# This file is part of dxtb.
#
# SPDX-Identifier: Apache-2.0
# Copyright (C) 2024 Grimme Group
#
# 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
# limitations under the License.
"""
Vibrational Analysis: Raman Spectra
===================================
Calculate Raman intensities and the depolarization ratio from the geometric
polarizability derivative.
"""
from __future__ import annotations
import torch
from tad_mctc import storch
from tad_mctc.math import einsum
from tad_mctc.units import AU2AA4AMU
from dxtb._src.typing import Any, Literal, NoReturn, Tensor
from .result import BaseResult
__all__ = ["raman_ints_depol", "RamanResult"]
[docs]
class RamanResult(BaseResult):
"""
Data from the calculation of a Raman spectrum.
- Vibrational frequencies
- Raman activities (intensities)
- Depolarization ratios
"""
converter_ints: dict[str, float] = {
"a.u.": 1.0,
"A^4/amu": AU2AA4AMU,
}
__slots__ = ["_ints", "_ints_unit", "_depol", "_depol_unit"]
def __init__(
self,
freqs: Tensor,
ints: Tensor,
depol: Tensor,
device: torch.device | None = None,
dtype: torch.dtype | None = None,
):
"""
Initialize the Raman result.
Parameters
----------
freqs : Tensor
Vibrational frequencies in atomic units.
ints : Tensor
IR intensities (activities) in atomic units.
depol : Tensor
Depolarization ratio (unitless).
device : torch.device | None, optional
Device of the tensors. If ``None``, the device of `freqs` is used.
Defaults to ``None``.
dtype : torch.dtype | None, optional
Data type of the tensors. If ``None``, the data type of `freqs` is
used. Defaults to ``None``.
"""
super().__init__(
freqs=freqs,
device=device if device is not None else freqs.device,
dtype=dtype if dtype is not None else freqs.dtype,
)
self._ints = ints
self._ints_unit = "a.u."
self._depol = depol
self._depol_unit = None
# intensities
@property
def ints(self) -> Tensor:
return self._ints * self.converter_ints[self._ints_unit]
@ints.setter
def ints(self, *_: Any) -> NoReturn:
raise RuntimeError(
"Setting Raman intensities (activities) is not supported. "
"Internally, the intensities should always be stored in atomic "
"units. Use the `to_unit` method to convert to a different unit "
"or set the `ints_unit` attribute."
)
@property
def ints_unit(self) -> str:
return self._ints_unit
@ints_unit.setter
def ints_unit(self, value: str) -> None:
if value not in self.converter_ints:
raise ValueError(f"Unsupported intensity unit: {value}")
self._ints_unit = value
# depolarization ratio
@property
def depol(self) -> Tensor:
return self._depol
@depol.setter
def depol(self, *_: Any) -> NoReturn:
raise RuntimeError("Setting depolarization ratios is not supported.")
@property
def depol_unit(self) -> None:
return self._depol_unit
@depol_unit.setter
def depol_unit(self, *_: Any) -> NoReturn:
raise RuntimeError("The depolarization ratios are unitless.")
# conversion
[docs]
def to_unit(
self, value: Literal["freqs", "ints", "depol"], unit: str
) -> Tensor:
"""
Convert a value from one unit to another based on the converter
dictionary.
Parameters
----------
value : Literal['freqs', 'ints', 'depol']
The value (stored property) to convert.
unit : str
The unit to convert to.
Returns
-------
Tensor
The converted value.
Raises
------
NotImplementedError
If the value is "depol", because the depolarization ratio is
unitless.
ValueError
If the value (name of the stored property) does not exist.
"""
if value == "freqs":
return self._convert(self.freqs, unit, self.converter_freqs)
if value == "ints":
return self._convert(self.ints, unit, self.converter_ints)
if value == "depol":
raise NotImplementedError("Depolarization ratio is unitless.")
raise ValueError(f"Unsupported value for conversion: {value}")
[docs]
def use_common_units(self) -> None:
"""
Convert the frequencies and intensities to common units, that is,
`cm^-1` for frequencies and `A^4/amu` for intensities.
"""
self.freqs_unit = "cm^-1"
self.ints_unit = "A^4/amu"
[docs]
def raman_ints_depol(da_dr: Tensor, modes: Tensor) -> tuple[Tensor, Tensor]:
r"""
Calculate static Raman activities (intensities) and the depolarization
ratios from the geometric polarizability derivative (Raman susceptibility
tensor :math:`\chi`).
Formula taken from `here <https://doi.org/10.1080/00268970701516412>`__.
Parameters
----------
da_dr : Tensor
Geometric polarizability derivative tensor of shape `(..., 3, 3, nat, 3)`.
modes : Tensor
Normal modes of shape `(..., nat*3, nmodes)`.
Returns
-------
tuple[Tensor, Tensor]
Static Raman activities (intensities) of shape `(..., nfreqs)` and
depolarization ratios of shape `(..., nfreqs)`.
"""
# reshape for matmul: (..., 3, 3, nat, 3) -> (..., 3, 3, nat*3)
da_dr = da_dr.view(*(*modes.shape[:-2], 3, 3, -1))
# convert cartesian to internal coordinate derivatives
# (..., 3, 3, nat*3) @ (..., nat*3, nmodes) = (..., 3, 3, nmodes)
da_dq = da_dr @ modes
# Eq.3 with alpha' = a (trace of the polarizability derivative)
a = einsum("...iij->...j", da_dq)
a2 = torch.pow(a, 2.0)
# Eq.4 with (gamma')^2 = g = 0.5 * (g1 + g2 + g3 + 6.0*g4)
g1 = (da_dq[0, 0] - da_dq[1, 1]) ** 2
g2 = (da_dq[0, 0] - da_dq[2, 2]) ** 2
g3 = (da_dq[2, 2] - da_dq[1, 1]) ** 2
g4 = da_dq[0, 1] ** 2 + da_dq[1, 2] ** 2 + da_dq[2, 0] ** 2
g = g1 + g2 + g3 + 6.0 * g4
# Eq.1 (the 1/3 from Eq.3 is squared, yielding 45 * 1/9 = 5; the 7 is
# halfed by the 0.5 from Eq.4)
ints = 5 * a2 + 3.5 * g
# original formula: 3 * gamma^2 / (45 * alpha^2 + 4 * gamma^2)
depol = torch.where(
a2 > 1e-8, # avoid division by tiny values...verify correctness?
storch.divide(1.5 * g, 5 * a2 + 2.0 * g),
torch.tensor(0.0, device=a.device, dtype=a.dtype),
)
return ints, depol
