The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.     

Electrostatic DFT map for the complete vibrational amide band of NMA

An anharmonic vibrational Hamiltonian for the amide I, II, III, and A modes of N-methyl acetamide (NMA), recast in terms of the 19 components of an external electric field and its first and second derivative tensors (electrostatic DFT map), is calculated at the DFT(BPW91/6-31G(d,p)) level. Strong correlations are found between NMA geometry and the amide frequency fluctuations calculated using this Hamiltonian together with the fluctuating solvent electric field obtained from the MD simulations in TIP3 water. The amide I and A frequencies are strongly positively correlated with the C=O and N-H bond lengths. The C=O and C-N amide bond lengths are negatively correlated, suggesting the solvent-induced fluctuations of the contribution of zwitterionic resonance form. Sampling the global electric field in the entire region of the transition charge densities (TCDs) is required for accurate infrared line shape simulations. Collective electrostatic solvent coordinates which represent the fluctuations of the 10 lowest amide fundamental and overtone states are reported. Normal-mode analysis of an NMA-3H(2)O cluster shows that the 660 cm(-1) to 1100 cm(-1) oscillation found in the frequency autocorrelation functions of the amide modes may be ascribed to the two bending vibrations of intermolecular hydrogen bonds with the amide oxygen of NMA.     

Infrared Spectral Assignment of Pyrimidine and Pyrazine in the CH Stretching Region by an Effective Spectroscopic Hamiltonian

Mid-Infrared spectra of pyrimidine (PM) and pyrazine (PZ) were recorded in the gas phase using a multi-pass long path gas cell. The IR band structure of these compounds above and below 3000 cm⁻¹ is very broad and contains many humps and shoulders. These humps and shoulders are due to various higher quantum excitation of low-frequency vibrational modes, which participate in Fermi resonance with the nearby CH stretch fundamentals and appears in this region. We constructed an Effective Spectroscopic Hamiltonian (ESH) in a mixed local mode (LM) normal mode (NM) basis to assign the various overtone and combination bands in the CH stretching region of these compounds. The CH stretching vibrations of both PZ and PM were treated as symmetrized anharmonic Morse oscillators in local coordinates and the in-plane deformations down to 1000 cm⁻¹ were treated as normal coordinates. The ESHs were diagonalized and the resulting eigenvalues were subsequently fitted in a given parameter space with the experimentally observed bands. The eigenvalues of the converged Hamiltonian are the anharmonic frequencies and the transition intensities were obtained by summing the squared eigenvector components. The overtone and combination transitions near 3000 cm⁻¹ of both PM and PZ were identified and assigned from the eigenvector coefficients of the ESH matrix. The wavefunctions of a pure CH stretch, overtone of the HCC in-plane bend and due to Type 1 Fermi coupling (resonance between a fundamental with an overtones of a low frequency mode, in this case resonance between the CH strech and the overtone of HCC in-plane bending modes) has been demonstrated pictorially.     

Vibrational spectroscopy and DFT calculations of 1,3-dibromo-2,4,6-trimethylbenzene: Anharmonicity,coupling and methyl group tunneling

The Raman, IR and INS spectra of 1,3-dibromo-2,4,6-trimethylbenzene (DBMH) were recorded in the 80–3200 cm⁻¹ range. The molecular conformation and vibrational spectra of DBMH were computed at the MPW1PW91/LANL2DZ level. Except for the methyl 2 environment, the agreement between the DFT calculations and the neutron diffraction structure is almost perfect (deviations < 0.01 Å for bond lengths, <0.2° for angles). The frequencies of the internal modes of vibration were calculated with the harmonic and anharmonic approximations; the later method yields results that are in remarkable agreement with the spectroscopic data, resulting in a confident assignment of the vibrational bands. Thus, no scaling is necessary. The coupling, in phase or anti-phase, of the motions of symmetrical CBr and CMe bonds is highlighted. Our DFT calculations suggest that the torsion of methyl groups 4 and 6 is hindered in deep wells, whereas methyl group 2 is a quasi-free rotor. The failure of the calculations to determine the frequencies of the methyl torsional modes is explained as follows: DFT does not consider the methyl spins and assumes localization of the protons, whereas the methyl groups must be treated as quantum rotors.     

Vibrational relaxation pathways of amide I and amide II modes in N-methylacetamide

We studied the vibrational energy relaxation mechanisms of the amide I and amide II modes of N-methylacetamide (NMA) monomers dissolved in bromoform using polarization-resolved femtosecond two-color vibrational spectroscopy. The results show that the excited amide I vibration transfers its excitation energy to the amide II vibration with a time constant of 8.3 ± 1 ps. In addition to this energy exchange process, we observe that the excited amide I and amide II vibrations both relax to a final thermal state. For the amide I mode this latter process dominates the vibrational relaxation of this mode. We find that the vibrational relaxation of the amide I mode depends on frequency which can be well explained from the presence of two subbands with different vibrational lifetimes (~1.1 ps on the low frequency side and ~2.7 ps on the high frequency side) in the amide I absorption spectrum.     

On the temperature dependence of amide I frequencies of peptides in solution

The temperature dependence of the amide I vibrational frequencies of peptides in solution was investigated. In D2O, the amide I' bands of both an alpha-helical oligopeptide, the random-coil poly(L-lysine), and the simplest amide, N-methyl acetamide (NMA), exhibit linear frequency shifts of approximately 0.07 cm(-1)/degrees C with increasing temperature. Similar amide I frequency shifts are also observed for NMA in both polar (acetonitrile and DMSO) and nonpolar (1,4-dioxane) organic solvents, thus ruling out hydrogen-bonding strength as the cause of these effects. The experimental NMA amide I frequencies in the organic solvents can be accurately described by a simple theory based on the Onsager reaction field with temperature-dependent solvent dielectric properties and a solute molecular cavity. DFT-level calculations (BPW91/cc-pVDZ) for NMA with an Onsager reaction field confirm the significant contribution of the molecular cavity to the predicted amide I frequencies. Comparison of the computations to experimental data shows that the frequency-dependent response of the reaction field, taken into account by the index of refraction, is crucial for describing the amide I frequencies in polar solvents. The poor predictions of the model for the NMA amide I band in D2O might be due, in part, to the unknown temperature dependence of the refractive index of D2O in the mid-IR range, which was approximated by the available values in the visible region.     

Vibrational relaxation pathways of AI and AII modes in N-methylacetamide clusters

We studied the pathways of vibrational energy relaxation of the amide I (~1660 cm?1) and amide II (~1560 cm?1) vibrational modes of N-methylacetamide (NMA) in CCl? solution using two-color femtosecond vibrational spectroscopy. We measured the transient spectral dynamics upon excitation of each of these amide modes. The results show that there is no energy transfer between the amide I (AI) and amide II (AII) modes. Instead we find that the vibrational energy is transferred on a picosecond time scale to a common combination tone of lower-frequency modes. By use of polarization-resolved femtosecond pump-probe measurements we also study the reorientation dynamics of the NMA molecules and the relative angle between the transition dipole moments of the AI and AII vibrations. The spectral dynamics at later times after the excitation (>40 ps) reveal the presence of a dissociation process of the NMA aggregates, trimers, and higher order structures into dimers and monomers. By measuring the dissociation kinetics at different temperatures, we determined the activation energy of this dissociation E(a) = 35 ± 3 kJ mol?1.     

Matrix isolation infrared spectroscopic and quantum chemical studies on the rotational isomers of orotic acid (6-carboxyuracil)

The infrared spectrum of orotic acid (6-carboxyuracil) isolated in a low-temperature argon matrix is presented, for the first time. This molecule is a key precursor in the biosynthesis of all pyrimidine nucleotides in living organisms. The comprehensive theoretical studies on the rotational isomerism of orotic acid have been performed by an ab initio MP2 and three density functional methods (B3LYP, M06 and M06-2X). All theoretical methods have predicted that four possible conformers of orotic acid may exist in the gas phase. The calculated barrier height for rotation of the COOH group around the CC bond (37 kJ mol⁻¹, M06-2X) is much lower than the barriers for the OH rotation around the CO bond (47 and 51 kJ mol⁻¹). The Gibbs free energies, relative stabilities and the mole fractions of isomers at different temperatures, in the gas phase, have been determined.The anharmonic vibrational frequencies, infrared intensities and potential energy distributions (PEDs) were computed for two isomers of the lowest energy (A and B) using the B3LYP method with the aug-cc-pVTZ basis set. The theoretical anharmonic IR spectra are in excellent agreement with the experiment. It is concluded that the most stable conformer (A) is the predominant form in a low-temperature argon matrix, while the mole fraction of the less stable B conformer can be assessed as ca. 15%. No spectral indications of the presence of other isomers (C and D) in the matrix were detected.     

Computational spectroscopy of ubiquitin: comparison between theory and experiments

Using the constrained molecular dynamics simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, the authors have established computational schemes for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and two-dimensional (2D) IR photon echo spectra of the protein ubiquitin in water. Vibrational characteristic features of these spectra in the amide I vibration region are discussed. From the semiempirical quantum chemistry calculation results on an isolated ubiquitin, amide I local mode frequencies and vibrational coupling constants were fully determined. It turns out that the amide I local mode frequencies of ubiquitin in both gas phase and aqueous solution are highly heterogeneous and site dependent. To directly test the quantitative validity of thus obtained spectroscopic properties, they compared the experimentally measured amide I IR, 2D IR, and electronic circular dichroism spectra with experiments, and found good agreements between theory and experiments. However, the simulated VCD spectrum is just qualitatively similar to the experimentally measured one. This indicates that, due to delicate cancellations between the positive and negative VCD contributions, the prediction of protein VCD spectrum is critically relied on quantitative accuracy of the theoretical model for predicting amide I local mode frequencies. On the basis of the present comparative investigations, they found that the site dependency of amide I local mode frequency, i.e., diagonal heterogeneity of the vibrational Hamiltonian matrix in the amide I local mode basis, is important. It is believed that the present computational methods for simulating various vibrational and electronic spectra of proteins will be of use in further refining classical force fields and in addressing the structure-spectra relationships of proteins in solution.     

Observation of sub-surface phenyl rings in polystyrene with vibrationally resonant sum-frequency generation

The use of vibrationally resonant sum-frequency generation (VR-SFG) spectroscopy to investigate the structure of surfaces and interfaces generally relies on the assumption that only the surface/interface is probed and that the vibrational mode assignments are known and correct. To make vibrational mode assignments, two fundamental aspects of the technique must be dealt with. First, not all vibrational modes observed in linear spectroscopic techniques, such as IR and Raman, are necessarily present in the VR-SFG spectrum. Second, while it is generally assumed that VR-SFG only probes the surface, this technique in actuality is sensitive to molecules in any environment with broken symmetry. Previously published assignments for the aromatic CH stretching modes of polystyrene surfaces are contradictory, and one purpose of this work is to revisit those assignments. In addition to thin films of polystyrene, we have collected VR-SFG spectra of dimethylphenyl silane, polystyrene covered with a layer of poly(methyl methacrylate) (PMMA), and plasma-treated polystyrene to aid our mode assignments. Density functional theory calculations were also performed on styrene oligomers. Based on these experimental and theoretical results, we have determined that not all the expected vibrational modes are observed in the VR-SFG spectrum of polystyrene. We have also found that one particular mode, the ν₂ symmetric stretch, accounts for two of the observed peaks, one from the exposed surface and a second feature from a subsurface layer within the polymer thin film. These two features appear at separate frequencies (11 cm⁻¹ separation) because this mode is very sensitive to the local density, which is higher in the bulk than at the surface. With these experimentally validated mode assignments, VR-SFG spectra in the aromatic CH stretching region can be interpreted more reliably. More importantly, these results demonstrate that great care must be taken in assigning VR-SFG spectra. These results also show that VR-SFG can be used to interrogate more than just free surfaces and buried interfaces; any area of broken symmetry is probed with this technique.     

Study of the hydrogen bonding of 1,4-bis[(3,4,5-trihexyloxyphenyl)hydrazide]phenylene in crystalline and liquid crystalline phases using infrared,Raman, and two-dimensional correlation spectroscopy

The vibrational bands of a dihydrazide derivative, 1,4-bis[(3,4,5-trihexyloxyphenyl)hydrazide]phenylene (TC6), observed in the Raman and infrared spectra were assigned. The intermolecular hydrogen bonding vibrational bands due to CO and NH groups in the low-frequency Raman spectra were observed at 111 and 94 cm⁻¹ in the crystalline and liquid crystalline (LC) phases, respectively. The sequential order of changes in the hydrogen bonding and alkyl chains was opposite in the crystalline and LC phases. The modifications in the hydrogen bonding occurred prior to conformational changes in the hydrocarbon chains in the crystalline phase; however, a reverse trend was observed in the LC phase. Simultaneously, the two-dimensional (2D) IR and Raman correlation spectroscopic analysis showed that the amide I band of TC6 in the LC phase comprised at least five distinct bands. In addition, the hetero 2D correlation between the NH and CO groups confirmed that no free NH and CO groups existed in the LC phase.     

Structural and vibrational studies of molecular conductors using quantum mechanical methods: 1,3-Dithiole-2-thione, 1,3-dithiole-2-one, 1,3-dioxole-2-one and 1,3-dioxole-2-thione

Computations were carried out by employing the RHF and density functional theory (DFT) methods to investigate the geometries, atomic charges, harmonic vibrational frequencies for the 1,3-dithiole-2-thione (DTT), 1,3-dithiole-2-one (DTO), 1,3-dioxole-2-thione (DOT) and 1,3-dioxole-2-one (DOO) molecules and their radical cations. The geometrical parameters and atomic charges on various atomic sites of the DTT and DOT molecules and their radical cations suggest extended conjugation in these systems. Contrary to this, for the DOO⁺ and DTO⁺ ions there is no evidence in favour of such conjugation, however, the neutral molecules exhibit some conjugation. Harmonic forced field and vibrational mode calculations provided convincing theoretical evidence for the reassignment of some fundamental vibrational modes for all the four molecules. In going from the neutral species to the charged ions for all the four cases the CC stretching frequency is found to decrease drastically. The CS stretching frequency reduces drastically for the DTT and DOT molecules as compared to their radical cations whereas the CO stretching frequency is found to increase in going from the neutral molecule to its radical cation for the DOO and DTO molecules. The ring stretching mode with a₁ symmetry and CC and CO/S stretching modes in these molecules appear to help in conversion of neutral molecule into respective radical cation and neighbouring radical cation into respective neutral molecule. Thus, there appears the feasibility of stretching vibrational mode coupling with electron transfer.     

Vibrational spectroscopy for glycine adsorbed on silicon clusters: Harmonic and anharmonic calculations for models of the Si(1 0 0)-2 × 1 surface

The vibrational spectroscopy of a glycine molecule adsorbed on a silicon surface is studied computationally, using different clusters as models for the surface. Harmonic frequencies are computed using density functional theory (DFT) with the B3LYP functional. Anharmonic frequency calculations are carried out using vibrational self-consistent field (VSCF) algorithms on an improved PM3 potential energy surface. The results are compared with experiments on Glycine@Si(1 0 0)-2 × 1.

The main findings are: (1) Agreement of the computed frequencies with experiment improves with cluster size. (2) The anharmonic calculations are generally in better agreement with experiment than the harmonic ones. The improvements due to anharmonicity are most significant for hydrogenic stretching. (3) An important part of the anharmonic effects is due to anharmonic coupling between different normal modes of the system. (4) The anharmonic coupling between glycine vibrational modes is much larger than the anharmonic coupling between glycine and “phonon” (cluster) modes.

Implications of the results for surface vibrational spectroscopy are discussed.     

Vibrational spectroscopy of protonated imidazole and its complexes with water molecules: ab initio anharmonic calculations and experiments

The results of anharmonic frequency calculations on neutral imidazole (C3N2H4, Im), protonated imidazole (ImH+), and its complexes with water (ImH+)(H2O)n, are presented and compared to gas phase infrared photodissociation spectroscopy (IRPD) data. Anharmonic frequencies are obtained via ab initio vibrational self-consistent field (VSCF) calculations taking into account pairwise interactions between the normal modes. The key results are: (1) Prediction of anharmonic vibrational frequencies on an MP2 ab initio potential energy surface show excellent agreement with experiment and outstanding improvement over the harmonic frequencies. For example, the ab initio calculated anharmonic frequency for (ImH+)(H2O)N2 exhibits an overall average percentage error of 0.6% from experiment. (2) Anharmonic vibrational frequencies calculated on a semiempirical potential energy surface fitted to ab initio harmonic data represents spectroscopy well, particularly for water complexes. As an example, anharmonic frequencies for (ImH+)H2O and (ImH+)(H2O)2 show an overall average deviation of 1.02% and 1.05% from experiment, respectively. This agreement between theory and experiment also supports the validity and use of the pairwise approximation used in the calculations. (3) Anharmonic coupling due to hydration effects is found to significantly reduce the vibrational frequencies for the NH stretch modes. The frequency of the NH stretch is observed to increase with the removal of a water molecule or replacement of water with N2. This result also indicates the ability of the VSCF method to predict accurate frequencies in a matrix environment. The calculation provides insights into the nature of anharmonic effects in the potential surface. Analysis of percentage anharmoncity in neutral Im and ImH+ shows a higher percentage anharmonicity in the NH and CH stretch modes of neutral Im. Also, we observe that anharmonicity in the NH stretch modes of ImH+ have some contribution from coupling effects, while that of neutral Im has no contribution whatsoever from mode-mode coupling. It is concluded that the incorporation of anharmonic effects in the calculation brings theory and experiment into much closer agreement for these systems.     

Harmonic analysis of large systems. I. Methodology

Methods have been developed for the determination of vibrational frequencies and normal modes of large systems in the full conformational space (including all degrees of freedom) and in a reduced conformational space (reducing the number of degrees of freedom). The computational method, which includes Hessian generation and storage, full and iterative diagonalization techniques, and the refinement of the results, is presented. A method is given for the quasiharmonic analysis and the reduced basis quasiharmonic analysis. The underlying principle is that from the atomic fluctuations, an effective harmonic force field can be determined relative to the dynamic average structure. Normal mode analysis tools can be used to characterize quasiharmonic modes of vibration. These correspond to conventional normal modes except that anharmonic effects are included. Numerous techniques for the analyses of vibrational frequencies and normal modes are described. Criteria for the analysis of the similarity of low-frequency normal modes is presented. The approach to determining the natural frequencies and normal modes of vibration described here is general and applicable to any large system. © 1995 John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

Vibrational spectroscopic determination of local solvent electric field, solute-solvent electrostatic interaction energy, and their fluctuation amplitudes

IR probes have been extensively used to monitor local electrostatic and solvation dynamics. Particularly, their vibrational frequencies are highly sensitive to local solvent electric field around an IR probe. Here, we show that the experimentally measured vibrational frequency shifts can be inversely used to determine local electric potential distribution and solute-solvent electrostatic interaction energy. In addition, the upper limits of their fluctuation amplitudes are estimated by using the vibrational bandwidths. Applying this method to fully deuterated N-methylacetamide (NMA) in D(2)O and examining the solvatochromic effects on the amide I' and II' mode frequencies, we found that the solvent electric potential difference between O(═C) and D(-N) atoms of the peptide bond is about 5.4 V, and thus, the approximate solvent electric field produced by surrounding water molecules on the NMA is 172 MV/cm on average if the molecular geometry is taken into account. The solute-solvent electrostatic interaction energy is estimated to be -137 kJ/mol, by considering electric dipole-electric field interaction. Furthermore, their root-mean-square fluctuation amplitudes are as large as 1.6 V, 52 MV/cm, and 41 kJ/mol, respectively. We found that the water electric potential on a peptide bond is spatially nonhomogeneous and that the fluctuation in the electrostatic peptide-water interaction energy is about 10 times larger than the thermal energy at room temperature. This indicates that the peptide-solvent interactions are indeed important for the activation of chemical reactions in aqueous solution.     

Molecular structure and vibrational assignment of 2-,4-,6-methylquinoline by density functional theory (DFT) and ab initio Hartree-Fock (HF) calculations

The molecular geometry, the normal mode frequencies and corresponding vibrational assignments of 2-,4-,6-methylquinoline (2-,4-,6-mq) in the ground state were performed by HF and DFT/B3LYP levels of theory using the 6-31++G(d,p) basis set. Harmonic and anharmonic vibrational frequencies were calculated. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method by using parallel quantum mechanic solutions program. The general agreements between the observed and calculated frequencies are shown.