Perturbation theory London

The dispersion attractive interactions were first characterized by London (1930) and arise from the rapid fluctuations in electron density in one atom, which induce an electrical moment in a neighbouring atom. By making use of quantum-mechanical perturbation theory, London arrived at the well-known expression for the potential energy, eD(r), of two isolated atoms separated by a distance r ... 

Using quantum mechanics and perturbation theory, London developed the following expression for the energy of attraction of symmetric molecules i andj ... 

Perturbation theory is a natural tool for the description of intemioleciilar forces because they are relatively weak. If the interactmg molecules (A and B) are far enough apart, then the theory becomes relatively simple because tlie overlap between the wavefiinctions of the two molecules can be neglected. This is called the polarization approximation. Such a theory was first fomuilated by London [3, 4], and then refomuilated by several others [5, 6 and 7]. 

Smith W R 1972 Perturbation theory in the classical statistical mechanics of fluids Specialist Periodical Report vol 1 (London Chemical Society)... 

The key element in London s approach is the expansion of the electrical potential energy in multipole series. Since neutral molecules or portions of molecules are involved, the leading term is that for dipole-dipole interaction. While attention has been given to higher-order terms, these are usually small, and the greater need seems to be for improved treatment of the dipole-dipole terms. London used second order perturbation theory in his treatment, but Slater and Kirkwood38,21 soon followed with a variation method treatment which yielded similar results. Other individual papers will be mentioned later, but the excellent review of Mar-genau26 should not be overlooked. 

Hubbard, J., Proc. Roy. Soc. London) A240, 539, The description of collective motions in terms of many-body perturbation theory. ... 

From this starting point, London employed standard techniques of Rayleigh-Schrodinger perturbation theory to evaluate the leading effects of the intermolecular... 

The last important contribution to intermolecular energies that will be mentioned here, the dispersion energy (dEnis). is not accessible in H. F. calculations. In our simplified picture of second-order effects in the perturbation theory (Fig. 2), d mS was obtained by correlated double excitations in both subsystems A and B, for which a variational wave function consisting of a single Slater determinant cannot account. An empirical estimate of the dispersion energy in Li+...OH2 based upon the well-known London formula (see e.g. 107)) gave a... 

Peierls R (1973) Perturbation theory for projected states. Proc Royal Soc (London) A, 333 157-170... 

Polymeropoulos EE, Adams WH (1978) Exchange perturbation theory. II. Eisenschitz-London type. Phys Rev A 17 18-23... 

Dalgarno A, Lewis JT (1955) The exact calculation of long-range forces between atoms by perturbation theory. Proc Roy Soc (London) A 233 70-74... 

According to SAPT formulation of the first-order interaction energy, the Heitler-London term consists of electrostatic and exchange contributions (the former obtained from the perturbation theory formula) ... 

Statistical theory of electron densities - multiple-scattering perturbation theory. Proc. Roy. Soc. London A 435, 245-255 (1991). 

From the work of Casimir, Lifshitz, London and many others [229] we know that the perturbation expression for the dispersion interaction between separated systems can be related to the electric polarizabilities of the interacting species, and also to the correlation of fluctuating electric multipoles on the two systems. In the Present TDDFT context, a useful polarizability form for the second-order dispersion interaction was given by Zaremba and Kohn [231] who derived it directly from second-order perturbation theory ... 

Figure 5.2 i Anisotropy of various contributions to the 3-body forces for the cyclic water trimer . See Fig. 5.19 for definition of a. HL refers to Heitler-London term which prohibits modification of the charge clouds of each molecule in the presence of the others, and SCF-def to the result of such deformation, both at the SCF level. Three-body induction is computed directly via perturbation theory. 

In the 1930s, Eisenschitz and London did analytical calculations with the perturbation theory in quantum mechanics and estimated the interaction energy between two induced dipoles as... 

Blinder, S. M. (1974). Foundations of Quantum Dynamics, Academic Press, London. The author s earlier monograph on the fundamental principles of time-dependent quantum mechanics, including transitions and time-dependent perturbation theory. 

Dalgarno, A. Perturbation theory for atomic systems. Proc. Roy. Soc. (London) A251, 282-290 (1959)... 

The energy components are most naturally divided into long-range and short-range terms. The long-range terms may be defined in terms of London s perturbation theory leading to electrostatic, induction and... 

This relation shows how the action of the antisymmetrizer can mix different orders in perturbation theory. Secondly, the projected functions AglO ) 0 > do not form an orthogonal set in the antisymmetric subspace of the Hilbert space L2(r3N) if we take all excited states a > and b > in order to obtain a complete set a > b >, the projections As a > b > form a linearly dependent set. Expanding a given (antisymmetric) function in this overcomplete set is always possible, but the expansion coefficients are not uniquely defined. How the different symmetry adapted perturbation theories that have been formulated since the original treatment by Eisenschitz and London in 1930 , actually deal with these two problems can be read in the following reviews Usually, the first order interaction... 

Although the London equation can only be derived using quantum mechanical perturbation theory, it is instructive to use a simple approach on how these interactions take place, using the one-electron Bohr atom where the shortest distance between the electron and proton is known as the first Bohr radius, rB, at which the Coulomb energy (e2/47T rB) is equal to 2h t0, so that we can calculate rB as... 

Perturbation theory. A comparison with results obtained in the Heitler London approximation... 

A straightforward hut approximate application of second-order perturbation theory by R. Eisenschitz and F. London gave the value 6.47 for this coefficient [Z. f. Phys. 60, 491 (1930)]. The first attack on this problem was made by S. C. Wang, Phys. Z. 28, 663 (1927). The value found by him for the coefficient, = 8.68, must be in error (as first pointed out... 

On the other hand, people took a closer look at the symmetrized perturbation theory of Eisenschitz and London, which in principle can give a full potential energy surface (PES), not just the long range of it. 

A quantum-mechanical calculation of da(ry) and fH/tj) for large ry (ry - oo) can be carried out via perturbation theory. This calculation is the analog of the calculation of London-dispersion forces. The important asymptotic results are... 

The London theory uses second-order perturbation theory in its usual (R.S.) form an infinite sum over a complete basis set. The set taken for the composite system of two interacting molecules a and b consists of all products of the complete set of eigenfunctions of a and b separately. Thus, the London theory not only assumes that there is no overlap between the ground-state atoms but also that there is no overlap between any of the virtual atomic excited states. ... 

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