#include <molecule.h>

Collaboration diagram for madness::Molecule:

[legend]

Classes
struct	apply_c2
	Apply to (x,y,z) a C2 rotation about an axis thru the origin and (xaxis,yaxis,zaxis) More...

struct	apply_inverse

struct	apply_sigma
	Apply to (x,y,z) a reflection through a plane containing the origin with normal (xaxis,yaxis,zaxis) More...

struct	GeometryParameters

Public Member Functions
	Molecule ()
	Makes a molecule with zero atoms. More...

	Molecule (std::vector< Atom > atoms, double eprec, CorePotentialManager core_pot={}, madness::Tensor< double > field=madness::Tensor< double >(3L))
	makes a molecule from a list of atoms More...

	Molecule (World &world, const commandlineparser &parser)
	makes a molecule using contents of `parser` More...

void	add_atom (double x, double y, double z, double q, int atn)

void	add_atom (double x, double y, double z, double q, int atn, bool psat)

double	atomic_attraction_potential (int iatom, double x, double y, double z) const
	nuclear attraction potential for a specific atom in the molecule More...

double	bounding_cube () const
	Returns the half width of the bounding cube. More...

void	center ()
	Moves the center of nuclear charge to the origin. More...

Tensor< double >	center_of_mass () const
	compute the center of mass More...

double	core_derivative (int atom, int axis, unsigned int core, int m, double x, double y, double z) const

double	core_eval (int atom, unsigned int core, int m, double x, double y, double z) const

double	core_potential_derivative (int atom, int axis, double x, double y, double z) const

std::vector< std::string >	cubefile_header () const
	print out a Gaussian cubefile header More...

madness::Tensor< double >	get_all_coords () const

std::vector< madness::Vector< double, 3 > >	get_all_coords_vec () const

const Atom &	get_atom (unsigned int i) const

unsigned int	get_atom_charge (unsigned int i) const

unsigned int	get_atomic_number (unsigned int i) const

const std::vector< Atom > &	get_atoms () const

double	get_core_bc (unsigned int atn, unsigned int c) const

unsigned int	get_core_l (unsigned int atn, unsigned int c) const

double	get_eprec () const

std::string	get_pointgroup () const

bool	get_pseudo_atom (unsigned int i) const

std::vector< double >	get_rcut () const

void	get_structure ()

std::string	guess_file () const

hashT	hash () const

double	inter_atomic_distance (unsigned int i, unsigned int j) const

bool	is_potential_defined (unsigned int atn) const

bool	is_potential_defined_atom (int i) const

Tensor< double >	massweights () const
	compute the mass-weighting matrix for the hessian More...

double	mol_nuclear_charge_density (double x, double y, double z) const

double	molecular_core_potential (double x, double y, double z) const

Tensor< double >	moment_of_inertia () const

unsigned int	n_core_orb (unsigned int atn) const

unsigned int	n_core_orb_all () const

size_t	natom () const

double	nuclear_attraction_potential (double x, double y, double z) const
	nuclear attraction potential for the whole molecule More...

double	nuclear_attraction_potential_derivative (int atom, int axis, double x, double y, double z) const

double	nuclear_attraction_potential_second_derivative (int atom, int iaxis, int jaxis, double x, double y, double z) const
	the second derivative of the (smoothed) nuclear potential Z/r More...

double	nuclear_charge_density (double x, double y, double z) const

double	nuclear_dipole (int axis) const
	compute the dipole moment of the nuclei More...

Tensor< double >	nuclear_dipole_derivative (const int atom, const int axis) const
	compute the derivative of the nuclear dipole wrt a nuclear displacement More...

double	nuclear_repulsion_derivative (size_t iatom, int axis) const

double	nuclear_repulsion_energy () const

Tensor< double >	nuclear_repulsion_hessian () const
	return the hessian matrix of the second derivatives d^2/dxdy V More...

double	nuclear_repulsion_second_derivative (int iatom, int jatom, int iaxis, int jaxis) const
	compute the nuclear-nuclear contribution to the second derivatives More...

void	orient (bool verbose=false)
	Centers and orients the molecule in a standard manner. More...

void	print () const

void	read (std::istream &f)

void	read_core_file (const std::string &filename)

void	read_file (const std::string &filename)

void	read_structure_from_library (const std::string &name)

void	read_xyz (const std::string filename)

void	rotate (const Tensor< double > &D)
	rotates the molecule and the external field More...

template<typename Archive >
void	serialize (Archive &ar)

void	set_all_coords (const madness::Tensor< double > &newcoords)

void	set_atom_charge (unsigned int i, double zeff)

void	set_atom_coords (unsigned int i, double x, double y, double z)

void	set_core_eprec (double value)

void	set_core_rcut (double value)

void	set_pseudo_atom (unsigned int i, bool psat)

void	set_rcut (double value)

double	smallest_length_scale () const

std::string	symmetrize_and_identify_point_group (const double symtol)

json	to_json () const

double	total_nuclear_charge () const

void	translate (const Tensor< double > &translation)
	translate the molecule More...

void	update_rcut_with_eprec (double value)
	updates rcuts with given eprec More...

Static Public Member Functions
static std::string	get_structure_library_path ()

static std::istream &	position_stream_in_library (std::ifstream &f, const std::string &name)

static void	print_parameters ()

Public Attributes
std::vector< double >	atomic_radii

GeometryParameters	parameters

Private Member Functions
template<typename opT >
int	find_symmetry_equivalent_atom (int iatom, opT op, const double symtol) const

void	swapaxes (int ix, int iy)

template<typename opT >
void	symmetrize_for_op (opT op, const double symtol)

bool	test_for_c2 (double xaxis, double yaxis, double zaxis, const double symtol) const

bool	test_for_inverse (const double symtol) const

template<typename opT >
bool	test_for_op (opT op, const double symtol) const

bool	test_for_sigma (double xaxis, double yaxis, double zaxis, const double symtol) const

Private Attributes
std::vector< Atom >	atoms

CorePotentialManager	core_pot

madness::Tensor< double >	field

std::string	pointgroup_ ="c1"
	The molecular point group is automatically assigned in the identify_pointgroup function. More...

std::vector< double >	rcut

Constructor & Destructor Documentation

◆ Molecule() [1/3]

madness::Molecule::Molecule ( )

inline

Makes a molecule with zero atoms.

◆ Molecule() [2/3]

madness::Molecule::Molecule	(	std::vector< Atom >	atoms,
		double	eprec,
		CorePotentialManager	core_pot = `{}`,
		madness::Tensor< double >	field = `madness::Tensor<double>(3L)`
	)

makes a molecule from a list of atoms

References atomic_radii, madness::constants::atomic_unit_of_length, madness::AtomicData::covalent_radius, e(), madness::get_atomic_data(), and update_rcut_with_eprec().

◆ Molecule() [3/3]

madness::Molecule::Molecule	(	World &	world,
		const commandlineparser &	parser
	)

makes a molecule using contents of parser

References madness::WorldGopInterface::broadcast_serializable(), madness::Molecule::GeometryParameters::field(), field, get_structure(), madness::World::gop, MADNESS_CHECK, parameters, madness::QCCalculationParametersBase::print(), and madness::World::rank().

Member Function Documentation

◆ add_atom() [1/2]

void madness::Molecule::add_atom	(	double	x,
		double	y,
		double	z,
		double	q,
		int	atn
	)

References atomic_radii, madness::constants::atomic_unit_of_length, atoms, c, madness::AtomicData::covalent_radius, e(), madness::get_atomic_data(), get_eprec(), q(), rcut, and madness::smoothing_parameter().

Referenced by main(), read(), read_xyz(), and madness::InitParameters::readnw().

◆ add_atom() [2/2]

void madness::Molecule::add_atom	(	double	x,
		double	y,
		double	z,
		double	q,
		int	atn,
		bool	psat
	)

References atomic_radii, madness::constants::atomic_unit_of_length, atoms, c, madness::AtomicData::covalent_radius, e(), madness::get_atomic_data(), get_eprec(), q(), rcut, and madness::smoothing_parameter().

◆ atomic_attraction_potential()

double madness::Molecule::atomic_attraction_potential	(	int	iatom,
		double	x,
		double	y,
		double	z
	)		const

nuclear attraction potential for a specific atom in the molecule

References atoms, madness::distance(), rcut, madness::smoothed_potential(), and madness::sum().

Referenced by madness::NuclearCorrelationFactor::square_times_V_functor::operator()().

◆ bounding_cube()

double madness::Molecule::bounding_cube ( ) const

Returns the half width of the bounding cube.

The molecule will be contained in the cube [-L,+L].

References atoms, L, and max.

Referenced by main().

◆ center()

void madness::Molecule::center ( )

Moves the center of nuclear charge to the origin.

References atoms, and translate().

Referenced by orient().

◆ center_of_mass()

Tensor< double > madness::Molecule::center_of_mass ( ) const

compute the center of mass

References get_atom(), madness::Atom::mass, natom(), madness::Atom::x, madness::Atom::y, and madness::Atom::z.

Referenced by projector_external_dof(), and madness::MolecularOptimizer::projector_external_dof().

◆ core_derivative()

double madness::Molecule::core_derivative	(	int	atom,
		int	axis,
		unsigned int	core,
		int	m,
		double	x,
		double	y,
		double	z
	)		const

References atoms, axis, madness::CorePotentialManager::core_derivative(), core_pot, m, and xi.

Referenced by madness::CoreOrbitalDerivativeFunctor::operator()().

◆ core_eval()

double madness::Molecule::core_eval	(	int	atom,
		unsigned int	core,
		int	m,
		double	x,
		double	y,
		double	z
	)		const

References atoms, madness::CorePotentialManager::core_eval(), core_pot, and m.

Referenced by madness::CoreOrbitalFunctor::operator()().

◆ core_potential_derivative()

double madness::Molecule::core_potential_derivative	(	int	atom,
		int	axis,
		double	x,
		double	y,
		double	z
	)		const

References atoms, axis, core_pot, madness::distance(), natom(), madness::CorePotentialManager::potential_derivative(), and xi.

Referenced by madchem::CorePotentialDerivativeFunctor::operator()().

◆ cubefile_header()

std::vector< std::string > madness::Molecule::cubefile_header ( ) const

print out a Gaussian cubefile header

References get_atom(), madness::Atom::get_atomic_number(), madness::Atom::get_coords(), and natom().

Referenced by madness::cubefile_header(), and main().

◆ find_symmetry_equivalent_atom()

template<typename opT >

int madness::Molecule::find_symmetry_equivalent_atom	(	int	iatom,
		opT	op,
		const double	symtol
	)		const

private

References atoms, madness::distance(), and op().

Referenced by symmetrize_for_op(), and test_for_op().

◆ get_all_coords()

madness::Tensor< double > madness::Molecule::get_all_coords ( ) const

References c, get_atom(), natom(), madness::Atom::x, madness::Atom::y, and madness::Atom::z.

Referenced by madness::Znemo::gradient(), main(), madness::MolecularEnergy::output_calc_info_schema(), run_all_calculations(), test_read_restartaodata(), test_read_restartdata(), and madness::Znemo::value().

◆ get_all_coords_vec()

std::vector< madness::Vector< double, 3 > > madness::Molecule::get_all_coords_vec ( ) const

References c, get_atom(), natom(), madness::Atom::x, madness::Atom::y, and madness::Atom::z.

Referenced by GaussianNucleusFunctor::GaussianNucleusFunctor(), madness::Znemo::recompute_factors_and_potentials(), MolecularPotentialFunctor::special_points(), madchem::MolecularGuessDensityFunctor::special_points(), madness::MolecularPotentialFunctor::special_points(), madness::MolecularCorePotentialFunctor::special_points(), and madness::write_molecules_to_file().

◆ get_atom()

const Atom & madness::Molecule::get_atom ( unsigned int i ) const

References atoms.

Referenced by madness::GTHPseudopotential< Q >::apply_potential(), madness::GTHPseudopotential< Q >::apply_potential_simple(), center_of_mass(), madness::PotentialManager::core_projection(), madness::PotentialManager::core_projector_derivative(), cubefile_header(), madness::SCF::derivatives(), get_all_coords(), get_all_coords_vec(), madness::Znemo::gradient(), madness::BasisFunctions::guess_virtuals_internal(), madness::SCF::initial_guess(), madness::GTHPseudopotential< Q >::load_pseudo_from_file(), madness::GTHPseudopotential< Q >::make_pseudo_potential(), massweights(), madchem::AtomicAttractionFunctor::operator()(), projector_external_dof(), madness::MolecularOptimizer::projector_external_dof(), madchem::AtomicAttractionFunctor::special_points(), madchem::MolecularDerivativeFunctor::special_points(), madchem::MolecularSecondDerivativeFunctor::special_points(), and test_ethylene().

◆ get_atom_charge()

unsigned int madness::Molecule::get_atom_charge ( unsigned int i ) const

References atoms.

Referenced by madness::SCF::initial_guess().

◆ get_atomic_number()

unsigned int madness::Molecule::get_atomic_number ( unsigned int i ) const

References atoms.

Referenced by GaussianNucleusFunctor::GaussianNucleusFunctor(), get_structure(), madness::SCF::initial_guess(), madness::Localizer::localize_new(), and madness::write_molecules_to_file().

◆ get_atoms()

const std::vector<Atom>& madness::Molecule::get_atoms ( ) const

inline

References atoms.

Referenced by madness::Znemo::custom_guess(), madness::BasisFunctions::guess_contracted_virtuals_from_file(), madness::BasisFunctions::guess_virtuals_from_file(), madness::make_atom_vec(), madness::BasisFunctions::predefined_guess(), and DF::print_molecule().

◆ get_core_bc()

double madness::Molecule::get_core_bc	(	unsigned int	atn,
		unsigned int	c
	)		const

inline

References c, core_pot, and madness::CorePotentialManager::get_core_bc().

Referenced by madness::PotentialManager::core_projection(), and madness::PotentialManager::core_projector_derivative().

◆ get_core_l()

unsigned int madness::Molecule::get_core_l	(	unsigned int	atn,
		unsigned int	c
	)		const

inline

References c, core_pot, and madness::CorePotentialManager::get_core_l().

Referenced by madness::PotentialManager::core_projection(), and madness::PotentialManager::core_projector_derivative().

◆ get_eprec()

double madness::Molecule::get_eprec ( ) const

inline

References madness::Molecule::GeometryParameters::eprec(), and parameters.

Referenced by madness::GaussSlater::GaussSlater(), madness::GradientalGaussSlater::GradientalGaussSlater(), madness::LinearSlater::LinearSlater(), madness::poly4erfc::poly4erfc(), madness::Polynomial< N >::Polynomial(), madness::PseudoNuclearCorrelationFactor::PseudoNuclearCorrelationFactor(), madness::Slater::Slater(), add_atom(), read_core_file(), madness::NuclearCorrelationFactor::smoothed_unitvec(), and update_rcut_with_eprec().

◆ get_pointgroup()

std::string madness::Molecule::get_pointgroup ( ) const

inline

References pointgroup_.

◆ get_pseudo_atom()

bool madness::Molecule::get_pseudo_atom ( unsigned int i ) const

References atoms.

Referenced by get_structure(), and madness::SCF::initial_guess().

◆ get_rcut()

std::vector<double> madness::Molecule::get_rcut ( ) const

inline

References rcut.

Referenced by madchem::AtomicAttractionFunctor::operator()().

◆ get_structure()

void madness::Molecule::get_structure ( )

References madness::Molecule::GeometryParameters::core_type(), madness::QCCalculationParametersBase::get(), get_atomic_number(), madness::get_charge_from_file(), get_pseudo_atom(), MADNESS_EXCEPTION, natom(), madness::Molecule::GeometryParameters::no_orient(), orient(), parameters, read(), read_core_file(), read_structure_from_library(), read_xyz(), set_atom_charge(), set_pseudo_atom(), madness::Molecule::GeometryParameters::source_name(), and madness::Molecule::GeometryParameters::source_type().

Referenced by Molecule().

◆ get_structure_library_path()

std::string madness::Molecule::get_structure_library_path ( )

static

Referenced by position_stream_in_library(), and madness::Molecule::GeometryParameters::set_derived_values().

◆ guess_file()

std::string madness::Molecule::guess_file ( ) const

inline

References core_pot, and madness::CorePotentialManager::guess_file().

◆ hash()

hashT madness::Molecule::hash ( ) const

inline

References atoms, h(), madness::hash_combine(), madness::hash_range(), pointgroup_, and rcut.

◆ inter_atomic_distance()

double madness::Molecule::inter_atomic_distance	(	unsigned int	i,
		unsigned int	j
	)		const

References atoms, and madness::distance().

Referenced by nuclear_repulsion_derivative(), nuclear_repulsion_energy(), and nuclear_repulsion_second_derivative().

◆ is_potential_defined()

bool madness::Molecule::is_potential_defined ( unsigned int atn ) const

inline

References core_pot, and madness::CorePotentialManager::is_defined().

◆ is_potential_defined_atom()

bool madness::Molecule::is_potential_defined_atom ( int i ) const

inline

References atoms, core_pot, and madness::CorePotentialManager::is_defined().

Referenced by madness::SCF::derivatives().

◆ massweights()

Tensor<double> madness::Molecule::massweights ( ) const

inline

compute the mass-weighting matrix for the hessian

use as mass_weighted_hessian=inner(massweights,inner(hessian,massweights));

References get_atom(), and natom().

Referenced by compute_frequencies(), madness::Nemo::compute_IR_intensities(), and compute_reduced_mass().

◆ mol_nuclear_charge_density()

double madness::Molecule::mol_nuclear_charge_density	(	double	x,
		double	y,
		double	z
	)		const

References atoms, madness::distance(), rcut, and madness::smoothed_density().

Referenced by NuclearDensityFunctor::operator()().

◆ molecular_core_potential()

double madness::Molecule::molecular_core_potential	(	double	x,
		double	y,
		double	z
	)		const

References atoms, core_pot, madness::distance(), madness::CorePotentialManager::is_defined(), natom(), madness::CorePotentialManager::potential(), and madness::sum().

Referenced by madness::MolecularCorePotentialFunctor::operator()().

◆ moment_of_inertia()

Tensor< double > madness::Molecule::moment_of_inertia ( ) const

References atoms, I, k, and q().

Referenced by projector_external_dof(), and madness::MolecularOptimizer::projector_external_dof().

◆ n_core_orb()

unsigned int madness::Molecule::n_core_orb ( unsigned int atn ) const

inline

References core_pot, madness::CorePotentialManager::is_defined(), and madness::CorePotentialManager::n_core_orb_base().

Referenced by madness::PotentialManager::core_projection(), and madness::PotentialManager::core_projector_derivative().

◆ n_core_orb_all()

unsigned int madness::Molecule::n_core_orb_all ( ) const

References atoms, core_pot, madness::CorePotentialManager::is_defined(), madness::CorePotentialManager::n_core_orb(), natom(), and madness::sum().

Referenced by madness::SCF::initial_guess(), and madness::SCF::load_mos().

◆ natom()

size_t madness::Molecule::natom ( ) const

inline

References atoms.

Referenced by NuclearVector::NuclearVector(), center_of_mass(), madness::Nemo::compute_all_cphf(), compute_frequencies(), madness::Nemo::compute_IR_intensities(), compute_reduced_mass(), core_potential_derivative(), madness::PotentialManager::core_projection(), cubefile_header(), madness::SCF::derivatives(), get_all_coords(), get_all_coords_vec(), get_structure(), madness::Znemo::gradient(), madness::BasisFunctions::guess_virtuals_internal(), madness::Nemo::hessian(), madness::SCF::initial_guess(), madness::GTHPseudopotential< Q >::load_pseudo_from_file(), madness::Localizer::localize_new(), madness::Nemo::make_incomplete_hessian(), madness::Nemo::make_incomplete_hessian_response_part(), madness::GTHPseudopotential< Q >::make_pseudo_potential(), massweights(), molecular_core_potential(), n_core_orb_all(), nuclear_generator(), nuclear_repulsion_hessian(), madness::MolecularEnergy::output_calc_info_schema(), print(), projector_external_dof(), madness::MolecularOptimizer::projector_external_dof(), read_core_file(), read_xyz(), set_all_coords(), madness::ResponseParameters::set_derived_values(), madness::SCF::solve(), madness::Nemo::solve_cphf(), to_json(), madness::MolecularEnergy::value(), madness::Znemo::value(), and madness::write_molecules_to_file().

◆ nuclear_attraction_potential()

double madness::Molecule::nuclear_attraction_potential	(	double	x,
		double	y,
		double	z
	)		const

nuclear attraction potential for the whole molecule

References atoms, madness::distance(), field, rcut, madness::smoothed_potential(), and madness::sum().

Referenced by MolecularPotentialFunctor::operator()(), and madness::MolecularPotentialFunctor::operator()().

◆ nuclear_attraction_potential_derivative()

double madness::Molecule::nuclear_attraction_potential_derivative	(	int	atom,
		int	axis,
		double	x,
		double	y,
		double	z
	)		const

References atoms, axis, madness::distance(), madness::dsmoothed_potential(), field, and rcut.

Referenced by madness::NuclearCorrelationFactor::square_times_V_derivative_functor::operator()(), and madchem::MolecularDerivativeFunctor::operator()().

◆ nuclear_attraction_potential_second_derivative()

double madness::Molecule::nuclear_attraction_potential_second_derivative	(	int	atom,
		int	iaxis,
		int	jaxis,
		double	x,
		double	y,
		double	z
	)		const

the second derivative of the (smoothed) nuclear potential Z/r

$V(R,r_{el}) -V(r) =\frac{Z}{|R-r_{el}|} \approx Z u(r)$

with

$\frac{\partial^2 V}{\partial X_i\partial X_j} = Z \left(\frac{\partial^2 u(r)}{\partial r^2} \frac{\partial r}{\partial X_i} \frac{\partial r}{\partial X_j} + \frac{\partial u}{\partial r} \frac{\partial^2 r}{\partial X_i \partial X_j}\right)$

References atoms, madness::d2smoothed_potential(), madness::Vector< T, N >::normf(), rcut, madness::smoothed_potential(), and u().

Referenced by madchem::MolecularSecondDerivativeFunctor::operator()().

◆ nuclear_charge_density()

double madness::Molecule::nuclear_charge_density	(	double	x,
		double	y,
		double	z
	)		const

References atoms, madness::distance_sq(), rcut, and madness::smoothed_density().

Referenced by NuclearDensityFunctor::operator()().

◆ nuclear_dipole()

double madness::Molecule::nuclear_dipole ( int axis ) const

compute the dipole moment of the nuclei

Parameters

[in] axis the axis (x, y, z)

References atoms, axis, core_pot, madness::CorePotentialManager::is_defined(), MADNESS_EXCEPTION, madness::CorePotentialManager::n_core_orb(), and madness::sum().

Referenced by madness::SCF::dipole().

◆ nuclear_dipole_derivative()

Tensor< double > madness::Molecule::nuclear_dipole_derivative	(	const int	atom,
		const int	axis
	)		const

compute the derivative of the nuclear dipole wrt a nuclear displacement

Parameters

[in]	atom	the atom which will be displaced
[in]	axis	the axis where the atom will be displaced

Returns: a vector which all 3 components of the dipole derivative

References atoms, and axis.

Referenced by madness::Nemo::compute_IR_intensities().

◆ nuclear_repulsion_derivative()

double madness::Molecule::nuclear_repulsion_derivative	(	size_t	iatom,
		int	axis
	)		const

References atoms, axis, core_pot, inter_atomic_distance(), madness::CorePotentialManager::is_defined(), madness::CorePotentialManager::n_core_orb(), and madness::sum().

Referenced by madness::SCF::derivatives().

◆ nuclear_repulsion_energy()

double madness::Molecule::nuclear_repulsion_energy ( ) const

References atoms, core_pot, inter_atomic_distance(), madness::CorePotentialManager::is_defined(), madness::CorePotentialManager::n_core_orb(), and madness::sum().

Referenced by madness::Znemo::compute_energy(), main(), and madness::SCF::solve().

◆ nuclear_repulsion_hessian()

Tensor< double > madness::Molecule::nuclear_repulsion_hessian ( ) const

return the hessian matrix of the second derivatives d^2/dxdy V

compute the nuclear-nuclear contribution to the molecular hessian

no factor 0.5 included

References natom(), and nuclear_repulsion_second_derivative().

Referenced by madness::Nemo::hessian(), and madness::Nemo::make_incomplete_hessian().

◆ nuclear_repulsion_second_derivative()

double madness::Molecule::nuclear_repulsion_second_derivative	(	int	iatom,
		int	jatom,
		int	iaxis,
		int	jaxis
	)		const

compute the nuclear-nuclear contribution to the second derivatives

Parameters

[in]	iatom	the i-th atom (row of the hessian)
[in]	jatom	the j-th atom (column of the hessian)
[in]	iaxis	the xyz axis of the i-th atom
[in]	jaxis	the xyz axis of the j-th atom return the (3iatom + iaxis, 3jatom + jaxis) matix element of the hessian
[in]	iatom	the i-th atom (row of the hessian)
[in]	jatom	the j-th atom (column of the hessian)
[in]	iaxis	the xyz axis of the i-th atom
[in]	jaxis	the xyz axis of the j-th atom return the (3iatom + iaxis, 3jatom + jaxis) matix element