Heterocyclic thioamide derivatives of coinage metals (Cu, Ag): Synthesis, structures and spectroscopy

Heterocyclic thioamides, namely, imidazolidine-2-thione (imdzSH), 1-methyl-1, 3-imidazoline-2-thione (mimzSH), thiazolidine-2-thione (tzdSH) and 2,4-dithiouracil (dtucH₂) with silver(I)/copper(I) salts in presence of triphenyl phosphine (PPh₃) have yielded complexes of different nuclearity: mononuclear, [Ag(η¹-S-HL)(PPh₃)₂Cl] (HL = imdzSH 1, mimzSH 2, tzdSH 3), dinuclear, [Ag₂(η¹-S-tzdSH)₂(μ-S-tzdSH)₂(PPh₃)₂](NO₃)₂4, and polynuclear, {Cu(μ-S,S-dtucH₂)(PPh₃)₂X} (X = Cl 5, Br 6, I 7). All complexes have been characterized using analytical data, IR and multinuclear NMR spectroscopy (¹H, ¹³C and ³¹P) and single crystal X-ray crystallography. The thio-ligands are bonded to the metal centers as neutral sulfur donors. The geometry around each metal center is distorted tetrahedral. Complexes 5-7 represent first examples of polymers of 2,4-dithiouracil in its coordination chemistry with metal salts. The hydrogen bonding interactions lead to the formation of 1D (2, 3, 7) and 2D (1, 4-6) sheet structures.     

Studies in the sphingolipids series,XXXII : Synthesis and resolution into optical antipodes of C20-phytosphingosine

C₂₀-Phytosphingosine, D(+)-ribo-2-amino-1, 3, 4-trihydroxyeicosane (8a), is synthesized through the following intermediates: 2-Methoxyoctadecanoic acid chloride (1)→Ethyl 2-methoxyoctadecanoylacetoacetate (2)→Ethyl (2-p-nitrophenylhydrazono)-2,3-dioxo-4-methoxyeicosanoate (3)→Ethyl 2-acetamido-3-oxo-4-methoxyeicosanoate (4)→Ethyl 2-acetamido-3-hydroxy-4-methoxyeicosanoate (5)→2-Acetamido-3-hydroxy-4-methoxyeicosanoic acid (6), 2-Amino-3-hydroxyeicosanoic acid 1,4-lactone hydrobromide (7a, b)→DL-ribo (8a) and DL-xylo(?)-2-amino-1,3,4-trihydroxyeicosane (8b). The resolution of the racemic base (8a) has been effected through its salts with D-tartaric acid.     

The phenyl - and -L-idopyranosiduronic acids and some other aryl glycopyranosiduronic acids

Condensation of 1,2,3,4,6-penta-O-acetyl-á-l-idopyranose (1) with phenol yielded phenyl 2,3,4,6-tetra-O-acetyl-α- (2) and α-l-idopyranoside (4). Deacetylation of 2 and 4 afforded phenyl α and β-l-idopyranosides (3 and 5), respectively, the structures of which were verified by periodate oxidation studies. A platinum-catalyzed oxidation of 3 and 5 produced the amorphous phenyl α- and β-L-idopyranosiduronic acids (9 and 11), respectively, which were isolated as the crystalline cyclohexylammonium salts. Phenyl β- and α-d-glucopyranosiduronic acids are apparent minor byproducts of the catalytic oxidations, resulting from an inversion at C-5. _p-Nitrophenyl α-d-mannopyranosiduronic acid and _p-nitrophenyl α- and β-d-galactopyranosiduronic acids are also described.     

Synthesis, structures and spectroscopic properties of platinum(II), copper(I) and zinc(II) complexes bearing 4-(p-dimethylaminophenyl)-6-phenyl-2,2′-bipyridine ligand

The reactions of 4-(p-dimethylaminophenyl)-6-phenyl-2,2′-bipyridine (HL) with three metal salts of platinum(II), copper(I) and zinc(II) provide the new complexes [Pt(L)(PPh₃)]ClO₄ (1), [Cu(HL)₂]BF₄ (2), [Cu(HL)(PPh₃)]BF₄ (3) and [Zn(HL)₂](ClO₄)₂ (4). All the structures of these four complexes have been characterized by single crystal X-ray diffraction, and their spectroscopic properties were investigated. Especially for complex 1, upon protonation, the excited state can be tuned from the intraligand charge transfer (ILCT) to the metal-to-ligand charge transfer (MLCT), and such switching in the excited state is acid/base reversible. The time-dependent density functional theory (TD-DFT) calculation was used to interpret the absorption spectra of complex 1, and the calculated result is consistent with those of experiments results. In contrast with 1, the lowest energy absorption at 410-650 nm of complexes 2 and 3 can be assigned to MLCT excited state. In solid state or solution complex 4 exhibits intense photoluminescence attributed to a ILCT transition in nature.     

Silver coordination complexes of 2-(diphenylphosphinomethyl)pyridine and their bipyridine derivatives

Reaction of 2-(diphenylphosphinomethyl)pyridine (PMP-21) with the silver(I) salts of tetrafluoroborate , triflate (Otf⁻), and trifluoroacetate (tfa⁻) affords dinuclear complexes (2-4), where the ligand bridges the two silver centers, and the anions interact with the metal centers to varying degrees. Further reaction of AgBF₄ and AgOtf with reaction solutions containing PMP-21 and either the bidentate 5,5′-dimethyl-2,2′-bipyridine or 4,4′-bipyridine ligands produce dimeric and bridged structural motifs. The ability of 5,5′-dimethyl-2,2′-bipyridine to chelate and the 4,4′-bipyridine to serve as a connector between metal centers, allows the construction of coordinative structures where the effect of ligand ratio and either interacting or non interacting anions influence the silver coordination environment, allowing it to take on several geometries including trigonal bipyramidal, 5, both T-shaped and tetrahedral in a single structure, 6 and 8, trigonal pyramidal, 7, and trigonal planar, 9. Structures 2, 3, and 4 display comparable Ag-Ag contacts ranging from 2.7979(10) to 3.0538(4) Å, with a corresponding weakening of the metallophilic interaction when a bipyridine ligand is coordinated. Low-temperature luminescence spectra were collected for all compounds and are compared.     

Exploring the chelating potential of 1,3-bis(furyl)-1,1,3,3-tetramethyldisilazides

A range of furyl-substituted silylamides of the group 1 metals have been isolated and structurally characterized. The lithium salts of the neutral compounds (RMe₂Si)₂NH [1H, R = furyl; 2H, R = 2-methylfuryl; 3H, R = 2-trimethylsilylfuryl] are formed directly in a one-pot reaction between the chloraminosilane, (ClMe₂Si)₂NH and three equivalents of the appropriate furyl lithium species. Conversion of the Li-salts to the neutral compounds 1H and 2H by quenching with NH₄Cl, and reaction of the unpurified products with KNH₂ afforded the corresponding potassium salts K{1} and K{2}. The crystal structures of [Li{2}]₂, [Li{3}]₂(THF), [K{1}(toluene)]₂ and [K{2}(toluene)]₂ have been determined, in which, as predicted, the ability of the furyl group to coordinate to the metal is related to the size of the substituent in the 2-position.     

Dopamine release and molecular modeling study of some coumarin derivatives

4-aryl-2-amino-6-(4-hydroxy-2-oxo-2H-chromen-3-yl)-pyridin-3-carbonitrile (1), 4-aryl-2-oxo-6-(4-hydroxy-2-oxo-2H-chromen-3-yl)-pyridin-3-carbonitriles (2a-2c), 3-(6-aryl-1,2,5,6- tetrahydro-2-thioxopyrimidin-4-yl)-4-hydroxy-2H-chromen-2-one (3a, 3b) and pyrazol-3-yl-4-hydroxycoumarin derivatives (4a-4c, 5, 6a, 6b, 7a, 7b, and 8a-8c) were prepared in order to measure their % change dopamine release in comparison to amphetamine as reference, using PC-12 cells in different concentrations. In addition, the molecular modeling study of the compounds into 3BHH receptor was also demonstrated. The calculated inhibition constant (k_i) implemented in the AutoDock program revealed identical correlation with the experimental results to that obtained binding free energy (ΔG_b) as both parameters revealed reasonable correlation coefficients (R²) being 0.51 involving 10 compounds; (1, 2b, 2c, 3a, 3b, 4a, 4b, 6a, and 8c).     

Synthesis, in vitro antimalarial and cytotoxicity of artemisinin-aminoquinoline hybrids

Dihydroartemisinin (DHA) was coupled to different aminoquinoline moieties forming hybrids 9-14, which were then treated with oxalic acid to form oxalate salts (9a-14a). Compounds 9a, 10a, 12, 12a, and 14a showed comparable potency in vitro to that of chloroquine (CQ) against the chloroquine sensitive (CQS) strain, and were found to be more potent against the chloroquine resistant CQR strain. Hybrids 12 and its oxalate salt 12a were the most active against CQR strain, being 9- and 7-fold more active than CQ, respectively (17.12 nM; 20.76 nM vs 157.9 nM). An optimum chain length was identified having 2 or 3 Cs with or without an extra methylene substituent.     

Synthesis and characterization of nickel and palladium complexes containing hetero-multidentate PNO ligands

Formation of mono- and dinuclear complexes containing ligands stemmed from the condensation of 2,6-diformyl-4-methylphenol derivatives with 2-(diphenylphosphino)aniline (P∼N) was investigated. Condensation of P∼N with 2,6-diformyl-4-methylanisole yielded the desired bis(imine-phosphine) L₃, but provided the cyclized benzoazaphospholium compound with 2,6-diformyl-4-methylphenol. Complexation of L₃ with (COD)PdCl₂ gave the dinuclear complex 4. On the other hand, L₃ underwent the intramolecular cyclization in the presence of (DME)NiCl₂ via the formation of benzoazaphospholium rings. Template condensation of 2,6-diformyl-4-methylphenol with P∼N in the presence of metal ions yielded the mononuclear nickel(II) and palladium(II) complexes, respectively.     

Addition of secondary amines to activated alkenes promoted by Pd(II) complexes: Use of ammonium salts as cocatalysts

The complexes [Pd(acac)₂] 1, [Pd(hfa)₂] 2 (hfa = hexafluoroacetylacetonate), [Pd(CF₃CO₂)₂] 3 and [Pd₃(CH₃CO₂)₆] 4 exhibit very different catalytic efficiency in the reaction between secondary amines and activated alkenes. Complexes 1 and 4 generally show an enhanced activity when catalytic amounts of NH₄X salts (X⁻ = low-coordinating anion) are added to the reaction mixtures. On the contrary, the activity of the perfluorurate analogues 2 and 3, which is much higher than that of 1 and 4, is generally scarcely affected by the presence of the NH₄X additive. The cocatalytic effect of NH₄X is comparable with that of strong acids such as CF₃SO₃H. The ammonium salts alone can behave as a catalyst giving an almost quantitative yield of the hydroamination product.     

Unusual reactivity of copper(I) complexes of functionalised calix[4]arenes

Two functionalised calix[4]arenes, 5,11,17,23-tetra-tert-butyl-25,27-bis(2-pyridylmethoxy)calix[4]arene (L¹) and 5,11,17,23-tetra-tert-butyl-25,27-bis(2-pyridylmethoxy)-26,28-dibutoxycalix[4]arene (L³), were prepared and characterised. The copper(I) complexes of both calix[4]arenes were synthesised and their reactivities were analysed and compared. The presence of the metal induced a radical in the case of L¹ whereas no such radical was observed in the metal complex of ligand L³.     

(Pyrazolylmethyl)pyridine platinum(II) and gold(III) complexes: Synthesis, structures and evaluation as anticancer agents

Reactions of 2-(3,5-dimethylpyrazol-1-ylmethyl)pyridine (L1), 2-(3,5-diphenylpyrazol-1-ylmethyl)pyridine (L2), 2-(3,5-di-tert-butylpyrazol-1-ylmethyl)pyridine (L3) and 2-(3-p-tolylpyrazol-1-ylmethyl)pyridine (L4) with K₂[PtCl₄] in a mixture of ethanol and water formed the dichloro platinum complexes [PtCl₂(L1)] (1), [PtCl₂(L2)] (2), [PtCl₂(L3)] (3) and [PtCl₂(L4)] (4). Complex 1, [PtCl₂(L1)], could also be prepared in a mixture of acetone and water. Performing the reactions of L2 and L3 in a mixture of acetone and water, however, led to C-H activation of acetone under mild conditions to form the neutral acetonyl complexes [Pt(CH₂COCH₃)Cl(L2)] (2a) and [Pt(CH₂COCH₃)Cl(L3)] (3a). The same ligands reacted with HAuCl₄ · 4H₂O in a mixture of ethanol and water to form the gold salts [AuCl₂(L1)][AuCl₄] (5) [AuCl₂(L2)][Cl] (6) [AuCl₂(L3)][Cl] (7) and [AuCl₂(L4)][AuCl₄] (8); however, with the pyrazolyl unit in the para position of the pyridinyl ring in 4-(3,5-dimethylpyrazol-1-ylmethyl)pyridine (L5), 4-(3,5-diphenylpyrazol-1-ylmethyl)pyridine (L6) neutral gold complexes [AuCl₃(L5)] (9) and [AuCl₂(L6)] (10) were formed; signifying the role the position of the pyrazolyl group plays in product formation in the gold reactions. X-ray crystallographic structural determination of L6, 2, 33a, 8 and 10 were very important in confirming the structures of these compounds; particularly for 3a and 8 where the presence of the acetonyl group confirmed C-H activation and for 8 where the counter ion is . Cytotoxicity studies of L2, L4 and complexes 1-10 against HeLa cells showed the Au complexes were much less active than the Pt complexes.     

Non-cannabinoid constituents from a high potency Cannabis sativa variety

Six new non-cannabinoid constituents were isolated from a high potency Cannabis sativa L. variety, namely 5-acetoxy-6-geranyl-3-n-pentyl-1,4-benzoquinone (1), 4,5-dihydroxy-2,3,6-trimethoxy-9,10-dihydrophenanthrene (2), 4-hydroxy-2,3,6,7-tetramethoxy-9,10-dihydrophenanthrene (3), 4,7-dimethoxy-1,2,5-trihydroxyphenanthrene (4), cannflavin C (5) and β-sitosteryl-3-O-β-d-glucopyranoside-2′-O-palmitate (6). In addition, five known compounds, α-cannabispiranol (7), chrysoeriol (8), 6-prenylapigenin (9), cannflavin A (10) and β-acetyl cannabispiranol (11) were identified, with 8 and 9 being reported for the first time from cannabis. Some isolates displayed weak to strong antimicrobial, antileishmanial, antimalarial and anti-oxidant activities. Compounds 2-4 were inactive as analgesics.     

X-ray powder and single crystal structures of two unprecedented families of bpca-based 1-D magnetic chains (Hbpca = bis(2-pyridylcarbonyl)amine)

Two unprecedented families of bpca-based mono-dimensional complexes Cu(bpca)(X) (X = CN, 1; N₃, 2) and [Cu_1 − xFe_x(bpca)](ClO₄) (x = 0, 3; 0.23, 4) were synthesised. The structure of 1 was solved ab initio from X-ray powder diffraction data and refined by Rietveld methods. The complexes 3-4 were characterised by X-ray single crystal diffraction. In 1 the cyano ligand coordinates the metal centres, the Cu centres forming a zigzag 1-D chain along the (0 0 1) direction, while in 3-4, the bpca ligand itself acts as the link towards the metal ions which are arranged in a linear 1-D chain running parallel to the (0 0 1) direction. An infrared spectroscopy study confirmed these coordination modes. The magnetic properties of both chain families were studied. 1-2 do not show significant magnetic interactions, whereas the magnetic behaviour for 3-4 suggests dominant antiferromagnetic interactions between the metal ions within the chains. The magnetic behaviour of 3 was analysed using the Padé approximation of the Bonner-Fisher model for S = 1/2 antiferromagnetic chains. The J value was estimated as 10 K.     

Four coordination polymers constructed from a multicarboxylate ligand and metal centers various from Ba, Cu, Zn to Gd: Syntheses, crystal structures and properties

Hydrothermal reactions between H₄ODPA (2,2′,3,3′-oxydiphthalic acid) and metal ion salts of Ba²⁺, Cu²⁺, Zn²⁺ and Gd³⁺ afford four novel coordination polymers [Ba(H₂ODPA)(H₂O)₄] · H₂O (1), [Cu₂(ODPA)(H₂O)₃] · H₂O (2), Zn₂(ODPA)(H₂O)₂ (3) and [Gd(HODPA)(H₂O)_3.5] · H₂O (4), accordingly. These polymers show great differences in regard to their structures and properties originated from the variation of size and coordination geometry of the metal ions. Compound 1 presents puckered achiral layer structure with (4.8²) topology with helices, 2 has a 6³ topology with copper tetramer as SBUs, 3 has chiral layer with two kinds of helices built up from Zn-binuclear “paddle-wheel” like SBUs, and 4 features a simple 1D helix with opposite chirality. Compound 3 shows obvious fluorescent emissions upon excitation. Compound 2 shows ferromagnetic interactions between Cu^II centers bridged by carboxylate groups, whereas compound 4 presents weak ferromagnetic interaction between Gd^III ions.     

Iridium assisted S-H and C-H activation of benzaldehyde thiosemicarbazones. Synthesis, structure and electrochemical properties of the resulting complexes

Reaction of five 4-R-benzaldehyde thiosemicarbazones (R = OCH₃, CH₃, H, Cl and NO₂) with [Ir(PPh₃)₃Cl] in refluxing ethanol in the presence of a base (NEt₃) affords complexes of three different types, viz. 1-R, 2-R and 3-R. In the 1-R complexes the thiosemicarbazone is coordinated to iridium as a monoanionic bidentate N,S-donor forming a four-membered chelate ring. Two triphenylphosphines, a hydride and a chloride are also coordinated to the metal center. The 2-R complexes are very similar in composition and stereochemistry to the corresponding 1-R complexes, except that a second hydride is bound to iridium instead of the chloride. In the 3-R complexes, the thiosemicarbazones are coordinated to iridium as dianionic tridentate C,N,S-donors forming two adjacent five-membered chelate rings. Two triphenylphosphines and a hydride are also coordinated to the metal center. Structures of the 1-NO₂, 2-NO₂ and 3-NO₂ complexes have been determined by X-ray crystallography. Reaction of the same 4-R-benzaldehyde thiosemicarbazones with [Ir(PPh₃)₃Cl] in refluxing toluene in the presence of NEt₃ affords complexes of two types, viz. 3-R and 4-R. The 4-R complexes are very similar in composition and stereochemistry to the corresponding 3-R complexes, except that a chloride is bound to iridium instead of the hydride. Structure of the 4-CH₃ complex has been determined by X-ray crystallography. In all the complexes the two PPh₃ ligands are trans. All the complexes show intense MLCT transitions in the visible region. Cyclic voltammetry on the complexes shows an Ir(III)-Ir(IV) oxidation on the positive side of SCE followed by an oxidation of the coordinated thiosemicarbazone. A reduction of the coordinated thiosemicarbazone is also observed on the negative side of SCE.     

Mn(II) coordination architectures with mixed ligands of 3-(2-pyridyl)pyrazole and carboxylic acids bearing different secondary coordination donors and pendant skeletons

In our efforts to investigate the factors that affect the formation of coordination architectures, such as secondary coordination donors and pendant skeletons of the carboxylic acid ligands, as well as H-bonding and other weak interactions, two kinds of ligands: (a) 3-(2-pyridyl)pyrazole (L¹) with a non-coordinated N atom as a H-bonding donor, a 2,2′-bipyridyl-like chelating ligand, and (b) four carboxylic ligands with different secondary coordination donors and/or pendant skeletons, 1,4-benzenedicarboxylic acid (H₂L²), 4-sulfobenzoic acid (H₂L³), quinoline-4-carboxylic acid (HL⁴) and fumaric acid (H₂L⁵), have been selected to react with Mn(II) salts, and five new complexes, [Mn(L¹)₂(SO₄)]₂ (1), [Mn(L¹)₂(L²)]_∞ (2), [Mn(L¹)(HL³)₂]_∞ (3), Mn(L¹)₂(L⁴)₂ (4), and [Mn(L¹)₂(L⁵)]_∞ (5), have been obtained and structurally characterized. The structural differences of 1-5 can be attributed to the introduction of the different carboxylic acid ligands (H₂L², H₂L³, HL⁴, and H₂L⁵) with different secondary coordination donors and pendant skeletons, respectively. This result also reveals that the typical H-bonding (i.e. N-H?O and O-H?O) and some other intra- or inter-molecular weak interactions, such as C-H?O weak H-bonding and π?π interactions, often play important roles in the formation of supramolecular aggregates, especially in the aspect of linking the multi-nuclear discrete subunits or low-dimensional entities into high-dimensional supramolecular networks.     

Examining the impact of steric and electronic variation in N2S scorpionate ligands on the properties of zinc(II) and cadmium(II) complexes

A series of LZn(II)Br (1-4) and LCd(II)Cl complexes (9-11) has been prepared by the reaction of metal halide precursors with the lithium salts of the N₂S⁻ ligands bis(3,5-diisopropylpyrazol-1-yl)dithioacetate (L¹), bis(3,5-di-tert-butylpyrazol-1-yl)dithioacetate (L²), N-phenyl-2,2-bis(3,5-diisopropylpyrazol-1-yl)thioacetamide (L³) and N-phenyl-2,2-bis(3,5-di-tert-butylpyrazol-1-yl)thioacetamide (L⁴). Characterization by X-ray crystallography and DOSY NMR studies indicate that LZnBr complexes 1-4 are mononuclear both in the solid state and in solution. Steric differences between ligands L¹-L⁴ result in distortion from an ideal tetrahedral geometry for each complex, with the degree of distortion depending on the bulk of the ligand substituents. In contrast, the related complex L³CdCl was shown by X-ray crystallography to dimerize in the solid state to form the chloride-bridged five-coordinate complex [L³CdCl]₂ (10). Despite 10 having a dinuclear structure in the solid state, DOSY NMR studies indicate 9-11 exist as mononuclear LCdCl species in solution. In addition, Zn(II) cyanide complexes of the form LZnCN [L = L¹ (5), L³ (7), L⁴ (8)] have been characterized and the X-ray structure of 8 determined. Moreover, density functional theory calculations have been conducted which yield important insight into the bonding in 1-4 and 5-8 and the electronic impact of ligands L¹-L⁴ on the zinc(II) ion and its ability to function as a Lewis acid catalyst.     

Solvent-controlled generation of two pairs of mononuclear single-strand helical copper(II) complexes of 2,6-pyridinediylbis(2-pyridinyl)methanone: metal-promoted hydrolysis and solvolysis with asymmetric induction

Two pairs of stable mononuclear single-strand helical complexes were obtained through controlled self-assembly using 2,6-pyridinediylbis(2-pyridinyl)methanone (L) and copper(II) salts. CuL(NO₃)₂ (1) and [CuL′(H₂O)](NO₃)₂ (2) represent a pair in which L takes the diketo form in 1 but hydrolyzed in 2, while CuLCl₂ (3) and [CuL″Cl]Cl (4) constitute another pair in which L remains intact in 3 but solvolyzed in 4. A mechanism of the metal-promoted hydrolysis and solvolysis of ligand L with asymmetric induction is proposed through studies on the crystal structures of these complexes.     

Insights into electronic and structural properties of novel Pd(II) salen-type complexes

Novel palladium(II) complexes with salen-type ligands based on 3-methylsalicyladehyde and a set of aliphatic diamines (C1 to C4) have been synthesised and characterized by spectroscopic techniques (UV-Vis and FTIR), Density Functional Theory (DFT) calculations and single-crystal X-ray diffraction for C1 and C4. X-ray diffraction analysis of these complexes was focused on coordination sphere and supramolecular arrangements. In the two compounds, the molecules form dimers, being the most relevant intermolecular interactions the hydrogen bonds of the type C-H?O, C-H?π and π?π stacking interactions between the six-membered metallocycles.Electronic spectra of all Pd(II) complexes are dominated by charge transfer and intraligand bands at λ < 400 nm. DFT calculations showed that the HOMO is ligand-dominated, with the metal contribution being ∼18% for all complexes. This suggests that the structural/electronic differences between the ligands do not influence significantly the participation of metal orbitals in HOMO. All the complexes exhibit dipole moments with the same direction, from the aldehyde moiety towards the imine bridge with C2 and C3 showing quite similar values, μ_C2 = 5.49 and μ_C3 = 5.54 D, whereas complexes C1 and C4 show slightly higher values: μ_C1 = 5.79 and μ_C4 = 6.17 D. The magnitude of bond lengths and angles predicted by DFT calculations are comparable to those determined by X-ray crystallography.The experimental vibrational frequencies of the Pd(II) complexes were correlated with the values estimated by DFT calculations. The good agreement between the experimental and theoretical vibrational data allowed the assignment of relevant IR bands to molecular vibration modes.