Relaxation effects accompanying core ionization in diatomic molecules

The influence of electronic relaxation on the bond-length charges following inner-shell ionisation in diatomic molecules is studied. CO and N₂ are treated explicitly. Transition operators are used for predicting renormalized vibrational coupling constants and slopes of relaxation energy surfaces.     

On the correlation between bond-length change and vibrational frequency shift in halogen-bonded complexes

The C-Hal (Hal = Cl, Br, or I) bond-length change and the corresponding vibrational frequency shift of the C-Hal stretch upon the C-Hal···Y (Y is the electron donor) halogen bond formation have been determined by using density functional theory computations. Plots of the C-Hal bond-length change versus the corresponding vibrational frequency shift of the C-Hal stretch all give straight lines. The coefficients of determination range from 0.94366 to 0.99219, showing that the correlation between the C-Hal bond-length change and the corresponding frequency shift is very good in the halogen-bonded complexes. The possible effects of vibrational coupling, computational method, and anharmonicity on the bond-length change-frequency shift correlation are discussed in detail.     

Structural dependence of the cohesive-energy, abundancy and bond-length of transition-metal clusters

We calculate the size-dependence of the cohesive-energy, abundancy and average bond-length of small Fe_n- and Ni_n-clusters. A tight-binding Hubbard Hamiltonian in the Hartree-Fock approximation together with the second moment approximation is used. Results for different assumed cluster structures are compared and discussed. In particular we obtain that bcc- like clusters with n = 6 and 15, and fcc-like clusters with n = 5, 7, 13 and 19 are particularly stable, in agreement with experimental observations for Fe_n and Ni_n, respectively. Allowing uniform relaxation for each assumed structure we obtain for small clusters a reduction of the equilibrium bond-length of about 10% with respect to bulk. The role of magnetism for the stability of the clusters and limitations of the present calculations are discussed.     

Vibrational structure of endohedral fullerene Sc3N@C78 (D3h'): evidence for a strong coupling between the Sc3N cluster and C78 cage.

The vibrational structure of the endohedral cluster fullerene Sc(3)N@C(78) is studied by FTIR spectroscopy, Raman spectroscopy and DFT-based quantum chemical calculations. Remarkably good agreement between experimental and calculated spectra is achieved and a full assignment of the Sc(3)N-based vibrational modes is given. Significant differences in the vibrational structure of the endohedral cluster fullerene Sc(3)N@C(78) and the empty, charged C(78) (6-): 5 (D(3h)') are rationalized by the strong coupling between the Sc(3)N cluster and the fullerene cage. This coupling has its origin in a significant overlap of the Sc(3)N and C(78) molecular orbitals, and causes atomic-charge and bond-length redistributions compared to the neutral C(78) and the C(78) (6-) anion. An ionic model is not sufficient to describe the electronic, geometric and vibrational structure of the Sc(3)N@C(78) nitride cluster fullerene.     

Distorted wave calculations of the vibrational relaxation of CO in collision with He atoms

Cross sections are calculated for vibrational relaxation of the CO/He system. The calculations use the exponential distorted wave, the distorted wave and close-coupling techniques for the vibrational motion. Rotational motion is treated with the infinite-order sudden approximation. Good agreement is shown between the distorted wave methods and the close-coupled calculations. Vibrational relaxation rate constants are calculated and compared with experimentally determined values. The distorted wave approximation is shown to provide results of useful accuracy.     

A compact model system for electron–phonon calculations in discotic materials

Electron–phonon coupling underlies the unwanted rapid relaxation of electrically excited states in potential organic solar-cell materials. A compact model for the vibrational dynamics of 2,3,6,7,10,11-hexakishexyloxytriphenylene (HAT6) is derived from the combined use of inelastic neutron scattering (INS) spectroscopy and first-principles calculations. Because this model reproduces the essential features of the vibrational dynamics and electronic structure on the aromatic core of HAT6 it can be used as a basis for future calculations of the relaxation mechanisms of the electronically excited states.     

End-cap effects on vibrational structures of finite-length carbon nanotubes

Vibrational structures of C60-related finite-length nanotubes, C(40+20n) and C(42+18n) (1 < or = n < or = 4), in which n is, respectively, the number of cyclic cis- and trans-polyene chains inserted between fullerene hemispheres, are analyzed from density functional theory (DFT) calculations. To illuminate the end-cap effects on their vibrational structures, the corresponding tubes terminated by H atoms C(20n)H20 and C(18n)H18 (1 < or = n < or = 5) are also investigated. DFT calculations show a broad range of vibrational frequencies for the finite-size nanotubes: high-frequency modes (1100-1600 cm(-1)) containing oscillations along tangential directions (tangential modes), medium-frequency modes (700-850 cm(-1)) whose oscillations are located on the edges or end caps, and low-frequency modes (300-600 cm(-1)) involving oscillations along the radial directions (radial modes). Broadening of the calculated frequencies is due to the number of nodes in the standing waves of normal modes in the finite-size tubes. In the capped tubes, calculated vibrational frequencies are insensitive to the number of chains (n), whereas in the uncapped tubes, most vibrational frequencies change significantly with an increase in tube length. The discrepancy in the size dependency is reasonably understood by their C-C bonding networks; the capped tubes have similar bond-length alternation patterns within the polyene chains irrespective of n, whereas the uncapped tubes have various bond-deformation patterns. Thus, DFT calculations illuminate that the edge effects have strong impacts on the vibrational frequencies in the finite-size nanotubes.     

A new ab initio potential energy surface for studying vibrational relaxation in NO(v) + NO collisions

A new ab initio potential energy surface for the ground state of the NO-NO system has been calculated within a reduced dimensionality model. We find an unusually large vibrational dependence of the interaction potential which explains previous spectroscopic observations. The potential can be used to model vibrational energy transfer, and here we perform quantum scattering calculations of the vibrational relaxation of NO(v). We show that the vibrational relaxation for v = 1 is 4 orders of magnitude larger than that for the related O(2)(v) + O(2) system without having to invoke nonadiabatic mechanisms as had been suggested in the past. For highly vibrationally excited states, we predict a strong dependence of the rates on the vibrational quantum number as has been observed experimentally, although there remain important quantitative differences. The importance of a chemically bound isomer on the relaxation mechanism is analyzed, and we conclude it does not play a role for the values of v considered in the experiment. Finally, the intriguing negative temperature dependence of the vibrational relaxation rate constants observed in experiments was studied using an statistical model to include the presence of many asymptotically degenerate spin-orbit states.     

Vibrational relaxation in SO2

SSH—Tanczos calculations are carried out to estimate the energy transfer probabilities and the slow vibrational relaxation time in SO₂ in the temperature range 300–2000 K. The theoretical results suggest a series process below 1000 K, and a complex series/parallel process above that temperature for the vibrational relaxation in SO₂. The theoretical results are compared with the known experimental data.     

On the correlation between bond-length change and vibrational frequency shift in hydrogen-bonded complexes: a computational study of Y...HCl dimers (Y = N2, CO, BF)

The H-Cl bond-length change and the harmonic vibrational frequency shift of the H-Cl stretch on formation of the linear isoelectronic Y...H-Cl complexes (Y = N(2), CO, BF) have been determined by ab initio computations at different levels of theory. These shifts are in agreement with predictions from a model based on perturbation theory and involving the first and second derivatives of the interaction energy with respect to displacement of the H-Cl bond length from its equilibrium value in the isolated monomer. At the highest level of theory, blue shifts were obtained for BF...HCl and CO...HCl, while red shifts were obtained for FB...HCl, OC...HCl, and N(2)...HCl. These vibrational characteristics are rationalized by considering the balance between the interaction energy derivatives obtained from the perturbative model. The widely believed correlation between the bond-length change and the sign of the frequency shift obtained on complexation is discussed and found to be unreliable.     

Concerted hydrogen exchange tunneling in formic acid dimer

The effect of conformational relaxation on the quantum dynamics of the hydrogen exchange tunneling is studied in the D2h subspace of formic acid dimer. The fully coupled quantum dynamics in up to six dimensions are derived for potential energy hypersurfaces interpolated directly from hybrid density functional calculations with and without geometry relaxation. For a calculated electronic barrier height of 35.0 kJ/mol the vibrational ground state shows a tunneling splitting of 0.0013 cm(-1). The results support the vibrational assignment of Madeja and Havenith [J. Chem. Phys. 2002, 117, 7162-7168]. Fully coupled ro-vibrational calculations demonstrate the compatibility of experimentally observed inertia defects with in-plane hydrogen exchange tunneling dynamics in formic acid dimer.     

Ab initio computation of vibrational relaxation rate coefficients for the collisions of CO2 with helium and neon atoms

Ab initio calculations of rate coefficients are reported for the vibrational relaxation of CO₂ molecules in collision with helium and neon atoms. Self consistent-field computations have been performed to parameterise simple three-dimensional potential energy functions which have been used in vibrational close-coupling, rotational infinite-order-sudden calculations of rate coefficients. Excellent agreement is obtained between the calculated and experimental rate coefficients for the deactivation of the (01₁0) vibrational level in the He + CO₂ system at temperatures of 300 K and above. The ab initio predictions of rate coefficients for relaxation of CO₂ vibrational levels such as (10⁰0) and (02⁰0) should be useful in computer simulations of CO₂ lasers.     

Theoretical studies of solute vibrational energy relaxation at liquid interfaces

Recent advances in the theoretical understanding of solute vibrational energy relaxation at liquid interfaces and surfaces are described. Non-equilibrium molecular dynamics simulations of the relaxation of an initially excited solute molecule are combined with equilibrium force autocorrelation calculations to gain insight into the factors that influence the vibrational relaxation rate. Diatomic and triatomic nonpolar, polar, and ionic solute molecules adsorbed at the liquid/vapor interface of several liquids as well as at the water/CCl(4) liquid/liquid interface are considered. In general, the vibrational relaxation rate is significantly slower (a factor of 3 to 4) at the liquid/vapor and liquid/liquid interface than in the bulk due to the reduced density, which gives rise to a reduced contribution of the repulsive solvent-solute forces on the vibrational mode. The surface effects on the ionic solutes are much smaller (50% or less slower relaxation relative to the bulk). This is due to the fact that ionic solutes at the interface are able to keep part of their solvation shell to a degree that depends on their size. Thus, a significant portion of the repulsive forces is maintained. A high degree of correlation is found between the peak height of the solvent-solute radial distribution function and the vibrational relaxation rate. The relaxation rate at the liquid/liquid interface strongly depends on the location of the solute across the interface and correlates with the change in the density and polarity profile of the interface.     

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.     

Vibrational contributions to static linear and nonlinear optical coefficients: from two-level to two-band systems

The importance of vibrational contributions to the static linear and nonlinear optical coefficients is investigated. We apply the exact sum-over-state (SOS) formulas for polarizabilities and hyperpolarizabilities expressed in terms of vibronic states to a two-level system with a single vibrational mode. The Herzberg–Teller expansion is applied to the SOS formulas including vibrational energy levels without employing the Placzek’s approximation within both the Born–Oppenheimer approximation and electrical and mechanical harmonicities. The results include not only the vibrational contribution from the lattice relaxation expression but also the contribution arising from the higher-order correction terms. Model calculations on a diatomic system with two electronic states show that the contribution of these correction terms is small. Moreover, most of these higher-order terms are negligible in the solid-state limit. In polyacetylene, the contribution of the lattice relaxation expression is much larger than that in the diatomic case. Within the tight-binding approximation, the contribution of the lattice relaxation expression is 44% of the pure electronic contribution for the second hyperpolarizability.     

Experimental and theoretical study of the rovibrational relaxation of CH4 and CD4 by Ar

Experimental results are reported for the vibrational relaxation of the lowest bending modes of CH₄ and CD₄ br Ar in the temperature range of 140–376 K. Theoretical calculations are carried out in the framework of the semiclassical coupled-states approximation using asymptotic expressions of (3j) symbols and a first-order perturbation treatment. The confrontation of experimental and theoretical rate constants confirms the crucial role of rotational energy transfer upon the vibrational relaxation transfer.     

Vibrational energy relaxation of large-amplitude vibrations in liquids

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.     

A modified landau-teller model for vibrational relaxation of small molecular ions

We report a new interpretation of vibrational relaxation of molecular ions based on a modified Landau-Teller model. Distorted wave calculations show the relaxation to be dominated by repulsive forces. The ion-induced-dipole forces alter the steepness of the repulsive force and increase the effective collision energy. Incorporating these modifications into the Landau-Teller model correctly predicts the observed dependence of the cross sections on collision energy.     

Spin-Phonon Coupling and Slow-Magnetic Relaxation in Pristine Ferrocenium

We report the spin dynamic properties of non-substituted ferrocenium complexes. Ferrocenium shows a field-induced single-molecule magnet behaviour in DMF solution while cobaltocene lacks slow spin relaxation neither in powder nor in solution. Multireference quantum mechanical calculations give a non-Aufbau orbital occupation for ferrocenium with small first excitation energy that agrees with the relatively large measured magnetic anisotropy for a transition metal S=1/2 system. The analysis of the spin relaxation shows an important participation of quantum tunnelling, Raman, direct and local-mode mechanisms which depend on temperature and the external field conditions. The calculation of spin-phonon coupling constants for the vibrational modes shows that the first vibrational mode, despite having a low spin-phonon constant, is the most efficient process for the spin relaxation at low temperatures. In such conditions, vibrational modes with higher spin-phonon coupling constants are not populated. Additionally, the vibrational energy of this first mode is in excellent agreement with the experimental fitted value obtained from the local-mode mechanism.