PetiteList is a petite list (see Dupuis & King, IJQC 11,613,(1977) ) that can be used for constructing symmetry-adapted basis functions (`‘symmetry orbitals’', SO for short) as well as transforming operators and functions from AO to SO basis, and vice versa. More...

#include <chemistry/qc/basis/petite.h>

Inheritance diagram for sc::PetiteList:

Public Member Functions
	PetiteList (const Ref< GaussianBasisSet > &, const Ref< Integral > &)

Ref< GaussianBasisSet >	basis ()

Ref< Integral >	integral ()

Ref< PetiteList >	clone ()

int	nirrep () const

int	order () const

int	atom_map (int n, int g) const

int	shell_map (int n, int g) const

int	lambda (int ij) const

int	lambda (int i, int j) const

int	in_p1 (int n) const

int	in_p2 (int ij) const

int	in_p2 (int i, int j) const
	Same as previous, except for it takes i and j separately.

int	in_p4 (int ij, int kl, int i, int j, int k, int l) const

int	in_p4 (int i, int j, int k, int l) const
	Same as previous, except for doesn't assume ij > kl and recomputes them.

int	nfunction (int i) const

int	nblocks () const

void	print (std::ostream &=ExEnv::out0(), int verbose=1)

RefSCDimension	AO_basisdim ()
	blocked AO dimension (if symmetry = c1, equivalent to SO_basisdim(); otherwise number of blocks = 1, the lone subdimension is blocked by shells)

RefSCDimension	SO_basisdim ()
	blocked SO dimension (number of blocks = order of the point group, each subdimension has 1 block)

RefSCMatrix	r (int g)
	return the basis function rotation matrix R(g) More...

SO_block *	aotoso_info ()

RefSCMatrix	aotoso ()

RefSCMatrix	sotoao ()

void	symmetrize (const RefSymmSCMatrix &skel, const RefSymmSCMatrix &sym)

RefSymmSCMatrix	to_SO_basis (const RefSymmSCMatrix &O_ao)
	converts an operator matrix from AO to SO basis. More...

RefSymmSCMatrix	to_AO_basis (const RefSymmSCMatrix &O_so)
	converts an operator matrix from SO to AO basis. More...

RefSCMatrix	evecs_to_AO_basis (const RefSCMatrix &)
	converts a set of functions (vectors) from SO to AO basis. More...

RefSCMatrix	evecs_to_SO_basis (const RefSCMatrix &)
	converts a set of functions (vectors) from AO to SO basis. More...

Public Member Functions inherited from sc::RefCount
size_t	identifier () const
	Return the unique identifier for this object that can be compared for different objects of different types. More...

int	lock_ptr () const
	Lock this object.

int	unlock_ptr () const
	Unlock this object.

void	use_locks (bool inVal)
	start and stop using locks on this object

refcount_t	nreference () const
	Return the reference count.

refcount_t	reference ()
	Increment the reference count and return the new count.

refcount_t	dereference ()
	Decrement the reference count and return the new count.

int	managed () const

void	unmanage ()
	Turn off the reference counting mechanism for this object. More...

Additional Inherited Members
Protected Member Functions inherited from sc::RefCount
	RefCount (const RefCount &)

RefCount &	operator= (const RefCount &)

Detailed Description

PetiteList is a petite list (see Dupuis & King, IJQC 11,613,(1977) ) that can be used for constructing symmetry-adapted basis functions (`‘symmetry orbitals’', SO for short) as well as transforming operators and functions from AO to SO basis, and vice versa.

N.B. Same basis set assumed for all centers. If need generalization for different basis sets see GPetiteList2 and GPetiteList4.

Member Function Documentation

◆ aotoso()

RefSCMatrix sc::PetiteList::aotoso ( )

Returns: the AO->SO coefficient matrix. The columns correspond to SOs (see SO_basisdim() ) and rows to AOs (see AO_basisdim() ).

This matrix can be used to transform operators from AO to SO basis and functions from SO to AO basis. An operator in the SO basis is obtained by $ X^T O_ao X$ , where $X$ is the return value of this function and $ O_ao $ is the operator in the AO basis. A function in the AO basis is obtained by $ X F_so $ , where $ F_so $ is the function in the SO basis.

◆ aotoso_info()

SO_block* sc::PetiteList::aotoso_info ( )

Returns: information about the transformation from AOs to SOs

◆ evecs_to_AO_basis()

RefSCMatrix sc::PetiteList::evecs_to_AO_basis ( const RefSCMatrix & )

converts a set of functions (vectors) from SO to AO basis.

Parameters

F_so	vectors in SO basis

Returns: non-blocked AO basis vectors

◆ evecs_to_SO_basis()

RefSCMatrix sc::PetiteList::evecs_to_SO_basis ( const RefSCMatrix & )

converts a set of functions (vectors) from AO to SO basis.

Parameters

F_ao	vectors in AO basis, blocked or nonblocked.

Returns: blocked SO basis vectors

◆ r()

RefSCMatrix sc::PetiteList::r ( int g )

return the basis function rotation matrix R(g)

Parameters

g	index of the group operation

◆ sotoao()

RefSCMatrix sc::PetiteList::sotoao ( )

Returns: the SO->AO coefficient matrix (the inverse of AO->SO; for Abelian point groups it is a transpose of AO->SO matrix). The columns correspond to AOs (see AO_basisdim() ) and rows to SOs (see SO_basisdim() ).

This matrix can be used to transform operators from SO to AO basis and functions from AO to SO basis. An operator in the AO basis is obtained by $ X^T O_so X$ , where $X$ is the return value of this function and $ O_so $ is the operator in the SO basis. A function in the SO basis is obtained by $ X F_ao $ , where $ F_ao $ is the function in the AO basis.