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CAS+EN OK
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CI/CI.ml
136
CI/CI.ml
@ -385,7 +385,9 @@ let make ?(n_states=1) det_space =
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let pt2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states } =
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let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states }
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i_o1_alfa alfa_o2_i w_alfa =
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let mo_basis = Ds.mo_basis det_space in
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let mo_basis = Ds.mo_basis det_space in
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@ -400,17 +402,16 @@ let pt2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states } =
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)
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)
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in
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in
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(* Only the gournd state is computed here *)
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let psi0, e0 = Lazy.force eigensystem in
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let psi0 =
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let psi0 =
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let psi0, _ = Lazy.force eigensystem in
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let stream =
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let stream =
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Ds.determinant_stream det_space
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Ds.determinant_stream det_space
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in
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in
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Array.init (Ds.size det_space) (fun i ->
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Array.init (Ds.size det_space) (fun i ->
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Stream.next stream, psi0.{i+1,1})
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Stream.next stream, psi0.{i+1,1})
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in
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in
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let e0 = e0.{1} in
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(*
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(*
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let is_internal =
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let is_internal =
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@ -445,7 +446,7 @@ let pt2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states } =
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let psi_filtered_idx =
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let psi_filtered_idx =
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let rec aux accu = function
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let rec aux accu = function
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| j when j <= i -> List.rev accu
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| j when j < i -> List.rev accu
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| j -> if Determinant.degree (fst psi0.(i)) (fst psi0.(j)) < 4 then
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| j -> if Determinant.degree (fst psi0.(i)) (fst psi0.(j)) < 4 then
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aux (j::accu) (j-1)
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aux (j::accu) (j-1)
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else
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else
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@ -457,10 +458,27 @@ let pt2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states } =
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List.map (fun i -> psi0.(i)) psi_filtered_idx
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List.map (fun i -> psi0.(i)) psi_filtered_idx
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in
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in
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let psi_h alfa =
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let symmetric = i_o1_alfa == alfa_o2_i in
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let hij = h_ij mo_basis alfa in
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let psi_h_alfa alfa =
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List.fold_left (fun accu (det, coef) ->
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List.fold_left (fun accu (det, coef) ->
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accu +. coef *. (hij det)) 0. psi_filtered
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accu +. coef *. (i_o1_alfa det alfa)) 0. psi_filtered
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in
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let alfa_h_psi =
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if symmetric then
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psi_h_alfa
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else
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fun alfa ->
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List.fold_left (fun accu (det, coef) ->
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accu +. coef *. (alfa_o2_i alfa det)) 0. psi_filtered
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in
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let psi_h_alfa_alfa_h_psi alfa =
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if symmetric then
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let x = psi_h_alfa alfa in x *. x
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else
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(psi_h_alfa alfa) *. (alfa_h_psi alfa)
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in
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in
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let is_internal alfa =
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let is_internal alfa =
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@ -483,13 +501,15 @@ let pt2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states } =
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in
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in
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let det_i = fst psi0.(i) in
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let det_i = fst psi0.(i) in
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let w_alfa = w_alfa det_i in
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let same_spin =
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List.fold_left (fun accu spin ->
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accu +.
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List.fold_left (fun accu particle ->
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List.fold_left (fun accu particle ->
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accu +.
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accu +.
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List.fold_left (fun accu hole ->
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List.fold_left (fun accu hole ->
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if hole = particle then accu else
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if hole = particle then accu else
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accu +.
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List.fold_left (fun accu spin ->
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let alfa =
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let alfa =
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Determinant.single_excitation spin hole particle det_i
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Determinant.single_excitation spin hole particle det_i
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in
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in
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@ -497,39 +517,113 @@ let pt2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states } =
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let single =
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let single =
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if already_generated alfa then 0. else
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if already_generated alfa then 0. else
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let h_aa = h_ij mo_basis alfa alfa in
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w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
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let psi_h_alfa = psi_h alfa in
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psi_h_alfa *. psi_h_alfa /. (e0 -. h_aa)
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in
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in
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let double =
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let double =
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List.fold_left (fun accu particle' ->
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List.fold_left (fun accu particle' ->
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if particle' > particle then
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accu
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else
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accu +.
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accu +.
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List.fold_left (fun accu hole' ->
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List.fold_left (fun accu hole' ->
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accu +.
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if hole' = particle' || hole' < hole then
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List.fold_left (fun accu spin' ->
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accu
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else
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let alfa =
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let alfa =
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Determinant.double_excitation
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Determinant.double_excitation
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spin hole particle
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spin hole particle
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spin' hole' particle' det_i
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spin hole' particle' det_i
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in
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in
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if Determinant.is_none alfa ||
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if Determinant.is_none alfa ||
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already_generated alfa then
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already_generated alfa then
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accu
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accu
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else
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else
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let h_aa = h_ij mo_basis alfa alfa in
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accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
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let psi_h_alfa = psi_h alfa in
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accu +. psi_h_alfa *. psi_h_alfa /. (e0 -. h_aa)
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) 0. [ Spin.Alfa ; Spin.Beta ]
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) 0. mo_indices
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) 0. mo_indices
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) 0. mo_indices
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) 0. mo_indices
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in
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in
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accu +. single +. double
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accu +. single +. double
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) 0. mo_indices
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) 0. mo_indices
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) 0. [ Spin.Alfa ; Spin.Beta ]
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) 0. [ Spin.Alfa ; Spin.Beta ]
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in
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let opposite_spin =
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List.fold_left (fun accu particle ->
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accu +.
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List.fold_left (fun accu hole ->
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if hole = particle then accu else
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let alfa =
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Determinant.single_excitation Spin.Alfa hole particle det_i
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in
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if Determinant.is_none alfa then accu else
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let double =
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List.fold_left (fun accu particle' ->
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accu +.
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List.fold_left (fun accu hole' ->
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if hole' = particle' then accu else
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let alfa =
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Determinant.double_excitation
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Spin.Alfa hole particle
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Spin.Beta hole' particle' det_i
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in
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if Determinant.is_none alfa ||
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already_generated alfa then
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accu
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else
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accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa
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) 0. mo_indices
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) 0. mo_indices
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) 0. mo_indices
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) 0. mo_indices
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in
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in
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accu +. double
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) 0. mo_indices
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) 0. mo_indices
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in
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same_spin +. opposite_spin
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in
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Array.mapi (fun i (_,c_i) -> c_i *. det_contribution i) psi0
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Array.mapi (fun i (_,c_i) -> c_i *. det_contribution i) psi0
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|> Array.fold_left (+.) 0.
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|> Array.fold_left (+.) 0.
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let pt2_en ci =
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let mo_basis = Ds.mo_basis ci.det_space in
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let _psi0, e0 = Lazy.force ci.eigensystem in
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let i_o1_alfa = h_ij mo_basis in
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let w_alfa _ =
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let e0 = e0.{1} in
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let h_aa alfa = h_ij mo_basis alfa alfa in
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fun alfa ->
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1. /. (e0 -. h_aa alfa)
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in
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second_order_sum ci i_o1_alfa i_o1_alfa w_alfa
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let pt2_mp ci =
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let mo_basis = Ds.mo_basis ci.det_space in
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let i_o1_alfa = h_ij mo_basis in
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let eps = MOBasis.mo_energies mo_basis in
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let w_alfa det_i alfa=
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match Excitation.of_det det_i alfa with
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| Excitation.Single (_, { hole ; particle ; spin })->
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1./.(eps.{hole} -. eps.{particle})
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| Excitation.Double (_, { hole=h ; particle=p ; spin=s },
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{ hole=h'; particle=p'; spin=s'})->
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1./.(eps.{h} +. eps.{h'} -. eps.{p} -. eps.{p'})
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| _ -> assert false
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in
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second_order_sum ci i_o1_alfa i_o1_alfa w_alfa
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@ -99,6 +99,16 @@ let double_of_det t t' =
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| _ -> assert false
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| _ -> assert false
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let of_det t t' =
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match Determinant.degree t t' with
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| 0 -> if Determinant.phase t = Determinant.phase t' then
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Identity Phase.Pos
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else
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Identity Phase.Neg
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| 1 -> single_of_det t t'
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| 2 -> double_of_det t t'
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| _ -> multiple_of_det t t'
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let pp_s_exc ppf t =
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let pp_s_exc ppf t =
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Format.fprintf ppf "@[T^{%s}_{%d->%d}@]"
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Format.fprintf ppf "@[T^{%s}_{%d->%d}@]"
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(match t.spin with
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(match t.spin with
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@ -40,19 +40,19 @@ let two_e_ints t = Lazy.force t.ee_ints
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let one_e_ints t = Lazy.force t.one_e_ints
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let one_e_ints t = Lazy.force t.one_e_ints
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let mo_energies t =
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let mo_energies t =
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let f =
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let m_C = mo_coef t in
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let m_C = mo_coef t in
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let f =
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let m_N = Mat.of_diag @@ mo_occupation t in
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let m_N = Mat.of_diag @@ mo_occupation t in
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let m_P =
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let m_P = x_o_xt m_N m_C in
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gemm m_C @@ (gemm m_N m_C ~transb:`T)
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in
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match t.mo_type with
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match t.mo_type with
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| RHF -> Fock.make_rhf ~density:m_P (ao_basis t)
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| RHF -> Fock.make_rhf ~density:m_P (ao_basis t)
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| ROHF -> Fock.make_uhf ~density_same:m_P ~density_other:m_P (ao_basis t)
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| ROHF -> (Mat.scal 0.5 m_P;
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Fock.make_uhf ~density_same:m_P ~density_other:m_P (ao_basis t))
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| _ -> failwith "Not implemented"
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| _ -> failwith "Not implemented"
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in
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in
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let m_F = Fock.fock f in
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let m_F0 = Fock.fock f in
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Vec.init (size t) (fun i -> m_F.{i,i})
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xt_o_x m_F0 m_C
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|> Mat.copy_diag
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let mo_matrix_of_ao_matrix ~mo_coef ao_matrix =
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let mo_matrix_of_ao_matrix ~mo_coef ao_matrix =
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@ -49,6 +49,10 @@ val two_e_ints : t -> ERI.t
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val size : t -> int
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val size : t -> int
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(** Number of molecular orbitals in the basis *)
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(** Number of molecular orbitals in the basis *)
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val mo_energies : t -> Vec.t
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(** Fock MO energies *)
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(** {1 Creators} *)
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(** {1 Creators} *)
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val make : simulation:Simulation.t ->
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val make : simulation:Simulation.t ->
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@ -5,7 +5,7 @@ let make ?(frozen_core=true) hf =
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MOBasis.of_hartree_fock hf
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MOBasis.of_hartree_fock hf
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in
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in
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let epsilon =
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let epsilon =
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HartreeFock.eigenvalues hf
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MOBasis.mo_energies mo_basis
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in
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in
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let mo_class =
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let mo_class =
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MOClass.cas_sd mo_basis 0 0
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MOClass.cas_sd mo_basis 0 0
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@ -95,8 +95,18 @@ let density t =
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| _ -> failwith "Not implemented"
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| _ -> failwith "Not implemented"
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let occupation t =
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let occupation t =
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density t
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let n_alfa, n_beta =
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|> Mat.copy_diag ~n:(Mat.dim2 @@ eigenvectors t)
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El.n_alfa @@ Simulation.electrons @@ simulation t,
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El.n_beta @@ Simulation.electrons @@ simulation t
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in
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match kind t with
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| RHF -> Vec.init (Mat.dim2 @@ eigenvectors t) (fun i ->
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if i <= nocc t then 2.0 else 0.0)
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| ROHF -> Vec.init (Mat.dim2 @@ eigenvectors t) (fun i ->
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if i <= n_beta then 2.0 else
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if i <= n_alfa then 1.0 else
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0.0)
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| _ -> failwith "Not implemented"
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let energy t =
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let energy t =
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@ -72,7 +72,7 @@ let () =
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let ci = CI.make space in
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let ci = CI.make space in
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Format.fprintf ppf "CAS-CI energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion s);
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Format.fprintf ppf "CAS-CI energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion s);
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let pt2 = CI.pt2 ci in
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let pt2 = CI.pt2_en ci in
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Format.fprintf ppf "CAS-EN2 energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion s +. pt2)
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Format.fprintf ppf "CAS-EN2 energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion s +. pt2)
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(*
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(*
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let s2 = Util.xt_o_x ~o:(CI.s2_matrix ci) ~x:(CI.eigenvectors ci) in
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let s2 = Util.xt_o_x ~o:(CI.s2_matrix ci) ~x:(CI.eigenvectors ci) in
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