A theoretical study of three and four proton donors on linear HX···BeH2···HX and bifurcate BeH2···2HX trimolecular dihydrogen-bonded complexes with X?=?CN and NC

The interaction phenomenon H^−δ···H^+δ between two hydrogen atoms binding each other is well-known in dihydrogen-bonded complexes. Either by experimental or theoretical viewpoint, dihydrogen bonds are often known as directional or bifurcate interactions. Regarding the beryllium hydride BeH₂, its capacity to form bimolecular complexes with proton donors has been demonstrated, but in some cases, trimolecular complexes are also characterized in a minimum of the potential energy surface. As such, in this work is presented a theoretical study about the formation of trimolecular dihydrogen complexes with three hydrogen centers. By taking into account the beryllium hydride BeH₂ as proton acceptor, two classical proton donors were chosen, HCN and HNC. The great goal of this work is the analysis of two dihydrogen complexes types: bifurcate BeH₂···2HX and linear HX···BeH₂···HX. In these systems, it is discussed the capacity of one hydride H^−δ (H–Be–H^−δ) to interact simultaneously with two proton donors, as well as when two hydrides H^−δ (^−δH–Be–H^−δ) form linear dihydrogen bonds. In this context, the analysis of the vibrational harmonic spectrum at B3LYP/6-311 ++G(3d,3p) level of theory and the interpretation of the topological parameters derived from Quantum Theory of Atoms in Molecules (QTAIM) aided us to determine which is the most stable trimolecular complex, either bifurcate or linear. Moreover, quantification of charge transfer measured by the QTAIM formalism as well as by ChelpG calculations also were used with the purpose to justify infrared effects, such as red-shift and blue-shift stretch modes on donors (HCN and HNC) and acceptors (BeH₂) of protons.     

Can BB double bond be as potential proton acceptor: A UB3LYP and UMP2 theoretical study on unusual intermolecular T-shaped XH…π interactions between the triplet state HBBH and HF, HCl, HCN or H2C2

The unusual weak T-shaped XH…π hydrogen bonds are found between the BB double bond of the triplet state HBBH and the acid hydrogen of HF, HCl, HCN and H₂C₂ using UMP2 and UB3LYP methods at 6-311++G(2df,2p) and aug-cc-pVTZ levels. The binding energies follow the order of HBBH…HF > HBBH…HCl > HBBH…HCN > HBBH…H₂C₂, and the hydrogen-bonded interactions in the triplet state complexes HBBH…HX (³B₁) are found to be weaker than those in HCCH…HX and OCBBCO…HX. The analyses of natural bond orbital (NBO) and the electron density shifts reveal that the nature of the T-shaped XH…π hydrogen-bonded interaction is that the lost density from the π-orbital of BB bond is shifted toward the hydrogen atom of HX, leading to the electron density accumulation and the formation of the hydrogen bond. The atoms in molecules (AIM) theory has been also applied to characterize bond critical points and confirm that it is difficult for the ground electronic state of HBBH to be as the hydrogen-bond proton acceptor, perhaps due to the nature of electron-deficient BB double bond.     

Hydrogen bond CH…O in a methanolic solution of hydrogen chloride

The existence of a hydrogen bond in which a methyl group of the (MeOH)₂H⁺ ion acts as a proton donor is examined. The fundamental vibration frequencies of this ion were calculated for different numbers and strengths of CH…O bonds. The atomic charges in neutral ((MeOH) _n ,n=1–4) and protonated ((MeOH) _m H⁺,m=2–6) associates of methanol molecules were also calculated. The experimentally observed decrease in the v(CH) vibration frequencies of the (MeOH)₂H⁺ ion to 2890 cm⁻¹ and 2760 cm⁻¹ is attributable to the fact that each methyl group of the ion is involved in formation of two CH…O bonds with strength of −12.5 kJ mol⁻¹. The proton-donating ability of the CH bond depends on the charge on its H atom; however, it does not correlate with the dipole moment of this bond. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 306–312, February, 1999.     

Analysis of relaxation on polypropyleneglycols above vitrification temperature

The dielectric spectra of polypropyleneglycols H-(C₃H₆O) _{N p} -OH (PPGs), where N _p = 1, 2, 3, 7, 12, 17, 20, 34, 69, were analyzed in terms of the Dissado Hill (DH) cluster model above the vitrification temperatures. In PPGs, the structural clusters are associates formed by intra- and intermolecular hydrogen bonds. The activation processes of cleavage and formation of intermolecular hydrogen bonds in clusters, when the total number of intermolecular hydrogen bonds changes, are characterized by the parameter n _DH. The fluctuation processes of simultaneous exchange of molecules between adjacent clusters correspond to redistributions of intermolecular hydrogen bonds between clusters, when only the position but not the total number of intermolecular hydrogen bonds changes, and are characterized by the parameter m _DH. The relaxation time τ_DH at 303 K and 423 K and the parameters n _DH and m _DH of the dielectric spectra were calculated. The activation energies of relaxation in the range 210–323 K were determined. The mean statistic squares of the dipole moments of clusters 〈μ_c²〉 and di-PG, PPG-425 (N _p = 7), and PPG-2025 (N _p = 34) molecules 〈μ_m²〉 at 303 K and 423 K were calculated. The number of the units of the oxypropylene chains involved in relaxation was determined. The dependence of the parameters of the DH model, relaxation energies, 〈μ_c²〉 and 〈μ_m²〉 on N _p were studied.     

A theoretical study of keto-enol isomerism and internal rotation in the H<Subscript>2</Subscript>Salen molecule,N,N′-ethylene-bis(salicylidenimine) — schiff base

Geometric parameters, vibrational spectra, and the energies of isomerization of seven keto-enol isomeric forms of the H₂Salen molecule (N,N′-ethylene-bis(salicylidenimine)) are calculated using electron density functional theory (DFT/B3LYP) and correlation consistent valence triple-zeta Gaussian basis sets (cc-pvtz). The isomer with two enol groups (EE₁) and C ₂ symmetry configuration is most energetically favorable. Calculations of the keto-enol equilibrium show that at T ≥ 250 K the H₂Salen gas phase is a mixture of four conformers (rotamers of the main isomer EE₁). The contribution of other isomers does not exceed a few percent. The NBO analysis reveals that the system of π-conjugated bonds involves not only the atoms of the benzene moiety, but also the O, C, and N atoms nearest to the benzene ring. The energy stabilization of the isomer EE₁ is shown to be due to the presence of two strong intramolecular N...H hydrogen bonds. Intramolecular N...H and O...H hydrogen bonds are observed in all other isomers. The bathochromic shift of O-H and N-H vibrational frequencies, caused by the effect of hydrogen bonds, is 520–790 cm⁻¹.     

Theoretical investigation on the structural and electronic properties of complexes formed by thymine and 2′-deoxythymidine with different anions

Hydrogen bonding interactions between thymine nucleobase and 2′-deoxythymidine nucleoside (dT) with some biological anions such as F⁻ (fluoride), Cl⁻ (chloride), OH⁻ (hydroxide), and NO₃ ⁻ (nitrate) have been explored theoretically. In this study, complexes have been studied by density functional theory (B3LYP method and 6-311++G (d,p) basis set). The relevant geometries, energies, and characteristics of hydrogen bonds (H-bonds) have been systematically investigated. There is a correlation between interaction energy and proton affinity for complexes of thymine nucleobase. The nature of all the interactions has been analyzed by means of the natural bonding orbital (NBO) and quantum theory atoms in molecules (QTAIM) approaches. Donors, acceptors, and orbital interaction energies were also calculated for the hydrogen bonds. Excellent correlations between structural parameter (δR) and electron density topological parameter (ρ _b) as well as between E(2) and ρ _b have been found. It is interesting that hydrogen bonds with anions can affect the geometry of thymine and 2′-deoxythymidine molecules. For example, these interactions can change the bond lengths in thymine nucleobase, the orientation of base unit with respect to sugar ring, the furanose ring puckering, and the C1′–N1 glycosidic linkage in dT nucleoside. Thus, it is necessary to obtain a fundamental understanding of chemical behavior of nucleobases and nucleosides in presence of anions.     

DFT calculation of α-cyclodextrin dimers. contribution of hydrogen bonds to the energy of formation

The structures and energies of formation of α-cyclodextrin (α-CD) dimers formed according to the “head-to-head” (HH), “head-to-tail” (HT), and “tail-to-tail” (TT) modes, harmonic vibrational frequencies, and intensities of IR bands of the IR transitions were calculated by the DFT/PBE density functional method with full geometry optimization without symmetry restrictions. The spectral data were transformed into spectral patterns. An α-CD molecule can exist in two isomeric forms close in energy, namely, α-CD⁻ and α-CD⁺, with different directions of the ring intramolecular hydrogen bonds. Among the three α-CD⁻ dimers, the highest dimerization energy (E _d/kcal mol⁻¹) belongs to the HH⁻ (68.9), TT⁻ (43.4), and HT⁻ (24.8) dimers. The strength of the α-CD⁺ dimers decreases in the series: TT⁺ (56.7), HT⁺ (49.4), and HH⁺ (42.4). The energies E _H of hydrogen bonds were calculated from the low-frequency shifts of bands of stretching vibrations of the OH groups involved in the formation of these hydrogen bonds. The E _H value for each dimer correlates with E _d. A possibility of formation of intermolecular hydrogen bonds is a driving force of association of α-CD molecules in aqueous solutions. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1289–1296, August, 2006.     

Synthesis and properties of <Emphasis Type="Italic">O,O</Emphasis>-dialkyl [1-hydroxy-3-(dialkylamino)-2,2-dimethylpropyl]phosphonates

O,O-Dialkyl [1-hydroxy-3-(dialkylamino)-2,2-dimethylpropyl]phosphonates were prepared for the first time. By means of NMR ¹H, IR spectroscopy and quantum-chemical calculations the presence in them of various H-bonds was established. In the crystalline state P=O…HO intermolecular hydrogen bonds favor the formation of cyclic dimer associates D _P=O. In the liquid state and concentrated solutions P=O…HO and N…HO intermolecular hydrogen bonds cause the formation of cyclic dimer associates D _P=O and D_N, and intramolecular hydrogen bonds provide the existence of different conformations of the monomer form MN, the most stable among them with the non-strained six-membered …NCCCOH… ring.     

Reactions of proton transfer and exchange with the participation of OH,SH, and CH acids and amines

A comparison of proton exchange reactions between OH, SH, and CH acids and the NH groups of trialkylammonium ions showed that regardless of the nature of the acid XH, the mechanism of exchange includes transfer of a proton in the ion pair N-H⁺ ... X^– as the slow step. At the fast steps of proton exchange XH- N⁺H, i.e., molecular exchange with breaking of a hydrogen bond X-H ... N and transfer of a proton along these bonds, differences appear in the properties of XH acids. In the sequence from OH to SH and CH acids, the hydrogen bonds X-H ... N are weakened. As a result of this, in the same sequence the kinetic acidity (k₂) decreases but the rate of molecular exchange (k_H) increases. The ratio between the values of k₂ and k_H is inverted when the strong bonds O-H ... N (k₂/k_H 1) are replaced by weak bonds C-H ... N (k₂/k_H 1). It was also established that the kinetic stability of the anions increases as the oxygen atoms are replaced by sulfur in the series RCOO^– < RCOS^– < R₂PSS^– as a result of the more effective delocalization of the negative charge on the diffuse orbitals of sulfur.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 4, pp. 471–475, July–August 1987.     

Structure of BaTiO<Subscript>3</Subscript> phases is studied by comparing neutron diffraction and Raman spectroscopy data

Considering the structural unit of the rhombohedral BaTiO₃ phase in the form of Ti(-O...Ti)₆ which was constructed by neutron diffraction data, we revealed an atomic group in the form of a pyramidal complex anion TiO₃²⁻. Inspection of the Raman spectra of this phase showed symmetry group C _s for this complex anion. From the similarity of the Raman spectra of all ferroelectric BaTiO₃ phases, we inferred that the orthorhombic phase and tetragonal phase are also built of TiO₃²⁻ complex anions. In the paraelectric cubic phase, TiO₃²⁻ complex anions decompose to oxygen ions O²⁻ and Ti²⁺(O⁻)₂ molecules, which are randomly oriented over 12 possible positions. Average Ti-O distances derived from neutron diffraction data were used to calculate Ti-O⁻ and Ti=O bond lengths in TiO₃²⁻ complex anions of the ferroelectric BaTiO₃ phases. Two types of Ti-O...Ti bridges were found to exist; they belong to weak and strong intermolecular bonds, which are similar to weak and strong hydrogen bonds (H-bonds) in ferroelectrics. Weak bonds exist in all of the three ferroelectric phases; strong bonds are only in the orthorhombic phase and the tetragonal phase. As a result of a low potential barrier height in strong bonds, an oxygen atom persistently hops from one potential well to an adjacent one, which is responsible for bands appearing below 100 cm⁻¹ in the Raman spectra of the tetragonal phase and orthorhombic phase. The data obtained on the structure of the ferroelectric BaTiO₃ phases were used to interpret their spontaneous polarization, repolarization, and permittivity.     

Two polymorphs of bis(2‐carbamoylguanidinium) fluorophosphonate dihydrate

Two polymorphs of bis(2‐carbamoylguanidinium) fluorophosphonate dihydrate, 2C₂H₇N₄O⁺·FO₃P²⁻·2H₂O, are presented. Polymorph (I), crystallizing in the space group Pnma, is slightly less densely packed than polymorph (II), which crystallizes in Pbca. In (I), the fluorophosphonate anion is situated on a crystallographic mirror plane and the O atom of the water molecule is disordered over two positions, in contrast with its H atoms. The hydrogen‐bond patterns in both polymorphs share similar features. There are O—H...O and N—H...O hydrogen bonds in both structures. The water molecules donate their H atoms to the O atoms of the fluorophosphonates exclusively. The water molecules and the fluorophosphonates participate in the formation of R⁴₄(10) graph‐set motifs. These motifs extend along the a axis in each structure. The water molecules are also acceptors of either one [in (I) and (II)] or two [in (II)] N—H...O hydrogen bonds. The water molecules are significant building elements in the formation of a three‐dimensional hydrogen‐bond network in both structures. Despite these similarities, there are substantial differences between the hydrogen‐bond networks of (I) and (II). The N—H...O and O—H...O hydrogen bonds in (I) are stronger and weaker, respectively, than those in (II). Moreover, in (I), the shortest N—H...O hydrogen bonds are shorter than the shortest O—H...O hydrogen bonds, which is an unusual feature. The properties of the hydrogen‐bond network in (II) can be related to an unusually long P—O bond length for an unhydrogenated fluorophosphonate anion that is present in this structure. In both structures, the N—H...F interactions are far weaker than the N—H...O hydrogen bonds. It follows from the structure analysis that (II) seems to be thermodynamically more stable than (I).     

Syntheses, structural determination and binding studies of nine-coordinate mononuclear (EnH2)1.5 [ErIII(Ttha)] · 3H2O and (EnH2)[ErIII(Egta)(H2O)]2 · 6H2O

In this work, the title complexes, (EnH₂)_1.5[Er^III(Ttha)] · 3H₂O (I) and (EnH₂)[Er^III(Egta)(H₂O)]₂ · 6H₂O (II), where En = ethylenediamine, H₆Ttha = triethylenetetramine-N,N,N′,N″,N″’,N″′-hexaacetic acid, H₄Egta = ethyleneglycol-bis-(2-aminoethylether)-N,N,N′,N′-tetraacetic acid, have been successfully synthesized. Their structures have been characterized by IR spectroscopy and single-crystal X-ray diffraction techniques. The X-ray diffraction reveals that I is nine-coordinated and crystallizes in the monoclinic crystal space group P2/n with cell dimensions a = 17.6058(16), b = 9.6249(9), c = 20.560(2) ?, β = 109.7440(10)°, and V = 3279.1(5) ?³. Compound II is also nine-coordinated and crystallizes in the monoclinic crystal space group P2₁/n with the cell dimensions a = 12.938(6), b = 12.651(5), c = 14.943(6) ?, β = 105.441(5)°, and V = 2357.5(17) ?³. In I, each EnH₂²⁺ cation connects three adjacent [Er^III(Egta)(H₂O)]⁻ complex anions through hydrogen bonds, while in I, there are two types of EnH₂ ²⁺ anions. One is highly symmetrical, forming hydrogen bonds with two neighboring [Er^III(Ttha)]³⁻ complex anions. The other anion connects three adjacent [Er^III(Ttha)]³⁻ complex anions through hydrogen bonds. These hydrogen bonds lead to the formation of 2D ladder-like layer structure.     

Synthesis,structure and bonding of 2-aminopyridinium heptamolybdate trihydrate

Summary 2-aminopyridinium heptamolybdate trihydrate crystallizes in the monoclinic system with space group P2₁/n and Z=4 (R=0.030). The unit cell dimensions area=14.8161(4) Å,b=17.5073(4) Å,c=20.8492(6) Å, =107.503(2)°, V=5157.7(2) ų. The [Mo₇O₂₄]^6– anions in the 2-aminopyridinium, ammonium⁽⁴⁾, guanidium⁽²⁾, propyl- and isopropyl-ammonium⁽¹⁾ molybdates, while similar, show slightly differences in several bond lengths and angles. The distinguishing features of 2-aminopyridinium heptamolybdate trihydrate structure is its extensive hydrogen bonding. The planar cations and the water molecules are positioned so as to be able to form hydrogen bonds with either molybdate oxygen atoms or water oxygen atoms. Four different types of hydrogen bonds have been found-: N-H... O (mono- and bifurcated), N-H... Ow (monofurcated), Ow-Hw... O (mono- and bi-furcated) and Ow-Hw...OW (monofurcated). The closest approach distances associated with 27 of these potential hydrogen bonds vary from 2.67 to 3.24 Å^(7,8)). The proposed strong hydrogen bonding interactions appear to stabilize the structure and explain the way of three water molecules are lost upon heating. Some of these hydrogen bonds can play an important role in the possible photochromism of this compound.     

Vibrational spectra and structure of some oxalic acid/substituted pyridine (methyl-, amino-, and dihalogeno-) complexes: Hydrogen bond features

The Raman and infrared spectra of some polycrystalline substituted pyridine/oxalic acid complexes have been investigated and assignments in terms of group frequencies are given. Various hydrogen bonds (NH?O, OH?O, OH?N) are distinguished and crystal structures are proposed. For the stronger bases (methyl- or aminopyridines with pk_a ≈ 6) proton transfer occurs. The 1/1 complex contains infinite chains of hydrogen oxalate ions linked by strong OH?O hydrogen bonds with vOH between 2000 and 800 cm⁻¹. R_OH?O distances are 2.47–2.62 Å). The substituted pyridinium cations are linked to the chain backbone by medium NH?O hydrogen bonds with NH?O lengths of 2.71–2.81 Å. The 3,5-dichloropyridine forms a 2/1 adduct without proton transfer, in accordance with its pk_a (0.6), and strong OH?N hydrogen bonds occur (vOH about 2000 cm⁻¹ and ). Finally, the 2,6-dihalogenopyridine derivatives do not form complex with oxalic acid, presumably because of steric hindrance.     

Matrix IR studies on hydrogen-bonded complexes of hydrogen chloride and hydrogen bromide with ketene

Infrared spectra of matrices codeposited Ar/HX (X=Cl, Br) with Ar/H₂CCO mixtures have been examined. Isotopic substitutions (HX, DX, H₂CCO, D₂CCO) showed that ketene formed the 1:1 hydrogen-bonded complex with HX. The HX stretching modes were observed at 2684 cm⁻¹ in the H₂CCO–HCl complex and at 2384 cm⁻¹ in the H₂CCO–HBr complex. The ν₁ modes of the ketene submolecules were shifted to low frequency and the ν₉ modes to high frequency. It was proposed for the structure of the complex that the acid proton is bonded to the C=C pi electron system.     

Non-alkane behavior of cyclopropane and its derivatives: characterization of unconventional hydrogen bond interactions

Eight cyclopropane derivatives (Δ − R) have been modeled, with R = −H, −CH₃, −NH₂, −C ≡ CH, −C ≡ CCH₃, −OH, −F and −C ≡ N. All geometries have been fully optimized at the MP2/ AUG-cc-pVTZ level of calculations. Natural bond orbital analyses reveal extra p character (sp^λ, λ > 3) in the C-C bonds of the cyclopropyl rings. The banana-like σ _CC bonds in the rings are described in detail. Alkene-like complexes between Δ − R molecules and hydrogen fluoride are identified. These weakly bonded complexes are formed through unconventional hydrogen bond interactions between the hydrogen atom in the HF molecule and the carbon–carbon bonds in the cyclopropane ring. A topological analysis of the electronic charge density and its Laplacian has been used to characterize the interactions. The possible relevance of such complexes in the modeling of substrate–receptor interactions in some anti-AIDS drugs is discussed. Contribution to the Serafin Fraga Memorial Issue.     

Kinetics of protonation of tungsten hydrides WH(CO)2(NO)L2 by weak OH-acids

The kinetics of protonation of tungsten hydrides WH(CO)₂(NO)L₂ (1, L = PMe₃, PEt₃, P(OPri)₃, PPh₃) by weak OH-acids (PhOH, (CF₃)₂CHOH, (CF₃)₃COH) in hexane was studied by IR spectroscopy. The study of the reactions of compounds 1 with OH-acids at 190–270 K revealed that the first step involves the formation of dihydrogen-bonded W(CO)₂(NO)L₂(H)...HOR complexes. When the temperature increases to ambient, the proton transfer and evolution of molecular hydrogen occur, affording the final products: organyloxy derivatives W(OR)(CO)₂(NO)L₂. The study of the kinetics at 298 K found that the proton transfer is the rate-determining step. The rate constants k _app are 2.2·10⁻⁵–6.3·10⁻⁴ s⁻¹, and the free activation energies are ΔG ^≠ _298K = 22–23 kcal mol⁻¹. The rate constants depend on the proton-accepting properties of the hydride and the acidic properties of the OH-proton donor and increase in the same order as the enthalpy of hydrogen bond formation. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 837–841, May, 2007.     

Proton transfer involving nucleic acids: A temperature-jump study of the systems sulphonephthaleins–double stranded poly(A) and sulphonephthaleins–double stranded poly(C)

The kinetics of proton transfer between poly(A—AH) (partially protonated double-stranded polyadenylic acid) and CPR (chlorophenol red), and between poly(C—H—C) (partially protonated double-stranded polycytidylic acid) and the indicators CPR, BCP (bromocresol purple), and BCG (bromocresol green) have been investigated at 25°C and ionic strength 0.1 M (NaClO₄) by the temperature-jump method. The acidic proton of poly(C—H—C) is engaged in a hydrogen bond (N₃H⁺––––N₃) which is believed to contribute to stabilizing the double-strand conformation, whereas the acidic proton of poly(A—A—H) does not form hydrogen bonds. The analysis of the dependence of the relaxation times on the concentrations of the reactants has enabled the evaluation of the rate constants for the direct proton transfer and for the protolysis paths. The rate constants for proton recombination with the deprotonated forms of the polynucleotides and the indicators are of the order of magnitude expected for diffusion controlled processes involving oppositely charged ions (k₂=(0.2−1.6)×1010 M⁻¹s⁻¹). The direct proton transfer from poly(C—H—C) to BCG is thermodynamically disfavored and its rate constant, k₁, is lower than k₂ by about three orders of magnitude. The (thermodynamically favored) proton transfers from poly(A—A—H) to CPR and from poly(C—H—C) to CPR and BCP are characterized by similar values of k₁. This result indicates that the hydrogen bonds in poly(C—H—C) are very weak and suggests that the stabilization of the double-stranded conformation of this polynucleotide could be ascribed to the large number of hydrogen bonds rather than to their specific strength. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet: 30: 161–169, 1998.     

Study of geometrical parameters in N-H...N type of hydrogen bonds

Geometrical parameters associated with N-H ... N types of hydrogen bonds have been analysed using crystal structure data on nucleic acids, amino acids and related compounds. Histograms depicting the frequency distribution of N-H ... N length (l) and H-N ... N angle (θ) have been drawn and conclusions on the favoured geometry of such bonds have been arrived at. The distribution ofl shows a pronounced maximum in the range between 2.9? and 3.0? with an overall average of 2.98 ?. The θ distribution shows a pronounced maximum for the hydrogen bond angle in the range 0°-10°, with a rapid fall-off in frequency for nonlinear hydrogen bonds. The frequency shows a cos⁶θ dependence as compared to cos²θ dependence term used earlier to predict the angular dependence of hydrogen bond potential energy in proteins and polypeptides.     

Thermal decomposition of ammonium dinitramide and mechanism of anomalous decay of dinitramide salts

Thermal decomposition of ammonium dinitramide proceedsvia homolytic rupture of the N−NO₂ bond and partially by the proton transfer reaction. The monomolecular decay of the anion to N₂O and NO₃ ⁻ in the solid state at 60 °C occurs with higher rates than those in the melt. This is related to a change in the reactivity of the anion due to the violation of its symmetry on going to the solid state. The absence of hydrogen bonds between the anion and cations or water molecules is an additional condition for the fast decay. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 50–54, January, 1999.