Open-shell calculation

For an open-shell system, try converging the closed-shell ion of the same molecule and then use that as an initial guess for the open-shell calculation. Adding electrons may give more reasonable virtual orbitals, but as a general rule, cations are easier to converge than anions. 

When it has been shown that the errors introduced by spin contamination are unacceptable, restricted open-shell calculations are often the best way to obtain a reliable wave function. 

A spin projected result does not give the energy obtained by using a restricted open-shell calculation. This is because the unrestricted orbitals were optimized to describe the contaminated state, rather than the spin-projected state. In cases of very-high-spin contamination, the spin projection may fail, resulting in an increase in spin contamination. 

Many transition metal systems are open-shell systems. Due to the presence of low-energy excited states, it is very common to experience problems with spin contamination of unrestricted wave functions. Quite often, spin projection and annihilation techniques are not sufficient to correct the large amount of spin contamination. Because of this, restricted open-shell calculations are more reliable than unrestricted calculations for metal system. Spin contamination is discussed in Chapter 27. 

Both HF and DFT calculations can be performed. Supported DFT functionals include LDA, gradient-corrected, and hybrid functionals. Spin-restricted, unrestricted, and restricted open-shell calculations can be performed. The basis functions used by Crystal are Bloch functions formed from GTO atomic basis functions. Both all-electron and core potential basis sets can be used. 

Open shell systems—for example, those with unequal numbers of spin up and spin down electrons—are usually modeled by a spin unrestricted model (which is the default for these systems in Gaussian). Restricted, closed shell calculations force each electron pair into a single spatial orbital, while open shell calculations use separate spatial orbitals for the spin up and spin down electrons (a and P respectively) ... 

In Gaussian, open shell calculations are requested by prepending the method keyword with a U (for unrestricted) similarly, closed shell calculations use an initial R (for example, RHF versus UHF, RMP2 versus UMP2 and so on). ... 

Since we knew molecular oxygen is a triplet, we should have performed this calculation as an open shell calculation. 

Hurst, R. P., Gray, J. D., Brigman, G. H., and Matsen, F. A., Mol. Phys. 1, 189, "Open shell calculations for two- and three-electron ions." The improvement over closed shell calculations becomes less with increasing atomic number. 

For all results in this paper, spin-orbit coupling corrections have been added to open-shell calculations from a compendium given elsewhere I0) we note that this consistent treatment sometimes differs from the original methods employed by other workers, e.g., standard G3 calculations include spin-orbit contributions only for atoms. In the SAC and MCCM calculations presented here, core correlation energy and relativistic effects are not explicitly included but are implicit in the parameters (i.e., we use parameters called versions 2s and 3s in the notation of previous papers 11,16,18)). 

The coupled cluster calculations involved in Wlc theory were carried out using MOLPRO 2002.3. (7P) (For the open-shell calculations on the constituent atoms, the definition of the open-shell CCSD and CCSD(T) energies in Ref. (20) was employed.) The density functional calculations were carried out using a modified version of Gaussian 98 rev. All (27), as were the Gn theory (22-24) and CBS-n (25) calculations. 

Kroto and Santy sl> have used the CNDO/2 method to calculate bond angles of a few molecules in their excited states. Again their results seem good. Subsequently 68>, they performed a far more laborious open-shell calculation which resulted in only slightly improved bond angles. 

Open-shell calculations, 13 Optimization methods, 3 Organometallics, 6... 

Open-shell calculations have also been carried out on derivatives of 2 in order to compare their calculated and experimental ionization potentials (Section IX.B) (89JA1181). Although Koopman s theorem (69IJMS419) proposes an absolute correspondence between the orbital energies and the ionization potentials, it is not observed in this case the first ionization potentials are consistently some 1.5-2 eV too high. This is discussed more fully in Section IX.B. 

Very interesting information from high-resolution ESR or from ENDOR spectroscopy concerns the distribution of the unpaired electron in the paramagnetic molecular cation the spin population can be determined experimentally from the electron/nuclear spin coupling, whereas the charge distribution has to be approximated by (open-shell) calculations. As concerns Me3SiCH2-substituted n radical cations, the spin population pn... 

Refer also to the discussion of open shell calculations in Chapter 1 (page 10). 

The SCF method of Longuet-Higgins and Pople 20) (LHP) became rather popular in semiempirical open-shell treatments and the majority of the reported semiempirical open-shell calculations have been based on it, thus we consider it expedient to describe it in detail in this section. Longuet-Higgins and Pople formulated 20) the following effective Hamiltonian... 

The position of the benzene radical ions among the other benzenoid systems is somewhat exceptional. The presence of the degenerate frontier molecular orbitals makes it difficult to perform standard open-shell calculations because the LHP method is inherently incapable of accommodating systems of this type and the Roothaan procedure diverges here The simple Cl treatments based on the HMO computational... 

In the case of a planar (C2v) formaldehyde molecule, direct open-shell calculations are then possible for the Ai mz ), Az(nK ),... 

Furthermore, the frontier spin orbital diagram which was obtained from the unrestricted open-shell calculation suggests that the interaction in both the highest occupied spin orbitals was responsible for N—N bond in the hyponitrite moiety (Figure 59). 

In the final Section 3.8, we leave the restricted closed-shell formalism and derive and illustrate unrestricted open-shell calculations. We do not discuss restricted open-shell calculations. By procedures that are strictly analogous to those used in deriving the Roothaan equations of Section 3.4, we derive the corresponding unrestricted open-shell equations of Pople and Nesbet. To illustrate the formalism and the results of unrestricted calculations, we apply our standard basis sets to a description of the electronic structure and ESR spectra of the methyl radical, the ionization potential of N2, and the orbital structure of the triplet ground state of O2. Finally, we describe in some detail the application of unrestricted wave functions to the improper behavior of restricted closed-shell wave functions upon dissociation. We again use our minimal basis H2 model to make the discussion concrete. 

In this subsection, we describe restricted closed-shell calculations on the ground state of H2. As we will see, there is a very basic deficiency in such calculations at long bond lengths. Later in this chapter, when we describe unrestricted open-shell calculations, we will return to minimal basis H2 and partially correct this deficiency. Some of the results obtained here will also be used in later chapters when we use the minimal basis H2 model to illustrate procedures that go beyond the Hartree-Fock approximation. 

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