Classes
struct	CCIntegrals
	Restricted (closed-shell, spatial-MO) integral blocks in chemist notation (pq\|rs), plus a vvvv-ladder callable. More...

struct	CCSDOptions

struct	CCSDResult

struct	LaplaceGrid
	Least-squares "Laplace" quadrature for the inverse function on a range: 1/x ~= sum_k weights(k) * exp(-x * points(k)) for x in [xmin, xmax]. More...

struct	ThcFactors
	THC factors for the spatial MOs: (pq\|rs) ~ sum_PQ X(p,P) X(q,P) V(P,Q) X(r,Q) X(s,Q). More...

struct	ThcMP2Options

struct	ThcMP2Result

struct	ThcOptions

struct	UCCIntegrals
	Spin-blocked spatial MO integrals for spin-adapted unrestricted CCSD, in chemist notation, matching the PySCF UCCSD `_ChemistsERIs` block layout. More...

struct	UCCSDOptions

struct	UCCSDResult

struct	UThcFactors
	Cross-spin THC factors for unrestricted CCSD. More...

Enumerations
enum class	IsdfMethod { QR , Cholesky }
	Interpolation-point selection for ISDF. More...

enum class	ThcRegType { Eig , Tikhonov }
	Regularisation of the (ill-conditioned) LS-THC metric inverse. More...

enum class	ThcSelectBasis { AO , MO }
	Which functions' products the interpolation points must span. More...

Functions
CCSDResult	ccsd (const CCIntegrals &eris, const CCSDOptions &opts={})
	Restricted (closed-shell, spin-adapted) CCSD against a canonical reference.

double	ccsd_energy (const Eigen::Tensor< double, 2 > &t1, const Eigen::Tensor< double, 4 > &t2, const CCIntegrals &eris)
	CCSD correlation energy for given amplitudes (exposed for testing).

void	pgemm (Eigen::Ref< occ::Mat > C, Eigen::Ref< const occ::Mat > A, Eigen::Ref< const occ::Mat > B, bool accumulate=false, bool transA=false)
	C(m x n) = A(m x k) * B(k x n).

Eigen::Map< const occ::Mat >	mat_view (const Eigen::Tensor< double, 4 > &t, Eigen::Index r, Eigen::Index c)
	View a contiguous (column-major) 4-tensor's data as an (r x c) matrix.

template<int N>
void	ppermute (double out, const double A, const Eigen::array< Eigen::Index, N > &Adims, const Eigen::array< int, N > &perm)
	Parallel tensor permute (transpose): writes contiguous `out` = A.shuffle(perm) – out has dims Odim[k] = Adims[perm[k]] and out(j...) = A(source).

Eigen::Tensor< double, 4 >	pcon2 (const Eigen::Tensor< double, 4 > &A, int a0, int a1, const Eigen::Tensor< double, 4 > &B, int b0, int b1)
	Parallel two-index contraction of two 4-tensors – a drop-in, multithreaded replacement for `A.contract(B, {(a0,b0),(a1,b1)})`.

template<int RA, int RB, int NC>
Eigen::Tensor< double, RA+RB - 2 *NC >	pcon (const Eigen::Tensor< double, RA > &A, const Eigen::Tensor< double, RB > &B, const std::array< Eigen::IndexPair< int >, NC > &pairs)
	General N-index parallel tensor contraction – a drop-in, multithreaded replacement for `A.contract(B, pairs)` that routes through pgemm (BLAS), so it parallelises where Eigen's tensor contract() (serial gebp_kernel) does not.

int	num_frozen_core (const AOBasis &basis)
	Number of frozen-core spatial orbitals for `basis` (chemical core: 1s for Li-Ne, [Ne] for Na-Ar, [Ar] for Sc+), matching the standard CCSD(T) default.

CCIntegrals	exact_eris (const AOBasis &basis, const MolecularOrbitals &mo, int n_frozen=0, size_t memory_budget=(size_t(1)<< 30))
	Exact backend: all blocks (incl.

CCIntegrals	df_eris (const AOBasis &basis, const AOBasis &aux_basis, const MolecularOrbitals &mo, int n_frozen=0, size_t memory_budget=(size_t(1)<< 30))
	Density-fitted (RI) backend: every block from the metric-folded DF B-tensor; the ladder is contracted through B so (ac\|bd) is never formed.

CCIntegrals	thc_eris (const AOBasis &basis, const AOBasis &aux_basis, const MolecularOrbitals &mo, const ThcOptions &opts={}, int n_frozen=0, size_t memory_budget=(size_t(1)<< 30))
	THC backend: the <=2-virtual blocks come from DF (scalable); ovvv and the vvvv ladder are applied through the THC factors (X, V) – the ladder as three GEMMs, never forming vvvv.

LaplaceGrid	laplace_grid (double xmin, double xmax, int n)
	Build an n-point Laplace grid approximating 1/x over [xmin, xmax] (require 0 < xmin <= xmax).

double	laplace_max_rel_error (const LaplaceGrid &grid, double xmin, double xmax, int n_sample=64)
	Max relative error max_x \|1 - x * sum_k w_k e^{-x t_k}\| of `grid`, sampled on `n_sample` log-spaced x in [xmin, xmax] (testing / diagnostics).

ThcFactors	build_thc (const AOBasis &basis, const AOBasis &aux_basis, const MolecularOrbitals &mo, const ThcOptions &opts={})
	Build THC factors (X, V) for the spatial MOs of `mo`.

ThcFactors	build_thc_from_B (const AOBasis &basis, const MolecularOrbitals &mo, const ThcOptions &opts, const Mat &B)
	As build_thc, but using a precomputed metric-folded DF reference tensor `B` (nmo^2 x naux, row p*nmo+q).

UThcFactors	build_uthc (const AOBasis &basis, const Mat &Ca, const Mat &Cb, const Mat &Ba, const Mat &Bb, const ThcOptions &opts)

std::vector< int >	select_isdf_points (const Mat &coll, IsdfMethod method, int target, double tol)
	Indices of interpolation grid points spanning products of the columns of `coll` (npts x nfunc).

Mat	thc_select_collocation (const AOBasis &basis, const MolecularOrbitals &mo, const ThcOptions &opts)
	Point-selection half of build_thc: select ISDF interpolation points (AO- or MO-based per opts.select_basis, geometry-only) and return the MO collocation X (nmo x n_isdf) = MO value at each selected point.

Mat	fit_core (const Mat &X, const Mat &B, double reg, ThcRegType reg_type, double condition_out=nullptr, int n_kept_out=nullptr)
	Regularised least-squares THC core fit.

Mat	fit_core_ov (const Mat &Xo, const Mat &Xv, const Mat &B_ov, double reg, ThcRegType reg_type, double condition_out=nullptr, int n_kept_out=nullptr)
	LS-THC core fit restricted to the occupied-virtual block – the only integrals MP2 needs.

Eigen::Tensor< double, 4 >	reconstruct_eri (const Mat &X, const Mat &V)
	THC-reconstructed chemist integrals (pq\|rs) as a dense nmo^4 tensor (testing).

Eigen::Tensor< double, 4 >	mo_eri_general (const IntegralEngine &engine, const Mat &C_L, const Mat &C_q, const Mat &C_r, const Mat &C_s, size_t budget=(size_t(1)<< 28))
	Semidirect AO->MO transform (chemist (pq\|rs)) for arbitrary MO coefficient blocks.

double	reconstruction_error (const AOBasis &basis, const MolecularOrbitals &mo, const Mat &X, const Mat &V)
	Relative Frobenius error of the THC-reconstructed MO integrals vs exact.

ThcMP2Result	thc_mp2 (const AOBasis &basis, const AOBasis &aux_basis, const MolecularOrbitals &mo, const ThcMP2Options &opts={})
	LS-THC-MP2 correlation energy (restricted or unrestricted, dispatched on mo.kind).

double	ccsd_t (const Eigen::Tensor< double, 2 > &t1, const Eigen::Tensor< double, 4 > &t2, const CCIntegrals &eris)
	Restricted closed-shell perturbative triples (T) correction.

UCCSDResult	uccsd (const AOBasis &basis, const MolecularOrbitals &mo, const UCCSDOptions &opts={})
	Spin-adapted unrestricted CCSD(T) for a UHF (or RHF) reference.

UCCSDResult	uccsd (const AOBasis &basis, const AOBasis &aux_basis, const MolecularOrbitals &mo, const UCCSDOptions &opts={})
	df/thc backends need an auxiliary basis; "exact" is also accepted here.

UCCSDResult	uccsd_so (const AOBasis &basis, const MolecularOrbitals &mo, int n_frozen=0, bool with_triples=true, int max_cycle=100, double tol=1e-9)
	Spin-orbital CCSD(T) for an open- or closed-shell reference.

double	uccsd_t_via_so (const AOBasis &basis, const MolecularOrbitals &mo, int n_frozen, const Eigen::Tensor< double, 2 > &t1a, const Eigen::Tensor< double, 2 > &t1b, const Eigen::Tensor< double, 4 > &t2aa, const Eigen::Tensor< double, 4 > &t2ab, const Eigen::Tensor< double, 4 > &t2bb)
	Perturbative (T) correction for converged spin-adapted UCCSD amplitudes, evaluated through the validated spin-orbital triples kernel.

UCCIntegrals	u_exact_eris (const AOBasis &basis, const MolecularOrbitals &mo, int n_frozen=0, std::size_t memory_budget=(std::size_t(1)<< 30))
	Exact (full AO->MO) spin-blocked integrals.

UCCIntegrals	u_df_eris (const AOBasis &basis, const AOBasis &aux_basis, const MolecularOrbitals &mo, int n_frozen=0, std::size_t memory_budget=(std::size_t(1)<< 30))
	Density-fitted spin-blocked integrals.

UCCIntegrals	u_thc_eris (const AOBasis &basis, const AOBasis &aux_basis, const MolecularOrbitals &mo, const ThcOptions &opts={}, int n_frozen=0, std::size_t memory_budget=(std::size_t(1)<< 30))
	THC spin-blocked integrals: cheap blocks (<= 2 virtuals + ovvv) come from DF, and the three vvvv ladders use cross-spin THC factors (one ISDF point set, per-spin X and three cores Vaa/Vbb/Vab).

double	uccsd_t (const UCCIntegrals &e, const Eigen::Tensor< double, 2 > &t1a, const Eigen::Tensor< double, 2 > &t1b, const Eigen::Tensor< double, 4 > &t2aa, const Eigen::Tensor< double, 4 > &t2ab, const Eigen::Tensor< double, 4 > &t2bb)
	Perturbative (T) correction for spin-adapted unrestricted CCSD, evaluated natively from the spin-blocked UCCIntegrals (no spin-orbital integral build).

Enumeration Type Documentation

◆ IsdfMethod

enum class occ::qm::cc::IsdfMethod

strong

Interpolation-point selection for ISDF.

Enumerator
QR	pivoted QR on the pair-density collocation (accurate, O(N^4))
Cholesky	pivoted Cholesky of the grid Gram with lazy columns (cheaper)

◆ ThcRegType

enum class occ::qm::cc::ThcRegType

strong

Regularisation of the (ill-conditioned) LS-THC metric inverse.

Enumerator
Eig	drop eigenvalues below reg*lambda_max (truncated pinv)
Tikhonov	shift (S + reg*lambda_max I)^-1

◆ ThcSelectBasis

enum class occ::qm::cc::ThcSelectBasis

strong

Which functions' products the interpolation points must span.

Enumerator
AO	AO pair products: geometry-only / SCF-free (default)
MO	MO pair products (needs converged MOs for selection)

Function Documentation

◆ build_thc()

ThcFactors occ::qm::cc::build_thc	(	const AOBasis &	basis,
		const AOBasis &	aux_basis,
		const MolecularOrbitals &	mo,
		const ThcOptions &	opts = `{}`
	)

Build THC factors (X, V) for the spatial MOs of mo.

basis : AO basis of the molecule aux_basis : density-fitting auxiliary basis (the LS-THC reference)

◆ build_thc_from_B()

ThcFactors occ::qm::cc::build_thc_from_B	(	const AOBasis &	basis,
		const MolecularOrbitals &	mo,
		const ThcOptions &	opts,
		const Mat &	B
	)

As build_thc, but using a precomputed metric-folded DF reference tensor B (nmo^2 x naux, row p*nmo+q).

Lets a caller that already holds a DFIntegrals reuse it instead of rebuilding the 3-center store.

◆ build_uthc()

UThcFactors occ::qm::cc::build_uthc	(	const AOBasis &	basis,
		const Mat &	Ca,
		const Mat &	Cb,
		const Mat &	Ba,
		const Mat &	Bb,
		const ThcOptions &	opts
	)

◆ ccsd()

CCSDResult occ::qm::cc::ccsd	(	const CCIntegrals &	eris,
		const CCSDOptions &	opts = `{}`
	)

Restricted (closed-shell, spin-adapted) CCSD against a canonical reference.

Backend-agnostic: eris may be exact / DF / THC. Returns the correlation energy and converged t1/t2 amplitudes.

◆ ccsd_energy()

double occ::qm::cc::ccsd_energy	(	const Eigen::Tensor< double, 2 > &	t1,
		const Eigen::Tensor< double, 4 > &	t2,
		const CCIntegrals &	eris
	)

CCSD correlation energy for given amplitudes (exposed for testing).

◆ ccsd_t()

double occ::qm::cc::ccsd_t	(	const Eigen::Tensor< double, 2 > &	t1,
		const Eigen::Tensor< double, 4 > &	t2,
		const CCIntegrals &	eris
	)

Restricted closed-shell perturbative triples (T) correction.

Port of the thc_cct reference rtriples.py (PySCF ccsd_t_slow, JCP 94, 442 (1991)). Memory-frugal: it loops over virtual triples (a>=b>=c) and forms only O(nocc^3) intermediates per triple – the full O(o^3 v^3) triples array is never materialised. The only 3-virtual integral needed is ovvv, which is supplied by the (exact / DF / THC) backend, so (T) works for all three.

Returns the (T) energy correction for the given converged CCSD amplitudes.

◆ df_eris()

CCIntegrals occ::qm::cc::df_eris	(	const AOBasis &	basis,
		const AOBasis &	aux_basis,
		const MolecularOrbitals &	mo,
		int	n_frozen = `0`,
		size_t	memory_budget = `(size_t(1)<< 30)`
	)

Density-fitted (RI) backend: every block from the metric-folded DF B-tensor; the ladder is contracted through B so (ac|bd) is never formed.

◆ exact_eris()

CCIntegrals occ::qm::cc::exact_eris	(	const AOBasis &	basis,
		const MolecularOrbitals &	mo,
		int	n_frozen = `0`,
		size_t	memory_budget = `(size_t(1)<< 30)`
	)

Exact backend: all blocks (incl.

ovvv and the dense vvvv ladder) from a semidirect AO->MO transform (no nao^4 tensor). Reference for the others. n_frozen lowest occupied orbitals are excluded from the correlation space.

◆ fit_core()

Mat occ::qm::cc::fit_core	(	const Mat &	X,
		const Mat &	B,
		double	reg,
		ThcRegType	reg_type,
		double *	condition_out = `nullptr`,
		int *	n_kept_out = `nullptr`
	)

Regularised least-squares THC core fit.

B is the metric-folded DF tensor (nmo^2 x naux) with row p*nmo+q, so (pq|rs) = sum_A B(p*nmo+q,A) B(r*nmo+s,A).

◆ fit_core_ov()

Mat occ::qm::cc::fit_core_ov	(	const Mat &	Xo,
		const Mat &	Xv,
		const Mat &	B_ov,
		double	reg,
		ThcRegType	reg_type,
		double *	condition_out = `nullptr`,
		int *	n_kept_out = `nullptr`
	)

LS-THC core fit restricted to the occupied-virtual block – the only integrals MP2 needs.

Fits V so (ia|jb) ~ sum_PQ Xo(i,P)Xv(a,P) V(P,Q) Xo(j,Q)Xv(b,Q). Xo (o x P) / Xv (v x P) are the occ/virt rows of the THC collocation; B_ov is the metric-folded DF tensor for the ov pairs (o*v x naux, row i*v+a) = build_b_tilde(C_occ, C_virt). Metric is the ov Gram S = (Xo^T Xo) o (Xv^T Xv). Much cheaper (o*v << nmo^2) and more accurate for MP2 than the all-pairs fit_core.

◆ laplace_grid()

LaplaceGrid occ::qm::cc::laplace_grid	(	double	xmin,
		double	xmax,
		int	n
	)

Build an n-point Laplace grid approximating 1/x over [xmin, xmax] (require 0 < xmin <= xmax).

Derivation: the canonical inverse on [1,R] with R=xmax/xmin satisfies 1/x' = \int_0^1 u^{x'-1} du; applying n-point Gauss-Legendre on [0,1] and undoing the x'=x/xmin scaling gives t_k = -ln(u_k)/xmin, w_k = omega_k/(u_k*xmin).

◆ laplace_max_rel_error()

double occ::qm::cc::laplace_max_rel_error	(	const LaplaceGrid &	grid,
		double	xmin,
		double	xmax,
		int	n_sample = `64`
	)

Max relative error max_x |1 - x * sum_k w_k e^{-x t_k}| of grid, sampled on n_sample log-spaced x in [xmin, xmax] (testing / diagnostics).

◆ mat_view()

Eigen::Map< const occ::Mat > occ::qm::cc::mat_view	(	const Eigen::Tensor< double, 4 > &	t,
		Eigen::Index	r,
		Eigen::Index	c
	)

inline

View a contiguous (column-major) 4-tensor's data as an (r x c) matrix.

r*c must equal the tensor size; the caller is responsible for having laid the tensor out (via .shuffle()) so that this flat reinterpretation is meaningful.

◆ mo_eri_general()

Eigen::Tensor< double, 4 > occ::qm::cc::mo_eri_general	(	const IntegralEngine &	engine,
		const Mat &	C_L,
		const Mat &	C_q,
		const Mat &	C_r,
		const Mat &	C_s,
		size_t	budget = `(size_t(1)<< 28)`
	)

Semidirect AO->MO transform (chemist (pq|rs)) for arbitrary MO coefficient blocks.

Blocks the left index by budget and uses IntegralEngine::ao_direct_half_transform, so the nao^4 AO tensor is never materialised. Returns G(L, q, r, s) with L over the columns of C_L.

◆ num_frozen_core()

int occ::qm::cc::num_frozen_core ( const AOBasis & basis )

Number of frozen-core spatial orbitals for basis (chemical core: 1s for Li-Ne, [Ne] for Na-Ar, [Ar] for Sc+), matching the standard CCSD(T) default.

◆ pcon()

template<int RA, int RB, int NC>

Eigen::Tensor< double, RA+RB - 2 *NC > occ::qm::cc::pcon	(	const Eigen::Tensor< double, RA > &	A,
		const Eigen::Tensor< double, RB > &	B,
		const std::array< Eigen::IndexPair< int >, NC > &	pairs
	)

General N-index parallel tensor contraction – a drop-in, multithreaded replacement for A.contract(B, pairs) that routes through pgemm (BLAS), so it parallelises where Eigen's tensor contract() (serial gebp_kernel) does not.

Each pair (a,b) contracts A axis a with B axis b. Result is returned in Eigen's contract output order (A free axes ascending, then B free axes ascending), so any existing trailing .shuffle() still applies.

◆ pcon2()

Eigen::Tensor< double, 4 > occ::qm::cc::pcon2	(	const Eigen::Tensor< double, 4 > &	A,
		int	a0,
		int	a1,
		const Eigen::Tensor< double, 4 > &	B,
		int	b0,
		int	b1
	)

inline

Parallel two-index contraction of two 4-tensors – a drop-in, multithreaded replacement for A.contract(B, {(a0,b0),(a1,b1)}).

Pairs A axis a0 with B axis b0 and a1 with b1; returns the (A-free..., B-free...) tensor in Eigen's contract output order (so an existing trailing .shuffle() still applies). Reshapes each operand once (free indices grouped as the GEMM's outer dim, contracted indices as the shared dim) and dispatches to pgemm.

◆ pgemm()

void occ::qm::cc::pgemm	(	Eigen::Ref< occ::Mat >	C,
		Eigen::Ref< const occ::Mat >	A,
		Eigen::Ref< const occ::Mat >	B,
		bool	accumulate = `false`,
		bool	transA = `false`
	)

inline

C(m x n) = A(m x k) * B(k x n).

With accumulate, C += A*B. With transA, A is passed as (k x m) and A^T*B is formed.

Whether to parallelise here depends on the GEMM backend:

On Apple with Accelerate, the GEMM runs on the AMX matrix co-processor, which is shared per CPU cluster: one dgemm already saturates it (measured: 8 concurrent dgemms = 1.2x one) and a single AMX call (~346 GFLOP/s) beats Eigen NEON on all 8 cores (~237). So issue exactly ONE call – TBB-blocking would only spawn contending AMX calls.
Everywhere else (Linux default has no system BLAS; we do not assume a Linux BLAS is threaded) the underlying GEMM is single-threaded (Eigen's own NEON/AVX, ~52 GFLOP/s), so we parallelise over output blocks of the larger dimension ourselves (measured ~4.6x on 8 cores).

◆ ppermute()

template<int N>

void occ::qm::cc::ppermute	(	double *	out,
		const double *	A,
		const Eigen::array< Eigen::Index, N > &	Adims,
		const Eigen::array< int, N > &	perm
	)

inline

Parallel tensor permute (transpose): writes contiguous out = A.shuffle(perm) – out has dims Odim[k] = Adims[perm[k]] and out(j...) = A(source).

The strided gather from A is split across TBB over contiguous output blocks. This replaces Eigen's serial .shuffle(): in a transpose-GEMM (TTGT) contraction the permutation is the bottleneck (Matthews, TBLIS, arXiv:1607.00291), so it must run on all cores even though the GEMM is handed to a black-box BLAS.

◆ reconstruct_eri()

Eigen::Tensor< double, 4 > occ::qm::cc::reconstruct_eri	(	const Mat &	X,
		const Mat &	V
	)

THC-reconstructed chemist integrals (pq|rs) as a dense nmo^4 tensor (testing).

◆ reconstruction_error()

double occ::qm::cc::reconstruction_error	(	const AOBasis &	basis,
		const MolecularOrbitals &	mo,
		const Mat &	X,
		const Mat &	V
	)

Relative Frobenius error of the THC-reconstructed MO integrals vs exact.

◆ select_isdf_points()

std::vector< int > occ::qm::cc::select_isdf_points	(	const Mat &	coll,
		IsdfMethod	method,
		int	target,
		double	tol
	)

Indices of interpolation grid points spanning products of the columns of coll (npts x nfunc).

target<=0 falls back to the tol rank cut.

◆ thc_eris()

CCIntegrals occ::qm::cc::thc_eris	(	const AOBasis &	basis,
		const AOBasis &	aux_basis,
		const MolecularOrbitals &	mo,
		const ThcOptions &	opts = `{}`,
		int	n_frozen = `0`,
		size_t	memory_budget = `(size_t(1)<< 30)`
	)

THC backend: the <=2-virtual blocks come from DF (scalable); ovvv and the vvvv ladder are applied through the THC factors (X, V) – the ladder as three GEMMs, never forming vvvv.

aux_basis is the DF/LS-THC reference basis.

◆ thc_mp2()

ThcMP2Result occ::qm::cc::thc_mp2	(	const AOBasis &	basis,
		const AOBasis &	aux_basis,
		const MolecularOrbitals &	mo,
		const ThcMP2Options &	opts = `{}`
	)

LS-THC-MP2 correlation energy (restricted or unrestricted, dispatched on mo.kind).

The denominator is made separable by a Laplace quadrature so the THC factors collapse the orbital sums into n_isdf x n_isdf contractions: opposite-spin (Coulomb) is O(n_isdf^3) per Laplace point, same-spin exchange O(n_isdf^4). aux_basis is the density-fitting basis used both for the cheap DF reference and the LS-THC core fit (as in thc_eris).

◆ thc_select_collocation()

Mat occ::qm::cc::thc_select_collocation	(	const AOBasis &	basis,
		const MolecularOrbitals &	mo,
		const ThcOptions &	opts
	)

Point-selection half of build_thc: select ISDF interpolation points (AO- or MO-based per opts.select_basis, geometry-only) and return the MO collocation X (nmo x n_isdf) = MO value at each selected point.

The caller then fits the core: fit_core over all pairs (CCSD), or fit_core_ov over the occ-virt block (MP2).

◆ u_df_eris()

UCCIntegrals occ::qm::cc::u_df_eris	(	const AOBasis &	basis,
		const AOBasis &	aux_basis,
		const MolecularOrbitals &	mo,
		int	n_frozen = `0`,
		std::size_t	memory_budget = `(std::size_t(1)<< 30)`
	)

Density-fitted spin-blocked integrals.

All blocks come from the metric-folded DF B-tensor (one 3-center store, shared aux basis), and the three vvvv ladders contract through the per-spin B-tensors so no O(V^4) block is ever formed.

◆ u_exact_eris()

UCCIntegrals occ::qm::cc::u_exact_eris	(	const AOBasis &	basis,
		const MolecularOrbitals &	mo,
		int	n_frozen = `0`,
		std::size_t	memory_budget = `(std::size_t(1)<< 30)`
	)

Exact (full AO->MO) spin-blocked integrals.

Builds the three spatial chemist tensors (alpha, beta, alpha-beta) and materialises the vvvv blocks for the ladder closures. Reference backend. n_frozen frozen-core spatial orbitals are dropped from each spin's occupied space.

◆ u_thc_eris()

UCCIntegrals occ::qm::cc::u_thc_eris	(	const AOBasis &	basis,
		const AOBasis &	aux_basis,
		const MolecularOrbitals &	mo,
		const ThcOptions &	opts = `{}`,
		int	n_frozen = `0`,
		std::size_t	memory_budget = `(std::size_t(1)<< 30)`
	)

THC spin-blocked integrals: cheap blocks (<= 2 virtuals + ovvv) come from DF, and the three vvvv ladders use cross-spin THC factors (one ISDF point set, per-spin X and three cores Vaa/Vbb/Vab).

No O(V^4) block is ever formed.

◆ uccsd() [1/2]

UCCSDResult occ::qm::cc::uccsd	(	const AOBasis &	basis,
		const AOBasis &	aux_basis,
		const MolecularOrbitals &	mo,
		const UCCSDOptions &	opts = `{}`
	)

df/thc backends need an auxiliary basis; "exact" is also accepted here.

◆ uccsd() [2/2]

UCCSDResult occ::qm::cc::uccsd	(	const AOBasis &	basis,
		const MolecularOrbitals &	mo,
		const UCCSDOptions &	opts = `{}`
	)

Spin-adapted unrestricted CCSD(T) for a UHF (or RHF) reference.

Amplitudes and integrals are organised by spin into spatial blocks (t1a,t1b; t2aa,t2ab,t2bb) – the formulation production codes use for open shell. ~2-4x less work/memory than the spin-orbital path (uccsd_so) and, for the df/thc backends, never forms the O(V^4) vvvv block. Exact backend only via this overload; df/thc take an auxiliary basis (see the aux overload).

◆ uccsd_so()

UCCSDResult occ::qm::cc::uccsd_so	(	const AOBasis &	basis,
		const MolecularOrbitals &	mo,
		int	n_frozen = `0`,
		bool	with_triples = `true`,
		int	max_cycle = `100`,
		double	tol = `1e-9`
	)

Spin-orbital CCSD(T) for an open- or closed-shell reference.

Builds the antisymmetrised spin-orbital MO integrals from the (UHF or RHF) coefficients – spin orbitals are sorted by energy – then runs the textbook spin-orbital CCSD (Stanton-Gauss-Watts-Bartlett 1991) and, optionally, the perturbative (T) (Crawford project-6 formulas). Works for any reference but is ~4-8x the work of the spin-adapted unrestricted path; kept as an independent oracle for validating the spin-adapted uccsd and as a fallback for references the spin-adapted path does not handle (e.g. ROHF). n_frozen is the number of frozen-core spatial orbitals (2*n_frozen spin orbitals are frozen). Exact integrals only.

◆ uccsd_t()

double occ::qm::cc::uccsd_t	(	const UCCIntegrals &	e,
		const Eigen::Tensor< double, 2 > &	t1a,
		const Eigen::Tensor< double, 2 > &	t1b,
		const Eigen::Tensor< double, 4 > &	t2aa,
		const Eigen::Tensor< double, 4 > &	t2ab,
		const Eigen::Tensor< double, 4 > &	t2bb
	)

Perturbative (T) correction for spin-adapted unrestricted CCSD, evaluated natively from the spin-blocked UCCIntegrals (no spin-orbital integral build).

Port of PySCF uccsd_t_slow.py (4 spin cases aaa/bbb/baa/bba); a canonical UHF reference is assumed so the f_vo disconnected terms drop.

◆ uccsd_t_via_so()

double occ::qm::cc::uccsd_t_via_so	(	const AOBasis &	basis,
		const MolecularOrbitals &	mo,
		int	n_frozen,
		const Eigen::Tensor< double, 2 > &	t1a,
		const Eigen::Tensor< double, 2 > &	t1b,
		const Eigen::Tensor< double, 4 > &	t2aa,
		const Eigen::Tensor< double, 4 > &	t2ab,
		const Eigen::Tensor< double, 4 > &	t2bb
	)

Perturbative (T) correction for converged spin-adapted UCCSD amplitudes, evaluated through the validated spin-orbital triples kernel.

The spatial spin-block amplitudes (t1a,t1b; t2aa,t2ab,t2bb) are mapped into the energy-sorted spin-orbital basis built from the MOs, then so_triples runs.

Classes

Enumerations

Functions

Enumeration Type Documentation

◆ IsdfMethod

◆ ThcRegType

◆ ThcSelectBasis

Function Documentation

◆ build_thc()

◆ build_thc_from_B()

◆ build_uthc()

◆ ccsd()

◆ ccsd_energy()

◆ ccsd_t()

◆ df_eris()

◆ exact_eris()

◆ fit_core()

◆ fit_core_ov()

◆ laplace_grid()

◆ laplace_max_rel_error()

◆ mat_view()

◆ mo_eri_general()

◆ num_frozen_core()

◆ pcon()

◆ pcon2()

◆ pgemm()

◆ ppermute()

◆ reconstruct_eri()

◆ reconstruction_error()

◆ select_isdf_points()

◆ thc_eris()

◆ thc_mp2()

◆ thc_select_collocation()

◆ u_df_eris()

◆ u_exact_eris()

◆ u_thc_eris()

◆ uccsd() [1/2]

◆ uccsd() [2/2]

◆ uccsd_so()

◆ uccsd_t()

◆ uccsd_t_via_so()