Hartree open-shell species

So far there have not been any restrictions on the MOs used to build the determinantal trial wave function. The Slater determinant has been written in terms of spinorbitals, eq. (3.20), being products of a spatial orbital times a spin function (a or /3). If there are no restrictions on the form of the spatial orbitals, the trial function is an Unrestricted Hartree-Fock (UHF) wave function. The term Different Orbitals for Different Spins (DODS) is also sometimes used. If the interest is in systems with an even number of electrons and a singlet type of wave function (a closed shell system), the restriction that each spatial orbital should have two electrons, one with a and one with /3 spin, is normally made. Such wave functions are known as Restricted Hartree-Fock (RHF). Open-shell systems may also be described by restricted type wave functions, where the spatial part of the doubly occupied orbitals is forced to be the same this is known as Restricted Open-shell Hartree-Fock (ROHF). For open-shell species a UHF treatment leads to well-defined orbital energies, which may be interpreted as ionization potentials. Section 3.4. For an ROHF wave function it is not possible to chose a unitary transformation which makes the matrix of Lagrange multipliers in eq. (3.40) diagonal, and orbital energies from an ROHF wave function are consequently not uniquely defined, and cannot be equated to ionization potentials by a Koopman type argument. 

The common way to treat free radicals is with the unrestricted Hartree-Fock method or UHF method. In this method, we employ separate spatial orbitals for the oc and the jl electrons, giving two sets of MO s, one for oc and one for fj electrons. Less commonly, free radicals are treated by the restricted open-shell Hartree-Fock or ROHF method, in which electrons occupy MO s in pairs as in the RHF method, except for the unpaired electron(s). The theoretical treatment of open-shell species is discussed in various places in references [1] and in [12]. 

DODS) is also sometimes used. If the interest is in systems with an even number of electrons and a singlet type of wave function (a closed shell system), the restriction that each spatial orbital should have two electrons, one with a and one with j3 spin, is normally made. Such wave functions are known as Restricted Hartree-Fock (RHF). Open-shell systems may also be described by restricted type wave functions, where the spatial part of the doubly occupied orbitals is forced to be the same this is known as Rp.strirted Open-shell Hartree-Fock (RQHF). For open-shell species a UHF treatment... 

Brouwer and Wilbrandt have applied resonance Raman spectroscopy and calculations to questions of structure of amine radical cations [73]. Well-resolved Raman spectra of trialkylamine radical cations that are so short-lived that their electrochemical oxidation waves are irreversible may be obtained at room temperature in solution by photoionization and time-resolved detection. Comparison of the observed spectrum with calculations for various isomers provides a powerful method of answering structural questions. Density-functional calculations prove much easier to apply to open-shell species than Hartree-Fock calculations, which require cumbersome and expensive corrections to introduce suffieient electron correlation to eonsider questions like the charge distribution of disubstituted piperazine (1,4-diazacyclohexane) radical cations. The dimethyl- and diphenyl-substituted piperazine radical cations are delocalized, but charge is localized on one ArN unit of the dianisyl-substituted compound [73dj. 

G bases, except for the anions for which the MP2 energies were calculated in the former basis set only. Excitations from the core electrons were not included in the MP2 treatment. The restricted Hartree-Fock (RHF) method was used for the closed-shell molecules (parents and anions) and the unrestricted Hartree-Fock (UHF) method was applied to the spin doublet open-shell species (radicals and cations). Both methods are variants of the SCF approximation. A fuller description and explanation of the basis set and methods has been given previously8. 

PCMODEL contains sixty atom types and generalized parameters, as well as functions and parameters for transition metals, and thus the built-in MMX force field minimizations provide some of the most complete molecular modeling available. Unrestricted Hartree-Fock tt calculations for conjugated systems provide unparalleled accuracy for molecular mechanics calculations of open-shell species. Standard RHF n calculations can be used to model closed-shell species containing carbon, nitrogen, and oxygen. Also, specific aromatic carbon types provide excellent aromatic geometries without n calculations. 

Although P3 procedures perform well for a variety of atomic and molecular species, caution is necessary when applying this method to open-shell reference states. Systems with broken symmetry in unrestricted Hartree-Fock orbitals should be avoided. Systems with high multireference character are unlikely to be described well by the P3 or any other diagonal approximation. In such cases, a renormalized elec-... 

Many molecules of acute chemical interest are charged in particular many species containing transition metal atoms are anions. Sometimes these anions are closed-shell, sometimes open-shell. There exists a formal proof that the solutions of the (differential, GUHF) Hartree-Fock equations actually exist for neutral systems and cations. The proof apparently cannot be extended to anions all that can be proved is that a molecule with n -t-1 electrons is stable if the net nuclear charge sum is n 4- where may be small but non-zero. This means that the existence of the solutions of the Hartree-Fock equations for anions is contingent on the particular case in some cases the solutions will exist, in other cases not. Clearly, it is extremely unlikely that the Hartree-Fock equations for multiply charged anions will exist. 

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