Closed-shells calculations

Choose UHF (spin Unrestricted Hartree-Fock) or RHF (spin Restricted Hartree-Fock) calculations according to your molecular system. HyperChem supports UHF for both open-shell and closed-shell calculations and RHF for closed-shell calculations only. The closed-shell UHF calculation may be useful for studying dissociation of molecular systems. ROHF (spin Restricted Open-shell Hartree-Fock) is not supported in the current version of HyperChem (for ab initio calculations). 

Although not strictly part of a model chemistry, there is a third component to every Gaussian calculation involving how electron spin is handled whether it is performed using an open shell model or a closed shell model the two options are also referred to as unrestricted and restricted calculations, respectively. For closed shell molecules, having an even number of electrons divided into pairs of opposite spin, a spin restricted model is the default. In other words, closed shell calculations use doubly occupied orbitals, each containing two electrons of opposite spin. 

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). ... 

The simplest antisymmetric function that is a combination of molecular orbitals is a determinant. Before forming it, however, we need to account for a factor we ve neglected so far electron spin. Electrons can have spin up i+Vi) or down (-V2). Equation 20 assumes that each molecular orbital holds only one electron. However, most calculations are closed shell calculations, using doubly occupied orbitals, holding two electrons of opposite spin. For the moment, we will limit our discussion to this case. 

Part 2, Model Chemistries, begins with Chapter 5, Basis Set Effects. This chapter discusses the most important standard basis sets and presents principles for basis set selection. It also describes the distinction between open shell and closed shell calculations. 

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. 

Formerly, we used for < the value of 11.22 eV, which is commonly employed in closed-shell calculations, but a correct interpretation of ionization potentials requires (34) that Ic be equated to the ionization potential of methyl radical, 9.84 eV. This change, however, does not affect the values of transition energies. 

Generally only closed-shell calculations are required,... 

A comparison between BS and closed-shell calculations was shown for diamagnetic [Fe(CN)2(L)] (L = pentane-2,4-dione-bisGS-alkylisothiosemicarbazonato)) (1) (91,92). Through the... 

We note that the basis orbitals k(r) are common for both a and / spin electrons, therefore, the evaluation of one- and two-electron integrals has to be performed only once (or they can be taken over from the corresponding closed-shell calculations). The procedure analogous to the one applied for the closed-shell case leads to a set of coupled complex pseudo-eigenvalue equations of the form... 

Since most of the quantum mechanical calculations performed on bicyclobutane were closed shell calculations, they were incapable of revealing whether a biradical character exists in its central bond. Recently a calculation made by Schleyer and coworkers on the GVB/3-21G optimized geometry of bicyclobutane, assigned a 4% biradical character to this bond. 

Computer programs were MOLCAS 3 program system (25) for SCF, CASSCF, and CASPT2 calculations and the program TITAN for closed shell calculations (26). The new version of the COMENIUS program was used for open shell CCSD(T) calculations based on the spin adapted singly and doubly excited amplitudes (15, 27-29). These codes were supplemented by the generator of the no-pair hamiltonian written by B. A. Hess in all DK calculations. 

Go on and generate some integral calculation utilities so that we can do closed-shell calculations on any system... 

A GUHF calculation will involve twice as many basis functions as (e g.) a closed-shell calculation because the spin-basis functions axe used, not simply the spatial basis functions. However, unless one wants to be very eccentric and use different spatial basis functions in the definition of the spin-basis functions involving different spin factors, the basis is simply doubled Each spatial basis function is simply multiplied by the two spin factors to form a convenient spin-basis set. 

The physical interpretation of the MO coefficients is made easier if we have the information from the closed-shell calculation on the ground state of the neutral molecule available here it is in the same format. Notice that, in this case, there are only seven spatial basis functions in the expansion. 

The only way in which these codes differ from our earlier versions are in the definitions of CLOSED SHELL CALCULATION and UHF-CALCULATION which are defined to be two arbitrary (but different) integers. A small modification to the calculation of the total energy is required since, in the closed-shell case, the orbitals are doubly-occupied while in the UHF case they are just singly-occupied hence the multiplication of the total energy E by 0.5. 

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. 

At the beginning of this chapter we derived and discussed formal properties of the Hartree-Fock equations independent of any particular form for the spin orbitals. We then introduced a set of restricted spin orbitals and have since been concerned solely with restricted closed-shell calculations of the type... 

We give now the expressions for spin-restricted closed-shell calculations. For four fixed spatial orbitals referred to as p, q, r, and s, the Bethe-Salpeter kernel has the following spin structure ... 

The results of open- and closed-shell calculations implied that, ...the TSs should be regarded as closed-shell species with relatively little biradical character... . It was furthermore predicted that the rearrangement proceeds through a chair-like... 

All complexes, in both open-shell and closed shell calculations, are treated as single conjugated systems of Ti-electrons and the calculations are carried out within the tt-electron approximation. The aromatic rings are placed in parallel planes, and the atomic centers on each component of the complex are considered as non-neighbors... 

---