Van der Waals dimer

A very interesting field of research covers the spectroscopy of van der Waals molecules in search of more detailed information about the long range potential and the polarizability. Raman spectra of van der Waals dimers in argon have been observed and a vibrational frequency shift for I2-molecules from 213 cm" to 197 cm has been measured for I2 -Ar-complexes. 

Substituent effects on intermolecular J(H,H) and J(C,H) couplings in van der Waals dimers were studied by Scorrano et al375 by performing both... 

Figure 1.2 illustrates the difference between the transitions involved in van der Waals dimer bands which Welsh and associates hoped to find, and the collision-induced absorption spectra that were discovered instead. Intermolecular interaction is known to be repulsive at near range and attractive at more distant range. As a consequence, a potential well exists which for most molecular pairs is substantial enough to support bound states. Such a bound state is indicated in Fig. 1.2 (solid curve b). When infrared radiation of a suitable frequency is present, the dimer may undergo various transitions from the initial state (solid curve) to a final state which may have a rather similar interaction potential (dashed curve b ) and dimer level spacings. Such transitions (marked bound-bound) often involve a change of the rotovibrational state(s) EVj of one or both molecule(s),... 

Near the line centers, the spectral functions have sometimes been approximated by a Lorentzian. The far wings, on the other hand, may be approximated by exponential functions as Fig. 3.2 might suggest. However, better model profiles exist see Chapters 5 and 6 [421, 102, 320], Model profiles have been useful for fitting experimental spectra, for an extrapolation of measured profiles to lower or higher frequencies (which is often needed for the determination of spectral moments) and for a prediction of spectra at temperatures for which no measurements exist. We note that van der Waals dimer structures (which appear at low frequencies and low pressures) modify the Lorentzian-like appearance more or less, as we will see. 

Figure 3.41 compares the spectra of similar van der Waals dimers, from... 

The second term describes the bound-to-bound contributions, that is the rotovibrational bands of the van der Waals dimer. If the system does not form dimers, this term and the following two terms all vanish. For practical use, the d function in this term should be replaced by an instrumental slit function, or perhaps with some Lorentzian if pressure broadening affects the individual lines (as will often be the case). In any case, the d function is symbolic for the relatively sharp dimer lines that... 

At lower temperature, striking features arise from van der Waals dimers that have been studied experimentally [422, 259, 334,412] and theoretically [161, 150] by a number of investigators. 

The anisotropy of the interaction couples the translational and rotational states of collisional systems. This in turn couples the various dipole components. Instead of computing for each set of expansion parameters X XiSL one general profile for all rotational components associated with that set, one now has a much more complex computational task to compute the induced absorption continua. Moreover, the energy level diagrams as well as the spectra of van der Waals dimers are much more complex when the anisotropy of the interaction is accounted for. 

K. Yamanouchi Recently, we investigated the interatomic potential VRyd(/ ) of the Rydberg states of a HgNe van der Waals dimer by optical-optical double-resonance spectroscopy. It was demonstrated that VRyd(/ ) sensitively varies as a function of the principal quantum number n [J. Chem. Phys., 98, 2675 (1993) ibid., 101, 7290 (1995) ibid., 102, 1129 (1995)], and in the lowest Rydberg states of Hg(7 3S )Ne and Hg(7 5o)Ne, the interatomic potentials exhibit a distinct barrier at around R 4 A. The existence of the barrier was interpreted in terms of a repulsive interaction caused by the Is Rydberg... 

The foregoing examples show how the resonant coupling can be used to deduce proximity of C02 molecules, and in favorable cases, a reasonably adequate description of their relative positions. In fact, many vibrational spectroscopists who study van der Waals dimers in matrices rely almost entirely on the intermolecular coupling to assess structure [89]. Our... 

The microwave spectrum of the normal argon-acetaldehyde and of the Ar-CHsCDO van der Waals dimer has been used to determine their structure646 which was found to be a non-planar skew, with the Ar binding on top of the C—C—O triangle. The planar or nearly so structure of the Ar-formic acid van der Waals dimer has also been determined647 from assigning the rotation spectrum of normal, Ar, DCOOH and HCOOH isotopomers. 

The determination of a one-dimensional ladder molecular array structure of O2 molecules was first performed using in situ synchrotron powder XRD measurements on CPL-1 accommodating O2 molecules.77 78 The intermolecular distance of the adsorbed O2 molecules (3.28(4) A) is close to the nearest distance in the solid a-02 phase, whose close-packed structure appears below 24 K. This result indicates that O2 molecules adsorbed in the nanochannels form van der Waals dimers, (02)2- The X-ray structural analysis shows that 02 molecules are in the solid state rather than the liquid state, even at 130 K and 80kPa, which are much higher than the boiling point of bulk O2 at atmospheric pressure, 54.4 K. This result is ascribed to the strong confinement effect of CPL-1. 

Equation (1-13) or its body-fixed equivalent is of little use for Van der Waals complexes, as it discriminates one nuclear coordinate, e.g. y = 1. Specific mathematical forms of Hamiltonians describing the nuclear motions in Van der Waals dimers have been developed (7). This point will be discussed in more details in Section 12.4. Here we only want to stress that whatever the mathematical form of the Hamiltonian is used to solve the problem of nuclear motions, the results will be the same, if the Schrodinger equation is solved exactly. However, in weakly bound complexes there is a hierarchy of motions due to the strong intramolecular forces which determine the internal vibrations of the molecules, and to much weaker intermolecular forces which determine their relative translations and rotations. This hierarchy allows to make a separation between the intramolecular vibrations with high frequencies and the intermolecular modes with much lower frequencies. Such a separation of the fast intramolecular vibrations and slow rotation-vibration-tunneling motions can be performed if a suitable form of the Hamiltonian for the nuclear motions in Van der Waals molecules is used. 

Prengel AT, Gornall WS (1976) Raman scattering from colliding molecules and Van der Waals dimers in gaseous methane. Phys Rev A 13 253-262... 

However, the importance of good stacking should not be exaggerated The 12.5 K superconductor k-(ET)2Cu[N(CN)2]C1 has a layer of donors which form van der Waals "dimers" of two ET species with charge p = 1/2 each, with good intra-dimer overlap but bad interdimer overlap, and yet the system is superconducting ... 

M.R de Lara-Castells, et at, Complete basis set extrapolation limit for electronic structure calculations Energetic and nonenergetic properties of HeBr and HeBr2 van der Waals dimers, /. Chem. Phys. 115 (22) (2001) 10438-10449. 

A van-der-Waals dimer (N2)2 with a dissociation energy of only about IkJmol has been detected experimentally. Another N4 species, which was prepared by neutralizing N4+, was detected mass spectrometrically, and is beheved to be the C triplet because of its fragmentation pattern. The geometry of the starting material N4+ also points to a linear structure. 

We have studied the potential hypersuifaces for the Van der Waals dimers ( 2 (CjH by varying all the independent internal coordinates (in the rigid molecule cq>proximation, 3 angles for (Nj), 5 angles for and the distance R in both... 

Leaving aside this dynamical problem, we can make some further remarks about the equilibrium structure of Van der Waals molecules. Some attempts have been made to predict this structure from the molecular properties, multipole moments, polarizabilities, which are reflected in the long range interactions (electrostatic, dispersion). Other authors have assumed that the equilibrium structure of Van der Waals dimers resembles the structure of nearest neighbour pairs in molecular crystals. The latter approach could possibly be justified by packing considerations (short range repulsion). An example of the first approach is the prediction of a T-shaped (0 = 90°, 0 = < ) = 0°) equilibrium structure for the Nj-dimer, mainly... 

In the very same way as the Bom-Oppenheimer approximation allows the definition of a potential energy surface for a Van der Waals molecule, it enables, too, the conceit of an interaction tensor field. This is a field dependent on the relative coordinates of the monomers and transforming as a tensor under rotation of the complex as a ole. (The potential energy surface is an example of a rank zero interaction tensor field). In the case of tensor fields it is also convenient to base the theory on irreducible tensors and to use an e7q>ansion in terms of a complete set of functions of the five angular coordinates describing a Van der Waals dimer. 

It is possible to apply the mxiltipole e q>ansion and perturbation theory in order to derive long range expressions for Tj (R), thus relating this quantity to monomer I operties. A simple example of sudi a procedure can be found in the appendix of ref. where the induction contribution to the dipole moment (J = 1) of an arbitrary Van der Waals dimer has been evaluated. 

The dipole momwit of a Van der Waals dimer consists in principle of three contributions the dipole moments of the two monomers and the interaction dipole moment. In tl usual Van der Waals molecules the interaction dipole is in the order of 0.1 which for a large part arises from induction. That is, permanent... 

A barely touched field of research is the use of Raman spectroscopy for the study of van der Waals dimers (and of higher bound complexes). In the low-density limit, to a large extent, CILS is the spectroscopy of the unbound molecular pairs in collisional interaction. However, it is well known that theoretically for most gases, even at room temperature, a small percentage of the observable intensities of the so-called collision-induced Raman spectra arises from bound-bound and bound-free transitions involving van der... 

Waals dimers [266, 267, 302, 328], The theoretically predicted dimer Raman spectra [262, 263] have hitherto not been observed in the laboratory, presumably because of the substantial width (%10GHz) of the 5145- and 4880-A argon laser lines commonly employed in such work and because the high gas densities used tend to broaden the rotational features and render them indiscernible [262], Nevertheless, the envelopes of the rotational van der Waals dimer bands have been seen in several gases and mixtures [229, 230, 266, 267, 328]. Under more favorable jet expansion conditions, high-resolution argon dimer spectra have been obtained recently [280], There seems to be little room for doubt that eventually van der Waals dimer spectra will be obtained with ordinary Raman or third-order nonlinear techniques [676]. 

Theory. If the invariants of the pair polarizability are known, along with a refined model of the intermolecular interaction potential, the lineshapes of binary spectra can be computed quite rigorously [227, 231, 271], Lineshape computations based on exact or approximate classical trajectories are known [196, 264, 276, 316, 337]. Such computations generate spectral functions that are symmetric, g — co) = g((o). For massive pairs at high enough temperatures, such classical profiles are often sufficient at frequency shifts much smaller than the average thermal energy, ha> < kT, albeit special precaution is necessary when the system forms van der Waals dimers [302]. 

L. Frommhold and R. Bain. Comments concerning the Raman spectra of van der Waals dimers in argon. J. Chem. Phys., 63 1700-1702 (1975). 

Table 5.4 Comparison of the model structural predictions with experiment. Reprinted from Journal of Molecular Structure THEOCHEM, 204, Magnasco, V. etal., A model for the elementary prediction of the angular shape of Van der Waals dimers. 229-246, Copyright (1990), with permission from Elsevier...

Magnasco, V., Costa, C., and Figari, G. (1989b) On the angular shape of van der Waals dimers of small polar molecules. Chem. Phys. Lett., 160, 469 178. 

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