Excited state structural dynamics and Herzberg–Teller coupling of tetraphenylporphine explored via resonance Raman spectroscopy and density functional theory calculation

Resonance Raman spectra of free-base tetraphenylporphine (TPP) were obtained with 397.9, 416, and 435.7 nm excitation wavelengths and density functional calculations were done to elucidate the electronic transitions and the resonance Raman spectra (RRs) of TPP. The RRs indicate that the Franck–Condon region photodynamics for S₀ → S₄ electronic state is predominantly along the C_m–ph stretch while that for S₀ → S₃ electronic state is predominantly along the porphin ring C_βC_β stretch. Non-totally symmetric vibrational modes were regularly presented in resonance Raman spectra: the shorter the excitation wavelengths were, the stronger intensity the modes had, which can be interpreted in terms of electric dipole transition moments caused by Franck–Condon and Herzberg–Teller coupling.Four non-total symmetry vibrational mode υ_52, υ₆₄, υ₉₇ and υ₁₃₀ in A₂ irreducible representative of TPP were observed in 397.9, 416 and 435.7 nm resonance Raman spectrum. With the shorter wavelength laser excitations at 416 or 397.9 nm, the A₂ vibrational modes show more enhanced Raman intensity by comparison with those in the TPP spectrum excited at 435.7 nm.     

DFT and Raman spectroscopy of porphyrin derivatives: Tetraphenylporphine (TPP)

Raman spectrum of the meso tetraphenylporphine (TPP) deposited onto smooth copper surface as thin film were recorded in the region 200–1700 cm⁻¹. To investigate the effect of meso-phenyl substitution rings on the vibrational spectrum of free base porphyrin, we calculated Raman and infrared (IR) spectra of the meso-tetraphenylporphine (TPP), meso tetramethylporphine (TMP), copper (II)porphine (CuPr) and free base porphine (FBP) at the B3LYP/6-311+G(d,p) level of the density functional theory (DFT). The observed Raman spectrum of the TPP is assigned based on the calculated its Raman spectrum in connection with the calculated spectra of the TMP, CuPr and FBP by taking into account of their corresponding vibrational motions of the Raman modes of frequencies. Results of the calculations clearly indicated that the meso tetraphenyl substitution rings are totally responsible for the observed Raman bands at ∼1593, 1234 and 1002 cm⁻¹. The calculated and observed Raman spectra also suggested that the observed Raman band with a medium intense at 962 cm⁻¹ might result from the surface plasmon effect. Furthermore, the observed Raman bands with medium intense at ∼334 and ∼201 cm⁻¹ are as results of the dimerization or aggregation of the TPP or would be that related to intramolecular interaction. We also calculated IR spectra of these molecules at same level of the theory. To investigate the solvent effect on the vibrational spectrum of porphine, the Raman and IR spectra of the TPP and FBP are calculated in solution phase where water used as solvent. The results of these calculation indicated that there is no any significant effect on the vibrational spectrum of the TPP.     

Vibrational and electronic properties of single-walled and double-walled boron nitride nanotubes

We calculated IR, nonresonance Raman spectra and vertical electronic transitions of the zigzag single-walled and double-walled boron nitride nanotubes ((0,n)-SWBNNTs and (0,n)@(0,2n)-DWBNNTs). In the low frequency range below 600 cm⁻¹, the calculated Raman spectra of the nanotubes showed that RBMs (radial breathing modes) are strongly diameter-dependent, and in addition the RBMs of the DWBNNTs are blue-shifted reference to their corresponding one in the Raman spectra of the isolated (0,n)-SWBNNTs. In the high frequency range above ∼1200 cm⁻¹, two proximate Raman features with symmetries of the A_1g (∼1355 ± 10 cm⁻¹) and E_2g (∼1330 ± 25 cm⁻¹) first increase in frequency then approach a constant value of ∼1365 and ∼1356 cm⁻¹, respectively, with increasing tubes’ diameter, which is in excellent agreement with experimental observations. The calculated IR spectra exhibited IR features in the range of 1200–1550 cm⁻¹ and in mid-frequency region are consistent with experiments. The calculated dipole allowed singlet–singlet and triplet–triplet electronic transitions suggesting a charge transfer process between the outer- and inner-shells of the DWBNNTs as well as, upon irradiation, the possibility of a system that can undergo internal conversion (IC) and intersystem crossing (ISC) processes, besides the photochemical and other photophysical processes.     

Gamma ray induced changes on vibrational spectroscopic properties of strontium alumino-borosilicate glasses

The present investigation reports the effect of influence of aluminum ions on radiation damage of strontium borosilicate glasses studied by means of spectroscopic (viz., optical absorption (OA), infrared and Raman spectra). The composition of the glasses chosen for the study is 40SrO–xAl₂O₃–(15-x) B₂O₃–40SiO₂ (x = 5, 7.5, 10), all in mol%. The glasses were synthesized by conventional melt quenching method. Later, the samples were exposed to gamma (γ) radiation dose of strengths 10 kGy and 30 kGy with a dose rate of 1.5 Gy/s using ⁶⁰Co as radiation source. The infrared spectra (IR), Raman spectra and optical absorption (OA) spectra of the samples were recorded at ambient temperature before and after irradiation. The OA spectra of the pre-irradiated samples do not exhibit any absorption bands in the UV–vis regions and IR and Raman spectra exhibited conventional vibrational bands due to different borate, silicate AlO₄ and AlO₆ structural units. The OA spectra of post irradiated samples exhibited a broad absorption band in the wavelength region 600–750 nm; it is attributed to electron trapped color centers. The intensity of this peak is observed to increase with increase of the γ-ray dose. Considerable changes in the intensities of various bands in the IR and Raman spectra were also observed. The changes were explained based on structural modifications taking place in the glass network due to γ-ray irradiation and finally it is concluded that the glasses mixed with 10.0 mol% of Al₂O₃ are relatively more radiation resistant.     

Vibrational spectra and structure of mixed alkali borotungstate glasses: Evidence of mixed alkali effect

Mixed alkali borotungstate glasses with xLi₂O–(30 − x)Na₂O–10WO₃–60B₂O₃ (0 ≤ x ≤ 30) composition were prepared by melt quench technique. FT-IR and Raman spectroscopic studies were employed to investigate the structure of all the prepared glasses. Acting as complementary techniques, both IR and Raman measurements revealed that the network structure of the present glasses mainly based on BO₃ and BO₄ units placed in different structural groups. Raman spectra confirm the IR results regarding the presence of tungsten ions mainly as WO₆ groups. In the present work, the mixed alkali effect (MAE) has been investigated in the above glass system using FTIR and Raman studies.     

Glass transition behaviour of ionic liquid, 1-butyl-3-methylimidazolium tetrafluoroborate–H2O mixed solutions

Here, we have measured the glass transition temperature (T_g) of the ionic liquid, 1-butyl-3-methylimidazolium tetrafluoroborate–H₂O mixed solutions as a function of H₂O concentration (x mol% H₂O). The glass-forming composition region was also determined. Contrary to the results of the quaternary ammonium type of ionic liquid, N,N-diethyl-N-methyl-N-(2-methoxyethyl) ammonium tetrafluoroborate–H₂O mixed solutions, we did not observed the multiple glass transition behaviour. We also measured the glassy Raman spectra of the solutions at T = 77 K. We find that the “nearly free” hydrogen bonded Raman band of water molecules in the aqueous [bmim][BF₄] solution exists up to around x = 60 mol% H₂O, even at T = 77 K.     

Electronic structure and Raman spectroscopy study of dibarium magnesium orthoborate,Ba2Mg(BO3)2

The samples of dibarium magnesium orthoborate Ba₂Mg(BO₃)₂ were synthesized by solid-state reaction. The X-ray diffraction (XRD) patterns and Raman spectra of the samples were collected. Electronic structure and vibrational spectroscopy of Ba₂Mg(BO₃)₂ were systematically investigated by first principle calculation. A direct band gap of 4.4 eV was obtained from the calculated electronic structure results. The top valence band is constructed from O 2p states and the low conduction band mainly consists of Ba 5d states. Raman spectra for Ba₂Mg(BO₃)₂ polycrystalline were obtained at ambient temperature. The factor group analysis results show the total lattice modes are 5E_u + 4A_2u + 5E_g + 4A_1g + 1A_2g + 1A_1u, of which 5E_g + 4A_1g are Raman-active. Furthermore, we obtained the Raman active vibrational modes as well as their eigenfrequencies using first-principle calculation. With the assistance of the first-principle calculation and factor group analysis results, Raman bands of Ba₂Mg(BO₃)₂ were assigned as E_g (42 cm⁻¹), A_1g (85 cm⁻¹), E_g (156 cm⁻¹), E_g (237 cm⁻¹), A_1g (286 cm⁻¹), E_g (564 cm⁻¹), A_1g (761 cm⁻¹), A_1g (909 cm⁻¹), E_g (1165 cm⁻¹). The strongest band at 928 cm⁻¹ in the experimental spectrum is assigned to totally symmetric stretching mode of the BO₃ units.     

Raman spectra of carriers in ionic-liquid-gated transistors fabricated with poly(2,5-bis(3-tetradecylthiophen-2-yl)thieno[3,2-b]thiophene)

We observed the Raman spectra of carriers, positive polarons and bipolarons, generated in a poly(2,5-bis(3-tetradecylthiophen-2-yl)thieno[3,2-b]thiophene) (PBTTT-C14) film by FeCl₃ vapor doping. Electrical conductivity and Raman measurements indicate that the dominant carriers in the conducting state were bipolarons. We identified positive polarons and bipolarons generated in an ionic-liquid-gated transistor (ILGT) fabricated with PBTTT-C14 as an active semiconductor and an ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide [BMIM][TFSI] as a gate dielectric using Raman spectroscopy. The relationship between the source−drain current (I_D) at a constant source−drain voltage (V_D) and the gate voltage (V_G) was measured. I_D increased above −V_G = 1.1 V and showed a maximum at −V_G = 2.0 V. Positive polarons were formed at the initial stage of electrochemical doping (−V_G = 0.8 V). As I_D increased, positive bipolarons were formed. Above V_G = −2.0 V, bipolarons were dominant. The charge density (n), the doping level (x), and the mobility of the bipolarons were calculated from the electrochemical measurements. The highest mobility (μ) of bipolarons was 0.72 cm² V⁻¹ s⁻¹ at x = 110 mol%/repeating unit (−V_G = 2.0 V), whereas the highest μ of polarons was 4.6 × 10⁻⁴ cm² V⁻¹ s⁻¹ at x = 10 mol%.     

Different level of fluorescence in Raman spectra of montmorillonites

The paper presents the study of selected montmorillonite standards by Raman spectroscopy and microscopy supported by elemental analysis, X-ray powder diffraction analysis and thermal analysis. Dispersive Raman spectroscopy with excitation lasers of 532 nm and 780 nm, dispersive Raman microscopy with excitation laser of 532 nm and 100× magnifying lens, and Fourier Transform-Raman spectroscopy with excitation laser of 1064 nm were used for the analysis of four montmorillonites (Kunipia-F, SWy-2, STx-1b and SAz-2). These mineral standards differed mainly in the type of interlayer cation and substitution of octahedral aluminium by magnesium or iron. A comparison of measured Raman spectra of montmorillonite with regard to their level of fluorescence and the presence of characteristic spectral bands was carried out. Almost all measured spectra of montmorillonites were significantly affected by fluorescence and only one sample was influenced by fluorescence slightly or not at all. In the spectra of tested montmorillonites, several characteristic Raman bands were found. The most intensive band at 96 cm⁻¹ belongs to deformation vibrations of interlayer cations. The band at 200 cm⁻¹ corresponds to deformation vibrations of the AlO₆ octahedron and at 710 cm⁻¹ can be assigned to deformation vibrations of the SiO₄ tetrahedron. The band at 3620 cm⁻¹ corresponds to the stretching vibration of structural OH groups in montmorillonites.     

A Raman spectroscopic study of the antimonite mineral peretaite Ca(SbO)4(OH)2(SO4)2·2H2O

Raman spectra of mineral peretaite Ca(SbO)₄(OH)₂(SO₄)₂·2H₂O were studied, and related to the structure of the mineral. Raman bands observed at 978 and 980 cm^?1 and a series of overlapping bands observed at 1060, 1092, 1115, 1142 and 1152 cm^?1 are assigned to the SO₄^2? ν₁ symmetric and ν₃ antisymmetric stretching modes. Raman bands at 589 and 595 cm^?1 are attributed to the SbO symmetric stretching vibrations. The low intensity Raman bands at 650 and 710 cm^?1 may be attributed to SbO antisymmetric stretching modes. Raman bands at 610 cm^?1 and at 417, 434 and 482 cm^?1 are assigned to the SO₄^2? ν₄ and ν₂ bending modes, respectively. Raman bands at 337 and 373 cm^?1 are assigned to O–Sb–O bending modes. Multiple Raman bands for both SO₄^2? and SbO stretching vibrations support the concept of the non-equivalence of these units in the peretaite structure.     

In-plane chemical pressure in (U1−yCey)O2 studied by Raman spectroscopy

We investigate the nature of bonding and charge states in (U_1−yCe_y)O₂ (y = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) by Raman spectroscopy. Raman spectrum of UO₂ exhibits two prominent bands below 1000 cm⁻¹, a F_2g mode at 446 cm⁻¹ and a F_1u LO mode at 578 cm⁻¹. As y is increased from 0 to 0.6, the F_1u exhibits a large blue shift of 90 cm⁻¹, and from y = 0.6 to 1.0, a red shift of 54 cm⁻¹. We show that our results can be interpreted as arising from anisotropic compression/relaxation of the lattice under Ce substitution and this can give an indication of its charge states. Alternate interpretations have been given in the literature on the effect of substituents and dopants to the Raman spectra of UO₂ and CeO₂. The present interpretation of chemical stress effects can be taken as another plausible explanation.     

A Raman scattering study of structural changes in LaMn1−xCoxO3+δ system

We present results of Raman scattering studies on LaMn_1−xCo_xO_3+δ over a wide range of doping content (x = 0.1–0.75) and temperature range of 20–300 K. Powder X-ray diffraction patterns show that there is a structural change from orthorhombic to rhombohedral at x = 0.5 as x increases. Raman spectra of all LaMn_1−xCo_xO_3+δ samples show peaks near 260, 500, and 650 cm⁻¹. However, the Raman spectra are not drastically different from each other across the structural phase transition at x = 0.5. On the other hand, the peak frequencies of the modes near 260 and 500 cm⁻¹ as functions of Co content (x) show slope changes at x = 0.5. The full-width at the half-maximum (FWHM) of the mode near 650 cm⁻¹ as a function of Co content (x) shows minimum at x = 0.5. Normally, larger values of FWHM are expected at near x = 0.5, if the mode were affected by the structural disorder at the phase boundary. Therefore, it is likely due to lowest charge concentration at x = 0.5, which results in lowest screening effect. This is consistent with the fact that the intensity of the phonons is strongest at x = 0.5. As the temperature decreases, the two peaks near 500 and 650 cm⁻¹ of different Co contents, related with octahedral distortions, are found to shift to lower frequencies unlike the usual temperature behavior. However, no abrupt change in the peak frequencies and the FWHM is observed across measured temperature range, regardless of the Co content.     

High-pressure Raman scattering of MgMoO4

In this paper, we present results of high-pressure Raman scattering studies in β-MgMoO₄ from atmospheric to 8.5 GPa. The experiments were carried out using methanol–ethanol as pressure medium. By analyzing the pressure dependence of the Raman data (change in the number of lattice modes, splitting of bands and wavenumber discontinuities) we were able to observe a phase transition undergone by the β-MgMoO₄ at 1.4 GPa, which is only completed at ∼5 GPa. The transition was observed to be irreversible and the modifications in the Raman spectra were attributed to the changes in coordination of Mo ions from tetrahedral to octahedral. The transition possibly changes the original C2/m symmetry to C2/m or to P2/c. Implication on the phase transition for similar molybdate structures, such as α-MnMoO₄, is also highlighted.     

Vibrational spectroscopic study of syngenite formed during the treatment of liquid manure with sulphuric acid

Syngenite (K₂Ca(SO₄)₂·H₂O), formed during treatment of manure with sulphuric acid, was studied by infrared, near-infrared (NIR) and Raman spectroscopy. C_s site symmetry was determined for the two sulphate groups in syngenite (P2₁/m), so all bands are both infrared and Raman active. The split ν₁ (two Raman+two infrared bands) was observed at 981 and 1000 cm⁻¹. The split ν₂ (four Raman+four infrared bands) was observed in the Raman spectrum at 424, 441, 471 and 491 cm⁻¹. In the infrared spectrum, only one band was observed at 439 cm⁻¹. From the split ν₃ (six Raman+six infrared) bands three 298 K Raman bands were observed at 1117, 1138 and 1166 cm⁻¹. Cooling to 77 K resulted in four bands at 1119, 1136, 1144 and 1167 cm⁻¹. In the infrared spectrum, five bands were observed at 1110, 1125, 1136, 1148 and 1193 cm⁻¹. From the split ν₄ (six infrared+six Raman bands) four bands were observed in the infrared spectrum at 604, 617, 644 and 657 cm⁻¹. The 298 K Raman spectrum showed one band at 641 cm⁻¹, while at 77 K four bands were observed at 607, 621, 634 and 643 cm⁻¹. Crystal water is observed in the infrared spectrum by the OH-liberation mode at 754 cm⁻¹, OH-bending mode at 1631 cm⁻¹, OH-stretching modes at 3248 (symmetric) and 3377 cm⁻¹ (antisymmetric) and a combination band at 3510 cm⁻¹ of the H-bonded OH-mode plus the OH-stretching mode. The near-infrared spectrum gave information about the crystal water resulting in overtone and combination bands of OH-liberation, OH-bending and OH-stretching modes.     

Raman spectroscopic study of CuO–V2O5–P2O5–CaO glass system

In order to evidence the structural changes induced by CuO and V₂O₅ in the phosphate glass network and their modifier or former role, x(CuO·V₂O₅)(100 − x)[P₂O₅·CaO] glass system was prepared and investigated using Raman spectroscopy (0 ≤ x ≤ 40 mol%).Raman spectra of the studied glasses present the specific bands of the phosphate glasses at low concentration of transition metal (TM) ions, but at higher concentration (x > 7 mol%) a strong depolymerization of the phosphate network appears; non-bridging oxygen atoms are involved in VOP and CuOP bonds and new short units are formed. For a high concentration of V₂O₅ (x > 10 mol%) the Raman bands of V₂O₅ prevail in the spectra; this fact suggests that vanadium oxide imposes its structural units in the network acting thus as a network glass former.2D correlation analysis was also applied for the concentration-dependent Raman spectra in order to verify the assignments of the vibration modes and to find correlations in the changes induced by TM ions content. 2D correlation maps indicate a good correlation between the bands at ∼705 cm⁻¹ assigned to POP stretching vibration and at ∼1175 cm⁻¹ assigned to PO₂ groups which suggest the depolymerization of the phosphate network. The correlation between the 1270 cm⁻¹ and 930 cm⁻¹ bands also suggests that V₂O₅ oxide is responsible for PO bonds breaking and POV formation.     

Structures and spectroscopic properties of meso-tetrasubstituted porphyrin complexes: Meso-substitutional and central metallic effect study based on density functional theory calculations

Effects of the meso-substituents and central metals on the molecular structures, atomic charges, molecular orbital energy gaps, electronic absorption spectra, and infrared (IR) spectra of 12 meso-tetrasubstituted porphyrin complexes including metal-free porphyrins H₂P or (Por = TPP, TFPP, TClPP, TPyP) (1–4) and their metal complexes MPor (M = Mg, Zn; Por = TPP, TFPP, TClPP, TPyP) (5–12) [TPP = meso-tetrakis(phenyl)porphyrinate; TFPP = meso-tetrakis(4-fluorophenyl)porphyrinate; TClPP = meso-tetrakis(4-chlorophenyl)porphyrinate; TPyP = meso-tetrakis(4-pyridyl) porphyrinate] are systematically studied by density functional theory calculations at the B3LYP/6-31G(d) level. Good consistency was found between the calculated molecular structures and the experimental X-ray crystallography ones for 1, 3, and 4, and between the simulated electronic absorption and IR spectra and the experimental ones for 1 and 4. The calculation results reveal that introducing substituents at the meso positions of porphyrin induces increasing change in the molecular structures, atomic charges distribution, HOMO and LUMO energy, electronic absorption spectra, and IR spectra along with the increase in the electron-withdrawing ability of substituents in the order of phenyl, 4-fluorophenyl, 4-chlorophenyl, and pyridyl group. Furthermore, the central metal in porphyrins displays much significant influence on the structure and spectroscopic properties of meso-substituted porphyrin complexes. The electronic absorption and IR spectra of 1–12 are compared and assigned in detail. The present work should be not only helpful towards understanding the meso-substitutional and central metallic effects on the structure and spectroscopic properties of meso-substituted porphyrin complexes, but also useful in correctly assigning electronic absorption and IR spectra for porphyrin complexes.     

Raman study on pentacene:C60 bulk heterojunction films

We measured 785 nm excited Raman and infrared spectra of pentacene-d₁₄. The observed spectra were assigned on the basis of the Raman and infrared spectra calculated by the density functional theory (DFT) method at the B3LYP/6⬜311 + G** level. We measured 785 nm excited Raman spectrum of a pentacne-d₁₄:C₆₀ bulk heterojunction film. The spectrum was assigned on the basis of the wavenumber shifts upon deuteration of pentacene. The assignments of the 1462 and 493 cm^↙1 A_g bands of C₆₀ were confirmed. The 511, 453, and 256 cm^↙1 bands, which were observed only in pentacene:C₆₀ bulk heterojunction films, did not show large deuteration shifts. This result indicates that the 511, 453, and 256 cm^↙1 bands are attributed to activation of the silent modes of C₆₀ due to symmetry lowering_.     

Characterization of a new magnesium hydrogen orthophosphate salt,Mg3.5H2(PO4)3, synthesized in supercritical water

Beige crystals of a new magnesium hydrogen orthophosphate salt, Mg_3.5H₂(PO₄)₃, as well as nanoparticles of an amorphous, non-Mg-containing phosphate material, Fe_1−yK_yPO₄ (0 < y < 1), have been produced by hydrothermal reactions in supercritical water (SCW) of equivalent quantities of aqueous MgCl₂·6H₂O (2 M), and K₄P₂O₇ (1 M) in concentrated HCl in a stainless-steel batch reactor at 400–450 °C and 25–32 MPa. The new salt has been characterized by single-crystal X-ray diffraction and IR and Raman spectroscopies. It crystallizes in the triclinic space group Pī, Z = 2 with the following unit-cell parameters: a = 6.438(1), b = 7.856(1), c = 9.438(1) Å; α = 104.57(1), β = 108.61(1), γ = 101.28(1)°, V = 739.99 Å³. The effects of the SCW conditions on the nature of the products and their yields and morphologies have been studied by IR and Raman spectroscopies, X-ray powder diffraction, X-ray energy dispersive analysis, scanning electron microscopy, transmission electron microscopy and inductively coupled plasma analysis.     

Investigation of the phonon band gap effect on Raman-active optical phonons in SrMoO4 crystal

The phonon dispersions of SrMoO₄ crystal are calculated using the lattice dynamical calculations approach. Spontaneous Raman spectra in the SrMoO₄ were measured in the temperature range from 10 K to 295 K, and the temperature dependence of the linewidth of the B_g (95 cm⁻¹) and A_g (888 cm⁻¹) Raman modes was analyzed using the lattice dynamical perturbative approach. We found that different behaviors of these two modes in the case of temperature broadening could be attributed to the large energy band gap in the phonon spectrum resulting in different anharmonic interactions. The calculated temperature dependence of the linewidth of A_g (888 cm⁻¹) mode was well accounted for the experimental one by including both down-conversion by the cubic term and the dephasing by quartic term. The dephasing processes are increased only at high temperatures and the effect of dephasing is related to the size of a large phonon band gap.     

Study of the stability of 5,10,15,20-tetraphenylporphine (TPP) and metalloporphyrins NiTPP,CoTPP, CuTPP,and ZnTPP by differential scanning calorimetry and thermogravimetry

In this work, the stability of 5,10,15,20-tetraphenylporphine (TPP) and its metallic derivatives, NiTPP, CoTPP, CuTPP, and ZnTPP has been studied through differential scanning calorimetry and thermogravimetry. The decomposition temperatures are (712, 710, 708, 702, and 671) K for NiTPP, CoTPP, CuTPP, ZnTPP, and TPP, respectively. These values are in correspondence with the N–M bond length d_M–N, of the metalloporphyrins. The corresponding molar enthalpies of melting Δ_fusH_m, were determined as (58, 57, 55, 52, and 44) kJ · mol^?1 for the same series. These values are discussed in terms of the crystallographic features in the solid state.