Second-order Vibrational Perturbation Theory Research Articles

Изотопные эффекты в спектрах комплексов с водородными связями. Расчет колебательных спектров поглощения димеров (D-=SUB=-2-=/SUB=-CO)-=SUB=-2-=/SUB=- и D-=SUB=-2-=/SUB=-CO·sDF и тримеров D-=SUB=-2-=/SUB=-CO·s(DF)-=SUB=-2-=/SUB=- и (D-=SUB=-2-=/SUB=-CO)_2·sDF

The frequencies and intensities for the vibrational bands of absorption spectra of hydrogen-bonded (D2CO)2 and D2CO∙∙∙DF dimers, two D2CO∙∙∙(DF)2 trimers and four (D2CO)2∙∙∙DF trimers are calculated in the MP2/aug-cc-pVTZ approximation with the basis set superposition error taken into account. Anharmonic values of spectral parameters were obtained using the vibrational second-order perturbation theory. The influence of hydrogen bonds on the spectral parameters was determined from comparison of the values calculated for monomers, dimers, and trimers in the same approximation. The data obtained were compared with the results of previous calculations of (H2CO)2 and H2CO∙∙∙HF dimers and H2CO∙∙∙(HF)2 and (H2CO)2∙∙∙HF trimers. It was shown that one D2CO∙∙∙(DF)2 trimer and two (D2CO)2∙∙∙DF trimers have significant binding energies and strong absorption bands, which makes them promising candidates for detection by spectroscopic methods.

Theoretical Spectroscopic Study of Two Ketones of Atmospheric Interest: Methyl Glyoxal (CH3COCHO) and Methyl Vinyl Ketone (CH3COCH═CH2).

Two ketones of atmospheric interest, methyl glyoxal and methyl vinyl ketone, are studied using explicitly correlated coupled cluster theory and core–valence correlation-consistent basis sets. The work focuses on the far-infrared region. At the employed level of theory, the rotational constants can be determined to within a few megahertz of the experimental data. Both molecules present two conformers, trans/cis and antiperiplanar (Ap)/synperiplanar (Sp), respectively. trans-Methyl glyoxal and Ap-methyl vinyl ketone are the preferred structures. cis-Methyl glyoxal is a secondary minimum of very low stability, which justifies the unavailability of experimental data in this form. In methyl vinyl ketone, the two conformers are almost isoenergetic, but the interconversion implies a relatively high torsional barrier of 1798 cm–1. A very low methyl torsional barrier was estimated for trans-methyl glyoxal (V3 = 273.6 cm–1). Barriers of 429.6 and 380.7 cm–1 were computed for Ap- and Sp-methyl vinyl ketone. Vibrational second-order perturbation theory was applied to determine the rovibrational parameters. The far-infrared region was explored using a variational procedure of reduced dimensionality. For trans-methyl glyoxal, the ground vibrational state was estimated to split by 0.067 cm–1, and the two low excited energy levels (1 0) and (0 1) were found to lie at 89.588 cm–1/88.683 cm–1 (A2/E) and 124.636 cm–1/123.785 cm–1 (A2/E). For Ap- and Sp-methyl vinyl ketone, the ground vibrational state splittings were estimated to be 0.008 and 0.017 cm–1, respectively.

Quantum chemical rovibrational analysis of aminoborane and its isotopologues.

Aminoborane, H2 NBH2 and its isotopologues, H2 N10 BH2 , D2 NBD2 , and D2 N10 BD2 , have been studied by high-level ab initio methods. All calculations rely on multidimensional potential energy surfaces and dipole moment surfaces including high-order mode coupling terms, which have been obtained from electronic structure calculations at the level of explicitly correlated coupled-cluster theory, CCSD(T)-F12, or the distinguishable cluster approximation, DCSD. Subsequent vibrational structure calculations based on second-order vibrational perturbation theory, VPT2, and vibrational configuration interaction theory, VCI, were used to determine rotational constants, centrifugal distortion constants, vibrationally averaged geometrical parameters and (an)harmonic vibrational frequencies. The impact of core-correlation effects is discussed in detail. Rovibrational VCI calculations were used to simulate the gas phase spectra of these species and an in-depth analysis of the ν7 band of aminoborane is provided. Color-coding is used to reveal the identity of the individual progressions of the rovibrational transitions for this particular mode.

Rotational and Vibrational Spectra of the Pyridyl Radicals: A Coupled-Cluster Study.

Pyridyl is a prototypical nitrogen-containing aromatic radical that may be a key intermediate in the formation of nitrogen-containing aromatic molecules under astrophysical conditions. On meteorites, a variety of complex molecules with nitrogen-containing rings have been detected with nonterrestrial isotopic abundances, and larger nitrogen-containing polycyclic aromatic hydrocarbons (PANHs) have been proposed to be responsible for certain unidentified infrared emission bands in the interstellar medium. In this work, the three isomers of pyridyl (2-, 3-, and 4-pyridyl) have been investigated with coupled cluster methods. For each species, structures were optimized at the CCSD(T)/cc-pwCVTZ level of theory and force fields were calculated at the CCSD(T)/ANO0 level of theory. Second-order vibrational perturbation theory (VPT2) was used to derive anharmonic vibrational frequencies and vibrationally corrected rotational constants, and resonances among vibrational states below 3500 cm-1 were treated variationally with the VPT2+K method. The results yield a complete set of spectroscopic parameters needed to simulate the pure rotational spectrum of each isomer, including electron-spin, spin-spin, and nuclear hyperfine interactions, and the calculated hyperfine parameters agree well with the limited available data from electron paramagnetic resonance spectroscopy. For the handful of experimentally measured vibrational frequencies determined from photoelectron spectroscopy and matrix isolation spectroscopy, the typical agreement is comparable to experimental uncertainty. The predicted parameters for rotational spectroscopy reported here can guide new experimental investigations into the yet-unobserved rotational spectra of these radicals.

Accurate Quantum Chemical Spectroscopic Characterization of Glycolic Acid: A Route Toward its Astrophysical Detection.

The first step to shed light on the abiotic synthesis of biochemical building blocks, and their further evolution toward biological systems, is the detection of the relevant species in astronomical environments, including earthlike planets. To this end, the species of interest need to be accurately characterized from structural, energetic, and spectroscopic viewpoints. This task is particularly challenging when dealing with flexible systems, whose spectroscopic signature is ruled by the interplay of small- and large-amplitude motions (SAMs and LAMs, respectively) and is further tuned by the conformational equilibrium. In such instances, quantum chemical (QC) calculations represent an invaluable tool for assisting the interpretation of laboratory measurements or even observations. In the present work, the role of QC results is illustrated with reference to glycolic acid (CH2OHCOOH), a molecule involved in photosynthesis and plant respiration and a precursor of oxalate in humans, which has been detected in the Murchison meteorite but not yet in the interstellar medium or in planetary atmospheres. In particular, the equilibrium structure of the lowest-energy conformer is derived by employing the so-called semiexperimental approach. Then, accurate yet cost-effective QC calculations relying on composite post-Hartree–Fock schemes and hybrid coupled-cluster/density functional theory approaches are used to predict the structural and ro-vibrational spectroscopic properties of the different conformers within the framework of the second-order vibrational perturbation theory. A purposely tailored discrete variable representation anharmonic approach is used to treat the LAMs related to internal rotations. The computed spectroscopic data, particularly those in the infrared region, complement the available experimental investigations, thus enhancing the possibility of an astronomical detection of this molecule.

Isotope Effects in the Spectra of Hydrogen-Bonded Complexes. Calculation of the Structure and Vibrational Absorption Spectra of the H-=SUB=-2-=/SUB=-O...HF, H-=SUB=-2-=/SUB=-O...DF, D-=SUB=-2-=/SUB=-O...HF, and D-=SUB=-2-=/SUB=-O...DF Complexes

The frequencies and intensities of IR absorption bands of the H2O...HF, H2O...DF, D2O...HF, and D2O...DF hydrogen-bonded complexes are calculated using the second-order vibrational perturbation theory. The MP2/aug-cc-pVTZ method with the basis set superposition error taken into account is used to calculate the electronic wave functions in determining the equilibrium configuration, the potential energy and dipole moment surfaces of these complexes, as well as in calculating spectral parameters. It is shown that upon complexation the frequencies and intensities of the stretching vibration of HF (DF) molecules and the intensities of stretching vibrations of H2O (D2O) molecules change most significantly. A variational calculation of librational motion of the water molecule in the two-well potential explained the reason for the higher value of the fundamental transition frequency of the ν1(H-F) mode as compared to the frequency of this mode upon hot transition from the first excited librational state. The dependence of the intermode anharmonic interaction on isotope substitution was analyzed. Keywords: hydrogen bond, calculations of spectra of molecular complexes, anharmonic interactions, isotope effects.

An integrated protocol to study hydrogen abstraction reactions by atomic hydrogen in flexible molecules: application to butanol isomers.

This work presents a protocol designed to study hydrogen abstraction reactions by atomic hydrogen in molecules with multiple conformations. The protocol starts with the search and location of the conformers of the equilibrium structures using the TorsiFlex program. By a simple modification of the starting geometry of reactants, a Python script generates the input for the hydrogen abstraction transition states. Initially, the search of the stationary points (reactants and transition states) is carried out at a low-level employing firstly a preconditioned search and secondly a random search. The low-level conformers were reoptimized using a higher level electronic structure method. This information allows the evaluation of the multistructural harmonic-oscillator partition functions, which are corrected for zero-point energy anharmonicity by the hybrid degeneracy-corrected second-order vibrational perturbation theory and for torsional anharmonicity by the multistructural torsional method, as implemented in the MsTor program. The structural information of the stationary points is used by Pilgrim to evaluate the multipath canonical variational transition state theory thermal rate constants with multidimensional small-curvature corrections for tunneling. Therefore, the thermal rate constants include variational (recrossing) and tunneling effects in addition to the effect of multiple conformations on the thermal rate constants. These features grant the applicability of the method to a wide range of temperatures. The method was applied to each of the hydrogen abstraction sites of the four isomers of butanol. The methodology employed allowed us to calculate the thermal rate constants in the temperature range of 250-2500 K and to accurately fit them to analytical expressions. The variety of abstraction sites shows that the protocol is robust and that it can be employed to study hydrogen abstraction reactions in molecules containing carbon and oxygen as heavy atoms.

Slow monomer vibrations in formic acid dimer: Stepping up the ladder with FTIR and Raman jet spectroscopy.

In an effort to extend the cold gas phase spectroscopic database of the cyclic formic acid dimer (FAD), we present and analyze the jet-cooled vibrational infrared and Raman spectrum of (HCOOH)2 in the monomer fingerprintregion between 600 and 1500 cm-1. The present study bridges the gap between the intermolecular dimerization-induced and the carbonyl stretching fundamentals that have already been reexamined using jet-cooled or high-resolution spectroscopy. This completes the characterization of the jet-cooled vibrational (HCOOH)2 spectrum below the complex OH (CH) stretching fundamentals, and we report resonance-induced FAD combination/overtone transitions that will serve as a valuable reference for a theoretical modeling of its vibrational dynamics. As a by-product, several new formic acid trimer fundamentals are identified in the jet spectra and assigned with the help of second-order vibrational perturbation theory (VPT2). The polar formic acid dimer still eludes detection in a supersonic jet, but we are able to estimate an experimental upper-bound of the polar dimer-to-trimer-to-cyclic dimer intensity ratio to about 1:10:100 under typical expansion conditions. Using VPT2 with resonance treatment (VPT2+K), we reinvestigate the notorious ν22 resonance triad. Generally, we find that VPT2, which is, of course, inadequate for modeling the resonance-rich OH stretching spectrum of FAD, is performing very satisfactorily in predicting fundamental and two-quantum state term values for the slower modes below 1500 cm-1. As these modes are the building blocks for the ultrafast energy dissipation in the OH stretching region, the present work opens the door for its quantitative understanding.

Fundamental vibrational frequencies of isolated 2-phosphaethynolate and 2-phosphaethynthiolate anions: OCP– and SCP–

Both second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) theory have been employed to compute the fundamental vibrational frequencies of the isolated 2-phosphaethynolate and 2-phosphaethynthiolate anions (OCP and SCP) near the CCSD(T) complete basis set (CBS) limit. Our best estimates of the fundamental frequency associated with the doubly degenerate bending mode of these linear triatomic ions () are 492 cm for OCP and 362 cm for SCP. Due to strong coupling, the stretching motions of SCP are best described as pseudo-symmetric () and pseudo-antisymmetric () stretches that we estimate to be 588 cm and 1367 cm, respectively. For OCP, our best predictions are 792 cm for and 1795 cm for , with the latter having predominantly CO stretching character. In the absence of experimental gas-phase vibrational spectra for these species, these computed anharmonic frequencies provide important reference values to help quantify spectroscopic perturbations induced by environmental effects such as those from solvents or counter ions.

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.

Molecular vibrational frequencies from analytic Hessian of constrained nuclear-electronic orbital density functional theory.

Nuclear quantum effects are important in a variety of chemical and biological processes. The constrained nuclear-electronic orbital density functional theory (cNEO-DFT) has been developed to include nuclear quantum effects in energy surfaces. Herein, we develop the analytic Hessian for cNEO-DFT energy with respect to the change in nuclear (expectation) positions, which can be used to characterize stationary points on energy surfaces and compute molecular vibrational frequencies. This is achieved by constructing and solving the multicomponent cNEO coupled-perturbed Kohn-Sham (cNEO-CPKS) equations, which describe the response of electronic and nuclear orbitals to the displacement of nuclear (expectation) positions. With the analytic Hessian, the vibrational frequencies of a series of small molecules are calculated and compared to those from conventional DFT Hessian calculations as well as those from the vibrational second-order perturbation theory (VPT2). It is found that even with a harmonic treatment, cNEO-DFT significantly outperforms DFT and is comparable to DFT-VPT2 in the description of vibrational frequencies in regular polyatomic molecules. Furthermore, cNEO-DFT can reasonably describe the proton transfer modes in systems with a shared proton, whereas DFT-VPT2 often faces great challenges. Our results suggest the importance of nuclear quantum effects in molecular vibrations, and cNEO-DFT is an accurate and inexpensive method to describe molecular vibrations.

Unravelling the diarsenic hydrides: Reactivity and spectroscopic properties

Diarsenic hydrides in the ground state are among the simplest molecular systems, with an arsenic-arsenic bond. This investigation aimed to characterize the structural and electronic properties of diarsenic hydrides, as well as the relative stability between their isomers. The As2Hn (n=1-4) structures are represented by hydrogen diarsenide (As2H), the equilibrium structures of diarsene isomers (As2H2), a trihydride diarsenic species (diarsenium, As2H3), and the diarsine molecule (H2AsAsH2) and its ylide isomer (H3AsAsH). The energetic profile calculated at the CCSD(T)/CBS level indicated trans-HAsAsH as the global minimum structure among the dihydrides, and diarsine as the most stable configuration among the tetrahydrides, lying 33 kcal mol−1 below H3AsAsH. The diarsenic bonds were characterized with σ (2.362−2.490 Å) and π (2.177-2.268 Å) bond characters corroborated by natural bond orbital (NBO) and bond order index analyses. The accuracy to reproduce the experimental data was also evaluated at the DFT and MP2 levels using a training set of 8 arsenic-bearing molecules. The results showed that B97D functional showed the best performance in reproducing observable frequencies with slight differences among cc-pVnZ and aug-cc-pVnZ basis sets (n=D, T). On the other hand, B2PLYP/aug-cc-pVTZ achieve the best agreement with experimental results by using vibrational second-order perturbation theory (VPT2) to rationalize the vibrational results.

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., -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.

Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities Issuing From Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

Vibrational spectroscopy represents an active frontier for the identification and characterization of molecular species in the context of astrochemistry and astrobiology. As new missions will provide more data over broader ranges and at higher resolution, especially in the infrared region, which could be complemented with new spectrometers in the future, support from laboratory experiments and theory is crucial. In particular, computational spectroscopy is playing an increasing role in deepening our understanding of the origin and nature of the observed bands in extreme conditions characterizing the interstellar medium or some planetary atmospheres, not easily reproducible on Earth. In this connection, the best compromise between reliability, feasibility and ease of interpretation is still a matter of concern due to the interplay of several factors in determining the final spectral outcome, with larger molecular systems and non-covalent complexes further exacerbating the dichotomy between accuracy and computational cost. In this context, second-order vibrational perturbation theory (VPT2) together with density functional theory (DFT) has become particularly appealing. The well-known problem of the reliability of exchange-correlation functionals, coupled with the treatment of resonances in VPT2, represents a challenge for the determination of standardized or “black-box” protocols, despite successful examples in the literature. With the aim of getting a clear picture of the achievable accuracy and reliability of DFT-based VPT2 calculations, a multi-step study will be carried out here. Beyond the definition of the functional, the impact of the basis set and the influence of the resonance treatment in VPT2 will be analyzed. For a better understanding of the computational aspects and the results, a short summary of vibrational perturbation theory and the overall treatment of resonances for both energies and intensities will be given. The first part of the benchmark will focus on small molecules, for which very accurate experimental and theoretical data are available, to investigate electronic structure calculation methods. Beyond the reliability of energies, widely used for such systems, the issue of intensities will also be investigated in detail. The best performing electronic structure methods will then be used to treat larger molecular systems, with more complex topologies and resonance patterns.

Transfer Learning to CCSD(T): Accurate Anharmonic Frequencies from Machine Learning Models.

The calculation of the anharmonic modes of small- to medium-sized molecules for assigning experimentally measured frequencies to the corresponding type of molecular motions is computationally challenging at sufficiently high levels of quantum chemical theory. Here, a practical and affordable way to calculate coupled-cluster quality anharmonic frequencies using second-order vibrational perturbation theory (VPT2) from machine-learned models is presented. The approach, referenced as "NN + VPT2", uses a high-dimensional neural network (PhysNet) to learn potential energy surfaces (PESs) at different levels of theory from which harmonic and VPT2 frequencies can be efficiently determined. The NN + VPT2 approach is applied to eight small- to medium-sized molecules (H2CO, trans-HONO, HCOOH, CH3OH, CH3CHO, CH3NO2, CH3COOH, and CH3CONH2) and frequencies are reported from NN-learned models at the MP2/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ, and CCSD(T)-F12/aug-cc-pVTZ-F12 levels of theory. For the largest molecules and at the highest levels of theory, transfer learning (TL) is used to determine the necessary full-dimensional, near-equilibrium PESs. Overall, NN + VPT2 yields anharmonic frequencies to within 20 cm-1 of experimentally determined frequencies for close to 90% of the modes for the highest quality PES available and to within 10 cm-1 for more than 60% of the modes. For the MP2 PESs only ∼60% of the NN + VPT2 frequencies were within 20 cm-1 of the experiment, with outliers up to ∼150 cm-1, compared to the experiment. It is also demonstrated that the approach allows to provide correct assignments for strongly interacting modes such as the OH bending and the OH torsional modes in formic acid monomer and the CO-stretch and OH-bend mode in acetic acid.

Vibrational spectroscopy of H2He+ and D2He+

Vibrational modes of the relatively strongly bound H2He+ molecular ion and its deuterated congener D2He+ are investigated by low-resolution multi-photon photodissociation spectroscopy, using a combination of a 4 K cryogenic ion-trap machine and the free-electron-laser FELIX. The band origins obtained are fully explained by accurate variational calculations of the rovibrational states of H2He+ and D2He+ based on the three-dimensional potential energy surface of Koner et al. (2019). Results from second-order vibrational perturbation theory, based on a linear H–H–He equilibrium structure, agree well with those of the variational calculations for energies up to about 1300 cm−1. This suggests that H2He+ and D2He+ may either be considered as linear triatomic molecules with a degenerate bending mode, or as Van der Waals complexes with a strongly hindered rotation of He around the H2+ and D2+ subunits. The variational calculations show that in states close to the dissociation limits, 1794 and 1852 cm−1 for para- and ortho-H2He+, respectively, the angular internal motion becomes delocalized. The low-resolution experiments corroborate the linear structure of the ions and identify the bright IR-active HH-stretch fundamental in H2He+ at about 1840 cm−1 and the DD-stretch fundamental in D2He+ at about 1309 cm−1, both with an uncertainty of 0.5%, in good agreement with the calculations. The experiments also confirm the H2+–He bend and stretch fundamentals calculated at 632 and 732 cm−1 and the D2+–He bend and stretch fundamentals at 473 and 641 cm−1, respectively.

How to VPT2: Accurate and Intuitive Simulations of CH Stretching Infrared Spectra Using VPT2+K with Large Effective Hamiltonian Resonance Treatments.

This article primarily discusses the utility of vibrational perturbation theory for the prediction of X-H stretching vibrations with particular focus on the specific variant, second-order vibrational perturbation theory with resonances (VPT2+K). It is written as a tutorial, reprinting most important formulas and providing numerous simple examples. It discusses the philosophy and practical considerations behind vibrational simulations with VPT2+K, including but not limited to computational method selection, cost-saving approximations, approaches to evaluating intensity, resonance identification, and effective Hamiltonian structure. Particular attention is given to resonance treatments, beginning with simple Fermi dyads and gradually progressing to arbitrarily large polyads that describe both Fermi and Darling-Dennison resonances. VPT2+K combined with large effective Hamiltonians is shown to be a reliable framework for modeling the complicated CH stretching spectra of alkenes. An error is also corrected in the published analytic formula for the VPT2 transition moment between the vibrational ground state and triply excited states.

Coupled Cluster Characterization of 1-, 2-, and 3-Pyrrolyl: Parameters for Vibrational and Rotational Spectroscopy.

Pyrrolyl (C4H4N) is a nitrogen-containing aromatic radical that is a derivative of pyrrole (C4H5N) and is an important intermediate in the combustion of biomass. It is also relevant for chemistry in Titan's atmosphere and may be present in the interstellar medium. The lowest-energy isomer, 1-pyrrolyl, has been involved in many experimental and theoretical studies of the N-H photodissociation of pyrrole, yet it has only been directly spectroscopically detected via electron paramagnetic resonance and through the photoelectron spectrum of the pyrrolide anion, yielding three vibrational frequencies. No direct measurements of 2- or 3-pyrrolyl have been made, and little information is known from theoretical calculations beyond their relative energies. Here, we present an ab initio quantum chemical characterization of the three pyrrolyl isomers at the CCSD(T) level of theory in their ground electronic states, with an emphasis on spectroscopic parameters relevant for vibrational and rotational spectroscopy. Equilibrium geometries were optimized at the CCSD(T)/cc-pwCVTZ level of theory, and the quadratic, cubic, and partial quartic force constants were evaluated at CCSD(T)/ANO0 for analysis using second-order vibrational perturbation theory to obtain harmonic and anharmonic vibrational frequencies. In addition, zero-point-corrected rotational constants, electronic spin-rotation tensors, and nuclear hyperfine tensors are calculated for rotational spectroscopy. Our computed structures and energies agree well with earlier density functional theory calculations, and spectroscopic parameters for 1-pyrrolyl are compared with the limited existing experimental data. Finally, we discuss strategies for detecting these radicals using rotational and vibrational spectroscopy on the basis of the calculated spectroscopic constants.

Theoretical and matrix isolation studies of infrared spectra of the H2CO∙∙∙HF hydrogen-bonded complex

The equilibrium geometry, the binding energy, and harmonic and anharmonic spectral parameters of H2CO and HF monomers and the H2CO∙∙∙HF complex are calculated in the MP2/6-311++G(3df,3pd) approximation with the basis set superposition error taken into account. Anharmonic calculations are carried out using the second-order vibrational perturbation theory. The changes in transition frequencies and intensities of monomeric IR bands upon formation of the 1:1 complex are analyzed. A high intensity value (53 km mol–1) is predicted for the overtone band of the out-of-plane HF libration. The variational method was used to solve anharmonic vibrational problems in 1D–4D subspaces involving the H–F stretch. The influence of anharmonicity on spectral and structural parameters was studied. The variational calculation confirmed the high intensity value for the overtone of the HF librational mode from the perturbative calculation. Matrix-isolation experiments were performed in N2 at T = 8 K to record the absorption spectra of pure H2CO and HF and H2CO/HF mixtures in the IR region. The spectral features related to the H–F, C=O, and C–H stretches and the in-plane HF librational motion were reliably identified. The predictions of our perturbative calculations for isolated compounds, especially for the band shifts upon complexation, are in satisfactory agreement with the experimental matrix-isolation findings. The only exception is the H–F stretching mode in the complex because of the high anharmonicity of HF and strong interaction of free HF molecules with a matrix environment. Of particular interest is the observation of a rather strong band at 1069 cm–1, which is close to 1072 cm–1 predicted for the overtone of HF out-of-plane librational mode.

Isotope Effects in the Spectra of Hydrogen-Bonded Complexes. Anharmonic Calculations of Isotopologues of the [F(HF)2]– Complex

The frequencies and intensities for IR absorption bands of symmetric and asymmetric hydrogen-bonded complexes [FL1FL2F]– (L1, L2 = K-meson Ka, proton H, deuteron D, and triton T) are calculated. The equilibrium configuration and the potential energy and dipole moment surfaces of [FL1FL2F]– isotopologues were calculated by the MP2/6-311++G(3df,3pd) method with the basis set superposition error taken into account. The calculations of spectral parameters with allowance for anharmonic interactions of all vibrations were carried out using the second-order vibrational perturbation theory. Variation of L1 and L2 masses over wide limits led to significant changes in the forms of normal vibrations and anharmonic interaction constants upon isotopic substitution. The trends in the changes of spectral parameters were determined both upon transition from one symmetric isotopologue to another and upon transition from symmetric to asymmetric isotopologues. The frequency of the D–F stretching band of [FHFDF]– was predicted in good agreement with experimental information, and the assignment of this band was improved.