Vibrational lifetimes and intramolecular energy randomisation of polyatomic molecules in liquids

Transient experiments with picosecond laser pulses give valuable information on the dynamic properties of polyatomic molecules in the electronic ground state. In small molecules the decay of vibrational energy occurs via individual lower energy states; in large molecules the experimental data support a statistical model.     

Vibrational relaxation induced population inversions in laser pumped polyatomic molecules

Conditions for population inversion in laser pumped polyatomic molecules are described. For systems which exhibit metastable vibrational population distributions [slow vibration—translation/rotation (V—T/R) relaxation], large, long lived inversions are possible even when the vibrational modes are strongly coupled by rapid collisional vibration—vibration (V—V) energy transfer. Overtone states of a hot mode are found to invert with respect to fundamental levels of a cold mode even at V—V steady state. Inversion persists for a V—T/R relaxation time. A gain of 4 m^?1 for the 2v₃ → v₂ transition in CH₃F (λ ≈ 15.9 μ) was found assuming a spontaneous emission lifetime of 10 s for this transition. General equations are derived which can be used to determine the magnitude of population inversion in any laser pumped, vibrationally metastable, polyatomic molecule. A discussion of factors controlling the population maxima of different vibrational states in optically pumped, V—V equilibrated metastable polyatomics is also given.     

Vibrational relaxation by collision in polyatomic molecules

A model of a harmonic oscillator with friction is used to discuss the conversion of translational energy to vibrational by collision of an atom with a polyatomic molecule. It is shown that adiabatic conversion implies that E ² may substantially exceed the value calculated, neglecting the interaction of the bond with the rest of the molecule.     

Vibrational spectra of polyatomic molecules assisted by quantum thermal baths

We assess the performance of colored-noise thermostats to generate quantum mechanical initial conditions for molecular dynamics simulations, in the context of infrared spectra of large polyatomic molecules. Comparison with centroid molecular dynamics simulations taken as reference shows that the method is accurate in predicting line shifts and band widths in the ionic cluster (NaCl)(32) and in the naphthalene molecule. As illustrated on much larger polycyclic aromatic hydrocarbons, the method also allows fundamental spectra to be evaluated in the limit of T = 0, taking into account anharmonicities and vibrational delocalization.     

Changes of vibrational lifetimes with minor structural modification of small polyatomic molecules

Substantial changes of population lifetimes of CH-stretching modes are observed when two atoms are exchanged in CH₂CCl₂ to form trans CHClCHCl and when three deuterons are substituted in C₆H₆ to form 1,3,5.-C₆H₃D₃. The measured lifetimes are in good agreement with estimates based on Fermi resonance-mixing which is inferred from infrared and Raman spectra.     

Vibrational excitation and relaxation of five polyatomic molecules in an electrical discharge

Vibrational excitation and relaxation of five linear polyatomic molecules, OCS, OC3S, HC3N, HC5N, and SiC2S, have been studied by Fourier transform microwave spectroscopy in a supersonic expansion after the application of a low-current dc electric discharge. For each chain, the populations in bending and stretching modes have been characterized as a function of the applied discharge current; for stable OCS and HC3N, vibrational populations were studied as well in the absence of a discharge. With no discharge present the derived vibrational temperatures are slightly below T, the temperature of the gas before the supersonic expansion (i.e., 300 K). In the presence of the discharge, vibrational excitation occurs via inelastic collisions with the electrons and the vibrational temperatures rise as the applied current increases. Global vibrational relaxation is governed by rapid vibration-vibration (VV) energy transfer and slow vibration-translation (VT) energy transfer. The latter process is rate-determining and depends primarily on the wave number of the vibration. Vibrational modes with wave numbers near and below kT/hc (where T = 300 K and kT/hc-210 cm(-1)) are efficiently cooled by VT transfer because a sufficient number of collisions occur in the initial stages of the supersonic expansion. Vibrational modes with wave numbers around 450 cm(-l) appear to be inefficiently cooled in the molecular beam; at these energies VV and VT rates are probably comparable. For high-frequency vibrations, VV energy transfer dominates. For the longer chains OC3S and HC5N, higher-lying modes are generally not detectable and vibrational temperatures of most lower-lying modes were found to be lower than those of OCS and HC3N, suggesting that as the size of the molecules increases, intermode VV transfer becomes more efficient, plausibly due to the higher density of vibrational levels. New high resolution spectroscopic data have been obtained for several vibrationally excited states of OC3S, HC3N, and HC5N. Rotational lines of the 13C and 15N isotopic species of HC5N have been measured, yielding improved rotational and centrifugal distortion constants; 14N nitrogen quadrupole coupling constants for the isotopic species of HC5N with 13C have been determined for the first time.     

Vibrational energy relaxation of small molecules and ions in liquids

A theoretical/computational framework for determining vibrational energy relaxation rates, pathways, and mechanisms, for small molecules and ions in liquids, is presented. The framework is based on the system—bath coupling approach, Fermi’s golden rule, classical time-correlation functions, and quantum correction factors. We provide results for three specific problems: relaxation of the oxygen stretch in neat liquid oxygen at 77 K, relaxation of the water bend in chloroform at room temperature, and relaxation of the azide ion anti-symmetric stretch in water at room temperature. In each case, our calculated lifetimes are in reasonable agreement with experiment. In the latter two cases, theory for the observed solvent isotope effects illuminates the relaxation pathways and mechanisms. Our results suggest several propensity rules for both pathways and mechanisms.     

Vibrational energy relaxation of polyatomic molecules in liquid solution via the linearized semiclassical method

Vibrational energy relaxation (VER) of polyatomic, as opposed to diatomic, molecules can occur via different, often solvent assisted, intramolecular and/or intermolecular pathways. In this paper, we apply the linearized semiclassical (LSC) method for calculating VER rates in the prototypical case of a rigid, symmetrical and linear triatomic molecule (A-B-A) in a monatomic liquid. Starting at the first excited state of either the symmetric or asymmetric stretches, VER can occur either directly to the ground state or indirectly via intramolecular vibrational relaxation (IVR). The VER rate constants for the various pathways are calculated within the framework of the Landau-Teller formalism, where they are expressed in terms of two-time quantum-mechanical correlation functions. The latter are calculated by the LHA-LSC method, which puts them in a "Wignerized" form, and employs a local harmonic approximation (LHA) in order to compute the necessary multidimensional Wigner integrals. Results are reported for the LHL/Ar model of Deng and Stratt [J. Chem. Phys. 2002, 117, 1735], as well as for CO(2) in liquid argon and in liquid neon. The LHA-LSC method is shown to give rise to significantly faster VER and IVR rates in comparison to the classical treatment, particularly at lower temperatures. We also find that the type and extent of the quantum rate enhancement is strongly dependent on the particular VER pathway. Finally, we find that the classical and semiclassical treatments can give rise to opposite trends when it comes to the dependence of the VER rates on the solvent.     

Ultrashort vibrational population lifetime of large polyatomic molecules in the vapor phase

A vibrational mode of a polyatomic molecule in the vapor phase is first excited by an ultrashort infrared pulse. The degree of excitation is monitored by a delayed probe pulse which promotes the excited molecules to the fluorescent first singlet state. The lifetime of an overtone at 5950 cm^?1 of coumarin 6 is found to be 4 ± 1 ps in the vapor phase at 1 torr.     

EPR breakup of polyatomic molecules

We explore the EPR experiment in the case of the breakup of a polyatomic molecule into two mutually entangled fragments. We give a derivation based on the properties of the dissociated wave function that no information is transferred, not even at a speed smaller than the speed of light, from one entangled partner to the other concerning its measurement or lack thereof. We also explain experiments that show that each separated fragment can retain coherences induced in its parent molecule by a broad band laser pulse, regardless of whether a measurement has been performed on its entangled partner.     

Model calculation on the pump-probe measurement of ultrafast electronic population decay in polyatomic molecules

We consider the common situation of strong vibronic coupling of an optically bright (in absorption from the ground state) excited electronic state to a lower-lying dark electronic state in a polyatomic molecule. It is shown that for sufficiently short pump and probe laser pulses a time-resolved experiment measures the total time-dependent population probability P(t) of the bright state. For a realistic model problem (representing the three lowest electronic states of the benzene cation) a conical intersection of the potential energy surfaces of the bright and the dark state causes an ultrafast initial decay of P(t) on a femtosecond time scale, followed by quasiperiodic recurrences. These recurrences show up as femtosecond quantum beats in the time-resolved pump-probe signal. The beating frequency is related to the vibrational frequency of the dominant accepting mode of the system.     

Valence-shell calculations on polyatomic molecules

Calculations using the CNDO/2, the Extended Hückel (EH) method, and an iterative Extended Hückel (IEH) method are reported for HF, H₂O, NH₃, CO, H₂CO, HCONH₂, HCOOH, HCOF and sydnone. For the IEH method, it is shown that if the dipole moment is calculated by including the atomic dipole moment and the overlap moment (homopolar dipole) as well as the term from the Mulliken populations, then, except for carbon monoxide, the IEH method gives results in good agreement with experiment. The non-iterative EH method predicts dipole moments that are much too high. For molecules with dipole moments smaller than 3 Debyes, the IEH and CNDO/2 methods give similar results, but for molecules with higher dipole moments (formamide and sydnone), the CNDO/2 method gives better agreement with experiment. Comparison of the calculations on sydnone with those on other carbonyl compounds suggests that sydnone is best represented as a resonance stabilized azo-methine imine rather than as a meso-ionic or betaine type compound.

---

Zusammenfassung Rechnungen mittels des CNDO/2- und des erweiterten Hückelverfahrens (iterativ und nichtiterativ) werden für HF, H₂O, NH₃, CO, H₂CO, HCONH₂, HCOOH, HCOF und Sydnon vorgelegt. Im Fall des iterativen Hückelverfahrens zeigt sich, daß die Dipolmomente (außer für CO) gut mit dem Experiment übereinstimmen, wenn man die atomaren Dipol- und die Überlappungsmomente sowie die Terme der Mulliken-Population berücksichtigt. Dagegen sind die entsprechenden Werte des nichtiterativen Verfahrens viel zu groß. Für Moleküle mit Dipolmomenten kleiner als 3 Debye liefert das CNDO/2-Verfahren ähnliche Werte wie die iterative Hückelmethode, für Moleküle mit größeren Dipolmomenten dagegen bessere Resultate. Vergleicht man die Rechnungen für Sydnon mit denen für andere Carbonylverbindungen, so scheint es, daß man es besser als resonanzstabilisiertes Azomethinimin und nicht als Betain auffassen sollte.

---

Résumé HF, H₂O, NH₃, CO, H₂CO, HCONH₂, HCOOH, HCOF et la Sydnone on été calculées en utilisant les méthodes CNDO/2, Hückel étendu (EH) et Hückel étendu itératif (IEH). On montre que, pour la méthode IEH, si l'on calcule le moment dipolaire en incluant le moment dipolaire atomique et le moment de recouvrement (dipôle homopolaire) ainsi que le terme provenant des populations de Mulliken, les résultats obtenus sont en bon accord avec l'expérience sauf pour l'oxyde de carbone. La méthode EH non itérative donne des moments dipolaires trop élevés. Pour les molécules de moment inférieur à 3 Debyes, IEH et CNDO/2 donnent des résultats similaires, mais pour les molécules à moments plus élevés (formamide et sydnone) la méthode CNDO/2 donne un meilleur accord avec l'expérience. La comparaison des calculs sur la sydnone avec ceux sur les autres composés carbonylés suggère que la sydnone est mieux représentée comme une azo-méthine imine stabilisée par résonance que comme un composé de type «méso-ionique» ou bétaïnique.

---

---

This work was supported by Grant No. MH-12951-02 from the National Institutes of Health, Bethesda, Maryland, USA.

---

NASA Research Trainee.     

Cold collisions of complex polyatomic molecules

We introduce a method for classical trajectory calculations to simulate collisions between atoms and large rigid asymmetric-top molecules. We investigate the formation of molecule-helium complexes in buffer-gas cooling experiments at a temperature of 6.5 K for molecules as large as naphthalene. Our calculations show that the mean lifetime of the naphthalene-helium quasi-bound collision complex is not long enough for the formation of stable clusters under the experimental conditions. Our results suggest that it may be possible to improve the efficiency of the production of cold molecules in buffer-gas cooling experiments by increasing the density of helium. In addition, we find that the shape of molecules is important for the collision dynamics when the vibrational motion of molecules is frozen. For some molecules, it is even more crucial than the number of accessible degrees of freedom. This indicates that by selecting molecules with suitable shape for buffer-gas cooling, it may be possible to cool molecules with a very large number of degrees of freedom.     

Vibrational lifetimes of molecular adsorbates on metal surfaces

We report density functional theory calculations of electron-hole pair induced vibrational lifetimes of diatomic molecules adsorbed on metal surfaces. For CO on Cu(100), Ni(100), Ni(111), Pt(100), and Pt(111), we find that the C-O internal stretch and the bending modes have lifetimes in the 1-6 ps range, and that the CO-surface stretch and the frustrated translational modes relax more slowly, with lifetimes >10 ps for all cases except CO on Ni(111). This strong mode selectivity confirms earlier calculations for CO on Cu(100) and demonstrates that the trends carry over to other metal substrates. In contrast, for NO adsorbed on Pt(111), whereas we still find that the bending mode has the shortest lifetime, about 1.3 ps, we predict the other three modes to have almost equal lifetimes of 8-10 ps. Similarly, for CN adsorbed on Pt(111), we calculate that the internal stretching and molecule-surface stretching modes have approximately equal lifetimes of about 15 ps. Our results are in reasonable agreement with experiment, where available. We discuss some of the underlying factors that may contribute to the observed mode selectivity with adsorbed CO and the altered selectivity with NO and CN.     

Potential energy functions of polyatomic molecules

A direct method is proposed for determining polyatomic potential energy functions, expressed in terms of normal coordinates, which yield a given set of vibrational excitation energies. The method is a modification of the semiclassical technique for computing vibrational energy levels of Percival and Pomphrey. The technique is used to derive potential functions for the NO₂, SO₂ and ClO₂ molecules. With these potentials twenty two higher vibrational excitations energies have been predicted for these molecules and these results differ from the experimental values by at most 3 cm^?1. The computed potential functions are not unique despite the apparent accuracy of the vibrational energy levels. Comparison with the RKR method indicates that the present method must be extended to include rotational perturbations.     

Low-energy dissociative recombination in small polyatomic molecules

Indirect dissociative recombination of low-energy electrons and molecular ions often occurs through capture into vibrationally excited Rydberg states. Properties of vibrational autoionization, the inverse of this capture mechanism, are used to develop some general ideas about the indirect recombination process, and these ideas are illustrated by examples from the literature. In particular, the Δv = -1 propensity rule for vibrational autoionization, i.e., that vibrational autoionization occurs by the minimum energetically allowed change in vibrational quantum numbers, leads to the prediction of thresholds in the dissociative recombination cross sections and rates at the corresponding vibrational thresholds. Capture into rotationally excited Rydberg states is also discussed in terms of recent low-temperature studies of the dissociative recombination of H(3)(+).