ewaldshapecorrection.h

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/*
 *            Copyright 2009-2026 The VOTCA Development Team
 *                       (http://www.votca.org)
 *
 *      Licensed under the Apache License, Version 2.0 (the "License")
 *
 * You may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *              http://www.apache.org/licenses/LICENSE-2.0
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 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
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 */
 
#pragma once
#ifndef VOTCA_XTP_EWALDSHAPECORRECTION_H
#define VOTCA_XTP_EWALDSHAPECORRECTION_H
 
// Standard includes
#include <utility>
#include <vector>
 
// Local VOTCA includes
#include "eeinteractor.h"
#include "eigen.h"
#include "ewaldregistry.h"

 
namespace votca {
namespace xtp {
 
enum class EwaldShape { Cube, Slab };
 
class EwaldShapeCorrection {
 public:
  EwaldShapeCorrection(double volume, const EwaldRegistry& registry,
                       EwaldShape shape);
 
  // Adds the (position-independent) depolarizing field into target's own
  // V()/V_noE() accumulator, generated by every segment in the registry
  // at charge state source_state (including target's own segment, if
  // registered -- see class documentation).
  template <enum Estatic CE>
  void AddFieldAt(PolarSite& target, EwaldChargeState source_state) const;
 
  // Shape/surface contribution to the PERMANENT-multipole interaction
  // energy between a supplied foreground (1) and the rest of the cell
  // (2). With
  //
  //   Q0 = sum_i q_i                                (net charge)
  //   Q1 = sum_i (q_i r_i + mu_i)                   (dipole moment)
  //   Q2 = sum_i (0.5 q_i r_i r_i^T + mu_i r_i^T)   (second moment)
  //
  // the cube/sphere and slab forms are
  //
  //   E = -(4*pi/(3*V)) * [ Q0_1 TrQ2_2 + Q0_2 TrQ2_1 - Q1_1 . Q1_2 ]
  //   E = -(4*pi/V)     * [ Q0_1 Q2_2zz + Q0_2 Q2_1zz - Q1_1z Q1_2z ]
  //
  // THE SECOND-MOMENT TERMS ARE NOT OPTIONAL. An earlier version of this
  // method kept only the Q1.Q1 piece, reasoning that the shape energy is
  // the shape FIELD contracted with the foreground's moments. That
  // reasoning holds only for a NEUTRAL foreground. As soon as Q0_1 is
  // nonzero, Q1_1 depends on where the origin is put, and so did that
  // energy -- which is a statement about a missing term, not about
  // physics. The full expression above is exactly origin-invariant:
  // under r -> r + a,
  //
  //   Q1    -> Q1 + Q0 a
  //   TrQ2  -> TrQ2 + Q1 . a + 0.5 Q0 a^2
  //
  // and the three pieces cancel to all orders in a. A unit test shifts
  // every position by an arbitrary vector and requires the answer not to
  // move; that test is the real guarantee here, and it fails on the
  // Q1.Q1-only form. This matches the legacy code's own U12_ShapeTerm,
  // which carries the same three pieces.
  //
  // PERMANENT moments only, on BOTH sides. The induced part of this
  // interaction is not missing; it belongs to the polar region, which
  // accounts for it as sum(mu_ind . V) from the field AddFieldAt
  // delivers. Including it here as well would count it twice. That is
  // the division of labour the real- and reciprocal-space energies
  // already follow, and it is why TotalDipoleMoment -- which does
  // include induced dipoles, correctly, for the FIELD -- is not reused.
  // Legacy splits the same way, into its _pp, _pu and _uu channels; this
  // is its _pp.
  //
  // Rank is capped at 1 (charge and dipole) because every other sum in
  // this Ewald implementation is: the real-space interactor and the
  // reciprocal structure factors both stop at the dipole. Legacy adds
  // the sites' intrinsic quadrupoles into Q2 as well. That difference
  // does not affect origin-invariance -- an intrinsic quadrupole is
  // itself translation-invariant -- but it is a real numerical
  // difference wherever the multipole files carry rank-2 moments.
  //
  // `background_exclusions` holds the foreground's own background copies
  // out of the background moments, matching the suppression the other
  // two sums apply.
  double CalcStaticEnergyBetween(
      const std::vector<std::pair<const PolarSite*, Eigen::Vector3d>>&
          foreground,
      const std::vector<const PolarSite*>& background_exclusions,
      EwaldChargeState source_state) const;
 
  // The same shape/surface cross term, with the background entering
  // through its INDUCED dipoles instead of its permanent moments. An
  // induced dipole carries no charge, so the background's moments
  // reduce to
  //
  //   Q0_bg = 0,  Q1_bg = sum mu_ind,  Q2_bg = sum mu_ind r^T
  //
  // and the bracket loses its Q0_bg TrQ2_fg piece. The foreground still
  // contributes its permanent moments, all three of them -- Q0_fg
  // TrQ2_bg survives and is the piece that matters for a charged
  // foreground, exactly as in the permanent case.
  //
  // This is the shape partner of
  // EwaldRealSpaceSum::CalcInducedSourceEnergyAt; see
  // EwaldRealSpaceInteractor::CalcInducedSourceEnergy for what the term
  // is. Undamped, like every shape contribution: this is a boundary
  // condition on an infinite sum, not a short-range interaction.
  double CalcInducedSourceEnergyBetween(
      const std::vector<std::pair<const PolarSite*, Eigen::Vector3d>>&
          foreground,
      const std::vector<const PolarSite*>& background_exclusions,
      EwaldChargeState source_state) const;
 
 private:
  Eigen::Vector3d TotalDipoleMoment(EwaldChargeState source_state) const;
 
  // The three permanent moments the shape energy is built from, to rank
  // 1. See CalcStaticEnergyBetween for the definitions and for why all
  // three are needed.
  struct Moments {
    double q0 = 0.0;
    Eigen::Vector3d q1 = Eigen::Vector3d::Zero();
    Eigen::Matrix3d q2 = Eigen::Matrix3d::Zero();
  };
 
  static void Accumulate(Moments& m, const PolarSite& site,
                         const Eigen::Vector3d& pos);
 
  // Permanent moments of every registered site at source_state, with the
  // listed sites held out.
  Moments BackgroundMoments(
      EwaldChargeState source_state,
      const std::vector<const PolarSite*>& exclusions) const;
 
  // As BackgroundMoments, but built from the sites' INDUCED dipoles.
  Moments BackgroundInducedMoments(
      EwaldChargeState source_state,
      const std::vector<const PolarSite*>& exclusions) const;
 
  double volume_;
  const EwaldRegistry& registry_;
  EwaldShape shape_;
};
 
}  // namespace xtp
}  // namespace votca
 
#endif  // VOTCA_XTP_EWALDSHAPECORRECTION_H