Note

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OPEN

Defines the distribution of electrons over partially occupied orbitals for open-shell Hartree-Fock calculations.

SYNTAX: OPEN(m,n)

Distribute \(m\) electrons uniformly over \(n\) orbitals.

In an open-shell RHF calculation, the total number of electrons minus \(m\) must be an even number so that they can doubly occupy the lowest-energy orbitals. The remaining \(m\) electrons are uniformly spread over the \(n\) lowest-energy unoccupied orbitals with an occupation of \(m/n\) per orbital. These fractional orbital occupations represent a statistical superposition over alpha and beta spins, with an independent \(m/(2n)\) probability of the orbital containing an alpha and beta electron. For valid occupation probabilities, \(m \le 2n\) must be satisfied.

The OPEN keyword in an RHF calculation also expands the set of active orbitals to include the partially occupied orbitals. The active space can be further expanded using the C.I. keyword, but the new active space must contain all partially occupied orbitals or MOPAC will report an error.

In a UHF calculation, the total number of alpha minus \(m\) fully occupy the lowest-energy alpha orbitals. The remaining \(m\) alpha electrons are uniformly spread over the \(n\) lowest-energy unoccupied alpha orbitals with an occupation over \(m/n\) per orbital. For valid occupation probabilities, \(m \le n\) must be satisfied. Fractional occupations can also be applied to minority-spin electrons by using negative values of MS (alpha becomes the minority spin type). Unlike in RHF calculations, MOPAC is unable to correct the Fock exchange penalties in UHF calculations with fractional occupations, and their potential energy surfaces can only be directly compared to other UHF calculations with the same OPEN settings.

The primary uses of the OPEN keyword are to approximate spin states in open-shell RHF calculations and to mimic the dynamic Jahn-Teller effect in UHF calculations. Jahn-Teller distortions open energy gaps within a set of degenerate orbitals that are partially occupied, inducing a subset of fully-occupied, lower-energy orbitals and a subset of unoccupied, higher-energy orbitals. By spreading electrons uniformly over these degenerate orbitals, the Jahn-Teller distortion can be suppressed.

For the use of OPEN to be physically meaningful in a ground-state calculation, the fractionally occupied orbitals should maintain an orbital energy degeneracy. Otherwise, with fractional occupations over orbitals of different energies, the ground-state energy could be further lowered by shifting occupations towards the lower-energy orbitals.