CollectiveDipoleDisplacement.hpp

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 * work.  Good starting points are:
 *
 * [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
 * [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
 * [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
 * [4] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 * [5] Kuang & Gezelter, Mol. Phys., 110, 691-701 (2012).
 * [6] Lamichhane, Gezelter & Newman, J. Chem. Phys. 141, 134109 (2014).
 * [7] Lamichhane, Newman & Gezelter, J. Chem. Phys. 141, 134110 (2014).
 * [8] Bhattarai, Newman & Gezelter, Phys. Rev. B 99, 094106 (2019).
 */
 
#ifndef APPLICATIONS_DYNAMICPROPS_COLLECTIVEDIPOLEDISPLACEMENT_HPP
#define APPLICATIONS_DYNAMICPROPS_COLLECTIVEDIPOLEDISPLACEMENT_HPP
 
#include "applications/dynamicProps/TimeCorrFunc.hpp"
#include "brains/Thermo.hpp"
 
namespace OpenMD {
  //! Calculates the collective dipole displacement function
  /*! This time correlation function is the Helfand moment conjugate
      to the current density. Helfand moments are used to calculate
      the Einstein-Helfand relations for transport that are formally
      equivalent to Green-Kubo expressions using a related flux.  In
      this case, the flux,
 
      \f[ \mathbf{J}(t) = \sum_{i=1}^{N} q_i \mathbf{v}_{\mathrm{cm},i}(t) \f]
 
      is normally used to calculate an ionic conductivity,
 
      \f[ \sigma = \frac{1}{3V k_b T} \int_0^\infty \left< \mathbf{J}(0) \cdot
     \mathbf{J}(t) \right> dt \f]
 
      The cm subscript denotes center of mass locations for all molecules.
 
      This class computes the collective translational dipole moment,
 
      \f[ \mathbf{M}_\mathrm{trans}(t) = \sum_{i=1}^{N} q_i
     \mathbf{r}_{\mathrm{cm},i}(t) \f]
 
      as well as total contributions to the system's net dipole moment
 
      \f[ \mathbf{M}_\mathrm{tot}(t) =  \sum_{i=1}^{N} \sum_{a} q_{ia}
     \mathbf{r}_{ia}(t) = \sum_{i=1}^{N} q_i \mathbf{r}_{\mathrm{cq},i}(t) \f]
 
      where cq denotes the molecular center of charge.  It also
      calculates the rotational contribution,
 
      \f[ \mathbf{M}_\mathrm{rot}(t) = \sum_{i=1}^{N} q_i \left[
     \mathbf{r}_{\mathrm{cq},i}(t) - \mathbf{r}_{\mathrm{cm},i}(t) \right] \f]
 
      The correlation functions are the displacements of these terms
      from their values at an earlier time,
 
      \f[ \left< \left| \mathbf{M}_\mathrm{trans}(t) -
     \mathbf{M}_\mathrm{trans}(0) \right|^2 \right> \f]
 
      and identical quantities for the total and rotational contributions.
  */
  class CollectiveDipoleDisplacement : public SystemACF<Vector3d> {
  public:
    CollectiveDipoleDisplacement(SimInfo* info, const std::string& filename,
                                 const std::string& sele1,
                                 const std::string& sele2);
 
  private:
    virtual void computeProperty1(int frame);
    virtual Vector3d calcCorrVal(int frame1, int frame2);
 
    Thermo* thermo_;
 
    std::vector<Vector3d> CRcm_;
    std::vector<Vector3d> CRtot_;
    std::vector<Vector3d> CRrot_;
  };
}  // namespace OpenMD
 
#endif