Anharmonic Vibrational Calculations Research Articles

Isomer-Specific, Cryogenic Ion Vibrational Spectroscopy Investigation of D2- and N2-Tagged, Protonated Formic Acid Complexes Using Two-Color, IR-IR Photobleaching.

Here we analyze cryogenic ion vibrational spectra of tagged protonated formic acid (PFA) with electronic structure and anharmonic vibrational calculations to establish the isomers generated by electrospray ionization (ESI) followed by buffer gas cooling to ∼25 K. Two isomers are identified (the trans form (E,Z) and the cis form (E,E)) and generated in comparable abundance despite the fact that the calculated E,E structure lies 6.40 kJ mol-1 above the E,Z form. A large (∼60 kJ mol-1) barrier separates them such that the E,E form can be kinetically trapped upon cooling in the ion trap. The anticooperativity between the H-bonds of the OH groups is explored by measuring the shift in the D2-bound OH fundamental when a second D2 is attached. Both isomers are observed in the N2-tagged counterparts, displaying the expected red-shifted OH bands. These results indicate that ESI generates both isomers and both must be considered when analyzing cluster spectra based on the PFA core ion.

Microwave Spectroscopy of Chiral Astrochemical Candidate Vinyloxirane: The Missing Gauche Conformer.

The recent detection of a chiral molecule, propylene oxide, in the interstellar medium provides impetus for investigation of related analogues as candidates for discovery of a second chiral species. Vinyloxirane (VO) shares many of the characteristics of propylene oxide that favored its remote detection such as modest size, appreciable dipole moment and modest adsorption to water ice. The microwave spectrum of vinyloxirane at room temperature has been studied in the 18 - 26 GHz region. Rotational transitions of the previously undetected gauche-1 conformer have been assigned and fitted. The quantum number range of anti conformer transitions has been greatly expanded, providing improved molecular constants. Vibrational satellite transitions were assigned and fitted for the lowest frequency ν27 torsion mode, for 2ν27, and for the ν26 C=CC bend of anti VO, along with ν27 satellites of gauche-1. The rovibrational analyses were assisted by anharmonic vibrational calculations at B3LYP-D3/aug-cc-PVTZ, B2PLYPD3/cc-pVTZ, and DSDPBEP86/cc-pVTZ levels. Experimental peak intensities provide a population ratio Ngauche-1/Nanti of 0.36 ± 0.06, corresponding to a Gibbs free energy difference of 2.5 ± 0.4 kJ mol-1 in favor of the anti conformer, in agreement with the density functional theory results. In the gauche-1 conformer, the torsional angle between vinyl group and oxirane ring, τC=CCM, is optimized at -35° to favor an intramolecular CvinylH11...O interaction. The gauche-2 conformer with τC=CCM of + 74° suffers from CvinylH11...HCcyclopropyl repulsion so that it is calculated to be 8-9 kJ mol-1 higher than gauche-1. Reinterpretation of earlier Raman spectra suggests that the gauche-2 conformer had not been observed as reported.

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.

Accuracy of Different Electronic Basis Set Families for Anharmonic Molecular Vibrations: A Comprehensive Benchmark Study.

In this work, the accuracy and convergence of different electronic basis set families for the computation of anharmonic molecular vibrational spectroscopic calculations are benchmarked. A series of 39 different basis sets from different families following their hierarchy are assessed on VSCF and VSCF-PT2 algorithms with commonly used MP2 and DFT based B3LYP-D potentials for a set of molecular systems. Such an effort has been validated in a previous work ( J. Phys. Chem. A 2020, 124, 9203-9221) with split-valence basis sets for fundamentals and intensities. Here, fundamental transitions, vibrationally excited states, and intensities are compared with the experimental data to estimate the accuracy for a series of Jensen, Dunning, Calendar, Karlsruhe, and Sapporo basis set families. The convergence of basis sets are also compared with the large ANO basis set. Comprehensive statistical error analysis in terms of accuracy and precision was carried out to assess the performance of each basis set. It is observed that the improvement for the calculated harmonic and anharmonic values from the smaller basis sets to the medium (i.e., triple-ξ) is considerable. Beyond this, from medium to large basis sets, the convergence is slow and mostly posits nearly converged values. Basis sets with and without diffuse functions offer characteristically different accuracies and convergence patterns. Finally, recommendations are given on the choice of basis set chosen as black-box which can balance between accuracy and computational time, estimation of the errors, and their selections especially for large molecules.

The importance of electron correlations on vibrational anharmonicities and potential energy surfaces

An assessment and importance of different‐order of electron correlation effects on anharmonic vibrational potential energy surfaces (PESs) is reported. Systematic construction of quadratic, cubic and quartic force-fields using CCSD(T), MP2 and HF methods are performed for anharmonic vibrational spectroscopic calculations. The accuracies and convergences are assessed for VPT2 and VCI methods. The level of electron correlation is found important for the accuracies of harmonic force-constants while its effects on anharmonicities are less significant. Following this, suitable hybrid PESs are suggested for better accuracy/cost ratio. For the hybrid PESs, a more accurate high-level and less accurate low-level electron- correlation methods are employed to compute the harmonic and anharmonic part of the potential, respectively. The estimated deviations for hybrid PESs are found a few wavenumbers with the highly correlated methods as well as experiment. That in turn shows the validity and applicability of such hybrid PESs for large molecular systems.

Matrix-isolation and cryosolution-VCD spectra of α-pinene as benchmark for anharmonic vibrational spectra calculations.

The inclusion of anharmonicity in vibrational spectral analyis remains associated to small molecular systems with up to a dozen of atoms, with half a dozen of non-hydrogen atoms, typically thesize of propylene oxide. One may see two reasons for this: first of all, larger systems are often thought to be computationally too demanding (high computational costs) for a full anharmonic vibrational analysis. Second, the identification of resonances and their correction is often considered something only expert theoreticians could address because of the lack of unequivocal criteria. In this contribution, we illustrate that resonances can indeed become a complex problem, which can be handled almost transparently thanks to recent advances in vibrational perturbation theory (VPT2). The study also emphasizes the importance and the central role played by experiment in benchmarking novel theoretical approaches. In fact, we herein provide the currently highest resolution VCD spectra available for α- and β-pinene obtained under matrix-isolation conditions and in liquid Xenon as solvent. They are interpreted by VPT2 with novel tests for the identification of resonances. Hence, the study demonstrates the mutual stimulation of advances in both experimental techniques and computational models.

Recent advances in quantum fragmentation approaches to complex molecular and condensed‐phase systems

AbstractQuantum mechanical (QM) calculations are critical in quantitatively understanding the relationship between the structure and physicochemical properties of various chemical systems. However, the sharply increasing computational cost with the system size has severely hindered applying direct QM calculations on large‐sized systems. Hence, linear‐scaling and/or fragmentation QM methods have been proposed to overcome this difficulty. In this review, we focus on the recent development and applications of the electrostatically embedded generalized molecular fractionation with the conjugate caps (EE‐GMFCC) method in probing various properties of complex large molecules and condensed‐phase systems. The EE‐GMFCC method is now capable of describing the localized excited states of biomolecules and molecular crystals with a chromophore. The EE‐GMF method is also combined with anharmonic vibrational calculations for accurate simulation of the infrared spectrum of the magic number H+(H2O)21 cluster at the coupled cluster level. With an adaptive fragmentation scheme, the EE‐GMF‐based ab initio molecular dynamics is able to directly simulate chemical reactions occurred in atmospheric molecular clusters. Furthermore, by combining the EE‐GMF(CC) method and deep machine learning techniques, neural network potentials can be efficiently constructed for accurate simulations of complex systems with the accuracy of high‐level wave function methods. The EE‐GMF(CC) method is expected to become a practical tool for quantitative description of complex large molecules and condensed‐phase systems with high‐level ab initio theories or ab initio quality potentials.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Computational Biochemistry and Biophysics Structure and Mechanism > Reaction Mechanisms and Catalysis

Theoretical Study of the Isotope and Homologue Effects on Nuclear Magnetic Shielding in Water and Hydrogen Sulfide Molecules

Abstract The hydrogen/deuterium isotope and oxygen/sulfur homologue effects on the absolute nuclear magnetic shielding constants were theoretically analyzed for five 17O-water isotopologues and five hydrogen sulfide isotopologues. Using both ab initio calculations and anharmonic vibrational structure calculations based on vibrational quantum Monte Carlo theory, we confirmed that the changes in the atomic charges are strongly correlated with the enhancements of the absolute nuclear magnetic shielding constants.

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.

Anharmonic Vibrational Calculations Based on Group-Localized Coordinates: Applications to Internal Water Molecules in Bacteriorhodopsin.

An efficient anharmonic vibrational method is developed exploiting the locality of molecular vibration. Vibrational coordinates localized to a group of atoms are employed to divide the potential energy surface (PES) of a system into intra- and inter-group contributions. Then, the vibrational Schrödinger equation is solved based on a PES, in which the inter-group coupling is truncated at the harmonic level while accounting for the intra-group anharmonicity. The method is applied to a pentagonal hydrogen bond network (HBN) composed of internal water molecules and charged residues in a membrane protein, bacteriorhodopsin. The PES is calculated by the quantum mechanics/molecular mechanics (QM/MM) calculation at the level of B3LYP-D3/aug-cc-pVDZ. The infrared (IR) spectrum is computed using a set of coordinates localized to each water molecule and amino acid residue by second-order vibrational quasi-degenerate perturbation theory (VQDPT2). Benchmark calculations show that the proposed method yields the N-D/O-D stretching frequencies with an error of 7 cm-1 at the cost reduced by more than five times. In contrast, the harmonic approximation results in a severe error of 150 cm-1. Furthermore, the size of QM regions is carefully assessed to find that the QM regions should include not only the pentagonal HBN itself but also its HB partners. VQDPT2 calculations starting from transient structures obtained by molecular dynamics simulations have shown that the structural sampling has a significant impact on the calculated IR spectrum. The incorporation of anharmonicity, sufficiently large QM regions, and structural samplings are of essential importance to reproduce the experimental IR spectrum. The computational spectrum paves the way for decoding the IR signal of strong HBNs and helps elucidate their functional roles in biomolecules.

Second-Order Analytic Derivatives for XYG3 Type of Doubly Hybrid Density Functionals: Theory, Implementation, and Application to Harmonic and Anharmonic Vibrational Frequency Calculations.

Analytic derivative methods in quantum chemistry are powerful tools for the calculation of molecular properties and simulation of chemical systems. While the derivatives of the well-established B2PLYP type of doubly hybrid (DH) density functionals can be generated by a straightforward combination between the Kohn-Sham density functional and the second-order perturbation theory (PT2), both of these two contributions have to be considered nonvariationally for the XYG3 type of DH functionals (xDHs). A total Lagrangian that includes both parts is therefore needed for the corresponding Z-vector equations for the first-order derivatives of xDHs. Starting from the differentiation of the Z-vector equations, a theory for the second-order derivatives for xDHs is developed here and is applied to the molecular harmonic and anharmonic vibrational frequency calculations. The results are generally of high quality, as compared to the well-established experimental and CCSD(T) counterparts. Further investigations on the fundamental frequency predictions prove the capability of the xDH functionals for an accurate calculation of spectroscopic properties for a wide range of medium-size molecules.

Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates.

Spatially localized vibrational normal mode coordinates are shown to reduce the importance of calculating the full set of two-electron terms in the molecular electronic Schrödinger equation. Electron correlation and dispersion interactions become less significant in (E,E)-1,3,5,7-octatetraene vibrational self-consistent field calculations when displacing remote atoms along multiple coordinates. Electron correlation interactions between spatially remote modes are also found to be less important compared to their corresponding uncorrelated interaction terms. Attenuation of the Coulomb operator indicates that the two-electron terms between remote electrons become less important for accurately describing the strongly contributing mode-coupling terms between sets of localized vibrational modes.

Vibrationally resolved coupled-cluster x-ray absorption spectra from vibrational configuration interaction anharmonic calculations.

Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the adaptive density-guided approach scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecules.

Comprehensive Benchmark Results for the Accuracy of Basis Sets for Anharmonic Molecular Vibrations.

The accuracy and convergence of a series of commonly used split-valence electronic basis sets are systematically investigated for the anharmonic molecular vibrational spectroscopic calculations using the second-order perturbative corrected vibrational self-consistent field theory. A series of 18 split-valence basis sets with increasing flexibility is assessed in conjunction with MP2 and density functional theory (DFT)-based dispersion-corrected B3LYP potentials and applied to a set of molecular systems with different electronic and vibrational characteristics. The computed fundamental transitions and intensities are compared with the experimental values to assess the accuracy of different basis sets. Comparisons with high levels of Dunning basis sets, aug-cc-pVQZ along with def2-TZVPP and aug-pc-2 type basis sets, are also tested to check the convergence. A full statistical error analysis has been performed, assessing the success and failure of each basis set in terms of both accuracy and precision. The general statement "the bigger the basis, the better the results" is not strictly followed for bigger basis sets that are nearly converged to the adiabatic ab initio limit. It is found that the basis set hierarchy holds good for minimal basis sets up to polarized double-ζ basis sets. Beyond that, the improvements in comparison to experimental results or with very high end aug-cc-pVQZ and others are found rather slow. Finally, a prescription regarding the choice of a basis set for a suitable balance between accuracy and the computational time is given, which can be further used to investigate specific normal modes and large molecules as a blackbox.

Tailored multilevel approaches in vibrational structure theory: A route to quantum mechanical vibrational spectra for complex systems

AbstractVibrational spectroscopies have emerged as important tools to elucidate structures and processes in life sciences. The interpretation of vibrational spectra requires, in most cases, computational assistance and account for anharmonic effects. Pushing the size limitations of anharmonic vibrational structure calculations is therefore of great interest. Fortunately, interpretation of the experimental results often requires only a limited part of the vibrational spectrum. Hence, it can be expected that multilevel approaches, focusing computational effort on the relevant parts, are highly beneficial. Still, such approaches are rather sparse in the field of vibrational structure theory. In this perspective, we outline the present status on multilevel static vibrational wave functions and rectilinear vibrational coordinates. We further foresee how those ingredients can be combined to formulate a comprehensive multilevel vibrational structure framework.

Infrared-Assisted Synthesis of Prebiotic Glycine.

A novel approach has been developed to synthesize complex organic molecules (COMs) relevant to prebiotic chemistry, using infrared (IR) radiation to trigger the reaction. An original laboratory reactor working at low gas density and using IR irradiation was developed. In this way, glycine, the simplest brick of life, has been synthesized by assisting ion-molecule reaction with IR laser light. The ion-molecule complex constituted by acetic acid and hydroxylamine was formed in a mass spectrometer reactor and then irradiated with IR photons. As photoproducts, we obtained both glycine structures and some of its isomers. Anharmonic vibrational frequency calculations and fragmentation dynamics simulations allow for a better interpretation of the experimental data. This novel approach can be now extended to study other new synthetic pathways responsible for the formation of further COMs also with potential prebiotic relevance.

Theoretical Studies of Two Key Low-Lying Carbenes of C5H2Missing in the Laboratory

The equilibrium geometries and spectroscopic properties of two key singlet carbenes, buta-1,3-diynylcarbene (6) and 2-methylenebicyclo[1.1.0]but-1(3)-en-4-ylidene (9), which have not been experimentally observed to date, are investigated using high-level coupled-cluster (CC) methods. The current theoretical study necessitates new experimental data on C5H2 isomers considering the relevance of these molecules to interstellar chemistry. Bent-pentadiynylidene (4) has been missing in the laboratory and the prime focus of our earlier theoretical work. The present theoretical study indicates that isomers 6 and 9 are also viable experimental targets. Apart from ethynylcyclopropenylidene (2), pentatetraenylidene (3), ethynylpropadienylidene (5), and 3-(didehydrovinylidene)cyclopropene (8), which are identified by Fourier transform microwave spectroscopy, the dipole moments of elusive 4, 6, and 9 are also nonzero (μ ≠ 0). The relative energies of these isomers, calculated at the CCSDT(Q)/CBS level of theory, with respect to linear triplet pentadiynylidene (1) reveal that they all lie within 25.1 kcal mol-1. Therefore, geometric, energetic, aromatic, and spectroscopic parameters are reported here, which may assist the efforts of molecular spectroscopists in the future. Anharmonic vibrational calculations on isomers 6 and 9 indicate that the former is loosely bound and would be challenging to be detected experimentally. Among the undetected carbenes, 9 may be considered as a potential target molecule considering its higher polarity and aromatic nature.

Overtones of νC≡N Vibration as a Probe of Structure of Liquid CH3CN, CD3CN, and CCl3CN: Combined Infrared, Near-Infrared, and Raman Spectroscopic Studies with Anharmonic Density Functional Theory Calculations.

The νCN band (νC≡N) is a sensitive probe of the state of molecules with nitrile groups. Hence, physicochemical properties of acetonitrile and its derivatives have been frequently investigated by means of vibrational (IR and Raman) spectroscopy. Near-infrared (NIR) spectroscopy combined with high-level quantum mechanical calculations offers deeper physical insight into the structure of liquid nitriles not available from the fundamental region. This results from unique information provided by the overtones of νCN. Here, we report an application of anharmonic vibrational calculations coupled with IR, NIR, and Raman spectroscopy for investigation of the structure of CH3CN, CD3CN, and CCl3CN in the liquid phase. The computational part was based on generalized vibrational second-order perturbation theory (GVPT2) applied on the density function theory (B3LYP, M06-2X, and B2PLYP) level to monomers as well as linear and cyclic dimers. The obtained data were refined by counterpoise-corrected MP2 calculations to mimic the aggregation in the liquid state. Our results evidence that the intensity variations between the fundamental, first and second overtones of the νCN band depend on the symmetry of aggregated species. The symmetry of the cyclic dimers in liquid nitriles was elucidated from the relative intensity of the 2νCN band. This work advances our understanding of the vibrational spectra of acetonitrile and its derivatives by providing detailed band assignment of IR, NIR, and Raman spectra. For the first time, we reported the position of the first and second overtones of the nitrile group.

Infrared spectra of neutral dimethylamine clusters: An infrared-vacuum ultraviolet spectroscopic and anharmonic vibrational calculation study.

Infrared-vacuum ultraviolet (IR-VUV) spectra of neutral dimethylamine clusters, (DMA)n (n = 2-5), were measured in the spectral range of 2600-3700 cm-1. The experimental IR-VUV spectra show NH stretch modes gradually redshift to 3200-3250 cm-1 with the increase in the cluster size and complex Fermi Resonance (FR) pattern of the CH3 group in the 2800-3000 cm-1 region. Ab initio anharmonic vibrational calculations were performed on low-energy conformers of (DMA)2 and (DMA)3 to examine vibrational coupling among CH/NH and to understand the Fermi resonance pattern in the observed spectra features. We found that the redshift of NH stretching mode with the size of DMA cluster is moderate, and the overtone of NH bending modes is expected to overlap in frequency with the CH stretching fundamental modes. The FR in CH3 groups is originated from the strong coupling between CH stretching fundamental and bending overtone within a CH3 group. Well-resolved experimental spectra also enable us to compare the performance of ab initio anharmonic algorithms at different levels.

First-principles anharmonic vibrational study of the structure of calcium silicate perovskite under lower mantle conditions

Calcium silicate perovskite (CaSiO$_3$) is one of the major mineral components of the lower mantle, but has been the subject of relatively little work compared to the more abundant Mg-based materials. One of the major problems related to CaSiO$_3$ that is still the subject of research is its crystal structure under lower mantle conditions - a cubic Pm$\bar{3}$m structure is accepted in general, but some have suggested that lower-symmetry structures may be relevant. In this paper, we use a fully first-principles vibrational self-consistent field method to perform high accuracy anharmonic vibrational calculations on several candidate structures at a variety of points along the geotherm near the base of the lower mantle to investigate the stability of the cubic structure and related distorted structures. Our results show that the cubic structure is the most stable throughout the lower mantle, and that this result is robust against the effects of thermal expansion.