Darling-Dennison Resonances Research Articles

Anharmonic vibrational frequencies of ammonia borane (BH3NH3).

The fundamental vibrational frequency of the B-N stretch in BH3NH3 has eluded gas-phase experimental observation for decades. This work offers a theoretical anharmonic prediction of this mode to be 644 cm-1, using a Cartesian quartic force field at the CCSD(T)-F12/cc-pVTZ-F12 level of theory. The other fundamental frequencies reported herein have a mean absolute error of only 5 cm-1 from the seven available gas-phase experimental frequencies, making the anharmonic vibrational frequencies and rotational constants the most accurate computational data available for BH3NH3 to date. The inclusion of Fermi, Coriolis, and Darling-Dennison resonances is a major source of this accuracy, with the non-resonance-corrected frequencies having a mean absolute error of 10 cm-1. In particular, the inclusion of the 2ν6 = ν5 type 1 Fermi resonance increases the B-N stretching frequency by 14 cm-1 compared to previous work. Ammonia borane also represents one of the largest molecules ever studied by quartic force fields, making this work an important step in extending the breadth of application for these theoretical rovibrational techniques.

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.

Fundamental Analysis of Singular and Resonance Phenomena in Vibrational Polyads of the Difluorosilylene Molecule

The singular structure of lower vibrational states of the difluorosilylene molecule (up to four total excitation quanta) is studied by expansion of energies of each state into series of the high-order Rayleigh–Schrodinger perturbation theory and analysis of their implicit properties of multiple-valuedness using Pade–Hermite fourth-order approximants. The quartic surface of potential energy in dimensionless normal coordinates is calculated quantum-mechanically at the MP2/cc-pVTZ level. It is shown that one of values of multiple-valued approximants reproduces the variational solution with a high accuracy, while other values (beginning with the fourth polyad) in many cases coincide with energies of other states of the same polyad. The Fermi and Darling–Dennison resonances are analyzed based on facts of coincidence of singular complex branch points of the approximants for mutually interacting states inside a unit circle or near it on the complex plane. It is found that a pair of states can have several coinciding branch points of the solutions (in particular, inside the unit circle). A conclusion is made that this approach is an effective method for the determination of the polyad structure of vibrational states. Calculation parameters necessary for the reproducibility of key results are selected. The calculations are carried out by means of a Fortran-based software package using an arithmetic calculation package with a long mantissa of real numbers (200 digits).

Фундаментальный анализ сингулярных и резонансных явлений в колебательных полиадах молекулы дифторсилилена

The singular structure of the lower vibrational states of the difluorosilylene molecule (up to four quanta of total excitation) was studied by expanding the energies of each state in the series of high-order Rayleigh-Schrödinger perturbation theory and analyzing their implicit multivalued properties using the fourth degree Padé-Hermite approximants. The quartic potential energy surface in dimensionless normal coordinates was calculated quantum-mechanically at the MP2/cc-pVTZ level. It is shown that one of the values of multivalued approximants reproduces the variational solution with high accuracy, while other values, starting from the fourth polyad, in many cases coincide with the energies of other states of the polyad. The Fermi and Darling-Dennison resonances are analyzed on the basis of the coincidence of the singular complex branch points of the approximants for interacting states inside or near a circle of unit radius on the complex plane. It was found that a pair of states can have several coinciding branch points of solutions, including those inside the unit circle. It is concluded that this approach is an effective method for determining the polyad structure of vibrational states. The calculation parameters are selected, which are necessary for the reproducibility of key results. The calculations were carried out using a software package in the Fortran language using a package of arithmetic calculations with a long mantissa of real numbers (200 digits).

Disentangling the IR spectra of 2,3,3,3-tetrafluoropropene using an ab initio description of vibrational polyads by means of canonical Van Vleck perturbation theory

The vibrational spectra of 2,3,3,3-tetrafluoropropene (2333TFP) are studied in the infrared experimentally and theoretically by the canonical second-order Van Vleck operator perturbation theory (CVPT2) and full quartic potential energy surface (PES). 2333TFP belongs to hydrofluoroolefins (HFOs) considered among the most promising alternatives to the hydrofluorocarbons presently in use in refrigeration. The medium resolution infrared spectra of gaseous 2333TFP were recorded in the range 9500–30 cm−1. The integrated IR intensities for all bands falling between 6300–400 cm−1 were accurately determined. Theoretical descriptions of up to four-quanta anharmonic vibrational states of 2333TFP are performed using the state-of-the-art numerical-analytic implementation of CVPT2. High quality harmonic frequencies, obtained at different coupled-cluster levels of theory up to the CCSD(T*)-F12c/VTZ-F12 model were combined with the full quartic MP2/cc-pVTZ anharmonic force field to form the hybrid PES. All Fermi and Darling-Dennison resonances were detected using a universal criterion and treated with the variational CVPT2/VCI stage by using two-, three-, and four-quanta harmonic oscillator basis sets. General recommendations for choosing such basis sets in future studies are formulated. In addition to all fundamentals and their resonance satellites, the vibrational analysis led to the assignment of virtually all observed first/second overtone and binary/ternary combination bands. Computed dipole moment first derivatives in the principal axis system yielded reliable predictions of band shapes for fundamental transitions in good agreement with observed counterparts. Computed anharmonic IR intensities showed an excellent agreement with observed data in the measured ranges. The fundamental spectroscopic effect of excited resonances is observed experimentally and explained theoretically as a universal mechanism of formation of vibrational polyads. The efficiency of the CVPT2/VCI approach employed is clearly demonstrated and can be considered as a benchmark for modeling vibrational states and interpretation of vibrational spectra of semi-rigid molecules.

The Role of Fermi and Darling–Dennison Resonances in the Formation of the Raman Spectra of Water and Water–Ethanol Solutions

Experimental studies show that Fermi and Darling–Dennison resonances make substantial contribution to the formation of Raman spectra of water and water–ethanol solutions. Based on the analysis of spectra with an optimization algorithm, constants of interactions W and contributions of Fermi resonance to Raman spectra of water and water–ethanol solutions are calculated at 25°C.

The Carrier of 3.3 μm Aromatic Infrared Bands: Anharmonicity and Temperature Effects on Neutral PAHs

Abstract Anharmonic infrared (IR) spectra are crucial for the study of interstellar polycyclic aromatic hydrocarbon (PAH) molecules. This work aims to provide a comprehensive study of the features that may influence the accuracy of anharmonic IR spectra of PAHs so that a reliable spectrum that incorporates all necessary features for interpreting the observational IR spectra can be obtained. Six PAHs are investigated: naphthalene, anthracene, pyrene, chrysene, 9,10-dimethylanthracene, and 9,10-dihydroanthracene. The NIST spectra and high-resolution IR absorption spectra are utilized as the reference for the comparisons. The influences of different resonances and resonant thresholds are studied. Four methods for electronic structure calculations are tested. The quantitative comparisons indicate that for the NIST data, B3LYP/N07D provides the best agreement with measured spectra concerning band positions and B3LYP/cc-pVTZ is superior in the description of the relative intensities. The importance of 1–3 Darling–Dennison resonances, which are required for generating triple combination bands, is investigated through a comparison to a high-resolution experimental spectrum. For interpreting the bandwidths and profiles of the observational spectra, the temperature effects are included through the Wand-Landau random walk technique. The comparisons between calculated high-temperature anharmonic and observational spectra indicate that small and compact PAHs might be responsible for the 3.3 μm aromatic infrared bands.

Contribution of Fermi and Darling–Dennison resonances to the formation of Raman spectra of water and water–ethanol solutions

As a result of the experimental study of water Raman spectra and water–ethanol solutions, it was established that Fermi resonance and Darling–Dennison resonance make significant contribution to the formation of Raman spectra. Basing on the analysis of the spectra using optimization algorithms, the coupling constants W and the contributions of Fermi resonance to spectra in water and aqueous ethanol solutions at various temperatures were calculated. The contribution of the resonance of Darling–Dennison to the formation of the spectra of solutions was analyzed. It was established that Fermi and Darling–Dennison resonances manifested stronger in a 20% solution of ethanol in water in comparison with pure water. These resonances weakened with increasing temperature. This effect was explained from the point of view of strength of hydrogen bonds. Copyright © 2017 John Wiley & Sons, Ltd.

Infrared laser spectroscopy of the n-propyl and i-propyl radicals: Stretch-bend Fermi coupling in the alkyl CH stretch region.

The n-propyl and i-propyl radicals were generated in the gas phase via pyrolysis of n-butyl nitrite [CH3(CH2)3ONO] and i-butyl nitrite [(CH3)2CHCH2ONO], respectively. Nascent radicals were promptly solvated by a beam of He nanodroplets, and the infrared spectra of the radicals were recorded in the CH stretching region. Several previously unreported bands are observed between 2800 and 3150 cm-1. The CH stretching modes observed above 3000 cm-1 are in excellent agreement with CCSD(T) anharmonic frequencies computed using second-order vibrational perturbation theory. However, between 2800 and 3000 cm-1, the spectra of n- and i-propyl radicals become congested and difficult to assign due to the presence of multiple anharmonic resonance polyads. To model the spectrally congested region, Fermi and Darling-Dennison resonances are treated explicitly using "dressed" Hamiltonians and CCSD(T) quartic force fields in the normal mode representation, and the agreement with experiment is less than satisfactory. Computations employing local mode effective Hamiltonians reveal the origin of the spectral congestion to be strong coupling between the high frequency CH stretching modes and the lower frequency CHn bending/scissoring motions. The most significant coupling is between stretches and bends localized on the same CH2/CH3 group. Spectral simulations using the local mode approach are in excellent agreement with experiment.

Ab Initio Anharmonic Analysis of Vibrational Spectra of Uracil Using the Numerical-Analytic Implementation of Operator Van Vleck Perturbation Theory.

The numerical-analytic implementation of the operator version of the canonical Van Vleck second-order vibrational perturbation theory (CVPT2) is employed for a purely ab initio prediction and interpretation of the infrared (IR) and Raman anharmonic spectra of a medium-size molecule of the diketo tautomer of uracil (2,4(1H,3H)-pyrimidinedione), which has high biological importance as one of the four RNA nucleobases. A nonempirical, semidiagonal quartic potential energy surface (PES) expressed in normal coordinates was evaluated at the MP2/cc-pVTZ level of theory. The quality of the PES was improved by replacing the harmonic frequencies with the "best" estimated CCSD(T)-based values taken from the literature. The theoretical method is enhanced by an accurate treatment of multiple Fermi and Darling-Dennison resonances with evaluation of the corresponding resonance constants W and K (CVPT2+WK method). A prediction of the anharmonic frequencies as well as IR and Raman intensities was used for a detailed interpretation of the experimental spectra of uracil. Very good agreement between predicted and observed vibrational frequencies has been achieved (RMSD ∼4.5 cm(-1)). The model employed gave a theoretically robust treatment of the multiple resonances in the 1680-1790 cm(-1) region. Our new analysis gives the most reliable reassignments of IR and Raman spectra of uracil available to date.

Global modeling of NO2 line positions

The global modeling of NO2 line positions has been performed within the effective operators method. One hundred and ninety five parameters of the polyade model of the effective Hamiltonian have been fitted to 28016 line positions collected from the literature for the 0.006–7916 cm−1 wavenumber range. The global root mean square residual of the fit is 0.017 cm−1. The effective Hamiltonian used explicitely takes into account both the spin-rotation interactions within each vibrational state and numerous vibrational-rotational resonances. Indeed, resonances due to the first and second order C-type Coriolis interactions and Fermi and Darling-Dennison resonances had to be considered because of the approximate relations ω1 ≈ ω3 ≈ 2ω2 between three harmonic frequencies of NO2.

Criteria for first- and second-order vibrational resonances and correct evaluation of the Darling-Dennison resonance coefficients using the canonical Van Vleck perturbation theory.

The second-order vibrational Hamiltonian of a semi-rigid polyatomic molecule when resonances are present can be reduced to a quasi-diagonal form using second-order vibrational perturbation theory. Obtaining exact vibrational energy levels requires subsequent numerical diagonalization of the Hamiltonian matrix including the first- and second-order resonance coupling coefficients. While the first-order Fermi resonance constants can be easily calculated, the evaluation of the second-order Darling-Dennison constants requires more complicated algebra for seven individual cases with different numbers of creation-annihilation vibrational quanta. The difficulty in precise evaluation of the Darling-Dennison coefficients is associated with the previously unrecognized interference with simultaneously present Fermi resonances that affect the form of the canonically transformed Hamiltonian. For the first time, we have presented the correct form of the general expression for the evaluation of the Darling-Dennison constants that accounts for the underlying effect of Fermi resonances. The physically meaningful criteria for selecting both Fermi and Darling-Dennison resonances are discussed and illustrated using numerical examples.

Theoretical interpretation of the vibrational spectrum of bicyclo[1.1.0]butane in terms of an ab initio anharmonic model

The anharmonic vibrational IR and Raman spectra of the bicyclo[1.1.0]butane molecule have been calculated in the range of up to 4000 cm−1 using a numerical and analytical realization of the van Vleck second-order operator perturbation theory. Cubic and quartic force constants in normal coordinates, as well as cubic surfaces of the dipole moment and polarizability, have been found by numerical differentiation of the corresponding first and second derivatives calculated by the MP2/cc-pVTZ quantum-mechanical method. In order to increase the prediction accuracy of vibrational transitions, corresponding harmonic frequencies have been obtained by the CCSD(T)/cc-pVTZ high-precision quantum mechanical method. The anharmonic intensities of the IR and Raman spectra have been calculated using canonical transformations of the operators of the dipole moment and polarizability expanded into a Taylor series around the equilibrium configuration. The assignment of experimental vibrational bands in the IR and Raman spectra has been analyzed. It has been shown that the anharmonic calculation based on the above-described procedure of combining more exact harmonic frequencies with the anharmonic force field obtained with a more economical method makes possible the reliable interpretation of the majority of spectral bands, including Fermi and Darling-Dennison resonances.

Reduced dimension rovibrational variational calculations of the S1 state of C2H2. II. The S1 rovibrational manifold and the effects of isomerization

Reduced dimension variational calculations have been performed for the rovibrational level structure of the S1 state of acetylene. The state exhibits an unusually complicated level structure, for various reasons. First, the potential energy surface has two accessible conformers, trans and cis. The cis conformer lies about 2700 cm(-1) above the trans, and the barrier to cis-trans isomerization lies about 5000 cm(-1) above the trans minimum. The trans vibrations ν4 (torsion) and ν6 (asym. bend) interact very strongly by Darling-Dennison and Coriolis resonances, such that their combination levels and overtones form polyads with unexpected structures. Both conformers exhibit very large x36 cross-anharmonicity since the pathway to isomerization is a combination of ν6 and ν3 (sym. bend). Near the isomerization barrier, the vibrational levels show an even-odd K-staggering of their rotational levels as a result of quantum mechanical tunneling through the barrier. The present calculations address all of these complications, and reproduce the observed K-structures of the bending and C-C stretching levels with good qualitative accuracy. It is expected that they will assist with the assignment of the irregular patterns near the isomerization barrier.

Anharmonic Vibrational Analysis of the Gas-Phase Infrared Spectrum of 1,1-Difluoroethylene Using the Operator Van Vleck Canonical Perturbation Theory

Anharmonic vibration frequencies of 1,1-difluoroethylene (11DFE) in the gas phase are predicted by means of the numerical-analytic operator version of the canonical van Vleck perturbation theory in the second and fourth orders (CVPT2 and CVPT4). The full quartic and "semi-diagonal" sextic rectilinear normal coordinate potential energy surfaces, needed for CVPT2 and CVPT4, respectively, were obtained with the MP2/cc-pVTZ quantum-mechanical model. CVPT2 is superior to the traditional second-order vibrational perturbation theory approach (VPT2) because of the uniform general treatment of the Fermi and second-order Darling-Dennison resonances. The fourth-order version, CVPT4, provides a more refined solution and proves convergence of the perturbative treatment. Labeling of the basis functions by polyad numbers breaks down the infinite Hamiltonian matrix into a block-diagonal form. The polyad expression for 11DFE has been determined as P = 14(ν1 + ν7) + 8ν2 + 6(ν3 + ν8) + 4(ν4 + ν9) + 3(ν6 + ν11 + ν12) + 2(ν5 + ν10), where the νi are quantum numbers. The theoretical prediction of anharmonic infrared absorption intensities corroborated an assignment of the majority of observed gas-phase bands up to 3500 cm(-1). The solution was refined by iteratively fitting harmonic frequencies, until predicted fundamental anharmonic frequencies matched the observed values. The average error for about 90 observed frequencies after fitting only fundamental frequencies is ∼1.05 cm(-1). The fitted "semi-experimental" harmonic frequencies agree very well the quantum-mechanical predictions based on the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ models.

Calculation of the intensities of vibrational hydrogen sulfide transitions for remote sensing of high-temperature media

Integral intensities of vibrational bands are calculated for hydrogen sulfide (H2S) taking into account the Fermi and Darling–Dennison resonances. Components of the dipole moment function in normal coordinates and parameters of the effective vibrational Hamiltonian borrowed from the literature are used as initial data. From several sets of the dipole moment function parameters, we have chosen the set of the parameters computations with which provide the closest agreement with the experimental integral intensities of the H2S bands. As a result, predictive computations of the vibrational band intensities (ΣΔυ i = 2) are carried out at temperatures in the range 600–1500 K.

FTS high resolution spectra of 16O3 in 3500 and 5500 cm−1 regions. First example of new theoretical modelling for a polyad of strongly coupled states

The infrared spectrum of 16O3 has been revisited in the ranges 3300–3600cm−1 and 5200–5600cm−1, recorded by the Fourier Transform Spectrometer of Reims, with an improved signal/noise ratio. In the lower spectral range the weak 2ν1+2ν2 band is observed and assigned for the first time. This allowed for completing the triad of strongly interacting (220), (121), and (022) states. The resonance interaction parameters for this triad were derived from the molecular potential energy surface using high-order Contact Transformation method. This involves Darling–Dennison resonances between (220) and (022) vibration A-states, and Coriolis resonances between (121) B-state and A-states. Altogether 18 coupling parameters were fixed to these theoretically predicted values that allowed avoiding problems of ambiguities while fitting strongly correlated parameters. The remaining small perturbations of a few Ka=5 transitions of the ν1+2ν2+ν3 band were explained by accidental Coriolis resonance of (121) with the (050) dark state. This mixed half theoretical/half empirical model (with 39 fitted and 77 theoretically constrained parameters) developed in this work for the first time allows an excellent description of 1897 line positions with the rms deviation ∼0.001cm−1 closed to the experimental precision. The intensities of two new hot bands ν2+4ν3−ν3 and ν1+ν2+3ν3−ν1 that fall in this range were also observed and modelled, thanks to a better signal to noise ratio.In addition, the 5200–5600cm−1 region has also been revisited, showing for the first time the (321) state which was considered as “dark” one in the previous analysis. Effective Hamiltonian parameters were derived for strongly coupled (213)/(114)/(321) upper states including (080) as a dark one.The transition moment parameters of all newly observed and assigned bands were derived resulting to average rms deviation for intensities of ∼8% and 13% for the cold and the hot bands, respectively, in the lower range and of ∼15% for the bands in the upper range that is close to experimental accuracy for weak transitions.

Calculation of vibrational energy levels of water molecule by summing divergent perturbation theory series

The Rayleigh-Schrodinger perturbation theory is applied to a calculation of vibrational energy levels of the H2O molecule for isolated states and the states involved in the anharmonic Fermi and Darling-Dennison resonances. It is shown that in spite of the rapid divergence of the perturbation theory series caused by the resonances, the use of the summation methods of Pade, Pade-Borel, and Pade-Hermite and the moments method allows one to obtain quite satisfactory results.

On the ν1/2 ν2 Resonance in the Complex of Carbon Dioxide with Dimethyl Ether

Infrared and Raman spectra of solutions in liquid argon and krypton containing dimethyl ether or its fully deuterated isotopomer and (12)CO(2) or (13)CO(2) are investigated. The spectra lead to new data on the nu(1) (CO(2) )/2 nu(2) (CO(2) ) resonances appearing in the complex of CO(2) with the ether. The experimental data, and their interpretation, is supported by MP2/6-311++G(2d,2p) calculations of the cubic and quartic force constants and of the first and higher order dipole moment derivatives required for the modelling of the Fermi and Darling-Dennison resonances observed.

Calculated stretching overtone levels and Darling–Dennison resonances in water: a triumph of simple theoretical approaches

The coupled-cluster singles and doubles treatment with a perturbative treatment of triple excitations known as CCSD(T) has been used in conjunction with a hierarchy of atomic natural orbital basis sets to study stretching levels in water up to 2 eV above the zero-point level. Agreement with experiment obtained with perturbation theory augmented by a simple treatment of resonances suggested by Lehmann is quite remarkable in spite of the well-known and strong Darling–Dennison resonances in this system. With the largest basis sets, deviation from experiment is ca. 20 cm−1 at energies in the 15,000–16,000 cm−1 range.