Molecular vibration electron diffraction

The molecular point groups of (CF3)2S02, ( 03)2802 and (CBr3)2S02 can be either C2V or C2 according to electron diffraction and vibrational spectroscopic data. The molecular model and projection formula for ( 13)2802 are shown in Figure 11. The molecular geometry of the bromine derivative has not been determined but its vibrational... 

In general, all observed intemuclear distances are vibrationally averaged parameters. Due to anharmonicity, the average values will change from one vibrational state to the next and, in a molecular ensemble distributed over several states, they are temperature dependent. All these aspects dictate the need to make statistical definitions of various conceivable, different averages, or structure types. In addition, since the two main tools for quantitative structure determination in the vapor phase—gas electron diffraction and microwave spectroscopy—interact with molecular ensembles in different ways, certain operational definitions are also needed for a precise understanding of experimental structures. 

The nature of the intemuclear distance, r, is the object of interest in this chapter. In Eq. (5.1) it has the meaning of an instantaneous distance i.e., at the instant when a single electron is scattered by a particular molecule, r is the value that is evoked by the measurement in accordance with the probability density of the molecular state. Thus, when electrons are scattered by an ensemble of molecules in a given vibrational state v, characterized by the wave function r /v(r), the molecular intensities, Iv(s), are obtained by averaging the electron diffraction operator over the vibrational probability density. 

In Eq. (5.2), the function i iv(r) 2/r = P(r)/r is an example of a so-called radial distribution (RD) function, in the form in which it is obtained from gas-electron diffraction, in this case for a particular vibrational state of a diatomic molecule. It is seen that the molecular intensity curve is the Fourier transform of Pf. The reverse, by inversion, the RD function is the Fourier transformation of the molecular intensities ... 

Equations (5.2)—(5.4) and Figs. 5.1-5.3 illustrate the nature of the structural observables obtained from gas-electron diffraction the intensity data provide intemuclear distances which are weighted averages of the expectation values of the individual vibrational molecular states. This presentation clearly illustrates that the temperature-dependent observable distribution averages are conceptually quite different from the singular, nonobservable and temperature independent equilibrium distances, usually denoted r -type distances, obtained from ab initio geometry optimizations. 

K. Kuchitsu and L. S. Bartell, Effects of Anharmonicity of Molecular Vibrations on The Diffraction of Electrons. II. Interpretation of Experimental Structural Parameters, J. Chem. Phys., 35 (1961) 1945-1949. 

The amount of high precision experimental structural data on conjugated polyenes is limited. Some structure results are presented in Table 5. In gas electron diffraction studies it is difficult to determine closely spaced bond distances accurately, because these parameters are highly correlated with the corresponding vibrational amplitudes. Today it is possible to calculate the vibrational amplitudes accurately, if the vibrational frequencies are known. This was, however, not the case when the GED studies presented in Table 5 were carried out. The observed differences between the terminal and central C=C bonds in the GED studies of traw.s-l,3,5-hexatriene and c/s-l,3,5-hexatricne are probably too large29. A very accurate X-ray study of traw.s-l,3,5-hexatriene has, however, been carried out also in connection with the preparation of this chapter4. Figure 4 shows the molecular structures of trans-1,3-butadiene and trans-l,3,5-hexatriene as found in the crystal lattice. 

Polymer films were produced by surface catalysis on clean Ni(100) and Ni(lll) single crystals in a standard UHV vacuum system H2.131. The surfaces were atomically clean as determined from low energy electron diffraction (LEED) and Auger electron spectroscopy (AES). Monomer was adsorbed on the nickel surfaces circa 150 K and reaction was induced by raising the temperature. Surface species were characterized by temperature programmed reaction (TPR), reflection infrared spectroscopy, and AES. Molecular orientations were inferred from the surface dipole selection rule of reflection infrared spectroscopy. The selection rule indicates that only molecular vibrations with a dynamic dipole normal to the surface will be infrared active [14.], thus for aromatic molecules the absence of a C=C stretch or a ring vibration mode indicates the ring must be parallel the surface. 

In conventional gas electron diffraction experiments, an effusive beam is used in which vibrational levels of molecules are thermally populated and the width of a peak in a radial distribution curve is determined by thermally averaged mean amplitudes. When a molecular beam or a free jet is used, mean amplitudes could become small, since the contribution from the vibrationally excited levels is reduced significantly. As a consequence, sharper peaks are expected in the radial distribution curve, and the spatial resolution of the snapshot could be improved. However, it seems that the observed peaks in the radial distribution curve are considerably broad even though a molecular beam is used. There could be some reasons to have such broadened peaks in the radial distribution curve. 

Femtosecond laser excitation makes it possible to produce in a synchronous manner accurate to within a few femtoseconds an ensemble of molecules in an excited state and observe thereafter the evolution of this ensemble in the subsequent processes of decay, relaxation, and so on, by means of other femtosecond pulses. Another femtosecond pulse is usually used as a probe pulse [1]. However, one can directly observe changes in the geometry of molecules, specifically in molecular vibrations, by the method of electron diffraction using ultrashort electron pulses. This was successfully demonstrated in Ref. 2. Whereas the production of synchronous probe laser pulses is a standard technique, the situation with femtosecond electron pulses is more complicated. I would like to call attention to the possibility of using intense femtosecond laser pulses to control electron beams, specifically to obtain femtosecond electron pulses and to focus and reflect them, and so on [3, 4]. 

The molecular structure of gaseous tetrahydropyran has been determined by electron diffraction the dimensions are presented in Figure 7 (79ACS(A)225). The molecule exists in the chair form with Cs symmetry consistent with the conclusions based on NMR, rotational and vibrational spectra. The torsional angles suggest that the heteroatom causes no flattening of the ring relative to that of cyclohexane. 

The shrinkage effect1 is treated in more detail elsewhere in the present article. Due to molecular vibrations interatomic distances observed by electron diffraction do not correspond to a set of distances calculated from a rigid geometrical model. Usually the shrinkage effect is routinely included in electron-diffraction least-squares refinement. In order to do so, it has been found appropriate to introduce a third distance type r defined as the distance between mean positions of atoms at a particular temperature. If the harmonic force field is known, iQ may be calculated from ra according to Eq. (12) ... 

As earlier indicated carbon suboxide has attracted considerable interest as to the study of shrinkage effect and large molecular motion. The molecule has been submitted to four independent electron-diffraction studies at this laboratory81,82,, 2c. The large shrinkage effect of carbon suboxide could not be explained from the known vibrational frequency at the time when the shrinkage effect was first ob-... 

At lower temperatures, molecular AsC12F3 is unstable with respect to the non-molecular substance AsCl AsFg. Complete electron diffraction analysis could not be performed for the whole range of molecules. However, full vibrational spectra were obtained guided by the results for PC1 F5 , the force constants thus extracted showed that the AsC1 F5 have the same structures. This illustrates the point that vibrational spectra can often be obtained in situations where diffraction data cannot. 

Kuchitsu K, Bartell LS (1961) Effects of anharmonicity of molecular vibrations on the diffraction of electrons. II. Interpretation of experimental structural parameters. J Chem Phys 35 1945-1949... 

The molecule is pyramidal, having C3v symmetry with the nitrogen atom at the apex. The molecular dimensions have been determined by electron diffraction (266) and by microwave spectroscopy (161,271). The molecule with this symmetry will have four fundamental vibrations allowed, both in the infrared (IR) and the Raman spectra. The fundamental frequency assignments in the IR spectrum are 1031, vt 642, v2 (A ) 907, v3 (E) and 497 cm-1, v4 (E). The corresponding vibrations in the Raman spectrum appear at 1050, 667, 905, and 515 cm-1, respectively (8, 223, 293). The vacuum ultraviolet spectrum has also been studied (177). The 19F NMR spectrum of NF3 shows a triplet at 145 + 1 ppm relative to CC13F with JNF = 155 Hz (146, 216, 220,249, 280). 

The equilibrium molecular geometry of thiophene has been determined from a combination of gas-phase electron diffraction (ED) vibrational and microwave data and ab initio and DFT calculations (Table 19) <2001JST(567)29>. 

---