gaussiankernel.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
 *
 * 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.
 *
 */
 
#pragma once
#ifndef VOTCA_XTP_GAUSSIANKERNEL_H
#define VOTCA_XTP_GAUSSIANKERNEL_H
 
// Standard includes
#include <cmath>
 
// Local VOTCA includes
#include "eigen.h"
 
namespace votca {
namespace xtp {

struct GaussianKernel {
  double B0 = 0.0;
  double B1 = 0.0;
  double B2 = 0.0;
 
  GaussianKernel(double r, double S) {
    if (S <= 0.0) {
      B0 = 1.0 / r;
      B1 = B0 * B0 * B0;
      B2 = 3.0 * B1 * B0 * B0;
      return;
    }
    const double x = r / S;
    constexpr double two_over_sqrtpi = 1.1283791670955126;
    if (x < 0.05) {
      // series in x (to x^8): avoids the cancellation of the closed form at
      // short range
      const double x2 = x * x;
      const double s1 = two_over_sqrtpi / S;
      B0 = s1 *
           (1.0 + x2 * (-1.0 / 3.0 +
                        x2 * (1.0 / 10.0 + x2 * (-1.0 / 42.0 + x2 / 216.0))));
      const double s3 = s1 / (S * S);
      B1 = s3 * (2.0 / 3.0 +
                 x2 * (-2.0 / 5.0 +
                       x2 * (1.0 / 7.0 + x2 * (-1.0 / 27.0 + x2 / 132.0))));
      const double s5 = s3 / (S * S);
      B2 = s5 * (4.0 / 5.0 +
                 x2 * (-4.0 / 7.0 +
                       x2 * (2.0 / 9.0 + x2 * (-2.0 / 33.0 + x2 / 78.0))));
      return;
    }
    const double g = std::exp(-x * x);
    B0 = std::erf(x) / r;
    const double r2 = r * r;
    B1 = (B0 - two_over_sqrtpi * g / S) / r2;
    B2 = (3.0 * B1 - 2.0 * two_over_sqrtpi * g / (S * S * S)) / r2;
  }

  Eigen::Matrix3d DipoleTensor(const Eigen::Vector3d& r) const {
    Eigen::Matrix3d T = -B2 * r * r.transpose();
    T.diagonal().array() += B1;
    return T;
  }
};
 
}  // namespace xtp
}  // namespace votca
 
#endif  // VOTCA_XTP_GAUSSIANKERNEL_H