ABC Is For Christmas by Jane Werner with illustrations by Sally Augustiny Watson

By Jane Werner with illustrations by Sally Augustiny Watson

ABC is for Christmas

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1-97) and (1-92). The 3 expression for Eind−disp B can be obtained from Eq. (1-101) by interchanging symbols pertaining to monomers A and B. It is worth noting that the inductiondispersion contribution can be obtained in a second-order perturbation treatment if in zeroth order the monomers are fully deformed by the induction effects 139 . This means that the induction-dispersion energy is a second-order intermolecular correlation effect. 3 The third-order dispersion energy Edisp is a true third-order intermolecular correlation term.

It was shown by Jeziorski, Schwalm, and Szalewicz 86 that for the H2+ ion the interpolation function corresponding to the MSMA theory has a real pole for a value of the parameter slightly small that one. This explains the success of Padé summation techniques applied to the MSMA perturbation series 93 . It is important to stress here that in each order of the SRS and MSMA theories the energy correction can be separated into the polarization and exchange parts, n n n E SRS/MSMA = Epol + E exch n (1-40) The exchange contributions E exch , vanish exponentially as a function of intermonomer distance in each order, so at large intermonomer separations the SRS and MSMA results coincide with the RS results.

MULTIPOLE EXPANSION OF THE INTERACTION ENERGY According to London’s theory 143,144 the interaction energy can be represented as an asymptotic expansion in powers of R−1 , Eint R A Cn R ∼ B A B R (1-104) Rn n=1 The Van der Waals constants Cn A B R depend on the Euler angles A and B specifying the orientation of the monomers in an arbitrary space-fixed frame, and on the polar angles R = determining the orientation of the intermolecular axis (R is assumed to join the monomer centers of mass) with respect to the same space-fixed frame.

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