File size: 6,617 Bytes
7cc6c4a
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
import torch
import torch.linalg as LA
import torch.nn as nn
import torch_scatter
from torch_geometric.data import Data

from ase.data import covalent_radii
from ase.units import _e, _eps0, m, pi
from e3nn.util.jit import compile_mode # TODO: e3nn allows autograd in compiled model


@compile_mode("script")
class ZBL(nn.Module):
    """Ziegler-Biersack-Littmark (ZBL) screened nuclear repulsion"""

    def __init__(
        self,
        trianable: bool = False,
        **kwargs,
    ) -> None:
        nn.Module.__init__(self, **kwargs)
        
        torch.set_default_dtype(torch.double)

        self.a = torch.nn.parameter.Parameter(
            torch.tensor(
                [0.18175, 0.50986, 0.28022, 0.02817], dtype=torch.get_default_dtype()
            ),
            requires_grad=trianable,
        )
        self.b = torch.nn.parameter.Parameter(
            torch.tensor(
                [-3.19980, -0.94229, -0.40290, -0.20162],
                dtype=torch.get_default_dtype(),
            ),
            requires_grad=trianable,
        )

        self.a0 = torch.nn.parameter.Parameter(
            torch.tensor(0.46850, dtype=torch.get_default_dtype()),
            requires_grad=trianable,
        )

        self.p = torch.nn.parameter.Parameter(
            torch.tensor(0.23, dtype=torch.get_default_dtype()), requires_grad=trianable
        )

        self.register_buffer(
            "covalent_radii",
            torch.tensor(
                covalent_radii,
                dtype=torch.get_default_dtype(),
            ),
        )

    def phi(self, x):
        return torch.einsum("i,ij->j", self.a, torch.exp(torch.outer(self.b, x)))

    def d_phi(self, x):
        return torch.einsum(
            "i,ij->j", self.a * self.b, torch.exp(torch.outer(self.b, x))
        )

    def dd_phi(self, x):
        return torch.einsum(
            "i,ij->j", self.a * self.b**2, torch.exp(torch.outer(self.b, x))
        )

    def eij(
        self, zi: torch.Tensor, zj: torch.Tensor, rij: torch.Tensor
    ) -> torch.Tensor:  # [eV]
        return _e * m / (4 * pi * _eps0) * torch.div(torch.mul(zi, zj), rij)

    def d_eij(
        self, zi: torch.Tensor, zj: torch.Tensor, rij: torch.Tensor
    ) -> torch.Tensor:  # [eV / A]
        return -_e * m / (4 * pi * _eps0) * torch.div(torch.mul(zi, zj), rij**2)

    def dd_eij(
        self, zi: torch.Tensor, zj: torch.Tensor, rij: torch.Tensor
    ) -> torch.Tensor:  # [eV / A^2]
        return _e * m / (2 * pi * _eps0) * torch.div(torch.mul(zi, zj), rij**3)

    def switch_fn(
        self,
        zi: torch.Tensor,
        zj: torch.Tensor,
        rij: torch.Tensor,
        aij: torch.Tensor,
        router: torch.Tensor,
        rinner: torch.Tensor,
    ) -> torch.Tensor:  # [eV]
        # aij = self.a0 / (torch.pow(zi, self.p) + torch.pow(zj, self.p))

        xrouter = router / aij

        energy = self.eij(zi, zj, router) * self.phi(xrouter)

        grad1 = self.d_eij(zi, zj, router) * self.phi(xrouter) + self.eij(
            zi, zj, router
        ) * self.d_phi(xrouter)

        grad2 = (
            self.dd_eij(zi, zj, router) * self.phi(xrouter)
            + self.d_eij(zi, zj, router) * self.d_phi(xrouter)
            + self.d_eij(zi, zj, router) * self.d_phi(xrouter)
            + self.eij(zi, zj, router) * self.dd_phi(xrouter)
        )

        A = (-3 * grad1 + (router - rinner) * grad2) / (router - rinner) ** 2
        B = (2 * grad1 - (router - rinner) * grad2) / (router - rinner) ** 3
        C = (
            -energy
            + 1.0 / 2.0 * (router - rinner) * grad1
            - 1.0 / 12.0 * (router - rinner) ** 2 * grad2
        )

        switching = torch.where(
            rij < rinner,
            C,
            A / 3.0 * (rij - rinner) ** 3 + B / 4.0 * (rij - rinner) ** 4 + C,
        )

        return switching

    def envelope(self, r: torch.Tensor, rc: torch.Tensor, p: int = 6):
        x = r / rc
        y = (
            1.0
            - ((p + 1.0) * (p + 2.0) / 2.0) * torch.pow(x, p)
            + p * (p + 2.0) * torch.pow(x, p + 1)
            - (p * (p + 1.0) / 2) * torch.pow(x, p + 2)
        ) * (x < 1)
        return y

    def _get_derivatives(self, energy: torch.Tensor, data: Data):
        egradi, egradij = torch.autograd.grad(
            outputs=[energy],  # TODO: generalized derivatives
            inputs=[data.positions, data.vij],  # TODO: generalized derivatives
            grad_outputs=[torch.ones_like(energy)],
            retain_graph=True,
            create_graph=True,
            allow_unused=True,
        )

        volume = torch.det(data.cell)  # (batch,)
        rfaxy = torch.einsum("ax,ay->axy", data.vij, -egradij)

        edge_batch = data.batch[data.edge_index[0]]

        stress = (
            -0.5
            * torch_scatter.scatter_sum(rfaxy, edge_batch, dim=0)
            / volume.view(-1, 1)
        )

        return -egradi, stress

    def forward(
        self,
        data: Data,
    ) -> dict[str, torch.Tensor]:
        # TODO: generalized derivatives
        data.positions.requires_grad_(True)

        numbers = data.numbers  # (sum(N), )
        positions = data.positions  # (sum(N), 3)
        edge_index = data.edge_index  # (2, sum(E))
        edge_shift = data.edge_shift  # (sum(E), 3)
        batch = data.batch  # (sum(N), )

        edge_src, edge_dst = edge_index[0], edge_index[1]

        if "rij" not in data or "vij" not in data:
            data.vij = positions[edge_dst] - positions[edge_src] + edge_shift
            data.rij = LA.norm(data.vij, dim=-1)

        rbond = (
            self.covalent_radii[numbers[edge_src]]
            + self.covalent_radii[numbers[edge_dst]]
        )

        rij = data.rij
        zi = numbers[edge_src]  # (sum(E), )
        zj = numbers[edge_dst]  # (sum(E), )

        aij = self.a0 / (torch.pow(zi, self.p) + torch.pow(zj, self.p))  # (sum(E), )

        energy_pairs = (
            self.eij(zi, zj, rij)
            * self.phi(rij / aij.to(rij))
            * self.envelope(rij, torch.min(data.cutoff, rbond))
        )

        energy_nodes = 0.5 * torch_scatter.scatter_add(
            src=energy_pairs,
            index=edge_dst,
            dim=0,
        )  # (sum(N), )

        energies = torch_scatter.scatter_add(
            src=energy_nodes,
            index=batch,
            dim=0,
        )  # (B, )

        # TODO: generalized derivatives
        forces, stress = self._get_derivatives(energies, data)

        return {
            "energy": energies,
            "forces": forces,
            "stress": stress,
        }