Van Der Waals Type Interactions Research Articles

Synthesis and crystal structures of (2E)-1,4-bis-(4-chloro-phen-yl)but-2-ene-1,4-dione and (2E)-1,4-bis-(4-bromo-phen-yl)but-2-ene-1,4-dione.

The mol-ecular structure of (2E)-1,4-bis-(4-chloro-phen-yl)but-2-ene-1,4-dione [C16H10Cl2O2, (1)] is composed of two p-chlorophenyl rings, each bonded on opposite ends to a near planar 1,4-trans enedione moiety [-C(=O)-CH=CH-(C=O)-] [r.m.s. deviation = 0.003 (1) Å]. (2E)-1,4-Bis(4-bromo-phen-yl)but-2-ene-1,4-dione [C16H10Br2O2, (2)] has a similar structure to (1), but with two p-bromophenyl rings and a less planar enedione group [r.m.s. deviation= 0.011 (1) Å]. Both mol-ecules sit on a center of inversion, thus Z' = 0.5. The dihedral angles between the ring and the enedione group are 16.61 (8) and 15.58 (11)° for (1) and (2), respectively. In the crystal, mol-ecules of (1) exhibit C-Cl⋯Cl type I inter-actions, whereas mol-ecules of (2) present C-Br⋯Br type II inter-actions. van der Waals-type inter-actions contribute to the packing of both mol-ecules, and the packing reveals face-to-face ring stacking with similar inter-planar distances of approximately 3.53 Å.

Structural diversity of homobinuclear transition metal complexes of the phenazine ligand: theoretical investigation

DFT/BP86 calculations have been carried out on a series of hypothetical binuclear compounds of general formula (L3M)2(C12N2H8) (M = Sc–Ni, L3 = (CO)3, (PH3)3 and Cp−, and C12N2H8 = phenazine ligand-denoted Phn). The various structures with syn and anti configurations have been investigated, in order to determine the phenazine’s coordination to first-row transition metals of various spin states with syn and anti conformations. The lowest energy structures depend on the nature of the metal, the spin state, and the molecular symmetry. This study has shown that the electronic communication between the metal centers depends on their oxidation state and the attached ligands. The tricarbonyl and the triphosphine ligands gave rise to comparable results in terms of stability order of isomers, metal-metal bond distances, and the coordination modes. Metal-metal multiple bonding has been evidenced for Sc, Ti, and V complexes to compensate the electronic deficiency. The Cr, Mn, Fe, Co, and Ni-rich metals prefer the anti conformation due to the enhancement of the metal valence electron count. The spin density values calculated for the triplet and quintet spin structures point out that the unpaired electrons are localized generally on the metal centers. The Wiberg bond indices are used to evaluate the metal-metal bonding. Furthermore, calculations using the BP86-D functional which take into account the attractive part of the van der Waals type interaction potential between atoms and molecules that are not directly connected to each other gave comparable results to those obtained by BP86 functional in terms of coordination modes, HOMO-LUMO gaps, metal-metal bond orders, and the stability order between isomers, but with slight deviation of M–C, M–N, and M–M bond distances not exceeding 3%.

$$\hbox {N}_{2}$$ N 2 adsorption on the inside and outside the single-walled carbon nanotubes by density functional theory study

The adsorption energies, bond order, atomic charge, optical properties, and electrostatic potential of nitrogen molecules of armchair single-walled carbon nanotubes (SWCNTs) and nitrogen-doped single-walled carbon nanotubes (N-SWCNTs) were investigated using density functional theory (DFT). Our results show that adsorption of the $$\hbox {N}_{2}$$ molecules on the external wall of a nanotube is more effective than on the internal wall in SWCNTs. The results show that $$\hbox {N}_{2}$$ molecule(s) are weakly bonded to SWCNTs and N-SWCNTs through van der Waals-type interactions. The interaction of $$\hbox {N}_{2}$$ molecules with SWCNTs and N-SWCNTs is physisorption as the adsorption energy and charge transfer are small, and adsorption distance is large. The electronic transitions from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) ( $$\hbox {H}\rightarrow \hbox {L}$$ ) have the maximum wavelength and the lowest oscillator strength. The potential sensor on the surface of pristine SWCNTs and N-SWCNTs for the adsorption of $$\hbox {N}_{2}$$ molecule(s) is investigated. The N-loaded single-walled carbon nanotube is introduced as a better $$\hbox {N}_{2}$$ molecule(s) detector when compared with SWCNTs.

Creation and detection of photonic molecules in Rydberg gases

We consider the propagation of photons in a gas of Rydberg atoms under conditions of electromagnetically induced transparency, where they form strongly interacting massive particles, termed Rydberg polaritons. Depending on the strength of the van der Waals-type interactions of the atoms either bunching or anti-bunching of photons can be observed when driving the atoms off-resonantly. The bunching is associated with the formation of bound states. We employ a Green's function approach and numerical wave-function simulations to analyze the conditions for the creation and the dynamics of these photonic molecules and their interplay with the scattering continuum which can also show photon bunching. Analytic solutions of the pair-propagation problem obtained from a pseudopotential approximation and verified numerically provide a detailed understanding of bound and scattering states. We find that the scattering contributions acquire asymptotically a robust relative phase which can be employed to separate bound-state and scattering contributions by a homodyne detection scheme.

Structural and electronic properties of MoS2, WS2, and WS2/MoS2 heterostructures encapsulated with hexagonal boron nitride monolayers

In this study, we investigate the structural and electronic properties of MoS2, WS2, and WS2/MoS2 structures encapsulated within hexagonal boron nitride (h-BN) monolayers with first-principles calculations based on density functional theory by using the recently developed non-local van der Waals density functional (rvv10). We find that the heterostructures are thermodynamically stable with the interlayer distance ranging from 3.425 Å to 3.625 Å implying van der Waals type interaction between the layers. Except for the WS2/h-BN heterostructure which exhibits direct band gap character with the value of 1.920 eV at the K point, all proposed heterostructures show indirect band gap behavior from the valence band maximum at the Γ point to the conduction band minimum at the K point with values varying from 0.907 eV to 1.710 eV. More importantly, it is found that h-BN is an excellent candidate for the protection of intrinsic properties of MoS2, WS2, and WS2/MoS2 structures.

Effects of different inorganic nanoparticles on the structural, dielectric and ion transportation properties of polymers blend based nanocomposite solid polymer electrolytes

Nanocomposite solid polymer electrolyte (NSPE) films consisted of poly(ethylene oxide) (PEO) and poly(methyl methacrylate) (PMMA) blend (50/50wt%) as host polymer matrix with 20wt% lithium perchlorate (LiClO4) as dopant salt and 3wt% inorganic nanoparticles (i.e., Al2O3, SiO2, SnO2 or ZnO) as filler have been prepared by solution cast method followed by melt-press technique. The X-ray diffraction (XRD) study confirms that the electrolyte films without nanofiller and with Al2O3 and SiO2 nanofillers have predominantly amorphous structures, whereas the characteristic diffraction peaks of SnO2 and ZnO crystallites are observed in the respective NSPEs. Fourier transform infra-red (FTIR) spectra of these NSPE films confirm the formation of ion-dipolar coordination between the functional groups of polymers and the lithium ions throughout the material which completely suppressed the crystalline region absorption peaks of the PEO. The metal oxides of the nanoparticles mainly exhibit van der Waals type interaction with the polymers chains and the ions in the NSPE materials. Effects of a lithium salt as a dopant and the nanoparticles as fillers on the crystalline phase and thermal behaviour of PEO–PMMA blend in these electrolyte materials have also been examined by their differential scanning calorimetry (DSC) measurements.Dielectric and electrical dispersion behaviour of the NSPE films have been characterized by employing dielectric relaxation spectroscopy (DRS) over the frequency range from 20Hz to1MHz and at temperatures 27, 35, 45 and 55°C. The single relaxation peak appeared in the dielectric loss tangent spectra of these electrolytes confirms the ion-dipolar coordinated coupled cooperative chain segmental motion of the PEO and PMMA macromolecules. Lowering in the values of dielectric polarization strength and ionic conductivity has been observed for all the NSPE films as compared to that of the SPE film without nanofiller. A linear correlation between the crystallite sizes of different nanofillers and the dielectric permittivity of NSPE materials has been revealed. It is found that the cooperative polymers chain segmental dynamics becomes slower with the dispersion of nanoparticles in the ion-dipolar complexes which causes a decrease of ionic conductivity of the NSPE films. The correlation observed between the dielectric relaxation time and the ionic conductivity confirms that the ions transport occurs by intra- and inter-chain hopping in these PEO–PMMA blend based electrolytes. Temperature dependent values of relaxation time and dc ionic conductivity of the electrolyte films obey the Arrhenius relation and their activation energies are found in the range 0.22eV to 0.40eV which differ with the types of inorganic nanoparticles dispersed in the NSPEs. The comparative results confirm that the polymers chain segmental dynamics mask the effect of amorphous phase of these materials which contributes in the lithium ions transportation and their mobility. Linear correlation observed between the dielectric permittivity and ionic conductivity values of these NSPEs suggests that the strength of dielectric polarization also plays an important role for the ion transportation process in the solid ion-dipolar complexes. The room temperature ionic conductivity values of these NSPE films are found of the order of 10−5Scm−1 which confirms their suitability as potential candidates in the design and development of all-solid-state devices including the rechargeable lithium-ion batteries. Finally, these experimental results explain in depth the fundamental issues of nanomaterials science that confront the use of various kind of inorganic nanoparticles in the preparation of NSPEs, and the dependence of their ion transportation process on the amorphous phase, dielectric permittivity and the cooperative polymers chain segmental motion, especially for the polymers blend based electrolytes.

First-principles modeling of GaN/MoSe$_{2}$ van der Waals heterobilayer

We investigate structural and electronic properties of the graphene-like gallium nitride (GaN) monolayer deposited on a MoSe$_{2}$ monolayer by using density functional theory with the inclusion of the nonlocal van der Waals correction. The GaN is bound weakly to the MoSe$_{2}$ monolayer with adsorption energy of 49 meV/atom. We find that the heterobilayer is energetically favorable with the interlayer distance of 3.302 {\AA} indicating van der Waals (vdW) type interaction and the most stable stacking configuration is verified with different deposition sequences. The heterostructure of GaN/MoSe$_{2}$ is found to be indirect band gap semiconductor with gap value of 1.371 eV. Our results demonstrate the potential design of new two-dimensional nanoelectronic devices based on the vdW heterostructure.

Effect of Cross-Linking with Aloe vera Gel on Surface and Physicochemical Properties of Edible Films Made from Plantain Flour

Films made from plantain flour with incorporation of different concentrations (0, 2, 4 and 6 %) of a natural filler (Aloe vera gel - Av gel) were obtained by the casting method. The aim of this paper was to characterize the surface and physicochemical properties on plantain flour edible films. The average molecular weight, moisture, infrared spectroscopy, contact angle and mechanical properties were determined. Also, microstructural characterization was performed by atomic force microscopy and scanning electron microscopy. The Av gel produced cross-linking on the starch that is found in plantain flour, resulting in films with the following characteristics: smoother, more transparent, more rigid and plastics, less moist and with more hydrophobic surfaces. Finally, the surface properties of these materials were defined by the surface energy of material, which depends on the intermolecular interactions such as van der Waals-type interactions (hydrogen bond) and new bonds (cross-linking) formed between biopolymeric chains (plantain flour).

Tuning Up an Electronic Structure of the Subphthalocyanine Derivatives toward Electron-Transfer Process in Noncovalent Complexes with C60 and C70 Fullerenes: Experimental and Theoretical Studies.

Noncovalent π-π interactions between chloroboron subphthalocyanine (1), 2,3-subnaphthalocyanine (3), 1,4,8,11,15,18-(hexathiophenyl)subphthalocyanine (4), or 4-tert-butylphenoxyboron subphthalocyanine (2) with C60 and C70 fullerenes were studied by UV-vis and steady-state fluorescence spectroscopy, as well as mass (APCI, ESI, and CSI) spectrometry. Mass spectrometry experiments were suggestive of relatively weak interaction energies between compounds 1-4 and fullerenes. The formation of a new weak charge-transfer band in the NIR region was observed in solution only for subphthalocyanine 4 when titrated with C60 and C70 fullerenes. Molecular structures of the subphthalocyanines 2 and 4 as well as cocrystallite of 4 with C60 fullerene (4···C60) were studied using X-ray crystallography. One of the C60 fullerenes in the crystal structure of 4···C60 was found in the concave region between two subphthalocyanine cores, while the other three fullerenes are aligned above individual isoindole fragments of the aromatic subphthalocyanine. The excited-state dynamics in noncovalent assemblies were studied by transient absorption spectroscopy. The time-resolved photophysics data suggest that only electron-rich subphthalocyanine 4 can facilitate an electron-transfer to C60 or C70 fullerenes, while no electron-transfer from the photoexcited receptors 1-3 to fullerenes was observed in UV-vis and transient spectroscopy experiments. DFT calculations using the CAM-B3LYP exchange-correlation functional and the 6-31+G(d) basis set allowed an estimation of interaction energies for the noncovalent 1:1 and 1:2 (fullerene:subphthalocyanine) complexes. Theoretical data suggest that the weak (∼3.5-10.5 kcal/mol) van der Waals-type interaction energies tend to increase with an increase of the electron density at the subphthalocyanine core with compound 4 being the best platform for noncovalent interactions with fullerenes. DFT calculations also indicate that 1:2 (fullerene:subphthalocyanine) noncovalent complexes are more stable than the corresponding 1:1 assemblies.

The Effect of Graphene Shape on its Ability to Separate Gases

A new integrable modification of the LJ-potential and a continual approach are used to investigate the interaction between a thin film (graphene) and gas molecules. It is shown that this technique allows determining the characteristics of a van der Waals-type interaction between molecules and graphene films of a variety of shapes. It is found that an unperforated graphene (planar or buckled) is impermeable for molecules with the energies consistent to the room temperature of a gaseous medium; hence, it has to be perforated in order to be used as a separator. Penetration of the molecules through the openings in a buckled graphene is somewhat different from that through a planar graphene, though these differences are insignificant. It is demonstrated that the data obtained on the planar graphene (most useful for theoretical research) are also valid for the really existing buckled (ruled-surface or chessboard) graphenes. When a graphene is used as a separator, its shape does not play the leading role in determining its principal property – permeability.

Compact two-electron wave function for bond dissociation and Van der Waals interactions: a natural amplitude assessment.

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r12) depending on the interelectronic distance r12. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r12) needs to diverge for large r12 at large internuclear distances while for shorter bond distances it increases as a function of r12 to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.

Origin of chains of Au-PbS Nano-Dumbbells in space

Self-assembled, one-dimensional (1D) nanomaterials are amenable building blocks for bottom-up nanofabrication processes. A current shortcoming in the self-assembly of 1D nanomaterials in solution phase is the need for specific linkers or templates under very precise conditions to achieve a handful of systems. Here we report on the origin of a novel self-assembly of 1D dumbbells consisting of Au tipped PbS nanorods into stable chains in solution without any linkers or templates. A realistic multi-particle model suggests that the mesophase comprises 1D dumbbells arrayed in chains formed by anisotropic van der Waals type interactions. We demonstrate an alternative recognition mechanism for directing the assembly of the 1D dumbbells, based on effective interaction between the neighboring dumbbells consisting of Au tips with complementary crystallographic facets that guides the entire assembly in space.

Spectroscopic investigation of tolmetin interaction with human serum albumin

The interaction of tolmetin (TOL) with human serum albumin (HSA) in physiological buffer solution (pH 7.4) was studied by fluorescence and UV–vis absorption spectroscopy at different temperatures, combined with time-resolved fluorescence measurements. The experimental results showed that there was a strong fluorescence quenching of HSA by tolmetin. Using the continuous variation method, a single class of binding sites for TOL on HSA was put in evidence. The binding constants Ka were calculated at different temperatures, using a nonlinear fit to the experimental data, and the thermodynamic parameters ΔH0, ΔS0 and ΔG0 were given. The obtained thermodynamic signature suggests that at least van der Waals and electrostatic type interactions are present. Quenching efficiency calculations, based on steady state and time-resolved spectroscopy, indicate that both static and dynamic quenching mechanisms are present.

DFT Studies of Pristine Hexagonal Ge1Sb2Te4(0001), Ge2Sb2Te5(0001), and Ge1Sb4Te7(0001) Surfaces

Ternary alloys of germanium, antimony, and tellurium (GexSbyTez) are not only prominent phase-change data-storage materials with intriguing properties; they also form precisely ordered crystal structures if one allows them to do so. Here, we study atomically pristine surfaces of representative GexSbyTez alloys using density functional theory (DFT) and suitable plane-wave-based slab models. In particular, we look at the hexagonal (0001) surfaces of Ge1Sb2Te4, Ge2Sb2Te5, and Ge1Sb4Te7 but with the intent to draw some general conclusions beyond those explicit compositions. The conditions for thermodynamic stability of the ternary surfaces (i.e., the space of permissible chemical potentials) are delineated, and a simple general expression to estimate the latter is given. Because of weak van der Waals-type interactions between Te atomic layers, we assess how surface energy computations are affected by the choice of exchange–correlation functional and also by the use of dispersion corrections (here, Grimme’s DFT+D2 scheme). LDA and PBE+D2 predicted surface energies are similar to a degree that is rather unexpected; generally, Te terminations are lowest in surface energy regardless of the compound and methodology. Implications for further surface studies of “less ideal’’ GexSbyTez surfaces are discussed.

Polymorph stabilization in processed acetaminophen powders

A novel approach has been developed to stabilize the metastable form II of acetaminophen (APAP) prepared from the melt of micronized and nano-silica coated APAP I. It is suggested that stabilization of form II APAP occurs by pinning via van der Waals-type interactions on low energy defects created by micronization and impinging particles during dry coating in form I APAP, heating to the melt phase, and cooling. The defects are likely to persist into the near-molten isotropic phase due to a permanent memory effect similar to that previously observed in silica-liquid crystal composites and re-crystallize together with form II APAP. Raman spectroscopy, scanning electron microscopy (SEM), powder X-ray diffraction (PXRD), and conventional as well as intrinsic dissolution have been used to characterize the stabilized APAP II obtained. Raman measurements up to 18 months and PXRD data for micronized form II APAP show no indication of APAP I formation. Aged samples of dry-coated APAP II however display Raman features indicative of APAP I within 5 months. PXRD and SEM techniques also detected small fractions of APAP I in dry-coated APAP II. Both micronized APAP II and dry-coated APAP II give rise to a time-dependent background scattering superimposed on the Raman spectra which increases in integrated intensity with time, saturates at 180 and 90 days, respectively, and then decreases in intensity with further aging. The time-dependent scattering background occurs in the stabilized form II APAP samples only after cooling from the melt and is more intense in micronized APAP II compared to dry-coated APAP II. It is assigned to disorder associated with slowly diffusing defects created by micronization and dry coating with impinging nano-silica particles in form I APAP. Intrinsic dissolution profiles for the stabilized APAP II samples showed measureable increases, particularly for micronized APAP II.

Nickel Carbide as a Source of Grain Rotation in Epitaxial Graphene

Graphene has a close lattice match to the Ni(111) surface, resulting in a preference for 1 × 1 configurations. We have investigated graphene grown by chemical vapor deposition (CVD) on the nickel carbide (Ni(2)C) reconstruction of Ni(111) with scanning tunneling microscopy (STM). The presence of excess carbon, in the form of Ni(2)C, prevents graphene from adopting the preferred 1 × 1 configuration and leads to grain rotation. STM measurements show that residual Ni(2)C domains are present under rotated graphene. Nickel vacancy islands are observed at the periphery of rotated grains and indicate Ni(2)C dissolution after graphene growth. Density functional theory (DFT) calculations predict a very weak (van der Waals type) interaction of graphene with the underlying Ni(2)C, which should facilitate a phase separation of the carbide into metal-supported graphene. These results demonstrate that surface phases such as Ni(2)C can play a major role in the quality of epitaxial graphene.

Understanding physical properties of hydrocarbon polymers using an equation of state developed from semi soft core potential function

A semi-soft core intermolecular potential function for hydrocarbon molecules has been developed that expands the Boltzmann angle average of the van der Waals type-interaction. The logarithmic form simplifies the many thermodynamic derivatives related to Boltzmann statistics and clarifies the concept of the collision diameter. Second and third virial coefficients were derived as closed expressions and both the additive and non-additive terms were derived, especially for the third virial coefficient. A virial equation of state (EOS) was derived using the newly developed virial coefficients and compared to experimentally observed compressibility factors of natural gases. A perturbation EOS is derived to obtain vapor–liquid equilibrium (VLE) using the present potential function and the method of statistical mechanics. The EOS was employed to explain the VLE of pure hydrocarbon molecules. To expand the applicable range from small molecules to long chain polymers, the perturbation EOS was modified to a polymer EOS by introducing chain terms. Despite the relatively short expressions, each of the developed EOSs developed in this study were comparable in accuracy to well-known EOSs for each field, which demonstrates the advantage of applying these EOSs to multicomponent mixtures and long chain molecules.

Novel Cooperative Interactions and Structural Ordering inH2S−H2

Hydrogen sulfide (${\mathrm{H}}_{2}\mathrm{S}$) and hydrogen (${\mathrm{H}}_{2}$) crystallize into a `guest-host' structure at 3.5 GPa and, at the initial formation pressure, the rotationally disordered component molecules exhibit weak van der Waals-type interactions. With increasing pressure, hydrogen bonding develops and strengthens between neighboring ${\mathrm{H}}_{2}\mathrm{S}$ molecules, reflected in a pronounced drop in S-H vibrational stretching frequency and also observed in first-principles calculations. At 17 GPa, an ordering process occurs where ${\mathrm{H}}_{2}\mathrm{S}$ molecules orient themselves to maximize hydrogen bonding and ${\mathrm{H}}_{2}$ molecules simultaneously occupy a chemically distinct lattice site. Intermolecular forces in the ${\mathrm{H}}_{2}\mathrm{S}+{\mathrm{H}}_{2}$ system may be tuned with pressure from the weak hydrogen-bonding limit to the ordered hydrogen-bonding regime, resulting in a novel clathrate structure stabilized by cooperative interactions.

Theoretical study of β and γ-cyclodextrins inclusion complexes with nineteen atropisomeric polychlorobiphenyls

Inclusion complexes of β and γ-cyclodextrins (CDs), chirally selective macrocycles, with 19 atropisomeric polychlorinated biphenyls (PCBs), stable at physiological temperatures, were studied by molecular mechanics optimized potential for liquid simulations and semi-empirical quantum AM1 methods. Bimodal manual docking, geometry optimization and single point calculations were done. PCB:CD complex formation was studied considering two ways of entry in the large base of CD cavity: with biphenyl C1–C1′ bond axis of PCBs oriented parallel and anti-parallel with the CD trunk height axis. A distance dependent dielectric constant was used to account for the solvent effect. The values of complexation and binding energies were calculated, confirming the existence of a specific van der Waals (vdW) type interaction. β and/or γ-CD chiral recognition of the 19 atropisomeric PCBs, is described by means of the complexation and binding energy values. The binding energy is a better discriminator of PCBs enantiomers than complexation energy considering the average energy differences between (+) and (−) PCB:β/γ-CD complexes. The chromatographic elution order of several PCB enantiomers from literature was correlated with the complexation and binding energies. The molecular modeling of inclusion complexes is recommended to be used as enantiomer identification tool in correlation with chromatographic data.

5-Chloro-1-phenyl-1H-pyrazol-4-amine

In the crystal structure of the title compound, C9H8ClN3, amino–pyrazole N—H⋯N hydrogen bonds connect the mol­ecules along the [010] direction; the chains interact with each other only by van der Waals-type inter­actions. The pyrazole and phenyl rings are inclined at a dihedral angle of 45.65 (6)°