CoupledCluster - Maple Help

QuantumChemistry

 CoupledCluster (Mac OS X and Linux Only)
 an electron correlation method based on excitations from the Hartree-Fock wavefunction

 Calling Sequence CoupledCluster(molecule, 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 options - (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

Description

 • 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).

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 coupled cluster energy and the Hartree-Fock energy ${t}\left[{\mathrm{mo_coeff}}\right]$ - Matrix -- coefficients expressing molecular (natural) orbitals (columns) in terms of atomic orbitals (rows) ${t}\left[{\mathrm{mo_occ}}\right]$ - Vector -- molecular (natural) orbital occupations ${t}\left[{\mathrm{e_tot_mp2}}\right]$ - float -- total electronic energy of the system calculated by MP2 method ${t}\left[{\mathrm{aolabels}}\right]$ - Vector -- string label for each atomic orbital consisting of the atomic symbol and the orbital name ${t}\left[{\mathrm{converged}}\right]$ - integer -- 1 or 0, indicating whether the calculation is converged or not ${t}\left[{\mathrm{t1}}\right]$ - Matrix -- coupled clusters' one-electron transition amplitudes ${t}\left[{\mathrm{t2}}\right]$ - Array -- coupled clusters' two-electron transition amplitudes ${t}\left[{\mathrm{nuclear_gradient}}\right]$ - Matrix -- the analytical nuclear gradients ${t}\left[{\mathrm{e_tot_ccsdt}}\right]$ - float -- the coupled cluster energy including single, double, and perturbative triple excitations [CCSD(T)] ${t}\left[{\mathrm{rdm1}}\right]$ - Matrix -- one-particle reduced density matrix (1-RDM) in molecular-orbital (MO) representation ${t}\left[{\mathrm{rdm2}}\right]$ - Array -- two-particle reduced density matrix (2-RDM) in molecular-orbital (MO) representation ${t}\left[{\mathrm{populations}}\right]$ - Matrix -- atomic-orbital populations ${t}\left[{\mathrm{dipole}}\right]$ - Vector -- dipole moment according to its x, y and z components ${t}\left[{\mathrm{charges}}\right]$ - Vector -- atomic charges from the populations

 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.
 • unit = string -- "Angstrom" or "Bohr". Default is "Angstrom".
 • max_memory = posint -- allowed memory in MB. Default is 4000.
 • frozen = set -- set of orbitals to be frozen.
 • 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.
 • 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".
 • 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".
 • ccsdt = boolean -- option to return the energy from CCSD(T).  Default is false.

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".

References

 1 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"
 2 R. J. Bartlett and M. Musiał, Rev. Mod. Phys. 79, 291 (2007). "Coupled-cluster theory in quantum chemistry"

Examples

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

A coupled cluster calculation of the  molecule

 >
 ${\mathrm{molecule}}{≔}\left[\left[{"H"}{,}{0}{,}{0}{,}{0}\right]{,}\left[{"F"}{,}{0}{,}{0}{,}{0.95000000}\right]\right]$ (1)
 >
 ${\mathrm{table}}{}\left({\mathrm{%id}}{=}{18446744078426156798}\right)$ (2)
 >