Asymmetric Isotopomers Research Articles

Efficient Method for an Approximate Treatment of the Coriolis Effect in Calculations of Quantum Dynamics and Spectroscopy, with Application to Scattering Resonances in Ozone.

A numerical approach is developed to capture the effect of rotation-vibration coupling in a practically affordable way. In this approach only a limited number of adjacent rotational components are considered to be coupled, while the couplings to other rotational components are neglected. This partially coupled (PC) approach permits to reduce the size of Hamiltonian matrix significantly, which enables the calculations of ro-vibrational states above dissociation threshold (scattering resonances) for large values of total angular momentum. This method is employed here to reveal the role of the Coriolis effect in the ozone formation reaction at room temperature, dominated by large values of total angular momentum states, on the order of J = 24 and 28. We found that, overall, the effect of ro-vibrational coupling is not minor for large J. Compared to the results of symmetric top rotor approximation, where the ro-vibrational coupling is neglected, we found that the widths of scattering resonances, responsible for the lifetimes of metastable ozone states, remain nearly the same (on average), but the number of these states increases by as much as 20%. We also found that these changes are nearly the same in symmetric and asymmetric ozone isotopomers 16O18O16O and 16O16O18O. Therefore, based on the results of these calculations, the Coriolis coupling does not seem to favor the formation of asymmetric ozone molecules and thus cannot be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes.

Four Isotope-Labeled Recombination Pathways of Ozone Formation.

A theoretical approach is developed for the description of all possible recombination pathways in the ozone forming reaction, without neglecting any process a priori, and without decoupling the individual pathways one from another. These pathways become physically distinct when a rare isotope of oxygen is introduced, such as 18O, which represents a sensitive probe of the ozone forming reaction. Each isotopologue of O3 contains two types of physically distinct entrance channels and two types of physically distinct product wells, creating four recombination pathways. Calculations are done for singly and doubly substituted isotopologues of ozone, eight rate coefficients total. Two pathways for the formation of asymmetric ozone isotopomer exhibit rather different rate coefficients, indicating large isotope effect driven by ΔZPE-difference. Rate coefficient for the formation of symmetric isotopomer of ozone (third pathway) is found to be in between of those two, while the rate of insertion pathway is smaller by two orders of magnitude. These trends are in good agreement with experiments, for both singly and doubly substituted ozone. The total formation rates for asymmetric isotopomers are found to be somewhat larger than those for symmetric isotopomers, but not as much as in the experiment. Overall, the distribution of lifetimes is found to be very similar for the metastable states in symmetric and asymmetric ozone isotopomers.

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone.

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational-vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric (18O16O18O) and asymmetric (18O18O16O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric (16O18O16O) and asymmetric (16O16O18O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone.

Several alternative methods for the description of the interaction between rotation and vibration are compared and contrasted using hyperspherical coordinates for a triatomic molecule. These methods differ by the choice of the z-axis and by the assumption of a prolate or oblate rotor shape of the molecule. For each case, a block-structure of the rotational-vibrational Hamiltonian matrix is derived and analyzed, and the advantages and disadvantages of each method are made explicit. This theory is then employed to compute ro-vibrational spectra of singly substituted ozone; roughly, 600 vibrational states of 16O18O16O and 16O16O18O isomers combined, with rotational excitations up to J = 5 and both inversion parities (21600 coupled ro-vibrational states in total). Splittings between the states of different parities, so-called K-doublings, are calculated and analyzed. The roles of the asymmetric-top rotor term and the Coriolis coupling term are determined individually, and it is found that they both affect these splittings, but in the opposite directions. Thus, the two effects partially cancel out, and the residual splittings are relatively small. Energies of the ro-vibrational states reported in this work for 16O18O16O and 16O16O18O are in excellent agreement with literature (available for low-vibrational excitation). New data obtained here for the highly excited vibrational states enable the first systematic study of the Coriolis effect in symmetric and asymmetric isotopomers of ozone.

Influence of the Coriolis effect on the properties of scattering resonances in symmetric and asymmetric isotopomers of ozone.

Scattering resonances above dissociation threshold are computed for four isotopically substituted ozone species: 16O18O16O, 16O16O18O, 18O16O18O and 16O18O18O, using a variational method with accurate treatment of the rotation-vibration coupling terms (Coriolis effect) for all values of the total angular momentum J from 0 to 4. To make these calculations numerically affordable, a new approach was developed which employs one vibrational basis set optimized for a typical rotational excitation (J,Λ), to run coupled rotation-vibration calculations at several desired values of J. In order to quantify the effect of Coriolis coupling, new data are contrasted with those computed using the symmetric-top rotor approximation, where the rotation-vibration coupling terms are neglected. It is found that, overall, the major properties of scattering resonances (such as their lifetimes, the number of these states, and their cumulative partition function Q) are all influenced by the Coriolis effect and this influence grows as the angular momentum J is raised. However, it is found that the four isotopically substituted ozone molecules are affected roughly equally by the Coriolis coupling. When the ratio η of partition functions for asymmetric over symmetric ozone molecules is computed, the Coriolis effect largely cancels, and this cancelation seems to occur for all values of J. Therefore, it does not seem grounded to attribute any appreciable mass-independent symmetry-driven isotopic fractionation to the Coriolis coupling effect.

Several Levels of Theory for Description of Isotope Effects in Ozone: Symmetry Effect and Mass Effect.

The essential components of theory for the description of isotope effects in recombination reaction that forms ozone are presented, including the introduction of three reaction pathways for symmetric and asymmetric isotopomers, a brief review of relevant experimental data for singly- and doubly substituted isotopologues, the definitions of ζ-effect and η-effect, and the introduction of isotopic enrichment δ. Two levels of theory are developed to elucidate the role of molecular symmetry, atomic masses, vibrational zero-point energies, and rotational excitations in the recombination process. The issue of symmetry is not trivial, since the important factors, such as 1/2 and 2, appear in seven different places in the formalism. It is demonstrated that if all these effects are taken into account properly, then no anomalous isotope effects emerge. At the next level of theory, a model is considered in which one scattering resonance (sitting right at the top of centrifugal barrier) is introduced per ro-vibrational channel. It is found that this approach is equivalent to statistical treatment with partition functions at the transition state. Accurate calculations using hyper-spherical coordinates show that no isotope effects come from difference in the number of states. In contrast, differences in vibrational and rotational energies lead to significant isotope effects. However, those effects appear to be local, found for the rather extreme values of rotational quantum numbers. They largely cancel when rate coefficients are computed for the thermal distribution of rotational excitations. Although large isotope effects (observed in experiments) are not reproduced here, this level of theory can be used as a foundation for more detailed computational treatment, with accurate information about resonance energies and lifetimes computed and included.

Analyses of infrared FT spectra of asymmetric ozone isotopologue 16O16O18O in the range 950–3850 cm−1

Fifteen bands of the most abundant asymmetric ozone isotopomer 16O16O18O were observed in new spectra generated from various 18O2/16O2 mixtures in the 950–3850 cm−1 range. These bands were fully analyzed, leading to the assignment of a total of 9976 transitions, corresponding to 7030 upper state rovibrational energy levels. The analyses include also six “dark” vibrational states perturbing upper states of the observed bands through anharmonic and Coriolis resonance coupling. The modeling of very congested spectra simultaneously containing lines of six isotopic species resulted to the root mean squares deviations that vary from 0.001 to 0.003 cm−1 in line positions, not exceeding the experimental accuracy. To this end, two different approaches both guided by the ab initio theory were employed. Below 2500 cm−1, all the interacting vibrational states involved in the usual polyad scheme corresponding to the same total stretching excitation were observed. In these cases all symmetry allowed Coriolis and anharmonic coupling terms were initially predicted from ab initio potential energy surface (PES) using the contact transformation method. The major coupling terms were then held fixed to theoretical values during the least-square fits of the observed transitions in order to avoid correlations among adjusted parameters. Above 2500 cm−1, some bands were too weak to be observed. In these cases, the observations did not permit including complete stretching polyads and we used truncated effective models, for which the theory helped to predict initial values of the band centers, their assignments and vibrational dependence of Av, Bv, Cv rotational constants. The final comparison of fifteen experimentally detected and ab initio band centers of 16O16O18O gave the rms deviation of 0.59 cm−1. This drops down to 0.09 cm−1 when using the PES that had been empirically optimized to 16O3 data. The (observed-predicted) rms deviation for Av and Bv is very small - about 0.1%. Average deviations for Cv are somewhat larger ∼0.8% as they are affected by Coriolis resonances. Effective dipole transition moment parameters were either fitted or estimated from a qualitative comparison of observed and simulated spectra involving overlapping contributions of various isotopic species. The line lists built from data reduction models containing about 51,100 transitions are provided in Supplementary Materials.

Retrievals of heavy ozone with MIPAS

Abstract. A method for retrieval of 18O-substituted isotopomers of O3 in the stratosphere with the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) is presented. Using a smoothing regularisation constraint, volume mixing ratio profiles are retrieved for the main isotopologue and the symmetric and asymmetric isotopomers of singly substituted O3. For the retrieval of the heavy isotopologues, two microwindows in the MIPAS A band (685–970 cm−1) and six in the AB band (1020–1170 cm−1) are used. As the retrievals are performed as perturbations on the previously retrieved a priori profiles, the vertical resolution of the individual isotopomer profiles is very similar, which is important when calculating the ratio between two isotopomers. The performance of the method is evaluated using 1044 vertical profiles recorded with MIPAS on 1 July 2003. The mean values are separated by latitude bands, along with estimates of their uncertainties. The asymmetric isotopomer shows a mean enrichment of ∼ 8 %, with a vertical profile that increases up to 33 km and decreases at higher altitudes. This decrease with altitude is a robust result that does not depend on retrieval settings, and it has not been reported clearly in previously published datasets. The symmetric isotopomer is considerably less enriched, with mean values around 3 % and with a large spread. In individual retrievals the uncertainty of the enrichment is dominated by the measurement noise (2–4 %), which can be reduced by averaging multiple retrievals; systematic uncertainties linked to the retrieval are generally small at ∼ 0.5 %, but this is likely underestimated because the uncertainties in key spectroscopic parameters are unknown. The variabilities in the retrieval results are largest for the Southern Hemisphere.

On stabilization of scattering resonances in recombination reaction that forms ozone.

Calculations of energy transfer in the recombination reaction that forms ozone are carried out within the framework of the mixed quantum/classical theory and using the dimensionally reduced 2D-model of ozone molecule, with bending motion neglected. Recombination rate coefficients are obtained at room temperature for symmetric and asymmetric isotopomers of singly and doubly substituted isotopologues. The processes of resonance formation, spontaneous decay, collisional dissociation, and stabilization by bath gas (Ar) are all characterized and taken into account within the steady-state approximation for kinetics. The focus is on stabilization step, where the mysterious isotopic η-effect was thought to originate from. Our results indicate no difference in cross sections for stabilization of scatteringresonances in symmetric and asymmetric isotopomers. As practical results, the general and simple analytic models for stabilization and dissociation cross sections are presented, which can be applied to resonances in any ozone molecule, symmetric or asymmetric, singly or doubly substituted. Present calculations show some isotope effect that looks similar to the experimentally observed η-effect, and the origin of this phenomenon is in the rates of formation/decay of scatteringresonances, determined by their widths, that are somewhat larger in asymmetric isotopomers than in their symmetric analogues. However, the approximate two-dimensional model used here is insufficient for consistent and reliable description of all features of the isotopic effect in ozone. Calculations using an accurate 3D model are still needed.

Deciphering the “chemical” nature of the exotic isotopes of hydrogen by the MC-QTAIM analysis: the positively charged muon and the muonic helium as new members of the periodic table

This report is a primarily survey on the chemical nature of some exotic species containing the positively charged muon and the muonic helium, i.e., the negatively charged muon plus helium nucleus, as exotic isotopes of hydrogen, using the newly developed multi-component quantum theory of atoms in molecules (MC-QTAIM) analysis, employing ab initio non-Born-Oppenhiemer wavefunctions. Accordingly, the "atoms in molecules" analysis performed on various asymmetric exotic isotopomers of the hydrogen molecule, recently detected experimentally [Science, 2011, 331, 448], demonstrates that both the exotic isotopes are capable of forming atoms in molecules and retaining the identity of hydrogen atoms. Various derived properties of atomic basins containing the muonic helium cast no doubt that apart from its short life time, it is a heavier isotope of hydrogen while the properties of basins containing the positively charged muon are more remote from those of the orthodox hydrogen basins, capable of appreciable donation of electrons as well as large charge polarization. However, with some tolerance, they may also be categorized as hydrogen basins though with a smaller electronegativity. All in all, the present study also clearly demonstrates that the MC-QTAIM analysis is an efficient approach to decipher the chemical nature of species containing exotic constituents, which are difficult to elucidate by experimental and/or alternative theoretical schemes.

UV Photolysis of N2O Isotopomers: Isotopic Fractionations and Product Rotational Quantum State Distributions

The time-dependent quantum wave packet method is used to study the dynamics of the photodissociation processes for the isotopomers 14N14N16O, 14N15N16O, 15N14N16O, 15N15N16O, 14N14N17O, and 14N14N18O. In general, the computed isotopic fractionation factors derived from the absorption cross sections of five heavy isotopomers are in good agreement with the experimental results. Relative to the 14N14N16O isotopomer, the N2 rotational state distributions for the isotopically nitrogen substituted N2O are found to be entirely shifted to higher rotational states. Similar to its isotopic fractionation factors, the N2 rotational state distributions for the asymmetric isotopomers 14N15N16O and 15N14N16O are found to be observably different.

Geometric H/D Isotope Effects and Cooperativity of the Hydrogen Bonds in Porphycene

We investigate the primary, secondary, and vicinal hydrogen/deuterium (H/D) isotope effects on the geometry of the two intramolecular hydrogen bonds in porphycene. Multidimensional potential energy surfaces describing the anharmonic motion in the vicinity of the trans isomer are calculated for the different symmetric (HH/DD) and asymmetric (HD) isotopomers. From the solution of the nuclear Schrödinger equation the ground-state wavefunction is obtained, which is further used to determine the quantum corrections to the classical equilibrium geometries of the hydrogen bonds and thus the geometric isotope effects. In particular, it is found that the hydrogen bonds are cooperative, that is, both expand simultaneously even in the case of an asymmetric isotopic substitution. The theoretical predictions compare favorably with NMR chemical-shift data.

Excited-State Double-Proton Transfer in the 7-Azaindole Dimer in the Gas Phase. 1. Evidence of Complete Localization in the Lowest Excited Electronic State of Asymmetric Isotopomers

The fluorescence excitation and UV-UV hole-burning spectra are measured for deuterated 7-azaindole dimers (7AI2), 7AI2-(h(N)h(C))-(h(N)d(C)), 7AI2-(d(N)h(C))-(h(N)d(C)), 7AI2-(h(N)h(C))-(d(N)h(C)), and 7AI2-(h(N)h(C))-(d(N)d(C)), where h and d indicate the H and D atoms, respectively, and the subscripts N and C designate the imino N-H (or N-D) and C-H (or C-D) bonds at the 3-position. The transitions of the isotopomers have been consistently assigned. It has been found that the excitation is completely localized on one monomer unit in the lowest excited electronic state of asymmetrical 7AI2 dimers except for 7AI2-(d(N)h(C))-(h(N)d(C)) in which the excitation is delocalized over the dimer. This indicates that the undeuterated 7AI2 dimer and its isotopomers that belong to the C2h symmetry point group should be treated by the weak coupling limit of the exciton theory.

Six-dimensional ab initio potential energy surfaces for H3O+ and NH3: Approaching the subwave number accuracy for the inversion splittings

New potential energy surfaces are calculated for the hydronium ion using high-order coupled cluster ab initio methods. Large basis sets are used especially for the inversion part of the full surface. Electronic energies obtained with different correlation consistent basis sets are extrapolated to the infinite basis set limit. Core-valence and first order relativistic effects are also included. The influence of these two contributions and basis set sizes on both the inversion barrier height and equilibrium geometry are investigated thoroughly. The same methods are also adopted for ammonia in order to further improve a recently published surface [J. Chem. Phys. 118, 6358 (2003)]. The vibrational eigenvalues are calculated variationally both for the symmetric and asymmetric isotopomers using exact six-dimensional kinetic energy operators and successive basis set contractions. With the new surfaces, the mean absolute deviations obtained for all experimentally observed inversion splittings for different isotopomers of H3O+ (8 states) and NH314 (17 states) are 0.78 and 0.25 cm−1, respectively. Inversion levels are calculated with almost similar accuracy. These results indicate that the calculated inversion barrier heights for H3O+ and NH3, 650 and 1792 cm−1, respectively, are close to the real values. The value for ammonia is also close to the height determined from published experimental data in our previous work. The lowest energies for the high-frequency modes are computed with the mean absolute deviation being less than 2 cm−1 for isotopomers of H3O+ and less than 4.5 cm−1 for NH314 with respect to experimental energies.

Vibrational energy levels for symmetric and asymmetric isotopomers of ammonia with an exact kinetic energy operator and new potential energy surfaces

A new vibrational Hamiltonian operator for ammonia is presented. The potential energy part is expressed in terms of symmetrized bond-angle valence coordinates and an inversion coordinate, which is a function of the bond angles. In the exact kinetic energy operator, the stretching part is instead given in terms of unsymmetrized bond displacement coordinates. Six-dimensional ammonia potential energy surfaces are calculated using high-level ab initio tools, the CCSD(T) method with aug-cc-pVQZ and aug-cc-pVTZ basis sets. The potential energy functions are constructed in two, two-dimensional steps. The surfaces are expressed as a Taylor-type series with respect to the doubly degenerate asymmetric stretching and bending coordinates. This representation is given along a two-dimensional surface of the totally symmetric stretching and inversion coordinates of ammonia. Vibrational energies are calculated variationally in a finite basis representation. Employing successive basis set contractions, it is possible to optimize some potential energy parameters simultaneously for seven symmetric and asymmetric isotopomers very effectively. The symmetric part of the surface is fitted to experimentally observed vibrational band centers up to 6000 cm−1. This reduces the mean absolute error from 7.84 cm−1 with a pure ab initio potential to 0.44 cm−1 compared to the experimental values for NH314. In addition, vibrational energy levels of NH314 have been calculated up to about 15 000 cm−1 using the pure ab initio surface obtained with the aug-cc-pVTZ basis set. The nuclear motion calculation converges all levels up to about 10 000 cm−1 to within 0.05 cm−1.

The rovibrational levels of ammonia

In this paper we report variational rovibrational studies on ammonia and its isotopomers. We use six internal coordinates (one of which describes the umbrella motion). The expansion functions are products of one-dimensional functions of these internal coordinates, multiplied by appropriate functions of the Euler angles to describe the rotational motion. We use a previously published high accuracy six-dimensional potential energy surface [LEONARD, C., HANDY, N. C., CARTER, S., and BOWMAN, J. M., 2002, Spectrachim. Acta, 58, 825]. We derive the full kinetic energy operator for the rovibrational motion in these coordinates. This operator has been completely checked to give a hermitian secular matrix. All matrix elements are evaluated numerically by quadrature. The symmetry of the expansion functions is fully described in D3h, C2v and Cs. It is not possible to perform the calculations in D3h, but complete degeneracy in the appropriate levels is obtained with the C2v program. The algebraic complexity of this program has been far greater than for any other variational study we have undertaken for a tetra-atomic molecule. We present J = 0, 1, 2 energy levels for the experimentally observed band origins of NH3, and J = 0, 1 energy levels for the ground state and fundamentals of NH2D, ND2H and ND3. For the asymmetric isotopomers, identical results are obtained for both C2v and Cs, thus confirming the validity of the method. The levels we obtain are completely converged. Agreement with observation is of the order of 0.5% (of course being dependent upon the accuracy of the potential energy surface); therefore the ordering of the rotational levels and their splitting is completely predicted and understood.

Six-dimensional variational calculations for vibrational energy levels of ammonia and its isotopomers

Results of six-dimensional variational calculations of vibrational energy levels are presented for ammonia using a Hamiltonian expressed in curvilinear internal bond coordinates. A two-dimensional potential energy surface, which was introduced in a preliminary study on the inversion motion, is combined with a surface by Martin et al. Both surfaces are calculated at the aug-cc-pVTZ/CCSD(T) ab initio level. The exact kinetic energy operator is an enlargement of the one used in the previous two-dimensional calculations. Eigenvalues are computed variationally using successive basis set contractions for some symmetric and asymmetric isotopomers of ammonia.

On the theory of the strange and unconventional isotopic effects in ozone formation

The strange mass-independent isotope effect for the enrichment of ozone and the contrastingly unconventional strong mass-dependent effect of individual reaction rate constants are studied using statistical (RRKM)-based theory with a hindered-rotor transition state. Individual rate constant ratios of recombination reactions and enrichments are calculated. The theory assumes (1) an “η-effect,” which can be interpreted as a small deviation from the statistical density of states for symmetric isotopomers, compared with the asymmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. A partitioning effect controls the recombination rate constant ratios. It arises from small differences in zero-point energies of the two exit channels of dissociation of an asymmetric ozone isotopomer, which are magnified into large differences in numbers of states in the two competing exit channel transition states. In enrichment experiments, in contrast, this partitioning factor disappears exactly [Hathorn and Marcus, J. Chem. Phys. 112, 9497 (2000)], and what remains is the η-effect. Both aspects can be regarded as “symmetry driven” isotopic effects. The two experiments, enrichments and rate constant ratios, thus reveal markedly different theoretical aspects of the phenomena. The calculated low-pressure ozone enrichments, the low-pressure recombination rate constant ratios, the effects of pressure on the enrichment, on the individual recombination rate constant ratios, and on the recombination rate constant are consistent with the experimental data. The temperature dependence of the enrichment and of the recombination rate constant ratios is discussed and a variety of experimental tests are proposed. The negative temperature dependence of the isotopic exchange rate constant for the reaction O+16O18O→18O16O+18O18 at 130 K and 300 K is used for testing or providing information on the nature of a variationally determined hindered-rotor transition state. The theory is not limited to ozone formation but is intended to apply to other reactions where a symmetrical stable or unstable gas phase molecule may be formed.

The anharmonic potential energy surface of methyl fluoride

A large experimental spectroscopic data set sensitive to the cubic anharmonic potential energy surface (PES) of methyl fluoride has been compiled from the literature for six symmetric and asymmetric top isotopomers of methyl fluoride: 12CH 3F, 13CH 3F, 12CD 3F, 13CD 3F, 12CHD 2F and 12CH 2DF. This empirical data set has been used to critically assess the best available literature ab initio cubic force field and various ‘improved’ theoretical force fields. A perturbation-resonance approach to the calculation of the observables from the force constants has been utilized and existing PESs were found to reproduce the data poorly. The careful treatment required for the correct theoretical reproduction of empirical spectroscopic constants arising from highly correlated least-squares fits to the original data is discussed. A new fit to the data has been performed (optimising 19 of the 38 cubic force constants) resulting in a much improved PES. The latter has been used to predict currently unknown spectroscopic constants for the least well-characterised isotopomer 12CH 2DF. The prospects for a future empirical determination of the complete cubic force field of methyl fluoride are discussed and new data most likely to yield new information on the PES identified.

Estimation of Vibrational Frequencies and Vibrational Densities of States in Isotopically Substituted Nonlinear Triatomic Molecules

For use in unimolecular reactions, a simple method is introduced for obtaining the unknown vibration frequencies of the many asymmetric isotopomers of a molecule from those of the symmetric ones. The method is illustrated for a triatomic molecule XYZ, ozone. It is based on the neglect of a single G matrix element in the GF expression for XYZ, yielding for it a block-factored expression of the XYX type for the frequencies of all the isotopomers XYZ. It agrees with available data to the accuracy needed, a few cm^(-1). The first-order perturbation vanishes. (The zeroth-order case is not a symmetric molecule since it contains all three masses.) A simple second-order perturbation result for the GF matrix using data for one asymmetric isotopomer then provides agreement to about 1 cm^(-1). The virtues of the method are its simplicity, transparency, and novelty, though normally one would use much more general methods such as ASYM 20 or 40. The method itself is not restricted to triatomic molecules.