An Efficient Coupled Dipole Method for the Accurate Calculation of van der Waals Interactions at the Nanoscale

  • Hye-Young Kim
Part of the Progress in Optical Science and Photonics book series (POSP, volume 2)


The van der Waals (VDW) force arises from purely quantum mechanical charge fluctuations and is variously called a dispersion or London or Casimir force. This often considered as weak, yet ubiquitous, attractive interaction is important in many nanoscale systems. This chapter provides an overview of the Coupled Dipole Method (CDM), an atomistic and accurate computational method widely adopted to predict the VDW forces between dielectric nanomaterials. There is a concern about the burden of memory and computing time needed to solve eigenvalue problems by either diagonalization or iteration, which have hindered the implementation of CDM for large systems. Here, an efficient way, named trace-CDM (TCDM), is presented. TCDM uses the simple fact that the trace of a square matrix is equal to the sum of its eigenvalues and thus calculates the accurate VDW energies without solving for the eigenvalues. Four examples are solved to demonstrate the advantages of the method.


van der Waals (VDW) forces and interactions Dispersion force London force Casimir force Coupled dipole method (CDM) Trace-CDM (TCDM) Nanoscale Dielectric nanomaterials Diagonalization Iteration VDW energies 



I am grateful to all my collaborators in research projects involving CDM—Milton Cole, Darrell Velegol, Amand Lucas, Jorge Sofo, and Paul Kent. I most gratefully acknowledge the significant contribution of Amand Lucas in guiding me through the initial formulations of CDM and TCDM. I thank the Louisiana Board of Regents-RCS grant (LEQSF(2012-15)-RD-A-19) for support.


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Copyright information

© Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of Chemistry and PhysicsSoutheastern Louisiana UniversityHammondUSA

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