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QuantumChemistry

 ActiveSpaceCI
 A configuration interaction (CI) method, operating on a subset of orbitals known as the active space

 Calling Sequence ActiveSpaceCI(molecule, active, options)

Parameters

 molecule - list of lists; each list has 4 elements, the string of an atom's symbol and atom's x, y, and z coordinates active - equation of the form active = [nelectrons, nact] or {set of active orbitals} options - (optional) equation(s) of the form option = value where option is one of state, symmetry, unit,  max_memory, natorb, conv_tol, nuclear_gradient, return_rdm, populations, canonicalization, initial_mo, fcisolver_conv_tol, fcisolver_davidson_only, fcisolver_level_shift, fcisolver_lindep, fcisolver_max_cycle, fcisolver_max_space, fcisolver_nroots, fcisolver_pspace_size, conv_tol_hf, diis_hf, diis_space_hf, diis_start_cycle_hf, direct_scf_hf, direct_scf_tol_hf, level_shift_hf, max_cycle_hf, nuclear_gradient_hf, populations_hf

Description

 • ActiveSpaceCI, also known as complete-active-space configuration interaction (CASCI), performs a full configuration interaction (FCI) calculation with a subset of the molecular orbitals (MOs) known as the active orbitals.  Molecular orbitals are selected to be active if they are expected to contribute significantly to the molecule's electron correlation.  The remaining inactive orbitals are treated as either fully occupied or fully unoccupied, and hence, they do not contribute to the description of the electron correlation.
 • The active keyword argument must be provided to perform an active-space calculation.  The active keyword can be assigned to a list of two elements [N,r] containing the number N of active electrons and the number r of active orbitals or a set containing the indices of the molecular orbitals to be treated as active.   If the active keyword is not assigned, then all of the molecular orbitals are considered active, and a FCI calculation is performed.
 • The state keyword can be assigned a nonnegative integer to compute the energy and properties of a ground or excited state.  If the state keyword is assigned to 0 (default), then the ground state is computed; if the state keyword is assigned to a positive integer n, then the nth excited state is computed.  Calculations are affected by the spin keyword whose default is 0.

Outputs

The table of following contents:

 ${t}\left[{\mathrm{e_tot}}\right]$ - float -- total electronic energy of the system ${t}\left[{\mathrm{e_corr}}\right]$ - float -- the difference between the CASCI energy and the Hartree-Fock energy ${t}\left[{\mathrm{mo_coeff}}\right]$ - Matrix -- coefficients expressing natural molecular orbitals (columns) in terms of atomic orbitals (rows) ${t}\left[{\mathrm{mo_occ}}\right]$ - Vector -- molecular (natural) orbital occupations ${t}\left[{\mathrm{aolabels}}\right]$ - Vector -- string label for each atomic orbital consisting of the atomic symbol and the orbital name ${t}\left[{\mathrm{active_orbitals}}\right]$ - list -- list of integers and/or integer ranges indicating the molecular orbitals that are active for correlation ${t}\left[{\mathrm{ci_coeff}}\right]$ - Matrix -- a matrix of CI coefficients whose rows represent α-spin coefficient indices and columns represent β-spin coefficient indices ${t}\left[{\mathrm{rdm1}}\right]$ - Matrix -- one-particle reduced density matrix (1-RDM) in the molecular-orbital (MO) representation ${t}\left[{\mathrm{rdm2}}\right]$ - Array -- two-particle reduced density matrix (2-RDM) in the molecular-orbital (MO) representation ${t}\left[{\mathrm{dipole}}\right]$ - Vector -- dipole moment according to its x, y and z components ${t}\left[{\mathrm{populations}}\right]$ - Matrix -- atomic-orbital populations ${t}\left[{\mathrm{charges}}\right]$ - Vector -- atomic charges from the populations ${t}\left[{\mathrm{nuclear_gradient}}\right]$ - Matrix -- analytical nuclear gradient ${t}\left[{\mathrm{spin_squared}}\right]$ - integer or fraction -- expectation value of the total spin S squared (= S(S+1))

Options

 • 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 finds the appropriate symmetry while false (default) does not use symmetry.
 • state = nonnegint -- sets the electronic state to be computed.  Default is 0, which is the ground state.
 • unit = string -- "Angstrom" or "Bohr". Default is "Angstrom".
 • max_memory = posint -- allowed memory in MB. Default is 4000.
 • natorb = boolean -- whether to restore the natural orbital during CASSCF optimization. Default is false.
 • conv_tol = float -- converge threshold. Default is ${10}^{-10}.$
 • nuclear_gradient = boolean -- option to return the analytical nuclear gradient if available. Default is false.
 • return_rdm = string -- options to return the 1-RDM and/or 2-RDM: "none", "rdm1", "rdm1_and_rdm2". Default is "rdm1".
 • populations = string -- atomic-orbital population analysis: "Mulliken" and "Mulliken/meta-Lowdin". Default is "Mulliken".
 • canonicalization = boolean -- whether to canonicalize orbitals. Default is true.
 • initial_mo = list -- initial molecular orbitals (MOs) as a list: [ t[mo_coeff], t[mo_symmetry] ] where t[mo_coeff] is the Matrix of MOs (columns) in terms of atomic orbitals (rows) and t[mo_symmetry] is the Vector of MO symmetries (see HartreeFock output).
 • fcisolver_conv_tol = float -- converge threshold. Default is ${10}^{-18}$.
 • fcisolver_davidson_only = boolean -- use the Davidson diagonalization method to find the ground-state eigenvalues.
 • fcisolver_level_shift = float -- level shift for the Davidson diagonalization. Default is ${10}^{-3}$.
 • fcisolver_lindep = float -- linear dependence threshold for AH solver. Default is ${10}^{-10}$.
 • fcisolver_max_cycle = posint -- max number of iterations. Default is 50.
 • fcisolver_max_space = posint -- space size to hold trial vectors. Default is 12.
 • fcisolver_nroots = posint -- number of eigenvalues to be computed. When nroots >1, it affects shape of the return value.
 • fcisolver_pspace_size = posint -- size of Hamiltonian to improve Davidson preconditioner. Default is 50.

Attributes for Hartree Fock:

 • conv_tol_hf = float -- converge threshold. Default is ${10}^{-10}.$
 • diis_hf = boolean -- whether to employ diis. Default is true.
 • diis_space_hf = posint -- diis's space size. By default, 8 Fock matrices and error vectors 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 au) 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".

References

 1 B. O. Roos, P. R. Taylor, and P. E.M. Siegbahn, Chem. Phys. 48, 157-173 (1980). "A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach"
 2 T. Helgaker, P. Jorgensen, and J. Olsen, Molecular Electronic-Structure Theory (John Wiley & Sons, New York, 2000).

Examples

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

An active space CI calculation of the  molecule

 >
 ${\mathrm{molecule}}{≔}\left[\left[{"H"}{,}{0}{,}{0}{,}{0}\right]{,}\left[{"F"}{,}{0}{,}{0}{,}{0.95000000}\right]\right]$ (1)
 > $\mathrm{output_hf}≔\mathrm{ActiveSpaceCI}\left(\mathrm{molecule},\left[6,4\right],\mathrm{basis}="dz"\right)$
 ${\mathrm{table}}{}\left({\mathrm{%id}}{=}{18446744890356437854}\right)$ (2)
 >