Anharmonicity in rotational and vibrational excitation of H2 by Li+ collisions

Integral cross sections for pure rotational and vibrational-rotational excitation of H₂(X¹Σ⁺_g) by Li⁺(¹S) impact are computed by close-coupling methods at 0.2, 0.6, and 1.2 eV in the c.m. system using vibrational functions that are numerical solutions of the one-dimensional radial Schrödinger equation for harmonic, Morse, and adiabatically corrected Kolos-Wolniewicz (KW) potential functions. Comparison of results employing KW and Morse functions shows excellent agreement for all transitions studied. Findings using harmonic oscillator functions, however, differ noticeably from KW and Morse values for vibrational (0 → 1) and very large rotational (Δj = 10) transitions, but are satisfactory for lower order (0 → 2, 4, 6, 8) rotational transitions.     

Tests of semiclassical treatments of vibrational-translational energy transfer collinear collisions of helium with hydrogen molecules

Three kinds of semiclassical theory are tested against quantum mechanical results for vibrational transition probabilities and average vibrational energy transfers in collinear collisions of atoms with harmonic and Morse vibrators for the He-H₂ mass combination. The interaction potential is assumed to be a repulsive exponential function with an exponential parameter which is realistic for He-H₂ collisions. The energy range studied is total energies of 2–8 in units of ?ω_e. The uniform semiclassical approximations of classical S matrix theory are tested only for classically allowed transitions, i.e., for transition probabilities greater than about 0.2. They are accurate quantitatively for both harmonic and Morse vibrators. The integral expressions of classical S matrix theory are found to be quantitatively accurate for classically allowed and weakly classically forbidden transitions, i.e., for transition probabilities greater than about 0.01–0.05, and to be unreliable for strongly classically forbidden transitions. Quasiclassical trajectory methods yield qualitatively accurate results only for classically allowed transitions but the phase-averaged energy transfer in quasiclassical collisions may be accurate even when classically forbidden transition probabilities are important for the calculation of the average energy transfer. Forced quantum oscillator methods using a classical path whose initial velocity is the average of the initial and final velocities corresponding to the transition of interest are accurate for transition probabilities as small as 4 × 10^?8 for harmonic vibrators but do not seem to accurately account for the effect of anharmonicity.     

Time-dependent quantum simulations of FH2 photoelectron spectra on new ab initio potential energy surfaces for the anionic and the neutral species

The photoelectron spectra (`transition state spectra') of FH₂⁻ generated experimentally from para- and normal-H₂ are simulated on new ab initio potential energy surfaces using standard quantum time-dependent wavepacket techniques, and compared directly to experimental spectra. Agreement between theory and experiment is improved compared to earlier simulations. Two factors are shown to contribute to this success: (1) the anharmonicity of the exact vibrational wavefunctions on a new ab initio surface for the anion and (2) a new spin–orbit correction applied to the ab initio surface for neutral FH₂. Possible reasons for the small remaining discrepancies are investigated and discussed. Finally, predictions are given for spectra obtainable in future high-resolution experiments of this system.     

Non-radiative transitions. I. S1 ⇝ S0 internal conversion calculations in benzene and deuterobenzene

Non-radiative rate calculations for the S₁ ⇝ S₀ transition are presented. Complete vibrational basis sets are used. A Morse oscillator potential is assumed, for both the ν₁ and ν₂ vibrations. It is shown that the ν₁ potential has a dominant influence on the excess energy behaviour of the rates similar to that of the ν₂. The increase of the normalized non-radiative rate curves with excess energy is consistent with experimental results. A comparison is made with the non-radiative rates determined using the local-mode approximation for the CH- and CD-stretch vibrations.     

Interpretation of resonance raman excitation profiles of iodine in chloroform

The observed Raman excitation profiles of iodine in chloroform are analysed in Terms of Morse potentials in the ground and excited states. It is shown that excitation profiles and absorption spectra peak at different frequencies due to the anharmonicity of the vibrations and that the vibrational potential in the B ³ν_o+u state is very sensitive to solvent interactions.     

An improved anharmonic force field for SF6 which includes FF nonbonded interactions

An anharmonic force field for SF₆ in which nonbonded FF interactions are explicitly included has been explored. The FF interaction force constants were modeled with a Lennard—Jones potential using values of the parameters transfered from quadratic force-constant calculations. A Morse function was used to model the anharmonicity in the valence-bond stretching coordinates. The parameters of the model have been adjusted by least squares to some of the available experimental data and have been used to predict energies of excited vibrational states in the v₃ manifold.     

Self-consistent potential energy curves for the A1Σ+ and X1Σ+ states of isotopic cesium hydrides

From the spectroscopic experimental data available in the literature we have determined the mass-reduced Dunham coefficients for the A¹Σ⁺ ↔ X¹Σ⁺ system of the isotopic species CsH and CsD. Based upon these results, for both ground and excited states of cesium hydride and deuteride we report new hybrid rotationless potential energy curves (PMO-RKR-van der Waals) up to the dissociation. As a consistency check on the accuracy of the potentials the eigenvalues were calculated by direct numerical integration of the radial Schrödinger equation and found to agree within the rms error 0.39 cm⁻¹ (X¹Σ⁺) and 0.41 cm⁻¹ (A¹Σ⁺) with the experimental vibrational energies. From the wavefunctions, the rotational constants B_υ, centrifugal distortion terms D_υ, H_υ and L_υ, Franck—Condon factors, and probability density distributions were obtained. The probability density distributions for the lowest vibrational levels of the A¹Σ⁺ show an anharmonicity associated with the anomalous behavior of that state.     

The structure of linear SiCC: An ab initio SCF CI study including vibrational effects

Large-scale SCF CI calculations have been performed for the ground ¹Σ⁺ state of linear SiCC. The calculation includes up to quadruple excitations in the valence space plus all single and double excitations from the valence localized orbitals of the single HF configuration. Vibrational wavefunctions have been derived from the CI potential surface. Vibrational frequencies including anharmonicity corrections are calculated together with the zero-point vibrational correction to the rotational constant. The large dipole moment, 4.62 D, should make this molecule suitable for radioastronomic searches.     

Applications of an adiabatic rotational model to the Ar…O2 van der Waals molecule

In this paper a separation of vibrational and rotational motions is applied to describe the metastable levels of the ArO₂ van der Waals molecule. The potential energy surface is written as a sum of atom—atom pairwise Morse functions, the parameters being obtained by fitting the potential of Pirani and Vecchiocattivi at the equilibrium configuration. The results agree fairly well with experimental data about infrared absorption, assuming a J = 2 → 1 transition, where J is the quantum number associated to the total angular momentum of the complex. Also, close coupling three-dimensional calculations about the ArO₂ collision show a good agreement with some energies previously calculated. The widths for rotational predissociation have been estimated by this procedure to be of the order of 1 cm^?1.     

The A1Σ+-X1Σ+ band system of the KH and KD molecules

The molecular constants of the A¹Σ⁺ and X¹Σ⁺ states of the KH and KD molecules have been determined using mass relations correspondent to a normal isotope shift. For the calculation we have used data of the laser-induced fluorescence spectrum by the Ar⁺ 4881 Å exciting line photographed in our laboratory, as well as previous data presented by other authors. From the spectroscopic terms, quantum-mechanical PMO-RKR-van der Waals hybrid potentials have been generated. Numerical calculations for the A¹Σ⁺ and X¹Σ⁺ states of the KH and KD species are comapred with quantum-mechanical values obtained by numerical solution of the radial Schrödinger equation. Vibrational wavefunctions appropriate to the potential curves yield values of E_υ and B_υ which are in close agreement with the experimental results. The probability distribution functions and Franck-Condon factors for the A¹Σ⁺ ↔ X¹Σ⁺ band system have also been determined. It is observed that the anomalous behaviour of the A state is clearly revealed with a changed anharmonicity for the lowest vibrational levels.     

Time-dependent close coupling for vibrational excitation in three dimensions: Application to H+ - H2

Impact parameter calculations for the non-reactive H⁺ + H₂ (n_i = 0) → H⁺ + H₂ (n_f) collision are reported for energies 10 eV ? E_cm ? 200 eV describing the rotational motion of the molecule in the sudden limit. The time-dependent Schrödinger equation for the vibrational motion has been solved by close coupling techniques expanding the vibrational wavefunction into both harmonic and numerically exact H₂ bound states. The convergence in vibrational basis sets, where up to six vibrational levels are considered, becomes worse with decreasing energy and increasing inelasticity. Furthermore, the harmonic wavefunctions are not suitable over a large range of energies to calculate proper cross sections. The various integral and differential cross sections have been compared with the classical results of Giese and Gentry.     

The vibrational energy manifold of the lowest lying bending mode of tricarbon oxide sulfide,OCCCS,as determined by relative intensity measurements

The determination of a precise vibrational energy level scheme for the two-dimensional bending mode of tricarbon oxide sulfide (3-thioxo-1,2-propadiene-1-one), OCCCS, has been carried out by relative intensity measurements of rotational transitions up to the seventh excited vibrational state of ν₇. The harmonic wavenumber ω₇ was determined to be 84.50 ± 0.63 cm^?1 while the anharmonicity constant χ₇₇ was found to be ?0.62 ± 0.11 cm^?1, respectively. A linear dependence of the expectation value of the electric dipole moment on the vibrational quantum number υ₇ was found. All results confirm that in O CCCS the potential function describing the two-dimensional oscillator of ν₇ is very harmonic without a perturbing barrier to linearity as was found in the case of OCCCO.     

Effects of anharmonicity on nonadiabatic electron transfer: a model

The effect of anharmonicity in the intramolecular modes of a model system for exothermic intramolecular nonadiabatic electron transfer is probed by examining the dependence of the transition probability on the exoergicity. The Franck-Condon factor for the Morse potential is written in terms of the Gauss hypergeometric function both for a ground initial state and for the general case, and comparisons are made between the first-order perturbation theory results for transition probability for harmonic and Morse oscillators. These results are verified with quantum dynamical simulations using wave-packet propagations on a numerical grid. The transition-probability expression incorporating a high-frequency quantum mode and low-frequency medium mode is compared for Morse and harmonic oscillators in different temperature ranges and with various coarse-graining treatments of the delta function from the Fermi golden rule expression. We find that significant deviations from the harmonic approximation are expected for even moderately anharmonic quantum modes at large values of exoergicity. The addition of a second quantum mode of opposite displacement negates the anharmonic effect at small energy change, but in the inverted regime a significantly flatter dependence on exoergicity is predicted for anharmonic modes.     

Vibrational corrections to the charge and momentum densities of H2

Vibrational corrections to the charge and momentum densities of H₂ are calculated using the Wang wavefunction and various expressions for the dependence of the effective nuclear charge on the interatomic distance. Both harmonic oscillator and Morse potentials are employed for the vibrational wavefunctions, and excited as well as ground vibrational states are considered. The corrections to the momentum density, though considerably smaller than the charge density corrections, appear to be somewhat more sensitive qualitatively to the choice of both nuclear and electronic wavefunctions.     

Intramolecular vibrational redistribution following optical excitation

We study the time-dependence of vibrational redistribution following the excitation of a zero-order harmonic state. Two models are considered: (i) the (unphysical) case of a unique anharmonic coupling matrix element gives rise to very strong coherence effects, resulting in a very slow redistribution, at the time scale of the recurrence time 2 π?, characteristic of the manifold; (ii) on the contrary, a random distribution of the coupling matrix elements results into a redistribution rate; Δ_a = 2 π? ΔV²_a — where ΔV²_a is the variance of the distribution — with no influence of its average value. This last model is extended to the case of an initial excitation of mixed states which result from a selective coupling of a radiative state with some vibronic states of a non-radiative manifold. The experimental results available in the literature are reviewed; redistribution following an optical excitation of large molecules, with a vibrational excess energy as high as 5000 to 10000 cm^?1, is generally a slow process (≤ 10⁷ s^?1), in contrast with vibrational relaxation in the condensed phases.     

The r-centroid approximation and molecular transitions

The implications of the r-centroid approximation on vibrational transition integrals are explored with reference to simple harmonic oscillator wavefunctions. It is quantitatively established for molecular bands of low vibrational quantum number that the existence of a localised well-developed uncancelled peak in the wavefunction product is necessary for the approximation to hold well.     

Investigations of nuclear dynamics of LaI<Subscript>3</Subscript> molecule. I. Potential functions of normal vibrations in harmonic and anharmonic approximations

The potential energy surface of the LaI₃ molecule is scanned along the normal coordinate by a B3LYP/SDD, SDD method. It is shown that a nonplanar ν₂(A ₂″) vibrational potential function is most anharmonic. The effect of anharmonicity on the root mean square amplitudes of vibrations and the vibrational molecule spectrum is stated.     

Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.     

Anharmonicity of a molecular oscillator

The phenomenon of anharmonicity has been proved to be an effect of coupling between the change of nuclear positions in molecular vibrations ( Q ) and the electronic degrees of freedom as represented by the chemical potential (μ) at constant number of electrons (N). The coupling parameters have well‐founded meaning in the conceptual density functional theory (DFT), first approximations to their numerical values have recently become available. The effect of coupling between normal vibrational modes also appears to be the direct consequence of the electron‐nuclear coupling. To show the pure anharmonic effect, calculations for a collection of diatomic molecules have been presented. The anharmonicity, described in the present work as d³E/d Q ³ ≠ 0, has been proved to be the intrinsic property of every oscillating molecular system. A small anharmonic contribution exists even for the “strong harmonic” oscillator, when for the force constant k both a = (?k/? Q )_N = 0 and λ = (?k/?N) _Q = 0. The latter derivative of the force constant appears to be primary factor determining the anharmonic property of a molecule. An estimate of its values has been provided from the experimental data on the anharmonicity of diatomic molecules. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004