Restricted open-shell

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). 

Another way of constructing wave functions for open-shell molecules is the restricted open shell Hartree-Fock method (ROHF). In this method, the paired electrons share the same spatial orbital thus, there is no spin contamination. The ROHF technique is more difficult to implement than UHF and may require slightly more CPU time to execute. ROHF is primarily used for cases where spin contamination is large using UHF. 

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. 

If spin contamination is small, continue to use unrestricted methods, preferably with spin-annihilated wave functions and spin projected energies. Do not use spin projection with DFT methods. When the amount of spin contamination is more significant, use restricted open-shell methods. If all else fails, use highly correlated methods. 

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. 

RHF (restricted Hartree-Fock) ah initio method for singlet systems ROHF (restricted open-shell Hartree-Fock) ah initio method for open-shell systems... 

It is also possible to define spin restricted open shell models (keyword prefix RO). See he Gaussian User s Reference for more information. 

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. 

In the unrestricted treatment, the eigenvalue problem formulated by Pople and Nesbet (25) resembles closely that of closed-shell treatments.-On the other hand, the variation method in restricted open-shell treatments leads to two systems of SCF equations which have to be connected in one eigenvalue problem (26). This task is not a simple one the solution was done in different ways by Longuet-Higgins and Pople (27), Lefebvre (28), Roothaan (29), McWeeny (30), Huzinaga (31,32), Birss and Fraga (33), and Dewar with co-workers (34). 

It is possible to construct a HF method for open-shell molecules that does maintain the proper spin symmetry. It is known as the restricted open-shell HF (ROHF) method. Rather than dividing the electrons into spin-up and spin-down classes, the ROHF method partitions the electrons into closed- and open-shell. In the easiest case of the high-spin wavefunction ( op = — electrons in op... 

Filatov, M., Shaik, S., 1999, Application of Spin-Restricted Open-Shell Kohn-Sham Method to Atomic and Molecular Multiplet States , J. Chem. Phys., 110, 116. 

Langer H, Doltsinis NL (2003) Excited state tautomerism of the DNA base guanine a restricted open-shell kohn-sham study. J Chem Phys 118 5400-5407... 

To distinguish between closed-shell and open-shell configurations (and determinants), one may generally include a prefix to specify whether the starting HF wavefunction is of restricted closed-shell (R), restricted open-shell (RO), or unrestricted (U) form. (The restricted forms are total S2 spin eigenfunctions, but the unrestricted form need not be.) Thus, the abbreviations RHF, ROHF, and UHF refer to the spin-restricted closed-shell, spin-restricted open-shell, and unrestricted HF methods, 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. 

---