Electrical Anharmonicity Research Articles

Vibrational properties of OH groups associated with divalent cations in corundum (α-Al2O3)

Abstract. The infrared spectra of synthetic corundum (α-Al2O3) samples either doped directly with divalent cations (Mg2+) or containing divalent cations formed by reduction of trivalent cations in H2 gas (Co2+, Ni2+) may display broad OH stretching bands at ∼3000 cm−1 due to the structural incorporation of trace amounts of hydrogen. Experimental spectra recorded from some natural sapphires display a similar absorption band associated with a dominant absorption at 3161 cm−1, and some beryllium-diffused corundum crystals show a band at 3060 cm−1. All of these also display smaller and generally narrower bands between 1900 and 2700 cm−1, whose natures are poorly defined. In this work, the atomic-scale structure, relative stability and infrared spectroscopic properties of a series of OH defects in corundum (α-Al2O3) are theoretically investigated at the density-functional-theory level. The investigated defects consist of interstitial H+ ions forming OH groups and compensating for the charge imbalance related to the presence of divalent cations (Be2+, Mg2+, Cr2+, Mn2+, Fe2+, Co2+, Ni2+) substituted for Al3+ at nearby octahedral sites. Bands occurring at ∼3000 cm−1 in experimental spectra are assigned to the OH stretching modes of some of these defects, with bands observed around 1900 and 2700 cm−1 being assigned to overtones of corresponding OH bending modes. The results also support the assignment of the so-called “3161 cm−1 series”, observed in experimental spectra of some rubies and yellow sapphires, to structural OH groups in association with Fe2+ ions, rather than Si4+, as has been previously proposed. These inferences are also supported by analysis of correlations between band areas in experimental infrared spectra extracted from a database of corundum gemstones. A qualitative explanation relating the anomalous intensity and the polarisation properties of the OH bending overtone bands to the electrical anharmonicity of OH groups involved in medium-strength H bonds is proposed.

Low-frequency anharmonic couplings in crystalline bromoform: Theory.

Theoretical calculations of the low-frequency anharmonic couplings of the β-phase of crystalline bromoform are presented based on density functional theory quantum chemistry calculations. The electrical and mechanical anharmonicities between intra- and intermolecular modes are calculated, revealing that the electrical anharmonicity dominates the cross-peak intensities in the 2D Raman-THz response and crystalline, as well as liquid, bromoform. Furthermore, the experimentally observed difference in relative cross-peak intensities between the two intramolecular modes of bromoform and the intermolecular modes can be explained by the C3v-symmetry of bromoform in combination with orientational averaging. The good agreement with the experimental results provides further evidence for our interpretation that the 2D Raman-THz response of bromoform is, indeed, related to the anharmonic coupling between the intra- and intermolecular modes.

Anharmonic Aspects in Vibrational Circular Dichroism Spectra from 900 to 9000 cm-1 for Methyloxirane and Methylthiirane.

Vibrational circular dichroism (VCD) spectra and the corresponding IR spectra of the chiral isomers of methyloxirane and of methylthiirane have been reinvestigated, both experimentally and theoretically, with particular attention to accounting for anharmonic corrections, as calculated by the GVPT2 approach. De novo recorded VCD spectra in the near IR (NIR) range regarding CH-stretching overtone transitions, together with the corresponding NIR absorption spectra, were also considered and accounted for, both with the GVPT2 and with the local mode approaches. Comparison of the two methods has permitted us to better describe the nature of active “anharmonic” modes in the two molecules and the role of mechanical and electrical anharmonicity in determining the intensities of VCD and IR/NIR data. Finally, two nonstandard IR/NIR regions have been investigated: the first one about ≈2000 cm–1, involving mostly two-quanta bending mode transitions, the second one between 7000 and 7500 cm–1 involving three-quanta transitions containing CH-stretching overtones and HCC/HCH bending modes.

Retinal Vibrations in Bacteriorhodopsin are Mechanically Harmonic but Electrically Anharmonic: Evidence From Overtone and Combination Bands.

Fundamental vibrations of the chromophore in the membrane protein bacteriorhodopsin (BR), a protonated Schiff base retinal, have been studied for decades, both by resonance Raman and by infrared (IR) difference spectroscopy. Such studies started comparing vibrational changes between the initial BR state (all-trans retinal) and the K intermediate (13-cis retinal), being later extended to the rest of intermediates. They contributed to our understanding of the proton-pumping mechanism of BR by exploiting the sensitivity of fundamental vibrational transitions of the retinal to its conformation. Here, we report on new bands in the 2,500 to 1,800 cm−1 region of the K-BR difference FT-IR spectrum. We show that the bands between 2,500 and 2,300 cm−1 originate from overtone and combination transitions from C-C stretches of the retinal. We assigned bands below 2,300 cm−1 to the combination of retinal C-C stretches with methyl rocks and with hydrogen-out-of-plane vibrations. Remarkably, experimental C-C overtone bands appeared at roughly twice the wavenumber of their fundamentals, with anharmonic mechanical constants ≤3.5 cm−1, and in some cases of ∼1 cm−1. Comparison of combination and fundamental bands indicates that most of the mechanical coupling constants are also very small. Despite the mechanical quasi-harmonicity of the C-C stretches, the area of their overtone bands was only ∼50 to ∼100 times smaller than of their fundamental bands. We concluded that electrical anharmonicity, the second mechanism giving intensity to overtone bands, must be particularly high for the retinal C-C stretches. We corroborated the assignments of negative bands in the K-BR difference FT-IR spectrum by ab initio anharmonic vibrational calculations of all-trans retinal in BR using a quantum-mechanics/molecular mechanics approach, reproducing reasonably well the small experimental anharmonic and coupling mechanical constants. Yet, and in spite accounting for both mechanical and electrical anharmonicities, the intensity of overtone C-C transitions was underestimated by a factor of 4–20, indicating room for improvement in state-of-the-art anharmonic vibrational calculations. The relatively intense overtone and combination bands of the retinal might open the possibility to detect retinal conformational changes too subtle to significantly affect fundamental transitions but leaving a footprint in overtone and combination transitions.

Are "Bright-State" Models Appropriate for Analyzing Fermi-Coupled Bands in Molecular Vibrational Spectra?

Bright-state models are often applied to "deperturb" Fermi-coupled bands in molecular vibrational spectra, in cases where a harmonically forbidden transition "borrows" intensity from an energetically nearby allowed transition. However, forbidden transitions can also acquire intensity through anharmonic couplings on the potential energy surface ("mechanical anharmonicity") or dipole moment surface ("electrical anharmonicity") that are not accounted for within the bright-state model. In this work, we compare deperturbation shifts obtained by analysis of experimental data with those predicted using the bright-state model, for a series of discrete encapsulated chloride hydrate isotopomers. Predicted band center shifts and Fermi coupling matrix elements obtained using the bright-state model are larger than those estimated from experimental data.

Graphene Domain Signature of Raman Spectra of sp2 Amorphous Carbons.

The standard D-G-2D pattern of Raman spectra of sp2 amorphous carbons is considered from the viewpoint of graphene domains presenting their basic structure units (BSUs) in terms of molecular spectroscopy. The molecular approximation allows connecting the characteristic D-G doublet spectra image of one-phonon spectra with a considerable dispersion of the C=C bond lengths within graphene domains, governed by size, heteroatom necklace of BSUs as well as BSUs packing. The interpretation of 2D two-phonon spectra reveals a particular role of electrical anharmonicity in the spectra formation and attributes this effect to a high degree of the electron density delocalization in graphene domains. A size-stimulated transition from molecular to quasi-particle phonon consideration of Raman spectra was experimentally traced, which allowed evaluation of a free path of optical phonons in graphene crystal.

Structure and Vibrational Spectra of ArnH+ (n = 2-3).

The structure and vibrational spectra of protonated Ar clusters ArnH+ (n = 2-3) are studied using potential energy surfaces at the CCSD(T)/aug-cc-pVTZ level and basis set. Ar binding energies, as well as position isomerism in Ar3H+, were investigated. In our previous work, the spectra of Ar2H+ reveal a strong progression of combination bands, which involves the asymmetric Ar-H+ stretch with multiple quanta of the symmetric Ar-H+ stretch. In this work, insights on the origin of such progression were examined using an adiabatic model. In addition, contributions from mechanical and electrical anharmonicity on the progressions' intensities were also examined. Comparison of the calculated spectrum for the bare and Ar-tagged ions reveals that the reduction of the symmetry group, from D∞h to either C∞v or C2v, results in a richer vibrational structure in the 500-1700 cm-1 region. When compared with previously reported action spectra (D. C. McDonald III, D. T. Mauney, D. Leicht, J. H. Marks, J. A. Tan, J.-L. Kuo, and M. A. Duncan, J. Chem. Phys., 2016, 145, 231,101), it appears that the position isomers, because of the binding of the weakly bound Ar messenger, are needed to account for the additional bands in the infrared photodissociation spectrum for Ar3H+. These findings demonstrate the active role of the messenger atom in relaxing some of the selection rules for the bare ion's vibrational transitions - resulting in an augmentation of the bands in the action spectrum.

A Feynman diagram description of the 2D-Raman-THz response of amorphous ice.

The 2D-Raman-THz response in all possible time-orderings (Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman) of amorphous water ice is calculated in two ways: from atomistic molecular dynamics simulations and with the help of a Feynman diagram model, the latter of which power-expands the potential energy surface and the dipole and polarizability surfaces up to leading order. Comparing both results allows one to dissect the 2D-Raman-THz response into contributions from mechanical anharmonicity, as well as electrical dipole and polarizability anharmonicities. Mechanical anharmonicity dominates the 2D-Raman-THz response of the hydrogen-bond stretching and hydrogen-bond bending bands of water, and dipole anharmonicity dominates that of the librational band, while the contribution of polarizability anharmonicity is comparably weak. A distinct echo of the hydrogen-bond stretching band is observed for the THz-Raman-THz pulse sequence, again dominated by mechanical anharmonicity. A peculiar mechanism is discussed, which is based on the coupling between the many normal modes within the hydrogen-bond stretching band and which will inevitably generate such an echo for an amorphous structure.

Structure and Dynamics of the Superprotonic Conductor Caesium Hydrogen Sulfate, CsHSO4

We have investigated caesium hydrogen sulfate, CsHSO4, in all three of its ambient pressure phases by total scattering neutron diffraction, inelastic neutron scattering (INS) and Raman spectroscopies and periodic density functional theory calculations. Above 140 °C, CsHSO4 undergoes a phase transition to a superprotonic conductor that has potential application in intermediate temperature fuel cells. Total scattering neutron diffraction data clearly show that all the existing structures of this phase are unable to describe the local structure, because they have either partial occupancies of the atoms and/or non-physical O–H distances. Knowledge of the local structure is crucial because it is this that determines the conduction mechanism. Starting from one of the previous models, we have generated a new structure that has no partial occupancies and reasonable O–H distances. After geometry optimisation, the calculated radial distribution function is in reasonable agreement with the experimental data, as are the calculated and observed INS and Raman spectra. This work is particularly notable in that we have measured INS spectra in the O–H stretch region above room temperature, which is extremely rare. The INS spectra have the enormous advantage that the electrical anharmonicity that complicates the infrared spectra is absent and the stretch modes are plainly seen.

Feynman diagram description of 2D-Raman-THz spectroscopy applied to water.

2D-Raman-THz spectroscopy of liquid water, which has been presented recently [J. Savolainen et al., Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)], directly probes the intermolecular degrees of freedom of the hydrogen-bond network. However, being a relatively new technique, its information content is not fully explored to date. While the spectroscopic signal can be simulated based on molecular dynamics simulation in connection with a water force field, it is difficult to relate spectroscopic signatures to the underlying microscopic features of the force field. Here, a completely different approach is taken that starts from an as simple as possible model, i.e., a single vibrational mode with electrical and mechanical anharmonicity augmented with homogeneous and inhomogeneous broadening. An intuitive Feynman diagram picture is developed for all possible pulse sequences of hybrid 2D-Raman-THz spectroscopy. It is shown that the model can explain the experimental data essentially quantitatively with a very small set of parameters, and it is tentatively concluded that the experimental signal originates from the hydrogen-bond stretching vibration around 170 cm-1. Furthermore, the echo observed in the experimental data can be quantified by fitting the model. A dominant fraction of its linewidth is attributed to quasi-inhomogeneous broadening in the slow-modulation limit with a correlation time of 370 fs, reflecting the lifetime of the hydrogen-bond networks giving rise to the absorption band.

Effective Inclusion of Mechanical and Electrical Anharmonicity in Excited Electronic States: VPT2-TDDFT Route.

We present a reliable and cost-effective procedure for the inclusion of anharmonic effects in excited-state energies and spectroscopic intensities by means of second-order vibrational perturbation theory. This development is made possible thanks to a recent efficient implementation of excited-state analytic Hessians and properties within the time-dependent density functional theory framework. As illustrated in this work, by taking advantage of such algorithmic developments, it is possible to perform calculations of excited-state infrared spectra of medium-large isolated molecular systems, with anharmonicity effects included in both the energy and property surfaces. We also explore the use of this procedure for the inclusion of anharmonic effects in the simulation of vibronic bandshapes of electronic spectra and compare the results with previous, more approximate models.

Signature of Congregated Effects of Mechanical and Electrical Anharmonicities, Fermi Resonances, and Dampings on the IR Spectra of Hydrogen Bonded Systems: Quantum Dynamic Study.

Theoretical IR spectral density of the high-frequency stretching mode of hydrogen bond (H-bond) systems is reported using a three-dimensional approach. The model, studied within the framework of linear response theory, involves the mechanical anharmonicity of the high-frequency stretching mode by contemplating its potential as an asymmetric double well potential, the mechanical anharmonicity of the H-bond Bridge by contemplating its potential as a Morse potential, Fermi resonances which occur between the high frequency stretching mode and the overtones of the bending modes, the electrical anharmonicity translated by the nonlinearity to second order in the electric dipole moment function of the fast mode, the second order modulation of the angular frequency and the equilibrium position of the fast mode on the slow mode coordinate, and direct and indirect relaxation mechanism. Moreover, the repulsive potential interposing in the fast mode potential is chosen in Gaussian form to account for the asymmetry of the fast mode potential and thereby elucidate the nature of the H-bond. The anharmonic coupling between the fast and slow frequency modes is handled within the strong anharmonic coupling theory. The direct relaxation of the fast mode and the indirect relaxation of the H-bond Bridge are consolidated using previous results [Rekik et al. Chem. Phys. 2008, 352, 65-76]. The infrared spectral density is calculated using the Fourier transform of the autocorrelation function of the transition dipole moment operator of the fast mode. The evolution of the infrared absorption is demonstrated, indicating that mixing of all these effects results in a broadening and complicated distribution of the spectral density. The result of this work underscores the necessity of simultaneously combining the maximum effects in H-bonded complexes for effectively modeling and interpreting their corresponding IR spectra.

Accurate Vibrational-Rotational Parameters and Infrared Intensities of 1-Bromo-1-fluoroethene: A Joint Experimental Analysis and Ab Initio Study.

The medium-resolution gas-phase infrared (IR) spectra of 1-bromo-1-fluoroethene (BrFC═CH2, 1,1-C2H2BrF) were investigated in the range 300-6500 cm-1, and the vibrational analysis led to the assignment of all fundamentals as well as many overtone and combination bands up to three quanta, thus giving an accurate description of its vibrational structure. Integrated band intensity data were determined with high precision from the measurements of their corresponding absorption cross sections. The vibrational analysis was supported by high-level ab initio investigations. CCSD(T) computations accounting for extrapolation to the complete basis set and core correlation effects were employed to accurately determine the molecular structure and harmonic force field. The latter was then coupled to B2PLYP and MP2 computations in order to account for mechanical and electrical anharmonicities. Second-order perturbative vibrational theory was then applied to the thus obtained hybrid force fields to support the experimental assignment of the IR spectra.

Electrical anharmonicity and dampings contributions to Cl-[formula omitted] stretching band in gaseous (CH3)2O…HCl complex: Quantum dynamic study and prediction of the temperature effects

In a previous work (Rekik et al., 2017), we demonstrated the ability of a simple anharmonic model of the dipole moment function of the X-H stretching band to explain a set of spectroscopic features of hydrogen bonding formation. Within the context of this model, we have shown that the origins of the broadening of the X-H→ stretching band is attributed to large terms in the expansion of the autocorrelation functions due to the electrical anharmonicity. However, the question remained as to the ability of this model to treat the more complex situation in which we take into account the relaxation mechanisms that look at the effect of the surroundings and thereby gives rise to signatures of the medium to the X-H→ stretching band lineshapes. Thus, in the present study, we investigated this situation by envisaging that the direct relaxation mechanism is due to the coupling between the fluctuating local electric field and the dipole moment of the complex as rationalized by Rosh and Ratner and the indirect damping resulting from the interaction of the X-H→ stretch with its environment via the H-bond bridge mode. Theoretical experiments show that mixing of all these effects results in a speard and complicated structure. Using an ensemble of physically sound parameters as input into this approach, we have captured the main features in the experimental Cl-H→ band in gaseous (CH3)2O…HCl complex and shown that the direct relaxation entrains a broadening of the spectra and is capable of qualitatively capturing the main features in the experimental spectra and quantitatively capturing the characteristic time scale of the vibrational dynamics of the Cl-H→ stretching band. Furthermore, due to the decent agreement obtained between the theoretical and experimental line shapes at 226K, the evolution of the IR spectra with the varaiation of temperature is proposed. The findings gained herein underscore the utility of combining simultaneously the effects of the electrical anharmonicity and the damping mechanisms for efficiently modeling the IR spectra of H-bonded systems and predicting its evolution with the temperature.

Electrical anharmonicity in hydrogen bonded systems: complete interpretation of the IR spectra of the Cl-H[combining right harpoon above] stretching band in the gaseous (CH3)2OHCl complex.

Following the previous developments to simulate the fully infrared spectra of weak hydrogen bond systems within the linear response theory, an extension of the adiabatic model is presented here. A general formulation including the electrical anharmonicities in the calculation of the damped autocorrelation function of weak H-bonds is adopted to facilitate the support of the additional properties, and thus the IR spectra of the Cl-H[combining right harpoon above] stretching band in the gaseous (CH3)2OHCl complex. We have explored the origins of the broadening of the Cl-H[combining right harpoon above] stretching band. We found that the main features of the lineshape are attributed to electrical anharmonicity as a consequence of the large mixed second derivatives of the dipole moment with respect to the Cl-H[combining right harpoon above] bond and of the intermonomer elongations . In addition to providing more accurate theoretical band shapes, inclusion of the electrical anharmonicity in the present model paves the way for a more complete interpretation by generating three new Franck-Condon superposed distributions.

Vibrational Fingerprints of Low-Lying Pt(n)P(2n) (n = 1-5) Cluster Structures from Global Optimization Based on Density Functional Theory Potential Energy Surfaces.

Vibrational fingerprints of small Pt(n)P(2n) (n = 1-5) clusters were computed from their low-lying structures located from a global exploration of their DFT potential energy surfaces with the GSAM code. Five DFT methods were assessed from the CCSD(T) wavenumbers of PtP2 species and CCSD relative energies of Pt2P4 structures. The eight first Pt(n)P(2n) isomers found are reported. The vibrational computations reveal (i) the absence of clear signatures made by overtone or combination bands due to very weak mechanical and electrical anharmonicities and (ii) some significant and recurrent vibrational fingerprints in correlation with the different PP bonding situations in the Pt(n)P(2n) structures.

A VPT2 route to near-infrared spectroscopy: the role of mechanical and electrical anharmonicity.

Following the previous developments to simulate fully anharmonic spectra within the vibrational second-order perturbation level of theory [ J. Chem. Phys. 2012 , 126 , 134108 ], an extension to transitions up to three quanta is presented here. A general formulation including the mechanical and electrical anharmonicities is adopted to facilitate the support of additional properties, and thus spectroscopies. In addition to providing more accurate theoretical band shapes, inclusion of overtones and combination bands up to three quanta paves the way to a more complete interpretation of near-infrared spectra.

Computational Chemistry Meets Experiments for Explaining the Behavior of Bibenzyl: A Thermochemical and Spectroscopic (Infrared, Raman, and NMR) Investigation.

The structure, conformational behavior, and spectroscopic parameters of bibenzyl have been investigated by a computational protocol including proper treatment of anharmonic and hindered rotor contributions. Conventional hybrid functionals overstabilize the anti conformer while low-order post-Hartree-Fock (MP2) approaches strongly favor the gauche conformer. However, inclusion of semiempirical dispersion effects in density functionals or coupled cluster post-Hartree-Fock models agree in forecasting the simultaneous presence of both conformers in the gas phase with a slightly larger stability (0.7 kcal·mol(-1)) of the gauche conformer. Addition of thermal and entropic effects finally leads to very close Gibbs free energies for both conformers and, thus, to a slight preference for the gauche form due to statistical factors (2 vs 1). The situation remains essentially the same in solution. On these grounds, perturbative vibrational computations including both electrical and mechanical anharmonicities lead to IR and Raman spectra in remarkable agreement with experiment. Full assignment of the IR spectra explains the presence of peaks from gauche or anti conformers. Comparison between computed and experimental Raman spectra confirms that both conformers are present in liquid phase, whereas the anti conformer seems to be preponderant in the solid state. Also computed NMR parameters are in good agreement with experiment.

Near-Infrared Study of the Hydrogen Bonding in Acetone-Methanol and Acetone-Ethanol Mixtures: Roles of Mechanical and Electrical Anharmonicities of Hydroxyl Oscillator

Near-infrared spectra of methanol-acetone and ethanol-acetone mixtures in the entire mole fraction range in increments of 0.1 were recorded in the region of 7500–6000 cm−1. The first overtone bands of the hydroxyl (OH) groups were assigned to the polymeric and oligomeric OH associations. In both solutions, the frequency of the polymeric OH band decreased with the increase in the mole fraction of alcohol, which indicated the increase in the hydrogen bonding strength. The integrated area of the polymeric OH band followed the opposite trend to the frequency with the mole fraction. The nonlinearity of the plot of the integrated band area of the polymeric OH band of methanol versus the mole fraction of acetone revealed the nonideal character of the methanol-acetone mixtures, whereas the opposite was observed for the ethanol-acetone mixtures. These observations have been explained in terms of mechanical and electrical anharmonicities of the OH oscillator.

Molecular structure and spectroscopic signatures of acrolein: theory meets experiment.

A comprehensive study of the molecular structure and IR spectrum of cis and trans acrolein has been performed by an integrated computational approach coupling methods rooted in the coupled-cluster ansatz and the density functional theory. From the one side, DFT anharmonic force fields allow us to determine very reliable semiexperimental structures for both isomers, which are in remarkable agreement with the geometries issuing from CCSD(T) computations accounting for the extrapolation to the complete basis set and core correlation. The same kind of coupled-cluster computations provide dipole moment, relative energies, and interconversion barrier in remarkable agreement with experiments. Finally, harmonic CCSD(T) results coupled to DFT evaluation of mechanical and electrical anharmonicity allow us, in the framework of second-order perturbative vibrational theory, to confirm most of the experimental assignments of IR spectra, and to suggest some additional interpretations for congested regions including fundamental bands together with overtones and combination bands.