# This file is part of tad-dftd3.
# SPDX-Identifier: Apache-2.0
#
# 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
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"""
Data: Expectation values
========================
PBE0/def2-QZVP atomic values calculated by S. Grimme in Gaussian (2010),
rare gases recalculated by J. Mewes with PBE0/aug-cc-pVQZ in Dirac (2018).
Also new super heavies Cn, Nh, Fl, Lv, Og and Am-Rg calculated at
4c-PBE/Dyall-AE4Z (Dirac 2022).
"""
from __future__ import annotations
import torch
__all__ = ["R4R2"]
[docs]
def R4R2(
dtype: torch.dtype | None = None, device: torch.device | None = None
) -> torch.Tensor:
"""
Returns the r⁴ over r² expectation values as a tensor.
Parameters
----------
dtype : torch.dtype | None, optional
The desired data type of the returned tensor. Defaults to None.
device : torch.device | None, optional
The desired device of the returned tensor. Defaults to None.
Returns
-------
Tensor
A tensor containing the r⁴ over r² expectation values.
"""
# Actually calculated r⁴ over r² expectation values
# fmt: off
_r4_over_r2 = [
0.0000, # None
8.0589, 3.4698, # H,He
29.0974,14.8517,11.8799, 7.8715, 5.5588, 4.7566, 3.8025, 3.1036, # Li-Ne
26.1552,17.2304,17.7210,12.7442, 9.5361, 8.1652, 6.7463, 5.6004, # Na-Ar
29.2012,22.3934, # K,Ca
19.0598,16.8590,15.4023,12.5589,13.4788, # Sc-
12.2309,11.2809,10.5569,10.1428, 9.4907, # -Zn
13.4606,10.8544, 8.9386, 8.1350, 7.1251, 6.1971, # Ga-Kr
30.0162,24.4103, # Rb,Sr
20.3537,17.4780,13.5528,11.8451,11.0355, # Y-
10.1997, 9.5414, 9.0061, 8.6417, 8.9975, # -Cd
14.0834,11.8333,10.0179, 9.3844, 8.4110, 7.5152, # In-Xe
32.7622,27.5708, # Cs,Ba
23.1671,21.6003,20.9615,20.4562,20.1010,19.7475,19.4828, # La-Eu
15.6013,19.2362,17.4717,17.8321,17.4237,17.1954,17.1631, # Gd-Yb
14.5716,15.8758,13.8989,12.4834,11.4421, # Lu-
10.2671, 8.3549, 7.8496, 7.3278, 7.4820, # -Hg
13.5124,11.6554,10.0959, 9.7340, 8.8584, 8.0125, # Tl-Rn
29.8135,26.3157, # Fr,Ra
19.1885,15.8542,16.1305,15.6161,15.1226,16.1576,14.6510, # Ac-Am
14.7178,13.9108,13.5623,13.2326,12.9189,12.6133,12.3142, # Cm-No
14.8326,12.3771,10.6378, 9.3638, 8.2297, # Lr-
7.5667, 6.9456, 6.3946, 5.9159, 5.4929, # -Cn
6.7286, 6.5144,10.9169,10.3600, 9.4723, 8.6641, # Nh-Og
]
# fmt: on
sqrtz = torch.sqrt(
torch.arange(len(_r4_over_r2), device=device, dtype=dtype)
)
return torch.sqrt(
0.5 * (torch.tensor(_r4_over_r2, device=device, dtype=dtype) * sqrtz)
)
