Abstract: The performance of over forty density functionals in predicting indirect spin-spin coupling
constants (SSCCs) in the Kohn-Sham limit was tested. For comparison, similar calculations
were performed using the RHF, SOPPA, SOPPA(CC2) and SOPPA(CCSD) methods and the
results were estimated toward the complete basis set limit (CBS). The SSCCs of nine small
molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6 and C6H6) were estimated using the
dedicated Jensenâs pcJ-n polarization-consistent basis sets toward the Kohn-Sham limit. These
CBS results were compared with calculations using the aug-cc-pVTZ-J basis set. Among the
41 studied DFT methods the tHCTHhyb, HSEh1PBE, HSE2PBE, wB97XD, wB97 and wB97XD functionals reproduced accurately the experimental 1J(XH) parameters and
3J(HH60) and 2J(HHgem) in ethane. Similarly, the functionals HSEh1PBE, HSE2PBE,
wB97XD, wB97 and wB97XD predicted accurately 1J(CC) and B98, B97-1, B97-2,
PBE1PBE, B1LYP, O3LYP calculated accurately 1J(CO) in the CO molecule. A very good
performance of the relatively small basis set aug-cc-pVTZ-J was observed closely reproducing
the CBS values.
Abstract: The solvent dependence of harmonic and anharmonic frequencies of water, formaldehyde and
formamide was studied using the B3LYP method. The results obtained with the Jensenâs
polarization-consistent basis sets were fitted with two-parameter formula toward the B3LYP
Kohn-Sham complete basis set limit (CBS). Anharmonic corrections have been obtained by a
second order perturbation treatment and vibrational configuration interaction (VCI) method.
The solvent environment was treated according to the SCRF PCM approach.
Abstract: The Raman optical activity (ROA) spectroscopic technique has been applied in the past to many
biologically relevant systems including peptides, proteins, sugars, and even viruses. However,
theoretical interpretation of the spectra relies on lengthy quantum-chemical computations, which are
difficult to extend to larger molecules. In the present study, ROA and Raman spectra of insulin under a
range of various conditions were measured and interpreted with the aid of the Cartesian-coordinate
tensor transfer (CCT) method. The CCT methodology yielded spectra of insulin monomer and dimer of
nearly ab initio quality, while at the same time reproducing the experimental data very well. The link
between the spectra and the protein structure could thus be studied in detail. Spectral contributions
from the peptide backbone and the amino acid side chains were calculated. Likewise, specific intensity
features originating from the α-helical, coil, β-sheet and 310-helical parts of the protein could be
deciphered. The assignment of the Raman and ROA bands to intrinsic molecular coordinates as based
on the harmonic force field calculation revealed their origin and degree of locality. Alternatively, the
relation of the structural flexibility of insulin to the inhomogeneous broadening of spectral bands was
studied by a combination of CCT and molecular dynamics (MD). The present study confirms the
sensitivity of the ROA technique to some subtle static and dynamic changes in molecular geometry,
and many previous ad hoc or semi-empirical spectral-structure assignments could be verified. On the
other hand, a limitation in longer-range tertiary structure sensitivity was revealed. Unlike for smaller
molecules with approximately equal contributions of the electric dipole (α), quadrupole (A), and
magnetic dipole (G') polarizabilities, only the electric dipolar polarization (α) interactions seem to
dominate in the protein ROA signal. The simulations concern the largest molecule for which such
spectra were interpreted by a priory procedures, and significantly enhance protein folding studies
undertaken by this technique.
Abstract: 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 that originated in the molecular structure. To obtain insight 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-atomic quantum and molecular
mechanics approach captures the overall influence of the temperature dependent solvent properties on the
amide I spectra and thus improve the accuracy and reliability of molecular structural studies.
Abstract: Correlated ab initio wave function calculations have been performed, using nonrelativistic frozen core MP2 complete basis set extrapolation model chemistry. The calculations have been made for three test sets of gas-phase saccharide conformations to provide reference values for their relative energies. The remaining correlation effects are estimated from frozen core coupledcluster singles and doubles [CCSD(T)] calculations. The test sets consist of 15 conformers of alpha- and beta-D-allopyranose, 15 of 3,6-anhydro-4-O-methyl-D-galactitol, and four of β-D-glucopyranose. For each set, conformational energies varied by about 7 kcal/mol. These benchmark quality relative conformational energies are used to re-evaluate the performance of the best density functional methods for conformational analyses of saccharides. Our results show that the B3PW91 and PBE0 relative energies are
systematically better than the B3LYP and M05-2X results. Overall, the functionals based on the exact constraints perform better for the relative energies of monosaccharide conformers than the empirically fitted functionals.
Abstract: Reliable modeling of protein and peptide circular dichroism (CD) spectra in the far UV
presents a challenge for current theoretical approaches. In this study, the time-dependent density
functional theory (TDDFT), configuration interaction with single excitation (CIS), and transition
dipole coupling (TDC), were used to asses the most important factors contributing to the CD spectra
of α-helical secondary structure. The roles of the peptide chain length, flexibility, and the solvent
environment were investigated on a model oligopeptide Ac-(Ala)N-NH-Me, (N=1â¦18) constrained
to an α-helical structure. Both the TDDFT and TDC-like methods suggest that the CD curve typical
for the α-helix arises gradually, but its basic characteristic is discernable already for peptides with
4-5 amino acid residues. The calculated dependence was in a qualitative agreement with
experimental spectra of short α-helices stabilized by the histidine-metal binding. The TDDFT
computations of the CD were found to be unusually sensitive to the basis set and solvent model,
which is partially given by the prevalent perpendicular orientation of the magnetic and electric
dipole moments in the n-Ï* and Ï-Ï* spectral regions. Explicit hydration and temperature
fluctuations of the peptide geometry, simulated with the aid of molecular dynamics (MD),
significantly influenced the CD and absorption spectral shapes. An extensive averaging over MD
configurations is thus required to obtain a converged spectral profile in cluster simulations. On the
other hand, both the TDDFT and TDC models indicate only a minor influence of the alanine sidechains
and helix-helix interaction on the CD spectral profiles. For a model system of two helices,
the CIS method predicted larger changes in the spectra than TDC, which suggest that interaction
across peptide chains can have a minor, but measurable, effect on the CD spectrum.
Abstract: It isshownthatalinear correlation existsbetweennuclear shieldingconstantsforninesmall inorganicandorganicmolecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6 and C6H6) calculated with 47methods (42 DFT methods, RHF, MP2, SOPPA, SOPPA(CCSD), CCSD(T)) and the aug-cc-pVTZ-J basis set and corresponding complete basis set results, estimated from calculations with the family of polarization-consistent pcS-n basis sets. This implies that the remaining basis set error of the aug-cc-pVTZ-J basis set is very similar in DFT and CCSD(T) calculations. As the aug-cc-pVTZ-J basis set is significantly smaller, CCSD(T)/aug-cc-pVTZ-J calculations allow in combination with affordable DFT/pcS-n complete basis set calculations the prediction of nuclear shieldings at the CCSD(T) level of nearly similar accuracy as those, obtained by fitting results obtained from computationally demanding pcS-n calculations at the CCSD(T) limit.Asignificant saving of computational efforts can thus be achieved by scaling inexpensive CCSD(T)/aug-cc-pVTZ-J calculations of nuclear isotropic shieldings with affordable DFT complete basis set limit corrections.
Abstract: Acid-catalyzed condensation of resorcinol with 3,5-diisopropoxybenzaldehyde and 3,5-dihydroxybenzaldehyde
afforded aryl substituted resorc[4]arenes 1a and 1b, respectively. All
16 hydroxyls in 1b were acetylated providing resorc[4]arene 1c. The conformational behaviour
of 1a, 1b and 1c was studied by NMR spectroscopy and quantum chemical calculations.
It was found that the stabilization of their conformations is an effect of competing Ï-Ï and
OH-Ï interactions, hydrogen bonding and steric features, respectively. As a result, C2 symmetrical
boat conformations 1a, 1b and 1c with aryls in axial positions were identified in all
cases. In case of 1c also the formation of C2 symmetrical conformation with aryls in equatorial
positions (boat-eq) was identified. Moreover, compounds 1a and 1b being able to create
hydrogen bonds, adopt also symmetrical C4 crown conformations. For 1c(boat-ax), the
boat-boat conversion with energy barrier of 80 kJ/mol was observed, while the 1c(boat-eq)
was found to be rigid in the whole accessible temperature range. Both conformers of 1c exhibit
also second dynamic process â rotation of bridge aryl rings (ÎGâ¡ = 66 kJ/mol).
Abstract: Convergence patterns and limiting values of isotropic nuclear magnetic shieldings and indirect magnetic spin-spin coupling constants (SSCC) were studied for several small molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6 and C6H6) in the Kohn-Sham limit. Individual results of calculations using dedicated families of Jensenâs basis sets (pcS-n and pcJ-n) and simple two-parameter formula were fitted toward the complete basis set limit (CBS) and ZPV correction applied. Several density functionals were used, and, for comparison purposes, calculations were performed using RHF, MP2, SOPPA and SOPPA(CCSD) methods and aug-cc-pVTZ-J basis set. Finally, the CBS estimated results were critically compared with earlier reported literature data and experiment.
Abstract: Hydration envelopes of metallic ions significantly influence their chemical properties and biological functioning. Previous computational studies, nuclear magnetic resonance (NMR), and other experiments indicate a strong affinity of the Mg2+ cation to water. We used the Raman spectroscopy to probe the magnesium hydration shell. In the measured Raman spectra of several salts (LiCl, NaCl, KCl, MgCl2, CaCl2, MgBr2 and MgI2 water solutions) only the spectroscopic imprint of the hydrated Mg2+ cation could clearly be identified as an exceptionally distinct peak at ~355 cm-1. The unexpectedly high vibrational frequency of this band was assigned to the Mg-O stretching motion on the basis of several models involving quantum chemical computations on metal/water clusters. Other minor Raman spectral features could also be explained. Ab initio and Fourier transform (FT) techniques coupled with the Car-Parinello molecular dynamics were adapted to provide the spectra from dynamical trajectories. The results suggest that even in concentrated solutions magnesium preferentially forms a [Mg(H2O)6]2+ complex of a nearly octahedral symmetry; nevertheless the Raman signal is primarily associated with the relatively strong metal-H2O bond. Partially covalent character of the Mg-O bond was confirmed by a natural bond orbital analysis. We find it interesting that although this and other monoatomic ions do not vibrate themselves, they cause notable changes in the water Raman signal. Although many spectral features of magnesium and the other salts could not be interpreted yet, the vibrational Raman spectroscopy exhibits a large potential to sense the ionic hydration patterns. The dynamical and cluster computational models provide the link between spectral shapes and specific ion-water interactions that govern the hydration shell structures.
Abstract: Recent experimental studies of trans-formic acid (FA) in solid para-hydrogen (pH2) highlighted the importance of vibrationally averaged dipole moments for the interpretation of the high resolution infrared (IR) spectra, in particular for the C=O stretch (v3) mode. In this report, dipole moments for the ï®3 ground (v=0) and excited (v=1, 2, 3 and 4) anharmonic vibrational states in trans-FA are investigated using two different approaches: a single mode approximation, where the vibrational states are obtained from the solution of the one-dimensional Schrödinger equation for the harmonic normal coordinate, and, second, a limited vibrational configuration interaction (VCI) approximation. Density functional theory (B3LYP, BPW91) and correlated ab initio (MP2 and CCSD(T)) electronic methods were employed with a number of double- and triple-ïºï¬ and correlation consistent basis sets. Both single mode and VCI approaches show comparable agreement with experimental data, which is more dependent on the level of theory used. In particular, the BPW91/cc-pVDZ level appears to perform remarkably well. Effects of solvation of FA in solid state Ar and pH2 matrices were simulated at the BPW91/cc-pVDZ level using a conductor-like polarized continuum model. The Ar and pH2 solid state matrices cause quite a substantial increase in the FA dipole moments. Compared to gas phase calculations, the CPCM model for pH2 better reproduces the experimental FA spectral shifts in solid pH2 caused by interaction with traces of ortho-hydrogen (oH2) species. The validity of the single mode approach is tested against the multidimensional VCI results, suggesting that the isolated (non-interacting) mode approximation is valid up to the third vibrationally excited state (v=3). Finally, the contribution of the ground anharmonic vibrational states of the remaining modes on the resulting v3 single mode dipole moments and IR intensities is examined and discussed.
Abstract: 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.
Abstract: 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.
Abstract: Raman scattering and its polarized extension, Raman optical activity (ROA), are commonly used for monitoring of molecular conformational equilibria in solutions. This is complicated for saccharides due to extensive motions of the hydroxyl groups and other molecular parts. Standard interpretation procedures involving ab initio spectral simulations for a limited set of conformers are not adequate. In this study, a more general approach is proposed for the gluconic acid anion taken as a model compound, where quantum simulations of the spectra are directly coupled with molecular dynamics (MD) techniques. Such a multiscale approach reveals how the structural information is encoded in the broadened spectral lines. The spectra were simulated for solvent-solute clusters generated by MD. Conformational averaging was enabled by a limited library of conformers for which the spectral parameters could be calculated ab initio and moved on the MD geometries by Cartesian coordinate tensor transfer techniques. The B3LYP/CPCM/6-31+G** approximation was used as a default for computation of the source force fields and polarizability derivatives. The spectra thus obtained relatively faithfully reproduced most of the experimental features. The Amber and polarizable Amoeba MD force fields produced similar results; application of the latter, however, was limited by the long time necessary
to achieve a converged conformational equilibrium. Both MD simulation and spectral averaging suggest that the hydroxyl groups as well as the backbone C-C bonds rotate relatively freely, with some restrictions in the vicinity of the carboxyl group. In spite of the averaging, spectral response of characteristic vibrational normal mode families, such as CH and OH bending, can clearly be identified in the spectra. The simulations thus confirm the experimental fact that flexible saccharides exhibit significant vibrational activity that reveals precious information about molecular structure and dynamics encoded in the Raman and ROA spectral shapes.
Abstract: 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. In vacuum the MP2, MP4 and CCST(T) wavefunction 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 non-planar 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 CH3 group rotations modeled by a rigid rotor model was found important for explaining some features of the spectra in solid hydrogen matrix. At room temperature the methyl rotation contributes to a non-specific inhomogeneous band broadening. The dependence of the amide group flexibility on the environment polarity may have interesting consequences for peptide and protein folding studies.
Abstract: 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 aminoacid. In comparison with a 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 NH2 residues to a similar degree as 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 15N and 13C-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.
Abstract: The relative energies of 95 conformers of four peptide models are studied using MP2 and LMP2 methods and correlation consistent basis sets ranging from double-zeta to augmented quintuple-zeta quality. It is found that both methods yield quite similar results, and the differences between MP2 and LMP2 decrease systematically with increasing basis set. Due to reduced intramolecular basis set superposition effects (BSSE), the LMP2 results converge more slowly to the basis set limit for most of these rather small systems. However, for larger peptides, the BSSE has a very large effect on the energy difference between extended and helical structures, leading to a very strong basis set dependence of the canonical MP2 results. It is demonstrated for alanine octapeptides that the basis set error exceeds 30 and 20kJ mol1, respectively, if augmented double-zeta and triple-zeta basis sets are used. On the other hand, the LMP2 results are only slightly affected by the basis set size, and, even with augmented double-zeta basis sets, reasonably accurate results are obtained. Furthermore, for the larger systems, the computation times for the LMP2 calculations are shown to be up to one order or magnitude shorter than for canonical MP2 calculations with the same basis set.
Abstract: The nucleophillic substitution is a common method for preparation of saccharide derivatives. For biologically active compounds, it is desirable that the stereochemistry is under control and the amount of byproducts is limited. Therefore, we studied the SN2 nucleophillic attacks of the azide anion on methyl 2,3-anhydro-a- and -b-L-erythrofuranoside, as well as on their epithio and epimino analogues, which are used as common intermediates in sugar chemistry. Geometry and energetics of the reactions were investigated in the gas phase and in two different solvents using the density functional theory methods. Equilibrium structures of the reactants, reaction-complexes, transition states and products were localized on the computed potential energy surfaces. According to the theory the methoxy group may suppress the substitutions at the 2-position, but detailed reaction rate is influenced by nature of the furanosides and the presence of solvent. Predicted substitution selectivity in the position 2 or 3 of the furanose sugars is in agreement with experimental data.
Abstract: 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 DZ basis set and relative energies estimated by extrapolation of results using double, triple, and QZ 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 DZ 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 TZ 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 cca 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 cca 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.
Abstract: Indirect spin-spin NMR 1H-1H coupling constants of newly synthesized furanose monosaccharide derivatives were interpreted on the basis of ab initio modeling. Epoxy, epithio, and epimino groups were inserted into the sugars and significantly limited their conformational flexibility, which was confirmed by a systematic conformer analysis. Because of the restriction, the performance of the computations and the dependence of the coupling constants on the geometry could be estimated more easily. Conventional Karplus equations are not optimized for this class of compounds and cannot be used for reliable interpretation of the NMR spectra. Fully analytical B3LYP/IGLOII computations of the coupling constants were performed including all the four important magnetic terms (SD, DSO, PSO, FC) in the Hamiltonian. Good agreement of the calculated and the experimental coupling constants was achieved, and computed structural parameters are consistent with available X-ray data. The influence of the different functional groups on the spin-spin coupling constants was discussed.
Abstract: Chiroptical Spectra explore different absorption, scattering, or dispersion of left- and right circularly polarized light on molecules.
Density Functional Theory (DFT) is an efficient method for computation of molecular energies, based on electronic density.
Response Theory is a general formulation of the quantum theory (including DFT) allowing to calculate molecular properties as energy derivatives.
Electronic Circular Dichroism (ECD, also CD or UVCD) is different absorption of left and right circularly polarized light by a chiral molecule (which has neither plane nor a center of symmetry).
Optical Rotatory Dispersion (ORD) is different dispersion of left and right circularly polarized light, measured also as a rotation of linearly polarized light.
Magnetic Circular Dichroism (MCD) is circular dichroism in the presence of a static magnetic field.
Vibrational Circular Dichroism (VCD) is circular dichroism in the infrared, based on vibrational transitions in molecules.
Raman Optical Activity (ROA) is different scattering of right and left circularly polarized light.
Vibrational Optical Activity (VOA) usually involves VCD and ROA.
