ROHF model

Naturally, this model is a restricted or constrained model of molecular electronic structure (Restricted Open-shell Hartree-Fock, ROHF, say), and so may be expected to have an energy lying above that of the best (GUHF) single determinant and may well have some quantitative difficulties (the ROHF model of the P, ls 2p state of the lithium atom, for example will have no Fermi contact nuclear-spin electron-spin coupling since the unpaired electron density is zero at the nucleus). 

The general theory outlined in Chapter 14 has been used in the ROHF model. It can also provide the basis for a whole class of multi-determinant models of molecular electronic structure which are constructed from sets o/doubly occupied orbitals. Two such models are outlined in this chapter Paired-Electron MCSCF (PEMCSCF) and the General Valence Bond (GVB). These pair expansion theories are based on the idea of natural orbitals which diagonalise the one-electron density matrix. 

Agreement with experiment is not particularly good, and the ROHF method cannot give regions of negative spin density, since the spin density is just the sum of the squares of the partially occupied orbitals in this model. Corresponding calculations with the UHF method give Table 18.4. 

The procedure we follow is very similar to that of Harriman " . Again, as in the case of the 2-Fe ferredoxin model," these two methods, i.e. ROHF and... 

More subtle constraints due to the model being used the most common is the UHF/ROHF example to be discussed later. 

GAMES S is a program for ab initio molecular quantum chemistiy which can compute self-consistent field (SCF) wave functions ranging from restricted Hartree-Fock (RHF), ROHF, UHF, GVB, and MCSCF [47], Computation of the Hessian energy permits prediction of vibrational frequencies with IR or Raman intensities. Solvent effects may be modeled by the discrete Effective Fragment potentials or continuum models such as the polarizable continuum model [48]. Numerous relativistic computations are available, including infinite order two component scalar corrections, with various spin-orbit coupling options [49]. 

The extension of the RHF, ROHF and UHF LCAO methods to periodic systems is considered in the next sections. We begin this consideration from the discussion of specific features of these methods when instead of a molecular system the cyclic model of a crystal is introduced. 

In addition to being based on an incorrect physical model, ROHF calculations require the construction of multiple energy operators to treat the interactions of the electrons within and between the different manifolds of singly and doubly occupied MOs. The formulation of MBP theories in terms of ROHF MOs is also difficult and not unambiguous. Finally, as described in the section on ROHF calculations, they frequently give unphysical results, because they often lead to an artifact called symmetry breaking. 

However, even if one is not interested in modeling ESR spectra, preventing electrons of opposite spin from having different spatial distributions imposes a constraint on ROHF wavefunctions that has energetic consequences. For example, if one compares the ROHF energy of the planar allyl radical in C2J, symmetry (cf. below), where spin polarization is quite important, to that of the twisted species, where spin polarization of the electrons in the n bond is almost absent, one obtains a rotational barrier that is far too low (see Table 1), compared to the experimental value of 15 kcal/mol. 

CC calculations do provide a safe means for navigating between the Scylla of UHF spin contamination and the Charybdis of ROHF symmetry breaking for radicals. Cost is the main disadvantage of CC calculations. If performed with large polarized basis sets of the type required to obtain results of chemical accuracy, CCSD(T) and even CCSD calculations rapidly become prohibitively expensive as the size of the molecules on which they are performed increases. When they cannot be applied directly to the molecules under study, CC calculations on smaller model systems can sometimes be employed to validate the use of lower level procedures on the actual molecules of interest. This protocol has, in fact, proven useful in several recent studies. ... 

Calculations [145] were performed at the ROHF/6-31G and ROHF/D95v//6-31G levels on several model radicals and scaled to the known experimental electron affinities. This scaling was subsequently used in estimating the electron affinities of the DNA base radical intermediates. The... 

The Koopmans estimates of the vertical ionization potentials of radicals can be calculated from the energy of the lowest unoccupied molecular orbital (LUMO) of the nonradical cations in the geometry of the radicals [145]. Employing this method and using the ROHF/6-31G and ROHF/D95v//6-31G basis sets, ionization potentials were calculated. These results were then scaled to results found for experimentally known ionization potentials of several model compounds. The final results gave the estimates of vertical ionization potentials of the DNA adducts (shown in Figure 6). 

Figure 8 Koopmans energies (bold lines) and corrected vertical energies (doited lines) of CH3SH, CH3S"(H20)n (n=l-4) in gas phase and aqueous solution calculated at the ROHF/6-31G basis set. The results in aqueous phase are obtained through the use of the SCRF model and the Born charge term. The calculated vertical values were scaled to experiment [164]. Reproduced with permission from ref. [164].

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