Photochemical syn-anti isomerization reactions in N2-hydroxyisocytosines--an experimental matrix isolation and theoretical study

N2-hydroxyisocytosine and 1-methyl-N2-hydroxyisocytosine were studied using a matrix isolation technique combined with infrared absorption spectroscopy. For N2-hydroxyisocytosine isolated in an Ar matrix (at 10 K), two imino-oxo isomers, one with the hydroxyimino =N-OH group directed toward the N1-H group (the form called further anti) and the second with the =N-OH group directed toward N3-H (syn), were observed in the ratio 1.4:1. The syn isomer is converted totally to the anti form after UV (lambda > 295 nm) irradiation of the matrix. A small amount of the N(3)H-hydroxy-amino tautomer of N2-hydroxyisocytosine was also detected in the matrix. This form did not react photochemically. For 1-methyl-N2-hydroxyisocytosine, only the syn form of the imino-oxo tautomer was observed after deposition of the matrix. UV (lambda > 295 nm) irradiation induced a photoreaction converting this isomer into the anti form. After 15% of the starting material had been converted into the product, a photostationary state was achieved, and no further progress of the reaction was observed. Subsequent UV irradiation (lambda > 335 nm) caused a back reaction, leading to a disappearance of the anti form and to the recovery of the initial syn isomer. All isomers were identified by comparing their experimental IR spectra with the spectra theoretically calculated at the DFT(B3LYP)/6-31G(d,p) level, where DFT is the density functional theory. Good agreement between the observed and predicted patterns of the spectral lines allowed for reliable identification. The experimental IR spectra were interpreted and discussed. The relative energies of the 12 isomers of N2-hydroxyisocytosine were calculated at the MP2/6-31G(d,p) and MP4//MP2/6-31G(d,p) levels. For six isomers of 1-methyl-N2-hydroxyisocytosine, the calculations were carried out at the MP2/6-31G(d,p) level. The anti form of the imino-oxo tautomer of N-hydroxyisocytosine and the syn form of the imino-oxo tautomer of 1-methyl-N2-hydroxyisocytosine were predicted to be the most stable.     

Conformational studies by dynamic NMR. 90. Structure and stereodynamics of the rotamers of di- and tri-alpha-naphthylphenyl derivatives

The crystal structure of 1,3,5-tris(4-methylnaphth-1-yl)benzene, 1, shows one naphthyl substituent in an anti relationship to the other two. On the other hand, low temperature (-70 degrees C) (1)H NMR spectra in solution show the presence of a second rotational conformer (rotamer) having all the three naphthyl substituents in a syn relationship. The interconversion barrier between the anti (77%) and syn (23%) rotamers of 1 was determined by line shape simulation of the temperature-dependent NMR spectra (Delta G(++) = 12.1 kcal mol(-1)). In the analogous disubstituted meta and paraderivatives, that is, 1,3- and 1,4-bis(4-methylnaphth-1-yl)benzene (2 and 3, respectively), the presence of both the anti and syn rotamers was also detected by low-temperature NMR spectroscopy. In the latter compounds, the proportions of the anti and syn forms are nearly equal, and the corresponding anti to syn interconversion barriers were found to be lower (11.4 and 11.1(5) kcal mol(-1), respectively) than those of the trisubstituted derivative 1.     

Determination of the solution structures of melamine-based bis- and tris-macrocyclic ligand copper(II) complexes

A combination of molecular mechanics (MM), electron paramagnetic resonance spectroscopy (EPR), and spectra simulation (MM-EPR) has been used to determine the solution structures of di- and trinuclear copper(II) complexes of melamine-based oligomacrocyclic ligands. The spin Hamiltonian parameters of the mononuclear, melamine-appended macrocyclic ligand copper(II) complex have been determined by EPR spectroscopy and were also studied with DFT methods. These spin Hamiltonian parameters, together with the structural parameters obtained from models optimized with MM, have been used for the simulation of the EPR spectra of the di- and trinuclear complexes. For the dinuclear complex, the syn isomer is preferred over the anti, for which an X-ray structure exists; for the trinuclear complex, the syn,syn isomer is preferred over the syn,anti form. Additional support for these assignments comes from DFT calculations, and this demonstrates that the MM-DFT-EPR method is a reliable approach for the determination of solution structures and for the analysis of spin Hamiltonian parameters of dipolar, coupled transition metal complexes (g and A tensors and J values).     

How many conformers determine the thymidine low-temperature matrix infrared spectrum? DFT and MP2 quantum chemical study

A comprehensive conformational analysis of isolated 2'-beta-deoxy-thymidine (T), canonical DNA nucleoside, has been performed by means of ab initio calculations at the MP2/6-311++G(d,p)//DFT B3LYP/6-31G(d,p) level of theory. At 298.15 K, all 92 conformers of isolated dT are within a 7.49 kcal/mol Gibbs energy range. Syn orientation for the base and South (S) conformers for the sugar dominate at this temperature: syn/anti = 61.6%:38.4% and S/N = 74.5%:25.5%. However, at 420 K, the majority of conformers contain anti base and the population of North (N) sugars increases: syn/anti = 38.0%:62.0% and S/N = 59.5%:40.5%. The whole conformational parameters (P, chi, gamma, delta, beta, epsilon, nu max) were analyzed as well as the energies of the OH...O intramolecular H-bonds on the basis of nu(OH) stretching vibrations. Convolution of calculated IR spectra of all of the T conformers appears consistent with its low-temperature matrix spectrum (Ivanov et al. Low Temp. Phys. 2003, 29, 809). The maximal discrepancy in frequencies between calculated and experimental spectra is less than 1%. A conclusion was made that for reliable reconstruction of the isolated nucleoside IR spectrum the quasi whole set of conformers should be taken into consideration. In essence, this result opens up a possibility to reconstruct IR spectra of isolated nucleosides at physiological temperatures with rather satisfactory probability.     

Photoisomerizations of N4-hydroxycytosines

A series of N4-hydroxycytosines, unsubstituted or substituted with methyl groups at N3 or C5 atoms of the heterocyclic ring, was studied using the matrix-isolation method. Depending on the absence or presence of the methyl substituent at N3 or C5 atoms (or at both of them) the syn or anti form of the compounds (or a mixture of both forms) was trapped from the gas phase into a low-temperature matrix. Upon UV (lambda > 295 nm) irradiation of the matrixes the syn --> anti as well as the anti --> syn photoisomerization reactions were observed. The syn and anti isomers of N4-hydroxycytosines were identified by comparing their experimental IR spectra with the theoretical spectra calculated at the DFT(B3LYP)/6-31G(d,p) level. For the majority of the studied compounds, the UV induced reactions led to a photostationary state. The position of the final photostationary state was found to be a sensitive function of weak interactions of a studied N4-hydroxycytosine with the matrix environment: solid argon or solid nitrogen. However, not all of the studied photoisomerizations led to a classical photostationary state. For some of the investigated N4-hydroxycytosines, the position of the photostationary state was shifted very strongly in favor of the photoproduct, whereas for some others the position was shifted so strongly in favor of the starting isomer that no photoisomerization was observed. These experimental findings were elucidated by theoretical investigations of the potential energy surfaces of the ground (S0) and first excited (S1) electronic states of N4-hydroxycytosine. The crucial result of these calculations (carried out at the CASSCF level) was the localization of a conical intersection between S0 and S1 at a structure with perpendicular orientation of the hydroxylimino group with respect to the heterocyclic ring.     

Conformational studies by dynamic NMR. 94.1 cogwheel pathway for the stereomutations of durene derivatives containing the mesityl ring

The low-temperature NMR spectra of 1,4-bis(mesitoyl)durene, 1, and of 1,4-bis(mesitylethenyl)durene, 2, reveal the presence of syn and anti rotamers at the equilibrium, their relative proportions depending on the dielectric constant of the solvent. In solution the more stable rotamer of 1 is the anti whereas, in the case of 2, the more stable is the syn. Depending on the crystallization solvent employed the more (anti) and the less stable (syn) rotamers were both observed (X-ray diffraction) in the solid state of 1. On the other hand, only the less stable rotamer (anti) was found to be present in the solid state of 2. As shown by MM calculations, the syn-to-anti interconversion occurs via a correlated process (cogwheel pathway) involving the mesityl-C and durene-C bond rotations: the dynamic NMR technique yields an experimental barrier of 8.2 kcal mol(-)(1) for 1 and 13.1 kcal mol(-)(1) for 2. In the case of derivative 2 a second barrier, due to a second type of correlated rotation process (torsion), was also determined (8.6 kcal mol(-)(1)). As a consequence of the restriction of this second torsional motion the anti rotamer of 2 displays two distinguishable NMR spectra at -133 degrees C, corresponding to a pair of conformers with different symmetry (anti C(i)() and anti C(2)).     

Arylbiphenylene atropisomers: structure, conformation, stereodynamics, and absolute configuration

Anti and syn conformers, due to restricted sp(2)-sp(2) bond rotation, were detected in hindered 1,8-diarylbiphenylenes, the aryl moieties being phenyl groups bearing 0micron-alkyl substituents such as Me, Et, i-Pr, and t-Bu. By means of low-temperature NOE experiments, the corresponding structures were assigned and were found to be in agreement with the results of single-crystal X-ray diffraction. The interconversion barriers of these conformers were determined by line-shape simulation of the variable-temperature NMR spectra and the experimental values were reproduced satisfactorily by DFT calculations. In the case of the bulkiest aryl substituent investigated (i.e., 2-methylnaphthalene), the syn and anti atropisomers were stable enough as to be separated at ambient temperature. The two enantiomers (M,M and P,P) of the isomer anti were also isolated by enantioselective HPLC, and the theoretical interpretation of the corresponding CD spectrum allowed the absolute configuration to be assigned.     

Product ion studies of diastereomeric benzo[ghi]fluoranthene tetraols by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry and post-source decay

The product ion formation characteristics of the four diastereomeric tetrahydroxy benzo[ghi]fluoranthene compounds formed by hydrolysis of the syn and anti diastereomers of trans-3,4-dihydroxy-5,5a-epoxy-3,4,5,5a-tetrahydrobenzo[ghi]fluoranthene are studied using matrix-assisted laser desorption/ionization and post-source decay (PSD) to determine a correlation between the fragmentation characteristics of these tetraols and the structures of the diol-epoxide diastereomers from which they are hydrolyzed. The tetraols formed by the trans ring opening of the diol epoxides during hydrolysis yield product ion spectra specific for the syn and anti configurations of their precursor diol epoxides. All four diastereomeric tetraols form product ions by the losses of one and/or two water molecules in varying proportions when lithium-cationized molecule ions (m/z 301) are selected for PSD product ion analysis. The differences in the PSD spectra of these four Li+-cationized molecules are rationalized in terms of a water loss mechanism that involves the 1,2 elimination of a hydrogen atom and hydroxyl group that are cis with respect to each other on adjacent carbons.     

Enhancement of diastereoselectivity in photodimerization of alkyl 2-naphthoates with chiral auxiliaries via inclusion within γ-cyclodextrin cavities

Irradiations of alkyl 2-naphthoates are known to result in four isomeric "cubane-like" photodimers: anti(HH)-2, syn(HH)-2, anti(HT)-2, and syn(HT)-2 where the anti(HH)-2, anti(HT)-2, and syn(HT)-2 consist of pairs of diastereomers. Here, chiral auxiliary and chiral microreactor strategies have been combined to achieve high diastereoselectivity in photodimerizations of an enantiomeric pair of 2-naphthoates with (R)- and (S)-1-methoxycarbonylethyl esters as chiral auxiliaries (1R and 1S). Thus, irradiations of their γ-cyclodextrin (γ-CD) complexes have been conducted. Fluorescence, IR, and NMR spectra of both enantiomers of 1 demonstrate that their γ-CD complexes are mainly 2:2 with the molecules of 1 in head-to-head orientations. Irradiation of the complexes in the solid state mainly resulted in anti(HH)-2. The absolute configuration of each diastereomer of anti(HH)-2 has been established for the first time here. The diastereomeric excesses (de's) of anti(HH)-2 from 1R and 1S were 94% and 86%, respectively. These de's are much higher than those found from irradiations in solution (55% for 1R and 1S), where the opposite diastereomeric form is in excess! Calculations of the energies of various conformations of the head-to-head 2:2 inclusion complexes were performed using the PM3 approach. The predicted major diastereomers based on the calculation are consistent with those found experimentally.     

RESONANCE-ENHANCED CARS SPECTROSCOPY OF BILIPROTEINS. INFLUENCE OF AGGREGATION and LINKER PROTEINS ON CHROMOPHORE STRUCTURE IN ALLOPHYCOCYANIN (Mastigocladus laminosus)

Abstract— Resonance-enhanced coherent anti-Stokes Raman spectra (CARS) are reported for monomers and for trimers with and without linker proteins of allophycocyanin isolated from Mastigocladus laminosus. The CARS spectrum of the monomer is independent of the presence of linker proteins and is very similar to that of phycocyanin monomers indicating that the equivalent chromophores exhibit like structures in both biliproteins. Large differences are, however, observed between the spectra of phycocyanin trimers and those of allophycocyanin trimers with or without linker proteins (L_c^8,9). The observed differences between monomer and trimer spectra are consistent with a change of the α-chromophore-protein arrangement upon aggregation without linker. If linker proteins are present in the trimer, then additional geometry changes of the β-chromophores are induced; these could relate to a transition from the 15Z- anti to 15Z- syn conformation.     

Infrared and ultraviolet spectral signatures and conformational preferences of jet-cooled serotonin

The ultraviolet and infrared spectroscopy of single conformations of neutral serotonin (5-hydroxytryptamine) have been studied in the gas phase using a combination of methods including laser-induced fluorescence, resonance-enhanced two-photon ionization, UV-UV hole-burning spectroscopy, and resonant ion-dip infrared spectroscopy. By comparison to its close analogue tryptamine, for which firm assignments to seven low-energy conformations have been made, UV and IR transitions due to eight conformations of serotonin are observed and assigned. The ultraviolet spectrum divides into two subsets of transitions separated from one another by approximately 230 cm-1 ascribable to syn and anti conformations of the 5-OH group. These two subsets are also distinguishable via their 5-OH stretch fundamentals, with the anti-OH subset shifted by approximately 4-5 cm-1 to lower frequency than those due to syn-OH conformers. The existing firm assignments for tryptamine play a decisive role in assignments in serotonin, where the alkyl CH stretch infrared spectrum is diagnostic of the conformation of the ethylamine side chain. Conformer A of serotonin (SERO(A)), with S1 <-- S0 origin transition at 32584 cm-1, is assigned to Gpy(out)/anti-OH, SERO(B) at 32548 cm-1 to Gpy(up)/anti, SERO(C) at 32545 cm-1 to Gph(out)/anti, SERO(D) at 32560 cm-1 to Anti(py)/anti, SERO(E) at 32537 cm-1 to Anti(up)/anti, SERO(F) at 32353 cm-1 to Gpy(out)/syn, SERO(G) at 32313 cm-1 to Gpy(up)/syn, and SERO(H) at 32282 cm-1 to Gph(out)/syn. The conformational preferences of serotonin differ from those of tryptamine most notably in the selective stabilization observed for the Gph(out)/anti-OH conformer SERO(C), which makes it the second-most intense transition in the ultraviolet spectrum, surpassed only by the Gpy(out)/anti-OH conformer SERO(A).     

Stacking effect of polyfluorene on the chemical shift and electron transport

We investigate the structures, NMR chemical shifts, absorption spectra, frontier molecular orbitals, and transition density matrices of pi-stacked polyfluorenes by ab initio calculations. For F1-F4, we consider two different conformations, syn and anti. The simulated 1H NMR chemical shifts are in good agreement with the previous experiment, and the significantly upfielded chemical shifts explain that the fluorene moieties are stacked on each other. It is found that the relative stability for syn and anti conformers is almost equivalent in B3LYP calculations; however, the syn conformer becomes much more stable than the anti conformer in MP2 calculations, which is consistent with the experimental finding that only the syn conformers are relevant. The vertical detachment energy, which is linearly proportional to the ionization potential, shows the same size dependence as the previous experiment. The electron attachment energy decreases exponentially as the size increases, which implies that the electron transport would be possible even for long chains such as F3 and F4. This was evident from the frontier molecular orbitals (HOMO and LUMO). Also, it is found that the syn conformers are very favorable for electron transport through the pi-stacked fluorene moieties.     

Atropisomers of hindered triarylisocyanurates: structure, conformation, stereodynamics, and absolute configuration

The syn and anti diastereoisomers of some 1,3,5-triarylisocyanurate derivatives were isolated and their configuration assigned by NOE experiments and by X-ray diffraction. The kinetics of the syn/anti interconversion were determined, and the experimental activation energies matched satisfactorily the values predicted by DFT computations. Low-temperature NMR spectra were employed to determine the rotation barrier of N-bonded unhindered aryl substituents: these barriers, too, are satisfactorily reproduced by DFT computations. In the case of racemic diastereoisomers, the two expected enantiomers (atropisomers) were isolated by enantioselective HPLC and the absolute configuration established by DFT simulation of the electronic and vibrational circular dichroism spectra.     

Study of exchange processes in 4,4,6-trimethyl-2-phenylamino-4H-1, 3-thiazine derivatives

It is shown that, in contrast to model structures with fixed amine and imine forms, the form and position of some of the signals in the PMR spectra of 4,4,6-trimethyl-2-phenylamino-4H-1, 3-thiazine derivatives depend on the temperature; this is associated with rotational isomerism about the nitrogen-heteroring bond, which is realized at a higher rate in the model derivative with an amine structure and is slowed down in the tautomeric derivatives owing to the formation of hydrogen bonds with solvent molecules (in deuteroacetone) or in dimeric associates (in deuterochloroform). According to data from the low-temperature spectra, the percentages of the syn and anti forms in acetone solutions are comparable. In chloroform solution, the equilibrium between the two rotational forms is shifted markedly to favor the anti isomer as the temperature is lowered because of the formation of cyclic dimeric structures.     

Influence of carrier ligand NH hydrogen bonding to the O6 and phosphate group of guanine nucleotides in platinum complexes with a single guanine ligand

Coordinated N,N',N"-trimethyldiethylenetriamine (Me3dien) has several possible configurations: two have mirror symmetry (R,S configurations at the terminal nitrogens) and the terminal N-Me's anti or syn with respect to the central N-Me (anti-(R,S) and syn-(R,S) isomers, respectively), and two are nonsymmetrical (R,R and S,S configurations at terminal nitrogens, rac denotes a 1:1 mixture of the two isomers). For each configuration, two Me3dienPtG atropisomers can be formed (anti or syn orientation of central N-Me and G 06, G = guanine derivative), and these can be observed since the terminal N-Me's decrease the rate of G rotation about the Pt-N7 bond. In symmetrical syn-(R,S)-Me3dienPtG derivatives with G = 9-EtG and 3'-GMP, the anti rotamer, which can form O6-NH H-bonds, was slightly favored over the syn rotamer but never more than 2:1. This anti rotamer is also favored by lower steric repulsion between the terminal N-Me's and G O6; thus, the contribution of O6-NH H-bonding to the stability of the anti rotamer could be rather small. With G = 5'-GMP, an O6-NH H-bond in the anti rotamer and a phosphate-NH H-bond in the syn rotamer can form. Only the syn rotamer was detected in solution, indicating that NH H-bonds to 5'-phosphate are far more important than to O6, particularly since steric factors favor the anti rotamer. Interconversion between rotamers was faster for syn-(R,S)- than for rac-Me3dien derivatives. This appears to be determined by a smaller steric impediment to G rotation of two "quasi equatorial" N-Me's, both on one side of the platinum coordination plane (syn-(R,S) isomer), than one "quasi equatorial" and one "quasi axial" N-Me on either side of the coordination plane (rac isomer).     

Exploring the electro‐optical properties of conjugated polymers based on oligo‐selenophene and oligo(3,4‐ethylenedioxyselenophene)

For seeking high‐efficiency narrow‐band‐gap donor materials to enhance short‐circuit current density for organic solar cells, a series of oligo‐selenophene (OS) and oligo(3,4‐ethylenedioxyselenophene) (OEDOS) with various chain lengths were designed and characterized using density functional theory (DFT) and time‐dependent DFT calculations. Based on the results, it can be seen that with increasing chain length of the oligomers in both syn‐ and anti‐adding manners, the bond length alternation is decreased which indicates that the π‐electron delocalization is increased. Also, when the chain length is increased the electronic energy gap and the optical energy gap are decreased. It can be concluded that the syn‐(OS)_n=10,14,15, anti‐(OS)_n=14 and anti‐(OEDOS)_n=7–12 oligomers can act as low‐band‐gap polymers. Therefore they can absorb more sunlight based on maximum wavelength (higher than 620 nm). Furthermore, a red shift in the simulated absorption spectra of (OS)_n and (OEDOS)_n donors is observed. It is found that (OS)_n=14,15 with syn configuration of the extended oligomers is the most suitable donor for the design of high‐performance organic solar cells possessing a narrow electronic band gap, high exciton lifetime and broad and intense absorption spectra that cover the solar spectrum leading to complete light‐harvesting efficiency.     

Early barriers in the matrix photochemical formation of syn-anti randomized FC(O)SeF from the OCSe:F(2) complex

The photochemically induced reaction of OCSe and F(2), isolated together in an Ar matrix at about 15 K, leads to formation of the hitherto-unknown fluorocarbonylselenyl fluoride FC(O)SeF. The reaction occurs via a van der Waals complex O=C=Se...F-F that favors very early formation of the anti conformer. The presence and subsequent decay of a band assigned to the F-F vibration correlated with perturbed OCSe bands seems to confirm this hypothesis. Subsequent irradiation of the matrix leads to randomized FC(O)SeF by a photochemically induced conformational equilibrium between syn and anti forms. Another photochemical reaction channel is the formation of CO and SeF(2) molecules, which are produced in the same matrix cage and then form a loose complex. The changes were monitored and the products characterized experimentally by their IR spectra, and the spectra analyzed in the light of the results of theoretical calculations.     

Better characterization of surface organometallic catalysts through resolution enhancement in proton solid state NMR spectra

Delayed-acquisition methods, namely, echo and constant-time-acquisition approaches, allow a significant improvement in resolution in the proton solid state NMR spectra of surface organometallic catalysts such as [syn-(SiO)Mo(=NAr)(=CH(t)Bu)(CH2(t)Bu)] and [(SiO)Re(C(t)Bu)(=CH(t)Bu)(CH2(t)Bu)] (syn/anti ratio = 1:1). This enables the observation of all of the proton resonances, which is not possible with the simple proton single-pulse technique under magic-angle spinning. For example, the methylene protons of the neopentyl ligands, buried in the large peak associated with all of the methyls in the 1H MAS spectrum, can easily be identified by recording a delayed-acquisition spectrum (resolution enhancement of a factor of 3 is obtained). Moreover, combining constant-time acquisition with heteronuclear carbon-proton correlation spectroscopy also improves the resolution of the 2D HETCOR spectra.     

The infrared spectra and normal coordinate analysis of syn and anti acetaldoxime

The infrared spectra of mixtures of syn and anti acetaldoxime and its deuterated analogues CH₃CHNOD, CD₃CHNOH, CD₃CDNOH and CH₃CDNOH have been recorded. The syn and anti isomers of CH₃CHNOH, CD₃CHNOH, CD₃CDNOH and CH₃CDNOH have been separated by gas chromatography [1]. The infrared spectra of separated isomers in CS₂ solution have been recorded and the assignment of ten in-plane vibrations made. From a normal coordinate analysis the Urey-Bradley force field, the potential energy distribution and additional information about assignments have been obtained.For the anti isomer the simple Urey-Bradley force field gives satisfactory agreement between the calculated and measured frequencies. For the syn isomer it is necessary to take into account the interactions between atoms separated by three bonds.     

Secondary deuterium kinetic isotope effect for aquation, solvolysis, and isomerization reactions of trans-[Co(en)2(OSMe2)N3]2+, and the resolution of a mechanistic anomaly

The two closely spaced NH signals in the (1)H NMR spectrum of trans-[Co(en)(2)(OSMe(2))(N(3))](2+) have been reassigned using 2D NMR and other techniques. Thus, the unusual syn to anti (to Co-N(3)) NH rearrangement on base catalyzed substitution of the selectively deuterated complex in ND(3)(l) has been reinterpreted as "normal", with inversion of the effective deprotonation site accompanying the act of substitution. The re-examination of this system required a repeat study of the secondary isotope effect for the acid hydrolysis reaction, previously used to assign syn and anti amine sites, and this has been extended to other solvents (Me(2)SO, MeCN). The relative NH proton exchange rates are also reconsidered. A systematic rate reduction for Me(2)SO substitution is observed for deuterium incorporation into the cis-NH centers, irrespective of whether these are syn or anti, and the effect is much greater in Me(2)SO than in water. The results are interpreted in terms of zero point energy effects and coupled vibrations.