Hartree Fock wave functions

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]

Spin orbitals are grouped in pairs for an RHF calculation. Each member of the pair differs in its spin function (one alpha and one beta), but both must share the same space function. For N electrons, N/2 different molecular orbitals (space functions) are doubly occupied, with one alpha (spin up) and one beta (spin down) electron forming a pair. [Pg.37]

The UHE wave function can also apply to singlet molecules. Usually, the results are the same as for the faster RHEmethod. That is, electrons prefer to pair, with an alpha electron sharing a molecular space orbital with a beta electron. Use the UHE method for singlet states only to avoid potential energy discontinuities when a covalent bond is broken and electrons can unpair (see Bond Breaking on page 46). [Pg.37]

Drowicz F W and W A Goddard IB 1977. The Self-Consistent Field Equations for Generalized Valence Bond and Open-Shell Hartree-Fock Wave Functions. In Schaeffer H F III (Editor). Modem Theoretical Chemistry III, New York, Plenum, pp. 79-127. [Pg.180]

Correlation can be added as a perturbation from the Hartree-Fock wave function. This is called Moller-Plesset perturbation theory. In mapping the HF wave function onto a perturbation theory formulation, HF becomes a hrst-order perturbation. Thus, a minimal amount of correlation is added by using the second-order MP2 method. Third-order (MP3) and fourth-order (MP4) calculations are also common. The accuracy of an MP4 calculation is roughly equivalent to the accuracy of a CISD calculation. MP5 and higher calculations are seldom done due to the high computational cost (A time complexity or worse). [Pg.22]

Configuration Interaction (or electron correlation) adds to the single determinant of the Hartree-Fock wave function a linear combination of determinants that play the role of atomic orbitals. This is similar to constructing a molecular orbital as a linear combination of atomic orbitals. Like the LCAO approximation. Cl calculations determine the weighting of each determinant to produce the lowest energy ground state (see SCFTechnique on page 43). [Pg.38]

Next, you choose a UHF or RHF calculation. HyperChem can compute open-shell (non-singlet) systems with either the half-electron RHF or the UHF method (see Hartree-Fock Wave Functions on page 37). [Pg.119]

A Hartree-Fock wave function can be written as a single Slater determinant, composed of a set of orthonormal MOs (eq. (3.20)). [Pg.227]

Hartree-Fock wave functions, 269 High resolution electron energy loss spectroscopy, HREELS, 43, 69 Highest occupied molecular orbital, HOMO, 269... [Pg.570]

The minimization of this functional presents a problem which for many component mixtures can be quite timeconsuming if the truly optimal form of the interface and free energy is to be found. One may use an iterative method of solution much like the famous scheme used to solve for the Hartree-Fock wave function in electronic structure calculations [4]. An alternative, much to be preferred when sufficiently accurate, is to use a simple parametrized form for the particle densities through the interface and then determine the optimal values of these parameters. The simplest possible scheme is, of course, to take the profile to be a step function. [Pg.105]

If an excited state is concerned, this is done under the restriction that the function should be orthogonal to all of the lower-energy states. We may specify these as the uni-configurational Hartree-Fock wave functions . The "best orbitals constructing the determinants in these wave functions are in general not orthogonal to each other. [Pg.7]

How does a rigorously calculated electrostatic potential depend upon the computational level at which was obtained p(r) Most ab initio calculations of V(r) for reasonably sized molecules are based on self-consistent field (SCF) or near Hartree-Fock wavefunctions and therefore do not reflect electron correlation in the computation of p(r). It is true that the availability of supercomputers and high-powered work stations has made post-Hartree-Fock calculations of V(r) (which include electron correlation) a realistic possibility even for molecules with 5 to 10 first-row atoms however, there is reason to believe that such computational levels are usually not necessary and not warranted. The Mpller-Plesset theorem states that properties computed from Hartree-Fock wave functions using one-electron operators, as is T(r), are correct through first order (Mpller and Plesset 1934) any errors are no more than second-order effects. [Pg.54]

As an aid in understanding the properties of a molecule, the concept of atomic charge is not a magnitude which can be directly determined from the Hartree-Fock wave function. Some scheme must be adopted to divide the total electronic charge among the atoms in a molecule. [Pg.163]

Here is the Hartree-Fock wave function of the solute immersed in the solution, and the four energy terms of equation (55) come directly from the corresponding Hamiltonian operators of equations (53) and (54). [Pg.168]

Bond Order Indices Calculated for Prototype Hydrocarbon Molecules Calculated from Hartree-Fock Wave Functions at the 6-31G Equilibrium... [Pg.308]

Formulas 21.1 through 21.3 are designed for Hartree-Fock wave functions. There are some attempts to define similar indices using wave functions obtained via methods including electron correlation [19]. Similarly, to the situation with respect to basis set improvement, the results based on correlated wave functions do not necessarily make the qualitative picture of bonding easier to understand. An exception is when there is a significant nondynamical correlation in the system,... [Pg.309]

The electron densities of the separate atoms are described by Hartree-Fock wave functions approximated by analytic extended (Slater-type) basis sets. [Pg.82]

A second example is the minimal-basis-set (MBS) Hartree-Fock wave function for the diatomic molecule hydrogen fluoride, HF (Ransil 1960). The basis orbitals are six Slater-type (i.e., single exponential) functions, one for each inner and valence shell orbital of the two atoms. They are the Is function on the hydrogen atom, and the Is, 2s, 2per, and two 2pn functions on the fluorine atom. The 2sF function is an exponential function to which a term is added that introduces the radial node, and ensures orthogonality with the Is function on fluorine. To indicate the orthogonality, it is labeled 2s F. The orbital is described by... [Pg.54]

The electrostatic Hellmann-Feynman theorem states that for an exact electron wave function, and also of the Hartree-Fock wave function, the total quantum-mechanical force on an atomic nucleus is the same as that exerted classically by the electron density and the other nuclei in the system (Feynman 1939, Levine 1983). The theorem thus implies that the forces on the nuclei are fully determined once the charge distribution is known. As the forces on the nuclei must vanish for a nuclear configuration which is in equilibrium, a constraint may be introduced in the X-ray refinement procedure to ensure that the Hellmann-Feynman force balance is obeyed (Schwarzenbach and Lewis 1982). [Pg.85]

The expansion of the Roothaan-Hartree-Fock wave functions for the ground-state atoms tabulated by Clementi and Roetti (1974) can be used for this purpose. [Pg.177]

J. B. Mann, Atomic Structure Calculations, Los Alamos Scientific Laboratory, Univ. California, Los Alamos, NM, Part I Hartree—Fock Energy Results for the Elements Hydrogen to Lawrencium, 1967 Part II Hartree-Fock Wave Functions and Radial Expectation Values, 1968. [Pg.220]

Problem 11-1. Consider three levels of approximation (a) Exact many-electron wave function, (b) Hartree-Fock wave function, (including all electrons), (c) Simple LCAO-MO valence electron wave function. For each of the following molecular properties, would you expect the Hartree-Fock approximation to give a correct prediction (to within 1% in the cases of quantitative predictions) Would you expect the LCAO-MO approximation to give a correct prediction ... [Pg.104]

A comparison of HF, MP2 and density functional methods in a system with Hartree-Fock wave function instabilities, ONO—OM (for M = Li, Na and K), shows that DFT methods are able to avoid the problems that ab initio methods have for this difficult class of molecules. The computed MP2 frequencies and IR intensities were more affected by instabilities than HF. The hybrid B3LYP functional reproduced the experimental frequencies most reliably. The cis,cis conformation of ONO—OM was highly preferred because of electrostatic attraction and was strongest in the case where M = Li. The small Li cation can fit in best in the planar five-membered ring. This is completely different from the nonionic... [Pg.9]

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