HartreeFock - Maple Help

QuantumChemistry

 HartreeFock
 compute the ground state energy of a molecule with each electron in the mean field of the other electrons

 Calling Sequence HartreeFock(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, conv_tol, diis, diis_space, diis_start_cycle, direct_scf, direct_scf_tol, level_shift_factor, max_cycle, nuclear_gradient, populations, excited_states, nstates

Description

 • The Hartree Fock (HF) method computes the energy of a many-electron atom or molecule with each electron in the mean field of the other electrons.
 • Formally, the many-electron wavefunction in HF is approximated as an antisymmetrized product of orbitals, known as a Slater determinant.  The Hartree-Fock energy is an upper bound on the ground-state energy by the variational principle.  It is the lowest energy possible from a trial wave function that is a single Slater determinant.
 • Practically, for an N-electron atom or molecule HF solves for a set of N orbitals that satisfy the Hartree-Fock equations that approximate the electron-electron repulsion as a effective one-electron potential.  The effective one-electron potential contains two terms known as Coulomb and exchange terms.
 • Because wavefunction from the Hartree-Fock method can be expressed as a product of orbitals, it is said to be not correlated.  The correlation energy of the Hartree-Fock method, by definition, is zero.
 • Excited states can be computed by setting the optional keyword excited_states to true (default is false) or one of the strings, "TDHF" or "CIS".  When set to true or "TDHF", the excited states are computed by the time-dependent Hartree-Fock (TDHF) method; when set to "CIS", they are computed by the configuration interaction singles (CIS) method.

Outputs

The table of following contents:

 ${t}\left[{\mathrm{e_tot}}\right]$ - float -- total electronic energy of the system ${t}\left[{\mathrm{mo_coeff}}\right]$ - Matrix -- coefficients expressing molecular orbitals (columns) in terms of atomic orbitals (rows) ${t}\left[{\mathrm{mo_occ}}\right]$ - Vector -- molecular orbital occupations ${t}\left[{\mathrm{mo_energy}}\right]$ - Vector -- energies of the molecular orbitals ${t}\left[{\mathrm{mo_symmetry}}\right]$ - Vector -- string labels of the irreducible representations of the molecular orbitals ${t}\left[{\mathrm{group}}\right]$ - string -- name of the molecule's point group symmetry ${t}\left[{\mathrm{aolabels}}\right]$ - 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 ${t}\left[{\mathrm{rdm1}}\right]$ - Matrix -- one-particle reduced density matrix (1-RDM) in the atomic-orbital basis set ${t}\left[{\mathrm{nuclear_gradient}}\right]$ - Matrix -- analytical nuclear gradient ${t}\left[{\mathrm{dipole}}\right]$ - 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 ${t}\left[{\mathrm{excited_state_energies}}\right]$ - Vector -- energies of excited states ${t}\left[{\mathrm{excited_state_spins}}\right]$ - Vector -- spin of excited states ${t}\left[{\mathrm{transition_dipoles}}\right]$ - Matrix -- transition dipoles ${t}\left[{\mathrm{oscillator_strengths}}\right]$ - Vector -- oscillator strengths ${t}\left[{\mathrm{rtm1}}\right]$ - Matrix -- 1-electron reduced transition matrices with each matrix stored as a column vector

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.
 • 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.
 • excited_states = boolean/string -- options to compute excited states: true ("TDHF"), false (default), "TDHF", and "CIS".
 • nstates = posint/list -- number of excited states: integer n or list [p,q] where p is the number of singlets and q is the number of triplets and n is interpreted as [n,n] (default is 6).

References

 1 D. R. Hartree, Math. Proc. Camb. Phil. Soc. 24, 111-132 (1928). The wave mechanics of an atom with a non-Coulomb central field. Part II. Some results and discussion
 2 V. Fock, Z. Physik 61, 126-148 (1930). Näherungsmethode zur lösung des quantenmechanischen mehrkörperproblems
 3 C. C. J. Roothaan, Rev. Mod. Phys. 23, 69–89 (1951). "New developments in molecular orbital theory"
 4 A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover Books, New York, 1996).

Examples

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

A Hartree-Fock calculation of the  molecule

 >
 ${\mathrm{molecule}}{≔}\left[\left[{"H"}{,}{0}{,}{0}{,}{0}\right]{,}\left[{"F"}{,}{0}{,}{0}{,}{0.95000000}\right]\right]$ (1)
 >
 ${\mathrm{table}}{}\left({\mathrm{%id}}{=}{18446745128648484254}\right)$ (2)
 >