CoupledCluster (Mac OS X and Linux Only)
an electron correlation method based on excitations from the Hartree-Fock wavefunction
list of lists; each list has 4 elements, the string of an atom's symbol and atom's x, y, and z coordinates
(optional) equation(s) of the form option = value where option is one of symmetry, unit, max_memory, frozen, max_cycle, conv_tol, conv_tol_normt, diis_space, diis_start_cycle, ccsdt, nuclear_gradient, return_rdm, populations, diis_start_energy_diff, 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, max_memory_scf_hf, nuclear_gradient_hf, populations_hf
The coupled cluster method includes electron correlation through a basis of excitations from the Hartree-Fock determinant wavefunction. Unlike truncated configuration interaction, the coupled cluster method includes the excitations through an exponential ansatz that ensures size extensivity. A method is size extensive if and only if its energy scales linearly with system size. Truncation of the excitations generates a hierarchy of coupled cluster methods. For example, the coupled cluster method with single and double excitations, known as CCSD, includes single and double excitations with higher excitations approximated as products of these lower excitations. The CoupledCluster command currently implements CCSD as the default. The energy from coupled cluster with a single, double, and perturbative triple excitations [CCSD(T)] can be computed by setting the keyword ccsdt = true. The CoupledCluster command is only available on the MacOS X and Linux platforms. The Parametric2RDM method can also be employed to obtain energies and properties with an accuracy similar to that of CCSD and CCSD(T).
The table of following contents:
float -- total electronic energy of the system
float -- the difference between the coupled cluster energy and the Hartree-Fock energy
Matrix -- coefficients expressing molecular (natural) orbitals (columns) in terms of atomic orbitals (rows)
Vector -- molecular (natural) orbital occupations
float -- total electronic energy of the system calculated by MP2 method
Vector -- string label for each atomic orbital consisting of the atomic symbol and the orbital name
integer -- 1 or 0, indicating whether the calculation is converged or not
Matrix -- coupled clusters' one-electron transition amplitudes
Array -- coupled clusters' two-electron transition amplitudes
Matrix -- the analytical nuclear gradients
float -- the coupled cluster energy including single, double, and perturbative triple excitations [CCSD(T)]
Matrix -- one-particle reduced density matrix (1-RDM) in molecular-orbital (MO) representation
Array -- two-particle reduced density matrix (2-RDM) in molecular-orbital (MO) representation
Matrix -- atomic-orbital populations
Vector -- dipole moment according to its x, y and z components
Vector -- atomic charges from the populations
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.
ccsdt = boolean -- option to return the energy from CCSD(T). Default is false.
frozen = set -- set of orbitals to be frozen.
unit = string -- "Angstrom" or "Bohr". Default is "Angstrom".
max_memory = posint -- allowed memory in MB. Default is 4000.
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.
initial_mo = Matrix -- Matrix of MOs (columns) in terms of atomic orbitals (rows) that defines the MO basis set.
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".
max_cycle = int -- max number of iterations. Default is 50.
conv_tol = float -- converge threshold. Default is 10−10.
conv_tol_normt = float -- converge threshold for norm of coupled cluster transition amplitude. Default is 10−5.
diis_space = int -- DIIS space size. By default, 8 Fock matrices and errors vector are stored
diis_start_cycle = int -- the step to start DIIS. Default is 0.
diis_start_energy_diff = float -- the energy difference threshold to start DIIS. Default is 10−10.
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".
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.
max_memory_scf_hf = posint -- allowed memory in MB. Default is 4000.
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".
G. D. Purvis III and R. J. Bartlett, J. Chem. Phys. 76, 1910 (1982). "A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples"
R. J. Bartlett and M. Musiał, Rev. Mod. Phys. 79, 291 (2007). "Coupled-cluster theory in quantum chemistry"
A coupled cluster calculation of the hydrogen fluoride HF molecule
molecule ≔ H,0,0,0,F,0,0,0.95;
output_hf ≔ CoupledClustermolecule, basis=dz;
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