Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. II. Infrared spectrum and vibrational dynamics

The infrared absorption spectrum of the protonated water dimer (H5O2+) is simulated in full dimensionality (15 dimensional) in the spectral range of 0-4000 cm(-1). The calculations are performed using the multiconfiguration time-dependent Hartree (MCTDH) method for propagation of wavepackets. All the fundamentals and several overtones of the vibrational motion are computed. The spectrum of H5O2+ is shaped to a large extent by couplings of the proton-transfer motion to large amplitude fluxional motions of the water molecules, water bending and water-water stretch motions. These couplings are identified and discussed, and the corresponding spectral lines are assigned. The large couplings featured by H5O2+ do not hinder, however, to describe the coupled vibrational motion by well defined simple types of vibration (stretching, bending; etc.) based on well defined modes of vibration, in terms of which the spectral lines are assigned. Comparison of our results to recent experiments and calculations on the system is given. The reported MCTDH IR spectrum is in very good agreement to the recently measured spectrum by Hammer et al. [J. Chem. Phys. 122, 244301 (2005)].     

Vibrational relaxation in simulated two-dimensional infrared spectra of two amide modes in solution

Two-dimensional infrared spectroscopy is capable of following the transfer of vibrational energy between modes in real time. We develop a method to include vibrational relaxation in simulations of two-dimensional infrared spectra at finite temperature. The method takes into account the correlated fluctuations that occur in the frequencies of the vibrational states and in the coupling between them as a result of interaction with the environment. The fluctuations influence the two-dimensional infrared line shape and cause vibrational relaxation during the waiting time, which is included using second-order perturbation theory. The method is demonstrated by applying it to the amide-I and amide-II modes in N-methylacetamide in heavy water. Stochastic information on the fluctuations is obtained from a molecular dynamics trajectory, which is converted to time dependent frequencies and couplings with a map from a density functional calculation. Solvent dynamics with the same frequency as the energy gap between the two amide modes lead to efficient relaxation between amide-I and amide-II on a 560 fs time scale. We show that the cross peak intensity in the two-dimensional infrared spectrum provides a good measure for the vibrational relaxation.     

Ultrafast Vibrational Dynamics and Local Interactions of Hydrated DNA

Biochemical processes occur mainly in aqueous environments, where interactions with water molecules play a key role for both the structure and function of biomolecules. Deoxyribonucleic acid (DNA), the basic carrier of genetic information, is characterized by an equilibrium double helix structure which is held together by intermolecular hydrogen bonds between base pairs and hydrated by an environment of water molecules with fluctuating hydrogen bonds. Basic vibrational motions of hydrated DNA and the fastest changes in the DNA–water interactions and hydration geometries occur in less than 1 ps. These processes can be accessed by mapping the vibrational dynamics of DNA and water in a time‐resolved way by nonlinear ultrafast vibrational spectroscopy. Recent studies provide a detailed understanding of DNA vibrations and their dynamics, and give insight into nonequilibrium properties and structures of hydrated DNA.     

Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability

We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.     

Direct identification and decongestion of Fermi resonances by control of pulse time ordering in two-dimensional IR spectroscopy

We show that it is possible to both directly measure and directly calculate Fermi resonance couplings in benzene. The measurement method used was a particular form of two-dimensional infrared spectroscopy (2D-IR) known as doubly vibrationally enhanced four wave mixing. By using different pulse orderings, vibrational cross peaks could be measured either purely at the frequencies of the base vibrational states or split by the coupling energy. This capability is a feature currently unique to this particular form of 2D-IR and can be helpful in the decongestion of complex spectra. Five cross peaks of the ring breathing mode nu13 with a range of combination bands were observed spanning a region of 1500-4550 cm(-1). The coupling energy was measured for two dominant states of the nu13+nu16 Fermi resonance tetrad. Dephasing rates were measured in the time domain for nu13 and the two (nu13+nu16) Fermi resonance states. The electronic and mechanical vibrational anharmonic coefficients were calculated to second and third orders, respectively, giving information on relative intensities of the cross peaks and enabling the Fermi resonance states of the combination band nu13+nu16 at 3050-3100 cm(-1) to be calculated. The excellent agreement between calculated and measured spectral intensities and line shapes suggests that assignment of spectral features from ab initio calculations is both viable and practicable for this form of spectroscopy.     

Vibrational dynamics of DNA. I. Vibrational basis modes and couplings

Carrying out density functional theory calculations of four DNA bases, base derivatives, Watson-Crick (WC) base pairs, and multiple-layer base pair stacks, we studied vibrational dynamics of delocalized modes with frequency ranging from 1400 to 1800 cm(-1). These modes have been found to be highly sensitive to structure fluctuation and base pair conformation of DNA. By identifying eight fundamental basis modes, it is shown that the normal modes of base pairs and multilayer base pair stacks can be described by linear combinations of these vibrational basis modes. By using the Hessian matrix reconstruction method, vibrational coupling constants between the basis modes are determined for WC base pairs and multilayer systems and are found to be most strongly affected by the hydrogen bonding interaction between bases. It is also found that the propeller twist and buckle motions do not strongly affect vibrational couplings and basis mode frequencies. Numerically simulated IR spectra of guanine-cytosine and adenine-thymine bases pairs as well as of multilayer base pair stacks are presented and described in terms of coupled basis modes. It turns out that, due to the small interlayer base-base vibrational interactions, the IR absorption spectrum of multilayer base pair system does not strongly depend on the number of base pairs.     

Theoretical study of the infrared and Raman line shapes of liquid methanol

Using a combined electronic structure and molecular dynamics simulation method, we calculated the infrared and Raman spectra for the OH vibrations in liquid CH(3)OH. The vibrational frequencies, transition dipole moments, and transition polarizabilities are obtained from density functional theory calculations and then mapped into an empirical relation to the electric field on the H atom along the OH bond. Vibrational couplings between OH chromophores on different molecules are treated using transition dipole interactions. The simulated infrared and Raman line shapes are in good agreement with experimental observations. We have also shown that the vibrations of non-hydrogen-bonded OH groups contribute significantly to the difference between the IR and Raman line shapes.     

Approximate vibrational corrections for NMR spectral parameters of partially oriented molecules

The NMR spectral parameters of partially oriented molecules, such as indirect couplings, chemical shifts and quadrupolar couplings, should be corrected for effects due to vibrational motions. A practicable method of correction, applicable to cases where the parameters are determined approximately by axially symmetric bonds, is described.     

Structures, energetics, and spectra of aqua-cesium (I) complexes: an ab initio and experimental study

The design of cesium-selective ionophores must include the nature of cesium-water interactions. The authors have carried out extensive ab initio and density functional theory calculations of hydrated cesium cations to obtain reasonably accurate energetics, thermodynamic quantities, and IR spectra. An extensive search was made to find the most stable structures. Since water...water interactions are important in the aqua-Cs+ clusters, the authors investigated the vibrational frequency shifts as a function of the number of water molecules and the frequency characteristics with and without the presence of outer-shell water molecules. The predicted vibrational frequencies were then compared with the infrared photodissociation spectra of argon-tagged hydrated cesium cluster ions. This comparison allowed the identification of specific hydrogen-bonding structures present in the experimental spectra.     

Prediction of accurate anharmonic experimental vibrational frequencies for water clusters, (H2O)n, n=2-5

Accurate anharmonic experimental vibrational frequencies for water clusters consisting of 2-5 water molecules have been predicted on the basis of comparing different methods with MP2/aug-cc-pVTZ calculated and experimental anharmonic frequencies. The combination of using HF/6-31G* scaled frequencies for intramolecular modes and anharmonic frequencies for intermolecular modes gives excellent agreement with experiment for the water dimer and trimer and are as good as the expensive anharmonic MP2 calculations. The water trimer, the cyclic Ci and S4 tetramers, and the cyclic pentamer all have unique peaks in the infrared spectrum between 500 and 800 cm-1 and between 3400 and 3700 cm-1. Under the right experimental conditions these different clusters can be uniquely identified using high-resolution IR spectroscopy.     

Anharmonic vibrational modes of nucleic acid bases revealed by 2D IR spectroscopy

Polarization-dependent two-dimensional infrared (2D IR) spectra of the purine and pyrimadine base vibrations of five nucleotide monophosphates (NMPs) were acquired in D(2)O at neutral pH in the frequency range 1500-1700 cm(-1). The distinctive cross-peaks between the ring deformations and carbonyl stretches of NMPs indicate that these vibrational modes are highly coupled, in contrast with the traditional peak assignment, which is based on a simple local mode picture such as C═O, C═N, and C═C double bond stretches. A model of multiple anharmonically coupled oscillators was employed to characterize the transition energies, vibrational anharmonicities and couplings, and transition dipole strengths and orientations. No simple or intuitive structural correlations are found to readily assign the spectral features, except in the case of guanine and cytosine, which contain a single local CO stretching mode. To help interpret the nature of these vibrational modes, we performed density functional theory (DFT) calculations and found that multiple ring vibrations are coupled and delocalized over the purine and pyrimidine rings. Generally, there is close correspondence between the experimental and computational results, provided that the DFT calculations include explicit waters solvating hydrogen-bonding sites. These results provide direct experimental evidence of the delocalized nature of the nucleotide base vibrations via a nonperturbative fashion and will serve as building blocks for constructing a structure-based model of DNA and RNA vibrational spectroscopy.     

Dual-frequency 2D IR on interaction of weak and strong IR modes

Dual-frequency 2D IR heterodyne photon-echo spectroscopy of C[triple bond]N and C=O stretching vibrational modes in 2-cyanocoumarin is reported. We have shown that the interaction among these modes provides convenient and useful structural constraints for molecules. Implementation of two pulse sequences, 4, 4, and 6 microm and 6, 6, and 4 microm, allowed the clear determination of contributions caused by vibrational relaxation. Positive correlation between C[triple bond]N and C=O frequency distributions was observed in 2-cyanocoumarin. Because C[triple bond]N modes are highly localized and have frequencies in a spectral region with minimal water absorption, the C[triple bond]N/C=O interactions have a strong potential for use as structural reporters in proteins. In addition to CN/CO peaks, the cross-peaks responsible for the C[triple bond]N/C=C interaction are also observed in the 2D IR spectra, where C=C is a coumarin ring stretching mode. We have demonstrated that 2D IR spectroscopy can utilize interactions of strong IR modes with weak local modes as structural reporters.     

Vibrational dynamics of DNA: IV. Vibrational spectroscopic characteristics of A-, B-, and Z-form DNA's

Linear and nonlinear IR spectroscopic studies of nucleic acids can provide crucial information on solution conformations of DNA double helix and its complex with other molecules. Carrying out density functional theory calculations of A-, B-, and Z-form DNA's, the authors obtained vibrational spectroscopic properties as well as coupling constants between different basis modes. The vibrational couplings that determine the extent of exciton delocalization are strongly dependent on DNA conformation mainly because the interlayer distance between two neighboring base pairs changes with respect to the DNA conformation. The Z-DNA has comparatively small interlayer vibrational coupling constants so that its vibrational spectrum depends little on the number of base pairs, whereas the A-DNA shows a notable dependency on the size. Furthermore, it is shown that a few distinctively different line shape changes in both IR and two-dimensional IR spectra as the DNA conformation changes from B to A or from B to Z can be used as marker bands and characteristic features distinguishing different DNA conformations.     

Nature of vibrational coupling in helical peptides: an isotopic labeling study

Infrared (IR) and vibrational circular dichroism (VCD) spectra were measured for a series of isotopically ((13)C on two or more amide Cdouble bond]O) labeled, 25 residue, alpha-helical peptides of the sequence Ac-(AAAAK)(4)AAAAY-NH(2) that were also studied in the previous paper. Theoretical IR and VCD simulations were performed for correspondingly isotopically labeled Ac-A(24)-NHCH(3) constrained to an alpha-helical conformation by use of property tensor transfer from density functional theory (DFT) calculations on Ac-A(10)-NHCH(3). The simulations predicted and experiments confirmed that the vibrational coupling constants between i, i + 1 and i, i + 2 residues differ in sign, thus leading to a reversal of the (13)C VCD pattern and explaining the large shift in the (13)C amide I frequency as reported in the previous paper. The sign of the coupling constant remained consistent for larger label separation (with the exception of i, i + 4) and for more labels with uniform separation. Such effects confirm that the isotopically labeled group vibrations are essentially only coupled to each other and are effectively uncoupled from those of the unlabeled groups. This development confirms the utility of isotopic labels for site-specific structural studies with vibrational spectra. Observed spectral effects cannot be explained by considering only transition dipole coupling (TDC) between amide oscillators, particularly for smaller label separations, but the TDC and ab initio predicted couplings roughly converge at large separation.     

Infrared and Raman line shapes for ice Ih. II. H2O and D2O

We present a theoretical study of infrared and Raman line shapes of polycrystalline and single crystal ice Ih, for both water and heavy water, at 1, 125, and 245 K. Our calculations involve a mixed quantum/classical approach, a new water simulation model with explicit three-body interactions, transition frequency and dipole maps, and intramolecular and intermolecular vibrational coupling maps. Our theoretical spectra are in reasonable agreement with experimental spectra (available only near the two higher temperatures). We trace the origins of the different spectral peaks to weak and strong intermolecular couplings. We also discuss the delocalization of the vibrational eigenstates in terms of the competing effects of disorder and coupling.     

Two-dimensional infrared spectral signatures of 3(10)- and alpha-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.     

Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath

Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.     

Theoretical study of the changes in the vibrational characteristics arising from the hydrogen bonding between Vitamin C (L-ascorbic acid) and H2O

The vibrational characteristics (vibrational frequencies, infrared intensities and Raman activities) for the hydrogen-bonded system of Vitamin C (L-ascorbic acid) with five water molecules have been predicted using ab initio SCF/6-31G(d,p) calculations and DFT (BLYP) calculations with 6-31G(d,p) and 6-31++G(d,p) basis sets. The changes in the vibrational characteristics from free monomers to a complex have been calculated. The ab initio and BLYP calculations show that the complexation between Vitamin C and five water molecules leads to large red shifts of the stretching vibrations for the monomer bonds involved in the hydrogen bonding and very strong increase in their IR intensity. The predicted frequency shifts for the stretching vibrations from Vitamin C taking part in the hydrogen bonding are up to -508 cm(-1). The magnitude of the wavenumber shifts is indicative of relatively strong OH...H hydrogen-bonded interactions. In the same time the IR intensity and Raman activity of these vibrations increase upon complexation. The IR intensity increases dramatically (up to 12 times) and Raman activity increases up to three times. The ab initio and BLYP calculations show, that the symmetric OH vibrations of water molecules are more sensitive to the complexation. The hydrogen bonding leads to very large red shifts of these vibrations and very strong increase in their IR intensity. The asymmetric OH stretching vibrations of water, free from hydrogen bonding are less sensitive to the complexation than the hydrogen-bonded symmetric OH stretching vibrations. The increases of the IR intensities for these vibrations are lower and red shifts are negligible.     

Anharmonic Vibrational Motions In C<Subscript>60</Subscript>: A Potential Energy Surface Derived From Vibrational Self-Consistent Field Calculations

A potential energy surface (PES) is developed for C₆₀ designed to describe vibrational motions valid in the anharmonic limit. The PES is based on a previously existing one that is fit to the harmonic fundamentals and is then modified to generate anharmonicity of all orders and in all terms, but without additional fitted parameters. The resulting Cartesian vibrational motions are decomposed into normal modes, and the anharmonic expansion coefficients are calculated including 2-mode couplings and up to 4th order. The resulting PES is used in a vibrational self-consistent field (VSCF) algorithm to calculate the anharmonically corrected fundamental frequencies. The parameters are then fit to fundamental infrared and Raman frequencies. While it is not possible to assign combination and overtone transitions with sufficient experimental accuracy, conclusions about the effects of anharmonic vibrational coupling in C₆₀ are described.