Using MPQC LCAO and AO Factory Interfaces

Operators

Mapping of operator labels to operator types is described in the documentation for class mpqc::Operator .

User called functions

• Return TiledArray array ao_integral.compute(std::wstring) mo_integral.compute(std::wstring)
• Return TiledArray expression ao_integral(std::wstring) mo_integral(std::wstring)

Atomic Integral

Space labels

• κ λ μ ν -> obs(primary orbital basis)
• Α Β Γ Δ -> vbs(secondary orbital basis)
• Κ Λ Μ Ν -> dfbs(density fitting basis)
• ε -> min(minimal basis)
• α β γ δ -> cabs(cabs basis)
• ρ σ τ υ -> ribs(obs + cabs)
• One Electron Integral

  cpp
  // Overlap
  ao_integral.compute(L"<κ|λ>");
  ao_integral.compute(L"<α|λ>");
  // Kinetic
  ao_integral.compute(L"<κ|T|λ>");
  // Nuclear
  ao_integral.compute(L"<κ|V|λ>");
  // H Core
  ao_integral.compute(L"<κ|H|λ>");
  // Inverse Square Root
  ao_integral.compute(L"<κ|λ>[inv_sqr]");

• Two Electron Two Center Integral

only chemical notation allowed

// Coulomb
ao_integral.compute(L"(Κ|G|Λ)");
// Inverse
ao_integral.compute(L"(Κ|G|Λ)[inv]");
// Inverse Square Root
ao_integral.compute(L"(Κ|G|Λ)[inv_sqr]");

• Two Electron Three Center Integral

only chemical notation allowed

density-fitting basis has to go the bra

// Coulomb
ao_integral.compute(L"(Κ|G| μ λ )");
// R12
ao_integral.compute(L"(Κ|R| μ λ )");

• Two Electron Four Center Integral

  // convention
  ao_integral.compute(L"<μ1 λ1|G| μ2 λ2 >");
  // density fitting
  ao_integral.compute(L"<μ1 λ1|G| μ2 λ2 >[df]");
  // chemical notation
  ao_integral.compute(L"(μ1 λ1|G| μ2 λ2 )");
  ao_integral.compute(L"(μ1 λ1|G| μ2 λ2 )[df]");

• J, K, and F

  // Fock
  ao_integral.compute(L"<κ|F|λ>");
  ao_integral.compute(L"<κ|F(α)|λ>");
  ao_integral.compute(L"<κ|F(β)|λ>");
  // Exchange
  ao_integral.compute(L"<κ|K|λ>");
  ao_integral.compute(L"<κ|K(α)|λ>");
  ao_integral.compute(L"<κ|K(β)|λ>");

LCAO Integral

Space labels:

• m, n -> occ(occupied)
• m', n' -> frozen_occ (inactive/core occupied)
• i,j,k,l -> active_occ (correlated occupied)
• x, y -> active (active orbital used in MR)
• e,f -> uocc (unoccupied in obs, aka virtual)
• e',f' -> frozen_uocc (frozen unoccupied in obs)
• a,b,c,d -> uocc (active unoccupied in obs)
• p,q,r,s -> any (orbital basis, obs)
• a', b', c', d' -> other_uocc (cabs = complete basis - orbital basis)
• A', B', C', D' -> complete_uocc (complete unoccupied = a + a')
• P',Q',R',S' -> complete_any (complete basis, cbs)
• One Electron Integral

  mo_integral.compute(L"<i|H|a>");
  mo_integral.compute(L"<i|F|a>");
  mo_integral.compute(L"<i|F(α)|a>");

• Two Electron Four Center Integral

  mo_integral.compute(L"<i j|G|a b>");
  mo_integral.compute(L"(i a|G|j b)");
  mo_integral.compute(L"<i j|R|P' Q'>");
  // density fitting
  mo_integral.compute(L"<i j|G|a b>[df]");

• Half Transformed Integral

  mo_integral.compute(L"(Κ|G|i a)");
  mo_integral.compute(L"<p q|G|μ ν>");