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//! Molecular symmetry element detection for asymmetric tops.
use anyhow::{self, ensure, format_err};
use itertools::Itertools;
use log;
use nalgebra::Vector3;
use crate::rotsym::RotationalSymmetry;
use crate::symmetry::symmetry_core::_search_proper_rotations;
use crate::symmetry::symmetry_element::{SymmetryElement, ROT, SIG, TRROT, TRSIG};
use crate::symmetry::symmetry_element_order::{ORDER_1, ORDER_2};
use super::{PreSymmetry, Symmetry};
impl Symmetry {
/// Performs point-group detection analysis for an asymmetric-top molecule.
///
/// The possible asymmetric top point groups are:
///
/// * $`\mathcal{C}_{1}`$ and $`\mathcal{C}_{2}`$,
/// * $`\mathcal{C}_{2v}`$,
/// * $`\mathcal{C}_{2h}`$,
/// * $`\mathcal{C}_{s}`$,
/// * $`\mathcal{D}_{2}`$,
/// * $`\mathcal{D}_{2h}`$, and
/// * $`\mathcal{C}_{i}`$.
///
/// These are all Abelian groups.
///
/// # Arguments
///
/// * `presym` - A pre-symmetry-analysis structure containing information about the molecular
/// system.
/// * `tr` - A flag indicating if time reversal should also be considered. A time-reversed
/// symmetry element will only be considered if its non-time-reversed version turns out to be
/// not a symmetry element.
#[allow(clippy::too_many_lines)]
pub(super) fn analyse_asymmetric(
&mut self,
presym: &PreSymmetry,
tr: bool,
) -> Result<(), anyhow::Error> {
let (_mois, principal_axes) = presym.recentred_molecule.calc_moi();
ensure!(
matches!(
presym.rotational_symmetry,
RotationalSymmetry::AsymmetricPlanar | RotationalSymmetry::AsymmetricNonPlanar
),
"Unexpected rotational symmetry -- expected: {} or {}, actual: {}",
RotationalSymmetry::AsymmetricPlanar,
RotationalSymmetry::AsymmetricNonPlanar,
presym.rotational_symmetry
);
_search_proper_rotations(presym, self, true, tr)?;
log::debug!("Proper elements found: {:?}", self.get_elements(&ROT));
log::debug!(
"Time-reversed proper elements found: {:?}",
self.get_elements(&TRROT)
);
// Classify into point groups
let count_c2 = self
.get_proper(&ORDER_2)
.map_or(0, |proper_elements| proper_elements.len());
ensure!(
count_c2 == 0 || count_c2 == 1 || count_c2 == 3,
"Unexpected number of C2 axes: {count_c2}."
);
let max_ord = self.get_max_proper_order();
if count_c2 == 3 {
// Dihedral, either D2h or D2.
log::debug!("Dihedral family (asymmetric top).");
ensure!(
max_ord == ORDER_2,
"Unexpected principal order -- expected: 2, actual: {max_ord}."
);
// Principal axis, which is C2, is also a generator.
// If the group is a black-white magnetic group, then one C2 axis is non-time-reversed,
// while the other two are. Hence, one C2 generator is non-time-reversed, and the other
// must be. We take care of this by sorting `c2s` to put any non-time-reversed elements
// first.
let mut c2s = self
.get_proper(&ORDER_2)
.ok_or_else(|| format_err!("No C2 elements found."))?
.into_iter()
.cloned()
.collect_vec();
c2s.sort_by_key(SymmetryElement::contains_time_reversal);
let mut c2s = c2s.into_iter();
let c2 = c2s
.next()
.ok_or_else(|| format_err!("No C2 elements found."))?;
self.add_proper(
max_ord,
c2.raw_axis(),
true,
presym.dist_threshold,
c2.contains_time_reversal(),
);
// One other C2 axis is also a generator.
let another_c2 = c2s
.next()
.ok_or_else(|| format_err!("No more C2s found."))?;
self.add_proper(
max_ord,
another_c2.raw_axis(),
true,
presym.dist_threshold,
another_c2.contains_time_reversal(),
);
let z_vec = Vector3::new(0.0, 0.0, 1.0);
if let Some(improper_kind) = presym.check_improper(&ORDER_2, &z_vec, &SIG, tr) {
// Inversion centre, D2h
log::debug!("Located an inversion centre.");
self.set_group_name("D2h".to_owned());
self.add_improper(
ORDER_2,
&z_vec,
false,
SIG,
None,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
// Add remaining mirror planes, each of which is
// perpendicular to a C2 axis.
let c2s = self
.get_proper(&ORDER_2)
.ok_or_else(|| format_err!("No C2 elements found."))?
.into_iter()
.cloned()
.collect_vec();
for c2 in &c2s {
let improper_check = presym.check_improper(&ORDER_1, c2.raw_axis(), &SIG, tr);
ensure!(
improper_check.is_some(),
"Expected improper element not found."
);
self.add_improper(
ORDER_1,
c2.raw_axis(),
false,
SIG,
None,
presym.dist_threshold,
improper_check
.ok_or_else(|| {
format_err!(
"Expected mirror plane perpendicular to `{}` not found.",
c2.raw_axis()
)
})?
.contains_time_reversal(),
);
}
let principal_element_axis = *self.get_proper_principal_element().raw_axis();
let improper_check =
presym.check_improper(&ORDER_1, &principal_element_axis, &SIG, tr);
ensure!(
improper_check.is_some(),
"Expected improper element not found."
);
self.add_improper(
ORDER_1,
&principal_element_axis,
true,
SIG,
None,
presym.dist_threshold,
improper_check
.ok_or_else(||
format_err!("Expected mirror plane perpendicular to the principal axis not found.")
)?
.contains_time_reversal(),
);
} else {
// Chiral, D2
self.set_group_name("D2".to_owned());
}
} else if count_c2 == 1 {
// Non-dihedral, either C2, C2v, or C2h
log::debug!("Non-dihedral family (asymmetric top).");
ensure!(
max_ord == ORDER_2,
"Unexpected principal order -- expected: 2, actual: {max_ord}."
);
// Principal axis, which is C2, is also a generator.
let c2s = self
.get_proper(&ORDER_2)
.ok_or_else(|| format_err!("No C2 elements found."))?;
let c2 = (*c2s
.iter()
.next()
.ok_or_else(|| format_err!("No C2 elements found."))?)
.clone();
self.add_proper(
max_ord,
c2.raw_axis(),
true,
presym.dist_threshold,
c2.contains_time_reversal(),
);
let z_vec = Vector3::new(0.0, 0.0, 1.0);
if let Some(improper_kind) = presym.check_improper(&ORDER_2, &z_vec, &SIG, tr) {
// Inversion centre, C2h
log::debug!("Located an inversion centre.");
self.add_improper(
ORDER_2,
&z_vec,
false,
SIG,
None,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
self.set_group_name("C2h".to_owned());
// There is one σh.
let c2 = (*self
.get_proper(&ORDER_2)
.ok_or_else(|| format_err!("No C2 elements found."))?
.iter()
.next()
.ok_or_else(|| format_err!("No C2 elements found."))?)
.clone();
let improper_check = presym.check_improper(&ORDER_1, c2.raw_axis(), &SIG, tr);
ensure!(
improper_check.is_some(),
"Expected improper element not found."
);
self.add_improper(
ORDER_1,
c2.raw_axis(),
false,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
improper_check
.as_ref()
.ok_or_else(|| {
format_err!(
"Expected mirror plane perpendicular to {} not found.",
c2.raw_axis()
)
})?
.contains_time_reversal(),
);
self.add_improper(
ORDER_1,
c2.raw_axis(),
true,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
improper_check
.ok_or_else(|| {
format_err!(
"Expected mirror plane perpendicular to {} not found.",
c2.raw_axis()
)
})?
.contains_time_reversal(),
);
} else {
// No inversion centres.
// Locate σ planes
let mut count_sigma = 0;
if matches!(
presym.rotational_symmetry,
RotationalSymmetry::AsymmetricPlanar
) {
// Planar system. The plane of the system (perpendicular to the highest-MoI
// principal axis) might be a symmetry element: time-reversed in the presence of
// a magnetic field (which must also lie in this plane), or both in the absence
// of a magnetic field.
if let Some(improper_kind) =
presym.check_improper(&ORDER_1, &principal_axes[2], &SIG, tr)
{
if presym.recentred_molecule.magnetic_atoms.is_some() {
ensure!(
improper_kind.contains_time_reversal(),
"Expected time-reversed improper element not found."
);
}
count_sigma += u32::from(self.add_improper(
ORDER_1,
&principal_axes[2],
false,
SIG,
Some("v".to_owned()),
presym.dist_threshold,
improper_kind.contains_time_reversal(),
));
}
}
let sea_groups = &presym.sea_groups;
for sea_group in sea_groups.iter() {
if count_sigma == 2 {
break;
}
if sea_group.len() < 2 {
continue;
}
for atom2s in sea_group.iter().combinations(2) {
if count_sigma == 2 {
break;
}
let normal = (atom2s[0].coordinates.coords - atom2s[1].coordinates.coords)
.normalize();
if let Some(improper_kind) =
presym.check_improper(&ORDER_1, &normal, &SIG, tr)
{
if c2.contains_time_reversal()
&& !improper_kind.contains_time_reversal()
{
log::debug!("The C2 axis is actually θ·C2. The non-time-reversed σv will be assigned as σh.");
count_sigma += u32::from(self.add_improper(
ORDER_1,
&normal,
false,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
improper_kind.contains_time_reversal(),
));
} else {
count_sigma += u32::from(self.add_improper(
ORDER_1,
&normal,
false,
SIG,
Some("v".to_owned()),
presym.dist_threshold,
improper_kind.contains_time_reversal(),
));
}
}
}
}
log::debug!(
"Located {} σ ({} σv and {} σh).",
count_sigma,
self.get_sigma_elements("v")
.map_or(0, |sigmavs| sigmavs.len()),
self.get_sigma_elements("h")
.map_or(0, |sigmavs| sigmavs.len()),
);
if count_sigma == 2 {
self.set_group_name("C2v".to_owned());
// In C2v, one of the σ's is also a generator. We prioritise the
// non-time-reversed one as the generator.
let mut sigmas = self
.get_sigma_elements("v")
.or_else(|| {
log::debug!("No σv found. Searching for σh instead.");
self.get_sigma_elements("h")
})
.ok_or_else(|| format_err!("No σv nor σh found."))?
.into_iter()
.chain(self.get_sigma_elements("h").unwrap_or_default().into_iter())
.cloned()
.collect_vec();
sigmas.sort_by_key(SymmetryElement::contains_time_reversal);
let sigma = sigmas
.first()
.ok_or_else(|| format_err!("No σv or σh found."))?;
self.add_improper(
ORDER_1,
sigma.raw_axis(),
true,
SIG,
Some(sigma.additional_subscript.clone()),
presym.dist_threshold,
sigma.contains_time_reversal(),
);
} else {
ensure!(
count_sigma == 0,
"Unexpected number of σ mirror planes: {count_sigma}."
);
self.set_group_name("C2".to_owned());
}
}
} else {
// No C2 axes, so either C1, Ci, or Cs
log::debug!("No C2 axes found.");
let z_vec = Vector3::new(0.0, 0.0, 1.0);
if let Some(improper_kind) = presym.check_improper(&ORDER_2, &z_vec, &SIG, tr) {
log::debug!("Located an inversion centre.");
self.set_group_name("Ci".to_owned());
self.add_improper(
ORDER_2,
&z_vec,
false,
SIG,
None,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
self.add_improper(
ORDER_2,
&z_vec,
true,
SIG,
None,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
);
} else {
log::debug!("No inversion centres found.");
// Locate mirror planes
let sea_groups = &presym.sea_groups;
let mut count_sigma = 0;
for sea_group in sea_groups.iter() {
if count_sigma > 0 {
break;
}
if sea_group.len() < 2 {
continue;
}
for atom2s in sea_group.iter().combinations(2) {
let normal = (atom2s[0].coordinates.coords - atom2s[1].coordinates.coords)
.normalize();
if let Some(improper_kind) =
presym.check_improper(&ORDER_1, &normal, &SIG, tr)
{
count_sigma += u32::from(self.add_improper(
ORDER_1,
&normal,
false,
SIG,
None,
presym.dist_threshold,
improper_kind.contains_time_reversal(),
));
}
}
}
if count_sigma == 0
&& matches!(
presym.rotational_symmetry,
RotationalSymmetry::AsymmetricPlanar
)
{
log::debug!("Planar molecule based on MoIs but no σ found from SEA groups.");
log::debug!("Locating the planar mirror plane based on MoIs...");
let sigma_check = presym.check_improper(&ORDER_1, &principal_axes[2], &SIG, tr);
if sigma_check.is_some() {
ensure!(
self.add_improper(
ORDER_1,
&principal_axes[2],
false,
SIG,
None,
presym.dist_threshold,
sigma_check
.ok_or_else(|| format_err!(
"Expected {}mirror plane perpendicular to the highest-MoI principal axis not found.",
if tr { "time-reversed " } else { "" }
))?
.contains_time_reversal(),
),
"Failed to add {}mirror plane perpendicular to the highest-MoI principal axis.",
if tr { "time-reversed " } else { "" }
);
log::debug!(
"Located one planar {}mirror plane based on MoIs.",
if tr { "time-reversed " } else { "" }
);
count_sigma += 1;
} else {
assert!(!tr, "The only way for a planar molecule to not have a planar mirror plane is when a magnetic field is present but time reversal is not considered.");
log::debug!("No additional planar mirror planes found.");
}
// Old algorithm
// for atom3s in presym.recentred_molecule.atoms.iter().combinations(3) {
// let normal = (atom3s[1].coordinates.coords - atom3s[0].coordinates.coords)
// .cross(&(atom3s[2].coordinates.coords - atom3s[0].coordinates.coords));
// if normal.norm() < presym.dist_threshold {
// if let Some(e_atoms) = &presym.recentred_molecule.electric_atoms {
// let normal = (atom3s[1].coordinates.coords
// - atom3s[0].coordinates.coords)
// .cross(
// &(e_atoms[1].coordinates.coords
// - e_atoms[0].coordinates.coords),
// );
// } else {
// continue;
// }
// }
// let normal = normal.normalize();
// if presym.check_improper(&ORDER_1, &normal, &SIG) {
// count_sigma += self.add_improper(
// ORDER_1,
// normal,
// false,
// SIG.clone(),
// None,
// presym.dist_threshold,
// ) as u32;
// break;
// }
// }
// assert_eq!(count_sigma, 1);
// log::debug!("Located one planar mirror plane based on MoIs.");
}
log::debug!("Located {} σ.", count_sigma);
if count_sigma > 0 {
ensure!(
count_sigma == 1,
"Unexpected number of σ mirror planes: {count_sigma}."
);
let old_sigmas = self
.get_elements_mut(&SIG)
.and_then(|sigmas| sigmas.remove(&ORDER_1))
.or_else(|| {
self.get_elements_mut(&TRSIG)
.and_then(|tr_sigmas| tr_sigmas.remove(&ORDER_1))
})
.ok_or_else(|| {
format_err!("No normal or time-reversed mirror planes found.")
})?;
ensure!(
old_sigmas.len() == 1,
"Unexpected number of old σ mirror planes: {}.",
old_sigmas.len()
);
let old_sigma = old_sigmas
.into_iter()
.next()
.ok_or_else(|| format_err!("No σ found."))?;
self.add_improper(
ORDER_1,
old_sigma.raw_axis(),
false,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
old_sigma.contains_time_reversal(),
);
self.add_improper(
ORDER_1,
old_sigma.raw_axis(),
true,
SIG,
Some("h".to_owned()),
presym.dist_threshold,
old_sigma.contains_time_reversal(),
);
self.set_group_name("Cs".to_owned());
} else {
let identity = (*self
.get_proper(&ORDER_1)
.ok_or_else(|| format_err!("No identity found."))?
.iter()
.next()
.ok_or_else(|| format_err!("No identity found."))?)
.clone();
self.add_proper(
ORDER_1,
identity.raw_axis(),
true,
presym.dist_threshold,
false,
);
self.set_group_name("C1".to_owned());
}
}
}
Ok(())
}
}