Excited Rovibrational States Research Articles

Thermally Averaged Spectroscopic Parameters of the Weakly Bound Dimers

Spectroscopic parameters in an ensemble of the weakly bound dimers are derived making use of the quantum and classical statistical average over thermally excited rovibrational states. Argon dimers and oxygen dimers are taken as examples. It is shown that thermally averaged characteristics of dimers rapidly change as temperature of a gas rises. In an ensemble of quasi-diatomic tightly bound dimers, the high-temperature limit of the effective dissociation energy amounts to roughly D0/3, where D0 is the dissociation energy from the ground state. It is demonstrated that the effective rotational Beff(T) constant for the oxygen dimers statistically averaged at near room temperature is merely one half of the ground state B0 value. This conclusion is in agreement with recent spectroscopic observations. Rotationally resolved spectroscopic probe of (O2)2 in the slit-nozzle expansion resulted in B0 = 0.095 cm−1, while bandshape analysis of the room-temperature collision-induced absorption in the oxygen fundamental allowed an estimate of Beff ≈ 0.038 cm−1. The role of anisotropy of intermolecular interaction and the formation of various types of metastable dimeric states are discussed.

Electron scattering on excited diatomic molecules in selected rovibrational states

A theoretical method to investigate cross sections of electron scattering for certain excited rovibrational states of diatomic molecules by electron impact is proposed. This method is based on the treatment of the collision as a few-body process, using quantum theory of scattering in few particles system. Comparison of the results of calculation of cross sections of different elastic and inelastic processes with available experimental data and other calculations is presented.

Determination of highly excited rovibrational states for N2O using generalized internal coordinates

Generalized internal vibrational coordinates are optimized and used to describe highly excited vibrational motions in the N2O molecule. These coordinates are defined as the magnitudes of two vectors, which are expressed as linear combinations of the internal displacement vectors and the angle formed between them. They depend on two parameters and contain, as particular cases, valence and orthogonal (Jacobi, Radau, etc.) coordinate systems. The coordinates are optimized by minimizing unconverged variationally computed vibrational energies with respect to the external parameters. A comparison of the optimal internal coordinates derived for N2O with valence and hyperspherical normal coordinates is made. The optimal internal coordinates are also used to determine a new potential energy function for N2O from the observed vibrational frequencies up to 15 000 cm−1 using fully variational calculations. The quality of the adjusted potential energy function is checked by computing vibrational-rotation energy levels and rotational constants for Σ, Π, Δ, Φ, and Γ states and comparing them with the observed values.

Dissociative attachment of electrons to sodium molecules

A method based on the quantum-mechanical theory of collisions in a three-body system is used to calculate the cross sections of the dissociative attachment of electrons to sodium molecules that are in the rovibrational-excited states. The results of calculations are compared to the available experimental data and the published results of other calculations.

Quadrupole Transition Probabilities for the Excited Rovibrational States of H 2

Accurate calculations of the quadrupole moment of H2, carried out with a 494 term variational representation of the electronic eigenfunction, are reported, and the quadrupole transition probabilities connecting all the bound rovibrational levels of H2 are presented.

Intracavity laser absorption spectroscopy of HOCl. II. High overtones, perturbations, and intramolecular dynamics

High resolution spectra of the 4ν1 and 5ν1 OH-stretch overtone and the weak 4ν1+ν2 combination band of transient HO35(37)Cl in the energy range 12 500–16 500 cm−1 have been recorded using ultrasensitive intracavity laser absorption spectroscopy (ICLAS). For this investigation, two different spectrometers, a titanium:sapphire and a dye-jet ICLA spectrometer have been employed. We report line assignments for both isotopomers, refined Dunham parameters, and the spectroscopic constants for the excited rovibrational states. Strong and weak Fermi-type resonances as well as Coriolis interactions at ≈65%–85% of the dissociation energy E0 have been found and the role of dark perturbers is discussed. The dark 2ν1+3ν2+3ν3 state has been analyzed and identified to be the perturber of 3ν1+2ν2. From the detailed analysis of the experimental data the anharmonicity parameters of the asymmetric stretch ν3 are refined. The 5ν1 band at about 85% of E0 has been found to be strongly mixed with the 4ν1+2ν2+ν3 zero order vibrational state, and both states are coupled to other background states by additional (weaker) interactions. The extent and the magnitude of perturbations in all Ka bands of the 5ν1/4ν1+2ν2+ν3 system and additional interactions with other background states may be regarded as the signature of the onset of efficient but restricted intramolecular vibrational energy redistribution (IVR) in the overtone spectrum of HOCl. The intramolecular dynamics of this small molecule after coherent short pulse excitation of the 5ν1 zero order state is discussed in terms of a simple tiers model.

A theoretical study of the valence- and dipole-bound states of the nitromethane anion

The valence- and dipole-bound states of CH3NO−2 are studied at the CCSD(T), HFDFT (B3LYP), and EA-EOMCC levels of theory. At both CCSD(T) and HFDFT levels, we have found a positive valence EA in nice agreement with the experimental data. The binding energy of the dipole-bound electron is about 13 meV according to the EA-EOMCC calculations. Interaction of the valence- and dipole-bound states (DBS) of CH3NO−2 is complicated, since the dipole-bound state exists at the equilibrium geometry of the anion and corresponds to an excited state of the valence-bound anion. Hence, excitations of the valence anionic state could lead to both the detachment of an electron or formation of a DBS, whose geometry is similar to the geometry of the neutral parent. At the equilibrium geometry of the anion, the energies of the dipole-bound and valence states are close to each other. Since typical lifetimes of rovibrational excited states of a DBS are two orders of magnitude higher than the lifetimes of ordinary vibrationally excited states, it might be possible to transform the DBS into the valence ground state under certain experimental conditions.

Intracavity laser absorption spectroscopy of HOCl overtones. I. The 3v1+2v2 band and numbers of vibrational states

The near infrared high-resolution spectra of the a-type transitions of the weak 3v1+2v2 combination band of transient HO35(37)Cl at 12 600 cm−1 has been recorded in an ultrasensitive titanium:sapphire intracavity laser absorption spectrometer (ICLAS). We report line assignments, new and refined anharmonicity parameters, and the spectroscopic constants for the excited rovibrational states of 3v1+2v2. The Fermi resonance perturbations in this five quanta region, where the internal energy of the molecule is already more than 2/3 of the dissociation energy E0, remain localized and they are the exception, while the extent of intermode mixing and thus intramolecular vibrational energy distribution (IVR) seems to be still small. A Dunham expansion is used for band origin predictions and representations of vibrational states N(E) of HO35Cl up to the dissociation threshold. The results are compared with harmonic and anharmonic numbers of states from a recently proposed stretch–bend coupling model.

Dispersed fluorescence spectroscopy of excited rovibrational states in S formaldehyde

Dispersed fluorescence (DF) spectroscopy is used to explore the rovibrational structure of highly excited S0 formaldehyde (H2CO). A narrowband laser excites formaldehyde molecules to a single S1 rovibronic quantum state, and the resulting fluorescence is dispersed with a monochromator. DF spectra of ten vibrational levels with excitation in ν2, the carbon–oxygen stretch, and ν4, the out-of-plane bend, have been recorded, and the effective A, B, and C rotational constants are extracted. Five of the effective A rotational constants and seven of the effective B and C rotational constants are new to the literature. The dependence of these effective rotational constants on vibrational state are both calculated and discussed with regard to both the present and previous experiments. Particular attention is given to the manner in which that the effective A rotational constant depends on increasing excitation in ν4 due to the strong A-axis ν4/ν6 Coriolis interaction. For states where v2 is less than two, quantitatively accurate values for the nonlinear dependence of the A rotational constant on quanta in ν2 and ν4 is achieved by a simultaneous consideration of the strong A-axis ν4/ν6 Coriolis interaction and the 11↔42, 11↔62, and 51↔2161 Fermi interactions.

Rotation-vibrational states of D3+computed using hyperspherical harmonics

Using the RKJK potential surface highly excited rovibrational states of D2H+ were calculated and characterized. Band origins are reported for energies up to 9300 cm-1. Term values of the 11 lowest vibrational states are presented with J upto J = 10 for the vibrational states (v 1,v 2,v 3) = (0,0,0) and (1,0,0),up to J = 8 for (0,1,0) and (0,0,1), up to J = 7 or J = 6 for (0,2,0), (2,0,0) and (0,3,0), and up to J = 4 for the states (0,0,2), (0,1,1), (1,1,0) and (1,0,1). Calculated transition frequencies for the ν1, ν2 and ν3 fundamental bands are compared with experimental data.

Circumventing the Heisenberg principle: A rigorous demonstration of filter-diagonalization on a LiCN model

In a previous paper [J. Chem. Phys. 93, 2611 (1990)] a new method, filter diagonalization, was introduced for extracting highly excited rovibrational states from an arbitrary Hamiltonian, in any desired energy range. In the method, an arbitrary initial wave packet is propagated for a short time and during the propagation a ‘‘short time filter’’ of the wave packet is accumulated at various energies in any desired ‘‘window,’’ yielding a small set of functions which span the eigenfunctions of the Hamiltonian in the desired range. A small Hamiltonian matrix is then evaluated in the filtered-functions basis, to yield the eigenvalues in the desired range. The combination of the time-dependent (TD) propagation with the small matrix diagonalization eliminates the uncertainty-relation limitation associated with a pure TD approach and the large-matrix diagonalization necessary in a purely time-independent approach. In this paper we give the first demonstration of the power of filter diagonalization for a molecular Hamiltonian exhibiting accidental near degeneracies, thereby supplying a stringent test of our approach. A two-dimensional model of LiCN (J=0) is used. Good agreement is established with previous results for high-energy states. For a further check of consistency, we perform a large-scale direct diagonalization of the Hamiltonian, and verify a very-high accuracy even for nearly degenerate levels. Extraction of these levels by a purely TD approach would have necessitated ≊700-fold increase in propagation time.

Infrared multiphoton excitation dynamics of CF3I. I. Populations and dissociation rates of highly excited rovibrational states

Transient detection of I(2P3/2) by resonantly enhanced multiphoton ionization (REMPI) was used to monitor in-pulse and after-pulse dissociation of CF3I excited by infrared (IR) multiphoton absorption. After-pulse reaction is characterized by time-dependent dissociation rate coefficients. The apparent reaction rates increase with increasing laser intensity. These observations are attributed to strong rotational dependencies of the specific dissociation rate constants k(E,J) and to CO2 laser-intensity-dependent rotational distributions of the excited CF3I. The corresponding rotational distributions are reconstructed from the observed experimental time profiles of the reaction rates. In addition to the detection of the I(2P3/2) dissociation product from infrared multiphoton excitation, populations of vibrationally highly excited CF3I* were identified via electronic excitation in the visible, subsequent fast dissociation and REMPI detection of the resulting I(2P1/2). At weak IR laser intensities these vibrational distributions were found to be strongly bimodal. However, the bimodal character weakens with increasing laser intensity, tending towards a single broad distribution at very high laser intensities.

Faraday research article. Why calculate the spectra of small molecules?

Calculations on the bound nuclear motion states of molecules are now making a contribution to many areas of physical science including astrophysics, planetary atmospheres and chemical kinetics. This article discusses the various uses made of ro-vibrational calculations on small, particularly triatomic, molecules. A non-technical theoretical overview compares the three main methods for performing these calculations: the traditional perturbation theory approach, basis set methods using the variational principle and a finite-element approach, the discrete variable representation (DVR). The reasons for maintaining parallel basis set and DVR programs are given. Applications of ro-vibrational calculations to the area of traditional high-resolution spectroscopy, i.e. low-lying states, are discussed. These include proving and developing potential-energy surfaces, predicting and assigning spectra, calculating transition intensities and generating data for the calculation of thermodynamic and emissivity parameters. The links between highly excited ro-vibrational states, reaction dynamics and quantum chaology are discussed and the importance for improved calculations in this energy region outlined.

Rovibrational states of Ar–HCN van der Waals complex: A localized representation calculation

All bound rovibrational states of Ar–HCN and Ar–DCN van der Waals complexes for J=0–10 are calculated, assuming frozen HCN (DCN). The calculations are performed using the recently developed approach for accurate and efficient computation of highly excited rovibrational states of floppy triatomic molecules [M. Mladenović and Z. Bac̆ić, J. Chem. Phys. 93, 3039 (1990)]. Matrix representation of the Hamiltonian in body-fixed Jacobi coordinates is formed by combining the discrete variable representation of the angular coordinate and distributed Gaussian basis for the radial degree of freedom. The coupled low-frequency large amplitude vibrations are treated accurately, without any dynamical approximation. Model 2-D (R,θ) potential surface by Dykstra, having two minima at collinear Ar–HCN and Ar–NCH geometries, is employed. Besides energy levels and wave functions, for each state we calculate expectation values of Jacobi coordinates, 〈R〉 and 〈θ〉, degree of wave function delocalization, and effective rotational constants (for some states). Majority of states of Ar–H/DCN are delocalized over both potential minima. Comparison is made with available experimental data and possible refinements of the present potential surface are briefly discussed.

ChemInform Abstract: Highly Excited Vibration‐Rotation States of Floppy Triatomic Molecules by a Localized Representation Method: The HCN/HNC Molecule.

All rovibrational levels of HCN/HNC up to ∼16 000 cm−1, relative to the HCN minimum, for J=0, 1, 2, have been calculated accurately. All internal degrees of freedom are included in these calculations, performed on the realistic, empirical potential surface by Murrel et al. [J. Mol. Spectrosc. 93, 307 (1982)]. Body‐fixed mass‐scaled Jacobi coordinates are employed, together with the discrete variable representation of the large amplitude motion (LAM) angular coordinate, and a 2‐D distributed Gaussian basis for the radial degrees of freedom. The successive diagonalization–truncation procedure results in a compact matrix representation of the full rovibrational Hamiltonian, allowing accurate and efficient determination of a large number (>350 for J=2, p=0 case) of highly excited LAM rovibrational states of HCN/HNC. This approach is suitable for a broad class of floppy, isomerizing triatomic molecules and van der Waals complexes. In addition to energy levels and wave functions, expectation values of Jacobi co...

Highly excited vibration–rotation states of floppy triatomic molecules by a localized representation method: The HCN/HNC molecule

All rovibrational levels of HCN/HNC up to ∼16 000 cm−1, relative to the HCN minimum, for J=0, 1, 2, have been calculated accurately. All internal degrees of freedom are included in these calculations, performed on the realistic, empirical potential surface by Murrel et al. [J. Mol. Spectrosc. 93, 307 (1982)]. Body-fixed mass-scaled Jacobi coordinates are employed, together with the discrete variable representation of the large amplitude motion (LAM) angular coordinate, and a 2-D distributed Gaussian basis for the radial degrees of freedom. The successive diagonalization–truncation procedure results in a compact matrix representation of the full rovibrational Hamiltonian, allowing accurate and efficient determination of a large number (>350 for J=2, p=0 case) of highly excited LAM rovibrational states of HCN/HNC. This approach is suitable for a broad class of floppy, isomerizing triatomic molecules and van der Waals complexes. In addition to energy levels and wave functions, expectation values of Jacobi coordinates, 〈R〉, 〈r〉, and 〈θ〉, are calculated for most states. The majority of calculated J=1,2 levels lie above the top of the isomerization barrier, and are delocalized to a varying degree over both local minima. Rotation appears to lower the energy threshold for extensive delocalization; for the states with J=1, or 2, it is ∼460–480 cm−1 below that for J=0 states. Moreover, increasing rotational excitation affects significantly the degree of localization of a given state.

Highly excited rovibrational states of small molecules

The use of first principles variational calculations for the calculation of high-lying energy levels, wavefunctions and transition intensities for triatomic molecules is considered. Theoretical developments are considered, including the use of generalized internal coordinates, the use of a two-step procedure for rotationally excited systems and a finite element method known as the discrete variable representation. Illustrative calculations are presented including ones for H 2, LiCN and the Ar-N2 Van der Waals molecule. A first principles ‘rotational’ spectrum of H 2D+ is computed using states up to J = 30. The transition intensities in this spectrum are reproduced accurately in a frozen dipole approximation but are poorly represented by models that involve approximating the wavefunction.

Highly excited rovibrational states using a discrete variable representation: The H+3 molecular ion

A formulation of the rovibrational problem in Jacobi coordinates is presented which employs a discrete variable representation for the angular internal coordinate. Rotational excitation is implemented via a two-step procedure and symmetry (for AB2 systems) included using a computationally efficient method. Energies for the lowest 180 vibrational states of H+3 are presented and their wavefunctions analyzed graphically. J=1←0 excitation energies are presented for the lowest 41 vibrational states. The significance of the regular states in the high-energy regime of H+3 is discussed.

The ion–molecule reactivity of the positive muon molecular ions HeMu+ and NeMu+

Thermal (300 K) ion–molecule reaction rates are measured, using the µSR (muon spin rotation) technique, for the muonated rare gas molecular ions HeMu+ and NeMu+ reacting with NO, O2, N2O, NH3, CF4, C2H4, TMS, and CH3NO2. In almost every case (excepting O2), both charge transfer (ke) and muon transfer (kµ) contribute to the reaction rate. Reaction is believed to occur from ro-vibrational excited states, [HeMu+]* and [NeMu+]*, due to the poor efficiency of He and Ne moderators for collisional deactivation. The total experimental rate constants, kexp = kµ + ke, are generally in excellent agreement with total capture rates predicted by the simple ADO theory, regardless of the degree of internal excitation. Comparisons with literature values for corresponding protonated ion reaction rates with O2 and C2H4 reveal little or no isotope effect, although it is noted that these reactions are dominated by proton transfer, in contrast to the µSR results.