A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies

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.

Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers

Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.

Vibrational Circular Dichroism Spectroscopy with a Classical Polarizable Force Field: Alanine in the Gas and Condensed Phases

Polarizable force fields are an essential component for the chemically accurate modeling of complex molecular systems with a significant degree of fluxionality, beyond harmonic or perturbative approximations. In this contribution we examine the performance of such an approach for the vibrational spectroscopy of the alanine amino acid, in the gas and condensed phases, from the Fourier transform of appropriate time correlation functions generated along molecular dynamics (MD) trajectories. While the infrared (IR) spectrum only requires the electric dipole moment, the vibrational circular dichroism (VCD) spectrum further requires knowledge of the magnetic dipole moment, for which we provide relevant expressions to be used with polarizable force fields. The AMOEBA force field was employed here to model alanine in the neutral and zwitterionic isolated forms, solvated by water or nitrogen, and as a crystal. Within this framework, comparison of the electric and magnetic dipole moments to those obtained with nuclear velocity perturbation theory based on density-functional theory for the same MD trajectories are found to agree well with one another. The statistical convergence of the IR and VCD spectra is examined and found to be more demanding in the latter case. Comparisons with experimental frequencies are also provided for the condensed phases.

Scaling-up VPT2: A feasible route to include anharmonic correction on large molecules

Vibrational analysis plays a crucial role in the investigation of molecular systems. Though methodologies like second-order vibrational perturbation theory (VPT2) have paved the way to more accurate simulations, the computational cost remains a difficult barrier to overcome when the molecular size increases. Building upon recent advances in the identification of resonances, we propose an approach making anharmonic simulations possible for large-size systems, typically unreachable by standard means. This relies on the fact that, often, only portions of the whole spectra are of actual interest. Therefore, the anharmonic corrections can be included selectively on subsets of normal modes directly related to the regions of interest. Starting from the VPT2 equations, we evaluate rigorously and systematically the impact of the truncated anharmonic treatment onto simulations. The limit and feasibility of the reduced-dimensionality approach are detailed, starting on a smaller model system. The methodology is then challenged on the IR absorption and vibrational circular dichroism spectra of an organometallic complex in three different spectral ranges.

Multiple-time scale integration method based on an interpolated potential energy surface for ab initio path integral molecular dynamics

A new multiple-time scale integration method is presented that propagates ab initio path integral molecular dynamics (PIMD). This method uses a large time step to generate an approximate geometrical configuration whose energy and gradient are evaluated at the level of an ab initio method, and then, a more precise integration scheme, e.g., the Bulirsch-Stoer method or velocity Verlet integration with a smaller time step, is used to integrate from the previous step using the computationally efficient interpolated potential energy surface constructed from two consecutive points. This method makes the integration of PIMD more efficient and accurate compared with the velocity Verlet integration. A Nosé-Hoover chain thermostat combined with this new multiple-time scale method has good energy conservation even with a large time step, which is usually challenging in velocity Verlet integration for PIMD due to the very small chain mass when a large number of beads are used. The new method is used to calculate infrared spectra and free energy profiles to demonstrate its accuracy and capabilities.

Performance of EOM-CCSD(T)(a)*-Based Quartic Force Fields in Computing Fundamental, Anharmonic Vibrational Frequencies of Molecular Electronically Excited States with Application to the Ã1A″ State of :CCH2 (Vinylidene)

Highly accurate anharmonic vibrational frequencies of electronically excited states are not as easily computed as their ground electronic state counterparts, but recently developed approximate triple excited state methods may be changing that. One emerging excited state method is equation of motion coupled cluster theory at the singles and doubles level with perturbative triples computed via the (a)* formalism, EOMEE-CCSD(T)(a)*. One of the most employed means for the ready computation of vibrational anharmonic frequencies for ground electronic states is second-order vibrational perturbation theory (VPT2), a theory based on quartic force fields (QFFs),fourth-order Taylor series expansions of the potential portion of the internuclear Watson Hamiltonian. The combination of these two is herein benchmarked for its performance for use as a means of computing rovibrational spectra of electronically excited states. Specifically, the EOMEE-CCSD(T)(a)* approach employing a complete basis set extrapolation along with core electron inclusion and relativity (the so-called "CcCR" approach) defining the QFF produces anharmonic fundamental vibrational frequencies within 2.83%, on the average, of reported gas-phase experimentally assigned values for the test set including the A ~ 1 A ″ states of HCF, HCCl, HSiF, HNO, and HPO. However, some states have exceptional accuracy in the fundamentals, most notably for ν2 of A ~ 1 A ″ HCCl in which the CcCR QFF value is within 1.8 cm-1 at 927.9 cm-1 (or 0.2%) of the experiment. Additionally, this approach produces rotational constants to, on the absolute average, within 0.41% of available experimental data, showcasing notable accuracy in the computation of rovibronic spectral data. Furthermore, utilizing a hybrid approach composed of harmonic CcCR force constants along with a set of simple EOMEE-CCSD(T)(a)*/aug-cc-pVQZ QFF cubic and quartic force constants is faster than using pure CcCR and better represents those modes that suffer from numerical instability in the anharmonic portion of the QFF, implying that this so-called "CcCR + QZ" QFF approach may be the best for future applications. Finally, complete, rovibrational spectral data are provided for A ~ 1 A 2 :CCH2, a molecule of potential astrochemical interest, in order to aid in its potential future experimental rovibronic characterization.

Methoxyacetone revisited

Conformational space of methoxyacetone (MA) was studied at the MP2/6-311++G(d,p) and DFT(B3LYP)/6-311++G(d,p) levels of theory. Computations predict MA to adopt four conformations, resulting from internal rotations around the O=C-C-O (Trans, Cis) and C-C-O-C (trans, gauche) dihedral angles. The Tt (Trans-trans) conformer is the most stable. The computed energies of two gauche (Tg and Cg) conformers fall in the 3-8 kJ mol-1 range above Tt and should account for 1/3 of the room-temperature gas-phase equilibrium. The energy of Ct form is 11 kJ mol-1 above Tt, and its expected population is negligible (below 1 %). In our earlier work, MA monomers were isolated in cryogenic argon matrices and characterized by infrared spectroscopy. In the experiment, only the most stable Tt conformer was detected in the sample. Signatures of the other conformers were not detected, either in freshly deposited samples, or in samples subjected to different UV irradiations. We rationalize those observations in terms of computed barriers for intramolecular torsions, indicating occurrence of conformational cooling during deposition. The experimental infrared spectrum of the Tt form is now assigned with the aid of anharmonic DFT computations. Exposure of MA to UV irradiation in the 300-260 nm range led to photolysis, according to the Norrish type II mechanism, resulting in dimer between enol acetone and formaldehyde observed as a cage-confined intermediate photoproduct. The subsequent photolysis resulted in the formation of carbon monoxide as the dominating photoproduct, formed in the Norrish type I photoreaction. Mechanistic interpretation of this photo decarbonylation reaction is presented.

Infrared Spectroscopy of Fluorenyl Cations at Cryogenic Temperatures

The notion of (anti)aromaticity is a successful concept in chemistry to explain the structure and stability of polycyclic hydrocarbons. Cyclopentadienyl and fluorenyl cations are among the most studied classical antiaromatic systems. In this work, fluorenyl cations are investigated by high-resolution gas-phase infrared spectroscopy in helium droplets. Bare fluorenyl cations are generated in the gas phase by electrospray ionization. After mass-to-charge selection, ions are captured in ultracold helium nanodroplets and probed by infrared spectroscopy using a widely tunable free-electron laser in the 600-1700 cm-1 range. The highly resolved cryogenic infrared spectra confirm, in combination with DFT computations, that all cations are present in their singlet states.

Reassignment of the Photoelectron Spectrum of Methylketene Using a Hybrid Model of Harmonic and Anharmonic Oscillators to Compute Franck-Condon Factors

We constructed a hybrid model of harmonic and anharmonic oscillators to compute Franck-Condon factors and interpret the photoelectron spectrum of methylketene. The equilibrium structures of methylketene and its cation were optimized, and then, the harmonic and anharmonic vibrational frequencies were computed using the B3LYP, PBE0, APFD, and ωB97XD approaches of the density functional theory. The photoelectron spectrum of methylketene was simulated by computing the Franck-Condon factors with both the harmonic and hybrid models. The adiabatic ionization energy of methylketene was computed by using the CCSD(T) approach extrapolating to the complete basis set limit. The simulated photoelectron spectra are consistent with those from the experiment for both the harmonic and hybrid models. However, the error in band positions is reduced by using the hybrid model. The computed adiabatic ionization energies of methylketene are in agreement with the experiment, with the smallest error being 0.017 eV. Our interpretation based on the theoretical spectrum led to the reassignment of the experimental photoelectron spectrum of methylketene.

Comparison of different density functional theory methods for the calculation of vibrational circular dichroism spectra

The determination of the absolute configuration (AC) of an organic molecule is still a challenging task for which the combination of spectroscopic with quantum-mechanical methods has become a promising approach. In this study, we investigated the accuracy of DFT methods (480 overall combinations of 15 functionals, 16 basis sets, and 2 solvation models) to calculate the VCD spectra of six chiral organic molecules in order to benchmark their capability to facilitate the determination of the AC.

Free Ethynylarsinidene and Ethynylstibinidene: Heavier Analogues of Nitrenes and Phosphinidenes

Until now, there has been very little experimental evidence for the existence of free arsinidenes and stibinidenes, apart from the hydrides, AsH and SbH. Here, we report on photogeneration of triplet ethynylarsinidene, HCCAs, and triplet ethynylstibinidene, HCCSb, from ethynylarsine and ethynylstibine, respectively, in solid argon matrices. The products were identified using infrared spectroscopy and the associated UV absorption spectra are interpreted with the aid of theoretical predictions.

Intramolecular hole-transfer in protonated anthracene

Excitation spectra of protonated and deuteronated anthracene are obtained by triple-resonance dissociation spectroscopy. Very cold cations, protonated/deuteronated exclusively at the 9-position, are generated from two-colour two-photon threshold ionisation of 9-dihydroanthracenyl radicals (C₁₄H₁₁). The excitation spectra reveal rich structure, not resolved in previous studies, that is assigned based on anharmonic and Herzberg-Teller coupling calculations. This work reveals that the excitation of protonated anthracene induces a symmetry-breaking intramolecular charge-transfer process along a Marcus-Hush coordinate, where the positively charged hole hops from the central bridging sp² carbon, onto one of the aromatic rings. Signatures of this charge-transfer event are observed in the excitation spectrum, through active Herzberg-Teller progressions.

Computational infrared and Raman spectra by hybrid QM/MM techniques: a study on molecular and catalytic material systems

Vibrational spectroscopy is one of the most well-established and important techniques for characterizing chemical systems. To aid the interpretation of experimental infrared and Raman spectra, we report on recent theoretical developments in the ChemShell computational chemistry environment for modelling vibrational signatures. The hybrid quantum mechanical and molecular mechanical approach is employed, using density functional theory for the electronic structure calculations and classical forcefields for the environment. Computational vibrational intensities at chemical active sites are reported using electrostatic and fully polarizable embedding environments to achieve more realistic vibrational signatures for materials and molecular systems, including solvated molecules, proteins, zeolites and metal oxide surfaces, providing useful insight into the effect of the chemical environment on the signatures obtained from experiment. This work has been enabled by the efficient task-farming parallelism implemented in ChemShell for high-performance computing platforms.  This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

pbqff: Push-Button Quartic Force Fields

pbqff is an open-source program for fully automating the production of quartic force fields (QFFs) and their corresponding anharmonic spectroscopic data. Rather than being a monolithic piece of code, it consists of several key modules including a generic interface to quantum chemistry codes and, notably, queuing systems; a molecular point group symmetry library; an internal-to-Cartesian coordinate conversion module; a module for the ordinary least-squares fitting of potential energy surfaces; and an improved second-order rotational and vibrational perturbation theory package for asymmetric and symmetric tops that handles type-1 and -2 Fermi resonances, Fermi resonance polyads, and Coriolis resonances. All of these pieces are written in Rust, a modern, safe, and performant programming language that has much to offer for scientific programming. This work introduces pbqff and its surrounding ecosystem, in addition to reporting new anharmonic vibrational data for c-(C)C₃H₂ and describing how the components of pbqff can be leveraged in other projects.

Infrared spectra of isoquinolinium (iso-C9H7NH+) and isoquinolinyl radicals (iso-C9H7NH and 1-, 3-, 4-, 5-, 6-, 7- and 8-iso-HC9H7N) isolated in solid para-hydrogen

Protonated polycyclic aromatic nitrogen heterocycles (H⁺PANH) are prospective candidates that may contribute to interstellar unidentified infrared (UIR) emission bands because protonation enhances the relative intensities of the bands near 6.2, 7.7 and 8.6 μm, and the presence of the N atom induces a blue shift of the ring-stretching modes so that the spectra of H⁺PANH match better with the 6.2 μm feature in class-A UIR spectra. We report the infrared (IR) spectra of protonated isoquinoline (the 2-isoquinolinium cation, iso-C₉H₇NH⁺), its neutral counterpart (the 2-isoquinolinyl radical, iso-C₉H₇NH), and another mono-hydrogenated product (the 6-isoquinolinyl radical, 6-iso-HC₉H₇N), produced on the electron-bombardment of a mixture of isoquinoline (iso-C₉H₇N) with excess para-hydrogen (p-H₂) during matrix deposition at 3.2 K. To generate additional isomers of hydrogenated isoquinoline, we irradiated iso-C₉H₇N/Cl₂/p-H₂ matrices at 365 nm to generate Cl atoms, followed by IR irradiation to generate H atoms via Cl + H₂ (v = 1) → HCl + H; the H atoms thus generated reacted with iso-C₉H₇N. In addition to iso-C₉H₇NH and 6-iso-HC₉H₇N observed in the electron-bombardment experiments, we identified six additional hydrogenated isoquinoline species, 1-, 3-, 4-, 5-, 7- and 8-iso-HC₉H₇N, via their IR spectra; hydrogenation on the N atom and all available carbon atoms except for the two sharing carbon atoms on the fused ring was observed. Spectral groupings were achieved according to their behaviors after maintenance of the matrix in darkness and on secondary photolysis at various wavelengths. The assignments were supported via comparison of the experimental results with the vibrational wavenumbers and IR intensities of possible isomers predicted using the B3LYP/6-311++G(d,p) method. The implications in the identification of the UIR band are discussed.

Dinitrogen Activation in the Gas Phase: Spectroscopic Characterization of C-N Coupling in the V3 C+ +N2 Reaction

We report on cluster-mediated C-N bond formation in the gas phase using N₂ as a nitrogen source. The V₃ C⁺ +N₂ reaction is studied by a combination of ion-trap mass spectrometry with infrared photodissociation (IRPD) spectroscopy and complemented by electronic structure calculations. The proposed reaction mechanism is spectroscopically validated by identifying the structures of the reactant and product ions. V₃ C⁺ exhibits a pyramidal structure of C₁ -symmetry. N₂ activation is initiated by adsorption in an end-on fashion at a vanadium site, followed by spontaneous cleavage of the N≡N triple bond and subsequent C-N coupling. The IRPD spectrum of the metal nitride product [NV₃ (C=N)]⁺ exhibits characteristic C=N double bond (1530 cm^-1 ) and V-N single bond (770, 541 and 522 cm^-1 ) stretching bands.

Vibrational resonance analysis of linear molecules using resummation of divergent Rayleigh-Schrödinger perturbation theory series

The large order Rayleigh-Schrödinger perturbation theory (RSPT) was applied for calculating vibrational states of linear molecules. Two molecules (CO₂ and C₂H₂) were used as test cases with using of isomorphic Watson Hamiltonian and quartic force fields. For CO₂ the Sayvetz condition can remove all degeneracies for purely vibrational states and the non-degenerate perturbation theory can be applied. However, an existence of two degenerate modes in C₂H₂ requires using the upgraded degenerate version of RSPT that was employed in this context for the first time. The dominating divergent behavior of such series requires the resummation technique that mimics the multivalued nature of the underlying solutions, and the applied quartic Padé-Hermite approximants (QPHA) provided full solution of the problem. Moreover, some mathematical properties of QPHA proved to be an efficient tool for studying resonance effects through the Katz theorem that controls the singular points of the eigenvalues on the complex plane. In the case of C₂H₂, not only all earlier observed classical resonances were confirmed and quantified, but also subtle interpolyad resonances (K_2/55,K_3/4555), proposed recently by Herman (2011) were described as well. Following the analysis, we found several novel resonances, of which we proposed one independent interpolyad resonance K_2/4444. The complete analysis of such critical points provided the full resonance picture of all studied molecules.

Dual Photochemistry of Benzimidazole

Monomers of benzimidazole trapped in an argon matrix at 15 K were characterized by vibrational spectroscopy and identified as 1H-tautomers exclusively. The photochemistry of matrix-isolated 1H-benzimidazole was induced by excitations with a frequency-tunable narrowband UV light and followed spectroscopically. Hitherto unobserved photoproducts were identified as 4H- and 6H-tautomers. Simultaneously, a family of photoproducts bearing the isocyano moiety was identified. Thereby, the photochemistry of benzimidazole was hypothesized to follow two reaction pathways: the fixed-ring and the ring-opening isomerizations. The former reaction channel results in the cleavage of the NH bond and formation of a benzimidazolyl radical and an H-atom. The latter reaction channel involves the cleavage of the five-membered ring and concomitant shift of the H-atom from the CH bond of the imidazole moiety to the neighboring NH group, leading to 2-isocyanoaniline and subsequently to the isocyanoanilinyl radical. The mechanistic analysis of the observed photochemistry suggests that detached H-atoms, in both cases, recombine with the benzimidazolyl or isocyanoanilinyl radicals, predominantly at the positions with the largest spin density (revealed using the natural bond analysis computations). The photochemistry of benzimidazole therefore occupies an intermediate position between the earlier studied prototype cases of indole and benzoxazole, which exhibit exclusively the fixed-ring and the ring-opening photochemistries, respectively.

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.

Spectroscopic and quantum mechanical study of a scavenger molecule: N,N-diethylhydroxylamine

We report a combination of quantum mechanical calculations and a range of spectroscopic measurements in the gas phase of N,N-diethylhydroxylamine, an important scavenger compound. Three conformers were observed by pulsed jet Fourier transform microwave spectroscopy in the 6.5-18.5 GHz frequency range. They are characterized by the hydroxyl hydrogen atom being in trans orientation with respect to the bisector of the CNC angle while the side alkyl chains can be both trans (global minimum, C_s symmetry, A = 7608.1078(4), B = 2020.2988(2) and C = 1760.5423(2) MHz) or one trans and the other gauche (second energy minimum, A = 5302.896(1), B = 2395.9822(4) and C = 1804.8567(3) MHz) or gauche' (third energy minimum, A = 5960.8025(6), B = 2273.6627(4) and C = 1975.8074(4) MHz). For the global minimum, the ¹³C_α,¹³C_β and ¹⁵N isotopologues were observed in natural abundance, allowing for an accurate partial structure determination. Moreover, several lines were detected by free jet absorption millimeter wave spectroscopy in the 59.6-74.4 GHz spectral range. The electron binding energies of the highest occupied molecular orbital and the next-to-highest occupied molecular orbital, determined by photoelectron spectroscopy, are 8.95 and 10.76 eV, respectively. Supporting calculations evidence that, (i) upon ionization of the HOMO, the molecular structure changes from an amine to an N-oxoammonium arrangement and (ii) the 0-0 of the HOMO-1 photoionization is 10.46 eV. The K-shell binding energies, determined by X-ray photoelectron spectroscopy, are 290.42 eV (C_β), 291.45 eV (C_α), 405.98 eV (N) and 538.75 eV (O). The Fourier transform near infrared spectrum is reported and a tentative assignment is proposed. The equilibrium wavenumber (ω̃ = 3811 cm^-1) and the anharmonicity constant (ω̃χ = -87.5 cm^-1) of the hydroxyl stretching mode were estimated using a quadratic model.

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.

Molecules of life: studying the interaction between water and phosphine in argon matrices

The interaction between water and phosphine isolated in solid argon matrices has been investigated. Infrared spectra of matrices containing water and phosphine, as well as their deuterium and ¹⁸O isotopologues, revealed that a weak hydrogen bonded complex is formed, with an O-H⋯P bonding motif. This was supported by high level ab initio calculations, which predict a binding energy of only 5.1 kJ mol^-1 (430 cm^-1).

A Computational Protocol for Vibrational Circular Dichroism Spectra of Cyclic Oligopeptides

Cyclic peptides are a promising class of compounds for next-generation antibiotics as they may provide new ways of limiting antibiotic resistance development. Although their cyclic structure will introduce some rigidity, their conformational space is large and they usually have multiple chiral centers that give rise to a wide range of possible stereoisomers. Chiroptical spectroscopies such as vibrational circular dichroism (VCD) are used to assign stereochemistry and discriminate enantiomers of chiral molecules, often in combination with electronic structure methods. The reliable determination of the absolute configuration of cyclic peptides will require robust computational methods than can identify all significant conformers and their relative population and reliably assign their stereochemistry from their chiroptical spectra by comparison with ab initio calculated spectra. We here present a computational protocol for the accurate calculation of the VCD spectra of a series of flexible cyclic oligopeptides. The protocol builds on the Conformer-Rotamer Ensemble Sampling Tool (CREST) developed by Grimme and co-workers ( Phys. Chem. Chem. Phys. 2020, 22, 7169-7192 and J. Chem. Theory. Comput. 2019, 15, 2847-2862) in combination with postoptimizations using B3LYP and moderately sized basis sets. Our recommended computational protocol for the computation of VCD spectra of cyclic oligopeptides consists of three steps: (1) conformational sampling with CREST and tight-binding density functional theory (xTB); (2) energy ranking based on single-point energy calculations as well as geometry optimization and VCD calculations of conformers that are within 2.5 kcal/mol of the most stable conformer using B3LYP/6-31+G*/CPCM; and (3) VCD spectra generation based on Boltzmann weighting with Gibbs free energies. Our protocol provides a feasible basis for generating VCD spectra also for larger cyclic peptides of biological/pharmaceutical interest and can thus be used to investigate promising compounds for next-generation antibiotics.

Matrix Isolation Study of Fumaric and Maleic Acids in Solid Nitrogen

Fumaric and maleic acids ((E)- and (Z)-HOOC-CH═CH-COOH, FA and MA) were studied experimentally by infrared spectroscopy in nitrogen matrixes and theoretically by quantum chemical calculations. The calculations, carried out at the DFT(B3LYP) and MP2 levels of theory, predicted the existence of at least 5 conformers of maleic acid and 10 conformers of fumaric acid. After the deposition of the matrixes, two conformers of maleic acid (I and II) and three conformers (I-III) of fumaric acid were observed and characterized vibrationally. Selective narrowband near-infrared (NIR) excitation of the first OH stretching overtones of the different conformers of maleic and fumaric acids initially present in the matrixes allowed the generation of higher-energy forms, never before observed experimentally. In the case of maleic acid, conformers I (a cis-trans form, where cis and trans designate the conformation of the carboxylic groups of the molecule) and II (cis-cis) were found to generate the novel conformers VI (trans-trans) and VII (cis-trans), respectively. The conversion of conformer II into the most stable conformer I was also observed. For fumaric acid, the cis-cis conformers I-III were found to give rise to the new cis-trans conformers IV-VII, respectively. The tunneling decay of the new conformers produced upon NIR excitation of the lowest-energy conformers initially trapped in the matrixes was observed, and their lifetimes in solid N₂ were determined. The increased stability of all of the observed high-energy conformers of the studied acids in the N₂ matrix, compared to the argon matrix, where they could not be observed experimentally, demonstrates the stabilizing effect of the interaction between the OH groups of the acids with the matrix N₂ molecules, in line with previous observations for other carboxylic acids. In addition, the photochemistry of matrix-isolated maleic and fumaric acids upon broad-band UV irradiation (λ > 235 nm) was also investigated. UV-induced isomerization of both acids around the C═C double bond was observed, together with their decarboxylation to acrylic acid.

Studying the Key Intermediate of RNA Autohydrolysis by Cryogenic Gas-Phase Infrared Spectroscopy

Over the course of the COVID-19 pandemic, mRNA-based vaccines have gained tremendous importance. The development and analysis of modified RNA molecules benefit from advanced mass spectrometry and require sufficient understanding of fragmentation processes. Analogous to the degradation of RNA in solution by autohydrolysis, backbone cleavage of RNA strands was equally observed in the gas phase; however, the fragmentation mechanism remained elusive. In this work, autohydrolysis-like intermediates were generated from isolated RNA dinucleotides in the gas phase and investigated using cryogenic infrared spectroscopy in helium nanodroplets. Data from both experiment and density functional theory provide evidence for the formation of a five-membered cyclic phosphate intermediate and rule out linear or six-membered structures. Furthermore, the experiments show that another prominent condensed-phase reaction of RNA nucleotides can be induced in the gas phase: the tautomerization of cytosine. Both observed reactions are therefore highly universal and intrinsic properties of the investigated molecules.

F12-TZ-cCR: A Methodology for Faster and Still Highly Accurate Quartic Force Fields

The F12-TZ-cCR quartic force field (QFF) methodology, defined here as CCSD(T)-F12b/cc-pCVTZ-F12 with further corrections for relativity, is introduced as a cheaper and even more accurate alternative to more costly composite QFF methods like those containing complete basis set extrapolations within canonical coupled cluster theory. F12-TZ-cCR QFFs produce B₀ and C₀ vibrationally averaged principal rotational constants within 7.5 MHz of gas-phase experimental values for tetraatomic and larger molecules, offering higher accuracy in these constants than the previous composite methods. In addition, F12-TZ-cCR offers an order of magnitude decrease in the computational cost of highly accurate QFF methodologies accompanying this increase in accuracy. An additional order of magnitude in cost reduction is achieved in the F12-DZ-cCR method, while also matching the accuracy of the traditional composite method's B₀ and C₀ constants. Finally, F12-DZ and F12-TZ are benchmarked on the same test set, revealing that both methods can provide anharmonic vibrational frequencies that are comparable in accuracy to all three of the more expensive methodologies, although their rotational constants lag behind. Hence, the present work demonstrates that highly accurate theoretical rovibrational spectral data can be obtained for a fraction of the cost of conventional QFF methodologies, extending the applicability of QFFs to larger molecules.

Infrared spectra of carbocations and CH4+ in helium

Infrared (IR) spectra of several hydrocarbon cations are reported, namely CH₃⁺, CH₄⁺, CH₅⁺, CH₅⁺(CH₄) and C₂H₅⁺. The spectra were generated from weakly-bound helium-cation complexes formed by electron ionization of helium nanodroplets doped with a neutral hydrocarbon precursor. Spectroscopic transitions were registered by photoexcitation of the complexes coupled with mass spectrometric detection of the bare ions. For CH₃⁺, we provide evidence showing that the helium-bound complexes contain 10-20 helium atoms (on average) and have a rotational temperature of ∼5 K. We show that this technique is well-suited to the study of highly symmetric or fluxional ionic species, as these intrinsic properties are preserved in the helium environment. This is in contrast to conventional tagging methods that use a single atom or molecule, which can change the point group or rigidity of the core ion and therefore the spectral profile. We demonstrate this for the highly fluxional molecular ion CH₅⁺, whose spectrum in the current study matches that of the gas phase ion, whereas the fluxionality is lost when a methane tag is added. Finally, we present the first IR spectrum of methane cation, CH₄⁺. The spectrum of this fundamental organic ion shows CH stretching bands consistent with a non-tetrahedral structure, a consequence of Jahn-Teller distortion.

Structural and Energetic Properties of Amino Acids and Peptides Benchmarked by Accurate Theoretical and Experimental Data

Structural, energetic, and spectroscopic data derived in this work aim at the setup of an "experimentally validated" database for amino acids and polypeptides conformers. First, the "cheap" composite scheme (ChS, CCSD(T)/(CBS+CV)^MP2) is tested for evaluation of conformational energies of all eight stable conformers of glycine, by comparing to the more accurate CCSD(T)/CBS+CV computations (Phys. Chem. Chem. Phys. 2013, 15, 10094-10111 and J Mol. Model. 2020, 26, 129). The recently proposed jun-ChS (J. Chem. Theory and Comput. 2020, 16, 988-1006), employing the jun-cc-pVnZ basis set family for CCSD(T) computations and CBS extrapolation, yields conformational energies accurate to 0.2 kJ·mol^-1, at reduced computational cost with respect to aug-ChS employing aug-cc-pVnZ basis sets. The jun-ChS composite scheme is further applied to derive conformational energies for three dipeptide analogues Ac-Gly-NH₂, Ac-Ala-NH₂, and Gly-Gly. Finally, dipeptide conformational energies and semiexperimental equilibrium rotational constants along with the CCSD(T)/(CBS+CV)^MP2 structural parameters (J. Phys. Chem. Lett. 2014, 5, 534-540) stand as the reference for benchmarking of selected density functional methodologies. The double-hybrid functionals B2-PLYP-D3(BJ) and DSD-PBEP86, perform best for structural and energetic characterization of all dipeptide analogues. From hybrid functionals CAM-B3LYP-D3(BJ) and ωB97X-D3(BJ) represent promising methods applicable for larger peptide-based systems for which computations with double-hybrid functionals are not feasible.

Modeling the infrared cascade spectra of small PAHs: the 11.2 μm band

The profile of the 11.2 μm feature of the infrared (IR) cascade emission spectra of polycyclic aromatic hydrocarbon (PAH) molecules is investigated using a vibrational anharmonic method. Several factors are found to affect the profile including: the energy of the initially absorbed ultraviolet (UV) photon, the density of vibrational states, the anharmonic nature of the vibrational modes, the relative intensities of the vibrational modes, the rotational temperature of the molecule, and blending with nearby features. Each of these factors is explored independently and influence either the red or blue wing of the 11.2 μm feature. The majority impact solely the red wing, with the only factor altering the blue wing being the rotational temperature.

Structural and Vibrational Properties of Amino Acids from Composite Schemes and Double-Hybrid DFT: Hydrogen Bonding in Serine as a Test Case

The structures, relative stabilities, and vibrational wavenumbers of the two most stable conformers of serine, stabilized by the O-H···N, O-H···O═C and N-H···O-H intramolecular hydrogen bonds, have been evaluated by means of state-of-the-art composite schemes based on coupled-cluster (CC) theory. The so-called "cheap" composite approach (CCSD(T)/(CBS+CV)^MP2) allowed determination of accurate equilibrium structures and harmonic vibrational wavenumbers, also pointing out significant corrections beyond the CCSD(T)/cc-pVTZ level. These accurate results stand as a reference for benchmarking selected hybrid and double-hybrid, dispersion-corrected DFT functionals. B2PLYP-D3 and DSDPBEP86 in conjunction with a triple-ζ basis set have been confirmed as effective methodologies for structural and spectroscopic studies of medium-sized flexible biomolecules, also showing intramolecular hydrogen bonding. These best performing double-hybrid functionals have been employed to simulate IR spectra by means of vibrational perturbation theory, also considering hybrid CC/DFT schemes. The best overall agreement with experiment, with mean absolute error of 8 cm^-1, has been obtained by combining CCSD(T)/(CBS+CV)^MP2 harmonic wavenumbers with B2PLYP-D3/maug-cc-pVTZ anharmonic corrections. Finally, a composite scheme entirely based on CCSD(T) calculations (CCSD(T)/CBS+CV) has been employed for energetics, further confirming that serine II is the most stable conformer, also when zero-point vibrational energy corrections are included.

Impact of fluorination and chlorination on the electronic structure, topology and in-plane ring normal modes of pyridines

Seven partially and fully fluorinated/chlorinated pyridines were investigated by means of FT-IR and Raman spectroscopy combined with quantum chemical calculations, mainly aiming to detect how the nature and position of F and Cl substituents affect the in-plane ring normal modes (RNMs) of pyridines in terms of vibrational wavenumbers, force constants, IR intensities and Raman activities. Taking pyridine as the reference, the RNMs and some derived RNMs through coupling with related C-X (X = F, Cl) stretching vibrations were identified on the basis of their composition in terms of internal coordinates. The impact of fluorination and chlorination on these RNMs was also discussed from the perspective of frontier molecular orbitals (MOs), maps of the molecular electrostatic potential (MEP) and the molecular topology. Natural bond orbital (NBO) analysis revealed the consequences of substitutions on the intramolecular charge delocalisation and consequently the ring bond strength. Moreover, the effects of anharmonicity of the potential on vibrational frequencies were presented and discussed.

Characterizing hydrogen and tetrel bonds in clusters of CO2 with carboxylic acids

The interaction between carbon dioxide and planar carboxylic acids has been investigated through the analysis of the microwave spectrum of the acrylic acid·CO2 complex and quantum chemical modeling of the R-COOH·(CO2)1,16 clusters, where R = H, CH2CH. As regards the 1 : 1 compounds, two species, involving the s-cis and s-trans conformers of acrylic acid were observed. For both of them, a similar bidentate interaction arises between the carbonyl group of CO2 and the carboxylic group of the organic acid, leading to the formation of a planar six-membered ring. The binding energy is estimated to be De ≃ 21 kJ mol-1, 1/3 being the energy contributions of the tetrel to hydrogen bonds, respectively. In the 1 : 16 clusters, the ring arrangement is broken, allowing for the interaction of the acid with several CO2 molecules. The CO2 molecules completely surround formic acid, whereas, in the case of acrylic acid, they tend to avoid the allyl chain.

Rotational and Vibrational Signatures of Astrophyscially relevant Gas-Phase Stereo-isomeric Species of Proteinogenic Amino acid Leucine

The search for life-supporting molecules in outer space is an ever-growing endeavour. Towards this, the computational chemistry supporting the astronomical spectroscopic observations is becoming a valuable tool to unravel the complex chemical network in interstellar medium (ISM). In the present work, quantum-mechanical computations, accounting for anharmonic effects, are performed to obtain the rotational and vibrational line-data for the gas-phase conformers of proteinogenic amino acid Leucine and its isomeric species predicted to be involved in its stereoinversion under the extreme environment of ISM. These species exhibit diverse chemistry including branched skeleton and zwitterionic ammonium ylides. A few of the species have significantly high dipole moment, which can act as tracer for the conformers of Leucine having low dipole moment. Besides this, the species, which are terrestrially less stable, can be of significant importance to the astronomers. Notably, the spectral database generated in this work can assist in the detection of proteinogenic Leucine and its isomeric species in different regions of ISM.

Evidence of IR-Induced Chemistry in a Neat Solid: Tautomerization of Thiotropolone by Thermal, Electronic, and Vibrational Excitations

Thiotropolone isolated in argon and xenon matrices (as monomers) or in a neat solid (as the crystalline or amorphous state) at low temperature was found to exist only in the thione-enol form. Visible light irradiation (λ ≥ 400 nm) leads to thione-enol → thiol-keto tautomerization in matrices and under neat solid conditions at 15 K. The assignment of the IR spectra of the two thiotropolone tautomers (thione-enol and thiol-keto) was carried out with the support of B3LYP/6-311+G(2d,p) computations. The thiol-keto form generated in situ in a neat solid was found to tautomerize back to the thione-enol upon annealing up to 100 K. Gaussian-4 (G4) computations estimate that such a tautomerization process has an energy barrier of ∼25 kJ mol^-1, which is consistent with the observations. Moreover, it was found that narrowband IR irradiation of the thiol-keto form in a neat solid, at the frequency of its CH stretching overtones/combination modes, also induces tautomerization to the thione-enol form. Such a result constitutes an important demonstration of vibrationally induced chemistry under neat solid conditions.

Structure and IR Spectra of 3(5)-Aminopyrazoles and UV-Induced Tautomerization in Argon Matrix

The prototropic tautomerism in 3(5)-aminopyrazoles was investigated by matrix isolation infrared (IR) spectroscopy, supported by DFT(B3LYP)/6-311++G(d,p) calculations. In consonance with the experimental data, the calculations predict tautomer 3-aminopyrazole (3AP) to be more stable than the 5-aminopyrazole (5AP) tautomer (calculated energy difference: 10.7 kJ mol^-1; Gibbs free energy difference: 9.8 kJ mol^-1). The obtained matrix isolation IR spectra (in both argon and xenon matrices) were interpreted, and the observed bands were assigned to the tautomeric forms with help of vibrational calculations carried out at both harmonic and anharmonic levels. The matrix-isolated compound (in argon matrix) was then subjected to in situ broadband UV irradiation (λ > 235 nm), and the UV-induced transformations were followed by IR spectroscopy. Phototautomerization of the 3AP tautomer into the 5AP form was observed as the strongly prevalent reaction.

General Perturb-Then-Diagonalize Model for the Vibrational Frequencies and Intensities of Molecules Belonging to Abelian and Non-Abelian Symmetry Groups

In this paper, we show that the standard second-order vibrational perturbation theory (VPT2) for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or threefold degenerate vibrations but rather handling in the proper way all the degeneracy issues and deriving the peculiar spectroscopic signatures of non-Abelian groups (e.g., l -doubling) by a posteriori transformations of the eigenfunctions. Comparison with the results of previous conventional implementations shows a perfect agreement for the vibrational energies of linear and symmetric tops, thus paving the route to the transparent extension of the equations already available for asymmetric tops to the energies of spherical tops and the infrared and Raman intensities of molecules belonging to non-Abelian symmetry groups. The whole procedure has been implemented in our general engine for vibro-rotational computations beyond the rigid rotor/harmonic oscillator model and has been validated on a number of test cases.

MULTIMODE Calculations of Vibrational Spectroscopy and 1d Interconformer Tunneling Dynamics in Glycine Using a Full-Dimensional Potential Energy Surface

A full-dimensional, permutationally invariant polynomial potential energy surface for glycine recently reported (R. Conte et al., J. Chem. Phys. 2020, 153, 244301) is used with the code MULTIMODE to determine the IR absorption spectra for Conformers I and II using a new separable dipole moment function. The calculated spectra agree well with the experimental ones. The full-dimensional nature of the potential allows us also to examine dynamical results, such as tunneling rates. Remarkably, using a one-dimensional path based on the potential energy surface to estimate the tunneling rate from Conformer VI to Conformer I, good agreement is found with the recent experimental measurement. Finally a brief comparison of our potential energy surface with a recently reported sGDML one is made.

Harmonic Infrared and Raman Spectra in Molecular Environments Using the Polarizable Embedding Model

We present a fully analytic approach to calculate infrared (IR) and Raman spectra of molecules embedded in complex molecular environments modeled using the fragment-based polarizable embedding (PE) model. We provide the theory for the calculation of analytic second-order geometric derivatives of molecular energies and first-order geometric derivatives of electric dipole moments and dipole-dipole polarizabilities within the PE model. The derivatives are implemented using a general open-ended response theory framework, thus allowing for an extension to higher-order derivatives. The embedding-potential parameters used to describe the environment in the PE model are derived through first-principles calculations, thus allowing a wide variety of systems to be modeled, including solvents, proteins, and other large and complex molecular environments. Here, we present proof-of-principle calculations of IR and Raman spectra of acetone in different solvents. This work is an important step toward calculating accurate vibrational spectra of molecules embedded in realistic environments.

Performance of the DLPNO-CCSD and recent DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals

In the present study, the performance of a set of density functionals: BP86, PBE, OLYP, BEEF, PBEpow, TPSS, SCAN, PBEGXPBE, M06L, MN15L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, mPW1PW, B98, TPSS0, PBE1KCIS, SCAN0, M06, M06-2X, MN15, CAM-B3LYP, ωB97x, B2PLYP, and the B3LYP/N07D and PBE/N07D schemes in the calculation of the ¹⁴N anisotropic hyperfine coupling (HFC) constants of a set of 23 nitroxide radicals is evaluated. The results are compared with those obtained with the DLPNO-CCSD method and experimental HFC values. Harmonic contribution to the ¹⁴N HFC vibrational correction was calculated at the revPBE0/def2-TZVPP level and included in the evaluation. With the vibrational correction, the DLPNO-CCSD method yielded HFC values in good agreement with the experiment (mean absolute deviation (MAD) = 0.3 G for the dipole-dipole contribution and MAD = 0.8 G for the contact coupling contribution). The best DFT results are obtained using the M06 functional with MAD = 0.2 G for the dipole-dipole contribution and MAD = 0.7 G for the contact coupling contribution. In general, vibrational correction significantly improved most DFT functionals' performance but did not change its overall ranking.