SingleReference_R12Intermediates computes R12/F12 intermediates using MPQC3 runtime. More...

#include <chemistry/qc/mbptr12/sr_r12intermediates.h>

Public Types
typedef TA::Array< T, 4 >	TArray4
	standard 4-index tensor

typedef TA::Array< T, 4, DA4_Tile< T > >	TArray4d
	4-index tensor with lazy tiles

typedef TA::Array< T, 2 >	TArray2
	standard 2-index tensor

typedef TA::Array< T, 2, DA4_Tile< T > >	TArray2d
	2-index tensor with lazy tiles

typedef TA::Array< TA::Tensor< T >, 2 >	TArray22
	2-index tensor with lazy tiles More...

typedef TA::Array< TA::Tensor< T >, 2, DA4_Tile34< T > >	TArray22d
	2-index tensor of lazy 2-index tensors

typedef TA::Array< T, 4, LazyTensor< T, 4, expressions::TGeminalGenerator< T > > >	TArray4Tg
	geminal T tensor

Public Member Functions
	SingleReference_R12Intermediates (madness::World &world, const Ref< R12WavefunctionWorld > &r12world)
	Constructs an SingleReference_R12Intermediates object. More...

const Ref< R12WavefunctionWorld > &	r12world () const

std::pair< TArray2, TArray2 >	V_diag ()
	computes diagonal (spin-restricted, for now) V intermediate More...

std::pair< TArray2, TArray2 >	X_diag ()
	computes diagonal (spin-restricted, for now) X intermediate More...

std::pair< TArray2, TArray2 >	B_diag ()
	computes diagonal (spin-restricted, for now) B intermediate More...

void	gf2_r12 (int orbital)
	Computes second-order Green's function IPs and EAs \parame orbital the index of the orbital, -1 = HOMO, +1 = LUMO.

TArray2	rdm1 ()
	returns the 1-particle reduced density matrix More...

void	compute_multipole ()

TArray2	XaiAddToXam (const TA::Array< double, 2 > &Xam, const TA::Array< double, 2 > &Xai)

TArray2	BPk_Qk (const char p, const char q, const double C_0, const double C_1)

TArray4	Bpr_qs (const char p, const char q)

TArray4	VPq_Rs (const char p, const char q, const char r, const char s, const double C_0, const double C_1)

TArray2	VRk_Sk (const char r, const char s, const double C_0, const double C_1)

TArray2	Xam_CabsSingles (const TArray2 &TmA, const TArray2 &Tma)

TArray2	Xam_mp2 (const TArray4 &T2_ijab, const TArray2 &Dij, const TArray2 &Dab)

TArray2	Xam_Cmp2f12 (const double C_0, const double C_1, const TArray4 &T2_ijab, const TArray4 &A_ijab, const TArray2 &Dij, const TArray2 &Dab, const TArray2 &RT_apb)

void	compute_Df12_XB (const double C_0, const double C_1, TArray2 &D_f12_ij, TArray2 &D_f12_ab, TArray2 &D_f12_apbp, TArray2 &D_f12_apb)

TArray2	Xam_Df12_XB (const double C_0, const double C_1, const TArray2 &Df12_ij, const TArray2 &Df12_ab, const TArray2 &Df12_apbp, const TArray2 &Df12_apb)

TArray2	Xam_V (const double C_0, const double C_1)

TArray2	Xam_X (const double C_0, const double C_1)

TArray2	Xam_B (const double C_0, const double C_1)

TArray2	Xiip_VBX (const double C_0, const double C_1)

TArray2	Xiip_CVT (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &T2)

TArray2	Xam_CT2_ccsd (const double C_0, const double C_1, const TArray4 &T2, const TArray2 &RT2_aPb)

TArray2	Xam_VT_ccsd (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &T2)

void	compute_T_cc2 (TArray2 &T1, TArray4 &T2)

void	compute_lambda_cc2 (const TArray2 &t1, const TArray4 &t2, TArray2 &L1, TArray4 &L2)

void	compute_lambda_cc2_2 (const TArray2 &t1, const TArray4 &t2, TArray2 &L1, TArray4 &L2)

void	compute_Delta_cc (const TA::TiledRange &TR_ai, const TA::TiledRange &TR_abij, TArray2 &D_ai, TArray4 &D_abij)

void	compute_intermediates_TFW_ccsd (const TArray2 &t1, const TArray4 &t2, const TArray4d &g_abij, const TArray4d &g_aikl, const TArray4d &g_aibj, const TArray4d &g_aijb, const TArray4d &g_abci, const TArray4d &g_ijkl, const TArray4d &g_abcd, TArray2 &TFkc, TArray2 &TFac, TArray2 &TFki, TArray4 &TW_KbCj_ab, TArray4 &TW_KbcJ_ba, TArray4 &TW_AbCd_ab, TArray4 &TW_KlIj_ab)

void	compute_intermediates_CW_ccsd (const TArray2 &t1, const TArray4 &t2, TArray2 &CFkc, TArray2 &CFac, TArray2 &CFki, TArray4 &CW_KbEj_ab, TArray4 &CW_KbeJ_ba, TArray4 &CW_AbCd_ab, TArray4 &CW_AbCi_ab, TArray4 &CW_KlIj_ab, TArray4 &CW_KbIj_ab, TArray4 &CW_KlIc_ab, TArray4 &CW_KliC_ab, TArray4 &CW_AkCd_ab)

void	compute_T_ccsd (TArray2 &t1, TArray4 &t2, const std::string method)

void	compute_lambda_ccsd (const TArray2 &t1, const TArray4 &t2, TArray2 &L1, TArray4 &L2, const std::string method)

void	compute_cc2_1rdm_amp (const TArray2 &T1_cc2, const TArray4 &T2_cc2, const TArray2 &L1_cc2, const TArray4 &L2_cc2, TArray2 &Dij_cc2, TArray2 &Dab_cc2, TArray2 &Dia_cc2, TArray2 &Dai_cc2)

void	compute_Gamma_ijab_ccsd (const TArray2 &T1, const TArray4 &T2, const TArray4 &tau_ab, const TArray2 &L1, const TArray4 &L2, TArray4 &Gamma_IjAb_ab)

void	compute_ccsd_1rdm_amp (const TArray2 &T1, const TArray4 &T2, const TArray2 &L1, const TArray4 &L2, TArray2 &Dij, TArray2 &Dab, TArray2 &Dia, TArray2 &Dai)

void	compute_Gamma2_ccsd (const TArray2 &T1, const TArray4 &T2, const TArray2 &L1, const TArray4 &L2, const TArray4 &tau_aa, const TArray4 &tau_ab, TArray4 &Gamma_IjKa_ab, TArray4 &Gamma_AbCi_ab, TArray4 &Gamma_iBjA_ab, TArray4 &Gamma_iBJa_ba, TArray4 &Gamma_AbCd_ab, TArray4 &Gamma_IjKl_ab, TArray4 &Gamma_IjAb_ab)

void	compute_Xam_ccsd (const TArray2 &T1, const TArray4 &T2, const TArray2 &L1, const TArray4 &L2, TArray2 &Xam_tot, TArray2 &Xiip)

void	compute_multipole_F12b_coupling ()

TArray4	VPQ_RS (const char p, const char q, const char r, const char s)

TArray2	Xam_CT2L2_f12b (const double C_0, const double C_1, const TArray4 &T2, const TArray2 &RT2_aPb, const TArray4 &L2, const TArray2 &RL2_aPb)

TArray2	Xam_VTL_f12b (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &T2, const TArray2 &L1, const TArray4 &L2)

TArray2	Xam_VT1T1_f12b (const double C_0, const double C_1, const TArray2 &T1)

TArray2	Xam_VT1T1_f12b_test (const double C_0, const double C_1, const TArray4 &tauT1_ab)

TArray2	Xam_VL2T1_f12b (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &L2)

TArray2	Xam_VL2T1_f12b_test (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &L2)

TArray2	Xam_VL2T1T1_f12b (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &L2)

TArray2	Xam_VL2T1T1_f12b_test (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &L2)

TArray2	Xiip_CVT_f12b (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &T2, const TArray2 &L1, const TArray4 &L2)

TArray2	Xiip_VT1T1_f12b (const double C_0, const double C_1, const TArray2 &T1, const TArray4 &T2, const TArray4 &L2)

TArray4	rdm2 ()
	returns the 2-particle density matrix More...

TArray4	V_spinfree (bool symmetrize_p1_p2=false)
	computes spin-free V intermediate More...

TArray4	X_spinfree (bool symmetrize_p1_p2=false)
	computes spin-free X intermediate More...

TArray4	B_spinfree (bool symmetrize_p1_p2=false)
	computes spin-free B intermediate More...

void	set_T1 (const RefSCMatrix &t1)
	provides T1 amplitude tensor More...

void	set_T1_cabs (const RefSCMatrix &t1_cabs)
	provides T1 CABS amplitude tensor More...

void	set_L1 (const RefSCMatrix &l1)
	provides Lambda1 amplitude tensor More...

void	set_T2 (const Ref< DistArray4 >(&t2)[NSpinCases2])
	provides T2 amplitudes More...

void	set_L2 (const Ref< DistArray4 >(&l2)[NSpinCases2])
	provides Lambda2 amplitudes More...

void	set_rdm2 (const Ref< SpinFreeRDM< Two > > &rdm2)
	provides (spin-free) RDM2 More...

TArray4d &	ijxy (const std::string &key)

TArray22d &	ij_xy (const std::string &key)

TArray2 &	xy (const std::string &key)

TArray2 &	sieve (const TArray2 &input, const std::string &output_annotation)
	sieves x\|o1\|y -> x'\|o1\|y' does not throw only if each tile of the result depends only on 1 tile of the input

TA::expressions::TsrExpr< const TArray4d, true >	_4 (const std::string &key)
	Given a descriptive `key`, creates a rank-4 Array of integrals, or other related quantities The syntax of `key` is similar to that used by ParsedTwoBodyInt and TwoBodyMOIntsRuntime, but with te_type embedded into key. More...

TA::expressions::TsrExpr< const TArray2, true >	_2 (const std::string &key)
	Given a descriptive `key`, creates a rank-2 Array of integrals, or other related quantities The syntax of `key` is similar to that used by ParsedOneBodyInt, but with oe_type embedded into key. More...

TA::expressions::TsrExpr< const TArray4Tg, true >	_Tg (const std::string &key)
	like _4, produces geminal T tensor

Detailed Description

template<typename T>
class sc::SingleReference_R12Intermediates< T >

SingleReference_R12Intermediates computes R12/F12 intermediates using MPQC3 runtime.

Template Parameters

T	the numeric type supporting all tensors

Member Typedef Documentation

◆ TArray22

template<typename T>

typedef TA::Array<TA::Tensor<T>, 2> sc::SingleReference_R12Intermediates< T >::TArray22

2-index tensor with lazy tiles

2-index tensor of 2-index tensors

Constructor & Destructor Documentation

◆ SingleReference_R12Intermediates()

template<typename T>

sc::SingleReference_R12Intermediates< T >::SingleReference_R12Intermediates	(	madness::World &	world,
		const Ref< R12WavefunctionWorld > &	r12world
	)

inline

Constructs an SingleReference_R12Intermediates object.

There can be many.

Parameters

world	MADNESS world in which the computed Arrays will live
r12world	R12WavefunctionWorld that provides computation of integrals and OrbitalSpace objects

Member Function Documentation

◆ _2()

template<typename T >

TA::expressions::TsrExpr< const typename SingleReference_R12Intermediates< T >::TArray2, true > sc::SingleReference_R12Intermediates< T >::_2 ( const std::string & key )

Given a descriptive key, creates a rank-2 Array of integrals, or other related quantities The syntax of key is similar to that used by ParsedOneBodyInt, but with oe_type embedded into key.

The following oe_types are understood:

mu_i : electric dipole integral $- \bf{r}_i$ (i = x,y,z)
q_ij : electric quadrupole integral $- \bf{r}_i \bf{r}_j$ (ij = xx, xy, xz, yy, yz, zz)
gamma : $\Gamma$ , 1-RDM of the reference wave function
T1 : 1-body excitation amplitudes, e.g. of the coupled-cluster method, provided by set_T1() and/or set_T1_cabs()
L1 : 1-body de-excitation amplitudes, e.g. of the coupled-cluster method, provided by set_L1()
I : identity matrix

Indices are interpreted using to_space().

Example1: <i|mu_x|p> will create an array of <act_occ| -x |obs> integrals Example2: <j_F(p')|q_xy|a'> will create an array of <cbs| -xy |cabs> integrals with the second index transformed using Fock matrix between act_occ and cbs spaces.

Note that the indices are used to create the resulting tensor expression, hence these keys can be used in composing expressions.

See also: _4(); xy()

◆ _4()

template<typename T >

TA::expressions::TsrExpr< const typename SingleReference_R12Intermediates< T >::TArray4d, true > sc::SingleReference_R12Intermediates< T >::_4 ( const std::string & key )

Given a descriptive key, creates a rank-4 Array of integrals, or other related quantities The syntax of key is similar to that used by ParsedTwoBodyInt and TwoBodyMOIntsRuntime, but with te_type embedded into key.

The following te_types are understood:

g : $r_{12}^{-1}$
r : $f(r_{12})$
gr : $r_{12}^{-1} f(r_{12})$
rTr : $[f(r_{12}), [ \hat{T}_1 , f(r_{12})]]$
gamma : $\Gamma$ , 2-RDM, provided by set_rdm2()
T2 : 2-body excitation amplitudes, e.g. of the coupled-cluster method, provided by set_T2()
L2 : 2-body de-excitation amplitudes, e.g. of the coupled-cluster method, provided by set_L2()

Indices are interpreted using to_space().

Example1: <i j|g|p a'> will create an array of <act_occ act_occ| r_{12}^{-1} |obs cabs> integrals Example2: <i j_F(p')|g|p a'> will create an array of <act_occ cbs| r_{12}^{-1} |obs cabs> integrals with the second index transformed using Fock matrix between act_occ and cbs spaces.

Note that the indices are used to create the resulting tensor expression, hence these keys can be used in composing expressions. For example, the full (non-diagonal) V intermediate of the R12 method without the CABS terms can be computed as follows: TArray4d V_ij_kl = _4("<i j|gr|k l>") - _4("<i j|g|p q>") * _4("<k l|r|p q>");

See also: ijxy()

◆ B_diag()

template<typename T >

std::pair< typename SingleReference_R12Intermediates< T >::TArray2, typename SingleReference_R12Intermediates< T >::TArray2 > sc::SingleReference_R12Intermediates< T >::B_diag ( )

computes diagonal (spin-restricted, for now) B intermediate

Returns: $B^{ij}_{ij}$ and $B^{ij}_{ji}$ , respectively

this is incomplete at the moment

◆ B_spinfree()

template<typename T >

SingleReference_R12Intermediates< T >::TArray4 sc::SingleReference_R12Intermediates< T >::B_spinfree ( bool symmetrize_p1_p2 = false )

computes spin-free B intermediate

Parameters

symmetrize_p1_p2 if yes, make sure this holds for the result: B^{ij}_{kl} = B^{ji}_{kl}

Returns: $B^{ij}_{kl}$

◆ compute_multipole()

template<typename T >

void sc::SingleReference_R12Intermediates< T >::compute_multipole ( )

< evaluator of preconditioner

References sc::Molecule::natom(), and sc::ExEnv::out0().

◆ compute_multipole_F12b_coupling()

template<typename T >

void sc::SingleReference_R12Intermediates< T >::compute_multipole_F12b_coupling ( )

< evaluator of preconditioner

References sc::ExEnv::out0().

◆ ij_xy()

template<typename T >

SingleReference_R12Intermediates< T >::TArray22d & sc::SingleReference_R12Intermediates< T >::ij_xy ( const std::string & key )

map operator to the index within the operator set

References sc::DistArray4::activate(), sc::TwoBodyMOIntsTransform::compute(), sc::TwoBodyMOIntsTransform::ints_distarray4(), sc::DistArray4::ni(), sc::DistArray4::nj(), sc::DistArray4::nx(), sc::DistArray4::ny(), and sc::DistArray4::tasks_with_access().

◆ ijxy()

template<typename T >

SingleReference_R12Intermediates< T >::TArray4d & sc::SingleReference_R12Intermediates< T >::ijxy ( const std::string & key )

See also: _4()

map operator to the index within the operator set

References sc::DistArray4::activate(), sc::DistArray4::clone(), sc::TwoBodyMOIntsTransform::compute(), sc::DistArray4::data_persistent(), sc::DistArray4::deactivate(), sc::TwoBodyMOIntsTransform::ints_distarray4(), sc::map(), sc::DistArray4::ni(), sc::DistArray4::nj(), sc::DistArray4::nx(), sc::DistArray4::ny(), sc::DistArray4::release_pair_block(), sc::DistArray4::retrieve_pair_block(), and sc::DistArray4::tasks_with_access().

◆ rdm1()

template<typename T >

SingleReference_R12Intermediates< T >::TArray2 sc::SingleReference_R12Intermediates< T >::rdm1 ( )

returns the 1-particle reduced density matrix

Returns: $\gamma^{p}_{q}$ , respectively

this is just an example of how to compute the density

◆ rdm2()

template<typename T>

TArray4 sc::SingleReference_R12Intermediates< T >::rdm2 ( )

returns the 2-particle density matrix

Returns: $\gamma^{pq}_{rs}$ , respectively

Referenced by sc::SingleReference_R12Intermediates< T >::set_rdm2().

◆ set_L1()

template<typename T>

void sc::SingleReference_R12Intermediates< T >::set_L1 ( const RefSCMatrix & l1 )

inline

provides Lambda1 amplitude tensor

Parameters

l1	act_occ by act_vir matrix

◆ set_L2()

template<typename T>

void sc::SingleReference_R12Intermediates< T >::set_L2 ( const Ref< DistArray4 >(&) l2[NSpinCases2] )

inline

provides Lambda2 amplitudes

Parameters

l2	array of Lambda2 amplitudes, for AlphaBeta, AlphaAlpha, and (optionally) BetaBeta

◆ set_rdm2()

template<typename T>

void sc::SingleReference_R12Intermediates< T >::set_rdm2 ( const Ref< SpinFreeRDM< Two > > & rdm2 )

inline

provides (spin-free) RDM2

Parameters

rdm2	a SpinFreeRDM<Two> object

References sc::SingleReference_R12Intermediates< T >::rdm2().

◆ set_T1()

template<typename T>

void sc::SingleReference_R12Intermediates< T >::set_T1 ( const RefSCMatrix & t1 )

inline

provides T1 amplitude tensor

Parameters

t1	act_occ by act_vir matrix

◆ set_T1_cabs()

template<typename T>

void sc::SingleReference_R12Intermediates< T >::set_T1_cabs ( const RefSCMatrix & t1_cabs )

inline

provides T1 CABS amplitude tensor

Parameters

t1	act_occ by allvir (or CABS) matrix

◆ set_T2()

template<typename T>

void sc::SingleReference_R12Intermediates< T >::set_T2 ( const Ref< DistArray4 >(&) t2[NSpinCases2] )

inline

provides T2 amplitudes

Parameters

t2	array of T2 amplitudes, for AlphaBeta, AlphaAlpha, and (optionally) BetaBeta

◆ V_diag()

template<typename T >

std::pair< typename SingleReference_R12Intermediates< T >::TArray2, typename SingleReference_R12Intermediates< T >::TArray2 > sc::SingleReference_R12Intermediates< T >::V_diag ( )

computes diagonal (spin-restricted, for now) V intermediate

Returns: $V^{ij}_{ij}$ and $V^{ij}_{ji}$ , respectively

◆ V_spinfree()

template<typename T >

SingleReference_R12Intermediates< T >::TArray4 sc::SingleReference_R12Intermediates< T >::V_spinfree ( bool symmetrize_p1_p2 = false )

computes spin-free V intermediate

Parameters

symmetrize_p1_p2 if yes, make sure this holds for the result: V^{ij}_{mn} = V^{ji}_{nm}

Returns: $V^{ij}_{mn}$ , where ij refer to the geminal indices

◆ X_diag()

template<typename T >

std::pair< typename SingleReference_R12Intermediates< T >::TArray2, typename SingleReference_R12Intermediates< T >::TArray2 > sc::SingleReference_R12Intermediates< T >::X_diag ( )

computes diagonal (spin-restricted, for now) X intermediate

Returns: $X^{ij}_{ij}$ and $X^{ij}_{ji}$ , respectively

◆ X_spinfree()

template<typename T >

SingleReference_R12Intermediates< T >::TArray4 sc::SingleReference_R12Intermediates< T >::X_spinfree ( bool symmetrize_p1_p2 = false )

computes spin-free X intermediate

Parameters

symmetrize_p1_p2 if yes, make sure this holds for the result: X^{ij}_{kl} = X^{ji}_{kl}

Returns: $X^{ij}_{kl}$

◆ xy()

template<typename T >

SingleReference_R12Intermediates< T >::TArray2 & sc::SingleReference_R12Intermediates< T >::xy ( const std::string & key )

See also: _2()

References sc::OrbitalSpace::coefs(), sc::map(), sc::overlap(), and sc::OrbitalSpace::rank().

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

src/lib/chemistry/qc/mbptr12/sr_r12intermediates.h
src/lib/chemistry/qc/mbptr12/sr_r12intermediates_util.h
src/lib/chemistry/qc/mbptr12/sr_r12intermediates_VXB_diag.h

Public Types

Public Member Functions

Detailed Description

template<typename T> class sc::SingleReference_R12Intermediates< T >

Member Typedef Documentation

◆ TArray22

Constructor & Destructor Documentation

◆ SingleReference_R12Intermediates()

Member Function Documentation

◆ _2()

◆ _4()

◆ B_diag()

◆ B_spinfree()

◆ compute_multipole()

◆ compute_multipole_F12b_coupling()

◆ ij_xy()

◆ ijxy()

◆ rdm1()

◆ rdm2()

◆ set_L1()

◆ set_L2()

◆ set_rdm2()

◆ set_T1()

◆ set_T1_cabs()

◆ set_T2()

◆ V_diag()

◆ V_spinfree()

◆ X_diag()

◆ X_spinfree()

◆ xy()

template<typename T>
class sc::SingleReference_R12Intermediates< T >