Density-fitted Coupled Cluster methods

DFCoupledCluster

Density-fitted coupled-cluster methods.

calc_df_lt_sos_mp2(EC::ECInfo)

Perform density-fitted Laplace-transformed SOS MP2 calculation.

Args: EC: ECInfo object

Returns: OutDict with keys "E", "ESS", "EOS", "EO" for MP2 correlation energy, SS, OS, and O contributions.

calc_dfmp2(EC::ECInfo)

Perform density-fitted MP2 calculation. Materialize T2 amplitudes only when they are needed for an explicit doubles save or for the MP2 lambda/property path.

Args: EC: ECInfo object

Returns: OutDict with keys "E", "ESS", "EOS", "EO" for MP2 correlation energy, SS, OS, and O contributions.

calc_dressed_3idx(EC::ECInfo, T1)

Calculate dressed integrals for 3-index integrals from file mmL.

calc_svd_dc(EC::ECInfo, method::AbstractString)

Calculate decomposed closed-shell DCSD or DCD with $T^{ij}_{ab}=U^{iX}_a U^{jY}_b T_{XY}$.

calc_svd_dc(EC::ECInfo, method::ECMethod)

Calculate decomposed closed-shell DCSD or DCD with $T^{ij}_{ab}=U^{iX}_a U^{jY}_b T_{XY}$.

Currently only DC methods are supported. DF integrals are used (have to be calculated before). The starting guess for SVD-coefficients is calculated without doubles, see calc_doubles_decomposition_without_doubles.

save_pseudodressed_3idx(EC::ECInfo)

Save non-dressed 3-index integrals from file mmL to dressed files.

calc_3idx_svd_decomposition(EC::ECInfo, voL::AbstractArray, tol2)

Calculate $U^{iX}_a$ from $v_a^{iL}$ using SVD.

Version without holding all $v_a^{iL}$ integrals in memory. voL is the full 3-index integral $v_a^{iL}$ (can be mmaped).

calc_MP2_amplitudes_from_3idx(EC::ECInfo, voL::AbstractArray, ishift)

Calculate MP2 amplitudes from $v_a^{iL}$.

The imaginary shift ishift is used in the denominator in the calculation of the MP2 amplitudes.

calc_MP2_from_3idx(EC::ECInfo, voL::AbstractArray, ishift)

Calculate MP2 energy from $v_a^{iL}$.

The imaginary shift ishift is used in the denominator in the calculation of the MP2 amplitudes. Returns total energy, SS, OS and Openshell (0.0) contributions as OutDict with keys (E,ESS,EOS,EO).

calc_SVD_DCD_doubles1(EC::ECInfo, UaiX, ϵX)

Perform one SVD-DCD iteration for the doubles amplitudes in the MP2 SVD space.

This routine is used in the second decomposition step of the SVD-DCD scheme. It takes the SVD space from MP2 doubles amplitudes $U^{iX}_a$ and corresponding "orbital" energies $ϵ_X$, constructs the necessary pseudo-dressed intermediates, and performs a single residual evaluation and amplitude update for the doubles amplitudes $T^{ij}_{ab}$.

As part of the iteration, the coupled-cluster options EC.options.cc.project_vovo_t2 and EC.options.cc.use_projx are temporarily modified (to use the amplitude projection in the $vovo$ block and to disable projx, respectively); their original values are restored before returning.

Returns

• T2: Updated doubles amplitudes $T^{ij}_{ab}$ after one SVD-DCD iteration.

calc_deco_doubles_energy(EC::ECInfo, T2)

Calculate closed-shell doubles energy using decomposed doubles amplitudes T2=$T_{XY}$ or T2=$T^{ij}_{ab}$ using density-fitted integrals.

Returns total energy, SS, OS and Openshell (0.0) contributions as OutDict with keys (E,ESS,EOS,EO).

calc_deco_hylleraas(EC::ECInfo, T1, T2, R1, R2)

Calculate closed-shell singles and doubles Hylleraas energy using contravariant decomposed doubles amplitudes T2=$T_{XY}$ or full contravariant doubles amplitude T2=$T^{ij}_{ab}$.

Returns total energy, SS, OS and Openshell (0.0) contributions as OutDict with keys (E,ESS,EOS,EO).

calc_df_doubles_energy(EC::ECInfo, T2)

Calculate closed-shell doubles energy using DF integrals and T2[a,b,i,j] = $T^{ij}_{ab}$.

Returns total energy, SS, OS and Openshell (0.0) contributions as OutDict with keys (E,ESS,EOS,EO).

calc_dfmp2_energy_components(store_doubles!, Lvo, ϵo, ϵv)

Accumulate the DF-MP2 energy components and call store_doubles! for each completed t_vvij block when doubles amplitudes must be materialized.

calc_doubles_decomposition(EC::ECInfo)

Decompose $T^{ij}_{ab}=U^{iX}_a U^{jY}_b T_{XY}$

calc_doubles_decomposition_with_doubles(EC::ECInfo)

Decompose $T^{ij}_{ab}=U^{iX}_a U^{jY}_b T_{XY}$ using explicit doubles amplitudes $T^{ij}_{ab}$.

calc_doubles_decomposition_without_doubles(EC::ECInfo)

Decompose $T^{ij}_{ab}=U^{iX}_a U^{jY}_b T_{XY}$ without explicit calculation of $T^{ij}_{ab}$.

The decomposition is done in two steps:

1. $\bar U^{i\bar X}_a$ is calculated from $v_a^{iL}$ using SVD (with threshold CcOptions.ampsvdtol×CcOptions.ampsvdfac);
2. MP2 doubles $T^{i}_{aX}$ are calculated from $v_a^{iL}$ and $U^{iX}_a$ and again decomposed using SVD and threshold CcOptions.ampsvdtol.

The SVD-basis is rotated to pseudocanonical basis to diagonalize orbital-energy differences, $ϵ_X = U^{iX}_{a}(ϵ_a-ϵ_i)U^{iX}_a$. The imaginary shift CcOptions.deco_ishiftp is used in the denominator in the calculation of the MP2 amplitudes. The orbital energy differences are saved in file e_X. The SVD-coefficients $U^{iX}_a$ are saved in file C_voX. The starting guess for doubles $T_{XY}$ is saved in file T_XX. Return full MP2 correlation energy, SS, OS, and Openshell(0.0) (using the imaginary shift) as OutDict with keys (E,ESS,EOS,EO).

calc_svd_dcsd_residual(EC::ECInfo, T1, T2)

Calculate decomposed closed-shell DCSD residual with $T^{ij}_{ab}=U^{iX}_a U^{jY}_b T_{XY}$ and $R_{XY}=U^{iX†}_a U^{jY†}_b R^{ij}_{ab}$. T2 contains decomposed amplitudes $T_{XY}$ or full amplitudes $T^{ij}_{ab}$.

If T2 is $T^{ij}_{ab}$, the residual is also returned in full form.

calc_voX(EC::ECInfo; calc_vᵥᵒˣ=false, calc_vᵛₒₓ=false)

Calculate $\hat v_a^{iX} = \hat v_{ak}^{ci} U^{kX}_c$ and/or $\hat v^c_{kX} = \hat v_{ak}^{ci} U^{†a}_{kX}$ with $\hat v_{ak}^{ci} = \hat v_a^{cL} \hat v_k^{iL}$ and $U^{kX}_c$ from file C_voX.

Return a tuple (vᵥᵒˣ, vᵛₒₓ) (not calculated intermediates are empty arrays).

contravariant_deco_doubles(EC::ECInfo, T2, projx=false)

Calculate contravariant doubles amplitudes $T̃^{ij}_{ab} = 2T^{ij}_{ab} - T^{ij}_{ba}$ with $T^{ij}_{ab} = U^{iX}_a U^{jY}_b T_{XY}$. If projx is true, the projected exchange is returned: $T̃_{XY} = U^{†a}_{iX} U^{†b}_{jY} T̃^{ij}_{ab}$

dress_df_fock(EC::ECInfo, T1)

Dress DF fock matrix with DF 3-index integrals.

The dress-contribution is added to the original fock matrix from file f_mm. The dressed fock matrix is stored in file df_mm. Additionally, the coulomb and exchange dressing contributions to $\hat f_k^c$ are stored in files dfc_ov and dfe_ov.

gen_vₓˣᴸ(EC::ECInfo)

Generate $v_X^{X'L} = v_a^{cL} U^{†a}_{kX} U^{kX'}_c$ using bare integrals.

The integrals and the SVD-coefficients are read from files mmL and C_voX, and the result is stored in file X^XL.

get_ssv_osvˣˣ(EC::ECInfo)

Return $ssv^{XY} = U^{kX}_c U^{lX}_d (v_{kl}^{cd} - v_{lk}^{cd} )$ and $osv^{XY} = U^{kX}_c U^{lX}_d v_{kl}^{cd}$ with $v_{kl}^{cd} = v_k^{cL} v_l^{dL'}δ_{LL'}$.

The integrals will be read from files ssd_^XX and osd_^XX. If the files do not exist, the integrals will be calculated and stored in files ssd_^XX and osd_^XX. vk^{cL} and U^{kX}c are read from files d_ovL and C_voX.

save_pseudo_dress_df_fock(EC::ECInfo)

Save non-dressed DF fock matrix from file f_mm to dressed file df_mm.