Non-linear Triatomic Molecules

AH2 Molecules, inclnding H3.—The simplest of these species is H, which has been the subject of a number of recent studies. Work previous to 1970 is listed by Borkman.426 The ground state is triangular (Dsn) and it has been studied using a basis set of elliptical orbitals. Contracted GTO basis sets were used in near-HF calculations by Harrison et a/.,430 and correlated wavefunctions were computed by Salmon and Poshusta,431 and by Handy.482 In the latter calculation a new form for the correlation factor was used, and the good results suggest that it might be useful for other small molecules. 

BH2 has been less studied than most of the first-row AH2 molecules, although BHs was studied some years ago by Kaufman et al.434 However, with the recent advances in computing power, more accurate calculations on open-shell systems are now feasible, and three separate studies of BH2 have appeared. 

A discussion of Walsh s rules and the first-row hydrides has been given by Wasserman now that quantitative calculations have been carried out.439 These rules have also been reviewed by Buenker11 and further studied by Davidson et a/.405 

the next hydride in the series, is the classic example of the power of ab initio calculations in that the clear prediction was of a non-linear geometry, and this led to a consequent revision of the experimental data by Herzberg. Several recent calculations on this species should be mentioned. 

The calculations prior to 1971 have been summarized in Schaefer s book, and some of the results of later work are given in Table 7. There are two particularly important questions (i) the ground-state geometry, and (ii) the energy 

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By contrast to the plethora of simple oxo-halides and thiohalides of P, the corresponding derivatives of P are fugitive species that require matrix isolation techniques for preparation and characterization ClPO, BrPO, FPS and BrPS all form non-linear triatomic molecules, as expected. The corresponding oxosulfide, BrP(0)S, and its thio-analogue, FP(S)S, have also recently been isolated. 

Structure. The ultraviolet emission spectrum of CF2 was first examined by Venkateswarlu 2 9, who prepared the molecule by passing an uncondensed transformer discharge through CF4. An extensive band system between 3250 and 2400 A was observed. The similarity of the band system to that of N02 suggested that a non-linear triatomic molecule was responsible for the spectrum. Venkateswarlu identified the band system with the transition 1B2 - 1 Aj. 

Yi, Xi-Zhang, Ding, Shi-liang and Deng, Cong-hao (1988), Lie Algebraic Approach to the Rotation-Vibrational Energy Levels for a Non-Linear Triatomic Molecule X3, Chinese J. Chem. Phys. 1, 255. 

Fig. 1. Normal modes of a non-linear triatomic molecule such as H 0 (schematic). v9 symmetric stretching, d symmetric bending, va asymmetric stretching...

Recent calculations (see Section 3.1) show that the activated complex is non-linear, that is, the average rotational energy is (3/2)ksT and Ea = Eq + (.E ib) — (E ib). %2 = 4395 cm-1 and the two vibrational frequencies associated with the activated complex are 3772 cm-1 and 296 cm-1, respectively (remember that the third vibrational degree of freedom of the non-linear triatomic molecule is the reaction coordinate which is not included in (/A). The thermal energies associated with the... 

For a non-linear triatomic molecule three parameters are needed to specify (the assumed) fixed geometry, but only two moments of inertia can be measured. The situation becomes rapidly worse for larger molecules. Isotopic substitution may be used to produce more data, but the situation where sufficient data are available for a unique solution is rare. In the final analysis measured spectra may well be consistent with an assumed molecular conformation, without excluding many other classical or non-classical possibilities. 

For a non-linear triatomic molecule (ABC) there are three degrees of freedom. The representation of the three degrees of freedom depends on how many reaction channels are open/relevant. A review of the choice of coordinates and the corresponding Hamiltonian is given in Ref. [75]. It is common to use either the Jacobi or the hyper-spherical coordinate representation. 

VIBRATION-ROTATION SPECTRA OF NON-LINEAR TRIATOMIC MOLECULES... 

Let us take as our example the three vibrational coordinates of a non-linear triatomic molecule, illustrated in Fig. 4.3. Each of them describes an in-plane motion, so they are necessarily distributed between aj and 6i, the two irreps of C2v that are symmetric to reflection in the molecular plane. The expression for the potential energy of the vibrating XYX molecule in the harmonic approximation is ... 

It is known that the changes of standard Gibbs free energy and of enthalpy in the reaction are A( Se8=4000 cal mol and AH298= 19 000 cal mol. No data are available on heat capacities, but A and C are diatomic molecules, B is a linear triatomic molecule cuid is a non-linear triatomic molecule. 

There is one vibrational coordinate, and it is the bond length. Changing the bond length is the only way to change the relative position of the two atoms. In a non-linear triatomic molecule, there are 3 3 — 6 = 3 vibrational coordinates, or vibrational modes. 

Taking the example of the water molecule, a non-linear triatomic, one expects three fundamental vibrations. If a simple harmonic potential is applied, one could write... 

Note that in a non-linear molecule, one of the vibrational modes of the linear molecule has been replaced by a rotational coordinate. As an illustration, let us consider two examples. For the stable linear triatomic molecule CO2, there are 3 x 3 — 5 = 4 internuclear coordinates, which corresponds to the vibrational degrees of freedom, namely the symmetric and antisymmetric stretch and two (degenerate) bending modes (see Appendix E). For the three atoms in the reaction D + H — H—> D — H + H, there are 3 x 3 — 6 = 3 internuclear coordinates. These coordinates can, for example, be chosen as a D H distance, the H H distance, and the I) II H angle. 

Shrinkage effect is a direct consequence of the molecular vibrations and it shows that the bonded and non-bonded interatomic distances measured by GED are not self-consistent, i.e., they do not correspond to a set of distances calculated from a rigid geometrical model. This phenomenon is illustrated on a simplified diagram below for a linear triatomic molecule AB2 (simplification in this case means that for this type of vibration while two B atoms move up, atom A moves down which is ignored in this diagram). 

Linear triatomic molecules also have two significant rotational degrees of freedom non-linear molecules have three. For non-linear polyatomic molecules, the number of vibrational degrees of freedom is 3N - 6, where N is the number of atoms in the molecule. 

A radical is defined to be a molecule in an open shell electronic state. It is often, although not necessarily, very reactive and short-lived in a laboratory environment. Several new species have been studied since the publication of the previous supplement, although the number for which microwave transition frequencies have been measured is still quite small. Many of the new observations have been made by radio astronomers who now have access to frequencies up to 350 GHz. Experiments employing double resonance techniques (simultaneous irradiation with microwaves and either infrared or visible radiation) have also made a contribution to the development of the field. The information about linear molecules, in 2, 2, and states, is contained in section 3.2.1. The non-linear radicals, almost all of which are triatomic, are presented in 3.2.2 (Non-Unear triatomic) and 3.2.3 (Non-linear larger molecules). 

Polyatomic molecules containing many (N) atoms will have 3N degrees of freedom. Looking first at the case of molecules containing three atoms, two groups of diatomic molecules may be distinguished, i.e. linear and non-linear. Two simple examples of linear and non-linear triatomics are represented by CO2... 

The fundamental vibrational frequencies of several polyatomic molecules are given in Table 8.3, together with local mode descriptions and symmetry labels for the modes. Despite the complications inherent in vibrating polyatomics, several features are predictable from our experience with diatomics and a fundamental knowledge of vibrational modes. For example, we know that the isotopes of H2O, a non-linear triatomic — 3) molecule, should each have... 

Theory of vibrational spectroscopy considers the energy of a vibrating molecule and the selection rules governing absorption and emission processes. We calculate the number of normal modes of vibration for linear and non-linear (bent) molecules, and view a computer simulation of the normal modes for both linear and bent triatomic molecules. 

Additional support for the existence of non-oxo uranyl analogues may be found in the reactions of uranium atoms with small molecules (N2, NO, CO, etc.) in argon matrices. Although not stable outside of the stabilizing matrix, vibrational spectroscopy is consistent with the formation of other linear triatomic species such as NUN, NUO, and... 

The most common protic solvent is water. It is also one of the most complex from the point of view of vibrational spectroscopy because of its highly structured nature. Since water is a triatomic, non-linear molecule it has three vibrational modes, which are illustrated in fig. 5.13. The Vj mode is the symmetrical stretch V2 is the bending mode and V3 is the asymmetrical stretch. All three vibrational modes for water are active in the infrared because they involve changes in the dipole moment. Activity in the Raman spectrum requires that the polarizability of the molecule changes during vibration. Analysis of this aspect of molecular properties is more difficult but it shows that all three modes are also Raman active. A summary of the frequencies of these vibrations for H2O, and the isotopes D2O, and HOD determined from gas phase spectra are given in table 5.7. 

In order to evidence variations in the molecular potential for isoelectronic molecules of very similar geometry, we consider now the triatomic non-linear molecules, ozone (XII) and nitrosyl fluoride (XIII). Potential maps in the molecular plane are reported for ozone in Fig. 16 and for FNO in Fig. 175>. Near the terminal oxygen atoms both molecules... 

Bosch et al. (1969) have performed a non-erapirical ab initio SCF—MO calculation on the CuF2 triatomic molecule, with some interesting results. A linear configuration was found to be most stable for the ground state, and for the first two excited states. The ground state was predicted to be in agreement with simple crystal field considerations however, the lowest-l5dng excited state was found to be and not Ilg as we... 

M. V. Basilevsky and V. M. Ryaboy, Direct calculation of resonant states in reactive scattering—application to linear triatomic systems. Int. J. Quantum Chem. 19 611 (1981) M. V. Basilevsky and V. M. Ryaboy, Decay dynamics of triatomic molecules. Quantum calculations for non-symmetric linear systems. Chem. Phys. 86 61 (1984). 

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