Individual Molecules

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

When the overlap between the wavefiinctions of the interacting molecules cannot be neglected, the zeroth-order wavefiinction must be anti-symmetrized with respect to all die electrons. The requirement of anti-synmietrization brmgs with it some difficult problems. If electrons have been assigned to individual molecules... 

The nonlinear response of an individual molecule depends on die orientation of the molecule with respect to the polarization of the applied and detected electric fields. The same situation prevails for an ensemble of molecules at an interface. It follows that we may gamer infonnation about molecular orientation at surfaces and interfaces by appropriate measurements of the polarization dependence of the nonlinear response, taken together with a model for the nonlinear response of the relevant molecule in a standard orientation. 

Fleury L, Gruber A, Draebenstedt A, Wrachtrup J and von Borczyskowski C 1997 Low-temperature confocal microscopy on individual molecules near a surface J. Phys. Chem. B 101 7933-8... 

One interesting new field in the area of optical spectroscopy is near-field scaiming optical microscopy, a teclmique that allows for the imaging of surfaces down to sub-micron resolution and for the detection and characterization of single molecules [, M]- Wlien applied to the study of surfaces, this approach is capable of identifying individual adsorbates, as in the case of oxazine molecules dispersed on a polymer film, illustrated in figure Bl.22,11 [82], Absorption and emission spectra of individual molecules can be obtamed with this teclmique as well, and time-dependent measurements can be used to follow the dynamics of surface processes. 

The statistics of the detected photon bursts from a dilute sample of cliromophores can be used to count, and to some degree characterize, individual molecules passing tlirough the illumination and detection volume. This can be achieved either by flowing the sample rapidly through a narrow fluid stream that intersects the focused excitation beam or by allowing individual cliromophores to diffuse into and out of the beam. If the sample is sufficiently dilute that... 

The ability to make optical measurements on individual molecules and submicroscopic aggregates, one at a time, is a valuable new tool in several areas of molecular science. By eliminating inlromogeneous broadening it allows pure spectroscopy to be perfonned witli unprecedented precision in certain condensed phase systems. As an analytical method it pennits tire rapid detection of certain analytes witli unmatched sensitivity. Finally, it is revolutionizing our... 

Moerner W E, Plakhotnik T, Irngartinger T, Wild U P, Pohl D W and Hecht B 1994 Near-field optical spectroscopy of individual molecules in solids Phys. Rev. Lett. 73 2764-7... 

Sonnieitner M, Schutz G J and Schmidt T 1999 Imaging individual molecules by two-photon excitation Chem. Phys. Lett 300 221-6... 

Skinner J L 1997 Theoretical models for the spectral dynamics of individual molecules in solids Single Molecule Optical Detection, Imaging and Spectroscopy ed T Basche, W E Moerner, M Orrit and U P Wild (Weinheim VCFI)... 

Geva E, Reilly P D and Skinner J L 1996 Spectral dynamics of individual molecules in glasses and crystals Acc. Chem. Res. 29 579-84... 

Myers A B, Tchenio P, Zgierski M Z and Moerner W E 1994 Vibronic spectroscopy of individual molecules in solids J. Chem. Phys. 98 10 377-90... 

Xue Q and Yeung E S 1995 Differences in the chemical reactivity of individual molecules of an enzyme Nature 373 681-3... 

The modem era of biochemistry and molecular biology has been shaped not least by the isolation and characterization of individual molecules. Recently, however, more and more polyfunctional macromolecular complexes are being discovered, including nonrandomly codistributed membrane-bound proteins [41], These are made up of several individual proteins, which can assemble spontaneously, possibly in the presence of a lipid membrane or an element of the cytoskeleton [42] which are themselves supramolecular complexes. Some of these complexes, e.g. snail haemocyanin [4o], are merely assembled from a very large number of identical subunits vimses are much larger and more elaborate and we are still some way from understanding the processes controlling the assembly of the wonderfully intricate and beautiful stmctures responsible for the iridescent colours of butterflies and moths [44]. 

Here t. is the intrinsic lifetime of tire excitation residing on molecule (i.e. tire fluorescence lifetime one would observe for tire isolated molecule), is tire pairwise energy transfer rate and F. is tire rate of excitation of tire molecule by the external source (tire photon flux multiplied by tire absorjDtion cross section). The master equation system (C3.4.4) allows one to calculate tire complete dynamics of energy migration between all molecules in an ensemble, but tire computation can become quite complicated if tire number of molecules is large. Moreover, it is commonly tire case that tire ensemble contains molecules of two, tliree or more spectral types, and experimentally it is practically impossible to distinguish tire contributions of individual molecules from each spectral pool. 

After that time, energy loss from any individual molecule most likely involves a stepwise relaxation, but ensemble... 

The biologiccJ function of a protein or peptide is often intimately dependent upon the conformation(s) that the molecule can adopt. In contrast to most synthetic polymers where the individual molecules can adopt very different conformations, a protein usually exists in a single native state. These native states are found rmder conditions typically found in Uving cells (aqueous solvents near neutred pH at 20-40°C). Proteins can be unfolded (or denatured) using high-temperature, acidic or basic pH or certain non-aqueous solvents. However, this unfolding is often reversible cind so proteins can be folded back to their native structure in the laboratory. 

Once a wave function has been determined, any property of the individual molecule can be determined. This is done by taking the expectation value of the operator for that property, denoted with angled brackets < >. For example, the energy is the expectation value of the Hamiltonian operator given by... 

Consider a quantity of some liquid, say, a drop of water, that is composed of N individual molecules. To describe the geometry of this system if we assume the molecules are rigid, each molecule must be described by six numbers three to give its position and three to describe its rotational orientation. This 6N-dimensional space is called phase space. Dynamical calculations must additionally maintain a list of velocities. 

The dielectric constant is a property of a bulk material, not an individual molecule. It arises from the polarity of molecules (static dipole moment), and the polarizability and orientation of molecules in the bulk medium. Often, it is the relative permitivity 8, that is computed rather than the dielectric constant k, which is the constant of proportionality between the vacuum permitivity so and the relative permitivity. 

The susceptibility tensors give the correct relationship for the macroscopic material. For individual molecules, the polarizability a, hyperpolarizability P, and second hyperpolarizability y, can be defined they are also tensor quantities. The susceptibility tensors are weighted averages of the molecular values, where the weight accounts for molecular orientation. The obvious correspondence is correct, meaning that is a linear combination of a values, is a linear combination of P values, and so on. 

This chapter focuses on the simulation of bulk liquids. This is a dilferent task from modeling solvation effects, which are discussed in Chapter 24. Solvation effects are changes in the properties of the solute due to the presence of a solvent. They are defined for an individual molecule or pair of molecules. This chapter discusses the modeling of bulk liquids, which implies properties that are not defined for an individual molecule, such as viscosity. 

Another way of predicting liquid properties is using QSPR, as discussed in Chapter 30. QSPR can be used to And a mathematical relationship between the structure of the individual molecules and the behavior of the bulk liquid. This is an empirical technique, which limits the conceptual understanding obtainable. However, it is capable of predicting some properties that are very hard to model otherwise. For example, QSPR has been very successful at predicting the boiling points of liquids. 

Solids can be crystalline, molecular crystals, or amorphous. Molecular crystals are ordered solids with individual molecules still identihable in the crystal. There is some disparity in chemical research. This is because experimental molecular geometries most often come from the X-ray dilfraction of crystalline compounds, whereas the most well-developed computational techniques are for modeling gas-phase compounds. Meanwhile, the information many chemists are most worried about is the solution-phase behavior of a compound. 

Specific Rotation. Optical rotation is caused by individual molecules of the optically active compound. The amount of rotation depends upon how many molecules the light beam encounters in passing through the tube. When allowances are made for the length of the tube that contains the sample and the sample concentration, it is found that the amount of rotation, as well as its direction, is a characteristic of each individual optically active compound. 

As indicated in the previous section, the adsorption of a gas by a solid is the outcome of the forces of attraction between the individual molecules of the gas and the atoms or ions composing the solid. These forces have been studied theoretically over a number of decades, and though impressive advances have been made in recent years these remain more in the nature of refinements than of fundamental changes in the ideas themselves. And since. 

The three levels of structure listed above are also useful categories for describing nonprotein polymers. Thus details of the microstructure of a chain is a description of the primary structure. The overall shape assumed by an individual molecule as a result of the rotation around individual bonds is the secondary structure. Structures that are locked in by chemical cross-links are tertiary structures. 

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