curvature.h File Reference

The C interface for LOSC curvature matrix. More...

#include <c_losc/matrix.h>
#include <stddef.h>

Go to the source code of this file.

Classes
struct	LoscCurvatureBase
	The C interface for LOSC curvature base class. More...
struct	LoscCurvatureV1
	The C interface for LOSC curvature class of version 1. More...
struct	LoscCurvatureV2
	The C interface for LOSC curvature class of version 2. More...

Macros
#define	losc_dfa_info_free(ptr)   _losc_DFAInfo_free(&(ptr))
	Free a LoscDFAInfo struct. More...
#define	losc_curvature_v1_free(ptr)   _losc_curvature_v1_free(&(ptr))
	Free a struct LoscCurvatureV1. More...
#define	losc_curvature_v2_free(ptr)   _losc_curvature_v2_free(&(ptr))
	Free a struct LoscCurvatureV2. More...

Typedefs
typedef struct LoscDFAInfo	LoscDFAInfo
	The DFA information. More...
typedef struct LoscCurvatureBase	LoscCurvatureBase
	The C interface for LOSC curvature base class. More...
typedef struct LoscCurvatureV1	LoscCurvatureV1
	The C interface for LOSC curvature class of version 1. More...
typedef struct LoscCurvatureV2	LoscCurvatureV2
	The C interface for LOSC curvature class of version 2. More...

Functions
LoscDFAInfo *	losc_dfa_info_create (double gga_x, double hf_x, const char *name)
	Create a struct LoscDFAInfo. More...
LoscCurvatureV1 *	losc_curvature_v1_create (const LoscDFAInfo *dfa, const losc_matrix *df_pii, const losc_matrix *df_Vpq_inv, const losc_matrix *grid_lo, const double *grid_weight)
	Create a struct LoscCurvatureV1. More...
LoscCurvatureV2 *	losc_curvature_v2_create (const LoscDFAInfo *dfa, const losc_matrix *df_pii, const losc_matrix *df_Vpq_inv, const losc_matrix *grid_lo, const double *grid_weight)
	Constructor of LoscCurvatureV2. More...

Detailed Description

The C interface for LOSC curvature matrix.

Macro Definition Documentation

#define losc_curvature_v1_free

(

ptr

)

_losc_curvature_v1_free(&(ptr))

Free a struct LoscCurvatureV1.

Parameters

[in,out]

ptr

a pointer with type LoscCurvatureV1 *. At exit, ptr is set to null.

#define losc_curvature_v2_free

(

ptr

)

_losc_curvature_v2_free(&(ptr))

Free a struct LoscCurvatureV2.

Parameters

[in,out]

ptr

a pointer with type LoscCurvatureV1 *. At exit, ptr is set to null.

#define losc_dfa_info_free

(

ptr

)

_losc_DFAInfo_free(&(ptr))

Free a LoscDFAInfo struct.

Parameters

[in,out]

ptr

a pointer with type LoscDFAInfo *. At exit, ptr is set to null.

Typedef Documentation

typedef struct LoscCurvatureBase LoscCurvatureBase

The C interface for LOSC curvature base class.

Note

This struct exports all the functions for LOSC curvature base class. This struct servers as helper class to avoid code duplication for the implementation of C interface. There is no need for C users to create a such struct in practice.

typedef struct LoscCurvatureV1 LoscCurvatureV1

The C interface for LOSC curvature class of version 1.

Curvature version 1 is defined as \( \kappa \) in Eq. 3 in the original LOSC paper (https://doi.org/10.1093/nsr/nwx11).

See also

losc_curvature_v1_create(): create a LosCurvatureV1 object.

losc_curvature_v1_free(): free a LosCurvatureV1 object.

typedef struct LoscCurvatureV2 LoscCurvatureV2

The C interface for LOSC curvature class of version 2.

The curvature matrix is defined as \(\tilde{\kappa}\) in Eq. 8 of the LOSC2 paper (J. Phys. Chem. Lett. 2020, 11, 4, 1528-1535).

See also

losc_curvature_v2_create(): create a LosCurvatureV2 object.

losc_curvature_v2_free(): free a LosCurvatureV2 object.

typedef struct LoscDFAInfo LoscDFAInfo

The DFA information.

Note

This is a incomplete declaration. You can not create a LoscDFAInfo variable by youself.

See also

losc_dfa_info_create(): create a LoscDFAInfo

losc_dfa_info_free(): free a LoscDFAInfo

Function Documentation

LoscCurvatureV1* losc_curvature_v1_create	(	const LoscDFAInfo *	dfa,
		const losc_matrix *	df_pii,
		const losc_matrix *	df_Vpq_inv,
		const losc_matrix *	grid_lo,
		const double *	grid_weight
	)

Create a struct LoscCurvatureV1.

Parameters

[in]	dfa	Type of DFA.
[in]	df_pii	Three-body integral \( \langle p |ii \rangle \) used in density fitting. Index p is for fitbasis and index i is for LOs. The dimension of df_pii is [nfitbasis, nlo].
[in]	df_Vpq_inv	Inverse of \( \langle p | 1/\mathbf{r} | q \rangle \) matrix used in density fitting. Index p and q are for LOs. The dimension of df_Vpq_inv is [nfitbasis, nfitbasis].
[in]	grid_lo	LOs' value on grid points with dimension of [npts, nlo].
[in]	grid_weight	Coefficient vector for numerical integral on grid with size of npts.

Returns

Create a struct LoscCurvatureV1 and return the pointer.

Note

This function requires all the matrices are allocated in advance. This could be memory consuming. For example, the grid_lo matrix can be very large.

LoscCurvatureV2* losc_curvature_v2_create	(	const LoscDFAInfo *	dfa,
		const losc_matrix *	df_pii,
		const losc_matrix *	df_Vpq_inv,
		const losc_matrix *	grid_lo,
		const double *	grid_weight
	)

Constructor of LoscCurvatureV2.

Parameters

[in]	dfa	Type of DFA.
[in]	df_pii	Three-body integral \( \langle p |ii \rangle \) used in density fitting. Index p is for fitbasis and index i is for LOs. The dimension of df_pii is [nfitbasis, nlo].
[in]	df_Vpq_inv	Inverse of \( \langle p | 1/\mathbf{r} | q \rangle \) matrix used in density fitting. Index p and q are for LOs. The dimension of df_Vpq_inv is [nfitbasis, nfitbasis].
[in]	grid_lo	LOs' value on grid points with dimension of [npts, nlo].
[in]	grid_weight	Coefficient vector for numerical integral on grid with size of npts.

Returns

Create a struct LoscCurvatureV2 and return the pointer.

Note

This function requires all the matrices are allocated in advance. This could be memory consuming. For example, the grid_lo matrix can be very large.

LoscDFAInfo* losc_dfa_info_create	(	double	gga_x,
		double	hf_x,
		const char *	name
	)

Create a struct LoscDFAInfo.

Parameters

[in]	gga_x	The total weights of all GGA and LDA type exchanges.
[in]	hf_x	The total weights of HF exchanges.
[in]	name	The name of the DFA. Default to an empty string.

Example

Taking B3LYP functional as an example. The B3LYP functional is

\[ E^{\rm{B3LYP}}_{\rm{xc}} = E^{\rm{LDA}}_{\rm{x}} + a_0 (E^{\rm{HF}}_{\rm{x}} - E^{\rm{LDA}}_{\rm{x}}) + a_x (E^{\rm{GGA}}_{\rm{x}} - E^{\rm{LDA}}_{\rm{x}}) + E^{\rm{LDA}}_{\rm{c}} + a_c (E^{\rm{GGA}}_{\rm{c}} - E^{\rm{LDA}}_{\rm{c}}), \]

in which exchanges end with suffix _x and correlations end with suffix _c, \( a_0=0.20 \), \( a_x=0.72 \) and \( a_c=0.81 \). Only the exchanges are considered and the correlations are ignored. The GGA and LDA exchanges are viewed as the same type. Therefore, the total weights of GGA and LDA exchanges are \( 1 - a_0 + a_x \times (1 - 1) = 1 - a_0 = 0.80 \), and the total weights of HF exchanges is \( a_0 = 0.20 \). To construct a DFAInfo object for B3LYP functional, one should do the following

b3lyp = losc_dfa_info_create(0.80, 0.20, "B3LYP")