Anharmonic effects in IR, Raman, and Raman optical activity spectra of alanine and proline zwitterions

Performance of Effective Harmonic Oscillator Approach for the Calculations of Vibrational Transition Energies of Large Molecules

The accuracy and performance of the effective harmonic oscillator approximation for the description of anharmonic vibrational structure calculations are tested for large molecular systems and compared with experimental values along with vibrational self-consistent field and second-order perturbation theories. The effective harmonic oscillator approach is an effective single-particle approximation where the variational parameters are the centroids and widths of the multidimensional Gaussian product functions posited as the vibrational wave functions. A comprehensive calculation for 849 transitions that include the fundamentals, two and three quanta overtone transitions, and several combination bands of three polyaromatic hydrocarbons and one DNA nucleobase with a total of 231 normal modes are assessed. A comparison of EHO results with the experimental values is done for the polyaromatic hydrocarbons, and a close agreement is found between the two results. It also offers anharmonic eigenstates and eigenfunctions that are nearly identical with vibrational self-consistent field theory. An extensive analysis on the resultant wave functions of the excited states is performed. The overall root-mean-square deviation (RMSD) between these two methods for 849 transitions understudy is only about 8.3 cm-1, suggesting the effective harmonic oscillator as a viable alternative for the reliable calculations of transition energies of large molecular systems.

Calculation of absolute Raman scattering cross-sections using vibrational self-consistent field/vibrational configuration interaction wave functions

In the present study, the differential scattering cross-sections, depolarization ratios and Raman shifts of small molecular systems are obtained from configuration iteration wave functions of vibrational self-consistent field (VSCF) states. The transition polarizabilities were modeled using the Placzek approximation, neglecting those contributions not arising from the electric dipole mechanism. This theoretical approach is considered a good approximation for samples that absorb in the UV range if the excitation radiation falls in the visible region, as is the case of the molecules selected for the present study, namely: water, methane, and acetylene. Potential energy and electronic polarizability surfaces are calculated by the CCSD(T) and CC3 methods with aug-cc-p(C)V(T,Q,5)Z basis sets. The vibrational Hamiltonian includes the vibrational angular momentum contribution of the Watson kinetic energy operator. As expected, due to the variational nature of the VSCF and vibrational configuration interaction (VCI) methods, the Raman transition wavenumbers are substantially improved over the harmonic predictions. Surprisingly, the scattering cross-sections obtained using the harmonic approximation or the VSCF method better agrees with the experimental values than those cross-sections predicted using VCI wave functions. The more significant deviations of the VCI results from the experimental reference may be related to the significant uncertainties of the measured cross-sections. Still, it may also indicate that the VCI Raman transition moments may require a more accurate description of the electronic polarizability surface. Finally, the depolarization ratios calculated for H₂ O and C₂ D₂ using harmonic and VCI wave functions have similar accuracy, whereas, for C₂ H₂ and C₂ HD, the VCI results are more accurate.

Theory and algorithms for chiroptical properties and spectroscopies of aqueous systems

Chiroptical properties and spectroscopies are valuable tools to study chiral molecules and assign absolute configurations. The spectra that result from chiroptical measurements may be very rich and complex, and hide much of their information content. For this reason, the interplay between experiments and calculations is especially useful, provided that all relevant physico-chemical interactions that are present in the experimental sample are accurately modelled. The inherent difficulty associated to the calculation of chiral signals of systems in aqueous solutions requires the development of specific tools, able to account for the peculiarities of water-solute interactions, and especially its ability to form hydrogen bonds. In this perspective we discuss a multiscale approach, which we have developed and challenged to model the most used chiroptical techniques.

Computing Bulk Phase Resonance Raman Spectra from ab Initio Molecular Dynamics and Real-Time TDDFT

We present our novel approach for computing resonance Raman (RR) spectra of periodic bulk phase systems from ab initio molecular dynamics, including solvent influence and some anharmonic effects. Based on real-time time-dependent density functional theory, we obtain the RR spectra for all laser wavelengths in one pass. We compute the RR spectrum of uracil in aqueous solution, which is in good agreement with experiment. This is the first simulation of a bulk phase RR spectrum.

Theory of Molecular Vibrational Zeeman Effects as Measured with Circular Dichroism

We present a general theory that enables the first nonempirical computation of molecular vibrational Zeeman effects as are detectable with magnetic vibrational circular dichroism spectroscopy (MVCD). In this method, the second derivatives of the molecular magnetic moment appear to be essential to determine the observable MVCD intensities. Using a quasiharmonic approximation, computations based on our method allowed a band-to-band comparison of simulated to measured spectra. Given this new possibility of its reliable interpretation, MVCD spectroscopy may develop as a useful tool to yield detailed information on molecular vibrational states and structure, including achiral systems.

Uncertainty quantification for quantum chemical models of complex reaction networks

For the quantitative understanding of complex chemical reaction mechanisms, it is, in general, necessary to accurately determine the corresponding free energy surface and to solve the resulting continuous-time reaction rate equations for a continuous state space. For a general (complex) reaction network, it is computationally hard to fulfill these two requirements. However, it is possible to approximately address these challenges in a physically consistent way. On the one hand, it may be sufficient to consider approximate free energies if a reliable uncertainty measure can be provided. On the other hand, a highly resolved time evolution may not be necessary to still determine quantitative fluxes in a reaction network if one is interested in specific time scales. In this paper, we present discrete-time kinetic simulations in discrete state space taking free energy uncertainties into account. The method builds upon thermo-chemical data obtained from electronic structure calculations in a condensed-phase model. Our kinetic approach supports the analysis of general reaction networks spanning multiple time scales, which is here demonstrated for the example of the formose reaction. An important application of our approach is the detection of regions in a reaction network which require further investigation, given the uncertainties introduced by both approximate electronic structure methods and kinetic models. Such cases can then be studied in greater detail with more sophisticated first-principles calculations and kinetic simulations.

Computing Bulk Phase Raman Optical Activity Spectra from ab initio Molecular Dynamics Simulations

We present our novel methodology for computing Raman optical activity (ROA) spectra of liquid systems from ab initio molecular dynamics (AIMD) simulations. The method is built upon the recent developments to obtain magnetic dipole moments from AIMD and to integrate molecular properties by using radical Voronoi tessellation. These techniques are used to calculate optical activity tensors for large and complex periodic bulk phase systems. Only AIMD simulations are required as input, and no time-consuming perturbation theory is involved. The approach relies only on the total electron density in each time step and can readily be combined with a wide range of electronic structure methods. To the best of our knowledge, these are the first computed ROA spectra for a periodic bulk phase system. As an example, the experimental ROA spectrum of liquid (R)-propylene oxide is reproduced very well.

Hydrogen Bonding Environment of the N3-H Group of Flavin Mononucleotide in the Light Oxygen Voltage Domains of Phototropins

The light oxygen voltage (LOV) domain is a flavin-binding blue-light receptor domain, originally found in a plant photoreceptor phototropin (phot). Recently, LOV domains have been used in optogenetics as the photosensory domain of fusion proteins. Therefore, it is important to understand how LOV domains exhibit light-induced structural changes for the kinase domain regulation, which enables the design of LOV-containing optogenetics tools with higher photoactivation efficiency. In this study, the hydrogen bonding environment of the N3-H group of flavin mononucleotide (FMN) of the LOV2 domain from Adiantum neochrome (neo) 1 was investigated by low-temperature Fourier transform infrared spectroscopy. Using specifically ¹⁵N-labeled FMN, [1,3-¹⁵N₂]FMN, the N3-H stretch was identified at 2831 cm^-1 for the unphotolyzed state at 150 K, indicating that the N3-H group forms a fairly strong hydrogen bond. The N3-H stretch showed temperature dependence, with a shift to lower frequencies at ≤200 K and to higher frequencies at ≥250 K from the unphotolyzed to the intermediate states. Similar trends were observed in the LOV2 domains from Arabidopsis phot1 and phot2. By contrast, the N3-H stretch of the Q1029L mutant of neo1-LOV2 and neo1-LOV1 was not temperature dependent in the intermediate state. These results seemed correlated with our previous finding that the LOV2 domains show the structural changes in the β-sheet region and/or the adjacent Jα helix of LOV2 domain, but that such structural changes do not take place in the Q1029L mutant or neo1-LOV1 domain. The environment around the N3-H group was also investigated.

Anharmonic Theoretical Vibrational Spectroscopy of Polypeptides

Because of the size of polypeptides and proteins, the quantum-chemical prediction of their vibrational spectra presents an exceptionally challenging task. Here, we address one of these challenges, namely, the inclusion of anharmonicities. By performing the expansion of the potential energy surface in localized-mode coordinates instead of the normal-mode coordinates, it becomes possible to calculate anharmonic vibrational spectra of polypeptides efficiently and reliably. We apply this approach to calculate the infrared, Raman, and Raman optical activity spectra of helical alanine polypeptides consisting of up to 20 amino acids. We find that while anharmonicities do not alter the band shapes, simple scaling procedures cannot account for the different shifts found for the individual bands. This closes an important gap in theoretical vibrational spectroscopy by making it possible to quantify the anharmonic contributions and opens the door to a first-principles calculation of multidimensional vibrational spectra.

First-principles anharmonic quantum calculations for peptide spectroscopy: VSCF calculations and comparison with experiments

First-principles quantum calculations for anharmonic vibrational spectroscopy of three protected dipeptides are carried out and compared with experimental data.

Vibrational Properties of the Phosphate Group Investigated by Molecular Dynamics and Density Functional Theory

The phosphate group (PO2(-)) is an important building block occurring in many components of living matter including nucleic acids. It provides distinct features in vibrational spectra and is useful as a local probe of NA conformation and interactions with the environment. For this purpose, it is desirable to explore in detail various factors influencing spectral shapes of characteristic phosphate vibrations. In the present study, effects of the solvent and conformational averaging are analyzed for simple model molecules, dimethylphosphate, ethylmethylphosphate, and ethylmethylthiophosphate. Infrared absorption (IR) and Raman spectra were measured and calculated using a combination of molecular dynamics (MD) and density functional theory (DFT). To fully understand the link between the structure and the spectra, the solvent has to be explicitly included in the computational modeling. The results indicate that vibrational properties of the phosphate moiety are very sensitive to its conformation and interactions with the aqueous environment indeed. Polarizable continuum solvent models without explicit water molecules provided significantly worse agreement with the experiment. The combined MD/DFT approach captures well spectral characteristics for the model systems and constitutes the most reliable basis for exploration of phosphate vibrational properties in biomolecular structural studies.

Calculation of Raman optical activity spectra for vibrational analysis

This review provides the necessary knowledge to accurately model ROA spectra of solvated systems and interpret their vibrational characteristics.

Synthesis and in vitro microbial evaluation of La(III), Ce(III), Sm(III) and Y(III) metal complexes of vitamin B6 drug

Metal complexes of pyridoxine mono hydrochloride (vitamin B6) are prepared using La(III), Ce(III), Sm(III) and Y(III). The resulting complexes are investigated. Some physical properties, conductivity, analytical data and the composition of the four pyridoxine complexes are discussed. The elemental analysis shows that the formed complexes of La(III), Ce(III), Sm(III) and Y(III) with pyridoxine are of 1:2 (metal:PN) molar ratio. All the synthesized complexes are brown in color and possess high melting points. These complexes are partially soluble in hot methanol, dimethylsulfoxide and dimethylformamide and insoluble in water and some other organic solvents. Elemental analysis data, spectroscopic (IR, UV-vis. and florescence), effective magnetic moment in Bohr magnetons and the proton NMR suggest the structures. However, definite particle size is determined by invoking the X-ray powder diffraction and scanning electron microscopy data. The results obtained suggested that pyridoxine reacted with metal ions as a bidentate ligand through its phenolate oxygen and the oxygen of the adjacent group at the 4'-position. The molar conductance measurements proved that the pyridoxine complexes are electrolytic in nature. The kinetic and thermodynamic parameters such as: Ea, ΔH(*), ΔS(*) and ΔG(*) were estimated from the DTG curves. The antibacterial evaluation of the pyridoxine and their complexes were also performed against some gram positive, negative bacteria as well as fungi.

CH Stretching Region: Computational Modeling of Vibrational Optical Activity

Most organic compounds provide vibrational spectra within the CH stretching region, yet the signal is difficult to interpret because of multiple difficulties in experiment and modeling. To better understand various factors involved, the ability of several harmonic and anharmonic computational approaches to describe these vibrations was explored for α-pinene, fenchone, and camphor as test compounds. Raman, Raman optical activity (ROA), infrared absorption (IR), and vibrational circular dichroism (VCD) spectra were measured and compared to quantum chemical computations. Surprisingly, the harmonic vibrational approach reasonably well reproduced the measured spectral patterns, including the vibrational optical activity (VOA). The CH stretching, however, appeared to be more sensitive to the basis set and solvent variations than lower-frequency vibrations. For a higher accuracy in frequencies and spectral shapes, anharmonic corrections were necessary. Accurate harmonic and anharmonic force fields were obtained with the mPW2PLYP double-hybrid functional. A limited vibrational configuration interaction (LVCI) where the CH stretching motion was decoupled from other vibrations provided the best simulated spectra. A balanced harmonic oscillator basis set had to be used, containing also states indirectly interacting with fundamental vibrations. A simpler second-order perturbational approach (PT2) appeared less useful. The modeling provided unprecedented agreement with experimental vibrational frequencies; spectral shapes were reproduced less faithfully. The possibility of ab initio interpretation of the CH spectral region for relatively large molecules further broadens the application span of vibrational spectroscopy.

Vibrational averaging of the chemical shift in crystalline α-glycine

Averaging of the chemical shift over the molecular motion improves the simulated data and provides additional information about the temperature dependence and system dynamics. However, crystal modeling is difficult due to the limited precision of the plane-wave density functional theory (DFT) methods and approximate vibrational schemes. On the glycine example, we investigate how the averaging can be achieved within the periodic boundary conditions at the DFT level. The nuclear motion is modeled with the vibrational configuration interaction, with other simplified quantum anharmonic schemes, and the classical Born-Oppenheimer molecular dynamics (BOMD). The results confirm a large vibrational contribution to the isotropic shielding values. Both the first and second derivatives of the shielding were found important for the quantum averaging. The first derivatives influence the shielding mostly due to the anharmonic character of the CH and NH stretching modes, whereas second derivatives produce most vibrational corrections associated with the lower-frequency vibrational modes. Temperature excitations of the lowest-frequency vibrational states and the expansion of the crystal cell both determine the temperature dependence of nuclear magnetic resonance parameters. The vibrational quantum approach as well as classical BOMD schemes provided temperature dependencies of the chemical shifts that are consistent with the previous experimental data.

Effects of alkyl side chains on properties of aliphatic amino acids probed using quantum chemical calculations

Effects of alkyl side chains (R-) on the electronic structural properties of aliphatic amino acids are investigated using quantum mechanical approaches. The carbon (C 1s) binding energy spectra of the aliphatic amino acids are derived from the C 1s spectrum of glycine (the parent spectrum) by the addition of spectral peaks, depending on the alkyl side chains, appearing in the lower energy region IP < 290 eV (where IP is the ionization potential). The two glycyl parent spectral peaks of the amide 291.0 eV [C((2))] and carboxylic 293.5 eV [C((1))] C atoms are shifted in the aliphatic amino acids owing to perturbations depending on the size and structure of the alkyl chains. The pattern of the N 1s and O 1s spectra in glycine is retained in the spectra of the other amino acids with small shifts to lower energy, again depending on the alkyl side chain. The Hirshfeld charge analyses confirm the observations. The alkyl effects on the valence binding energy spectra of the amino acids are concentrated in the middle valence energy region of 12-16 eV, and hence this energy region of 12-16 eV is considered as the `fingerprint' of the alkyl side chains. Selected valence orbitals, either inside or outside of the alkyl fingerprint region, are presented using both density distributions and orbital momentum distributions, in order to understand the chemical bonding of the amino acids. It is also observed that the HOMO-LUMO energy gaps of the aliphatic amino acids are reduced with the growth of the alkyl side chain.

On the limited precision of transfer of molecular optical activity tensors

Transfer of molecular property tensors (force field, dipole derivatives, polarizabilities, etc.) from smaller fragments to bigger molecules is powerful tool to calculate molecular vibrational spectra. However, we found serious accuracy limits for valinomycin (Phys. Chem. Chem. Phys. 2010, 12, 11021), where the transfer of the Raman optical activity tensors (ROA) had to be avoided. Therefore, in this study, the individual polarizable group model is analyzed for a model water dimer, and the corrections stemming from mutual group polarizations neglected in the transfer are estimated ab initio. The electric dipole polarizability was found more local and less sensitive to the interaction of distant molecular parts than the optical activity tensors (G′, A), which can partially explain the error observed during the transfer. In the second part of the study, tensor derivatives are transferred from smaller fragments to model valinomycin and insulin molecules, and the resultant tensor derivatives and ROA spectra compared to benchmark computations. The results confirmed that the error is caused by mutual polarization of molecular parts, more significant in insulin than in valinomycin, and could only partially be improved by increased size of the fragments.

DFT and MP2 investigations of L-proline and its hydrated complexes

A theoretical study of L-proline-nH(2)O (n = 1-3) has been performed using the hybrid DFT-B3LYP and MP2 methods together with the 6-311++G(d,p) basis set. The results show that the P2 conformer is energetically favorable when forming a hydrated structure, and the hydration of the carboxyl group leads to the greatest stability. For hydrated complexes, the adiabatic and vertical singlet-triplet excitation energies tend to decrease with the addition of water molecules. The hydration energy indicates that in the hydrated complexes the order of stability is: binding site 2 > binding site 1 > binding site 3, and binding site 12 > binding site 23 > binding site 13. As water molecules are added, the stabilities of these hydrated structures gradually increase. In addition, an infrared frequency analysis indicated that there are some differences in the low-frequency range, which are mainly dominated by the O-H stretching or bending vibrations of different water molecules. All of these results should aid our understanding of molecular behavior and provide reference data for further studies of biological systems.

Anharmonic oscillation effect on the Davydov-Scott monomer in a thermal bath

The dynamics of Davydov-Scott monomer in a thermal bath with higher order amide-site's displacement leads to anharmonic oscillation effect is investigated using full-quantum approach and the Lindblad formulation of master equation. The specific heat is calculated based on the thermodynamic partition function using the path integral method. The temperature dependence of the specific heat is studied. In the model the specific heat anomaly as pointed out in recent works by Ingold [Phys. Rev. E 79, 061105 (2009)] is also observed. However, it is found that the anomaly occurs at high-temperature region, and the anharmonic oscillation restores the positivity of specific heat.

Vibrational Raman optical activity of 1-phenylethanol and 1-phenylethylamine: revisiting old friends

The samples used for the first observations of vibrational Raman optical activity (ROA) in 1972, namely both enantiomers of 1-phenylethanol and 1-phenylethylamine, have been revisited using a modern commercial ROA instrument together with state-of-the-art ab initio calculations. The simulated ROA spectra reveal for the first time the vibrational origins of the first reported ROA signals, which comprised similar couplets in the alcohol and amine in the spectral range approximately 280-400 cm(-1). The results demonstrate how easy and routine ROA measurements have become, and how current ab initio quantum-chemical calculations are capable of simulating experimental ROA spectra quite closely provided sufficient averaging over accessible conformations is included. Assignment of absolute configuration is, inter alia, completely secure from results of this quality. Anharmonic corrections provided small improvements in the simulated Raman and ROA spectra. The importance of conformational averaging emphasized by this and previous related work provides the underlying theoretical background to ROA studies of dynamic aspects of chiral molecular and biomolecular structure and behavior.

Theoretical Study of Vibrationally Averaged Dipole Moments for the Ground and Excited C═O Stretching States of trans-Formic Acid

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 (ν3) mode. In this report, dipole moments for the ν3 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 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-ζ 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 (CPCM). 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 caused by interaction with traces of ortho-hydrogen (oH2) species in solid pH2. The validity of the single mode approach is tested against the multidimensional VCI results, suggesting that the isolated (noninteracting) 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 to the resulting ν3 single mode dipole moments is examined and discussed.

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.