DiracSpinor

Stores radial Dirac spinor: F_nk = (f, g) More...

#include <DiracSpinor.hpp>

Public Types
using	Index = uint16_t

Public Member Functions
	DiracSpinor (int in_n, int in_kappa, std::shared_ptr< const Grid > in_rgrid)
	Constructor: Requires n (PQN), kappa (Dirac QN), and grid (shared pointer, as it's a shared resource)
int	n () const
	Principal quantum number, n.
int	kappa () const
	Dirac quantum number, kappa.
int	l () const
	Orbital angular momentum Q number.
double	jjp1 () const
	j(j+1)
int	twoj () const
int	twojp1 () const
	2j+1
int	parity () const
	(-1)^l, returns +/- 1
int	k_index () const
	kappa index (see AtomData)
Index	nk_index () const
	(n,kappa) index (see AtomData)
std::string	symbol (bool gnuplot=false) const
	Single-electron term symbol (e.g., 6s_1/2). Gnuplot=true => 6s_{1/2}.
std::string	shortSymbol () const
	e.g., 6p_1/2 => 6p-, 6p_3/2 => 6p+
void	set_new_kappa (int new_kappa)
	Changes 'kappa' angular quantum number. Use with caution!
const Grid &	grid () const
	Resturns a const reference to the radial grid.
std::shared_ptr< const Grid >	grid_sptr () const
	Resturns copy of shared_ptr to grid [shared resource] - used when we want to construct a new DiracSpinor that shares this grid.
double	en () const
	Single-particle energy, not including rest energy.
double &	en ()
const std::vector< double > &	f () const
	Upper (large) radial component function, f.
std::vector< double > &	f ()
double	f (std::size_t i) const
	Upper (large) radial component, f(r_i)
double &	f (std::size_t i)
const std::vector< double > &	g () const
	Lower (small) radial component function, g.
std::vector< double > &	g ()
double	g (std::size_t i) const
	Lower (small) radial component, g(r_i)
double &	g (std::size_t i)
auto	min_pt () const
	First non-zero point (index for f[i])
auto &	min_pt ()
auto	max_pt () const
	Effective size(); index after last non-zero point (index for f[i])
auto &	max_pt ()
double	r0 () const
	r0 = r[min_pt] (in atomic units) XXX Kill this?
double	rinf () const
	rinf = r[max_pt]
auto	its () const
	Number of iterations until energy convergence (for latest routine only)
auto &	its ()
auto	occ_frac () const
	Occupation fraction. =1 for closed shells. =1/(2j+1) for valence.
auto &	occ_frac ()
auto	eps () const
	Fractional energy convergence: eps = |(en'-en)/en|.
auto &	eps ()
const DiracSpinor &	scale (const double factor)
	Scales DiracSpinor (f and g) by constant.
const DiracSpinor &	scale (const std::vector< double > &v)
	Scales DiracSpinor (f and g) by function of r.
void	normalise (double norm_to=1.0)
	By default normalises to 1, but can normalise to other number.
void	zero_boundaries ()
	Forces f(r) and g(r) to be zero outside of [p0,pinf)
double	norm () const
	Returns the norm, defined: Norm = Sqrt[<a|a>].
double	norm2 () const
	Returns the norm^2, defined: Norm2 = <a|a>
std::pair< double, double >	r0pinfratio () const
	Returns [f[p0]/f_max , f[pinf]/f_max] - for tests.
std::vector< double >	rho () const
	rho(r) = sum_m |Psi^2|(r) = (2j+1) * x_occ * |F^2|(r)
int	num_electrons () const
	Number of occupied electrons: (2j+1)*occ_frac.
DiracSpinor &	operator+= (const DiracSpinor &rhs)
	Addition of two DiracSpinors - must have same kappa.
DiracSpinor &	operator-= (const DiracSpinor &rhs)
DiracSpinor &	operator*= (const double x)
	Scalar multiplication.
DiracSpinor &	operator*= (const std::vector< double > &v)
	Multiplication by array (function)

Static Public Member Functions
static bool	comp_l (const DiracSpinor &lhs, const DiracSpinor &rhs)
	Custom comparitors (for sorting): l, j, kappa_index, energy.
static bool	comp_j (const DiracSpinor &lhs, const DiracSpinor &rhs)
static bool	comp_ki (const DiracSpinor &lhs, const DiracSpinor &rhs)
static bool	comp_n (const DiracSpinor &lhs, const DiracSpinor &rhs)
static bool	comp_en (const DiracSpinor &lhs, const DiracSpinor &rhs)
static std::pair< double, std::string >	check_ortho (const std::vector< DiracSpinor > &a, const std::vector< DiracSpinor > &b)
	Returns worst |<a|b>| (or |<a|b>-1| for a=b) {val, state_names}.
static void	orthonormaliseOrbitals (std::vector< DiracSpinor > &orbs, int num_its=1)
	(approximately) OrthoNormalises a set of any orbitals. More...
static DiracSpinor	orthogonaliseWrt (const DiracSpinor &Fin, const std::vector< DiracSpinor > &orbs)
	Forces Fin to be orthogonal to orbs. If Fn (i.e., {n,k}) in in orbs, replaces Fin with that from orbs.
static DiracSpinor	orthonormaliseWrt (const DiracSpinor &Fin, const std::vector< DiracSpinor > &orbs)
	As orthogonaliseWrt(), but normalises Fin afterwards.
static std::string	shortSymbol (int n, int kappa)
	e.g., 6p_1/2 => 6p-, 6p_3/2 => 6p+
static std::string	state_config (const std::vector< DiracSpinor > &orbs)
	Returns formatted states string (e.g., '7sp5d') given list of orbs.
static DiracSpinor	exactHlike (int n, int k, std::shared_ptr< const Grid > rgrid, double zeff, double alpha=0.0)
	Constructs H-like (pointlike) DiracSpinor - mainly for testing.
static const DiracSpinor *	find (int n, int k, const std::vector< DiracSpinor > &orbs)
	Searches for {n,k} in list of orbitals, returns pointer (may be null)
static int	max_tj (const std::vector< DiracSpinor > &orbs)
	Returns maximum (2j) found in {orbs}.
static int	max_l (const std::vector< DiracSpinor > &orbs)
	Returns maximum l found in {orbs}.
static int	max_n (const std::vector< DiracSpinor > &orbs)
	Returns maximum n found in {orbs}.
static int	max_kindex (const std::vector< DiracSpinor > &orbs)
	Returns maximum kappa_index found in {orbs}.
static std::pair< std::vector< DiracSpinor >, std::vector< DiracSpinor > >	split_by_energy (const std::vector< DiracSpinor > &orbitals, double energy, int n_min_core=1)
static std::pair< std::vector< DiracSpinor >, std::vector< DiracSpinor > >	split_by_core (const std::vector< DiracSpinor > &orbitals, const std::vector< DiracSpinor > &core, int n_min_core=1)

Friends
double	operator* (const DiracSpinor &Fa, const DiracSpinor &Fb)
	Returns radial integral (Fa,Fb) = Int(fa*fb + ga*gb)
DiracSpinor	operator+ (DiracSpinor lhs, const DiracSpinor &rhs)
DiracSpinor	operator- (DiracSpinor lhs, const DiracSpinor &rhs)
DiracSpinor	operator* (DiracSpinor Fa, const double x)
DiracSpinor	operator* (const double x, DiracSpinor Fa)
DiracSpinor	operator* (const std::vector< double > &v, DiracSpinor Fa)
bool	operator== (const DiracSpinor &lhs, const DiracSpinor &rhs)
	Comparitor overloads (compares n, then kappa):
bool	operator!= (const DiracSpinor &lhs, const DiracSpinor &rhs)
bool	operator< (const DiracSpinor &lhs, const DiracSpinor &rhs)
bool	operator> (const DiracSpinor &lhs, const DiracSpinor &rhs)
bool	operator<= (const DiracSpinor &lhs, const DiracSpinor &rhs)
bool	operator>= (const DiracSpinor &lhs, const DiracSpinor &rhs)
std::ostream &	operator<< (std::ostream &ostr, const DiracSpinor &Fa)
	Writes short symbol to ostream.

Detailed Description

Stores radial Dirac spinor: F_nk = (f, g)

\[ \psi_{n\kappa m} = \frac{1}{r} \begin{pmatrix} f_{n\kappa}(r)\,\Omega_{\kappa m}\\ g_{n\kappa}(r)\,\Omega_{-\kappa m} \end{pmatrix}, \quad F_{n\kappa} = \begin{pmatrix} f_{n\kappa}(r)\\ g_{n\kappa}(r) \end{pmatrix} \]

Construction.

Takes in constant n and k=kappa values + grid

• A shared pointer to the Grid is stored (to avoid many copies of Grid)

Operator Overloads

• Intuative operator overloads are provided (Fa, Fb are DiracSpinors):
• v * Fa, where v is a double or vector works the obvious way
• Fa * Fb = <Fa|Fb>
• Fa == Fb returns true if {na,ka}=={nb,kb}
• Fa > Fb : first compares n, and then kappa (via kappa_index)
• Fa +/- Fb : Adds/subtracts the two spinors (and updates p0/pinf)
• You can make copies: auto Fnew = Fa
• And you can re-asign: Fb = Fa (provided Fa and Fb have same n and kappa!)
• n and kappa are constant, cannot be changed. Avoids angular errors.
• all 'set_' functions return mutable references to variables

Member Function Documentation

orthonormaliseOrbitals()

void DiracSpinor::orthonormaliseOrbitals ( std::vector< DiracSpinor > &  orbs, int  num_its = 1  )

static

(approximately) OrthoNormalises a set of any orbitals.

Note: only updates orbs, not energies

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The documentation for this class was generated from the following files:

• Wavefunction/DiracSpinor.hpp
• Wavefunction/DiracSpinor.cpp