Quantum field theoretical methods in chemically bonded systems

Abstract

Calculations of potential-energy curves based on a field-theoretic model of chemical bonding are reported for H,, F,, LiH, FH, and N,. All interactions are represented by Feynman diagrams. Conservation principles are incorporated as side conditions. A sum of Hartree, exchange, and pairing interactions, plus any terms from the side conditions, is used to set up an effective 1-particle potential and model Hamiltonian. The solutions to the potential are determined self-consistently. Many-body interactions are added as perturbative corrections expressed as scattering events among the 1-particle solutions. The resulting model, termed BCSLN after Bardeen, Cooper, Schrieffer, Lipkin, and Nogami, gives results which are in good agreement with experiment when many-body processes are included through third order.Landau (Nozihres 1964, ch 1) was the first to recognise that quantised many-body systems may be described with quasiparticles and elementary excitations which interact weakly compared to bare particles and fields. A microscopic model of these can be derived with the methods of quantum field theory (second quantisation). The model provides a unified theory which is formulated as a simple (but non-trivial) extension of ordinary non-relativistic 1-particle quantum theory (Scadron 1979). It is called many-body perturbation theory ( MBFT) (Inkson 1984).If MBPT is convergent, the total interaction can be divided into strong and weak parts without changing the final answer (Nozihres 1964, pp 232-7 and 0 7.4.c). The strong and weak forces can then be handled differently (Inkson 1984, 00 6.6, 6.7 and 8.7). Strong forces are used to set up effective potentials which are analogous to the potentials of 1-particle theory except the equations of motion must be solved selfconsistently. Solutions to the effective-potential problem are optimal 1-particle-type approximations to the many-body motion, and this enables them to represent quasiparticles or oscillations of the field (elementary excitations). The effective 1-particle motion may or may not resemble the motion of free particles or oscillations. Weak forces are included as interactions among the quasiparticles or elementary excitations. These interactions are represented by non-redundant scattering diagrams known as Feynman diagrams ( FD). They include the so-called many-body interactions. The FD furnish an exact order-by-order series expansion for the many-body system in terms of such scattering processes. There are general rules for expressing the diagrams

On the use of Brillouin-Wigner perturbation theory for many-body systems

“…We note that the two-state problem contains the essential ingredients required for the theoretical description of bond breaking for single bonds. Multiply bonded systems can be handled by 'solving the two-state problem' for each bond (cf the special Bogoliubov-Valatin transformation used by Sorensen et al [55][56][57][58][59] to develop a Bardeen-Cooper-Schrieffer reference model).…”

On the accuracy of the algebraic approximation in molecular electronic structure calculations: V. Electron correlation in the ground state of the nitrogen molecule

“…It is known that by using localized orbitals, both occupied and unoccupied, the many-body perturbation theoretic approach can provide a useful technique for large molecules which can be further improved by exploiting techniques such as Feenberg scaling [66][67][68][69][70][71][72][73][74][75][76][77][78][79]. The use of superfluid reference functions opens the route to treatments of dissociative processes [137,138]. The relativistic extension of the present approach via the Furry picture boundstate picture of quantum electrodynamics is well established [20][21][22][23].…”

Valence states of the cyano radical Feynman's way

“…7.4.5). If no diagram is counted unless at least one quasiparticle is outside the valence space, the theory is third order and can be used to make ground‐state calculations 27, 29–32. If diagrams with ODLRO are counted diagram by diagram with the help of a suggestion by Kinoshita and Nambu 33 (3, see also Fig.…”