fundamental functionality for linear algebra, utilities, molecules and more More...

Namespaces
namespace	charges

namespace	diis

namespace	graph

namespace	linalg

namespace	numpy

namespace	opt

namespace	rotor

Classes
struct	Atom
	Class representing and holding data for an Atom in 3D space. More...

class	Combinations
	Class to generate all possible combinations of a integers. More...

struct	ConditioningOrthogonalizerResult

class	Dimer
	Storage class for relevant information of a dimer (pair) of Molecule objects. More...

class	ElasticTensor
	Class for computation of properties based on an elasticity tensor. More...

class	Element
	Utility class representing and holding data for a chemical element. More...

class	EnergyComponents
	Storage class for components of energy, separated by the dot character. More...

class	Fraction
	Class representing and holding data a rational number i.e. More...

struct	GenSqrtInvResult

class	Interpolator1D
	Class for interpolating one-dimensional functions. More...

struct	KalmanEstimator

class	MolecularAxisCalculator
	Molecular axis calculator class. More...

struct	MolecularAxisResult
	Structure to hold molecular axis calculation results. More...

class	MolecularPointGroup
	Storage class for a point group describing a Molecule. More...

class	Molecule
	Storage class for relevant information of a Molecule. More...

struct	Multipole
	Templated storage class for Multipole expansions. More...

struct	NeighcrysAxisInfo
	Structure for neighcrys-compatible axis file information. More...

class	PointCharge

class	ProgressTracker

struct	SymmetryMappingResult
	Result of attempting a transformation with grouped permutations. More...

struct	SymOp
	Structure/utility class for a point group symmetry operation. More...

struct	TerminalSize

struct	VibrationalModes
	Results from vibrational frequency analysis. More...

Typedefs
template<typename NumericType >
using	KDTree = nanoflann::KDTreeEigenMatrixAdaptor< Eigen::Matrix< NumericType, 3, Eigen::Dynamic >, 3, nanoflann::metric_L2, false >

Enumerations
enum	DomainMapping { Linear , SquareRoot , Log }
	An enum to specify the mapping of the domain of inputs for interpolation. More...

enum class	AxisMethod { None , Neighcrys , PCA , MOI }
	Enumeration of molecular axis calculation methods. More...

enum class	PointGroup { C1 , Ci , Cs , C2 , C3 , C4 , C5 , C6 , C8 , Coov , Dooh , C2v , C3v , C4v , C5v , C6v , C2h , C3h , C4h , C5h , C6h , D2 , D3 , D4 , D5 , D6 , D7 , D8 , D2h , D3h , D4h , D5h , D6h , D7h , D8h , D2d , D3d , D4d , D5d , D6d , D7d , D8d , S4 , S6 , S8 , T , Td , Th , O , Oh , I , Ih }

enum class	MirrorType { None , H , D , V }

Functions
bool	operator== (const Atom &atom1, const Atom &atom2)
	returns true if two Atoms have the same element and are at the exact same point in space

template<typename AtomIterator >
void	rotate_atoms (AtomIterator &atoms, const Mat3 &rotation)
	Rotate a range of atoms about the origin.

template<typename AtomIterator >
void	translate_atoms (AtomIterator &atoms, const Vec3 &translation)
	translate a range of atoms

void	set_bond_tolerance (float t)

double	get_bond_tolerance ()

ConditioningOrthogonalizerResult	conditioning_orthogonalizer (Eigen::Ref< const Mat >, double)

std::string	chemical_formula (const std::vector< Element > &elements)
	The chemical formula of a given std::vector of Elements e.g.

GenSqrtInvResult	gensqrtinv (Eigen::Ref< const Mat >, bool symmetric=false, double max_condition_number=1e8)

Mat3	inertia_tensor (Eigen::Ref< const Vec > masses, Eigen::Ref< const Mat3N > positions)

template<typename T >
OCC_ALWAYS_INLINE T	lerp (T v0, T v1, T t)

std::pair< Mat, Mat >	meshgrid (const Vec &, const Vec &)

SymmetryMappingResult	try_transformation_with_grouped_permutations (const IVec &labels_A, const Mat3N &positions_A, const IVec &labels_B, const Mat3N &positions_B, const Mat3 &transformation, double rmsd_threshold=1e-3)
	Attempts to find a transformation mapping from one set of atoms to another using grouped permutations based on provided labels.

void	label_molecules_by_chemical_formula (std::vector< occ::core::Molecule > &molecules)

constexpr unsigned int	num_unique_multipole_components (int L)
	The number of unique multipole components for a given angular momentum.

constexpr unsigned int	num_multipole_components_tensor (int L)
	The number of tensor multipole components for a given angular momentum.

constexpr unsigned int	total_num_multipole_components (int L)
	The total number of unique multipole components up to and including a given angular momentum.

std::vector< PointCharge >	make_point_charges (const std::vector< Atom > &atoms)

constexpr unsigned int	num_multipole_components (unsigned int order)

template<unsigned int order = 0>
auto	compute_multipoles (const std::vector< PointCharge > &charges, const Vec3 &origin=Vec3::Zero())

PointGroup	dihedral_group (int, MirrorType)

PointGroup	cyclic_group (int, MirrorType)

Mat	quasirandom_kgf (size_t ndims, size_t count, size_t seed=0)
	Generate an D dimensional Korobov type quasi-random vector based on the generalized Fibonacci sequence.

VibrationalModes	compute_vibrational_modes (const Mat &hessian, const Vec &masses, const Mat3N &positions=Mat3N(), bool project_tr_rot=false)
	Perform vibrational frequency analysis on a Hessian matrix.

VibrationalModes	compute_vibrational_modes (const Mat &hessian, const Molecule &molecule, bool project_tr_rot=false)
	Convenience function for molecular vibrational analysis.

Mat	mass_weighted_hessian (const Mat &hessian, const Vec &masses)
	Construct mass-weighted Hessian matrix.

Mat	mass_weighted_hessian (const Mat &hessian, const Molecule &molecule)
	Convenience function for molecular mass-weighted Hessian.

Vec	eigenvalues_to_frequencies_cm (const Vec &eigenvalues)
	Convert frequency eigenvalues to cm⁻¹

Vec	frequencies_cm_to_hartree (const Vec &frequencies_cm)
	Convert frequencies from cm⁻¹ to Hartree.

Mat	construct_translation_vectors (const Vec &masses)
	Construct translational projection vectors.

Mat	construct_rotation_vectors (const Vec &masses, const Mat3N &positions)
	Construct rotational projection vectors.

Mat	project_tr_rot_modes (const Mat &mass_weighted_hessian, const Vec &masses, const Mat3N &positions)
	Project out translational and rotational modes from mass-weighted Hessian.

Mat	construct_translation_vectors (const Molecule &molecule)
	Convenience functions for molecular systems.

Mat	construct_rotation_vectors (const Molecule &molecule)

Mat	project_tr_rot_modes (const Mat &mass_weighted_hessian, const Molecule &molecule)

void	to_json (nlohmann::json &j, const Molecule &)

void	from_json (const nlohmann::json &j, Molecule &)

void	to_json (nlohmann::json &j, const VibrationalModes &)

void	from_json (const nlohmann::json &j, VibrationalModes &)

Variables
double	covalent_bond_tolerance = 0.4

constexpr size_t	max_leaf = 10

constexpr std::array< const char *, 35 >	multipole_component_names
	The names of multipole components in order.

Detailed Description

fundamental functionality for linear algebra, utilities, molecules and more

No dependencies on other modules in occ

Typedef Documentation

◆ KDTree

template<typename NumericType >

using occ::core::KDTree = typedef nanoflann::KDTreeEigenMatrixAdaptor< Eigen::Matrix<NumericType, 3, Eigen::Dynamic>, 3, nanoflann::metric_L2, false>

Enumeration Type Documentation

◆ AxisMethod

enum class occ::core::AxisMethod

strong

Enumeration of molecular axis calculation methods.

Enumerator
None	No axis calculation.
Neighcrys	Neighcrys method using 3 specified atoms.
PCA	Principal component analysis.
MOI	Moment of inertia tensor eigenvectors.

◆ DomainMapping

enum occ::core::DomainMapping

An enum to specify the mapping of the domain of inputs for interpolation.

Can help improve precision of linear interpolation while minimizing number of points.

Enumerator
Linear	The typical f(x) mapping.
SquareRoot	Make f a function of x^2 -> f(x*x) mapping.
Log	Make f a function of e^x -> f(e^x) mapping.

◆ MirrorType

enum class occ::core::MirrorType

strong

Enumerator
None
H
D
V

◆ PointGroup

enum class occ::core::PointGroup

strong

Enumerator
C1	No rotational symmetry.
Ci	Ci = S2 No rotational symmetry, but with inversion.
Cs	Cs = C1h No rotational symmetry, but a mirror plane.
C2	open book geometry, two-fold rotational symmetry
C3	propeller, three-fold rotational symmetry
C4	four-fold rotational symmetry
C5	five-fold rotational symmetry
C6	six-fold rotational symmetry
C8	eight-fold rotational symmetry
Coov	Linear, infinite rotational symmetry.
Dooh	Linear, with an inversion center.
C2v	angular, see-saw, T-shape, two-fold rotational symmetry with mirror plane parallel to axis of rotation
C3v	trigonal pyramidal, three-fold rotational symmetry with mirror plane parallel to axis of rotation
C4v	square pyramidal, four-fold rotational symmetry with mirror plane parallel to axis of rotation
C5v	milking stool, five-fold rotational symmetry with mirror plane parallel to axis of rotation
C6v	six-fold rotational symmetry with mirror plane parallel to axis of rotation
C2h	two-fold rotational symmetry with mirror plane orthogonal to axis of rotation
C3h	three-fold rotational symmetry with mirror plane orthogonal to axis of rotation
C4h	four-fold rotational symmetry with mirror plane orthogonal to axis of rotation
C5h	five-fold rotational symmetry with mirror plane orthogonal to axis of rotation
C6h	six-fold rotational symmetry with mirror plane orthogonal to axis of rotation
D2	twist, two-fold rotational symmetry with an inversion
D3	three-fold rotational symmetry with an inversion
D4	four-fold rotational symmetry with an inversion
D5	five-fold rotational symmetry with an inversion
D6	six-fold rotational symmetry with an inversion
D7	seven-fold rotational symmetry with an inversion
D8	eight-fold rotational symmetry with an inversion
D2h	planar + inversion center, two-fold rotational symmetry with an and mirror plane orthogonal to axis of rotation
D3h	trigonal planar, trigonal bipyramidal, three-fold rotational symmetry with an inversion and mirror plane orthogonal to axis of rotation
D4h	square planar, four-fold rotational symmetry with an inversion and mirror plane orthogonal to axis of rotation
D5h	pentagonal
D6h	hexagonal
D7h	heptagonal
D8h	octagonal
D2d	90 degree twist
D3d	60 degree twist
D4d	45 degree twist
D5d	36 degree twist
D6d	30 degree twist
D7d
D8d
S4
S6
S8
T
Td	tetrahedral
Th	pyritohedron
O
Oh	octahedral, cubic
I
Ih	icosahedral, dodecahedral

Function Documentation

◆ chemical_formula()

std::string occ::core::chemical_formula ( const std::vector< Element > & elements )

The chemical formula of a given std::vector of Elements e.g.

"H2O"

The result is in plain ASCII characters (i.e. no subscripts) and elements with a count of 1 the number suffix is omitted. i.e. H2O not H2O1

Parameters

elements a std::vector of Elements used to calculate the chemical formula

Returns: a string representing the chemical formula

◆ compute_multipoles()

template<unsigned int order = 0>

auto occ::core::compute_multipoles	(	const std::vector< PointCharge > &	charges,
		const Vec3 &	origin = `Vec3::Zero()`
	)

inline

◆ compute_vibrational_modes() [1/2]

VibrationalModes occ::core::compute_vibrational_modes	(	const Mat &	hessian,
		const Molecule &	molecule,
		bool	project_tr_rot = `false`
	)

Convenience function for molecular vibrational analysis.

Parameters

hessian	3N×3N Hessian matrix in atomic units (Hartree/Bohr²)
molecule	Molecule object containing atomic masses and positions
project_tr_rot	Project out translational and rotational modes (like ORCA's PROJECTTR)

Returns: VibrationalModes Complete vibrational analysis results

◆ compute_vibrational_modes() [2/2]

VibrationalModes occ::core::compute_vibrational_modes	(	const Mat &	hessian,
		const Vec &	masses,
		const Mat3N &	positions = `Mat3N()`,
		bool	project_tr_rot = `false`
	)

Perform vibrational frequency analysis on a Hessian matrix.

Parameters

hessian	3N×3N Hessian matrix in atomic units (Hartree/Bohr²)
masses	Vector of atomic masses in AMU (length N for N atoms)
positions	3×N matrix of atomic positions in Bohr (optional, for projection)
project_tr_rot	Project out translational and rotational modes (like ORCA's PROJECTTR)

Returns: VibrationalModes Complete vibrational analysis results

◆ conditioning_orthogonalizer()

ConditioningOrthogonalizerResult occ::core::conditioning_orthogonalizer	(	Eigen::Ref< const Mat >	,
		double
	)

◆ construct_rotation_vectors() [1/2]

Mat occ::core::construct_rotation_vectors ( const Molecule & molecule )

◆ construct_rotation_vectors() [2/2]

Mat occ::core::construct_rotation_vectors	(	const Vec &	masses,
		const Mat3N &	positions
	)

Construct rotational projection vectors.

Parameters

masses	Vector of atomic masses in AMU (length N for N atoms)
positions	3×N matrix of atomic positions in Bohr

Returns: 3N×3 matrix with rotation vectors as columns

◆ construct_translation_vectors() [1/2]

Mat occ::core::construct_translation_vectors ( const Molecule & molecule )

Convenience functions for molecular systems.

◆ construct_translation_vectors() [2/2]

Mat occ::core::construct_translation_vectors ( const Vec & masses )

Construct translational projection vectors.

Parameters

masses Vector of atomic masses in AMU (length N for N atoms)

Returns: 3N×3 matrix with translation vectors as columns

◆ cyclic_group()

PointGroup occ::core::cyclic_group	(	int	,
		MirrorType
	)

◆ dihedral_group()

PointGroup occ::core::dihedral_group	(	int	,
		MirrorType
	)

◆ eigenvalues_to_frequencies_cm()

Vec occ::core::eigenvalues_to_frequencies_cm ( const Vec & eigenvalues )

Convert frequency eigenvalues to cm⁻¹

For positive eigenvalues: ν = sqrt(λ) * conversion_factor For negative eigenvalues: ν = -sqrt(-λ) * conversion_factor (imaginary frequencies)

Parameters

eigenvalues Eigenvalues from mass-weighted Hessian (Hartree/AMU/Bohr²)

Returns: Frequencies in cm⁻¹

◆ frequencies_cm_to_hartree()

Vec occ::core::frequencies_cm_to_hartree ( const Vec & frequencies_cm )

Convert frequencies from cm⁻¹ to Hartree.

Parameters

frequencies_cm Frequencies in cm⁻¹

Returns: Frequencies in Hartree

◆ from_json() [1/2]

void occ::core::from_json	(	const nlohmann::json &	j,
		Molecule &
	)

◆ from_json() [2/2]

void occ::core::from_json	(	const nlohmann::json &	j,
		VibrationalModes &
	)

◆ gensqrtinv()

GenSqrtInvResult occ::core::gensqrtinv	(	Eigen::Ref< const Mat >	,
		bool	symmetric = `false`,
		double	max_condition_number = `1e8`
	)

◆ get_bond_tolerance()

double occ::core::get_bond_tolerance ( )

inline

◆ inertia_tensor()

Mat3 occ::core::inertia_tensor	(	Eigen::Ref< const Vec >	masses,
		Eigen::Ref< const Mat3N >	positions
	)

◆ label_molecules_by_chemical_formula()

void occ::core::label_molecules_by_chemical_formula ( std::vector< occ::core::Molecule > & molecules )

◆ lerp()

template<typename T >

OCC_ALWAYS_INLINE T occ::core::lerp	(	T	v0,
		T	v1,
		T	t
	)

◆ make_point_charges()

std::vector< PointCharge > occ::core::make_point_charges ( const std::vector< Atom > & atoms )

inline

◆ mass_weighted_hessian() [1/2]

Mat occ::core::mass_weighted_hessian	(	const Mat &	hessian,
		const Molecule &	molecule
	)

Convenience function for molecular mass-weighted Hessian.

Parameters

hessian	3N×3N Hessian matrix in atomic units
molecule	Molecule object containing atomic masses

Returns: Mass-weighted Hessian matrix

◆ mass_weighted_hessian() [2/2]

Mat occ::core::mass_weighted_hessian	(	const Mat &	hessian,
		const Vec &	masses
	)

Construct mass-weighted Hessian matrix.

The mass-weighted Hessian is constructed as: H_mw[3i+a][3j+b] = H[3i+a][3j+b] / sqrt(m_i * m_j) where m_i is the mass of atom i in AMU

Parameters

hessian	3N×3N Hessian matrix in atomic units
masses	Vector of atomic masses in AMU (length N for N atoms)

Returns: Mass-weighted Hessian matrix

◆ meshgrid()

std::pair< Mat, Mat > occ::core::meshgrid	(	const Vec &	,
		const Vec &
	)

◆ num_multipole_components()

constexpr unsigned int occ::core::num_multipole_components ( unsigned int order )

constexpr

◆ num_multipole_components_tensor()

constexpr unsigned int occ::core::num_multipole_components_tensor ( int L )

inlineconstexpr

The number of tensor multipole components for a given angular momentum.

Parameters

L	the angular momentum.

Returns: an unsigned int with the count of the number of components.

◆ num_unique_multipole_components()

constexpr unsigned int occ::core::num_unique_multipole_components ( int L )

inlineconstexpr

The number of unique multipole components for a given angular momentum.

Parameters

L	the angular momentum.

Returns: an unsigned int with the count of the number of components.

◆ operator==()

bool occ::core::operator==	(	const Atom &	atom1,
		const Atom &	atom2
	)

inline

returns true if two Atoms have the same element and are at the exact same point in space

◆ project_tr_rot_modes() [1/2]

Mat occ::core::project_tr_rot_modes	(	const Mat &	mass_weighted_hessian,
		const Molecule &	molecule
	)

◆ project_tr_rot_modes() [2/2]

Mat occ::core::project_tr_rot_modes	(	const Mat &	mass_weighted_hessian,
		const Vec &	masses,
		const Mat3N &	positions
	)

Project out translational and rotational modes from mass-weighted Hessian.

Parameters

mass_weighted_hessian	Mass-weighted Hessian matrix
masses	Vector of atomic masses in AMU (length N for N atoms)
positions	3×N matrix of atomic positions in Bohr

Returns: Projected Hessian matrix

◆ quasirandom_kgf()

Mat occ::core::quasirandom_kgf	(	size_t	ndims,
		size_t	count,
		size_t	seed = `0`
	)

Generate an D dimensional Korobov type quasi-random vector based on the generalized Fibonacci sequence.

Based on the R_1, R_2 sequences available here: https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/

Parameters:

Parameters

ndims	number of dimensions to sample
count	the number of points in space to generate
seed	the seed (offset) into the sequence, default = 0

Returns: a ndims dimensional sampling point

◆ rotate_atoms()

template<typename AtomIterator >

void occ::core::rotate_atoms	(	AtomIterator &	atoms,
		const Mat3 &	rotation
	)

inline

Rotate a range of atoms about the origin.

◆ set_bond_tolerance()

void occ::core::set_bond_tolerance ( float t )

inline

◆ to_json() [1/2]

void occ::core::to_json	(	nlohmann::json &	j,
		const Molecule &
	)

◆ to_json() [2/2]

void occ::core::to_json	(	nlohmann::json &	j,
		const VibrationalModes &
	)

◆ total_num_multipole_components()

constexpr unsigned int occ::core::total_num_multipole_components ( int L )

inlineconstexpr

The total number of unique multipole components up to and including a given angular momentum.

Parameters

L	the angular momentum.

Returns: an unsigned int with the count of the number of components.

◆ translate_atoms()

template<typename AtomIterator >

void occ::core::translate_atoms	(	AtomIterator &	atoms,
		const Vec3 &	translation
	)

inline

translate a range of atoms

◆ try_transformation_with_grouped_permutations()

SymmetryMappingResult occ::core::try_transformation_with_grouped_permutations	(	const IVec &	labels_A,
		const Mat3N &	positions_A,
		const IVec &	labels_B,
		const Mat3N &	positions_B,
		const Mat3 &	transformation,
		double	rmsd_threshold = `1e-3`
	)

Attempts to find a transformation mapping from one set of atoms to another using grouped permutations based on provided labels.

This function applies the given transformation matrix to positions B and then finds permutations within atom groups to match reference positions A. Groups are formed by the provided labels (e.g., asymmetric unit indices or atomic numbers). The transformed positions are automatically aligned by centroid.

Parameters

labels_A	The labels for reference atoms (A)
positions_A	The reference positions (A) to match against
labels_B	The labels for atoms to transform (B)
positions_B	The positions (B) to transform and permute
transformation	The transformation matrix to apply to positions_B
rmsd_threshold	The RMSD threshold for considering a match (default: 1e-3)

Returns: SymmetryMappingResult containing success status, permutation, and RMSD

Variable Documentation

◆ covalent_bond_tolerance

double occ::core::covalent_bond_tolerance = 0.4

inline

◆ max_leaf

constexpr size_t occ::core::max_leaf = 10

constexpr

◆ multipole_component_names

constexpr std::array<const char *, 35> occ::core::multipole_component_names

inlineconstexpr

Initial value:

{
    "q",     "Dx",    "Dy",    "Dz",    "Qxx",   "Qxy",   "Qxz",
    "Qyy",   "Qyz",   "Qzz",   "Oxxx",  "Oxxy",  "Oxxz",  "Oxyy",
    "Oxyz",  "Oxzz",  "Oyyy",  "Oyyz",  "Oyzz",  "Ozzz",  "Hxxxx",
    "Hxxxy", "Hxxxz", "Hxxyy", "Hxxyz", "Hxxzz", "Hxyyy", "Hxyyz",
    "Hxyzz", "Hxzzz", "Hyyyy", "Hyyyz", "Hyyzz", "Hyzzz", "Hzzzz"}

The names of multipole components in order.

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ KDTree

Enumeration Type Documentation

◆ AxisMethod

◆ DomainMapping

◆ MirrorType

◆ PointGroup

Function Documentation

◆ chemical_formula()

◆ compute_multipoles()

◆ compute_vibrational_modes() [1/2]

◆ compute_vibrational_modes() [2/2]

◆ conditioning_orthogonalizer()

◆ construct_rotation_vectors() [1/2]

◆ construct_rotation_vectors() [2/2]

◆ construct_translation_vectors() [1/2]

◆ construct_translation_vectors() [2/2]

◆ cyclic_group()

◆ dihedral_group()

◆ eigenvalues_to_frequencies_cm()

◆ frequencies_cm_to_hartree()

◆ from_json() [1/2]

◆ from_json() [2/2]

◆ gensqrtinv()

◆ get_bond_tolerance()

◆ inertia_tensor()

◆ label_molecules_by_chemical_formula()

◆ lerp()

◆ make_point_charges()

◆ mass_weighted_hessian() [1/2]

◆ mass_weighted_hessian() [2/2]

◆ meshgrid()

◆ num_multipole_components()

◆ num_multipole_components_tensor()

◆ num_unique_multipole_components()

◆ operator==()

◆ project_tr_rot_modes() [1/2]

◆ project_tr_rot_modes() [2/2]

◆ quasirandom_kgf()

◆ rotate_atoms()

◆ set_bond_tolerance()

◆ to_json() [1/2]

◆ to_json() [2/2]

◆ total_num_multipole_components()

◆ translate_atoms()

◆ try_transformation_with_grouped_permutations()

Variable Documentation

◆ covalent_bond_tolerance

◆ max_leaf

◆ multipole_component_names