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

Vibrational second-order perturbation theory based on curvilinear coordinates: Thermochemical applications

This work improves and extends a general and robust workflow for the computation of anharmonic vibrational frequencies to thermodynamic functions, paving the way toward the study of large flexible molecules. The key new feature is the extension of closed-form expressions for both zero-point vibrational energies and partition functions to second-order vibrational perturbation theory based on curvilinear internal coordinates. The use of curvilinear coordinates enables the reduction of couplings between different degrees of freedom, enriching the arsenal of existing vibrational approaches, and can lead to effective, low-dimensional linear-scaling models. The accuracy of the results obtained for some prototypical systems paves the way toward the systematic use of this new implementation in the study of molecules containing a few dozen atoms, as exemplified by the test cases of a molecular motor, a nucleoside, and two hormones.

Accurate Structures and Spectroscopic Parameters of CN-Substituted Polycyclic Hydrocarbons at DFT Cost

The structures, isomerization energies, and rotational and vibrational spectra of prototypical CN-substituted polycyclic hydrocarbons in the gas phase have been analyzed using a general computational strategy based on Pisa composite schemes (PCS) and second-order vibrational perturbation theory (VPT2). The final results obtained in this way show, in most cases, relative average deviations with respect to experimental rotational constants close to 0.1%, corresponding to errors of around 1 mÅ and 0.1° for bond lengths and valence angles, respectively. At the same time, fundamental IR absorption bands are reproduced with average deviations below 10 cm-1 without any scaling factor. In addition to the intrinsic interest of the studied molecules, this work confirms that spectroscopic studies of large systems can be supported by unsupervised computational tools that couple accuracy with reasonable cost.

Structures and Rotational Constants of Monocyclic Monoterpenes at DFT Cost by Pisa Composite Schemes and Vibrational Perturbation Theory

The structures and rotational constants of prototypical monocyclic terpenes and terpenoids have been analyzed by a general computational strategy based on recent Pisa composite schemes (PCS) and vibrational perturbation theory at second order (VPT2). Concerning equilibrium geometries, a one-parameter empirical correction is added to bond lengths obtained by the revDSD-PBEP86 double hybrid functional in conjunction with a slightly modified cc-pVTZ-F12 basis set. The same functional and basis set give accurate harmonic frequencies, whereas the cheaper B3LYP hybrid functional in conjunction with a double-ζ basis set is employed to compute the semidiagonal cubic force constants needed to obtain vibrational corrections to the rotational constants in the framework of the VPT2 model. The final results obtained in this way show in most cases average deviations with respect to the experiment close to 0.1%, which correspond to errors around 1 mÅ and 0.1° for bond lengths and valence angles, respectively. The accuracy of the results has produced reliable estimates for species not analyzed yet experimentally. In addition to the intrinsic interest of the studied molecules, this article confirms that high-resolution spectroscopic studies of quite large systems can now be aided by a very accurate yet robust and user-friendly computational tool.

Accurate Structure and Spectroscopic Properties of Azulene and Its Derivatives by Means of Pisa Composite Schemes and Vibrational Perturbation Theory to Second Order

The structural and spectroscopic properties in the gas phase of azulene and some of its N-bearing derivatives have been analyzed by a general computational strategy based on the recent Pisa composite schemes (PCSs). First of all, an accurate semiexperimental equilibrium structure has been derived for azulene and employed to validate the geometrical parameters delivered by different quantum chemical methods. Next, different isomerization energies (azulene to naphthalene, 1-aza-azulene to quinoline and to other isomers) have been computed by an explicitly correlated PCS version employing frozen natural orbitals. Accurate geometries have been obtained by a cheaper PCS variant based on a double-hybrid functional improved by one-parameter bond corrections, with the same functional providing also remarkable harmonic frequencies. The corresponding equilibrium rotational constants show average deviations within 0.1% from experimental results when taking into account anharmonic vibrational corrections obtained by a global hybrid functional. Therefore, reliable computational estimates have been produced for the rotational constants of several nitrogen derivatives (isomeric aza-azulenes and guaiazulene), whose non-negligible dipole moments could allow experimental microwave characterizations. An analogous approach delivers infrared spectra in remarkable agreement with their experimental counterparts for naphthalene, quinoline, and azulene, together with reliable predictions for the still-unknown spectrum of 1-aza-azulene. In addition to their intrinsic interest, the results of this paper further confirm that a very accurate yet robust and user-friendly tool is now available for aiding high-resolution spectroscopic studies of quite large systems of current technological and/or biological interest.

Structural and Electronic Evolution of Ethanolamine upon Microhydration: Insights from Hyperfine Resolved Rotational Spectroscopy

Ethanolamine hydrates containing from one to seven water molecules were identified via rotational spectroscopy with the aid of accurate quantum chemical methods considering anharmonic vibrational corrections. Ethanolamine undergoes significant conformational changes upon hydration to form energetically favorable hydrogen bond networks. The final structures strongly resemble the pure (H2O)3-9 complexes reported before when replacing two water molecules by ethanolamine. The 14N nuclear quadrupole coupling constants of all the ethanolamine hydrates have been determined and show a remarkable correlation with the strength of hydrogen bonds involving the amino group. After addition of the seventh water molecule, both hydrogen atoms of the amino group actively contribute to hydrogen bond formation, reinforcing the network and introducing approximately 21-27 % ionicity towards the formation of protonated amine. These findings highlight the critical role of microhydration in altering the electronic environment of ethanolamine, enhancing our understanding of amine hydration dynamics.

Toward the identification of cyano-astroCOMs via vibrational features: benzonitrile as a test case

The James Webb Space Telescope (JWST) opened a new era for the identification of molecular systems in the interstellar medium (ISM) by vibrational features. One group of molecules of increasing interest is cyano-derivatives of aromatic organic molecules, which have already been identified in the ISM on the basis of the analysis of rotational signatures, and so, are plausible candidates for the detection by the JWST. Benzonitrile considered in this work represents a suitable example for the validation of a computational strategy, which can be further applied for different, larger, and not-yet observed molecules. For this purpose, anharmonic simulations of infrared (IR) spectra have been compared with recent FTIR experimental studies. The anharmonic computations using the generalized second-order vibrational perturbation theory (GVPT2) in conjunction with a hybrid force field combining the harmonic part of revDSD-PBEP86-D3/jun-cc-pVTZ with anharmonic corrections from B3LYP-D3/SNSD show very good agreement with those in the experiment, with a mean error of 11 c m - 1 for all fundamental transitions overall and only 2 c m - 1 for the C ≡ N stretching fundamental at 4.49 μ m . The inclusion of overtones up to three-quanta transitions also allowed the prediction of spectra in the near-infrared region, which shows distinct features due to C ≡ N overtones at the 2.26 μ m and 1.52 μ m . The remarkable accuracy of the GVPT2 results opens a pathway for the reliable prediction of spectra for a broader range of cyano-astroCOMs.

Accurate Vibrational and Ro-Vibrational Contributions to the Properties of Large Molecules by a New Engine Employing Curvilinear Internal Coordinates and Vibrational Perturbation Theory to Second Order

The unbiased comparison between theory and experiment requires approaches more sophisticated than the basic harmonic-oscillator rigid-rotor model, for taking into account vibrational averaging effects and ro-vibrational couplings in molecules of increasing size. Second-order vibrational perturbation theory based on curvilinear internal coordinates (ICs) offers a remarkable compromise between accuracy and computational cost, thanks to the reduction of mode-mode couplings with respect to their counterparts based on Cartesian coordinates. Therefore, we have developed, implemented, and validated a general engine employing ICs, which allows the accurate evaluation of vibrational averages and ro-vibrational couplings for molecules containing up to about 50 atoms beyond the harmonic approximation. After validation of the new tool for relatively small molecules, the effectiveness of ICs has been demonstrated for some flexible and/or quite large molecular bricks of life.

Accurate structures and rotational constants of bicyclic monoterpenes at DFT cost by means of the bond-corrected Pisa composite scheme (BPCS)

The structural, conformational, and spectroscopic properties in the gas phase of 20 bicyclic monoterpenes and monoterpenoids have been analyzed by a new accurate, reduced-cost computational strategy. In detail, the revDSD-PBEP86 double-hybrid functional in conjunction with the D3BJ empirical dispersion corrections and a suitable triple-zeta basis set provides accurate geometrical parameters, whence equilibrium rotational constants, which are further improved by proper account of core-valence correlation. Average deviations within 0.1% between computed and experimental rotational constants are reached when taking into account the vibrational corrections obtained by the B3LYP functional in conjunction with a double-zeta basis set in the framework of second-order vibrational perturbation theory. In addition to their intrinsic interest, the studied terpenes further extend the panel of systems for which the proposed strategy has provided accurate results at density functional theory cost. Therefore, a very accurate yet robust and user-friendly tool is now available for systematic investigations of the role of stereo-electronic effects on the properties of large systems of current technological and/or biological interest by experimentally oriented researchers.

Toward Accurate Quantum Chemical Methods for Molecules of Increasing Dimension: The New Family of Pisa Composite Schemes

The new versions of the Pisa composite scheme introduced in the present paper are based on the careful selection of different quantum chemical models for energies, geometries, and vibrational frequencies, with the aim of maximizing the accuracy of the overall description while retaining a reasonable cost for all the steps. In particular, the computation of accurate electronic energies has been further improved introducing more reliable complete basis set extrapolations and estimation of core-valence correlation, together with improved basis sets for third-row atoms. Furthermore, the reduced-cost frozen natural orbital (FNO) model has been introduced and validated for large molecules. Accurate molecular structures can be obtained avoiding complete basis set extrapolation and evaluating core-valence correlation at the MP2 level. Unfortunately, analytical gradients are not available for the FNO version of the model. Therefore, for large molecules, an accurate reduced-cost alternative is offered by evaluation of valence contributions with a double-hybrid functional in conjunction with the same MP2 contribution for core-valence correlation or by means of a one-parameter approximation. The same double-hybrid functional and basis set are employed to evaluate zero-point energies and partition functions. After the validation of the new models for small systems, a panel of molecular bricks of life has been used to analyze their performances for problems of current fundamental or technological interest. The fully black-box implementation of the computational workflow paves the way toward the accurate yet not prohibitively expensive study of medium- to large-sized molecules also by experimentally oriented researchers.

Infrared spectroscopy of the syn-methyl-substituted Criegee intermediate: A combined experimental and theoretical study

An IR-vacuum ultraviolet (VUV) ion-dip spectroscopy method is utilized to examine the IR spectrum of acetaldehyde oxide (CH3CHOO) in the overtone CH stretch (2νCH) spectral region. IR activation creates a depletion of the ground state population that reduces the VUV photoionization signal on the parent mass channel. IR activation of the more stable and populated syn-CH3CHOO conformer results in rapid unimolecular decay to OH + vinoxy products and makes the most significant contribution to the observed spectrum. The resultant IR-VUV ion-dip spectrum of CH3CHOO is similar to that obtained previously for syn-CH3CHOO using IR action spectroscopy with UV laser-induced fluorescence detection of OH products. The prominent IR features at 5984 and 6081 cm-1 are also observed using UV + VUV photoionization of OH products. Complementary theoretical calculations utilizing a general implementation of second-order vibrational perturbation theory provide new insights on the vibrational transitions that give rise to the experimental spectrum in the overtone CH stretch region. The introduction of physically motivated small shifts of the harmonic frequencies yields remarkably improved agreement between experiment and theory in the overtone CH stretch region. The prominent features are assigned as highly mixed states with contributions from two quanta of CH stretch and/or a combination of CH stretch with an overtone in mode 4. The generality of this approach is demonstrated by applying it to three different levels of electronic structure theory/basis sets, all of which provide spectra that are virtually indistinguishable despite showing large deviations prior to introducing the shifts to the harmonic frequencies.

Unbiased Comparison between Theoretical and Experimental Molecular Structures and Properties: Toward an Accurate Reduced-Cost Evaluation of Vibrational Contributions

The tremendous development of hardware and software is constantly increasing the role of quantum chemical (QC) computations in the assignment and interpretation of experimental results. However, an unbiased comparison between theory and experiment requires the proper account of vibrational averaging effects. In particular, high-resolution spectra in the gas phase are now available for molecules containing up to about 50 atoms, which are too large for a brute-force approach with the available QC methods of sufficient accuracy. In the present paper, we introduce hybrid approaches, which allow the accurate evaluation of vibrational averaging effects for molecules of this size beyond the harmonic approximation, with special attention being devoted to rotational constants. After the validation of new tools for relatively small molecules, the β-estradiol hormone and a prototypical molecular motor have been considered to witness the feasibility of accurate computations for large molecules.

Accurate Structures and Rotational Constants of Steroid Hormones at DFT Cost: Androsterone, Testosterone, Estrone, β-Estradiol, and Estriol

A comprehensive analysis of the structural, conformational, and spectroscopic properties in the gas phase has been performed for five prototypical steroid hormones, namely, androsterone, testosterone, estrone, β-estradiol, and estriol. The revDSD-PBEP86 double-hybrid functional in conjunction with the D3BJ empirical dispersion and a suitable triple-ζ basis set provides accurate conformational energies and equilibrium molecular structures, with the latter being further improved by proper account of core-valence correlation. Average deviations within 0.1% between computed and experimental ground state rotational constants are reached when adding to those equilibrium values vibrational corrections obtained at the cost of standard harmonic frequencies thanks to the use of a new computational tool. Together with the intrinsic interest of the studied hormones, the accuracy of the results obtained at DFT cost for molecules containing about 50 atoms paves the way toward the accurate investigations of other flexible bricks of life.

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.

DFT Meets Wave-Function Methods for Accurate Structures and Rotational Constants of Histidine, Tryptophan, and Proline

A new computational strategy has been applied to the conformational and spectroscopic properties in the gas phase of amino acids with very distinctive features, ranging from different tautomeric forms (histidine) to ring puckering (proline), and heteroaromatic structures with non-equivalent rings (tryptophan). The integration of modern double-hybrid functionals and wave-function composite methods has allowed us to obtain accurate results for a large panel of conformers with reasonable computer times. The remarkable agreement between computations and microwave experiments allows an unbiased interpretation of the latter in terms of stereoelectronic effects.

Accurate Structures and Spectroscopic Parameters of Guanine Tautomers in the Gas Phase by the Pisa Conventional and Explicitly Correlated Composite Schemes (PCS and PCS-F12)

A general strategy for the accurate computation of structural and spectroscopic properties of biomolecule building blocks in the gas phase is proposed and validated for tautomeric equilibria. The main features of the new model are the inclusion of core-valence correlation in geometry optimizations by a double hybrid functional and the systematic use of wave-function composite methods in conjunction with cc-pVnZ-F12 basis sets with separate extrapolation of MP2 and post-MP2 contributions. The resulting Pisa composite scheme employing conventional (PCS) or explicitly correlated (PCS-F12) approaches is applied to the challenging problem of guanine tautomers in the gas phase. The results are in remarkable agreement with the experimental structures, relative stabilities, and spectroscopic signatures of different tautomers. The accuracy of the results obtained at reasonable cost by means of black-box parameter-free approaches paves the way toward systematic investigations of other molecular bricks of life also by non-specialists.

DFT Meets Wave-Function Composite Methods for Characterizing Cytosine Tautomers in the Gas Phase

A general strategy for the accurate computation of structural and spectroscopic properties of biomolecule building blocks in the gas phase has been further improved and validated with a special reference to tautomeric equilibria. The main improvements concern the use of the cc-pVTZ-F12 basis set in both DFT and CCSD(T)-F12 computations, the inclusion of core-valence correlation in geometry optimizations by double hybrid functionals, and the use of the cc-pVQZ-F12 basis set for complete basis set extrapolation at the MP2-F12 level. The resulting model chemistry is applied to the challenging problem of cytosine tautomers in the gas phase. The results are in remarkable agreement with experiment concerning both rotational and vibrational spectroscopic parameters and permit their unbiased interpretation in terms of structural and thermochemical features. Together with the intrinsic interest of the studied molecule, the accuracy of the results obtained at reasonable cost without any empirical parameter suggests that the proposed composite method can be profitably employed for accurate investigations of other molecular bricks of life.

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.

Perturb-Then-Diagonalize Vibrational Engine Exploiting Curvilinear Internal Coordinates

The present paper is devoted to the implementation and validation of a second-order perturbative approach to anharmonic vibrations, followed by variational treatment of strong couplings (GVPT2) based on curvilinear internal coordinates. The main difference with respect to the customary Cartesian-based formulation is that the kinetic energy operator is no longer diagonal, and has to be expanded as well, leading to additional terms which have to be taken into proper account. It is, however, possible to recast all the equations as well-defined generalizations of the corresponding Cartesian-based counterparts, thus achieving a remarkable simplification of the new implementation. Particular attention is paid to the treatment of Fermi resonances with significant number of test cases analyzed fully, validating the new implementation. The results obtained in this work confirm that curvilinear coordinates strongly reduce the strength of inter-mode couplings compared to their Cartesian counterparts. This increases the reliability of low-order perturbative treatments for semi-rigid molecules and paves the way toward the reliable representation of more flexible molecules where small- and large-amplitude motions can be safely decoupled and treated at different levels of theory.

Exploring Expansions of the Potential and Dipole Surfaces Used for Vibrational Perturbation Theory

A scheme for evaluating expansions of the potential and dipole moment surfaces for vibrational perturbation theory is described. The approach is based on numerical differentiation of the Hessian in the coordinates of interest. It is shown that performing these calculations in internal coordinates generates expansions that are transferable among isotopologues of the molecule of interest. Additionally, re-expressing the expansion of the potential in terms of functions of the internal coordinates, for example, cosines of angles or exponential functions of the bond length displacements, provides expansions that can be used for higher-order perturbation theory calculations. The approach is explored and the results are discussed for water, HOD, ammonia, isomers of HNO₃, and halogenated methane.

Helium Droplet Infrared Spectroscopy of the Butyl Radicals

Butyl radicals ( n-, s-, i-,} and tert-butyl) are formed from the pyrolysis of stable precursors (1-pentyl nitrite, 2-methyl-1-butyl nitrite, isopentyl nitrite, and azo- tert-butane, respectively). The radicals are doped into a beam of liquid helium droplets and probed with infrared action spectroscopy from 2700-3125 cm-1, allowing for a low temperature measurement of the CH stretching region. The presence of anharmonic resonance polyads in the 2800-3000 cm-1 region complicates its interpretation. To facilitate spectral assignment, the anharmonic resonances are modeled with two model Hamiltonian approaches that explicitly couple CH stretch fundamentals to HCH bend overtones and combinations: a VPT2+K normal mode model based on CCSD(T) quartic force fields and a semi-empirical local mode model. Both of these computational methods provide generally good agreement with the experimental spectra.

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.