File GeometryUtilities.h

Copyright

This code is licensed under the 3-clause BSD license.

Copyright ETH Zurich, Laboratory for Physical Chemistry, Reiher Group.

See LICENSE.txt for details.

namespace Scine

This header file contains functions that allow for common notation for common things that can be done at a different degree of derivatives.

This header contains alias definitions defining which classes to use for the different degrees of derivatives.

namespace Utils
namespace Geometry

Functionalities working with an entire geometry (PositionCollection).

Functions

PositionCollection translatePositions(const PositionCollection &positions, const Eigen::Ref<Eigen::RowVector3d> &translation)

Translates a set of postions by a given displacement.

Return

PositionCollection Returns the translated positions.

Parameters

  • positions: The original positions.

  • translation: The displacement to be added.

void translatePositionsInPlace(PositionCollection &positions, const Eigen::Ref<Eigen::RowVector3d> &translation)

Translates a set of positions by a given displacement.

The translation happens in-place.

Parameters

  • positions: The initial positions, will be transformed in-place.

  • translation: The displacement to be added.

int getIndexOfClosestAtom(const PositionCollection &positions, const Position &targetPosition, double squaredDistanceConsideredZero = -1.0)

Get the index of closest position (atom) to a given position in space.

Return

int The index of the closest atom to the given target.

Parameters

  • positions: A set of positions to be traversed.

  • targetPosition: The target position.

  • distanceConsideredZero: Squared distance between two positions resulting in them being considered equal and therefore skipping this position as it is already present in the given PositionCollection. The default is set to a negative value, so that all positions are considered as possible candidates for the closest one.

int getIndexOfAtomInStructure(const AtomCollection &structure, const Atom &atom, double squaredDistanceConsideredZero = 1e-4)

Get the index of a given atom in a given molecular structure.

Return

int The index of the given atom in the given molecular structure.

Parameters

  • structure: The structure to be traversed.

  • atom: The target atom that is tried to be found in the given structure.

  • distanceConsideredZero: Squared distance between two atoms resulting in them being considered equal.

Exceptions

  • std::runtime_error: Function throws error if the atom is not found in the given structure.

Eigen::MatrixXd positionVectorToMatrix(const Eigen::VectorXd &v)

Transforms a 3N-dimensional vector {x0, y0, z0, x1, y1, z1, …} to a Nx3 matrix.

Return

Eigen::MatrixXd Returns the final Nx3 matrix.

Parameters

  • v: The positions in vector form.

Eigen::VectorXd positionMatrixToVector(const Eigen::MatrixXd &m)

Transforms a Nx3 matrix to a 3N-dimensional vector {x0, y0, z0, x1, y1, z1, …}.

Return

Eigen::VectorXd Returns the final vector.

Parameters

  • m: The positions in matrix form.

void alignPositions(const PositionCollection &reference, PositionCollection &positions)

Rotate and translate positions so that it is as close as possible to referencePositions.

Parameters

  • reference: The reference positions.

  • positions: The positions to be aligned, will be transformed in place.

std::vector<double> getMasses(const ElementTypeCollection &elements)

Get a vector of all masses (in a.u.).

Return

std::vector<double> Returns the masses listed in a vector.

Parameters

  • elements: A collection of elements.

Position getCenterOfMass(const PositionCollection &positions, const std::vector<double> &masses)

Get the center of mass.

Return

Position Returns the center of mass (COM).

Parameters

  • positions: The positions.

  • masses: The masses (sorted according to the positions).

Position getCenterOfMass(const AtomCollection &structure)

Get the center of mass.

Return

Position Returns the center of mass (COM).

Parameters

  • structure: The structure (positions and masses are relevant).

Position getAveragePosition(const PositionCollection &positions)

Get the average Position.

(The average Position is identical to the center of mass if all masses are identical)

Return

Position Returns the average position.

Parameters

  • positions: The positions.

Eigen::Matrix3d calculateInertiaTensor(const PositionCollection &positions, const std::vector<double> &masses, const Position &centerOfMass)

Calculates the inertia tensor.

Return

Eigen::Matrix3d Returns the inertia tensor.

Parameters

  • positions: The positions.

  • masses: The masses (sorted according to the positions).

  • centerOfMass: The center of mass.

PrincipalMomentsOfInertia calculatePrincipalMoments(const PositionCollection &positions, const std::vector<double> &masses, const Position &centerOfMass)

Calculates the principal moments of inertia.

Return

PrincipalMomentsOfInertia Returns the principal moments of inertia.

Parameters

  • positions: The positions.

  • masses: The masses (sorted according to the positions).

  • centerOfMass: The center of mass.

Eigen::MatrixXd calculateTranslationAndRotationModes(const PositionCollection &positions, const ElementTypeCollection &elements)

Calculated the cartesian modes corresponding to translations and rotations of the entire system.

Return

Eigen::MatrixXd The rotation and translation modes. Translation modes (x,y,z) first-third column, rotation modes 3-final column (depending on the geometry)

Parameters

  • positions: The positions of all atoms.

  • elements: The ElemenetTypes of all atoms.

Eigen::MatrixXd calculateRotTransFreeTransformMatrix(const PositionCollection &positions, const ElementTypeCollection &elements, bool massWeighted = false)

Generates the matrix removing rotation and translation modes from the given geometry if applied.

Return

Eigen::MatrixXd The transformation matrix (applied as X^T*H*X to the Hessian).

Parameters

  • positions: The positions of all atoms.

  • elements: The ElemenetTypes of all atoms.

  • massWeighted: True if Hessian to be transformed is mass-weighted

class PrincipalMomentsOfInertia
#include <Geometry.h>

The principal moments of inertia stored.

Public Members

Eigen::Vector3d eigenvalues
Eigen::Matrix3d eigenvectors