On the Calculation of Vibrational Frequencies for Molecules in Solution Beyond the Harmonic Approximation

Vibrational Spectra Simulations in Amino Acid-Based Imidazolium Ionic Liquids

We present maximally localized Wannier functions and Voronoi tessellation to obtain dipole moment distributions for vibrational spectra in several important ionic liquids calculated by using ab initio molecular dynamics simulations. IR and Raman spectra of various imidazolium-based ionic liquids (ILs) paired with six amino acid anions are shown herein. For IR spectra, two approaches (Wannier and Voronoi) are in agreement with respect to the relative intensities and the overall shapes for the main peaks. Under Raman spectra, the polarizability of the covalent bonds is shown to affect the strength of the Raman scattering signal. The advantage of the Voronoi tessellation method, being that it does not have strong spikes in its time development, is demonstrated by the comparison of two theoretical methods (Wannier and Voronoi) with experimental data. We analyze the errors between theoretical and experimental spectroscopic data, with the Voronoi method shown to accurately reproduce experimental values. In addition, theoretical spectroscopy shows the ability to accurately separate components of a mixture. The combination of theoretical and experimental methods is utilized to understand the spectroscopic properties of amino acid-based imidazolium ILs.

Computational Spectroscopy of Aqueous Solutions: The Underlying Role of Conformational Sampling

Fully atomistic multiscale polarizable quantum mechanics (QM)/molecular mechanics (MM) approaches, combined with techniques to sample the solute-solvent phase space, constitute the most accurate method to compute spectral signals in aqueous solution. Conventional sampling strategies, such as classical molecular dynamics (MD), may encounter drawbacks when the conformational space is particularly complex, and transition barriers between conformers are high. This can lead to inaccurate sampling, which can potentially impact the accuracy of spectral calculations. For this reason, in this work, we compare classical MD with enhanced sampling techniques, i.e., replica exchange MD and metadynamics. In particular, we show how the different sampling techniques affect computed UV, electronic circular dichroism, nuclear magnetic resonance shielding, and optical rotatory dispersion of N-acetylproline-amide in aqueous solution. Such a system is a model peptide characterized by complex conformational variability. Calculated values suggest that spectral properties are influenced by solute conformers, relative population, and solvent effects; therefore, particular care needs to be paid for when choosing the sampling technique.

Dissecting amide-I vibrations in histidine dipeptide

The amide-I vibrational characteristics and conformational preferences of the model compound - histidine dipeptide (Ac-His-NHCH₃, HISD) in gas phase and solution have been revealed with the help of ab initio calculations and wavefunction analyses. The Gibbs free energy surfaces (FESs) of solvated HISD were smoothed by solvent effect to exhibit different structural populations concerning various external environments. It was shown that the most stable conformations of HISD in CHCl₃ and gas phase are C7eq, while those in DMSO and water are β and PPII, respectively. Compared with ALAD, the number of accessible conformational states on these FESs was predicted to be reduced due to the steric effect of imidazole group. The two amide-I normal modes of HISD were found to have intrinsically secondary structural dependencies, and be sensitive to surrounding environments. The average amide-I_a frequencies of HISD isomers in these environments were predicted to be almost the same as those of ALAD, while the amide-I_b mean frequencies were estimated to be lower than ALAD due to the intramolecular interactions between the imidazole group and amino-terminal amide unit. The good linear correlations between amide-I frequencies and the atomic electrostatic potentials (ESPs) of amide groups were also found to interpret the solvent-induced amide-I frequency shifts of HISD at the electronic structure level. These results allow us to gain a deep understanding of amide-I vibrations of HISD, and would be helpful for the site-specific conformational monitoring and spectral interpretation of solvated polypeptides.

Concerted nucleophilic aromatic substitutions

Nucleophilic aromatic substitution (SNAr) is one of the most widely applied reaction classes in pharmaceutical and chemical research, providing a broadly useful platform for the modification of aromatic ring scaffolds. The generally accepted mechanism for SNAr reactions involves a two-step addition-elimination sequence via a discrete, non-aromatic Meisenheimer complex. Here we use 12C/13C kinetic isotope effect (KIE) studies and computational analyses to provide evidence that prototypical SNAr reactions in fact proceed through concerted mechanisms. The KIE measurements were made possible by a new technique that leverages the high sensitivity of 19F as an NMR nucleus to quantitate the degree of isotopic fractionation. This sensitive technique permits the measurement of KIEs on 10 mg of natural abundance material in one overnight acquisition. As a result, it provides a practical tool for performing detailed mechanistic analyses of reactions that form or break C-F bonds.

Anharmonic vibrational spectra and mode-mode couplings analysis of 2-aminopyridine

Vibrational spectra of 2-aminopyridine (2AP) have been analyzed using the vibrational self-consistence field theory (VSCF), correlated corrected vibrational self-consistence field theory (CC-VSCF) and vibrational perturbation theory (VPT2) at B3LYP/6-311G(d,p) framework. The mode-mode couplings affect the vibrational frequencies and intensities. The coupling integrals between pairs of normal modes have been obtained on the basis of quartic force field (2MR-QFF) approximation. The overtone and combination bands are also assigned in the FTIR spectrum with the help of anharmonic calculation at VPT2 method. A statistical analysis of deviations shows that estimated anharmonic frequencies are closer to the experiment over harmonic approximation. Furthermore, the anharmonic correction has also been carried out for the dimeric structure of 2AP. The fundamental vibration bands have been assigned on the basis of potential energy distribution (PED) and visual look over the animated modes. Other important molecular properties such as frontier molecular orbitals and molecular electrostatics potential mapping have also been analyzed.

Effective Fully Polarizable QM/MM Approach To Model Vibrational Circular Dichroism Spectra of Systems in Aqueous Solution

We propose a methodology, based on the combination of classical Molecular Dynamics (MD) simulations with a fully polarizable Quantum Mechanical (QM)/Molecular Mechanics (MM)/Polarizable Continuum Model (PCM) Hamiltonian, to calculate Vibrational Circular Dichroism (VCD) spectra of chiral systems in aqueous solution. Polarization effects are included in the MM force field by exploiting an approach based on Fluctuating Charges (FQ). By performing the MD, the description of the solvating environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions. On the other hand, the QM/FQ/PCM calculation of the VCD spectrum ensures an accurate description of the electronic density of the solute and a proper account for the specific interactions in solution. The application of our approach to (R)-methyloxirane and (l)-alanine in aqueous solution gives calculated spectra in remarkable agreement with their experimental counterparts and a substantial improvement with respect to the same spectra calculated with the PCM.

Sticking to (first) principles: quantum molecular dynamics and Bayesian probabilistic methods to simulate aquatic pollutant absorption spectra

This work explores the relationship between theoretically predicted excitation energies and experimental molar absorption spectra as they pertain to environmental aquatic photochemistry. An overview of pertinent Quantum Chemical descriptions of sunlight-driven electronic transitions in organic pollutants is presented. Second, a combined molecular dynamics (MD), time-dependent density functional theory (TD-DFT) analysis of the ultraviolet to visible (UV-Vis) absorption spectra of six model organic compounds is presented alongside accurate experimental data. The functional relationship between the experimentally observed molar absorption spectrum and the discrete quantum transitions is examined. A rigorous comparison of the accuracy of the theoretical transition energies (ΔES0→Sn) and oscillator strength (fS0→Sn) is afforded by the probabilistic convolution and deconvolution procedure described. This method of deconvolution of experimental spectra using a Gaussian Mixture Model combined with Bayesian Information Criteria (BIC) to determine the mean (μ) and standard deviation (σ) as well as the number of observed singlet to singlet transition energy state distributions. This procedure allows a direct comparison of the one-electron (quantum) transitions that are the result of quantum chemical calculations and the ensemble of non-adiabatic quantum states that produce the macroscopic effect of a molar absorption spectrum. Poor agreement between the vertical excitation energies produced from TD-DFT calculations with five different functionals (CAM-B3LYP, PBE0, M06-2X, BP86, and LC-BLYP) suggest a failure of the theory to capture the low energy, environmentally important, electronic transitions in our model organic pollutants. However, the method of explicit-solvation of the organic solute using the quantum Effective Fragment Potential (EFP) in a density functional molecular dynamics trajectory simulation shows promise as a robust model of the hydrated organic pollutant. Furthermore, the described protocol can be extended using higher-level equilibration and vertical excitation methods to increase the numerical accuracy and describe multi-reference electronic transitions. Finally, a measure of the accuracy of theoretically derived absorption spectra is discussed as a tool to further develop our capacity to produce accurate a priori simulations of sunlight-driven photochemistry in natural waters.

Analytic calculations of anharmonic infrared and Raman vibrational spectra

Using a recently developed recursive scheme for the calculation of high-order geometric derivatives of frequency-dependent molecular properties [Ringholm et al., J. Comp. Chem., 2014, 35, 622], we present the first analytic calculations of anharmonic infrared (IR) and Raman spectra including anharmonicity both in the vibrational frequencies and in the IR and Raman intensities. In the case of anharmonic corrections to the Raman intensities, this involves the calculation of fifth-order energy derivatives-that is, the third-order geometric derivatives of the frequency-dependent polarizability. The approach is applicable to both Hartree-Fock and Kohn-Sham density functional theory. Using generalized vibrational perturbation theory to second order, we have calculated the anharmonic infrared and Raman spectra of the non- and partially deuterated isotopomers of nitromethane, where the inclusion of anharmonic effects introduces combination and overtone bands that are observed in the experimental spectra. For the major features of the spectra, the inclusion of anharmonicities in the calculation of the vibrational frequencies is more important than anharmonic effects in the calculated infrared and Raman intensities. Using methanimine as a trial system, we demonstrate that the analytic approach avoids errors in the calculated spectra that may arise if numerical differentiation schemes are used.

Anharmonic Effects on Vibrational Spectra Intensities: Infrared, Raman, Vibrational Circular Dichroism, and Raman Optical Activity

The aim of this paper is 2-fold. First, we want to report the extension of our virtual multifrequency spectrometer (VMS) to anharmonic intensities for Raman optical activity (ROA) with the full inclusion of first- and second-order resonances for both frequencies and intensities in the framework of the generalized second-order vibrational perturbation theory (GVPT2) for all kinds of vibrational spectroscopies. Then, from a more general point of view, we want to present and validate the performance of VMS for the parallel analysis of different vibrational spectra for medium-sized molecules (IR, Raman, VCD, ROA) including both mechanical and electric/magnetic anharmonicity. For the well-known methyloxirane benchmark, careful selection of density functional, basis set, and resonance thresholds permitted us to reach qualitative and quantitative agreement between experimental and computed band positions and shapes. Next, the whole series of halogenated azetidinones is analyzed, showing that it is now possible to interpret different spectra in terms of mass, electronegativity, polarizability, and hindrance variation between closely related substituents, chiral spectroscopies being particular effective in this connection.

Infrared and Raman Spectroscopy from Ab Initio Molecular Dynamics and Static Normal Mode Analysis: The C-H Region of DMSO as a Case Study

Carbon-hydrogen (C-H) vibration modes serve as key probes in the chemical identification of hydrocarbons and in vibrational sum-frequency generation spectroscopy of hydrocarbons at the liquid/gas interface. Their assignments pose a challenge from a theoretical viewpoint. In this work, we present a detailed study of the C-H stretching region of dimethyl sulfoxide using a new ab initio molecular dynamics (AIMD) module that we have implemented in NWChem. Through a combination of AIMD simulations and static normal mode analysis, we interpret experimental infrared and Raman spectra and explore the role of anharmonic effects in this system. Comprehensive anharmonic normal mode analysis of the C-H stretching region casts doubt upon previous experimental assignments of the shoulder on the symmetric C-H stretching peak. In addition, our AIMD simulations also show significant broadening of the in-phase symmetric C-H stretching resonance, which suggests that the experimentally observed shoulder is due to thermal broadening of the symmetric stretching resonance.

Dispersion corrected DFT approaches for anharmonic vibrational frequency calculations: nucleobases and their dimers

Computational spectroscopy techniques have become in the last few years an effective means to analyze and assign infrared (IR) spectra of molecular systems of increasing dimensions and in different environments. However, transition from compilation of harmonic data to fully anharmonic simulations of spectra is still underway. The most promising results for large systems have been obtained, in our opinion, by perturbative vibrational approaches based on potential energy surfaces computed by hybrid (especially B3LYP) density functionals and medium size (e.g. SNSD) basis sets. In this framework, we are actively developing a comprehensive and robust computational protocol aimed at quantitative reproduction of the spectra of nucleic acid base complexes and their adsorption on solid supports (organic/inorganic). In this contribution we report the essential results of the first step devoted to isolated monomers and dimers. It is well known that in order to model the vibrational spectra of weakly bound molecular complexes dispersion interactions should be taken into proper account. In this work we have chosen two popular and inexpensive approaches to model dispersion interactions, namely the semi-empirical dispersion correction (D3) and pseudopotential based (DCP) methodologies both in conjunction with the B3LYP functional. These have been used for simulating fully anharmonic IR spectra of nucleobases and their dimers through generalized second order vibrational perturbation theory (GVPT2). We have studied, in particular, isolated adenine, hypoxanthine, uracil, thymine and cytosine, the hydrogen-bonded and stacked adenine and uracil dimers, and the stacked adenine-naphthalene heterodimer. Anharmonic frequencies are compared with standard B3LYP results and experimental findings, while the computed interaction energies and structures of complexes are compared to the best available theoretical estimates.

Stereo-electronic, vibrational, and environmental contributions to polarizabilities of large molecular systems: a feasible anharmonic protocol

Reliable computations of linear and non-linear optical properties of molecular systems in condensed phases require a proper account of stereo-electronic, vibrational, and environmental effects. In the framework of density functional theory, these effects can be accurately introduced using second-order vibrational perturbation theory in conjunction with polarizable continuum models. We illustrate the combination of an anharmonic description of the ground-state potential energy surface with solvation effects treated with the polarizable continuum model (PCM) in the calculation of the electronic, zero-point, and pure vibrational polarizabilities of selected systems. The description of the solvation environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions through the inclusion of both electronic and vibrational non-equilbrium effects, as well as the direct effect of the solvent on the electric field that generates the molecular response (local field effect). This treatment yields accurate results which can be directly compared with experimental findings without the need of empirical corrections.

A robust and effective time-independent route to the calculation of Resonance Raman spectra of large molecules in condensed phases with the inclusion of Duschinsky, Herzberg-Teller, anharmonic, and environmental effects

We present an effective time-independent implementation to model vibrational resonance Raman (RR) spectra of medium-large molecular systems with the inclusion of Franck-Condon (FC) and Herzberg-Teller (HT) effects and a full account of the possible differences between the harmonic potential energy surfaces of the ground and resonant electronic states. Thanks to a number of algorithmic improvements and very effective parallelization, the full computations of fundamentals, overtones, and combination bands can be routinely performed for large systems possibly involving more than two electronic states. In order to improve the accuracy of the results, an effective inclusion of the leading anharmonic effects is also possible, together with environmental contributions under different solvation regimes. Reduced-dimensionality approaches can further enlarge the range of applications of this new tool. Applications to imidazole, pyrene, and chlorophyll a1 in solution are reported, as well as comparisons with available experimental data.

Conformational analysis of Gly-Ala-NHMe in D(2)O and DMSO solutions: a two-dimensional infrared spectroscopy study

A relevant number of experiments on short peptides has been performed in recent years. One of the major problems rises from the simultaneous presence of slightly different conformers at equilibrium in solution. In the present paper, the conformational characteristics of the Gly-l-Ala-Methyl amide dipeptide in D2O and DMSO solutions are investigated by nonlinear IR spectroscopy. The pump-probe scheme with ultrashort mid-infrared pulses, in the Amide I region, is used to determine the mutual orientation of the two C═O bonds and the dynamics due to solute-solvent interactions. The coupling between Amide I modes is evaluated from both linear and 2D spectra. The interconversion between the different conformations occurs on time scales longer than the vibrational lifetime, and the spectral diffusion observed in 2D spectra is attributed to the solvent dynamics. Quantum mechanical calculations and molecular dynamics simulations are performed to identify the most stable geometries. By comparing the experimental and the theoretical data, we establish the prevalence of β-like polar conformers in both water and DMSO solvents.

Development of a virtual spectrometer for chiroptical spectroscopies: the case of nicotine

The impressive advances of computational spectroscopy in most recent years are providing robust and user-friendly multifrequency virtual spectrometers, which can also be used by nonspecialists to complement experimental studies. At the heart of these developments there are latest-generation models based on Density Functional Theory for the proper treatment of stereo-electronic effects, coupled to the polarizable continuum model to deal with bulk solvent effects, and low-order perturbative treatments of anharmonic effects. Continuing our efforts to increase the range of application of virtual spectrometers, we report here about chiroptical spectroscopies with special reference to optical rotation and vibrational circular dichroism. The capabilities and possible limitations of our latest tool will be analyzed for the specific case of (S)-nicotine in vacuo and in different solvents.

Toward Ab Initio Anharmonic Vibrational Circular Dichroism Spectra in the Condensed Phase

The first implementation and calculation of anharmonic VCD rotational strengths for solvated systems is reported. Our approach, rooted in the polarizable continuum model (PCM) and in the second-order vibrational perturbation theory (VPT2), permits not only correction for anharmonicity in the signals associated with fundamental transitions but also calculation of rotational strengths of overtones and combination bands. This allows for a more physically consistent comparison between experiment and calculations together with the analysis of spectral regions dominated by anharmonic effects. The developed model is applied to a few test cases, and the computational outcomes are directly compared with experimental data.

Towards an accurate description of anharmonic infrared spectra in solution within the polarizable continuum model: reaction field, cavity field and nonequilibrium effects

We present a newly developed and implemented methodology to perturbatively evaluate anharmonic vibrational frequencies and infrared (IR) intensities of solvated systems described by means of the polarizable continuum model (PCM). The essential aspects of the theoretical model and of the implementation are described and some numerical tests are shown, with special emphasis towards the evaluation of IR intensities, for which the quality of the present method is compared to other methodologies widely used in the literature. Proper account of an incomplete solvation regime in the treatment of the molecular vibration is also considered, as well as inclusion of the coupling between the solvent and the probing field (cavity field effects). In order to assess the quality of our approach, comparison with experimental findings is reported for selected cases.

Raman spectra of long chain hydrocarbons: anharmonic calculations, experiment and implications for imaging of biomembranes

First-principles anharmonic vibrational calculations are carried out for the Raman spectrum of the C-H stretching bands in dodecane, and for the C-D bands in the deuterated molecule. The calculations use the Vibrational Self-Consistent Field (VSCF) algorithm. The results are compared with liquid-state experiments, after smoothing the isolated-molecule sharp-line computed spectra. Very good agreement between the computed and experimental results is found for the two systems. The combined theoretical and experimental results provide insights into the spectrum, elucidating the roles of symmetric and asymmetric CH(3) and CH(2) hydrogenic stretches. This is expected to be very useful for the interpretation of spectra of long-chain hydrocarbons. The results show that anharmonic effects on the spectrum are large. On the other hand, vibrational degeneracy effects seem to be rather modest at the resolution of the experiments. The degeneracy effects may have more pronounced manifestations in higher-resolution experiments. The results show that first-principles anharmonic vibrational calculations for hydrocarbons are feasible, in good agreement with experiment, opening the way for applications to many similar systems. The results may be useful for the analysis of CARS imaging of lipids, for which dodecane is a representative molecule. It is suggested that first-principles vibrational calculations may be useful also for CARS imaging of other systems.

Estimation of formamide harmonic and anharmonic modes in the Kohn-Sham limit using the polarization consistent basis sets

Formamide harmonic and anharmonic frequencies of fundamental vibrations in the gas phase and in several solvents were successfully estimated in the B3LYP Kohn-Sham complete basis set limit (KS CBS). CBS results were obtained by extrapolating a power function (two-parameter formula) to the results calculated with polarization-consistent basis sets. Anharmonic corrections using the second order perturbation treatment (PT2) and hybrid B3LYP functional combined with polarization consistent pc-n (n = 0, 1, 2, 3, 4) and several Pople’s basis sets were analyzed for all fundamental formamide vibrational modes in the gas phase and solution. Solvent effects were modeled within a PCM method. The anharmonic frequency of diagnostic amide vibration C = O in the gas phase and the CCl₄ solution calculated with the VPT2 method was significantly closer to experimental data than the corresponding harmonic frequency. Both harmonic and anharmonic frequencies of C = O stretching mode decreased linearly with solvent polarity, expressed by relative environment permittivity (ε) ratio (ε − 1)/(2ε + 1). However, an unphysical behavior of solvent dependence of some low frequency anharmonic amide modes of formamide (e.g., CN stretch, NH₂ scissoring, and NH₂ in plane bend) was observed, probably due to the presence of severe anharmonicity and Fermi resonance.

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