Hartree-Fock INDO

N2O and Other Nitrogen i) Species. The results of accurate configuration interaction calculations on the excited states of N2O have been used to provide accurate assignments of the observed excitation features. Current assignments of the N2O spectra have been compared, and results for the higher-lying valence states presented. This study also provides a comparison of the Hartree-Fock, INDO, and configuration interaction methods. ... 

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. 

On the basis of the optimized ground-slate geometries, we simulate the absorption speetra by combining the scmicmpirical Hartree-Fock Intermediate Neglect of Differential Overlap (INDO) Hamiltonian to a Single Configuration Interaction... 

Two philosophies have emerged in connection with the various semi-empirical methods (for a review, see Klopman and Evans, 1976). In both cases certain matrix elements are assumed to be negligible, others are computed, and others are chosen according to some criteria. According to one philosophy, the chosen parameters should lead to agreement with exact Hartree-Fock theory. Then, if desired, correlation can be added in some form. Methods called CNDO and INDO are examples of this. A more recent development is the partial retention of diatomic differential overlap (PRDDO) method (see Estreicher et al., 1989). 

We now consider the PPP, CNDO, INDO, and MINDO two-electron semiempirical methods. These are all SCF methods which iteratively solve the Hartree-Fock-Roothaan equations (1.296) and (1.298) until self-consistent MOs are obtained. However, instead of the true Hartree-Fock operator (1.291), they use a Hartree-Fock operator in which the sum in (1.291) goes over only the valence MOs. Thus, besides the terms in (1.292), f/corc(l) m these methods also includes the potential energy of interaction of valence electron 1 with the field of the inner-shell electrons rather than attempting a direct calculation of this interaction, the integrals of //corc(/) are given by various semiempirical schemes that make use of experimental data furthermore, many of the electron repulsion integrals are neglected, so as to simplify the calculation. 

The unrestricted L.C.A.O.—S.C.F. method reduces to the restricted method when a and electrons are assigned to spatially identical molecular orbitals. Thus under the INDO method the Hartree-Fock matrix elements for an open-shell system become... 

The widespread application of MO theory to systems containing a bonds was sparked in large part by the development of extended Hiickel (EH) theory by Hoffmann (I) in 1963. At that time, 7r MO theory was practiced widely by chemists, but only a few treatments of a bonding had been undertaken. Hoffmann s theory changed this because of its conceptual simplicity and ease of applicability to almost any system. It has been criticized on various theoretical grounds but remains in widespread use today. A second approximate MO theory with which we are concerned was developed by Pople and co-workers (2) in 1965 who simplified the exact Hartree-Fock equations for a molecule. It has a variety of names, such as complete neglect of differential overlap (CNDO) or intermediate neglect of differential overlap (INDO). This theory is also widely used today. 

It has been customary to classify methods by the nature of the approximations made. In this sense CNDO, INDO (or MINDO), and NDDO (Neglect of Diatomic Differential Overlap) form a natural progression in which the neglect of differential overlap is applied less and less fully. It is now clearer that there is a deeper division between methods, related to their objectives. On the one hand are approximate methods which set out to mimic the ab initio molecular orbital results. The objective here is simply to find a more economical method. On the other hand, some workers, recognizing the defects of the MO scheme, aim to produce more accurate results by the extensive use of parameters obtained from experimental data. This latter approach appears to be theoretically unsound since the formalism of the single-determinant wavefunction and the Hartree-Fock equations is retained. It can be argued that the use of the single-determinant wavefunction prevents the consistent achievement of predictions better than those obtained by the ab initio scheme where no further... 

To simplify the Hartree-Fock problem, Pople introduced CNDO/1 (1965), then CNDO/2 (1967), and then INDO (1967) to yield computer programs that mimic ab initio programs with a minimum of fuss. Jaffe66 improved CNDO to fit spectroscopic absorptions (with a minimum of Cl) this was CNDO/S (1968). Later, Dewar67 introduced MINDO/3 (1975), then MNDO (1977), AMI (1985), and PM3 (1989). For transition metals, Zerner68 introduced ZINDO (1984) these were progressive improvements on INDO, but parameterized to fit thermochemical data, dipole moments, absorption spectra, and so on, to the fitful extent that they are available from experiment. 

However, it should be emphasized that use of these less rigorous methods for the calculation of potential-energy surfaces should be viewed with great caution. Even for a system which dissociates properly in the Hartree-Fock approximation, recent research by Kaufman and co-workers [142] has shown that even the INDO method is not capable of giving an accurate or even realistic surface for Li+ + H2 when compared point by point to Lester s accurate Hartree-Fock surface [117]. 

In Sections 7 and 8 we present results for the more successful approaches. The calculations presented are of the Hartree-Fock self consistent field type utilizing the INDO/1 [14,15] model Hamiltonian. Although the force constants from... 

Up to now most quantum mechanical studies of the ground and excited states of model heme complexes have focused primarily on diamagnetic systems (36), with less frequent treatment of heme systems with unpaired spins (37-42). With the inclusion of a restricted Hartree-Fock treatment (37, 38) within an INDO formalism parameterized for transition metals (39, 40, ), it is now possible to calculate the relative energies of different spin states of ferric heme complexes in an evenhanded fashion at a semiempirical level. 

Local density functional (LDF) quantum mechanical calculations for materials science. deMon for density functional calculations. Turbomole for Hartree-Fock and MP2 ab initio calculations. ZINDO for extended Fliickel, PPP, CNDO, and INDO semiempirical molecular orbital calculations and prediction of electronic spectra. Plane Wave for band structures of semiconductors. ESOCS for electronic structure of solids. Silicon Graphics and IBM workstation versions. 

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