Buckingham formula

From the point of view of the Buckingham formula (Equation (2.23)) only the effect of long-range electrostatic and induction interactions crE of the solvent molecule with the reaction field is included in the traditional methods of the (n) group (continuum models). Contrary to that, the supermolecular approach (I) or combined MD/QM methods (III) includes the short-range term cra and the long-range crw and some of the [Pg.132]

A similar generalization was also made by Buckingham. He followed Kirk-i.s wood s idea" in deriving the electric moment of a dielectric specimen produced by a fixed molecule in its interior and Scholte s extension of the cavity field and the reaction field in the Onsager-Bbttcher theoiy " to an ellipsoidal cavity. Buckingham s formula involves the polarizability of the solute molecule and appears quite different from Eq. [10.2.2]. It was shown that the Buckingham formula reduces to Eq. [10.2.2],... 

While these equations are descriptive of the flume, they are reasonably close to the prediction model derived by Churchill, Elmore, and Buckingham from their analysis of atmospheric reaeration of streams in the Tennessee Valley (11). The Churchill et al. formula for prediction of k2 at 20°C is... 

Both types of functions are commonly used. Several sets of a, b, c, and d, coefficients are available [1-3]. Equally good results can be obtained using Lennard-Jones-type functions alone or Buckingham-type functions alone or mixtures of Lennard-Jones and Buckingham functions [4]. The attraction coefficients in these expressions are generally but not always calculated with the formula of Slater and Kirkwood [5] ... 

The reader will find the corresponding formulas in the article by A.D. Buckingham, Advan. Chem. Phys., 12, 107 (1967) or by AJ. Sadlej, Introduction to the theory of intemiolecular interactions Lund s Theoretical Chemistry Lecture Notes. Lund (1990). 

Dictionary of Organic Compounds, 6th ed., Buckingham, J., ed. Chapman Hall, New York, 1996. The DOC is an excellent source for physical and chemical data on over 100,000 organic compounds and derivatives. Entries also provide literature references for synthesis, characterization, spectra, and properties, making the DOC useful as a starting point in a literature search. The 6th edition is in nine volumes. Volumes 1-6 contain the data for the compounds. Volume 7 is a name index with cross-references. Volume 8 contains a molecular-formula index, and Volume 9 is a CAS RN index. Some institutions subscribe to a Web version of the DOC and similar compilations called the Combined Chemical Dictionary (CCD), part of the ChemNetBase system provided by Chapman Hall/CRC Press. 

Apart from motivating the definition of the electric moments, the importance of the multipole expansion in Eq. (4.10) lies in the fact that we can calculate the electrostatic potential 4> R) for any point R from the simple formula in Eq. (4.10) as soon as we know the electric multipole moments of the corresponding charge distribution p r) instead of evaluating the more complicated expression in Eq. (4.1) for each R. A major application of electric multipole moments is thus the description and calculation of intermolecular forces (Buckingham, 1967). 

Buckingham parameters must always be specified for Lennard-Jones parameters Examples given check with atom pairs. Por formulae. 

Whereas all the theoretical papers mentioned here discuss the vibrational contribution to the (hyper)polarizabilities, only Whitehouse and Buckingham [4] made an attempt to calculate these properties for the type of system in which we are interested. They used a much simplified pofenfial, in conjunction with a classical analysis— estimated to be valid above 20 K—to obtain a (temperature-dependent) expression for the vibrationally averaged dipole moment. Then, from the field-dependence of this expression, formulas for the vibrational linear polarizability and second hyperpolarizability were extracted and the former quantity was evaluated for the [Li C6o] ... 

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