Generic Slater-Type Orbital. More...

Collaboration diagram for GenericSTO< T >:

Public Types
using	real_type = T

Public Member Functions
	GenericSTO ()

	GenericSTO (int power, real_type z, real_type norm)
	constructor with a known contraction factor More...

	GenericSTO (int n, int l, real_type z)
	constructor with a set of quantum numbers More...

void	reset ()

void	setgrid (real_type r)

real_type	f (real_type r)

real_type	df (real_type r)

real_type	evaluate (real_type r, real_type rinv)
	return the value only More...

void	evaluateAll (real_type r, real_type rinv)

real_type	evaluate (real_type r, real_type rinv, real_type &drnl, real_type &d2rnl)

real_type	evaluate (real_type r, real_type rinv, real_type &drnl, real_type &d2rnl, real_type &d3rnl)

Public Attributes
int	ID

int	N
	Principal number. More...

int	Power
	N-l-1. More...

real_type	Z

real_type	Norm

real_type	Y

real_type	dY

real_type	d2Y

real_type	d3Y

Detailed Description

template<class T>
struct GenericSTO< T >

Generic Slater-Type Orbital.

This class evalaute $\frac{\chi_{n,\xi}(r)}{r^l}$ where a normalized STO is defined as $\chi_{n,\xi}(r) = C r^{n-1} \exp{-\xi r}$ C is a contraction factor. The physical principal quantum number n has to be a positive integer, where n-1 is the number of nodes.

Definition at line 57 of file SlaterTypeOrbital.h.

Member Typedef Documentation

◆ real_type

using real_type = T

Definition at line 60 of file SlaterTypeOrbital.h.

Constructor & Destructor Documentation

◆ GenericSTO() [1/3]

GenericSTO ( )

inline

Definition at line 71 of file SlaterTypeOrbital.h.

71 : N(-1), Power(0), Z(1.0), Norm(1.0) {}

GenericSTO::Power

int Power

N-l-1.

Definition: SlaterTypeOrbital.h:66

GenericSTO::Norm

real_type Norm

Definition: SlaterTypeOrbital.h:68

GenericSTO::N

int N

Principal number.

Definition: SlaterTypeOrbital.h:64

GenericSTO::Z

real_type Z

Definition: SlaterTypeOrbital.h:67

◆ GenericSTO() [2/3]

GenericSTO	(	int	power,
		real_type	z,
		real_type	norm
	)

inlineexplicit

constructor with a known contraction factor

Definition at line 75 of file SlaterTypeOrbital.h.

75 : N(-1), Power(power), Z(z), Norm(norm) {}

GenericSTO::Power

int Power

N-l-1.

Definition: SlaterTypeOrbital.h:66

norm

double norm(const zVec &c)

Definition: VectorOps.h:118

GenericSTO::Norm

real_type Norm

Definition: SlaterTypeOrbital.h:68

GenericSTO::N

int N

Principal number.

Definition: SlaterTypeOrbital.h:64

GenericSTO::Z

real_type Z

Definition: SlaterTypeOrbital.h:67

◆ GenericSTO() [3/3]

GenericSTO	(	int	n,
		int	l,
		real_type	z
	)

inlineexplicit

constructor with a set of quantum numbers

Parameters

n	principal quantum number
l	angular quantum number
z	exponent

Power = n-l-1 Contraction factor is the normalization factor evaluated based on N and Z.

Definition at line 85 of file SlaterTypeOrbital.h.

References GenericSTO< T >::reset().

85 : N(n), Power(n - l - 1), Z(z) { reset(); }

GenericSTO::Power

int Power

N-l-1.

Definition: SlaterTypeOrbital.h:66

qmcplusplus::n

int n

Definition: test_cuBLAS_LU.cpp:216

GenericSTO::N

int N

Principal number.

Definition: SlaterTypeOrbital.h:64

GenericSTO::reset

void reset()

Definition: SlaterTypeOrbital.h:87

GenericSTO::Z

real_type Z

Definition: SlaterTypeOrbital.h:67

Member Function Documentation

◆ df()

real_type df ( real_type r )

inline

Definition at line 100 of file SlaterTypeOrbital.h.

References qmcplusplus::exp(), GenericSTO< T >::Norm, qmcplusplus::pow(), GenericSTO< T >::Power, and GenericSTO< T >::Z.

   {
     real_type rnl = exp(-Z * r) * Norm;
     if (Power == 0)
     {
       return -Z * rnl;
     }
     else
     {
       return rnl * pow(r, Power) * (Power / r - Z);
     }
   }

◆ evaluate() [1/3]

real_type evaluate	(	real_type	r,
		real_type	rinv
	)

inline

return the value only

Parameters

r	distance
rinv	inverse of r

Definition at line 117 of file SlaterTypeOrbital.h.

References qmcplusplus::exp(), GenericSTO< T >::Norm, qmcplusplus::pow(), GenericSTO< T >::Power, GenericSTO< T >::Y, and GenericSTO< T >::Z.

Referenced by GenericSTO< T >::evaluateAll().

117 { return Y = Norm * pow(r, Power) * exp(-Z * r); }

GenericSTO::Power

int Power

N-l-1.

Definition: SlaterTypeOrbital.h:66

qmcplusplus::pow

MakeReturn< BinaryNode< FnPow, typename CreateLeaf< Vector< T1, C1 > >::Leaf_t, typename CreateLeaf< Vector< T2, C2 > >::Leaf_t > >::Expression_t pow(const Vector< T1, C1 > &l, const Vector< T2, C2 > &r)

Definition: OhmmsVectorOperators.h:316

qmcplusplus::exp

MakeReturn< UnaryNode< FnExp, typename CreateLeaf< Vector< T1, C1 > >::Leaf_t > >::Expression_t exp(const Vector< T1, C1 > &l)

Definition: OhmmsVectorOperators.h:80

GenericSTO::Y

real_type Y

Definition: SlaterTypeOrbital.h:69

GenericSTO::Norm

real_type Norm

Definition: SlaterTypeOrbital.h:68

GenericSTO::Z

real_type Z

Definition: SlaterTypeOrbital.h:67

◆ evaluate() [2/3]

real_type evaluate	(	real_type	r,
		real_type	rinv,
		real_type &	drnl,
		real_type &	d2rnl
	)

inline

Definition at line 121 of file SlaterTypeOrbital.h.

References qmcplusplus::exp(), GenericSTO< T >::Norm, qmcplusplus::pow(), GenericSTO< T >::Power, and GenericSTO< T >::Z.

   {
     real_type rnl = Norm * exp(-Z * r);
     if (Power == 0)
     {
       drnl  = -Z * rnl;
       d2rnl = rnl * Z * Z;
     }
     else
     {
       rnl *= pow(r, Power);
       real_type x = Power * rinv - Z;
       drnl        = rnl * x;
       d2rnl       = rnl * (x * x - Power * rinv * rinv);
     }
     return rnl;
   }

◆ evaluate() [3/3]

real_type evaluate	(	real_type	r,
		real_type	rinv,
		real_type &	drnl,
		real_type &	d2rnl,
		real_type &	d3rnl
	)

inline

Definition at line 139 of file SlaterTypeOrbital.h.

References qmcplusplus::exp(), GenericSTO< T >::Norm, qmcplusplus::pow(), GenericSTO< T >::Power, and GenericSTO< T >::Z.

   {
     real_type rnl = Norm * exp(-Z * r);
     if (Power == 0)
     {
       drnl  = -Z * rnl;
       d2rnl = rnl * Z * Z;
       d3rnl = -d2rnl * Z;
     }
     else
     {
       rnl *= pow(r, Power);
       real_type x = Power * rinv - Z;
       drnl        = rnl * x;
       d2rnl       = rnl * (x * x - Power * rinv * rinv);
       d3rnl       = rnl * (x * x * x + (2.0 * rinv - 3.0 * x) * Power * rinv * rinv);
     }
     return rnl;
   }

◆ evaluateAll()

void evaluateAll	(	real_type	r,
		real_type	rinv
	)

inline

Definition at line 119 of file SlaterTypeOrbital.h.

References GenericSTO< T >::d2Y, GenericSTO< T >::dY, GenericSTO< T >::evaluate(), and GenericSTO< T >::Y.

119 { Y = evaluate(r, rinv, dY, d2Y); }

GenericSTO::evaluate

real_type evaluate(real_type r, real_type rinv)

return the value only

Definition: SlaterTypeOrbital.h:117

GenericSTO::dY

real_type dY

Definition: SlaterTypeOrbital.h:69

GenericSTO::Y

real_type Y

Definition: SlaterTypeOrbital.h:69

GenericSTO::d2Y

real_type d2Y

Definition: SlaterTypeOrbital.h:69

◆ f()

real_type f ( real_type r )

inline

Definition at line 98 of file SlaterTypeOrbital.h.

References qmcplusplus::exp(), GenericSTO< T >::Norm, qmcplusplus::pow(), GenericSTO< T >::Power, and GenericSTO< T >::Z.

98 { return exp(-Z * r) * Norm * pow(r, Power); }

GenericSTO::Power

int Power

N-l-1.

Definition: SlaterTypeOrbital.h:66

qmcplusplus::pow

MakeReturn< BinaryNode< FnPow, typename CreateLeaf< Vector< T1, C1 > >::Leaf_t, typename CreateLeaf< Vector< T2, C2 > >::Leaf_t > >::Expression_t pow(const Vector< T1, C1 > &l, const Vector< T2, C2 > &r)

Definition: OhmmsVectorOperators.h:316

qmcplusplus::exp

MakeReturn< UnaryNode< FnExp, typename CreateLeaf< Vector< T1, C1 > >::Leaf_t > >::Expression_t exp(const Vector< T1, C1 > &l)

Definition: OhmmsVectorOperators.h:80

GenericSTO::Norm

real_type Norm

Definition: SlaterTypeOrbital.h:68

GenericSTO::Z

real_type Z

Definition: SlaterTypeOrbital.h:67

◆ reset()

void reset ( )

inline

Definition at line 87 of file SlaterTypeOrbital.h.

References GenericSTO< T >::N, GenericSTO< T >::Norm, and GenericSTO< T >::Z.

Referenced by GenericSTO< T >::GenericSTO().

   {
     if (N > 0)
     {
       STONorm<T> anorm(N);
       Norm = anorm(N - 1, Z);
     }
   }

◆ setgrid()

void setgrid ( real_type r )

inline

Definition at line 96 of file SlaterTypeOrbital.h.

96 {}

Member Data Documentation

◆ d2Y

real_type d2Y

Definition at line 69 of file SlaterTypeOrbital.h.

Referenced by GenericSTO< T >::evaluateAll().

◆ d3Y

real_type d3Y

Definition at line 69 of file SlaterTypeOrbital.h.

◆ dY

real_type dY

Definition at line 69 of file SlaterTypeOrbital.h.

Referenced by GenericSTO< T >::evaluateAll().

◆ ID

int ID

Definition at line 62 of file SlaterTypeOrbital.h.

◆ N

int N

Principal number.

Definition at line 64 of file SlaterTypeOrbital.h.

Referenced by GenericSTO< T >::reset().

◆ Norm

real_type Norm

Definition at line 68 of file SlaterTypeOrbital.h.

Referenced by GenericSTO< T >::df(), GenericSTO< T >::evaluate(), GenericSTO< T >::f(), and GenericSTO< T >::reset().

◆ Power

int Power

N-l-1.

Definition at line 66 of file SlaterTypeOrbital.h.

Referenced by GenericSTO< T >::df(), GenericSTO< T >::evaluate(), and GenericSTO< T >::f().

◆ Y

real_type Y

Definition at line 69 of file SlaterTypeOrbital.h.

Referenced by GenericSTO< T >::evaluate(), and GenericSTO< T >::evaluateAll().

◆ Z

real_type Z

Definition at line 67 of file SlaterTypeOrbital.h.

Referenced by GenericSTO< T >::df(), GenericSTO< T >::evaluate(), GenericSTO< T >::f(), and GenericSTO< T >::reset().

The documentation for this struct was generated from the following file:

/home/pk7/projects/qmc/for_cron_doxygen/qmcpack/src/Numerics/SlaterTypeOrbital.h

Public Types

Public Member Functions

Public Attributes

Detailed Description

template<class T> struct GenericSTO< T >

Member Typedef Documentation

◆ real_type

Constructor & Destructor Documentation

◆ GenericSTO() [1/3]

◆ GenericSTO() [2/3]

◆ GenericSTO() [3/3]

Member Function Documentation

◆ df()

◆ evaluate() [1/3]

◆ evaluate() [2/3]

◆ evaluate() [3/3]

◆ evaluateAll()

◆ f()

◆ reset()

◆ setgrid()

Member Data Documentation

◆ d2Y

◆ d3Y

◆ dY

◆ ID

◆ N

◆ Norm

◆ Power

◆ Y

◆ Z

template<class T>
struct GenericSTO< T >