙∙H moiety, atom in molecule (AIM) and electron density shifts methods.

A comparative theoretical investigation into the strength of the trigger-bond in the Na⁺, Mg²âº and HF complexes involving the nitro group of R-NO2 (R = -CH3, -NH2 and -OCH3) or the C = C bond of (E)-O2N-CH = CH-NO2.

A comparative theoretical investigation into the change in strength of the trigger-bond upon formation of the Na(+), Mg(2+) and HF complexes involving the nitro group of RNO2 (R = -CH3, -NH2, -OCH3) or the C = C bond of (E)-O2N-CH = CH-NO2 was carried out using the B3LYP and MP2(full) methods with the 6-311++G**, 6-311++G(2df,2p) and aug-cc-pVTZ basis sets. Except for the Mg(2+)⋯π system with (E)-O2N-CH = CH-NO2 (i.e., C2H2N2O4⋯Mg(2+)), the strength of the trigger-bond X-NO2 (X = C, N or O) was enhanced upon complex formation. Furthermore, the increment of bond dissociation energy of the X-NO2 bond in the Na(+) complex was far greater than that in the corresponding HF system. Thus, the explosive sensitivity in the former might be lower than that in the latter. For C2H2N2O4⋯Mg(2+), the explosive sensitivity might also be reduced. Therefore, it is possible that introducing cations into the structure of explosives might be more efficacious at reducing explosive sensitivity than the formation of an intermolecular hydrogen-bonded complex. AIM, NBO and electron density shifts analyses showed that the electron density shifted toward the X-NO2 bond upon complex formation, leading to a strengthened X-NO2 bond and possibly reduced explosive sensitivity.

3-(4,6-Dichloro-1,3,5-triazin-2-yl)-2,2-dimethyl-1,3-oxazolidine.

In the title compound, C(8)H(10)Cl(2)N(4)O, the dichloro-substituted triazine ring and the quasi-plane of the five-membered dimethyl-substituted oxazolidine unit, in which the O atom lies 0.228 (1) Šout of the least-squares plane, are close to being coplanar [dihedral angle = 4.99 (10)°]. In the crystal, mol-ecules are linked by inter-molecular C-H⋯Cl inter-actions, forming chains extend along the a axis. Also present are weak π-π inter-actions between triazine rings [minimum ring centroid separation = 3.7427 (11) Å].

2,2'-{[4,6-Bis(octyl-amino)-1,3,5-triazin-2-yl]aza-nedi-yl}diethanol.

In the title compound, C(23)H(46)N(6)O(2), the two hy-droxy groups are located on opposite sides of the triazine ring. One of the hy-droxy groups links with the triazine N atom via an intra-molecular O-H⋯N hydrogen bond. Inter-molecular O-H⋯N and N-H⋯O hydrogen bonding is observed in the crystal structure. π-π stacking is also observed between parallel triazine rings of adjacent mol-ecules, the centroid-centroid distance being 3.5944 (14) Å.

A B3LYP and MP2(full) theoretical investigation into explosive sensitivity upon the formation of the molecule-cation interaction between the nitro group of 3,4-dinitropyrazole and H+, Li+, Na+, Be2+ or Mg2+.

The explosive sensitivity upon the formation of molecule-cation interaction between the nitro group of 3,4-dinitropyrazole (DNP) and H(+), Li(+), Na(+), Be(2+) or Mg(2+) has been investigated using the B3LYP and MP2(full) methods with the 6-311++G** and 6-311++G(2df,2p) basis sets. The bond dissociation energy (BDE) of the C3-N7 trigger bond has also been discussed for the DNP monomer and the corresponding complex. The interaction between the oxygen atom of nitro group and H(+) in DNP…H(+) is partly covalent in nature. The molecule-cation interaction and bond dissociation energy of the C3-N7 trigger bond follow the order of DNP…Be(2+) > DNP…Mg(2+) > DNP…Li(+) > DNP…Na(+). Except for DNP…H(+), the increment of the trigger bond dissociation energy in comparison with the DNP monomer correlates well with the molecule-cation interaction energy, natural charge of the nitro group, electron density ρ(BCP(C3-N7)), delocalization energy E(2) and NBO charge transfer. The analyses of atoms in molecules (AIM), natural bond orbital (NBO) and electron density shifts have shown that the electron density of the nitro group shifts toward the C3-N7 trigger bond upon the formation of the molecule-cation interaction. Thus, the trigger bond is strengthened and the sensitivity of DNP is reduced.

2-Hydroxy-3-methoxybenzaldehyde 2,4-dinitrophenylhydrazone pyridine monosolvate.

The Schiff base molecule of the title compound, C(14)H(12)N(4)O(6)·C(5)H(5)N, was obtained from the condensation reaction of 2-hy-droxy-3-meth-oxy-benzaldehyde and 2,4-dinitro-phenyl-hydrazine. The C=N bond of the Schiff base has a trans arrangement and the dihedral angle between the two benzene rings is 3.49 (10)°. An intra-molecular N-H⋯O hydrogen bond generates an S(6) ring. In the crystal, O-H⋯O hydrogen bonds link the Schiff base mol-ecules.

3-Eth-oxy-2-hy-droxy-benzaldehyde 2,4-di-nitro-phenylhydrazone N,N-di-methyl-formamide monosolvate.

The Schiff base of the title compound, C(15)H(14)N(4)O(6)·C(3)H(7)NO, was obtained from the condensation reaction of 3-eth-oxy-2-hy-droxy-benzaldehyde and 2,4-dinitro-phenyl-hydrazine. The dihedral angle between the benzene rings is 3.05 (10)° and intra-molecular N-H⋯O and O-H⋯O hydrogen bonds generate S(6) and S(5) ring motifs, respectively. In the crystal, the Schiff base and dimethyl-formamide solvent mol-ecules are linked by an O-H⋯O hydrogen bond.

A B3LYP and MP2 theoretical investigation into host-guest interaction between calix[4]arene and Li(+) or Na (+).

The DFT-B3LYP and MP2 methods with 6-311G** and 6-311++G** basis sets have been applied to study the complexation energies of the host-guest complexes between the cone calix[4]arene and Li(+) or Na(+) on the B3LYP optimized geometries. A comparison of the complexation energies obtained from the MP2(full) with those from MP2(fc) method is also carried out. The result shows that it is essential to introduce the diffuse basis set into the geometry optimizations and complexation energy calculations of the alkali-metal cation-pi interaction complexes of calix[4]arene, and the D (e) values show a maximum of 21.13 kJ mol(-1) (14.45% of relative error) between the MP2(full)/6-311++G** and MP2(fc)/6-311++G** method. For Li(+) cation, the complexation is mainly energetically stabilized by the lower rim/cation (namely O-Li(+)) interaction. However, binding energies and NBO analyses confirm that Na(+) cation prefers to enter the calix[4]arene cavity and the cation-pi interaction is predominant, which contradicts the previous low-level theoretical studies. Furthermore, the complexation with Li(+) is preferred over that with Na(+) by at least 12.70 kJ mol(-1) at MP2(full)/6-311++G**//B3LYP/6-311++G** level.

A theoretical study on unusual intermolecular T-shaped X-H...pi interactions between the singlet state HB=BH and HF, HCl, HCN or H2C2.

The unusual T-shaped X-H...pi hydrogen bonds are found between the B=B double bond of the singlet state HB=BH and the acid hydrogen of HF, HCl, HCN and H2C2 using MP2 and B3LYP methods at 6-311++G(2df,2p) and aug-cc-pVTZ levels. The binding energies follow the order of HB=BH...HF>HB=BH...HCl>HB=BH...HCN>HB=BH...H2C2. The hydrogen-bonded interactions in HB=BH...HX are found to be stronger than those in H2C=CH2...HX and OCB identical withBCO...HX. The analyses of natural bond orbital (NBO) and the electron density shifts reveal that the nature of the T-shaped X-H...pi hydrogen-bonded interaction is that much of the lost density from the pi-orbital of B=B bond is shifted toward the hydrogen atom of the proton donor, leading to the electron density accumulation and the formation of the hydrogen bond. The atoms in molecules (AIM) theory have also been applied to characterize bond critical points and confirm that the B=B double bond can be a potential proton acceptor.

3,6-Dibromo-9-(4-tert-butyl-benz-yl)-9H-carbazole.

In the title compound, C(23)H(21)Br(2)N, which was synthesized by the N-alkyl-ation of 1-tert-butyl-4-(chloro-meth-yl)benzene with 3,6-dibromo-9H-carbazole, the asymmetric unit contains two unique mol-ecules. Each carbazole ring system is essentially planar, with mean deviations of 0.0077 and 0.0089 Šfor the two mol-ecules. The carbazole planes make dihedral angles of 78.9 (2) and 81.8 (2)° with the planes of the respective benzene rings.