Vibrational band origins

Figure 1-9. Variation of the vibrational band origin Ai q, effective rotational constant B, and centrifugal distortion constant D with the size N of the cluster He -C02. Circles and dots indicate the experimental and theoretical results, respectively. The upper panel also includes for comparison the value of for clusters of He with OCS and N20. The inset in the middle panel shows the results calculated in an extended range of helium atoms in the cluster. The dashed lines indicate the nanodroplet results of Miller and collaborators 367...

The rotational intensity structure of a vibrational band provides information about the rotational population in the electronically excited state and the vibrational bands originating from an electronically excited state provide information about the corresponding vibrational population. Finally, the sum of the vibrational and rotational populations yields the population in the electronically excited state. 

Table 56 Vibrational band origins of C4H4S+ (X A observed in the ZEKE spectrum and assignments ...

For all but the smallest molecules, the procedure outlined in the previous paragraph is impractical. If we can locate or approximate the vibrational band origins from the experimental data, simplifications result. We then treat the J = 0 states in which case all terms in Eq. (3.1) involving rotational angular momenta vanish. Rewriting the pure vibrational term we obtain the vibrational kinetic energy Tv ... 

AB INITIO CALCULATIONS OF VIBRATIONAL BAND ORIGINS, Debra J. Searles and Ellak I. von Nagy-Felsobuki... 

TABLE 9.3 Variational vibrational band origins (VBOs, in cm with / = 0 up to the highest fundamental of 2 obtained with Chedin s [80] sextic empirical force held ... 

Each particular electronic or vibrational band originates from a quantum transition between two energy states i and j characterised by a transition dipole moment... 

A substantial number of calculations of force constants and vibrational frequencies have been reported. Many of the first studies were concerned with determining basis set and correlation effects so as to esublish the accuracy of various levels of treatment (see, for example, 118, 119). But a particularly encouraging glimpse of the current state-of-the-art is the set of calculations recently reported by Botsdiwina. " He claims (and shows ) that vibrational band origins can be obtained directly with an error range or uncertainty of around 25 cm and this applies, in his examples, not only to everyday molecules like ammonia, but also to cations, anions, and weakly bound complexes. 

Comparison of ab initio and experimental vibrational band origins... 

IR laser magnetic resonance spectroscopy on SiC showed that the vibrational band origin was at 953.32062(27) cm . The FTIR spectra of the products of... 

Table 10 Some vibrational band origins for FNO2 (/cm )...

In addition to the dependence of the intennolecular potential energy surface on monomer vibrational level, the red-shifting of the monomer absorption as a fiinction of the number of rare gas atoms in the cluster has been studied. The band origin for the Vppp = 1 -t— 0 vibration in a series of clusters Ar -HF, with 0 < n < 5, was measured and compared to the HF vibrational frequency in an Ar matrix (n = oo). The monomer vibrational frequency Vp p red shifts monotonically, but highly nonlinearly, towards the matrix value as sequential Ar atoms are added. Indeed, roughly 50% of the shift is already accounted for by n = 3. 

In addition to the characteristic XRD patterns and photoluminescence, UV-visible and X-ray absorption spectra, another fingerprint thought to indicate lattice substitution of titanium sites was the vibrational band at 960 cm-1, which has been recorded by infrared and Raman spectroscopy (33,34). Although there is some controversy about the origin of this band, its presence is usually characteristic of a good TS-1 catalyst, although it turned out to be experimentally extremely difficult to establish quantitative correlations between the intensity of the 960 cm-1 band and the Ti content of a Ti silicate and/or its catalytic activity. 

Efficient Calculation of Highly Excited Vibrational Energy Levels of Floppy Molecules The Band Origins of Hj up to 35000 cm-1. 

Figure 8.4 The v = 6 C-H overtone spectrum as determined by photoacoustic absorption (Hall, 1984) for increasing size alkynes. Each panel contains the molecular formula and the density of vibrational states per cm 1. The band origin does shift some with size but is roughly at 18450 cm"1 for all the molecules shown (see also Kerstel et al., 1991).

Table 4. Band origin, pure vibrational matrix element and strength of vibration-rotational...

Setting J = 0 in (4.67), we calculate the wave number of the band origin a0 for a transition from vibrational level t> to level v as... 

The appearance of a vibration-rotation band is shown in Fig. 4.9. Because A/=0 is forbidden, we have a gap at the wave number of the band origin o0. (We are considering only diatomic molecules in 2 electronic states for electronic states in which the electronic orbital angular-momentum quantum number A is nonzero, transitions with AJ=0 are allowed, giving a Q branch in each band. An example is NO, which has a 2n electronic ground term, -branch transitions also occur for vibration-rotation bands of polyatomic molecules see Chapter 6.) Under low resolution, an infrared band of a diatomic molecule looks like Fig. 4.10. 

---