Linear molecules, spectra

Figure 5.12 shows the J= — 0 transition of the linear molecule cyanodiacetylene (H—C=C—C=C—C=N) observed in emission in Sagittarius B2 (Figure 5.4 shows part of the absorption spectrum in the laboratory). The three hyperfine components into which the transition is split are due to interaction between the rotational angular momentum and the nuclear spin of the nucleus for which 1= 1 (see Table 1.3). The vertical scale is a measure of the change of the temperature of the antenna due to the received signal. 

Assuming reasonable bond lengths, estimate the frequency of the J= 15 — 14 transition in the linear molecule N=C—(C=C)6—H. In which region of the electromagnetic spectrum does it lie ... 

The envelope of the Stark structure of the rotator in a constant orienting field, calculated quantum-mechanically in [17], roughly reproduces the shape of the triplet (Fig. 0.5(c)). The appearance of the Q-branch in the linear rotator spectrum indicates that the axis is partially fixed, i.e. some molecules perform librations of small amplitude around the field. Only molecules with high enough rotational energy overcome the barrier created by the field. They rotate with the frequencies observed in the... 

The half-width (at half-height) and the shift of any vibrational-rotational line in the resolved spectrum is determined by the real and imaginary parts of the related diagonal element TFor linear molecules the blocks of the impact operator at k = 0,2 correspond to Raman scattering and that at k = 1 to IR absorption. The off-diagonal elements in each block T K, perform interference between correspond-... 

Fig. 6.1. A spectral exchange scheme between components of the rotational structure of an anisotropic Raman spectrum of linear molecules. The adiabatic part of the spectrum is shadowed. For the remaining part the various spectral exchange channels are shown ( - — ) between branches (<— ) within branches.

The IR spectra of linear molecules at low pressure do not contain a Q-branch at all. The intensity increases with 1/tj in the central part of this spectrum exclusively due to the exchange between P- and R-branches (Fig. 6.4). The secular simplification is inapplicable in this case. In order to describe the rise of intensity in a gap of the IR spectrum with increase of density, one has to know the exact solution of the problem, e.g. (6.45H6.47). Using it, one can calculate... 

In view of the accessibility of zeolite A (only linear molecules adsorb) the coupling will take place at the outer surface of the zeolite crystals. Indeed, Ag-Y and especially a Ag-loaded amorphous silica-alumina, containing a spectrum of wider pores, mrned out to be much better promoter-agents (ref. 28). The silica-alumina is etched with aqueous NaOH and subsequently exchanged with Ag(I). 

Hg(CN)2 in the solid state has a structure (I42d neutron diffraction), completely different from that of Cd(CN)2 Almost-linear molecules (r(Hg—C) 201.9, r(C—N) 116.0pm (corrected for thermal motion) a(C—Hg—C) 175.0°) are arranged such that four secondary bonds N" Hg (274.2 pm) yield the often-occurring 2 + 4 coordination around Hg.103 Analysis of the 199Hg MAS NMR spectrum of Hg(CN)2 has yielded the chemical shift and shielding tensor parameters.104... 

Methylzinc hydride was formed by the insertion of excited zinc atoms, in their 3Pi state, into the C-H bond of methane in an argon matrix.229 The MeZnH product was characterized on the basis of its infrared spectrum and determined to be a linear molecule with C v symmetry. The band at 1866.1 cm-1 is due the Zn-H stretch, while the band at 565.5 cm-1 was assigned to the Zn-C stretching vibration. Additional bands for isotopically labeled species were also reported. 

The number of fundamental vibrational modes of a molecule is equal to the number of degrees of vibrational freedom. For a nonlinear molecule of N atoms, 3N - 6 degrees of vibrational freedom exist. Hence, 3N - 6 fundamental vibrational modes. Six degrees of freedom are subtracted from a nonlinear molecule since (1) three coordinates are required to locate the molecule in space, and (2) an additional three coordinates are required to describe the orientation of the molecule based upon the three coordinates defining the position of the molecule in space. For a linear molecule, 3N - 5 fundamental vibrational modes are possible since only two degrees of rotational freedom exist. Thus, in a total vibrational analysis of a molecule by complementary IR and Raman techniques, 31V - 6 or 3N - 5 vibrational frequencies should be observed. It must be kept in mind that the fundamental modes of vibration of a molecule are described as transitions from one vibration state (energy level) to another (n = 1 in Eq. (2), Fig. 2). Sometimes, additional vibrational frequencies are detected in an IR and/or Raman spectrum. These additional absorption bands are due to forbidden transitions that occur and are described in the section on near-IR theory. Additionally, not all vibrational bands may be observed since some fundamental vibrations may be too weak to observe or give rise to overtone and/or combination bands (discussed later in the chapter). 

Here a third selection rule applies for linear molecules, transitions corresponding to vibrations along the main axis are allowed if Aj = 1. The A/=0 transition is only allowed for vibrations perpendicular to the main axis. Note that because of this selection rule the purely vibrational transition (called Q branch) appears in the gas phase spectrum of C(X but is absent in that of CO. In both cases, two branches of rotational side bands appear (called P and R branch) (see Fig. 8.3 for gas phase CO). 

Photolysis of H3NBH3 with 121.5 nm radiation yields imidoborane, HBNH, which has been of theoretical interest Spectral shifts observed for several isotopic species containing °B, N, and D show clearly that the spectrum is due to HNBH which is isoelectronic with HBO, HCN and HCCH. From the spectrum of the isolated species two of the and one of the tr-type vibration frequencies for a linear molecule have been obtained. The location of the missing S (B-H stretch) frequency has been calculated. A comparison of observed and calculated frequencies for HBNH is given in Table 7. Another isolated product observed in these experiments is identified as HNB. This radical may be generated by photodissociation of HNBH subsequent to its formation. In this respect the photolysis mechanism would be similar to the formation of C2H from acetylene. 

Group theory has been useful in chemistry in several ways. First, it has provided simple, qualitahve explanations for the behavior of matter. For example, why can the states of electrons in any atom be classified, to a good approximation, by the four quantum numbers n, I, rrii and m Why, in their ground states, is BeH2 a linear molecule but H2O bent Why do certain transitions not appear in an absorption spectrum Lengthy computations can provide correct but uninformative answers to these questions group theory can provide perspicuous explanations of the factors that determine these answers. 

Stoicheff investigated the pure rotational Raman spectrum of CS2. The first few lines could not be observed because of the width of the exciting line. The average values of the Stokes and anti-Stokes shifts for the first few observable lines (accurate to 0.02 cm-1) are Ap = 4.96, 5.87, 6.76, 7.64, and 8.50 cm-1, (a) Calculate the C=S bond length in carbon disulfide. (Assume centrifugal distortion is negligible. The rotational Raman selection rule for linear molecules in 2 electronic states is AJ = 0, 2.) (b) Is this an R0 or Re value (c) Predict the shift for the 7 = 0—>2 transition. 

I is the effective moment of inertia of a dipole (we consider here a linear molecule), determined by the relation (149). The spectral function L(z), calculated for thermal equilibrium, is linearly related to the spectrum C° of the dipolar autocorrelation function (ACF) C°(f) (VIG, p. 137 GT, p. 152) as... 

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