Rotation-vibration Coupling Research Articles

Communication: Creation of molecular vibrational motions via the rotation-vibration coupling.

Building on recent advances in the rotational excitation of molecules, we show how the effect of rotation-vibration coupling can be switched on in a controlled manner and how this coupling unfolds in real time after a pure rotational excitation. We present the first examination of the vibrational motions which can be induced via the rotation-vibration coupling after a pulsed rotational excitation. A time-dependent quantum wave packet calculation for the HF molecule shows how a slow (compared to the vibrational period) rotational excitation leads to a smooth increase in the average bond length whereas a fast rotational excitation leads to a non-stationary vibrational motion. As a result, under field-free postpulse conditions, either a stretched stationary bond or a vibrating bond can be created due to the coupling between the rotational and vibrational degrees of freedom. The latter corresponds to a laser-induced breakdown of the adiabatic approximation for rotation-vibration coupling.

Rovibrational energy transfer in the He–C3 collision: rigid bender treatment of the bending–rotation interaction and rate coefficients

C3 is a molecular chain which has been observed in interstellar clouds and in comets. It is also a very floppy molecule for which the vibrational bending transitions are in the same energy range as the rotational transitions. In this paper, we apply our recently developed quantum scattering method for treating atom rigid bender inelastic collisions at the Close Coupling level to the collision of C3 by helium. This method allows us to compute the rovibrational transitions induced by collisions. The purely rotational transitions have been also calculated, using the rigid monomer approximation. The accuracy of this last approximation in the case of a system with a significant vibrational–rotational coupling is discussed. The first evaluation of the cross-sections associated with the rovibrational transitions between levels belonging to different vibrational bending levels is also presented. We observe that the propensity rule for the rovibrational transitions is a competition between the smallest Δj and the smallest transition energy. As a consequence, cross-sections and rate coefficients of vibrationally inelastic transitions can be several orders of magnitude larger than for purely rotational transitions.

Accurate spectroscopy of polycyclic aromatic compounds: from the rotational spectrum of fluoren-9-one in the millimeter wave region to its infrared spectrum.

The rotational spectrum of fluoren-9-one, a small oxygenated polycyclic aromatic hydrocarbon, has been recorded and assigned in the 52-74.4 GHz region. The determined small negative value of the inertia defect (-0.3 u Å(2)) has been explained in terms of vibrational-rotational coupling constants calculated at the B3LYP/cc-pVTZ level of theory. Vibrational anharmonic analysis together with second-order vibrational perturbation theory approximation was applied both to fluorenone and its reduced form, fluorene, to predict the mid- and near-infrared spectra. The data presented here give precise indication on the fluorenone ground state structure, allow for an accurate spectral characterization in the millimeter wave and infrared regions, and hopefully will facilitate extensive radio astronomical searches with large radio telescopes.

Formation of cyanoallene (buta-2, 3-dienenitrile) in the interstellar medium: a quantum chemical and spectroscopic study

The interstellar medium, filling the vast space between stars, is a rich reservoir of molecular material ranging from simple diatomic molecules to more complex, astrobiologically important molecules such as vinylcyanide, methylcyanodiaccetylene, cyanoallene, etc. Interstellar molecular cyanoallene is one of the most stable isomers of methylcynoacetylene. An attempt has been made to explore the possibility of forming cyanoallene in interstellar space by radical-radical and radical-molecule interaction schemes in the gaseous phase. The formation of cyanoallene starting from some simple, neutral interstellar molecules and radicals has been studied using density functional theory. The reaction energies and structures of the reactants and products show that the formation of cyanoallene is possible in the gaseous phase. Both of the considered reaction paths are totally exothermic and barrierless, thus giving rise to a high probability of occurrence. Rate constants for each step in the formation process of cyanoallene in both the reaction paths are estimated. A full vibrational analysis has been attempted for cyanoallene in the harmonic and anharmonic approximations. Anharmonic spectroscopic parameters such as rotational constants, rotation-vibration coupling constants and centrifugal distortion constants have been calculated.

Rotational spectroscopy of pyridazine and its isotopologs from 235–360 GHz: Equilibrium structure and vibrational satellites

The rotational spectrum of pyridazine (o-C4H4N2), the ortho disubstituted nitrogen analog of benzene, has been measured and analyzed in the gas phase. For the ground vibrational state of the normal isotopolog, over 2000 individual rotational transitions have been identified between 238 and 360 GHz and have been fit to 13 parameters of a 6th-order centrifugal distortion Hamiltonian. All transitions in this frequency region can now be predicted from this model to near experimental accuracy, i.e., well enough for the purpose of any future radio-astronomical search for this species. Three isotopologs, [3-(13)C]-C4H4N2, [4-(13)C]-C4H4N2, and [1-(15)N]-C4H4N2, have been detected in natural abundance, and several hundred lines have been measured for each of these species and fit to 6th-order Hamiltonians. Ten additional isotopologs were synthesized with enhanced deuterium substitution and analyzed to allow for a complete structure determination. The equilibrium structure (Re) of pyridazine was obtained by correcting the experimental rotational constants for the effects of vibration-rotation coupling using interaction constants predicted from CCSD(T) calculations with an ANO0 basis set and further correcting for the effect of electron mass. The final Re structural parameters are determined with excellent accuracy, as evidenced by their ability to predict 28 independent moments of inertia (Ia and Ib for 14 isotopologs) very well from 9 structural parameters. The rotational spectra of the six lowest-energy fundamental vibrational satellites of the main isotopolog have been detected. The rotational spectra of the five lowest-energy vibrational satellites have been assigned and fit to yield accurate rotational and distortion constants, while the fit and assignment for the sixth is less complete. The resultant vibration-rotation interaction (α) constants are found to be in excellent agreement with ones predicted from coupled-cluster calculations, which proved to be the key to unambiguous assignment of the satellite spectra to specific vibration modes.

Rotational-vibrational coupling in the BPS Skyrme model of baryons

We calculate the rotational-vibrational spectrum in the BPS Skyrme model for the hedgehog skyrmion with baryon number one. The resulting excitation energies for the nucleon and delta Roper resonances are slightly above their experimental values. Together with the fact that in the standard Skyrme model these excitation energies are significantly lower than the experimental ones, this provides strong evidence for the conjecture that the inclusion of the BPS Skyrme model is required for a successful quantitative description of physical properties of baryons and nuclei.

Effect of vibration–rotation coupling on simultaneous extraction of temperature and species concentration from vibrational CARS spectra of hot gases

The coupling between vibration and rotation in light molecules changes the strength of the Raman response. From this standpoint, we consider high‐temperature molecular spectra obtained by means of coherent anti‐Stokes Raman scattering (CARS), whose spectral intensity is useful to extract thermometric information and species concentrations for applications in combustion science. In this context and unlike other studies on the subject that are exclusively focused on thermometry, the novelty of the current work lies in the determination of the mutual relationship among the free variables adopted in the analysis of CARS spectra when these do not include the effect of the vibration–rotation coupling. The relationship emerges from the comparison to a reference made of calculated vibrational spectra of nitrogen and oxygen subject to the coupling. These spectra are then fitted by means of spectra developed under the ordinary rigid‐rotor approximation that is usually adopted in any fitting procedure for such molecules. The results show that small changes of the fitted temperature correspond to larger deviations for the determination of concentrations and non‐resonant background. Copyright © 2013 John Wiley & Sons, Ltd.

Formylmethylene: The Triplet Ground State and the Lowest Singlet State

The ground triplet state and lowest singlet state of formylmethylene have been proposed as important intermediates in the Wolff rearrangement of α-diazo ketones into ketenes. The ground triplet state of formylmethylene has been examined experimentally, but the lowest singlet state has yet to be observed. We predict equilibrium geometries, energies, bonding, dipole moments, and harmonic vibrational frequencies for these two lowest states of formylmethylene at the cc-pVQZ CCSD(T) level of theory. The singlet-triplet energy difference [ΔE(S-T)] is quite sensitive to the level of theory. The highly accurate cc-pVQZ CCSD(T) level of theory yields the most reliable result of only 2.0 kcal mol(-1). An estimate based on the experimentally characterized CH2 molecule yields ΔE(S-T) = 1.27 kcal mol(-1). In addition, accurate quartic force fields have been determined at the cc-pVTZ CCSD(T) level of theory. Fundamental vibrational frequencies, anharmonic constants, and vibration-rotation coupling constants were determined using vibrational second-order perturbation theory (VPT2). Our results should aid in experimental detection and characterization of the lowest singlet state of formylmethylene, which is highly desirable for better understanding the mechanism of the Wolff rearrangement.

Using fixed-node diffusion Monte Carlo to investigate the effects of rotation-vibration coupling in highly fluxional asymmetric top molecules: Application to H2D+

A fixed-node diffusion Monte Carlo approach for obtaining the energies and wave functions of the rotationally excited states of asymmetric top molecules that undergo large amplitude, zero-point vibrational motions is reported. The nodal surfaces required to introduce rotational excitation into the diffusion Monte Carlo calculations are obtained from the roots of the asymmetric top rigid rotor wave functions calculated using the system's zero-point, vibrationally averaged rotational constants. Using H(2)D(+) as a model system, the overall accuracy of the methodology is tested by comparing to the results of converged variational calculations. The ability of the fixed-node diffusion Monte Carlo approach to provide insights into the nature and strength of the rotation-vibration coupling present in the rotationally excited states of highly fluxional asymmetric tops is discussed. Finally, the sensitivity of the methodology to the details of its implementation, such as the choice of embedding scheme, is explored.

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves (PECs) for the ground state (X2Σ+) and the four excited electronic states (A2Π, B2Π, C2Σ+, 4Π) of a BeH molecule are calculated using the multi-configuration reference single and double excited configuration interaction (MRCI) approach in combination with the aug-cc-pVTZ basis sets. The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm, and the equilibrium bond length Re and the vertical excited energy Te are determined directly. It is evident that the X2Σ+, A2Π, B2Π, C2Σ+ states are bound and 4Π is a repulsive excited state. With the potentials, all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero (J = 0) by numerically solving the radial Schrödinger equation of nuclear motion. Then the spectroscopic data are obtained including the rotation coupling constant ωe, the anharmonic constant ωexe, the equilibrium rotation constant Be, and the vibration-rotation coupling constant αe. These values are compared with the theoretical and experimental results currently available, showing that they are in agreement with each other.

Microwave spectrum of arsenic triphosphide

The microwave spectrum of AsP3 has been measured and assignments for three different vibrational states have been made. The symmetric top ΔJ=+1 transitions have been fit to obtain rotational constants, centrifugal distortion constants and quadrupole coupling strengths for the three vibrational states (I–III), BI=2201.394(1)MHz, eQqaaI=48.728(5)MHz, DJI=0.2(3)kHz, DJKI=0.5(1)kHz and σI=4kHz, BII=2192.26(1)MHz, eQqaaII=48.62(4)MHz, BIII=2183.93(2)MHz, eQqaaIII=48.53(4)MHz. The experimental vibration–rotation coupling constant, α(ν4)=9.20(3)MHz is compared with results from MP2/6-311G** calculations. The excited states (II and III) are tentatively assigned to the ν4 and 2ν4 excited vibrational states.

Equivalence of the three empirical potential energy models for diatomic molecules

It is found that the Manning–Rosen potential, Schiöberg potential and Deng–Fan potential are the same solvable empirical potential energy function for diatomic molecules. We calculate the anharmonicity ωexe and vibrational rotational coupling parameter αe for 16 molecules by choosing the experimental values of the dissociation energy De, equilibrium bond length re and vibrational frequency ωe as inputs. The results show that the Manning–Rosen potential, Deng–Fan potential and Schiöberg potential are not better than the traditional Morse potential.

Unraveling rotation-vibration mixing in highly fluxional molecules using diffusion Monte Carlo: Applications to ${\rm H}_3^+$H3+ and H3O+

A thorough examination of the use of fixed-node diffusion Monte Carlo for the study of rotation-vibration mixing in systems that undergo large amplitude vibrational motions is reported. Using H(3)(+) as a model system, the overall accuracy of the method is tested by comparing the results of these calculations with those from converged variational calculations. The effects of the presence of a large amplitude inversion mode on rotation-vibration mixing are considered by comparing the H(3)(+) results with those for H(3)O(+). Finally, analysis of the results of the fixed-node diffusion Monte Carlo calculations performed in different nodal regions is found to provide clear indications of when some of the methodology's underlying assumptions are breaking down as well as provide physical insights into the form of the rotation-vibration coupling that is most likely responsible.

Formation of 2-imino-malononitrile and diaminomaleonitrile in nitrile rich environments: A quantum chemical study

Nitriles and nitrile chemistry are found in a variety of astronomical environments and have been utilized in many areas of astronomy and planetary science. Cyanogen (NCCN) has been observed in Titan’s atmosphere though it is not detected in comets or interstellar space. Nitriles formed in the atmosphere of Titan are expected to precipitate down onto the satellite’s surface where cosmic radiations can convert them into other molecules. In view of the significance of the HCN tetramers diaminomaleonitrile (DAMN) and diaminofumaronitrile (DAFN) in reactions leading to the formation of adenine, the possibility of their formation from CN and H radicals, which are known to be abundant in the nitrile rich astronomical environments, has been explored on the basis of radical–radical and radical–molecule interaction schemes using quantum chemical methods. Global and local descriptors such as chemical potential, molecular hardness and softness, electrophilicity and condensed Fukui functions were used to understand the mechanistic aspects of chemical reaction and region-selectivity of the CN and H radical additions. The presence and nature of weak bonds in the reaction complexes and transition states formed during the reaction process have been ascertained using Bader’s quantum theory of atoms in molecules (QTAIM). The reaction leading to the formation of DAFN is found to be exothermic with a very large net energy gain but involves a potential barrier of about 4.75kcal/mol. The present reaction scheme shall provide a simpler route to the formation of 4-amino-1H-imidazole-5-carbonitrile (AICN) and adenine. This reaction involves the formation of a neutral intermediate 2-imino-malononitrile for which no structural or spectroscopic information is available. A full vibrational analysis has, therefore, been attempted for 2-imino-malononitrile in the harmonic and anharmonic approximations and spectroscopic parameters such as rotational constants, rotation–vibration coupling constants, and centrifugal distortion constants are being reported.

Conformational and vibrational studies of isomeric hydrogen cyanide tetramers by quantum chemical methods

The results of structural studies and detailed harmonic and anharmonic vibrational analysis on two hydrogen cyanide (HCN) tetramers diaminomaleonitrile (DAMN) and diaminofumaronitrile (DAFN), which are important molecules for understanding the chemistry of interstellar space and nitrile rich environments, are being reported on the basis of density functional theory using second-order perturbation theory. Both the molecules are found to have C1 symmetry. While all the heavy atoms of DAMN lie in the same plane (maximum deviation 6°), the two nitrogen atoms in DAFN are out of plane by about 15°. The two amino groups are tetrahedral and do not have significant bond angle anisotropy. Detailed conformational studies are reported on the two molecules and their possible rotational isomers are identified. Complete vibrational analysis based on harmonic and anharmonic frequencies, intensity of infrared and activity of Raman bands and potential energy distribution over the internal coordinates has been provided for the two molecules. Affect of hydrogen bonding on molecular geometry and frequencies of the NH stretch modes has been studied by calculations on the dimers of the two molecules. A close agreement has been observed between the experimental and calculated frequencies. Vibrational–rotational constants such as rotational constants in the ground vibrational state (A0, B0, C0) and the effective rotational constants (Ae, Be and Ce), including terms due to quartic centrifugal distortion constants, rotation–vibration coupling constants, Wilson and Nielsen's centrifugal distortion constants have been calculated using B3LYP and B97-1 functionals and 6-31G**, 6-311+G** and TZVP basis sets.

Microwave measurements of proton tunneling and structural parameters for the propiolic acid–formic acid dimer

Microwave spectra of the propiolic acid-formic acid doubly hydrogen bonded complex were measured in the 1 GHz to 21 GHz range using four different Fourier transform spectrometers. Rotational spectra for seven isotopologues were obtained. For the parent isotopologue, a total of 138 a-dipole transitions and 28 b-dipole transitions were measured for which the a-dipole transitions exhibited splittings of a few MHz into pairs of lines and the b-type dipole transitions were split by ~580 MHz. The transitions assigned to this complex were fit to obtain rotational and distortion constants for both tunneling levels: A(0+) = 6005.289(8), B(0+) = 930.553(8), C(0+) = 803.9948(6) MHz, Δ(0+)(J) = 0.075(1), Δ(0+)(JK) = 0.71(1), and δ(0+)(j) = -0.010(1) kHz and A(0-) = 6005.275(8), B(0-) = 930.546(8), C(0-) = 803.9907(5) MHz, Δ(0-)(J) = 0.076(1), Δ(0-)(JK) = 0.70(2), and δ(0-)(j) = -0.008(1) kHz. Double resonance experiments were used on some transitions to verify assignments and to obtain splittings for cases when the b-dipole transitions were difficult to measure. The experimental difference in energy between the two tunneling states is 291.428(5) MHz for proton-proton exchange and 3.35(2) MHz for the deuterium-deuterium exchange. The vibration-rotation coupling constant between the two levels, F(ab), is 120.7(2) MHz for the proton-proton exchange. With one deuterium atom substituted in either of the hydrogen-bonding protons, the tunneling splittings were not observed for a-dipole transitions, supporting the assignment of the splitting to the concerted proton tunneling motion. The spectra were obtained using three Flygare-Balle type spectrometers and one chirped-pulse machine at the University of Virginia. Rotational constants and centrifugal distortion constants were obtained for HCOOH···HOOCCCH, H(13)COOH···HOOCCCH, HCOOD···HOOCCCH, HCOOH···DOOCCCH, HCOOD···DOOCCCH, DCOOH···HOOCCCH, and DCOOD···HOOCCCH. High-level ab initio calculations provided initial rotational constants for the complex, structural parameters, and some details of the proton tunneling potential energy surface. A least squares fit to the isotopic data reveals a planar structure that is slightly asymmetric in the OH distances. The formic OH···O propiolic hydrogen bond length is 1.8 Å and the propiolic OH···O formic hydrogen bond length is 1.6 Å, for the equilibrium configuration. The magnitude of the dipole moment was experimentally determined to be 1.95(3) × 10(-30) C m (0.584(8) D) for the 0(+) states and 1.92(5) × 10(-30) C m (0.576(14) D) for the 0(-) states.

Herman–Wallis correction in vibrational CARS of oxygen

AbstractLight molecules are subject to vibration–rotation (VR) interaction, which implies corrections to the rigid rotor approximation and, in particular, corrections to spectral line intensities are related to the so‐called Herman–Wallis (HW) factor. This problem is outlined here for the spectral response of some medium‐weight diatomics in the gas phase and probed by means of vibrational coherent anti‐Stokes Raman scattering (CARS) used for diagnostic reasons in combustion science. However, different from other works on this subject, we specialized our analysis to oxygen and, since the peculiarity of its anti‐bonding molecular orbital, we find that the VR coupling is responsible for deviations that compete with the effect of Raman line widths typical of collisional environments of hot gases at room pressure. The HW correction is ultimately demonstrated to affect O2 CARS thermometry in such a manner that the accuracy for measurements at high temperatures can be improved. Copyright © 2011 John Wiley & Sons, Ltd.

Anharmonic rovibrational analysis for disilacyclopropenylidene (Si2CH2)

The global minimum on the Si(2)CH(2) electronic singlet potential energy surface has been theoretically predicted to be a peculiar hydrogen bridged (Si···H···Si) disilacyclopropenylidene structure (Si(2)CH(2)). An accurate quartic force field for Si(2)CH(2) has been determined employing ab initio coupled-cluster theory with single and double excitations and a perturbative treatment for triple excitations [CCSD(T)], in combination with the correlation consistent core-valence quadruple zeta (cc-pCVQZ) basis set. The vibration-rotation coupling constants, equilibrium and zero-point vibration corrected rotational constants, centrifugal distortion constants, and harmonic and fundamental vibrational frequencies for six isotopologues of Si(2)CH(2) are predicted using vibrational second-order perturbation theory (VPT2). The anharmonic corrections for the vibrational motions involving the H bridged bonds are found to be more than 5% with respect to the corresponding harmonic vibrational frequencies. In this light, an experimental detection and characterization of disilacyclopropenylidene (Si(2)CH(2)) is highly desired.

Transient laser absorption spectroscopy of CH 2 near 780 nm

Bands in the CH 2 b ˜ 1 B 1 – a ˜ 1 A 1 transition between 12 500 and 13 000 cm −1 were recorded at Doppler-limited resolution using a transient frequency-modulation (FM) laser absorption spectrometer. Rotational levels in seven upper vibronic states: a ˜ ( 0 , 11 , 0 ) 1 , 3 , a ˜ ( 2 , 6 , 0 ) 1 , b ˜ ( 0 , 2 , 0 ) 4 , b ˜ ( 1 , 1 , 0 ) 1 , 2 , and b ˜ ( 0 , 3 , 0 ) 1 were assigned with the assistance of optical–optical double resonance (OODR) and ground state combination differences. Perturbations due to rotation-vibration coupling, anharmonic couplings, ℓ-resonance, as well as the Renner–Teller effect are discussed as sources of the irregular rotational patterns observed in the b ˜ ( 0 , 3 , 0 ) 1 , b ˜ ( 1 , 1 , 0 ) 1 , and a ˜ ( 0 , 11 , 0 ) 3 vibronic levels.

Performance of W4 theory for spectroscopic constants and electrical properties of small molecules

Accurate spectroscopic constants and electrical properties of small molecules are determined by means of W4 and post-W4 theories. For a set of 28 first- and second-row diatomic molecules for which very accurate experimental spectroscopic constants are available, W4 theory affords near-spectroscopic or better predictions. Specifically, the root-mean-square deviations (RMSDs) from experiment are 0.04 pm for the equilibrium bond distances (r(e)), 1.03 cm(-1) for the harmonic frequencies (ω(e)), 0.20 cm(-1) for the first anharmonicity constants (ω(e)x(e)), 0.10 cm(-1) for the second anharmonicity constants (ω(e)y(e)), and 0.001 cm(-1) for the vibration-rotation coupling constants (α(e)). These RMSDs imply 95% confidence intervals of about 0.1 pm for r(e), 2.0 cm(-1) for ω(e), 0.4 cm(-1) for ω(e)x(e), and 0.2 cm(-1) for ω(e)y(e). We find that post-CCSD(T) contributions are essential to achieve such narrow confidence intervals for r(e) and ω(e), but have little effect on ω(e)x(e) and α(e), and virtually none on ω(e)y(e). Higher-order connected triples T(3)-(T) improve the agreement with experiment for the hydride systems, but their inclusion (in the absence of T(4)) tends to worsen the agreement with experiment for the nonhydride systems. Connected quadruple excitations T(4) have significant and systematic effects on r(e), ω(e), and ω(e)x(e), in particular they universally increase r(e) (by up to 0.5 pm), universally reduce ω(e) (by up to 32 cm(-1)), and universally increase ω(e)x(e) (by up to 1 cm(-1)). Connected quintuple excitations T(5) are spectroscopically significant for ω(e) of the nonhydride systems, affecting ω(e) by up to 4 cm(-1). Diagonal Born-Oppenheimer corrections have systematic and spectroscopically significant effects on r(e) and ω(e) of the hydride systems, universally increasing r(e) by 0.01-0.06 pm and decreasing ω(e) by 0.3-2.1 cm(-1). Obtaining r(e) and ω(e) of the pathologically multireference BN and BeO systems with near-spectroscopic accuracy requires large basis sets in the core-valence CCSD(T) step and augmented basis sets in the valence post-CCSD(T) steps in W4 theory. The triatomic molecules H(2)O, CO(2), and O(3) are also considered. The equilibrium geometries and harmonic frequencies (with the exception of the asymmetric stretch of O(3)) are obtained with near-spectroscopic accuracy at the W4 level. The asymmetric stretch of ozone represents a severe challenge to W4 theory, in particular the connected quadruple contribution converges very slowly with the basis set size. Finally, the importance of post-CCSD(T) correlation effects for electrical properties, namely, dipole moments (μ), polarizabilities (α), and first hyperpolarizabilities (β), is evaluated.