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WIREs Comput Mol Sci
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# Quantum electrodynamics effects in atoms and molecules

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Quantum electrodynamics (QED) is the fundamental theory describing the interaction of electrons and photons. Its characteristic feature is that both radiation and matter are treated quantum mechanically. For almost all atomic and molecular systems, which contain bound electrons moving at velocities considerably less than that of light, a non‐relativistic formulation of QED is appropriate. Termed molecular QED, its Hamiltonian operator can be constructed by starting from the classical Lagrangian function for the interaction of a charged particle with a radiation field on applying the variational calculus and carrying out the canonical quantization procedure. It is shown how the minimal‐coupling Lagrangian can be transformed to the chemically advantageous multipolar Hamiltonian in which matter couples to radiation directly through molecular multipole moments, with the ensuing interaction strictly causal. Applications include evaluation of transition rates for one‐ and two‐photon absorption, spontaneous and stimulated emission, and signal intensities for second‐ and third‐harmonic generation. Fundamental intermolecular interactions examined include resonance energy transfer, the van der Waals dispersion potential, and the change in energy shift of the pair induced by intense external radiation. The non‐relativistic contribution to the Lamb shift is also extracted. It is shown how a number of the above mentioned processes may be attributed to fluctuations of the vacuum electromagnetic field, which possesses zero‐point energy, a signature QED effect that has widespread implications for the structural and dynamical properties of atoms and molecules. WIREs Comput Mol Sci 2015, 5:178–201. doi: 10.1002/wcms.1211

• Electronic Structure Theory > Ab Initio Electronic Structure Methods
• Theoretical and Physical Chemistry > Spectroscopy
Single‐photon absorption.
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One of 48 diagrams contributing to radiation‐induced intermolecular energy shift via dynamic mechanism.
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The Lamb shift.
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One of 24 diagrams contributing to dispersion energy shift.
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Resonance energy transfer.
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Emission of light.
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