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Restricted Hartree Fock

A variation on the HF procedure is the way that orbitals are constructed to reflect paired or unpaired electrons. If the molecule has a singlet spin, then the same orbital spatial function can be used for both the a and P spin electrons in each pair. This is called the restricted Hartree-Fock method (RHF). [Pg.20]

Introductory descriptions of Hartree-Fock calculations [often using Rootaan s self-consistent field (SCF) method] focus on singlet systems for which all electron spins are paired. By assuming that the calculation is restricted to two electrons per occupied orbital, the computation can be done more efficiently. This is often referred to as a spin-restricted Hartree-Fock calculation or RHF. [Pg.227]

RHF (restricted Hartree-Fock) ah initio method for singlet systems ROHF (restricted open-shell Hartree-Fock) ah initio method for open-shell systems... [Pg.368]

Quantum mechanics calculations use either of two forms of the wave function Restricted Hartree-Fock (RHF) or Unrestricted Hartree-Fock (UHF). Use the RHF wave function for singlet electronic states, such as the ground states of stable organic molecules. [Pg.37]

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). [Pg.112]

You can order the molecular orbitals that are a solution to equation (47) according to their energy. Electrons populate the orbitals, with the lowest energy orbitals first. Anormal, closed-shell, Restricted Hartree Fock (RHF) description has a maximum of two electrons in each molecular orbital, one with electron spin up and one with electron spin down, as shown ... [Pg.220]

The Roothaan equations just described are strictly the equations for a closed-shell Restricted Hartree-Fock (RHF) description only, as illustrated by the orbital energy level diagram shown earlier. To be more specific ... [Pg.226]

A restricted Hartree-Fock description means that spin-up and spin-down electrons occupy the same spatial orbitals /j—there is no allowance for different spatial orbitals for different electron spins. [Pg.226]

This last Restricted Hartree-Fock (RHF) state, if allowed to go unrestricted, would probably result in the following UHF state ... [Pg.227]

A UHF wave function may also be a necessary description when the effects of spin polarization are required. As discussed in Differences Between INDO and UNDO, a Restricted Hartree-Fock description will not properly describe a situation such as the methyl radical. The unpaired electron in this molecule occupies a p-orbital with a node in the plane of the molecule. When an RHF description is used (all the s orbitals have paired electrons), then no spin density exists anywhere in the s system. With a UHF description, however, the spin-up electron in the p-orbital interacts differently with spin-up and spin-down electrons in the s system and the s-orbitals become spatially separate for spin-up and spin-down electrons with resultant spin density in the s system. [Pg.232]

Here we give the molecule specification in Cartesian coordinates. The route section specifies a single point energy calculation at the Hartree-Fock level, using the 6-31G(d) basis set. We ve specified a restricted Hartree-Fock calculation (via the R prepended to the HF procedure keyword) because this is a closed shell system. We ve also requested that information about the molecular orbitals be included in the output with Pop=Reg. [Pg.16]

So far, we have considered only the restricted Hartree-Fock method. For open shell systems, an unrestricted method, capable of treating unpaired electrons, is needed. For this case, the alpha and beta electrons are in different orbitals, resulting in two sets of molecular orbital expansion coefficients ... [Pg.264]

RHF Restricted Hartree-Fock (restricted means that there are no unpaired... [Pg.323]

Here, occ means occupied and virt means virtual. In the restricted Hartree-Fock model, each orbital can be occupied by at most one a spin and one (i spin electron. That is the meaning of the (redundant) Alpha in the output. In the unrestricted Hartree-Fock model, the a spin electrons have a different spatial part to the spin electrons and the output consists of the HF-LCAO coefficients for both the a spin and the spin electrons. [Pg.182]

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. [Pg.70]

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. [Pg.39]

Among the many ways to go beyond the usual Restricted Hartree-Fock model in order to introduce some electronic correlation effects into the ground state of an electronic system, the Half-Projected Hartree-Fock scheme, (HPHF) proposed by Smeyers [1,2], has the merit of preserving a conceptual simplicity together with a relatively straigthforward determination. The wave-function is written as a DODS Slater determinant projected on the spin space with S quantum number even or odd. As a result, it takes the form of two DODS Slater determinants, in which all the spin functions are interchanged. The spinorbitals have complete flexibility, and should be determined from applying the variational principle to the projected determinant. [Pg.175]

The Hartree-Fock description of the hydrogen molecule requires two spinorbitals, which are used to build the single-determinant two-electron wave function. In the Restricted Hartree-Fock method (RHF) these two spinorbitals are created from the same spatial... [Pg.189]

Whereas there are only two different bond lengths in Ceo, short between atoms 1 and 2 and long between atoms 2 and 3, there are seven different bond lengths in C. The Crobond lengths have been calculated here and previously [12] by the restricted Hartree-Fock method using an STO-3G basis set and are discussed in some detail... [Pg.442]

Table 2 Restricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts. AE is the difference in energy between the carbon allotrope and its adduct. In all cases, except where indicated by f, only the six carbon atoms in the immediate vicinity of the muon have had there positions optimised, f means that a full geometry optimisation has been carried out. The type specifies the defect and for C70 is identified in Table 1. is the spin density at the muon in atomic units (and the hyperfine coupling constant in MHz). JMuon constrained to lie in equatorial plane. indicates geometry not fully optimized. Table 2 Restricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts. AE is the difference in energy between the carbon allotrope and its adduct. In all cases, except where indicated by f, only the six carbon atoms in the immediate vicinity of the muon have had there positions optimised, f means that a full geometry optimisation has been carried out. The type specifies the defect and for C70 is identified in Table 1. is the spin density at the muon in atomic units (and the hyperfine coupling constant in MHz). JMuon constrained to lie in equatorial plane. indicates geometry not fully optimized.
In this chapter we make first contact with the electron density. We will discuss some of its properties and then extend our discussion to the closely related concept of the pair density. We will recognize that the latter contains all information needed to describe the exchange and correlation effects in atoms and molecules. An appealing avenue to visualize and understand these effects is provided by the concept of the exchange-correlation hole which emerges naturally from the pair density. This important concept, which will be of great use in later parts of this book, will finally be used to discuss from a different point of view why the restricted Hartree-Fock approach so badly fails to correctly describe the dissociation of the hydrogen molecule. [Pg.36]

This diagram is written in the sense of the "restricted Hartree-Fock scheme 18>. In the "unrestricted Hartree-Fock 19> sense each orbital of radical B is singly" occupied and LU is higher and HO is lower than the restricted Hartree-Fock SO, respectively (cf. Chap. 1)... [Pg.52]

In the former, electrons are assigned to orbitals in pairs, the total spin is zero, so the multiplicity is 1. In this case, the restricted Hartree-Fock method (RHF) can be applied. For radicals with doublet or triplet states, the unrestricted Hartree-Fock (UHF) has to be applied. In this method, a and, 3 electrons (spin up and spin down) are assigned to different spatial orbitals, so there are two distinct sets I and FJf... [Pg.7]

A theoretical study based on PM3 frontier molecular orbital (FMO) and potential energy surface (PES) analysis at the restricted Hartree-Fock (RHF)/6-31+G level was performed to examine the reaction of l-amino-2-ethoxycarbonyl-pyridinium mesitylenesulfonate and acrylonitrile in the presence of Hilnig s base leading to the formation of l,2-dihydropyrido[l,2-A]pyridazinium inner salt 17 <1999JOC9001>. The calculations indicated that both the [3+2] cycloaddition reaction and the ring expansion occurred in a concerted manner rather than through a stepwise mechanism via a zwitterionic intermediate 16 (Scheme 1). [Pg.82]


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