Restricted Open-shell Calculations

ROHF does not include spin polarization. Thus, it is not useful for some purposes, such as predicting EPR spectra. Also because of this, it cannot reliably predict spin densities. 

Within some programs, the ROMPn methods do not support analytic gradients. Thus, the fastest way to run the calculation is as a single point energy calculation with a geometry from another method. If a geometry optimization must be done at this level of theory, a non-gradient-based method such as the Fletcher-Powell optimization should be used. 

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. 

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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. 

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. 

Choose LHH(spin Unrestricted Hartree-Fock) or RHF (spin Restricted Ilartree-Fock) calculations according to your molecular system. HyperChem supports UHF for both open-sh el I and closed-shell calcii lation s an d RHF for cUised-shell calculation s on ly, Th e closed-shell LHFcalculation may be useful for studyin g dissociation of m olectilar system s. ROHF(spin Restricted Open-shell Hartree-Fock) is not supported in the current version of HyperChem (for ah initio calculations). 

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) ... 

Perturbative approximation methods are usually based on the Mpller-Plesset (MP) perturbation theory for correcting the HF wavefunction. Energetic corrections may be calculated to second (MP2), third (MP3), or higher order. As usual, the open- versus closed-shell character of the wavefunction can be specified by an appropriate prefix, such as ROMP2 or UMP2 for restricted open-shell or unrestricted MP2, respectively. 

Lately, the CP-MD approach has been combined with a mixed QM/MM scheme [10-12] which enables the treatment of chemical reactions in biological systems comprising tens of thousands of atoms [11, 26]. Furthermore, CP-MD and mixed QM/MM CP-MD simulations have also been extended to the treatment of excited states within a restricted open-shell Kohn-Sham approach [16, 17, 27] or within a linear response formulation of TDDFT [16, 18], enabling the study of biological photoreceptors [28] and the in situ design of optimal fluorescence probes with tailored optical properties [32]. Among the latest extensions of this method are also the calculation of NMR chemical shifts [14]. 

In this paper we present the approach [44] in more detail and add to the results obtained in Ref. [44] the results of calculation of the YBa2Cu307 ceramics at the restricted open shell Hartree-Fock (ROHF) level. The ROHF, UHF and MP2 calculations with the same basis set allow to study the influence of the electron correlation at different levels. As follows from the results obtained, the electron correlation has an essential or in some cases a crucial influence on charge and spin distributions in the superconducting YBa2Cu307 ceramics. 

The results obtained up to this point show that the amount of spin contamination was crucial to obtain good results for this system. We found that even small spin contamination leads, in some cases, to disparate charge distributions. Thus, we used the restricted open shell procedure (ROHF) to calculate an initial guess for the UHF calculation. Since the ROHF solution has the correct value of the spin, it was found that it provides a better starting point for the UHF procedure. Unfortunately it is not a final solution to this problem because we found some cases where even this procedure leads to a very large spin contamination. 

Calculated geometries for a small number of diatomic and small polyatomic free radicals are compared with experimental structures in Table 5-18. These have been drawn from a somewhat larger collection provided in Appendix A5 (Tables A5-50 to A5-57). Except for triplet oxygen, all radicals possess a single unpaired electron (they are doublets). The usual set of theoretical models has been examined. All calculations involve use of the unrestricted open-shell SCF approach, where electrons of different spin occupy different orbitals, as opposed to the restricted open-shell SCF approach, where paired electrons are confined to the same orbital (see Chapter 2 for more detailed discussion). 

EOMCCSD(T) calculations, while facilitating the open-shell implementation of the CR-EOMCCSD(T) method employing the restricted open-shell Hartree-Fock (ROHE) orbitals [59]. Indeed, the use of spin-orbital energy differences (ca -f -f Cc — — ej — e ) instead of the complete form of the diagonal matrix elements of involving triply excited determinants to... 

All the calculations of F2 are carried out with a simple basis set of double-zeta polarization type, the standard 6-31G(d) basis set, and are performed at a fixed interatomic distance of 1.44 A, which is approximately the optimized distance for a full Cl calculation in this basis set. Only the corresponding orbitals are referred to as the active orbitals , while the orbitals representing the lone pairs, so-called spectator orbitals , remain doubly occupied in all calculations. A common point to the various VB methods we use, except the VBCI method, is that at the dissociation limit, the methods converge to two F fragments at the restricted-open-shell Hartree Fock (ROHF) level. 

All calculations were carried out within the approximation of intermediate neglect of differential overlap (37-42) (INDO-RHF-SCF) which includes parameterization for transition metals. A restricted open-shell formalism, developed by Zerner et al. (37,38), was employed to prevent spin contamination and to make the quantitative evaluation of the relative spin state energies possible. This method has been used successfully to study simple transition metal complexes like [FeCl ]" (42), [CuCl ]2" ( ), and ferrocene ( ) as well as larger and more complicated systems like model oxyheme (61) and carbonylheme ( ) and model oxyhorseradish peroxidase ( ) complexes. 

Analytic Energy Gradients for Open-Shell Coupled-Cluster Singles and Doubles Calculations Using Restricted Open-Shell Hartree-Fock (ROHE) Reference Functions. 

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