ROHF Restricted Open Shell Hartree

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

ROHF Restricted open shell Hartree-Fock... 

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. 

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 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 common way to treat free radicals is with the unrestricted Hartree-Fock method or UHF method. In this method, we employ separate spatial orbitals for the oc and the jl electrons, giving two sets of MO s, one for oc and one for fj electrons. Less commonly, free radicals are treated by the restricted open-shell Hartree-Fock or ROHF method, in which electrons occupy MO s in pairs as in the RHF method, except for the unpaired electron(s). The theoretical treatment of open-shell species is discussed in various places in references [1] and in [12]. 

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. 

The choice of as the zeroth-order Hamiltonian requires the use of either a spin-restricted (closed-shell) Hartree-Fock (RHF) or spin-unrestricted Hartree-Fock (UHF) determinant as the zeroth-order (reference) wavefunction. Since spin-restricted open-shell Hartree-Fock (ROHF) reference functions are not eigenfunctions of the spin-orbital P, other partitionings are required (Refs. 127-134). 

Hes may be chosen, for example, as the restricted open-shell Hartree-Fock (ROHF) Hamiltonian of the many-electron system. 

Hyperfine couplings, in particular the isotropic part which measures the spin density at the nuclei, puts special demands on spin-restricted wave-functions. For example, complete active space (CAS) approaches are designed for a correlated treatment of the valence orbitals, while the core orbitals are doubly occupied. This leaves little flexibility in the wave function for calculating properties of this kind that depend on the spin polarization near the nucleus. This is equally true for self-consistent field methods, like restricted open-shell Hartree-Fock (ROHF) or Kohn-Sham (ROKS) methods. On the other hand, unrestricted methods introduce spin contamination in the reference (ground) state resulting in overestimation of the spin-polarization. 

The calculations on Ti2He were performed (30) using a basis set of triple zeta plus polarization quality, including / functions on Ti. For the singlet states, both restricted open-shell Hartree-Fock (ROHF) and FORS MCSCF reference wavefunctions were used, while ROHF reference wavefunctions were used for the triplet states. In order to account for dynamic electron correlation and obtain... 

As several density functionals became available in the Gaussian program (19, 20), it became possible to study their effect on the computed value of electron affinity with systematically enlarged basis sets. The plan of the present work is as follows (a) initial calculations were done using the Hartree-Fock methods (RHF, the restricted Hartree-Fock ROHF, the restricted open-shell Hartree-Fock UHF, the unrestricted open-shell Hartree-Fock), and various non-local density functionals, defined in Table 2, with several standard basis sets (Section 2) (b) a large, saturated sp basis set was systematically enlarged by adding polarization functions with exponents optimized in molecular Hartree-Fock and density-functional cal-... 

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