MOIntegrals - Maple Help

QuantumChemistry

 MOIntegrals
 compute the one- and two-electron integrals in the molecular-orbital basis set

 Calling Sequence MOIntegrals(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 basis, active, initial_mo, spin, charge, symmetry, frozen, unit, max_memory, conv_tol, diis, diis_space, diis_start_cycle, direct_scf, direct_scf_tol, level_shift_factor, max_cycle, nuclear_gradient, populations

Description

 • The MOIntegrals command generates the one- and two-electron integrals in the Hartree-Fock molecular-orbital basis set (default) or another molecular-orbital basis set specified by the optional keyword initial_mo.
 • If the active keyword is not specified, the output is a table of the following electron integrals: kinetic energy integrals, nuclear attraction integrals, overlap integrals, and electron repulsion integrals in chemistry notation ([ij,kl]) as well as the nuclear energy.
 • If the active keyword is specified, the output is a table of the following electron integrals: one-electron integrals and electron repulsion integrals in chemistry notation ([ij,kl]) as well as the nuclear and core energies.  Note that the core energy contains the energy of the core electrons as well as the nuclear energy.
 • The nuclear attraction integrals, kinetic energy integrals, and overlap integrals are one-electron integrals, and hence, they are returned as r×r matrices where r is the number of orbitals.
 • The electron repulsion integrals are organized in chemistry notation  ([ij,kl]) with only independent symmetric elements for both ij and kl pairs (i≥j and k≥l). For r orbitals the electron repulsion integrals are returned as a (r×(r+1)/2)×(r×(r+1)/2) Matrix M whose elements are given by M[k(k-1)/2+l,i(i-1)/2+j].

Outputs

The table has the following contents:

 ${t}\left[{\mathrm{electron_repulsion_integrals}}\right]$ - Matrix -- electron repulsion integrals - Matrix -- nuclear attraction integrals ${t}\left[{\mathrm{kinetic_energy_integrals}}\right]$ - Matrix -- kinetic energy integrals ${t}\left[{\mathrm{overlap_integrals}}\right]$ - Matrix -- overlap integrals ${t}\left[{\mathrm{nuclear_energy}}\right]$ - float -- nuclear energy

or with the active keyword given

 ${t}\left[{\mathrm{electron_repulsion_integrals}}\right]$ - Matrix -- electron repulsion integrals - Matrix -- nuclear attraction integrals ${t}\left[{\mathrm{core_energy}}\right]$ - float -- core energy including nuclear energy ${t}\left[{\mathrm{nuclear_energy}}\right]$ - float -- nuclear energy

Options

 • basis = string -- name of the basis set.  See Basis for a list of available basis sets.  Default is "sto-3g".
 • active = list -- [number of electrons, number of active orbitals]
 • initial_mo = list -- the basis of molecular orbitals (MOs) for the electron integrals can be specified 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).  If the keyword initial_mo is not given, then the electron integrals are computed with the Hartree-Fock MOs.
 • 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.
 • nuclear_gradient = boolean -- option to return the analytical nuclear gradient if available. Default is false.
 • populations = string -- atomic-orbital population analysis: "Mulliken" and "Mulliken/meta-Lowdin". Default is "Mulliken".
 • conv_tol = float -- converge threshold. Default is ${10}^{-10}.$
 • diis = boolean -- whether to employ diis. Default is true.
 • diis_space = posint -- diis's space size. By default, 8 Fock matrices and error vectors are stored.
 • diis_start_cycle = posint -- the step to start diis. Default is 1.
 • direct_scf = boolean -- direct SCF in which integrals are recomputed is used by default.
 • direct_scf_tol = float -- direct SCF cutoff threshold. Default is ${10}^{-13}.$
 • level_shift = float/int -- level shift (in au) for virtual space. Default is $0.$
 • max_cycle = posint -- max number of iterations. Default is 50.
 • frozen = set -- set of Hartree-Fock molecular orbitals to be frozen.

Examples

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

Consider the  molecule

 >
 ${\mathrm{molecule}}{≔}\left[\left[{"H"}{,}{0}{,}{0}{,}{0}\right]{,}\left[{"F"}{,}{0}{,}{0}{,}{0.95000000}\right]\right]$ (1)

Compute the MO integrals

 >
 ${\mathrm{table}}{}\left({\mathrm{%id}}{=}{36893488654136335900}\right)$ (2)

Or using the active keyword to specify a set of active electrons and orbitals

 >
 ${\mathrm{table}}{}\left({\mathrm{%id}}{=}{36893488654126190108}\right)$ (3)
 >