Longuet-Higgins-Pople

Modified Longuet-Higgins-Pople calculations of association. 

By employing the angle t defined by f68), the perturbative Hamiltonina H can be formulated in the form completely analogous to the Pople and Longuet-Higgins ansatz [69] ... 

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). 

In the approach of Dewar and co-workers (34), termed the half-electron method , a physical model is considered in which an unpaired electron is replaced by two hypothetical half-electrons of opposite spin. For radicals containing one unpaired electron, the eigenvalue problem of this method is, in our opinion, identical with the method of Longuet-Higgins and Pople (27) ... 

For reasons given later, we shall most frequently use in applications the method of Longuet-Higgins and Pople. Recently, the half-electron method was extended to the lowest-energy open-shell states of any given symmetry and multiplicity (57). 

Matrix elements for doublets constructed from the Longuet-Higgins and Pople SCF MO s are (10,27)... 

From the point of view of the present state of computational possibilities, an extension of open-shell methods to a and a + rr electronic systems is rather tempting. This extension is easy for the method of Longuet-Higgins and Pople e.g., the CNDO/2 method is amenable to radicals having one nondegenerate open shell if in the original terms for F matrix elements (66),... 

Figure 6. Potential curves for ethylene cation radical (full line) and ethylene anion radical (dashed line) calculated (68) by the method of Longuet-Higgins and Pople within the standard CNDO/2 approximation. The scale on the left-hand side concerns the total energy of the cation radical the scale on the right-hand side concerns the total energy of the anion radical.

Equilibrium valence angles calculated by unrestricted CNDO/2 (66) and INDO (85) methods for several AB2 and AB3 radicals are listed in Table III. We recalculated (68) this series of radicals by the restricted CNDO/2 method (Longuet-Higgins and Pople) and obtained results which are practically identical with those in Table III. The MINDO method also appears to give reasonable results (82, 83). 

Assuming the same molecular geometry and the same MO s for both the parent and ionized systems, the first ionization potential can be expressed in the SCF approach (Longuet-Higgins and Pople or Roothaan) (106) as... 

CNDO/2 with DelBene-Jaffe parametrization [for geometry, see (91)] open-shell method of Longuet-Higgins and Pople eq. (90). 

Figure 13. Orbital energy-level scheme for the biphenyl anion radical (A) and biphenyl cation radical (C) based on the SCF calculations (59) by the Pople and Longuet-Higgins method. Pairing of MO s is indicated. Thick lines with arrows represent the five lowest transition energies. All entries are given in eV.

Using the statistical mechanical theory, Longuet-Higgins and Pople obtained a correlation function for the velocities in a liquid consisting of... 

Pople-Longuet-Higgins model, Renner-Teller effect ... 

Actually, Eq. (6.14) is only correct for closed-shell systems, where rtf is equal to 2 for occupied orbitals and 0 for virtual orbitals. It is extended to open-shell systems with n( — 1 for singly occupied orbitals in the Longuet-Higgins and Pople approximation of the Roothaan SCF equations 66>. 

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