Vibrational Exciton Research Articles

Strong vibronic coupling effects in polarized IR spectra of the hydrogen bond in N-methylthioacetamide crystals

This paper presents the investigation results of the polarized IR spectra of the hydrogen bond in crystals of N-methylthioacetamide. The spectral studies were preceded by the determination of the crystal X-ray structure. The spectra were measured at 283 K and at 77 K by a transmission method, using polarized light. Theoretical analysis of the results concerned the linear dichroic effects, the H/D isotopic and temperature effects, observed in the solid-state IR spectra of the hydrogen and of the deuterium bond at the frequency ranges of the ν N–H and the ν N–D bands, respectively. The main spectral properties of the crystals can be interpreted satisfactorily in terms of the simple quantitative theory of the IR spectra of the hydrogen bond, i.e., the “ strong-coupling” theory on the basis of the hydrogen bond centrosymmetric dimer model. The spectra revealed that the strongest vibrational exciton coupling involved the closely spaced hydrogen bonds, each belonging to a different chain of associated N-methylthioacetamide molecules. The crystal spectral properties, along with an abnormal H/D isotopic effect in the spectra, were found to be strongly influenced by vibronic coupling mechanisms in these dimers. These mechanisms were considered as responsible for the activation in IR of the totally symmetric proton stretching vibrations in the dimers. On analyzing the spectra of isotopically diluted crystalline samples of N-methylthioacetamide, it was proved that a non-random distribution of the protons and deuterons took place in the hydrogen bond lattices. In an individual hydrogen-bonded chain in the crystals distribution of the hydrogen isotope atoms H and D was fully random. The H/D isotopic “ self-organization” mechanism, of a vibronic nature, involved a pair of hydrogen bonds from a unit cell, where each hydrogen bond belonged to a different chain of the associated molecules.

Two-Dimensional Infrared Spectral Signatures of 310- and α-Helical Peptides

Two-dimensional infrared (2D IR) spectra of Calpha-alkylated model octapeptides Z-(Aib)8-OtBu, Z-(Aib)5-L-Leu-(Aib)2-OMe, and Z-[L-(alphaMeVal)]8-OtBu have been measured in the amide I region to acquire 2D spectral signatures characteristic of 3(10)- and alpha-helical conformations. Phase-adjusted 2D absorptive spectra recorded with parallel polarizations are dominated by intense diagonal peaks, whereas 2D rephasing spectra obtained at the double-crossed polarization configuration reveal cross-peak patterns that are essential for structure determination. In CDCl3, all three peptides are of the 3(10)-helix conformation and exhibit a doublet cross-peak pattern. In 1,1,1,3,3,3-hexafluoroisopropanol, Z-[L-(alphaMeVal)]8-OtBu undergoes slow acidolysis and 3(10)-to-alpha-helix transition. In the course of this conformational change, its 2D rephasing spectrum evolves from an elongated doublet, characteristic of a distorted 3(10)-helix, to a multiple-peak pattern, after becoming an alpha-helix. The linear IR and 2D absorptive spectra are much less informative in discerning the structural changes. The experimental spectra are compared to simulations based on a vibrational exciton Hamiltonian model. The through-bond and through-space vibrational couplings are modeled by ab initio coupling maps and transition dipole interactions. The local amide I frequency is evaluated by a new approach that takes into account the effects of hydrogen-bond geometry and sites. The static diagonal and off-diagonal disorders are introduced into the Hamiltonian through statistical models to account for conformational fluctuations and inhomogeneous broadening. The sensitivity of cross-peak patterns to different helical conformations and the chain length dependence of the spectral features for short 3(10)- and alpha-helices are discussed.

Modulational instabilities in acetanilide taking into account both the N–H and the C=O vibrational self-trappings

A model of crystalline acetanilide, ACN accounting for the C=O and N–H vibrational self-trappings is presented. We develop a fully discrete version of ACN. We show that ACN can be described by a set of two coupled discrete nonlinear Schrödinger (DNLS) equations. Modulational instabilities (MI) are studied both theoretically and numerically. Dispersion laws for the wavenumbers and frequencies of the linear modulation waves are determined. We also derived the criterion for the existence of MI. Numerical simulations are carried out for a variety of selected wave amplitudes in the unstable zone. It is shown that instabilities grow as the wavenumbers and amplitudes of the modulated waves increase. MI grow faster in the N–H mode than in the C=O mode. Temporal evolution of the density probabilities of the vibrational excitons are obtained by the numerical integration of the coupled DNLS equations governing the ACN molecule. These investigations confirm the generation of localized modes by the phenomenon of MI and the predominance of the N–H vibrational mode in the MI process of the ACN.

“ Reversal” exciton coupling effect in the IR spectra of the hydrogen bond cyclic dimers; polarized IR spectra of 3-hydroxy-4-methyl-2(3H)-thiazolethione crystals

This paper presents the results of our investigation of the polarized IR spectra of the hydrogen bond in crystals of 3-hydroxy-4-methyl-2(3H)-thiazolethione. These spectra were measured at room temperature and at 77 K by a transmission method using polarized light. The spectral studies were preceded by re-determination of the crystal X-ray structure. Theoretical analysis of the results concerned linear dichroic effects, the H/D isotopic and temperature effects observed in the solid-state IR spectra of hydrogen and deuterium bonds at frequency ranges of the ν O H and the ν O D bands, respectively. Basic spectral properties of the crystals can be interpreted satisfactorily in terms of the “ strong-coupling” theory, when based on a hydrogen bond dimer model. This model sufficiently explains not only the two-branch structure of the ν O H and the ν O D bands and the temperature-induced evolution of the crystalline spectra, but also the linear dichroic effects observed in the band frequency ranges. A vibronic mechanism responsible for promotion of the symmetry forbidden transition in the IR for the totally symmetric proton stretching vibrations in centrosymmetric hydrogen bond dimers was analyzed. The crystal spectral properties were successfully interpreted on assuming a “ reversal” Davydow-splitting effect expressed by changing of the vibrational exciton interaction energy sign for hydrogen bond dimers in the lattice. These effects were ascribed to a considerable elongation of the dimeric O H ⋯ S bonds in the crystal due to the large atomic radius of sulfur determining the dimer geometry.

Size effects in the infrared spectra of NH3 ice nanoparticles studied by a combined molecular dynamics and vibrational exciton approach

Infrared extinction spectra of ammonia ice nanoparticles with radii between 2 and 10 nm show pronounced band shape variations depending on the conditions of particle formation by collisional cooling. We present experimental and theoretical evidence showing that the variations in the region of the nu2 (umbrella) fundamental are due to changes in the particle size. The effect is analyzed in terms of an explicit atomistic model of the particles' structure and vibrational dynamics. An explicit potential function combined with a novel extension of the vibrational exciton approach allows us to simulate extinction spectra for particles containing up to 16,000 atoms. It is shown that the particles formed under the conditions of our experiments consist of a crystalline core surrounded by an amorphous shell with an approximately constant thickness of 1-2 nm. For the nu2 fundamental, this shell gives rise to a broad band [full width at half maximum (FWHM) 72 cm(-1)] blueshifted by about 19 cm(-1) relative to a narrow peak (FWHM of 19 cm(-1)) which arises from the crystalline core.

Conformations of N-Acetyl-l-Prolinamide by Two-Dimensional Infrared Spectroscopy

Femtosecond two-dimensional infrared (2D IR) spectroscopy has been applied to study the conformations of a model dipeptide, N-acetyl-L-prolinamide (AcProNH2) in deuterated chloroform (CDCl3). Spectral features in the amide-I and -II regions are obtained by rephasing (R), nonrephasing (NR), and reverse photon echo (RPE) pulse sequences with two polarization conditions. The 2D spectra obtained by the RPE and NR sequences with (0, 0, 0, 0) polarization reveal new spectral features associated with the multiple conformers of AcProNH2 that are difficult to discern using R sequence and linear-IR spectroscopy. The high resolving power of the RPE sequence comes from destructive interference between the positive and negative peaks of nearby vibrators, similar to the NR sequence. The RPE response functions that are useful for 2D spectral simulations are evaluated, including the effects of vibrational frequency correlations. The 2D spectra obtained with (45, -45, 90, 0) polarization exhibit clear cross-peak patterns in the off-diagonal region for the R and RPE sequences but in the diagonal region for the NR sequence. These patterns, free from strong diagonal contributions, are crucial for structure determination. DFT calculations, normal-mode analysis, Hessian matrix reconstruction, and vibrational exciton Hamiltonian diagonalization yield molecular parameters needed for quantitative simulations of 2D spectra: angles between transition dipoles, coupling constants, and off-diagonal anharmonicities of the amide-I and -II modes are obtained for solvated trans-C7 and cis structures and for gas-phase trans conformers in the region of phi = -120 degrees to 0 degrees and psi = -100 degrees to 180 degrees in the Ramachandran space. Systematic simulations based on a 4:1 population ratio of the solvated trans-C7 and cis structures reproduce well the 2D spectral features obtained at both polarization conditions. However, better agreement between the experimental and simulated cross-peak patterns can be reached if the dihedral angles of the major trans conformer are close to (phi, psi) = (-80 degrees , 100 degrees ). Our results suggest that the major conformer of AcProNH2 in CDCl3 deviates from the gas-phase global minimum, the trans-C7 form, to an extended intermediate between the C7 and polyproline-II structure. These results are discussed in relationship with earlier findings obtained by NMR, transient IR studies, and MD simulations.

Vibrational dynamics of DNA. III. Molecular dynamics simulations of DNA in water and theoretical calculations of the two-dimensional vibrational spectra

A theoretical description of the vibrational excitons in DNA is presented by using the vibrational basis mode theory developed in Papers I and II. The parameters obtained from the density functional theory calculations, such as vibrational coupling constants and basis mode frequencies, are used to numerically simulate two-dimensional (2D) IR spectra of dG(n):dC(n) and dA(n):dT(n) double helices with n varying from 1 to 10. From the molecular dynamics simulations of dG(5)C(5) and dA(5)T(5) double helices in D(2)O solution, it is found that the thermally driven internal motions of these systems in an aqueous solution do not induce strong fluctuations of basis mode frequencies nor vibrational couplings. In order to construct the two-exciton Hamiltonian, the vibrational anharmonicities of eight basis modes are obtained by carrying out B3LYP6-31G(*) calculations for the nine basis modes. The simulated 2D IR spectra of dG(n):dC(n) double helix in D(2)O solution are directly compared with closely related experimental results. The 2D IR spectra of dG(n):dC(n) and dA(n):dT(n) are found to be weakly dependent on the number of base pairs. The present work demonstrates that the computational procedure combining quantum chemistry calculation and molecular dynamics simulation methods can be of use to predict 2D IR spectra of nucleic acids in solutions.

A systematic study of polarized IR spectra of the hydrogen bond in formic acid crystals

In this paper, we present the results of our investigation of the polarized IR spectra of the hydrogen bond in formic acid crystals, as well as in crystals of the three deuterium derivatives of the compound: DCOOH, HCOOD, and DCOOD. These spectra were measured by a transmission method, using polarized light at 273 K and also at the temperature of liquid nitrogen for the “ bc” crystalline face. Our studies mainly focused on spectral effects corresponding to the intensity distribution, the influence of temperature, the linear dichroism, and isotopic substitution of deuterium in formic acid molecules measured in the frequency range of the proton and the deuterium stretching vibration bands, ν O–H and ν O–D, respectively. The basic spectral properties of the hydrogen bond IR spectra of formic acid crystals were interpreted in a quantitative way in terms of the “strong-coupling” theory. On the basis of this theoretical model, we succeeded in explaining the fine structure patterns of the ν O–H and ν O–D polarized sub-bands, the temperature, the dichroic, and the H/D isotopic effects in the spectra. The spectra were interpreted as a result of vibrational exciton interactions involving two adjacent hydrogen bonds in one chain of the associated molecules. The hydrogen bonds from one unit cell belonging to different chains were found uncoupled. In the spectra of isotopically diluted crystalline samples of HCOOH and DCOOH we found no characteristic changes in the “residual” ν O–H band shapes, which could be attributed to a random distribution of protons and deuterons in open chains of the hydrogen bonded molecules. This fact proves the existence of strong dynamical co-operative interactions in the hydrogen bond chain system in the formic acid crystal lattices responsible for a non-random distribution of protons and deuterons in the chains.

Vibrational excitons in α-helical polypeptides: Multiexciton self-trapping and related infrared transient absorption

Based on the multiexciton expansion of a model Hamiltonian, an accurate quantum-dynamical description of vibrational states formed by amide modes in alpha-helical polypeptides is presented. Using the multiconfiguration time-dependent Hartree method, linear and pump-probe infrared absorption spectra are calculated by numerical time propagation of the exciton-chain vibrational wave function. The formation of self-trapped exciton states is discussed within the approximation of adiabatic excitons and within the full quantum description.

Local structure of beta-hairpin isotopomers by FTIR, 2D IR, and ab initio theory.

The 12-residue tryptophan zipper beta-hairpin (SWTWENGKWTWK) and two (13)C-isotopomers were examined in the amide-I region using FTIR and femtosecond two-dimensional infrared (2D IR) spectroscopies. Spectroscopic features of the labeled transitions with (13)C-substituted amide unit present in the terminal or turn region of the hairpin, including their frequency shifts and distributions, line broadenings, orientations, and anharmonicities of diagonal peaks, allow the peptide local structure and local environment to be examined. The results suggest a larger structure fluctuation in the terminal region than in the turn region as a result of the side chain effect and solvent-peptide interaction. The results also suggest that the uncoupled amide-I modes are not degenerate and that this is likely to be a common situation for solvated polypeptides. In addition, the amide-I states in the terminal and turn regions were found to be delocalized over several neighboring amide units. Cross-peaks between the various labeled and unlabeled structural regions were clearly observed in the 2D IR correlation spectra, allowing them to be characterized for monitoring structural changes. These results illustrate the sensitivity of 2D IR to the local environment of solvated peptides. The simulated 1D and 2D IR spectra of the hairpin, obtained by using the vibrational exciton model incorporating coupling constants from quantum chemical computations and semiempirical calculations, were found to reproduce the essential features of the experimental results.

Time-domain chirally-sensitive three-pulse coherent probes of vibrational excitons in proteins

The third-order optical response of Bosonic excitons is calculated using the Green’s function solution of the nonlinear exciton equations (NEE), which establish a quasi particle-scattering mechanism for optical nonlinearities. Both time-ordered and non-ordered forms of the response function which represent time and frequency domain techniques, respectively, are derived. New components of the response tensor are predicted for isotropic ensembles of periodic chiral structures to first order in the optical wavevector. The nonlocal nonlinear response function is calculated in momentum space. The finite exciton–exciton interaction length is used to greatly reduce the computational effort. Applications arc made to coupled anharmonic vibrations in the amide I infrared band of peptides. Chirally sensitive and non-sensitive signals for α helices and antiparallel β sheets are compared.

Anharmonicity of Amide Modes

The principal contributions to the anharmonic coupling of amide vibrations are explored with the objective of comparing recent experiments with density functional theory and evaluating simple models of mode coupling. Experimental information obtained by means of two-dimensional infrared spectroscopy (2D IR) is reasonably well predicted by the computed one- and two-quantum anharmonic modes of amide-A, -I, and -II types in mono-, di- and tripeptides. The expansion of the vibrational energy up to the cubic and quartic coupling of harmonic modes suggested criteria to assess how localized are the forces determining the anharmonicity. The off-diagonal anharmonicity between an amide-A and one other amide mode was shown to be mainly determined by forces involving only these two modes, whereas the off-diagonal anharmonicity of two amide-I modes in peptides depended significantly on forces due to motions other than those of the amide-I type. Both the diagonal and off-diagonal anharmonicities exhibit sensitivity to peptide structures. These results should prove useful in linking 2D IR experimental results to secondary structure. Further, the results are used to evaluate the vibrational exciton model for the mixed-mode anharmonicities of the amide-I transitions.

Characteristic two-dimensional IR spectroscopic features of antiparallel and parallel β-sheet polypeptides: Simulation studies

The antiparallel and parallel beta sheets are two of the most abundant secondary structures found in proteins. Although various spectroscopic methods have been used to distinguish these two different structures, the linear spectroscopic measurements could not provide incisive information for distinguishing an antiparallel beta sheet from a parallel beta sheet. After carrying out quantum-chemistry calculations and model simulations, we show that the polarization-controlled two-dimensional (2D) IR photon echo spectroscopy can be of critical use in distinguishing these two different beta sheets. Particularly, the ratio between the diagonal peak and the cross peak is found to be strongly dependent on the quasi-2D array of the amide I local-mode transition dipole vectors. The relative intensities of the cross peaks in the 2D difference spectrum of an antiparallel beta sheet are significantly larger than those of the diagonal peaks, whereas the cross-peak amplitudes in the 2D difference spectrum of a parallel beta sheet are much weaker than the main diagonal-peak amplitudes. A detailed discussion on the origin of the diagonal- and cross-peak intensity distributions of both the antiparallel and parallel beta sheets is presented by examining vibrational exciton delocalization, relative angles between two different normal-mode transition dipoles, and natures of the cross peaks in the 2D difference spectrum.

Adiabatic vibrational excitons: Amide I states in α-helices as an example

Based on a correct quantum dynamical description, exciton formation and self-trapping in α-helical polypeptides is reinvestigated. The studies are focused on the amide I high-frequency vibration of the peptide group and account for their modulation by longitudinal helix vibrations. First, the adiabatic single- and two-exciton states are analyzed for a chain of 10 peptide units, whereby the presence of two types of self-trapped amide I two-exciton states is confirmed. In a second step, by using the multi-configuration time-dependent Hartree method an exact quantum description is achieved for the complete exciton helix-vibrational states. The computational approach incorporating up to nine helix coordinates is used to calculate the infrared linear absorbance. Moreover, excitation energy motion through the chain is characterized.

Collective Oscillations and the Linear and Two-Dimensional Infrared Spectra of Inhomogeneous β-Sheets

We numerically calculate the collective amide I oscillations and the associated linear and two-dimensional infrared (2DIR) spectra for model antiparallel beta-sheets and study the effect of inhomogeneity. To visualize the collective vibrational exciton states, a new method is introduced, which proves very useful in classifying the optically dominant states with respect to their symmetry properties and phase relations, even in the absence of exact symmetries. We find that energy (diagonal) and interaction (off-diagonal) disorder may have profoundly different effects on the main peaks in the linear spectrum. We also show that in the 2DIR spectra energy disorder leads to diagonal stretching of the diagonal peaks, while the cross-peaks are typically stretched more horizontally. This offers an explanation for the recently observed overall Z-shape in experimental spectra. Finally, we find that the anharmonic splitting between associated positive and negative features in the 2DIR spectra scales inversely proportionally with the exciton delocalization size imposed by the disorder, thus offering a spectroscopic ruler for this size.

Vibrational Excitons in CH-Stretching Fundamental and Overtone Vibrational Circular Dichroism Spectra

A set of vibrational circular dichroism (VCD) spectra in the CH-stretching fundamental region for about twenty compounds belonging to the class of essential oils was empirically analyzed by the use of a sort of vibrational exciton mechanism, involving three centers. Through a general formula applicable to many coupled dipole oscillators, the rotational strengths of the previously identified vibrational excitons are evaluated. The results are then critically reviewed by the use of recent ab initio methodology, as applied to selected molecules of the original set. Further insight is gained by model calculations adding up the contribution of the coupling between electric dipole moments associated with normal mode behavior and that of the polarizability from polarizable groups. The former part is responsible for the excitonic behavior of the VCD spectra. For the same selected molecules we have also investigated whether some excitonic behavior is taking place in the second overtone region, and have concluded that this is not the case.

Temperature study of resonance intermolecular interaction in normal long-chain carboxylic acid crystals using IR absorption spectra

In the present paper we report on temperature dependent FTIR spectra studies of Davydov splitting value for the in-phase CH 2 rocking vibrations of crystal methylene chains of n-carboxylic acids CH 3(CH) n−2 COOH with odd ( n=15,17,19) and even ( n=10,14,16,22) numbers of carbon atoms, n, in the temperature region from 100 K to the crystal melting temperature. A statistic-dynamic model is proposed which provides an adequate description of the observed dependences. In the framework of this model, two different mechanisms are responsible for the temperature changes of the splitting value of vibrational modes. In addition to the thermal expansion of crystals under heating, the damping of vibrational excitons on orientational defects of different nature takes place. Genesis of such defects is connected with the excitation of conformational, librational and rotational degrees of freedom of H-bonded molecular dimers of studied acids at different temperatures. The theoretical analysis of the effect of the resonance dynamical intermolecular interaction on the spectra of intramolecular vibrations of the crystals was performed in terms of stochastic equations, taking into account mentioned mechanisms. The explicit expression for the theoretical dependence of Davydov splitting value on temperature was obtained. Computer simulation of such dependence was performed for crystalline long-chain n-carboxylic acids. Good agreement between the experimental and computer simulation results was obtained.

IR signature of (CO2)N clusters: size, shape and structural effects

The structure of carbon dioxide aggregates is investigated by means of direct absorption IR specroscopy in the region of the antisymmetric stretching vibration v3. The (CO2)N particles are generated under dynamic (supersonic cooling in Laval nozzles) and static (collisional cooling cells) conditions over a broad mean size range (20 < N < 10(5)). The vibrational exciton approach is used to interpret the observed spectral features. The particles generated by supersonic cooling remain globular in shape even for the largest explored aggregate sizes (N approximately 10(5)), thus highlighting the absence of agglomeration between primary clusters under our jet conditions. This is in contrast to collisional cooling where the primary particles strongly agglomerate after a few seconds. The spectra for the larger particles (N > 10(4)) are well reproduced by the simulations if cuboctahedral or octahedral rather than spherical aggregate shapes are assumed.

Peptide Secondary Structure Determination by Three-Pulse Coherent Vibrational Spectroscopies: A Simulation Study

Amide I mode vibrational spectra of four ideal secondary structural motiffs of peptides, α helix, 3 1 0 helix, parallel β sheet, and antiparallel β sheet, in response to three infrared pulses with wavevectors k 1 , k 2 , and k 3 are simulated using a vibrational exciton model. Correlation plots of the signals generated at -k 1 + k 2 + k 3 and +k 1 + k 2 - k 3 show a characteristic peak pattern for each motiff. Resolution is enhanced by applying specific polarization configurations of the optical fields to oriented peptides.

About the nature of phase transition in pure n-paraffin crystals

It is known that in long-chain aliphatic crystals a first order phase transition from three-dimensional translationally symmetric phase to one-dimensional translationally symmetric (hexagonal) one may occur in the temperature range below the melting point. During this transition, the molecules might be involved in torsion rotations around their long axes. It is clear that any distortions in periodic location of the atoms in the plane perpendicular to the long axis of the molecules must result in some peculiarities in the intermolecular interactions. In particular, one could expect changes in resonance dynamic intermolecular interaction (Davydov splitting of vibrational excitons) in orientationally disordered phase. Theoretical analysis of manifestation of resonance dynamical intermolecular interaction in the spectra of intramolecular vibrations in these crystals has been carried out in terms of stochastic equations with taking into consideration the above mentioned phase transition. We obtained the explicit expression for theoretical dependence of Davydov splitting value on temperature. We showed that at the transition to the high-temperature (hexagonal) phase, the absorption bands, which correspond to Davydov splitting components rapidly approach each other. This spectral effect is connected to the damping of vibrational excitons at their interaction with orientational defects in the crystal lattice. Such defects arise due to the thermal activation of molecular torsional-rotation degrees of freedom during the crystal transition to one-dimensional phase. Computer simulation of such dependence has been performed for some aliphatic compounds. Good agreement between the experimental and computer simulation results has been obtained. Theoretical approach developed in the present paper for resonance dynamical intermolecular interaction near the transition from three-dimensional to one-dimensional phase of crystalline n-paraffins is of general nature and may be applied to the description of some specific features observed in the vibrational spectra of rotary crystals.