QuantumChemistry
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compute the ground state energy of a molecule with each electron in the mean field of the other electrons
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Calling Sequence
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HartreeFock(molecule, options)
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Parameters
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molecule
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list of lists; each list has 4 elements, the string of an atom's symbol and atom's x, y, and z coordinates
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options
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(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
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Description
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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.
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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.
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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.
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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.
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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.
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Outputs
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The table of following contents:
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float -- total electronic energy of the system
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Matrix -- coefficients expressing molecular orbitals (columns) in terms of atomic orbitals (rows)
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Vector -- molecular orbital occupations
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Vector -- energies of the molecular orbitals
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Vector -- string labels of the irreducible representations of the molecular orbitals
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string -- name of the molecule's point group symmetry
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Vector -- string label for each atomic orbital consisting of the atomic symbol and the orbital name
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integer -- 1 or 0, indicating whether the calculation is converged or not
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Matrix -- one-particle reduced density matrix (1-RDM) in the atomic-orbital basis set
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Matrix -- analytical nuclear gradient
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Vector -- dipole moment according to its x, y and z components
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Matrix -- atomic-orbital populations
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Vector -- atomic charges from the populations
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Vector -- energies of excited states
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Vector -- spin of excited states
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Matrix -- transition dipoles
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Vector -- oscillator strengths
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Matrix -- 1-electron reduced transition matrices with each matrix stored as a column vector
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Options
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basis = string -- name of the basis set. See Basis for a list of available basis sets. Default is "sto-3g".
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spin = nonnegint -- twice the total spin S (= 2S). Default is 0.
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charge = nonnegint -- net charge of the molecule. Default is 0.
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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.
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unit = string -- "Angstrom" or "Bohr". Default is "Angstrom".
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max_memory = posint -- allowed memory in MB. Default is 4000.
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excited_states = boolean/string -- options to compute excited states: true ("TDHF"), false (default), "TDHF", and "CIS".
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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).
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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.
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nuclear_gradient = boolean -- option to return the analytical nuclear gradient if available. Default is false.
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populations = string -- atomic-orbital population analysis: "Mulliken" and "Mulliken/meta-Lowdin". Default is "Mulliken".
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conv_tol = float -- converge threshold. Default is
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diis = boolean -- whether to employ diis. Default is true.
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diis_space = posint -- diis's space size. By default, 8 Fock matrices and error vectors are stored.
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diis_start_cycle = posint -- the step to start diis. Default is 1.
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direct_scf = boolean -- direct SCF in which integrals are recomputed is used by default.
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direct_scf_tol = float -- direct SCF cutoff threshold. Default is
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level_shift = float/int -- level shift (in au) for virtual space. Default is
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max_cycle = posint -- max number of iterations. Default is 50.
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References
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4.
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A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover Books, New York, 1996).
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Examples
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>
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A Hartree-Fock calculation of the molecule
>
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