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# Source code for ase.calculators.tip4p

    import numpy as np

    from ase import units
    from ase.calculators.calculator import Calculator, all_changes
    from ase.calculators.tip3p import TIP3P, angleHOH, rOH

    __all__ = ['rOH', 'angleHOH', 'TIP4P', 'sigma0', 'epsilon0']

    # Electrostatic constant and parameters:
    k_c = units.Hartree * units.Bohr
    qH = 0.52
    A = 600e3 * units.kcal / units.mol
    B = 610 * units.kcal / units.mol
    sigma0 = (A / B)**(1 / 6.)
    epsilon0 = B**2 / (4 * A)
    # https://doi.org/10.1063/1.445869

    class TIP4P(TIP3P):
        def __init__(self, rc=7.0, width=1.0):
            """ TIP4P potential for water.

            :doi:`10.1063/1.445869`

            Requires an atoms object of OHH,OHH, ... sequence
            Correct TIP4P charges and LJ parameters set automatically.

            Virtual interaction sites implemented in the following scheme:
            Original atoms object has no virtual sites.
            When energy/forces are requested:

            * virtual sites added to temporary xatoms object
            * energy / forces calculated
            * forces redistributed from virtual sites to actual atoms object

            This means you do not get into trouble when propagating your system
            with MD while having to skip / account for massless virtual sites.

            This also means that if using for QM/MM MD with GPAW, the EmbedTIP4P
            class must be used.
            """

            TIP3P.__init__(self, rc, width)
            self.atoms_per_mol = 3
            self.sites_per_mol = 4
            self.energy = None
            self.forces = None

        def calculate(self, atoms=None,
                      properties=['energy', 'forces'],
                      system_changes=all_changes):
            Calculator.calculate(self, atoms, properties, system_changes)

            assert (atoms.numbers[::3] == 8).all()
            assert (atoms.numbers[1::3] == 1).all()
            assert (atoms.numbers[2::3] == 1).all()

            xpos = self.add_virtual_sites(atoms.positions)
            xcharges = self.get_virtual_charges(atoms)

            cell = atoms.cell
            pbc = atoms.pbc

            natoms = len(atoms)
            nmol = natoms // 3

            self.energy = 0.0
            self.forces = np.zeros((4 * natoms // 3, 3))

            C = cell.diagonal()
            assert (cell == np.diag(C)).all(), 'not orthorhombic'
            assert ((C >= 2 * self.rc) | ~pbc).all(), 'cutoff too large'

            # Get dx,dy,dz from first atom of each mol to same atom of all other
            # and find min. distance. Everything moves according to this analysis.
            for a in range(nmol - 1):
                D = xpos[(a + 1) * 4::4] - xpos[a * 4]
                shift = np.zeros_like(D)
                for i, periodic in enumerate(pbc):
                    if periodic:
                        shift[:, i] = np.rint(D[:, i] / C[i]) * C[i]
                q_v = xcharges[(a + 1) * 4:]

                # Min. img. position list as seen for molecule !a!
                position_list = np.zeros(((nmol - 1 - a) * 4, 3))

                for j in range(4):
                    position_list[j::4] += xpos[(a + 1) * 4 + j::4] - shift

                # Make the smooth cutoff:
                pbcRoo = position_list[::4] - xpos[a * 4]
                pbcDoo = np.sum(np.abs(pbcRoo)**2, axis=-1)**(1 / 2)
                x1 = pbcDoo > self.rc - self.width
                x2 = pbcDoo < self.rc
                x12 = np.logical_and(x1, x2)
                y = (pbcDoo[x12] - self.rc + self.width) / self.width
                t = np.zeros(len(pbcDoo))
                t[x2] = 1.0
                t[x12] -= y**2 * (3.0 - 2.0 * y)
                dtdd = np.zeros(len(pbcDoo))
                dtdd[x12] -= 6.0 / self.width * y * (1.0 - y)
                self.energy_and_forces(a, xpos, position_list, q_v, nmol, t, dtdd)

            if self.pcpot:
                e, f = self.pcpot.calculate(xcharges, xpos)
                self.energy += e
                self.forces += f

            f = self.redistribute_forces(self.forces)

            self.results['energy'] = self.energy
            self.results['forces'] = f

        def energy_and_forces(self, a, xpos, position_list, q_v, nmol, t, dtdd):
            """ energy and forces on molecule a from all other molecules.
                cutoff is based on O-O Distance. """

            # LJ part - only O-O interactions
            epsil = np.tile([epsilon0], nmol - 1 - a)
            sigma = np.tile([sigma0], nmol - 1 - a)
            DOO = position_list[::4] - xpos[a * 4]
            d2 = (DOO**2).sum(1)
            d = np.sqrt(d2)
            e_lj = 4 * epsil * (sigma**12 / d**12 - sigma**6 / d**6)
            f_lj = (4 * epsil * (12 * sigma**12 / d**13 -
                                 6 * sigma**6 / d**7) * t -
                    e_lj * dtdd)[:, np.newaxis] * DOO / d[:, np.newaxis]

            self.forces[a * 4] -= f_lj.sum(0)
            self.forces[(a + 1) * 4::4] += f_lj

            # Electrostatics
            e_elec = 0
            all_cut = np.repeat(t, 4)
            for i in range(4):
                D = position_list - xpos[a * 4 + i]
                d2_all = (D**2).sum(axis=1)
                d_all = np.sqrt(d2_all)
                e = k_c * q_v[i] * q_v / d_all
                e_elec += np.dot(all_cut, e).sum()
                e_f = e.reshape(nmol - a - 1, 4).sum(1)
                F = (e / d_all * all_cut)[:, np.newaxis] * D / d_all[:, np.newaxis]
                FOO = -(e_f * dtdd)[:, np.newaxis] * DOO / d[:, np.newaxis]
                self.forces[(a + 1) * 4 + 0::4] += FOO
                self.forces[a * 4] -= FOO.sum(0)
                self.forces[(a + 1) * 4:] += F
                self.forces[a * 4 + i] -= F.sum(0)

            self.energy += np.dot(e_lj, t) + e_elec

        def add_virtual_sites(self, pos):
            # Order: OHHM,OHHM,...
            # DOI: 10.1002/(SICI)1096-987X(199906)20:8
            b = 0.15
            xatomspos = np.zeros((4 * len(pos) // 3, 3))
            for w in range(0, len(pos), 3):
                r_i = pos[w]  # O pos
                r_j = pos[w + 1]  # H1 pos
                r_k = pos[w + 2]  # H2 pos
                n = (r_j + r_k) / 2 - r_i
                n /= np.linalg.norm(n)
                r_d = r_i + b * n

                x = 4 * w // 3
                xatomspos[x + 0] = r_i
                xatomspos[x + 1] = r_j
                xatomspos[x + 2] = r_k
                xatomspos[x + 3] = r_d

            return xatomspos

        def get_virtual_charges(self, atoms):
            charges = np.empty(len(atoms) * 4 // 3)
            charges[0::4] = 0.00  # O
            charges[1::4] = qH  # H1
            charges[2::4] = qH  # H2
            charges[3::4] = - 2 * qH  # X1
            return charges

        def redistribute_forces(self, forces):
            f = forces
            b = 0.15
            a = 0.5
            pos = self.atoms.positions
            for w in range(0, len(pos), 3):
                r_i = pos[w]  # O pos
                r_j = pos[w + 1]  # H1 pos
                r_k = pos[w + 2]  # H2 pos
                r_ij = r_j - r_i
                r_jk = r_k - r_j
                r_d = r_i + b * (r_ij + a * r_jk) / np.linalg.norm(r_ij + a * r_jk)
                r_id = r_d - r_i
                gamma = b / np.linalg.norm(r_ij + a * r_jk)

                x = w * 4 // 3
                Fd = f[x + 3]  # force on M
                F1 = (np.dot(r_id, Fd) / np.dot(r_id, r_id)) * r_id
                Fi = Fd - gamma * (Fd - F1)  # Force from M on O
                Fj = (1 - a) * gamma * (Fd - F1)  # Force from M on H1
                Fk = a * gamma * (Fd - F1)  # Force from M on H2

                f[x] += Fi
                f[x + 1] += Fj
                f[x + 2] += Fk

            # remove virtual sites from force array
            f = np.delete(f, list(range(3, f.shape[0], 4)), axis=0)
            return f