Tracking the Amide I and αCOO- Terminal ν(C=O) Raman Bands in a Family of l-Glutamic Acid-Containing Peptide Fragments: A Raman and DFT Study

The E-hook of β-tubulin plays instrumental roles in cytoskeletal regulation and function. The last six C-terminal residues of the βII isotype, a peptide of amino acid sequence EGEDEA, extend from the microtubule surface and have eluded characterization with classic X-ray crystallographic techniques. The band position of the characteristic amide I vibration of small peptide fragments is heavily dependent on the length of the peptide chain, the extent of intramolecular hydrogen bonding, and the overall polarity of the fragment. The dependence of the E residue's amide I ν(C=O) and the αCOO- terminal ν(C=O) bands on the neighboring side chain, the length of the peptide fragment, and the extent of intramolecular hydrogen bonding in the structure are investigated here via the EGEDEA peptide. The hexapeptide is broken down into fragments increasing in size from dipeptides to hexapeptides, including EG, ED, EA, EGE, EDE, DEA, EGED, EDEA, EGEDE, GEDEA, and, finally, EGEDEA, which are investigated with experimental Raman spectroscopy and density functional theory (DFT) computations to model the zwitterionic crystalline solids (in vacuo). The molecular geometries and Boltzmann sum of the simulated Raman spectra for a set of energetic minima corresponding to each peptide fragment are computed with full geometry optimizations and corresponding harmonic vibrational frequency computations at the B3LYP/6-311++G(2df,2pd) level of theory. In absence of the crystal structure, geometry sampling is performed to approximate solid phase behavior. Natural bond order (NBO) analyses are performed on each energetic minimum to quantify the magnitude of the intramolecular hydrogen bonds. The extent of the intramolecular charge transfer is dependent on the overall polarity of the fragment considered, with larger and more polar fragments exhibiting the greatest extent of intramolecular charge transfer. A steady blue shift arises when considering the amide I band position moving linearly from ED to EDE to EDEA to GEDEA and, finally, to EGEDEA. However, little variation is observed in the αCOO- ν(C=O) band position in this family of fragments.

On the SN2 reactions modified in vibrational strong coupling experiments: reaction mechanisms and vibrational mode assignments

Recent experiments have reported modified chemical reactivity under vibrational strong coupling (VSC) in microfluidic Fabry-Pérot cavities. In particular, the reaction rate of nucleophilic substitution reactions at silicon centers (S_N2@Si) has been altered when a vibrational mode of the reactant was coupled to a confined light mode in the strong coupling regime. In this situation, hybrid light-matter states known as polaritons are formed and seem to be responsible for the modified chemical kinetics. These results are very encouraging for future applications of polaritonic chemistry to catalyze chemical reactions, with the ability to manipulate chemical phenomena without any external excitation of the system. Still, there is no theory capable of explaining the mechanism behind these results. In this work we address two points that are crucial for the interpretation of these experiments. Firstly, by means of electronic structure calculations we report the reaction mechanism in normal conditions of the two recently modified S_N2@Si reactions, obtaining in both cases a triple-well PES where the rate-determining step is due to the Si-C and Si-O bond cleavage. Secondly, we characterize in detail the normal modes of vibration of the reactants. In the VSC experiments, reaction rates were modified only when specific vibrations of the reactants were coupled to a cavity mode. We find that these vibrations are highly mixed among the different fragments of the reactants leading to a completely new assignment of the IR peaks coupled to cavity modes in the original experimental works. Our results are fundamental for the interpretation of the VSC experiments given that in the absence of a theory explaining these results, the current phenomenological understanding relies on the assignment of the character of the vibrational IR peaks.

Assessing cluster models of solvation for the description of vibrational circular dichroism spectra: synergy between static and dynamic approaches

Solvation effects are essential for defining the shape of vibrational circular dichroism (VCD) spectra.

Frequency Range Selection Method for Vibrational Spectra

Theoretical calculations of vibrational properties are widely used to explain and predict experimental spectra. However, with standard quantum chemical methods all molecular motions are considered, which is rather time-consuming for large molecules. Because typically only a specific spectral region is of experimental interest, we propose here an efficient method that allows calculation of only a selected frequency interval. After a computationally cheap low-level estimate of the molecular motions, the computational time is proportional to the number of normal modes needed to describe this frequency range. Results for a medium-sized molecule show a reduction in computational time of up to 1 order of magnitude with negligible loss in accuracy. We also show that still larger computational savings are possible by using an additional intensity-selection procedure.

Accurate vibrational spectra via molecular tailoring approach: a case study of water clusters at MP2 level

In spite of the recent advents in parallel algorithms and computer hardware, high-level calculation of vibrational spectra of large molecules is still an uphill task. To overcome this, significant effort has been devoted to the development of new algorithms based on fragmentation methods. The present work provides the details of an efficient and accurate procedure for computing the vibrational spectra of large clusters employing molecular tailoring approach (MTA). The errors in the Hessian matrix elements and dipole derivatives arising due to the approximation nature of MTA are reduced by grafting the corrections from a smaller basis set. The algorithm has been tested out for obtaining vibrational spectra of neutral and charged water clusters at Møller-Plesset second order level of theory, and benchmarking them against the respective full calculation (FC) and/or experimental results. For (H2O)16 clusters, the estimated vibrational frequencies are found to differ by a maximum of 2 cm(-1) with reference to the corresponding FC values. Unlike the FC, the MTA-based calculations including grafting procedure can be performed on a limited hardware, yet take a fraction of the FC time. The present methodology, thus, opens a possibility of the accurate estimation of the vibrational spectra of large molecular systems, which is otherwise impossible or formidable.

Going clean: structure and dynamics of peptides in the gas phase and paths to solvation

The gas phase is an artificial environment for biomolecules that has gained much attention both experimentally and theoretically due to its unique characteristic of providing a clean room environment for the comparison between theory and experiment. In this review we give an overview mainly on first-principles simulations of isolated peptides and the initial steps of their interactions with ions and solvent molecules: a bottom up approach to the complexity of biological environments. We focus on the accuracy of different methods to explore the conformational space, the connections between theory and experiment regarding collision cross section evaluations and (anharmonic) vibrational spectra, and the challenges faced in this field.

Vibronic-structure tracking: a shortcut for vibrationally resolved UV/Vis-spectra calculations

The vibrational coarse structure and the band shapes of electronic absorption spectra are often dominated by just a few molecular vibrations. By contrast, the simulation of the vibronic structure even in the simplest theoretical models usually requires the calculation of the entire set of normal modes of vibration. Here, we exploit the idea of the mode-tracking protocol [M. Reiher and J. Neugebauer, J. Chem. Phys. 118, 1634 (2003)] in order to directly target and selectively calculate those normal modes which have the largest effect on the vibronic band shape for a certain electronic excitation. This is achieved by defining a criterion for the importance of a normal mode to the vibrational progressions in the absorption band within the so-called "independent mode, displaced harmonic oscillator" (IMDHO) model. We use this approach for a vibronic-structure investigation for several small test molecules as well as for a comparison of the vibronic absorption spectra of a truncated chlorophyll a model and the full chlorophyll a molecule. We show that the method allows to go beyond the often-used strategy to simulate absorption spectra based on broadened vertical excitation peaks with just a minimum of computational effort, which in case of chlorophyll a corresponds to about 10% of the cost for a full simulation within the IMDHO approach.

Efficient calculation of anharmonic vibrational spectra of large molecules with localized modes

The analysis and interpretation of the vibrational spectra of complex (bio)molecular systems, such as polypeptides and proteins, requires support from quantum-chemical calculations. Such calculations are currently restricted to the harmonic approximation. Here, we show how one of the main bottlenecks in such calculations, the evaluation of the potential energy surface, can be overcome by using localized modes instead of the commonly employed normal modes. We apply such local vibrational self-consistent field (L-VSCF) and vibrational configuration interaction (L-VCI) calculations to a cyclic water tetramer and a helical hexa-alanine peptide. The results show that the use of localized modes is equivalent to the commonly used normal modes, but offers several advantages. First, a faster convergence with respect to the excitation level is observed in L-VCI calculations. Second, the localized modes provide a reduced representation of the couplings between modes that show a regular coupling pattern. This can be used to disregard a significant number of small two-mode potentials a priori. Several such reduced coupling approximations are explored, and we show that the number of single-point calculations required to evaluate the potential energy surface can be significantly reduced without introducing noticeable errors in the resulting vibrational spectra.

Fully anharmonic IR and Raman spectra of medium-size molecular systems: accuracy and interpretation

Computation of full infrared (IR) and Raman spectra (including absolute intensities and transition energies) for medium- and large-sized molecular systems beyond the harmonic approximation is one of the most interesting challenges of contemporary computational chemistry. Contrary to common beliefs, low-order perturbation theory is able to deliver results of high accuracy (actually often better than those issuing from current direct dynamics approaches) provided that anharmonic resonances are properly managed. This perspective sketches the recent developments in our research group toward the development of a robust and user-friendly virtual spectrometer rooted in second-order vibrational perturbation theory (VPT2) and usable also by non-specialists essentially as a black-box procedure. Several examples are explicitly worked out in order to illustrate the features of our computational tool together with the most important ongoing developments.

PICVib: an accurate, fast and simple procedure to investigate selected vibrational modes and evaluate infrared intensities

The generalization of the PICVib approach for calculating selected infrared intensities is shown to be successful and to preserves its easiness of implementation and parallelization, flexibility and treatment of large systems and/or at high theoretical levels.

PICVib: an accurate, fast, and simple procedure to investigate selected vibrational modes at high theoretical levels

A new approach Procedure for Investigating Categories of Vibrations (PICVib) for estimating vibrational frequencies of selected modes using only the structure and energy calculations at a more demanding computational level is presented and explored. The PICVib has an excellent performance at only a small fraction of the computational demand required for a complete analytical calculation. The errors are smaller than ca. 0.5% when DFT functionals are combined with high level ab initio methods. The approach is general because it can use any quantum chemical program and electronic structure method. It is very robust because it was validated for a wide range of frequency values (ca. 20-4800 cm(-1)) and systems: XH(3) (D(3h) ) with X = B, Al, Ga, N, P, As, O, S, and Se, YH(4) (D(4h) ) with Y = C, Si, and Ge, conformers of RDX, S(N) 2 and E2 reactions, [W(dppe)(2)(NNC(5)H(10))] complex, carbon nanotubes, and hydrogen-bonded complexes including guanine-cytosine pair.

Theoretical determination of the infrared spectra of amorphous polymers

The simple procedure of calculating the infrared spectra of polymers is presented. It is based on selecting the relevant, medium-size representative fragments of a polymer, for which the vibrational frequencies are computed within the harmonic approximation, in conjunction with the multiparameter scaling techniques. Scaling is necessary to predict the reliable fundamentals, which, along with the calculated intensities and properly chosen band widths, reproduce the observed band shapes with high accuracy. Applications to the three polymers: poly(methyl methacrylate), poly(vinyl acetate), and poly(isopropenyl acetate) are presented. The simulated spectra are in good agreement with the experiment. The assignment of bands is reported. The obtained results indicate strong delocalization of the vibrational modes within polymers, which is in accord with the most recent experimental finding [Macromolecules2008, 41, 2494-2501]. Good agreement between the observed and the calculated spectra of deuterated PMMA confirms the correctness of our approach. The preliminary results obtained for the highly irregular macromolecular compound (vinyl-functionalized silica) are also shown.

Conformational transitions of glycine induced by vibrational excitation of the O-H stretch

Vibrational energy flow and conformational transitions following excitation of the OH stretching mode of the most stable conformer of glycine are studied by classical trajectories. "On the fly" simulations with the PM3 semiempirical electronic structure method for the potential surface are used. Initial conditions are selected to correspond to the ν=1 excitation of the OH stretch. The main findings are: (1) An an equilibrium-like ratio is established between the populations of the 3 lowest-lying conformers after about 10 picoseconds. (2) There is a high probability throughout the 150 ps of the simulations for finding the molecule in geometries far from the equilibrium structures of the lowest-energy conformers. (3) Energy from the initial excited OH (ν=1) stretch flows preferentially to 5 other vibrational modes, including the bending motion of the H atom. (4) RRK theory yields conformational transition rates that deviate substantially from the classical trajectory results. Possible implication of these results for vibrational energy flow and conformational transitions in small biological molecules are discussed.

Infrared spectroscopy of the alanine dipeptide analog in liquid water with DFT-MD. Direct evidence for P(II)/beta conformations

Following our previous work [J. Phys. Chem. B. Lett., 2009, 113, 10059], DFT-based molecular dynamics (DFTMD) simulations of 2-Ala peptide (i.e. Ac-Ala-NHMe dialanine peptide analog with methyl group caps at the extremities) immersed in liquid water at room temperature are reported. Our goal here is the theoretical calculation of the infrared spectrum of aqueous 2-Ala, in order to provide a definitive understanding of the average conformation adopted by this peptide in the liquid phase, taking into account solute and solvent at the same theoretical level of representation. We find that the experimental Amide I-II band predominantly results from a mixture of partially unfolded P(II) and unfolded beta conformational equilibrium of aqueous 2-Ala at room temperature.

Theoretical spectroscopy of floppy peptides at room temperature. A DFTMD perspective: gas and aqueous phase

Theoretical spectroscopy is mandatory for a precise understanding and assignment of experimental spectra recorded at finite temperature. We review here room temperature DFT-based molecular dynamics simulations for the purpose of interpreting finite temperature infrared spectra of peptides of increasing size and complexity, in terms of temperature-dependent conformational dynamics and flexibility, and vibrational anharmonicities (potential energy surface anharmonicities, vibrational mode couplings and dipole anharmonicities). We take examples from our research projects in order to illustrate the main key-points and strengths of dynamical spectra modeling in that context. The calculations are presented in relation to room temperature gas phase IR-MPD experiments and room temperature liquid phase IR absorption experiments. These illustrations of floppy polypeptides have been chosen in order to convey the following ideas: temperature-dependent spectra modeling is pivotal for a precise understanding of gas phase spectra recorded at room temperature, including conformational dynamics and vibrational anharmonicities; harmonic spectroscopy (as commonly performed in the literature) can be misleading and even erroneous for a proper interpretation of spectra recorded at finite temperature; taking into account vibrational anharmonicities is pivotal for a proper interplay between theory and experiments; amide I-III bands are not necessarily the most relevant fingerprints for unraveling the local structures of peptides and more complex systems; liquid phase simulations have unraveled relationships between the zwitterionic properties of the peptide bonds and infrared signatures. The review presents a state-of-the-art account of the domain and offers perspectives and new developments for future still more challenging applications.

Alanine polypeptide structural fingerprints at room temperature: what can be gained from non-harmonic Car-Parrinello molecular dynamics simulations

Structural infrared fingerprints of neutral gas phase alanine peptides of increasing size and complexity (dipeptide, octapeptide, and beta-strand peptide) are characterized through DFT-based Car-Parrinello molecular dynamics simulations. Harmonic and nonharmonic vibrational signatures are calculated from the time correlation of the dipole moment of the gas phase peptide in a direct way (without any approximation) respectively from low temperature (20 K) and room temperature (300 K) molecular dynamics. Our main purpose is to answer the two following questions: (i) Is the direct inclusion of temperature for the calculation of infrared spectra mandatory for the comprehension of the vibrational signatures experimentally recorded at room temperature? (ii) To what extent is the amide I, II, and III domain sensitive enough to the local structure of the peptides, to provide vibrational signatures that can be definitely used to assess the peptide conformation at 300 K?

Selective calculation of high-intensity vibrations in molecular resonance Raman spectra

We present an intensity-driven approach for the selective calculation of vibrational modes in molecular resonance Raman spectra. The method exploits the ideas of the mode-tracking algorithm [M. Reiher and J. Neugebauer, J. Chem. Phys. 118, 1634 (2003)] for the calculation of preselected molecular vibrations and of Heller's gradient approximation [Heller et al., J. Phys. Chem. 86, 1822 (1982)] for the estimation of resonance Raman intensities. The gradient approximation allows us to construct a basis vector for the subspace iteration carried out in the mode-tracking calculation, which corresponds to an artificial collective motion of the molecule that contains the entire intensity in the resonance Raman spectrum. Subsequently, the algorithm generates new basis vectors from which normal mode approximations are obtained. It is then possible to provide estimates for (i) the accuracy of the normal mode approximations and (ii) the intensity of these modes in the final resonance Raman spectrum. This approach is tested for the examples of uracil and a structural motif from the E colicin binding immunity protein Im7, in which a few aromatic amino acids dominate the resonance Raman spectrum at wavelengths larger than 240 nm.

QM/MM vibrational mode tracking

Vibrational spectroscopy is a powerful tool to investigate the structure and dynamics of biomolecules. When small subsystems of large molecules such as active centers of enzymes are studied, quantum chemical calculations based on quantum mechanics/molecular mechanics (QM/MM) coupling schemes are a valuable means to interpret the spectra. The goal of this work is a methodological pilot study on how to selectively and thus efficiently extract certain vibrational information for extended molecular systems described by QM/MM methods. This is achieved by an extension of the mode tracking algorithm and a comparison with the partial Hessian diagonalization approach. After validating the methodology for the CO stretching vibration of 2-butanone and a delocalized CO stretch in acetylacetone, the stretching and bending modes of the CO ligand in CO myoglobin are tracked. Such systems represent an ideal application for mode tracking, because only a few strongly localized vibrations are sought for, while the large remainder of the molecule is of interest only as far as it affects these local vibrations. This influence is treated exactly by mode tracking.