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By Brian Sutcliffe, R. Guy Woolley (auth.), Matti Hotokka, Erkki J. Brändas, Jean Maruani, Gerardo Delgado-Barrio (eds.)

Advances in Quantum tools and purposes in Chemistry, Physics, and Biology contains peer-reviewed contributions in line with rigorously chosen shows given on the seventeenth overseas Workshop on Quantum platforms in Chemistry, Physics, and Biology. New tendencies and cutting-edge advancements within the quantum conception of atomic and molecular structures, and condensed subject (including organic structures and nanostructures) are defined through lecturers of foreign distinction.

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4 Approximate Calculations It might have been hoped, in the light of the claim in the original paper by Born and Oppenheimer quoted in Sect. 1, that the eigensolutions of the κ → 0 limit 15 We assume that the centre-of-mass contributions are eliminated as usual. 22 B. G. 10) after separation of the centre-of-mass term, by letting the nuclear masses increase without limit. Although there are no analytically solved molecular problems, the work of Frolov [55] provides extremely accurate numerical solutions for a problem with two nuclei and a single electron.

33) while the nuclear kinetic energy part is: Tˆ N (t) = − 2 2 2 1 1 ∇ 2 (t) ≡ − ∇ 2 (t). 26). 35) remains essentially self-adjoint. 35). This divergence is discussed in some mathematical detail in the Appendix to Frolov [55]. It does not arise from the choice of a translationally invariant form for the electronic Hamiltonian; rather it is due to the lack of any kinetic energy term to dominate the Coulomb potential. 36) in the (te , tn ) position representation which is a formal solution, in the sense of distributions, of the Schrödinger equation for Hˆ elec .

29) As before its spectrum in general contains a discrete part below a continuum, σ (b) ≡ σ Kˆ b, ˆte o = E o (b)0 , . . , E o (b)m Λ(b), ∞ . 30) Note that for other than diatomic molecules, it is not possible to proceed further and separate out explicitly the rotational motion. For any choice of b the eigenvalues of Kˆ o will depend only upon the shape of the geometrical figure formed by the {ag }, being independent of its orientation. It is possible to introduce a so-called bodyfixed frame by transforming to a new coordinate system built out of the b consisting of three angular variables and 3M − 6 internal coordinates.

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