Rigorous vibrational Fermi resonance criterion revealed: two different approaches yield the same result

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.

Comprehensive quantum chemical analysis of the (ro)vibrational spectrum of thiirane and its deuterated isotopologue

The (ro)vibrational spectra of thiirane, c-C2H4S, and its fully deuterated isotopologue, c-C2D4S, have been studied by means of vibrational configuration interaction theory, VCI, its incremental variant, iVCI, and subsequent variational rovibrational calculations, RVCI, which rely on multidimensional potential energy surfaces of coupled-cluster quality including up to four-mode coupling terms. Accurate geometrical parameters, fundamental vibrational transitions and first overtones, rovibrational spectra and rotational spectroscopic constants have been determined from these calculations and were compared with experimental results whenever available. A number of tentative misassignments in the vibrational spectra could be resolved and most results for the deuterated thiirane are high-level predictions, which may guide experiments to come. Besides this, a new implementation of infrared intensities within the iVCI framework has been tested for the transitions of the title compounds and are compared with results obtained from standard VCI calculations.

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.

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.

Comparison of body definitions for incremental vibrational configuration interaction theory (iVCI)

Within incremental vibrational configuration interaction theory (iVCI), the vibrational state energy is determined by means of a many-body expansion, i.e., it is a sum of terms of increasing order, which allow for an embarrassingly parallel evaluation. The convergence of this expansion depends strongly on the definition of the underlying bodies, which essentially decompose the correlation space into fragments. The different definitions considered here comprise mode-based bodies, excitation level-based bodies, and energy-based bodies. An analysis of the convergence behavior revealed that accounting for resonances within these definitions is mandatory and leads to a substantial improvement of the convergence, that is, the expansions can be truncated at lower orders. Benchmark calculations and systematic comparisons of the different body definitions for a small set of molecules, i.e., ketene, ethene, and diborane, have been conducted to study the overall performance of these iVCI implementations with respect to accuracy and central processing unit time.

Fundamental studies of vibrational resonance phenomena by multivalued resummation of the divergent Rayleigh-Schrödinger perturbation theory series: deciphering polyad structures of three H216O isotopologues

A fundamental quantitative study of the vibrational resonances of three H₂¹⁶O H,D-isotopologues with a quartic Watson Hamiltonian was carried out using the resummation of the high-order (∼λⁿ, n ≤ 203) divergent Rayleigh-Schrödinger perturbation theory (RSPT) series by quartic Padé-Hermite multivalued diagonal approximants PH^[m,m,m,m,m], m ≤ 40. The resonance condition between a pair of states is formulated as the existence of a common complex energy solution branch point inside the unit circle: |E(λ_j)|,  Re(λ_j)² + Im(λ_j)² ≤ 1. For the matrix formulation of the vibrational problem (VCI), the existence of common branch points is governed by the Katz theorem and they can be found as roots of discriminant polynomials. The main branches of the Padé-Hermite approximants typically reproduce VCI energies with high accuracy while alternative branches often fit nearby resonant states. The resummation of the RSPT series for H₂O and D₂O (up to the tenth polyad) revealed not only Fermi and Darling-Dennison resonances, but also unusual (0,2,-5) and (5,-2,0) resonance effects matching the (5,2,5) polyad structure, while the (3,2,1) structure was rigorously confirmed for HDO. It is demonstrated that the (5,2,5) polyad structure ensures good organization of high-energy resonating states and breaks down the classic (2,1,2) structure. The advocated methodology of quantitative description of resonance phenomena and revealing polyad structures is suitable for larger molecules and can be adapted to linear molecules and symmetric tops. Its application ensures rigorous classification of vibrational states and can be used in quantitative vibration-rotation spectroscopy.