Overton Theory

General anesthetics are usually small solutes with relatively simple molecular structure. As overviewed before, Meyer and Overton have proposed that the potency of general anesthetics correlates with their solubility in organic solvents (the Meyer-Overton theory) almost a century ago. On the other hand, local anesthetics widely used are positively charged amphiphiles in solution and reversibly block the nerve conduction. We expect that the partition of both general and local anesthetics into lipid bilayer membranes plays a key role in controlling the anesthetic potency. Bilayer interfaces are crucial for the delivery of the anesthetics. 

The quantitative property-activity models, commonly referred to as those marking the beginning of systematic QSAR/QSPR studies [Richet, 1893], have come out from the search for relationships between the potency of local anesthetics and the oil/water partition coefficient [Meyer, 1899], between narcosis and chain length [Overton, 1901, 1991], and between narcosis and surface tension [Traube, 1904]. In particular, the concepts developed by Meyer and Overton are often referred to as the Meyer-Overton theory of narcotic action [Meyer, 1899 Overton, 1901]. 

The search for physical chemical correlates of drug action began as early as 1899 with the Meyer-Overton theory which stated that the potency of an anesthetic was directly proportional to its oil. water partition coefficient. The more lipid soluble the compound was, the more readily it was thought to penetrate the central nervous system. 

There have been many attempts to produce a unified theory detailing the mechanism of action of inhalation anaesthetics but no single theory has been accepted. Early theories on the mechanism of action of inhalation anaesthetics can by summarised by means of the Meyer-Overton theory, which indicated that the potency of anaesthetic action was related to the lipophilicity of an anaesthetic compound. The Meyer-Overton theory suggested that lipids within the brain could be dissolved by anaesthetic agents, thereby interfering with brain cell activity, leading to anaesthesia. 

Ha T-K, Lewerenz M, Marquardt R and Quack M 1990 Overtone Intensities and dipole moment surfaces for the Isolated CH chromophore In CHD3 and CHF3 experiment and ab initio theory J. Chem. Phys. 93 7097-109... 

Albrecht A C, Clark R J H, Oprescu D, Owens S J R and Svensen C 1994 Overtone resonance Raman scattering beyond the Condon approximation transform theory and vibronic properties J. Chem. Phys. 101 1890-903... 

The approach is ideally suited to the study of IVR on fast timescales, which is the most important primary process in imimolecular reactions. The application of high-resolution rovibrational overtone spectroscopy to this problem has been extensively demonstrated. Effective Hamiltonian analyses alone are insufficient, as has been demonstrated by explicit quantum dynamical models based on ab initio theory [95]. The fast IVR characteristic of the CH cliromophore in various molecular environments is probably the most comprehensively studied example of the kind [96] (see chapter A3.13). The importance of this question to chemical kinetics can perhaps best be illustrated with the following examples. The atom recombination reaction... 

The purpose of these comparisons is simply to point out how complete the parallel is between the Rouse molecular model and the mechanical models we discussed earlier. While the summations in the stress relaxation and creep expressions were included to give better agreement with experiment, the summations in the Rouse theory arise naturally from a consideration of different modes of vibration. It should be noted that all of these modes are overtones of the same fundamental and do not arise from considering different relaxation processes. As we have noted before, different types of encumbrance have different effects on the displacement of the molecules. The mechanical models correct for this in a way the simple Rouse model does not. Allowing for more than one value of f, along the lines of Example 3.7, is one of the ways the Rouse theory has been modified to generate two sets of Tp values. The results of this development are comparable to summing multiple effects in the mechanical models. In all cases the more elaborate expressions describe experimental results better. 

Professor Meyer was born at Dorpat, Estonia, on September 29, 1883, the elder son of Hans Horst Meyer—who held the chair of experimental pharmacology at the University of Vienna and formulated the modern theory of narcosis known as the Overton-Meyer theory. Two years later, his father became professor at Marburg/Lahn, and it was in this city that Kurt H. Meyer had his early education. The scholarly atmosphere in which he matured, where chemistry and medicine were always very much in the foreground, was to influence him throughout his lifetime. From his father, he inherited his desire for scientific study and research, and from his mother, his taste for the fine arts. His younger brother became a famous heart-surgeon. 

The number of fundamental vibrational modes of a molecule is equal to the number of degrees of vibrational freedom. For a nonlinear molecule of N atoms, 3N - 6 degrees of vibrational freedom exist. Hence, 3N - 6 fundamental vibrational modes. Six degrees of freedom are subtracted from a nonlinear molecule since (1) three coordinates are required to locate the molecule in space, and (2) an additional three coordinates are required to describe the orientation of the molecule based upon the three coordinates defining the position of the molecule in space. For a linear molecule, 3N - 5 fundamental vibrational modes are possible since only two degrees of rotational freedom exist. Thus, in a total vibrational analysis of a molecule by complementary IR and Raman techniques, 31V - 6 or 3N - 5 vibrational frequencies should be observed. It must be kept in mind that the fundamental modes of vibration of a molecule are described as transitions from one vibration state (energy level) to another (n = 1 in Eq. (2), Fig. 2). Sometimes, additional vibrational frequencies are detected in an IR and/or Raman spectrum. These additional absorption bands are due to forbidden transitions that occur and are described in the section on near-IR theory. Additionally, not all vibrational bands may be observed since some fundamental vibrations may be too weak to observe or give rise to overtone and/or combination bands (discussed later in the chapter). 

The anharmonicity of the O—H stretching oscillators changes with cluster size. For the monomer, the anharmonicity constant is on the order of 90 cm 1. A coarse deuteration analysis [16, 88] suggests that it increases by more than 20% upon trimer and tetramer formation [16]. More accurate overtone analyses are possible in a rare gas matrix [88], but the matrix shift complicates a direct comparison to theory. As an example, the overtone-deduced anharmonicity of methanol monomer in a nitrogen matrix [88] is 85 cm whereas in vacuum [16] it is 92 cm The deuteration-estimated anharmonicity is 91 cm 1 for the monomer and 97 cm 1 for the dimer donor in the nitrogen matrix, whereas it is 87 cm 1 for the monomer and 89 cm 1 for the dimer donor in vacuum. Clearly, only a vacuum overtone measurement would be fully conclusive, but as the matrix study [88]... 

The coefficient of partition of organic substances between water and lipins (these are fat-like constituents of the cell wall) is of great importance in biological processes (H. H. Meyer and Overton s theory of narcosis). 

Figure 6.9 Observed opto-thermal spectrum of the Avcw = 3 overtone of benzene (points with error bars) and a stick spectrum calculated by means of the algebraic theory. Labels indicate the most important states involved in borrowing intensity from the CH overtone. Adapted from Bassi et al. (1993).

The second set of problems in dynamics are those of scattering theory where the Hamiltonian is of the form H = H0 + V and the interaction V vanishes when the colliding particles are far apart. It is usually assumed that the H0 part is already solved and that the interesting or the hard part is to account for the role of V. For realistic systems, which are anharmonic, even the role of H() can be quite significant. An example that has received much recent attention is the reaction of vibrationally excited HOD with H atoms (Sinha et al., 1991 Figure 8.2). The large difference in the OH and OD vibrational frequencies means that the stretch overtones of HOD are primarily local in character (cf. Section 4.21). It follows that one can excite HOD to overtones localized preferentially on either one of the two bonds and that an approaching H atom will abstract prefer-... 

Halonen, L. (1989), Recent Developoments in the Local Mode Theory of Overtone Spectra, 7. Phys. Chem. 93, 3386. 

The Meyer-Overton hypothesis is the theory of anaesthetic action which proposes that the potency of an anaesthetic agent is related to its lipid solubility. 

At the same time (1902), a membrane theory was proposed for the electrical properties of cells and tissues by Overton [80] and Bernstein [8], whose principles remain valid to the present day. 

Dennis s rap drew on the theory of sound. If you pluck a string, it will sound in the octave in which it is struck, but it will also sound in octaves above and below its key. It has what are called harmonic overtones. If you strike the chord and then squelch it, you can still hear the harmonic overtones, a phenomenon that had fascinated Pythagoras. Dennis pointed out to us that one can use two sounds to cancel each other if the two sounds are exactly the same in relation to each other. 

Fig. 6.10. Absorption in the first overtone band of H2 by H2-H2 at 300 K. Comparison of theory (heavy line) and measurements (dots) [284].

Theory predicts that for a harmonic oscillator only a change from one vibrational energy level to the next higher is allowed, but for anharmonic oscillators weaker transitions to higher vibrational energy levels can occur. The resulting "overtones" are found at approximate multiples of the frequency of the fundamental. Combination frequencies representing sums... 

Dephasing Times Predicted from Fundamental Overtone of the C-I Stretching Mode in CH3I and C-H Stretching Mode in CHCL3 Using Mode Coupling Theory (MCT), the Hydrodynamics Theory (HT) [125], and the Experimental (Exptl)... 

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