The parametric 2-RDM method computes the ground-state energy of a molecule as a parametric functional of the two-electron reduced density matrix (2-RDM).  The parametrization approximately enforces N-representability conditions, which are necessary constraints for the 2-RDM to represent an N-electron density matrix.

Energies and properties from the parametric 2-RDM method typically have an accuracy between those from coupled cluster with single and double excitations (CCSD) and those from coupled cluster with single, double, and perturbative triple excitations [CCSD(T)].

The optional functional keyword controls the parametric functional employed in the calculation.  It can be set to the following strings: "CEPA", "K", and "M" (default).

The optional return_rdm keyword controls whether or not the spin-free 1- and/or 2-RDMs are returned.  If set to "rdm1" (default), the 1-RDM is returned, if set to "rdm1_and_rdm2", the 1- and 2-RDMs are returned, and if set to "none", RDMs are not returned.

The optional frozen keyword can be provided to prevent some orbitals from being correlated.  The keyword can be assigned to a set {} containing the indices of the molecular orbitals to be treated as frozen.  If the frozen keyword is not assigned, then all of the molecular orbitals are considered active, and a parametric 2-RDM calculation with all orbitals is performed.

basis = string -- name of the basis set.  See Basis for a list of available basis sets.  Default is "sto-3g".

spin = nonnegint -- twice the total spin S (= 2S). Default is 0.

charge = nonnegint -- net charge of the molecule. Default is 0.

symmetry = string/boolean -- is the Schoenflies symbol of the abelian point-group symmetry which can be one of the following:  D2h, C2h, C2v, D2, Cs, Ci, C2, C1. true (default) finds the appropriate symmetry while false does not use symmetry.

unit = string -- "Angstrom" or "Bohr". Default is "Angstrom".

ghost = list of lists -- each list has the string of an atom's symbol and the atom's x, y, and z coordinates.  See Ghost Atoms.

functional = string -- "CEPA", "K", or "M". Default is "M".

frozen = set -- set of orbitals to be frozen.

return_rdm = string -- options to return the 1-RDM and/or 2-RDM: "none", "rdm1", "rdm1_and_rdm2". Default is "rdm1".

return_t2t1 = boolean -- option to return the one- and two-electron transition amplitudes.  Default is false.

populations = string -- atomic-orbital population analysis: "Mulliken" and "Mulliken/meta-Lowdin". Default is "Mulliken".

nuclear_gradient = boolean -- option to return the analytical nuclear gradient if available. Default is false.

conv_tol = float -- converge threshold. Default is 5*${10}^{-5}\.$

max_memory = posint/boolean -- allowed memory in MB. Default is 4000.

verbose = posint -- positive integer between 1 and 5 that controls printing. Default is 1.

Attributes for Hartree Fock:

conv_tol_hf = float -- converge threshold. Default is ${10}^{-10}\.$

diis_hf = boolean -- whether to do diis. Default is true.

diis_space_hf = posinut -- diis's space size. By default, 8 Fock matrices and errors vector are stored.

diis_start_cycle_hf = posint -- the step to start diis. Default is 1.

direct_scf_hf = boolean -- direct SCF in which integrals are recomputed is used by default.

direct_scf_tol_hf = float -- direct SCF cutoff threshold. Default is ${10}^{-13}\.$

level_shift_hf = float/int -- level shift (in a.u.) for virtual space. Default is $0.$

max_cycle_hf = posint -- max number of iterations. Default is 50.

nuclear_gradient_hf = boolean -- option to return the analytical nuclear gradient. Default is false.

populations_hf = string -- atomic-orbital population analysis: "Mulliken" and "Mulliken/meta-Lowdin". Default is "Mulliken".

D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008). "Parametrization of the two-electron reduced density matrix for its direct calculation without the many-electron wave function"

D. A. Mazziotti, Phys. Rev. A 81, 062515 (2010). "Parametrization of the two-electron reduced density matrix for its direct calculation without the many-electron wave function: Generalizations and applications"

J. J. Foley IV and D. A. Mazziotti, J.Phys. Chem. A 117, 6712 (2013). "Cage versus prism: electronic energies of the water hexamer"

A. J. Valentine and D. A. Mazziotti, J. Phys. Chem. A 117, 9746 (2013). "Theoretical prediction of the structures and energies of olympicene and its isomers"

$\mathrm{with}\left(\mathrm{QuantumChemistry}\right)\:$

$\mathrm{molecule} ≔ \left[\left[''H''\,0\,0\,0\right]\,\left[''F''\,0\,0\,0.95\right]\right]\;$

$\mathrm{molecule}≔\left[\left[''H''\,0\,0\,0\right]\,\left[''F''\,0\,0\,0.95000000\right]\right]$

$\mathrm{output\_hf} ≔ \mathrm{Parametric2RDM}\left(\mathrm{molecule}\, \mathrm{basis}\=''dz''\right)\;$