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(*
Copyright (C) 2017 M.A.L. Marques
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
*)
(* nop scaling *)
s_scaling_0 := s -> s:
(* original scaling of Heyd *)
strans := 8.3:
smax := 8.572844:
sconst := 18.79622316:
s_scaling_1 := s -> my_piecewise3(
s < strans, s,
smax - sconst/s^2
):
(* first version of the scaling by TM Henderson, apparently used by Gaussian *)
s_scaling_2 := s -> my_piecewise3(
s < 1, s,
my_piecewise3(s > 15, smax, m_max(m_min(s, 15), 1) - log(1 + exp(m_max(m_min(s, 15), 1) - smax)))
):
(* second version of the scaling by TM Henderson *)
s_scaling_3 := s -> s - (1 - exp(-s))*log(1 + exp(s - smax)):
(* appendix of JCP 128, 194105 (2008) *)
s_p := [0.615482, 1.136921, -0.449154, 0.0175739*8.572844]:
s_q := [1.229195, -0.0269253, 0.313417, -0.0508314, 0.0175739]:
s_scaling_4 := s->
s*(1 + s^3*add(s_p[i]*s^i, i=1..4))/(1 + s^3*add(s_q[i]*s^i, i=1..5)):
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