Microwave, Raman and infrared spectra, r0 structural parameters, conformational stability, and ab initio calculations of cyclobutylisocyanate

The microwave spectrum of cyclobutylisocyanate, c-C₄H₇NCO, has been investigated from 21,000 to 11,000 MHz and 11 transitions for the more stable equatorial-trans conformer were assigned. The rotational constants of the ground vibrational state have been determined and the molecule has been shown to be a near symmetric prolate rotor (К = ?0.99). The B and C rotational constants have been confidently determined to be B = 1508.68(3) and C = 1476.55(2) MHz, respectively, whereas the value for the A rotational constant of 6,891(302) MHz had a large uncertainty. Variable temperature (?100 to ?55 °C) studies of the infrared spectra (3,500–400 cm^?1) of cyclobutylisocyanate dissolved in liquid xenon as well as the infrared spectra of the gas and solid have been recorded. In addition, the Raman spectra (3,600–100 cm^?1) of the liquid have been investigated. These spectral data indicated the present of three conformers in the fluid states which are the equatorial-trans, equatorial-gauche, and axial-trans forms. The second part of the conformational name refers to the relative position of the NCO moiety relative to the alpha hydrogen. By utilizing four conformer pairs, an enthalpy difference of 131 ± 13 cm^?1 (1.57 ± 0.16 kJ/mol) was obtained with the equatorial-trans conformer the more stable form, which is in good agreement with the ab initio predicted value of 137 ± 36 cm^?1 (1.64 ± 0.43 kJ/mol). To aid in the vibrational assignment, ab initio and DFT calculations have been carried out by using a variety of basis sets up to 6-311G(3df,3pd).     

Molecular structure and conformational preferences of 1-chloro-1-silacyclohexane,CH<Subscript>2</Subscript>(CH<Subscript>2</Subscript>CH<Subscript>2</Subscript>)<Subscript>2</Subscript>SiH-Cl,as studies by gas-phase electron diffraction and quantum chemistry

The molecular structure of axial and equatorial conformer of the 1-chloro-1-silacyclohexane molecule, CH₂(CH₂CH₂)₂SiH-Cl, as well as thermodynamic equilibrium between these species were investigated by means of gas-phase electron diffraction and quantum chemistry on the MP2(full)/AUG-cc-PVTZ level of theory. According to electron diffraction data, the compound exists in the gas-phase as a mixture of conformers possessing the chair conformation of the six-membered ring and Cs symmetry and differing in the axial and equatorial position of the Si-Cl bond at 352 K. NBO analysis revealed that axial conformer of 1-chloro-1-silacyclohexane molecule is an example of the stabilization of the form that is unfavorable from the point of view steric effects and effects of conjugations and that stabilization is achieved due to electrostatic interactions.     

Synthesis and NMR spectroscopic conformational analysis of esters of 4-hydroxy-cyclohexanone—the more polar the molecule the more stable the axial conformer

The esters of 4-hydroxy-cyclohexanone and a series of carboxylic acids R–COOH with R of different electronic and steric influence (R=Me, Et, n-Pr, i-Pr, n-Bu, i-Bu, sec-Bu, t-Bu, CF₃, CH₂Cl, CHCl₂, CCl₃, CH₂Br, CHBr₂, and CBr₃) were synthesized and the conformational equilibria studied by ¹H and ¹³C NMR spectroscopy at 103 K and at 295 K, respectively. The geometry of optimized structures of the axial/equatorial chair conformers was computed at the ab initio MO and DFT levels of theory. Only one preferred conformation was obtained for the axial and the equatorial conformer as well. When comparing the conformational equilibria of the cyclohexanone esters with those of the corresponding cyclohexyl esters a certain polarity contribution of the cyclohexanone framework was revealed, which is independent of the substituent effects and increases the stability of the axial conformers by a constant amount.     

Molecular structure and conformational preferences of 1-bromo-1-silacyclohexane, CH2(CH2CH2)2SiH-Br, as studies by gas-phase electron diffraction and quantum chemistry

The molecular structure of axial and equatorial conformer of the 1-bromo-1-silacyclohexane molecule, CH₂(CH₂CH₂)₂SiH-Br, as well as thermodynamic equilibrium between these species are investigated by means of gas-phase electron diffraction and quantum chemistry on the MP2(full)/SDB-AUG-cc-PVTZ level of theory. It is revealed that according to electron diffraction data, the compound exists in the gasphase as a mixture of conformers possessing the chair conformation of the six-membered ring and C _s symmetry and differing in the axial and equatorial position of the Si-Br bond (ax. = 80(5) mol %, eq. = 20(7) mol %) at 352 K, that corresponds to the value of A = (G _ax ^?? ? G _eq ^?? ) = ?0.82(32) kcal/mol. It is found that observed data agree well with theoretical ones. Using Natural Bond Orbital (NBO) analysis it is revealed that axial conformer of 1-bromo-1-silacyclohexane molecule is an example of the stabilization of the form that is unfavorable from the point of view of steric effects and effects of conjugations. It is concluded that stabilization is achieved due to electrostatic interactions.     

Quantum-chemical study of silacyclohexanes C5H10SiHCN, C5H10SiH(t-Bu), C5H10Si(t-Bu)CN, and C5H10SiHF

By quantum-chemical calculations at the M06-2X/aug-cc-pVTZ level of theory geometrical parameters, dipole moments, polarizabilities, first hyperpolarizabilities and relative energies of the axial and equatorial conformers in gaseous phase were determined for 1-cyano-1-silacyclohexane, 1-tert-butyl-1-silacyclohexane, 1-tert-butyl-1-cyano-1-silacyclohexane, and 1-fluoro-1-silacyclohexane. For the cyano group and fluorine atom the axial position is more preferable whereas for tert-butyl group, equatorial one. Polarizabilities of conformers are similar but optical anisotropy of equatorial conformers of C₅H₁₀SiHCN and C₅H₁₀SiH(t-Bu) molecules is much larger than that of axial conformers. Upon substitution in nitriles of C¹ atom by Si atom the hyperpolarizability is many times increased.     

Conformational Stability from Variable-Temperature Infrared Spectra of Krypton Solutions, Ab Initio Calculations, and r o Structural Parameters of Chlorocyclopentane

The infrared spectra (3500–400 cm^–1) of krypton solutions of chlorocyclopentane, c-C₅H₉Cl, at variable temperatures (–101 to –150°C) have been recorded and the fundamental vibrations of the axial conformer and several of those for the equatorial form have been assigned. Utilizing two pairs of fundamentals for the two conformers in the krypton solution, an enthalpy difference of 145±15 cm^–1 (1.73±0.18 kJ-mol^–1) has been obtained with the axial conformer the more stable form. It is estimated that there is 67±2% of the axial conformer present at ambient temperature. Convincing spectroscopic evidence shows that a significant percentage of the chlorocyclopentane molecules are undergoing pseudorotation at ambient temperature. The conformational stabilities, harmonic force constants, fundamental frequencies, infrared intensities, and Raman activities have been obtained from MP2/6-31G(d) calculations with full electron correlation and these quantities have been compared to the experimental values when appropriate. The optimized geometries and conformational stabilities have also been obtained from ab initio MP2 calculations as well as by density functional theory (DFT) by the B3LYP method with several different basis sets. The adjusted r ₀ structural parameters have been obtained for both conformers by combining the ab initio data with the previously reported microwave rotational constants. These new values of the structural parameters for both conformers are compared to those previously reported from electron diffraction and microwave studies. These results are compared to the corresponding quantities of some similar molecules.     

1-Phenyl-1-halo-1-silacyclohexanes

The approaches to synthesis of 1-phenyl-1-halo-1-silacyclohexanes C₅H₁₀Si(Ph)X (X = F, Cl, Br) have been examined. 1-Phenyl-1-chloro-1-silacyclohexane has been prepared via the known reaction of phenyltrichlorosilane with dimagnesium derivative of 1,5-dibromopentane; up to 20% of 1-bromo-1-phenyl-1-silacyclohexane admixture is formed along with the target product. The minor product formation has been prevented using an alternative method of chlorination of 1-phenyl-1-silacyclohexane with N-chlorosuccinimide. 1-Phenyl-1-fluoro-1-silacyclohexane has been obtained in close to quantitative yield via the reaction of 1-phenyl-1-chloro-1-silacyclohexane with SbF₃ and in 70% yield via its reaction with HF. The synthesis of 1-phenyl-1-bromo-1-silacyclohexane via bromination of 1-phenyl-1-chloro-1-silacyclohexane with N-bromosuccinimide has given the target product as a minor one, the major product being disiloxane formed due to hydrolysis of the Si–Br bond.     

Gas-phase molecular structure of 1,1,1,2-tetrabromo-2,2-dimethyldisilane: theoretical and experimental investigation of a super-halogenated disilane and computational investigation of the F, Cl and I analogues

The molecular structure of 1,1,1,2-tetrabromo-2,2-dimethyldisilane (Br₃SiSiBrMe₂) has been determined in the gas phase by electron diffraction and ab initio molecular-orbital calculations. The computational investigation was used to augment the experimental investigation using the Structure Analysis Restrained by Ab initio Calculations for Electron diffractioN (SARACEN) method. The structure was found to adopt a staggered structure with C _s symmetry by both theory and experiment. Important structural parameters (r _h1) include: rSi–Si 235.6(5) pm, rSi–C 185.4(3) pm, rSi–Br_av 220.3(1) pm, ∠Si–Si–Br(14) 106.1(4)°, ∠Si–Si–C 109.2(8)° and ?Br–Si–Si–Br 180.0°(fixed). These experimental observations are supported by theoretical predictions obtained at the MP2/6-311+G* level. An analogous theoretical investigation was also performed for the series X₃SiSiXMe₂ (X = F, Cl and I) and structural trends identified. The Si–X bond was observed to lengthen as a function of the halogen substituent, with corresponding changes to the Si–Si–X bond angles in the SiX₃ groups. The Si–Si–X bond angle in the SiXMe₂ groups displayed rather different behaviour, and was relatively stable to substitution until X = I. The flexible nature of bond angles about silicon atoms was observed, even in this relatively sterically unhindered system.     

Organomonophosphines in PtP<Subscript>2</Subscript>XY derivatives: structural aspects

This review covers over two hundred Pt(II) complexes with a PtP₂XY inner coordination sphere, in which the P-donor ligands are organomonophosphines. These complexes can be divided into six groups: PtP₂HX (X = O, N, B, Cl, S, Br, Se, Si, or I); PtP₂OX (X = N, Cl, S, or Se); PtP₂NX (X = CN, Cl, B, S, Br, Se, or Te); PtP₂BX (X = F, Cl, S, Br, or I); PtP₂ClX (X = S, Se, Si, As, or Te); and PtP₂SiX (X = Br or Te). The complexes crystallize in several crystal systems: hexagonal (×1), tetragonal (×1), orthorhombic (×22), triclinic (×78), and monoclinic (×130). There are complexes with cis-configuration and trans-configuration, the latter by far prevails. Besides monodentate ligands, there are also heterobidentate ligands with: O/N, O/S, O/Se, N/S, N/Se, and N/Te, donor sites. These chelating ligands form a wide variety of metallocyclic, four-, five-, and six-membered rings, and the effects of both steric and electronic factors can be seen from the values of the L–Pt–L bite angles. The structural parameters are analyzed and discussed with particular attention to trans-influences.     

A systematic density functional and wavefunction-based study on dicarboxyl dianions −O2C–R–CO2 − with R = C2, C2X2, C2X4, and C6X4 (X = H, F)

The possible existence of the gas phase cis- and trans-maleate, i.e. completely deprotonated maleic acid (O₂C–CΗ=CΗ–CO₂)^2–, is investigated by density functional (B3LYP) and ab-initio quantum chemical methods (MP2, CCSD(T)) using large basis sets. The calculations reveal that only the trans-isomer is Coulomb stable with respect to electron loss. The results are compared to other previously investigated dicarboxylate dianions of the general form ^?O₂C–R–CO₂ ^? with R = C₂, C₂X₂, C₂X₄, and C₆X₄ (X = H, F). Fluorine substitution on the carbon framework helps to stabilize these doubly charged systems, and we predict that all of the aromatic fluorine substituted dicarboxylate dianions are Coulomb stable in the gas phase. Only the highest levels of theory reveal the slight stabilization of both the succinate dianion and the ortho-isomer of the phthalic acid dianion in unprecedented agreement with experiments.     

Do halogen and methyl substituents have electronic effects on the structures of simple disilanes? An experimental and theoretical study of the molecular structures of the series X3SiSiMe3 (X = H, F, Cl and Br)

The gas-phase molecular structures of a series of halogen-substituted disilanes [X₃SiSiMe₃ (X = H, F, Cl and Br)], 1,1,1-trimethyldisilane (H₃SiSiMe₃), 1,1,1-trifluoro-2,2,2-trimethyldisilane (F₃SiSiMe₃), 1,1,1-trichloro-2,2,2-trimethyldisilane (Cl₃SiSiMe₃) and 1,1,1-tribromo-2,2,2-trimethyldisilane (Br₃SiSiMe₃), have been determined in the gas phase by electron diffraction. Ab initio calculations at the HF and MP2 level were used to support the experimental investigation using the SARACEN method. All of the investigated structures were determined to adopt a staggered structure with C _3v symmetry. The effect of substitution on the Si–Si bond and the Si–Si–X bond angle was investigated and these results were compared to results obtained from a recent study of halogen-substituted disilanes [X₃SiSiXMe₂ (X = F, Cl, Br and I)] to consider the effect of the methyl groups on the substituted disilanes.     

1-Methylthio-1-phenyl-1-silacyclohexane: Synthesis,conformational preferences in gas and solution by GED,NMR and theoretical calculations

1-Methylthio-1-phenyl-1-silacyclohexane 1, the first silacyclohexane with the sulfur atom at silicon, was synthesized and its molecular structure and conformational preferences studied by gas-phase electron diffraction (GED) and low temperature ¹³C and ²⁹Si NMR spectroscopy (LT NMR). Quantum-chemical calculations were carried out both for the isolated species and solvate complexes in gas and in polar medium. The predominance of the 1-MeS_axPh_eq conformer in gas phase (1-Ph_eq:1-Ph_ax = 55:45, ΔG° = 0.13 kcal/mol) determined from GED is consistent with that measured in the freon solution by LT NMR (1-Ph_eq:1-Ph_ax = 65:35, ΔG° = 0.12 kcal/mol), the experimentally measured ratios being close to that estimated by quantum chemical calculations at both the DFT and MP2 levels of theory.     

Synthesis,conformational preferences in gas and solution,and molecular gear rotation in 1-(dimethylamino)-1-phenyl-1-silacyclohexane by gas phase electron diffraction (GED), LT NMR and theoretical calculations

1-(Dimethylamino)-1-phenyl-1-silacyclohexane 1, was synthesized, and its molecular structure and conformational properties studied by gas-phase electron diffraction (GED), low temperature ¹³C NMR spectroscopy and quantum-chemical calculations. The predominance of the 1-Ph_ax conformer (1-Ph_eq:1-Ph_ax ratio of 20:80%, ΔG°(317?K)?=??0.87?kcal/mol) in the gas phase is close to the theoretically estimated conformational equilibrium. In solution, low temperature NMR spectroscopy showed analyzable decoalescence of C_ipso and C(1,5) carbon signals in ¹³C NMR spectra at 103?K. Opposite to the gas state in the freon solution employed (CD₂Cl₂/CHFCl₂/CHFCl₂?=?1:1:3), which is still liquid at 100?K, the 1-Ph_eq conformer was found to be the preferred one [(1-Ph_eq: 1-Ph_ax?=?77%: 23%, K?=?77/23?=?2.8; ?ΔG°?=??RT ln K (at 103?K)?=?0.44?±?0.1?kcal/mol]. When comparing 1 with 1-phenyl-1-(X)silacylohexanes (X?=?H, Me, OMe, F, Cl), studied so far, the trend of predominance of the Ph_ax conformer in the gas phase and of the Ph_eq conformer in solution is confirmed.     

2-Chloro and 2-fluoro ketones derived from the chiral-pool

Both (2R,5R)- and (2S,5R)-isomers of 2-chloro-2-isopropyl-5-methyl-, 2-chloro-2-methyl-5-isopropyl- and 2-fluoro-2-methyl-5-isopropylcyclohexanones have been synthesized and fully characterized. It is shown that a rapid overview of the ¹H NMR spectrum allows an unambiguous assignment of the axial or equatorial position of the halogen atom and that the IR ν_CO absorption does not differ from one isomer to the other.     

The <Emphasis Type="Italic">r</Emphasis><Subscript>0</Subscript> structural parameters of equatorial and axial chlorocyclobutane,conformational stability from temperature dependent infrared spectra of xenon solutions,and vibrational assignments

Variable temperature (?55 to ?100 °C) studies of the infrared spectra (4,000–400 cm^?1) of chlorocyclobutane, c-C₄H₇Cl, dissolved in liquid xenon have been carried out. The infrared spectrum (4,000–100 cm^–1) of the gas has also been recorded. For this puckered ring molecule the enthalpy difference between the more stable equatorial conformer and the axial form, has been determined to be 361 ± 17 cm^?1 (4.32 ± 0.20 kJ/mol). This stability order is consistent with that predicted by ab initio calculations but the ?H is much lower than the average energy value of 646 ± 73 cm^?1 obtained from the MP2 ab initio calculations or 611 ± 28 cm^?1 from the B3LYP density functional theory calculations. The percentage of the axial conformer present at ambient temperature is estimated to be 15 ± 1%. By utilizing previously reported microwave rotational constants for both conformers combined with ab initio MP2(full)/6–311+G(d,p) predicted structural values, adjusted r ₀ parameters have been obtained. The determined heavy atom structural parameters for the equatorial conformer are: the distances C–Cl = 1.783(5), C₁–C₄ = 1.539(3), C₄–C₆ = 1.558(3) Å, and angles ∠C₆C₄C₁ = 86.9(5), ∠C₄C₁C₅ = 89.7(5)°, and for the axial conformer are: the distances C–Cl = 1.803(5), C₁–C₄ = 1.547(3), C₄–C₆ = 1.557(3) Å, and angles ∠C₆C₄C₁ = 86.3(5), ∠C₄C₁C₅ = 88.9(5) and the puckering angles for the equatorial and axial conformers are 30.7(5)° and 22.3(5)°, respectively. The conformational stabilities, harmonic force fields, infrared intensities, Raman activities, depolarization ratios and vibrational frequencies have been obtained for both conformers from MP2(full)/6-31G(d) ab initio calculations and compared to experimental values where available. The results are discussed and compared to the corresponding properties of some similar molecules.     

Conformational preferences of Si–Ph,H and Si–Ph,Me silacyclohexanes and 1,3-thiasilacyclohexanes. Additivity of conformational energies in 1,1-disubstituted heterocyclohexanes

The conformational equilibria of 1-phenyl-1-silacyclohexane 1, 3-phenyl-1,3-thiasilacyclohexane 2, 1-methyl-1-phenyl-1-silacyclohexane 3, and 3-methyl-3-phenyl-1,3-thiasilacyclohexane 4 have been studied for the first time by low temperature ¹³C NMR spectroscopy at 103 K. Predominance of the equatorial conformer of compound 1 (Ph_eq/Ph_ax=78%:22%) is much less than in its carbon analog, phenylcyclohexane (nearly 100% of Ph_eq). And in contrast to 1-methyl-1-phenylcyclohexane, the conformers with the equatorial Ph group are predominant for compounds 3 and 4: at 103 K, Ph_eq/Ph_ax ratios are 63%:37% (3) and 68%:32% (4). As the Si–C bonds are elongated with respect to C–C bonds, the barriers to ring inversion are only between 5.2–6.0 (ax→eq) and 5.4–6.0 (eq→ax) kcal mol^?1. Parallel calculations at the DFT and MP2 level of theory (as well as the G2 calculations for compound 1) show qualitative agreement with the experiment. The additivity/nonadditivity of conformational energies of substituents on cyclohexane and silacyclohexane derivatives is analyzed. The geminally disubstituted cyclohexanes containing a phenyl group show large deviations from additivity, whereas in 1-methyl-1-phenyl-1-silacyclohexane and 3-methyl-3-phenyl-1,3-thiasilacyclohexane the effects of the methyl and phenyl groups are almost additive. The reasons for the different conformational preferences in carbocyclic and heterocyclic compounds are analyzed using the homodesmotic reactions approach.     

Conformational stability, r 0 structural parameters, barriers to internal rotation, ab initio calculations, and vibrational assignment for 2,2-difluoroethanol

The infrared spectra (4,000–30 cm^?1) of the gas and solid and the Raman spectrum of liquid 2,2-difluoroethanol as well as variable temperature infrared spectra of krypton/xenon solutions have been recorded. From all these data, two (Gg and Tg) out of the five possible stable conformers have been confidently identified. The order of the stabilities has been predicted to be Gg > Tg > Gt > Gg′ > Tt by utilizing ab initio MP2 (full) and DFT (B3LYP method) calculations, where the first indicator (capital letter) is in reference to rotation around the C–C bond (G = gauche or T = trans) and the second one (small letter) refers to the orientation of the hydroxyl group. The percentage of the minor conformer Tg, at ambient temperature, is estimated to be (16 ± 3%). The optimized geometries, fundamental frequencies, infrared intensities, Raman activities, and depolarization values as well as centrifugal distortion constants have been obtained from ab initio and density functional theory calculations by utilizing a variety of basis sets as well as those with diffuse functions. By utilizing the previously reported microwave rotational constants for two isotopomers of the Gg conformer combined with ab initio MP2(full)/6-311+G(d,p) predicted structural values, adjusted r ₀ parameters have been obtained. The determined heavy atom distances (Å) for the Gg conformer are: C₁–C₂ = 1.510(3), C₂–F₄ = 1.371(3), C₂–F₅ = 1.362(3), C₁–O₃ = 1.412(3) Å and angles ∠O₃C₁C₂ = 111.0(5), ∠F₄C₂C₁ = 108.8(5), ∠F₅C₂C₁ = 109.8(5), τF₄C₂C₁O₃ = 63.5(5), τF₅C₂C₁O₃ = 179.1(5)°. Barriers of internal rotation have been obtained and vibrational assignments for the Gg and Tg conformers are given. The five predicted centrifugal distortion constants compared to the experimental values are in reasonable agreement except for ?_K, which appears to be in error. The results are discussed and the structural parameters compared to the corresponding ones for 2-fluoroethanol and 2,2,2-trifluoroethanol where those for the latter molecule have been redetermined. The currently determined heavy atom parameters are quite different from the earlier assumed values, which led to poor values of the six adjusted parameters.     

Conformational preferences of RCH2CH2CN (R = CH3, F, Cl) cyanides and their corresponding isocyanides

The structure and relative stability of the different conformers of RCH₂CH₂CN (R = CH₃, F, Cl) cyanides and their corresponding isocyanides have been investigated through the use of high-level ab initio G4 theory as well as B3LYP/aug-cc-pVQZ and M06/aug-cc-pVQZ density functional theory calculations. This theoretical survey ratifies that the gauche conformer of butyronitrile is slightly more stable than the anti one, so that in the gas phase and at room temperature this compound should exist as a mixture of 57 % of the former and 43 % of the latter. Similar stability trends are predicted for the corresponding isocyanide isomer. Conversely, when the terminal methyl group of butyronitrile (or its isocyanide isomer) is replaced by F or Cl, the stability trends are reversed and the anti conformer becomes slightly more stable than the gauche one. These changes in relative stabilities could be traced through an analysis of the reduced density gradient which shows the existence of a stabilizing interaction between the terminal methyl group and the cyano (or isocyano) group in butyronitrile (or its isocyanide isomer), which becomes repulsive when this methyl group is replaced by F or Cl.     

Can the substituent in the para position of anilide ion influence the N−···H–F → N–H···F− switching: a quantum chemical study

The effect of substituents in the para position of anilide ion (An) on the N^?···H–F → N–H···F^? switching in X–An–HF (X = H, Me, CHO, CN, NO, F, NO₂, OH and OMe) complexes was investigated by means of B3LYP and MP2 quantum chemical methods. To delve into the mechanistic details of the proton transfer process, potential energy curve and further geometrical parameters involved in H-bonding during the course of the proton transfer process were evaluated at the MP2/6-311++G(2d,2p) level of theory. The changes in H-bond strength because of variation of substituents were well accompanied by changes in formation energy of complexes, structural parameter, electron density, natural charge and charge transfer between subunits. For X = H, Me, CHO, CN, NO, F and NO₂ substituents, our results at MP2/6-311++G(2d,2p) level showed that the minimum energy structures correspond to the N···HF H-bonded complexes without proton transfer occurring. On the other hand, for electron-donating substituents OH and OMe, proton is transferred from HF to anilide ion and the minimum energy structures are HNH···F^? H-bonded complexes. The nature of HN^?···HF and HN–H···F^? interactions in complexes was characterized by means of atoms in molecules and natural bond orbital analyses.