Jakub Kaminský

Force Field Modeling of Amino Acid Conformational Energies

The conformational degrees of freedom for four amino acids in a model peptide environment have been sampled with density functional and second-order Møller-Plesset methods. Geometries have been optimized with an augmented double-ζ basis set and relative energies estimated by extrapolation of results using double, triple, and quadruple-ζ basis sets and including higher order correlation effects. In addition, the effects of vibrational zero point energies and solvation have been considered. The density functional method is unable to locate all the minima found at the MP2 level, which most likely is due to the inability for describing dispersion interactions. The use of basis sets smaller than augmented polarized double-ζ with the MP2 method may also in some cases lead to artifacts. The effects on relative energies by enlarging the basis set beyond an augmented triple-ζ and including higher order correlation beyond MP2 is small. The MP2/aug-cc-pVTZ level is recommended as a level of theory capable of an accuracy of ∼1 kJ/mol for relative conformational energies. Eight different force fields are tested for reproducing the electronic structure reference data. Force fields that represent the electrostatic energy by fixed partial charges typically only account for half of the conformations, while the AMOEBA force field, which includes multipole moments and polarizability, can reproduce ∼80% of the conformations in terms of geometry. This not only suggests that multipole moments and polarizability are important factors in designing new force fields but also indicates that there is still room for improvements.

Structure of the Alanine Hydration Shell as Probed by NMR Chemical Shifts and Indirect Spin-Spin Coupling

The structure of the alanine hydration shell was modeled by Carr-Parinello molecular dynamics (CPMD) to explain subtle differences in NMR chemical shifts and indirect spin-spin coupling constants of the neutral (zwitterionic), cationic, and anionic forms of this amino acid. In comparison with classical molecular dynamics (MD), the quantum mechanical CPMD approach revealed a more structured solvent and significant differences in the radial and angular distributions of the water molecules around the solute. In particular, the solvent was predicted to be organized around the uncharged COOH and NH(2) residues to a similar degree as that for the charged ones. This was not the case with MD. For snapshot CPMD configurations, the NMR parameters were computed by density functional theory (DFT) and averaged. Obtained values were significantly closer to experimental parameters known for (15)N and (13)C isotopically labeled alanine than those calculated by the conventional implicit dielectric solvent model. The NMR results also quantitatively reflect a superiority of the CPMD over the MD explicit solvent treatment. A further improvement of the computed spin-spin coupling constants could be achieved by taking into account vibrational averaging beyond the harmonic approximation. Differently positioned water molecules in the clusters cause an unexpectedly large scattering of the NMR parameters. About 10-15 dynamics snapshots were required for a satisfactory convergence of the shifts and couplings. The NMR chemical shift was found to be much more sensitive to the molecular hydration than the coupling. The results thus indicate a large potential of the NMR spectroscopy and quantum simulations to probe not only the structure of molecules but also their interactions with the environment.

Relative importance of first and second derivatives of nuclear magnetic resonance chemical shifts and spin-spin coupling constants for vibrational averaging

Relative importance of anharmonic corrections to molecular vibrational energies, nuclear magnetic resonance (NMR) chemical shifts, and J-coupling constants was assessed for a model set of methane derivatives, differently charged alanine forms, and sugar models. Molecular quartic force fields and NMR parameter derivatives were obtained quantum mechanically by a numerical differentiation. In most cases the harmonic vibrational function combined with the property second derivatives provided the largest correction of the equilibrium values, while anharmonic corrections (third and fourth energy derivatives) were found less important. The most computationally expensive off-diagonal quartic energy derivatives involving four different coordinates provided a negligible contribution. The vibrational corrections of NMR shifts were small and yielded a convincing improvement only for very accurate wave function calculations. For the indirect spin-spin coupling constants the averaging significantly improved already the equilibrium values obtained at the density functional theory level. Both first and complete second shielding derivatives were found important for the shift corrections, while for the J-coupling constants the vibrational parts were dominated by the diagonal second derivatives. The vibrational corrections were also applied to some isotopic effects, where the corrected values reasonably well reproduced the experiment, but only if a full second-order expansion of the NMR parameters was included. Contributions of individual vibrational modes for the averaging are discussed. Similar behavior was found for the methane derivatives, and for the larger and polar molecules. The vibrational averaging thus facilitates interpretation of previous experimental results and suggests that it can make future molecular structural studies more reliable. Because of the lengthy numerical differentiation required to compute the NMR parameter derivatives their analytical implementation in future quantum chemistry packages is desirable.

Ramachandran Plot for Alanine Dipeptide as Determined from Raman Optical Activity.

Accessible values of the φ and ψ torsional angles determining peptide main chain conformation are traditionally displayed in the form of Ramachandran plots. The number of experimental methods making it possible to determine such conformational distribution is limited. In the present study, Raman optical activity (ROA) spectra of Ac-Ala-NHMe were measured and fit by theoretical curves. This revealed the most favored conformers and a large part of the potential energy surface (PES) of this model dipeptide. Such experimental PES compares well to quantum chemical computations, whereas molecular dynamics (MD) modeling reproduces it less faithfully. The surface shape is consistent with the temperature dependence of the spectra, as observed experimentally and predicted by MD. Despite errors associated with spectral modeling and the measurement, the results are likely to facilitate future applications of ROA spectroscopy.

Theoretical Modeling of Magnesium Ion Imprints in the Raman Scattering of Water

Hydration envelopes of metallic ions significantly influence their chemical properties and biological functioning. Previous computational studies, nuclear magnetic resonance (NMR), and vibrational spectra indicated a strong affinity of the Mg(2+) cation to water. We find it interesting that, although monatomic ions do not vibrate themselves, they cause notable changes in the water Raman signal. Therefore, in this study, we used a combination of Raman spectroscopy and computer modeling to analyze the magnesium hydration shell and origin of the signal. In the measured spectra of several salts (LiCl, NaCl, KCl, MgCl(2), CaCl(2), MgBr(2), and MgI(2) water solutions), only the spectroscopic imprint of the hydrated Mg(2+) cation could clearly be identified as an exceptionally distinct peak at approximately 355 cm(-1). The assignment of this band to the Mg-O stretching motion could be confirmed on the basis of several models involving quantum chemical computations on metal/water clusters. Minor Raman spectral features could also be explained. Ab initio and Fourier transform (FT) techniques coupled with the Car-Parrinello molecular dynamics were adapted to provide the spectra from dynamical trajectories. The results suggest that even in concentrated solutions magnesium preferentially forms a [Mg(H(2)O)(6)](2+) complex of a nearly octahedral symmetry; nevertheless, the Raman signal is primarily associated with the relatively strong metal-H(2)O bond. Partially covalent character of the Mg-O bond was confirmed by a natural bond orbital analysis. Computations on hydrated chlorine anion did not provide a specific signal. The FT techniques gave good spectral profiles in the high-frequency region, whereas the lowest-wavenumber vibrations were better reproduced by the cluster models. Both dynamical and cluster computational models provided a useful link between spectral shapes and specific ion-water interactions.

Efficient Modeling of NMR Parameters in Carbon Nanosystems.

Rapid growth of nanoscience and nanotechnology requires new and more powerful modeling tools. Efficient theoretical modeling of large molecular systems at the ab initio and Density Functional Theory (DFT) levels of theory depends critically on the size and completeness of the basis set used. The recently designed variants of STO-3G basis set (STO-3Gel, STO-3Gmag), modified to correctly predict electronic and magnetic properties were tested on simple models of pristine and functionalized carbon nanotube (CNT) systems and fullerenes using the B3LYP and VSXC density functionals. Predicted geometries, vibrational properties, and HOMO/LUMO gaps of the model systems, calculated with typical 6-31G* and modified STO-3G basis sets, were comparable. The (13)C nuclear isotropic shieldings, calculated with STO-3Gmag and Jensens polarization consistent pcS-2 basis sets, were also identical. The STO-3Gmag basis sets, being half the size of the latter one, are promising alternative for studying (13)C nuclear magnetic shieldings in larger size CNTs and fullerenes.

Solvent Dependence of the N-Methylacetamide Structure and Force Field

The N-methylacetamide molecule (NMA) is an important model for peptide and protein vibrational spectroscopy as it contains the main amide chromophore. In the past, some observed NMA geometry and spectral features could not be entirely explained at the harmonic level or by a single-conformer model. In particular, the spectra were found to be very dependent on molecular environment. In this work NMA Raman and infrared (IR) spectra in a variety of conditions were remeasured and simulated theoretically to separate the fundamental, dimer, and anharmonic bands. Under vacuum the MP2, MP4, and CCSD(T) wave function methods predicted a broad anharmonic potential energy well or even a double-well for the amide nitrogen out of plane motion, which density functional methods failed to reproduce. However, eventual nonplanar minima cannot support an asymmetric quantum state or explain band splittings observed in some experiments. In polar solvents the potential becomes more harmonic and the amide plane more rigid. On the other hand, solvent polarity enhances other anharmonic phenomena, such as the coupling between the carbonyl stretching (amide I) and lower frequency amide bending modes. The amide I band splitting is commonly observed experimentally. The influence of the CH(3) group rotations modeled by a rigid rotor model was found to be important for explaining some features of the spectra in a solid parahydrogen matrix. At room temperature the methyl rotation contributes to a nonspecific inhomogeneous band broadening. The dependence of the amide group flexibility on the environment polarity may have interesting consequences for peptide and protein folding studies.

Simulations of the temperature dependence of amide I vibration.

For spectroscopic studies of peptide and protein thermal denaturation it is important to single out the contribution of the solvent to the spectral changes from those originated in the molecular structure. To obtain insights into the origin and size of the temperature solvent effects on the amide I spectra, combined molecular dynamics and density functional simulations were performed with the model N-methylacetamide molecule (NMA). The computations well reproduced frequency and intensity changes previously observed in aqueous NMA solutions. An empirical correction of vacuum frequencies in single NMA molecule based on the electrostatic potential of the water molecules provided superior results to a direct density functional average obtained for a limited number of solute-solvent clusters. The results thus confirm that the all-atom quantum and molecular mechanics approach captures the overall influence of the temperature dependent solvent properties on the amide I spectra and can improve the accuracy and reliability of molecular structural studies.

3He NMR: from free gas to its encapsulation in fullerene

The 3He nuclear magnetic shieldings were calculated for single helium atom, its dimer, simple models of fullerene cages (He@Cn), and single wall carbon nanotubes. The performances of several levels of theory (HF, MP2, DFT‐VSXC, CCSD, CCSD(T), and CCSDT) were tested. Two sets of polarization‐consistent basis sets were used (pcS‐n and aug‐pcS‐n), and an estimate of 3He nuclear magnetic shieldings in the complete basis set limit using a two‐parameter fit was established. Theoretical 3He results reproduced accurately previously reported theoretical values for helium gas, dimer, and helium probe inside several fullerene cages. Excellent agreement with experimental values was achieved. 3He nuclear magnetic shieldings of single helium atom approaching various points of benzene ring were tested, and an impact of 3He confinement within fullerene cages of different size on the 3He chemical shift was determined. Copyright

Molecular dynamics with restrictions derived from optical spectra

The information about molecular structure coded in the optical spectra must often be deciphered by complicated computational procedures. A combination of spectral modeling with the molecular dynamic simulations makes the process simpler, by implicit accounting for the inhomogeneous band broadening and Boltzmann averaging of many conformations. Ideally, geometries of studied systems can be deduced by a direct confrontation of such modeling with the experiment. In this work, the comparison is enhanced by restrictions to molecular dynamics propagations based on the Raman and Raman optical activity spectra. The methodology is introduced and tested on model systems comprising idealized H2O2, H2O3 molecules, and the alanine zwitterion. An additional gradient term based on the spectral overlap smoothed by Fourier transformation is constructed and added to the molecular energy during the molecular dynamics run. For systems with one prevalent conformation the method did allow to enrich the Boltzmann ensemble by a spectroscopically favored structure. For systems with multiconformational equilibria families preferential conformations can be selected. An alternative algorithm based on the comparison of the averaged spectra with the reference enabling iterative updates of the conformer probabilities provided even more distinct distributions in shorter times. It also accounts for multiconformer equilibria and provided realistic spectra and conformer distribution for the alanine.