The Vacuum

The two theories of physics project a face of inscrutability to the uninitiated, which means virtually the entire world population. The science writers who have tried to bridge the gap did so in a woefully uncritical fashion. A notable exception was the philosopher Karl Popper (1965) who made a ruthless analysis of the near-dogmatic nature of quantum theory. 

The physics community have distanced themselves from the debate by accepting quantum theory as a mathematically useful tool, without agonizing over the physical interpretation. For the chemist who deals with three-dimensionally structured objects, like molecules, this approach creates a dilemma. Modern chemistry is best understood in terms of experimentally measured electron-density distributions, awkward, if not impossible, to visualize in terms of zero-dimensional objects. The alternative wave model, not only makes intuitive sense, but also eliminates poorly defined concepts such as probability densities and quantum jumps. 

The wave nature of the electron and the physical implications thereof were discussed recently in some detail (Boeyens, 2010). As in the theory of general relativity it is accepted that an empty universe is featureless and flat, but that curvature of space-time causes wavelike distortion of the vacuum. The equivalent of an infinite plane wave in flat space develops interference effects, like wave packets, in curved space, interpreted as units of mass and energy. 

The tangent curve follows the amplitude of the 1/r Coulomb potential, which reflects the actual charge density, except when r — 0. 

The secondary waves propagate with the group velocity Vg of the system and the primary waves have phase velocity v, such that VgV = 

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Vacuum distillation of the atmospheric residue complements primary distillation, enabli r.ecoyery of heavy distillate cuts from atmospheric residue that will un r o further conversion or will serve as lube oil bases. The vacuum residue containing most of the crude contaminants (metals, salts, sediments, sulfur, nitrogen, asphaltenes, Conradson carbon, etc.) is used in asphalt manufacture, for heavy fuel-oil, or for feed for others conversion processes. 

Deasphalting is a liquid-liquid separation operation that extracts the last of the easily convertible hydrocarbons from the vacuum residue. Solvents enipl ec) are light paraffins propane, butane, and pentane. The yimd In deasphalted oil increases with the molecular weight of the solvent, but its quality decreases. 5 uxct... 

As anode and cathode of the tube have to share the same vacuum envelope, and the insulating material has to insulate the high tension between these respective electrodes, the material is always part of the vacuum envelope of the tube. Therefore, the insulator has to be vacuum tight and must be able to carry the atmospheric pressure, which loads this envelope. 

The X-ray beam often leaves the tube envelope through a special beam window. This window also must be joined with the vacuum envelope. 

The material is brittle. There are relatively large radii to be obeyed to enable the vacuum envelope to withstand atmospheric pressure, and tubes must be handled carefully. 

Glass can be machined to a very limited extend only. Treatment of glass for the production of tubes is delicate and requires lots of special tools. The shape of the vacuum envelope can t be simply changed. Glass is more suitable for mass production of simple shaped goods. 

A related advantage of studying crystalline matter is that one can have synnnetry-related operations that greatly expedite the discussion of a chemical bond. For example, in an elemental crystal of diamond, all the chemical bonds are equivalent. There are no tenninating bonds and the characterization of one bond is sufficient to understand die entire system. If one were to know the binding energy or polarizability associated with one bond, then properties of the diamond crystal associated with all the bonds could be extracted. In contrast, molecular systems often contain different bonds and always have atoms at the boundary between the molecule and the vacuum. 

Since solids do not exist as truly infinite systems, there are issues related to their temiination (i.e. surfaces). However, in most cases, the existence of a surface does not strongly affect the properties of the crystal as a whole. The number of atoms in the interior of a cluster scale as the cube of the size of the specimen while the number of surface atoms scale as the square of the size of the specimen. For a sample of macroscopic size, the number of interior atoms vastly exceeds the number of atoms at the surface. On the other hand, there are interesting properties of the surface of condensed matter systems that have no analogue in atomic or molecular systems. For example, electronic states can exist that trap electrons at the interface between a solid and the vacuum [1]. 

The surface work fiincdon is fonnally defined as the minimum energy needed m order to remove an electron from a solid. It is often described as being the difference in energy between the Fenni level and the vacuum level of a solid. The work ftmction is a sensitive measure of the surface electronic structure, and can be measured in a number of ways, as described in section B 1.26.4. Many processes, such as catalytic surface reactions or resonant charge transfer between ions and surfaces, are critically dependent on the work ftmction. 

Other atoms and molecules also show similar series of lines, often in the vacuum ultraviolet region, which fit approximately a similar fonuula ... 

Herzberg G, Lagerquist A and Malmberg C 1969 New electronic transitions of the C2 molecule absorption in the vacuum ultraviolet region Can. J. Phys. 47 2735-43... 

Continuous wave (CW) lasers such as Ar and He-Ne are employed in conmionplace Raman spectrometers. However laser sources for Raman spectroscopy now extend from the edge of the vacuum UV to the near infrared. Lasers serve as an energetic source which at the same hme can be highly monochromatic, thus effectively supplying the single excitation frequency, v. The beams have a small diameter which may be... 

The vacuum requirements in the target chamber are relatively modest (10 Pa) and are comparable to those in the accelerator beam lines. All that is required is that the ion beam does not lose energy on its path to the sample and that there is minimal deposition of contaminants and hydrocarbons on the surface during analysis. 

This teclnhque can be used both to pennit the spectroscopic detection of molecules, such as H2 and HCl, whose first electronic transition lies in the vacuum ultraviolet spectral region, for which laser excitation is possible but inconvenient [ ], or molecules such as CH that do not fluoresce. With 2-photon excitation, the required wavelengdis are in the ultraviolet, conveniently generated by frequency-doubled dye lasers, rather than 1-photon excitation in the vacuum ultraviolet. Figure B2.3.17 displays 2 + 1 REMPI spectra of the HCl and DCl products, both in their v = 0 vibrational levels, from the Cl + (CHg) CD reaction [ ]. For some electronic states of HCl/DCl, both parent and fragment ions are produced, and the spectrum in figure B2.3.17 for the DCl product was recorded by monitoring mass 2 (D ions. In this case, both isotopomers (D Cl and D Cl) are detected. 

The homonuclear rare gas pairs are of special interest as models for intennolecular forces, but they are quite difficult to study spectroscopically. They have no microwave or infrared spectmm. However, their vibration-rotation energy levels can be detennined from their electronic absorjDtion spectra, which he in the vacuum ultraviolet (VUV) region of the spectmm. In the most recent work, Hennan et al [24] have measured vibrational and rotational frequencies to great precision. In the case of Ar-Ar, the results have been incoriDorated into a multiproperty analysis by Aziz [25] to develop a highly accurate pair potential. 

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

For the case of nonzero temperatures the vacuum averages in Eq.(7) should be replaced by thermal averages over phonon populations. Using (7) and (5) we obtain that the scattering of an exciton in the effective medium by the perturbation fi — v z)) is described by the following self-consistent condition... 

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section 7.2.3.6. 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

The explicit definition of water molecules seems to be the best way to represent the bulk properties of the solvent correctly. If only a thin layer of explicitly defined solvent molecules is used (due to hmited computational resources), difficulties may rise to reproduce the bulk behavior of water, especially near the border with the vacuum. Even with the definition of a full solvent environment the results depend on the model used for this purpose. In the relative simple case of TIP3P and SPC, which are widely and successfully used, the atoms of the water molecule have fixed charges and fixed relative orientation. Even without internal motions and the charge polarization ability, TIP3P reproduces the bulk properties of water quite well. For a further discussion of other available solvent models, readers are referred to Chapter VII, Section 1.3.2 of the Handbook. Unfortunately, the more sophisticated the water models are (to reproduce the physical properties and thermodynamics of this outstanding solvent correctly), the more impractical they are for being used within molecular dynamics simulations. 

For more efficient drying at elevated temperatures, the vacuum apparatus (Fig. 48(A)) is often used. The sample to be dried is placed in an inner tube surrounded by a heating jacket. 

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