SCF molecular orbitals

All three states were described by a single set of SCF molecular orbitals based on the occupied canonical orbitals of the X Z- state and a transformation of the canonical virtual space known as "K-orbitals" [10] which, among other properties, approximate the set of natural orbitals. Transition moments within orthogonal basis functions are easier to derive. For the X state the composition of the reference space was obtained by performing two Hartree-Fock single and double excitations (HFSD-CI) calculations at two typical intemuclear distances, i.e. R. (equilibrium geometry) and about 3Re,and adding to the HF... 

The SCF molecular orbital calculations were based on the structural model given in Figure 1. Detailed discussions of the calculations are given in references (1J.) and (24). We sum-... 

Returning to Figure 4, we note the two similar results obtained at 5.0 8 which indicate that the determination of from SCF molecular orbital wavefunctions is about the same... 

In the hands of Lipscomb and others 76,143, 145a, 153,189, 190), such localized bond schemes, particularly when obtained via self-consistent field (SCF) molecular orbital (MO) treatments, have proved particularly valuable for rationalizing the shapes and interatomic distances and estimating the charge distribution in many higher boranes. 

The SCF molecular orbital calculations are therefore unanimous that the direction of approach of the radical is perpendicular to the plane of the alkene and from above the attacked atom or on that side of it away from the double bond. Approach of the radical towards the centre of the double bond is... 

For the benzenoid aromatic molecules considered here, we wish to include electron correlation for the N electrons of the 7t-eleetron system but not for the 2n a electrons. This is achieved most readily if we first carry out a standard Hartree-Fock MO theory calculation, yielding a set of orthogonal self-consistent field (SCF) molecular orbitals tp(. The spin-coupled wavefunction may then be written... 

The 3dxz- and 3dyz-AOs on sulfur are included in the linear combination of atomic orbitals in a semi-empirical SCF MO study of thiophene. The extension of the SCF MO method to include more than one atomic orbital per atomic site is accomplished by a point-charge model for the evaluation of two-center repulsion integrals. A comparison of the SCF molecular orbitals with and without the inclusion of these higher atomic orbitals shows that the d orbitals participate in the 7t-electronic structure of thiophene to only a small extent, but that their participation affects the calculated electronic properties to a great extent <1966JA4804>. 

Similar results were calculated for the corresponding carbon compounds by the SCF molecular orbital method in the Gaussian approximation. It was found that the electron density on the carbon atom in CH and F CH" is by 0.32 and 0.12 e lower than that in CH and FCH, K... 

Table 4.10. The Si-O bond lengths (R(Si-O)] and vibrational frequencies calculated" using Hartree-Fock-Roothaan (SCF) molecular-orbital methods with different basis sets and compared with experimental properties of Si(OH)4 in Dj, symmetry...

Table 4.11. Hartree-Fock-Roothaan SCF molecular-orbital calculations of Si-O-Si angles (in degrees) for (SiH l O and (OH)3SiOSi(OH)3...

An approximate (non-SCF) molecular-orbital method involving extensive parametrization of the required integrals and with the overlap integral represented as a simple product of radial and angular terms... 

Thiacyclobutadienes such as 244 were suggested to be 6-vr electron systems and, therefore, aromatic . Ab initio SCF molecular orbital calculations indicate the contrary the thiacyclobutadienes are predicted to have considerable ylide character. ... 

A number of SCF molecular orbital calculations for cyclopropane have been reported, among them those of Skancke, Kochanski and Lehn ", Kao and Radom, Hase and colleaguesBasch and colleagues Collins and Gallup and von Niessen and colleagues the most accurate appear to be those of Skancke (Table 1). 

Table 17, LCAO coefficients and energies for SCF molecular orbitals in the azide ion, NaNt,N ... 

By means of a unitary transformation the set of SCF molecular orbitals has been converted to localized orbitals the or—tt separation... 

Orbitals (f>, are SCF molecular orbitals which are occupied in the ground states of A and of B respectively, and are excited orbitals of the... 

Stone and Hayeshave developed a method based upon the SCF molecular orbitals of the separate fragments. Single and double excitations are included. The secular determinant (cf. Eq. (55))... 

A sharp decrease in the transmitted current is seen at energies which correspond to the energies of the negative ion states of these molecules. In the context of Koopmans theorem (j(), these resonances are associated with the negative of the SCF molecular orbital energies of the neutral molecule. In order to accentuate the variations in the transmitted current, a small (20-50 meV) AC volt-age (J.) is applied to the collision chamber. Thus, the derivative of the transi tted current with respect to energy is obtained. 

In fact, the truncation of the atomic basis set prevents reaching the so-called Hartree-Fock limit, and Roothaan s procedure leads to SCF molecular orbitals. 

The SCF molecular orbitals of the neutral species, V, > give rise to the ground state wavefunction, 4>(P) = 11//,, while the SCF orbitals of the positive ion for the core-hole state produce a doublet state wavefunction, 2 (P+) = 1i//(. Koopmans Theorem6 assumes that there is no change in the molecular orbitals of the ground state and ionized species, xjsj = xp j, and that a vertical ionization energy can be obtained by the following expression ... 

For heteronuclear molecules, ab initio calculations of the Self-Consistent-Field (SCF) molecular orbitals are usually necessary to obtain the values of the Ck coefficients. The values of the spin-orbit constants depend on the effective charge on each atom, a positive charge causing a contraction of the atomic orbitals and an increase in C(atomic) a negative charge causes an opposite effect. In the simple case of an expansion of the molecular orbitals in terms of a large number of atomic orbitals associated with a single 1-value on each atom (Lefebvre-Brion and Moser, 1966),... 

Single determinant ab initio LCAO-SCF molecular orbital theory is used throughout this study (6,7), Molecular geometries were optimized with the minimal STO-3G basis set (8,9), and where possible the energy of the final structure was recalculated with the extended 4-31G basis set (9,10), Such a procedure has been shown to provide a reasonable description of the structures and energies of neutral organic molecules (11) and carbocations (12), The potential surface for the concerted elimination of hydrogen chloride from ethyl chloride also has been studied successfully (13) with this technique. 

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