/** compute potential and its derivative at squared distance 'rr' for particles of type 'a' and 'b' */
std::tuple<float_type, float_type> operator()(float_type rr, unsigned a, unsigned b) const
{
float_type sigma2 = sigma2_(a, b);
float_type rri = sigma2 / rr;
float_type r6i = rri * rri * rri;
float_type eps_r6i = epsilon_(a, b) * r6i;
float_type fval = 48 * rri * eps_r6i * (r6i - 0.5) / sigma2;
float_type en_pot = 4 * eps_r6i * (r6i - 1) - en_cut_(a, b);
return std::make_tuple(fval, en_pot);
}
/** compute potential and its derivatives at squared distance 'rr' for particles of type 'a' and 'b'
*
* @param rr squared distance between particles
* @returns tuple of unit "force" @f$ -U'(r)/r @f$, potential @f$ U(r) @f$
*
* @f{eqnarray*}{
* - U'(r) / r &=& 4 r^{-2} \epsilon (\sigma/r)^{n} \left[ m (\sigma/r)^{m-n} - n \right] \\
* U(r) &=& 4 \epsilon (\sigma/r)^{n} \left[ (\sigma/r)^{m-n} - 1 \right]
* @f}
*/
std::tuple<float_type, float_type> operator()(float_type rr, unsigned a, unsigned b) const
{
float_type sigma2 = sigma2_(a, b);
unsigned m_2 = index_m_2_(a, b);
unsigned n_2 = index_n_2_(a, b);
float_type rri = sigma2 / rr;
float_type rni = pow(rri, n_2);
float_type rmni = (m_2 - n_2 == n_2) ? rni : pow(rri, m_2 - n_2);
float_type eps_rni = epsilon_(a, b) * rni;
float_type fval = 8 * rri * eps_rni * (m_2 * rmni - n_2) / sigma2;
float_type en_pot = 4 * eps_rni * (rmni - 1);
return std::make_tuple(fval, en_pot);
}
std::tuple<float_type, float_type> impl_(float_type rr, unsigned a, unsigned b) const
{
// choose arbitrary index_ if template parameter index = 0
unsigned int n = const_index > 0 ? const_index : index_(a, b);
float_type rri = sigma2_(a, b) / rr;
// avoid computation of square root for even powers
float_type rni = (const_index > 0) ? fixed_pow<const_index / 2>(rri) : halmd::pow(rri, n / 2);
if (n % 2) {
rni *= std::sqrt(rri);
}
float_type eps_rni = epsilon_(a, b) * rni;
float_type fval = n * eps_rni / rr;
float_type en_pot = eps_rni - en_cut_(a, b);
return std::make_tuple(fval, en_pot);
}
