SCF LCAO

Later there was an attempt by ab initio calculation to fit the electron structure of diazirine into the Walsh model of cyclopropane (69MI50800). According to these SCF-LCAO-MO calculations three MOs add to the description of the lone electron pairs, all of which also contribute to some extent to ring bonding. As to strain, 7r-character and conjugative effect, the term pseudo-rr-character was used. 

The fundamental tool for the generation of an approximately transferable fuzzy electron density fragment is the additive fragment density matrix, denoted by Pf for an AFDF of serial index k. Within the framework of the usual SCF LCAO ab initio Hartree-Fock-Roothaan-Hall approach, this matrix P can be derived from a complete molecular density matrix P as follows. 

OH species, 30 249 olefin, 25 138, 139 on oxide semiconductors, 7 47 of oxygen, 27 192 relative contents of various forms of in absence of illumination, 23 161-164 on illumination, 23 164-170 SCF-LCAO-MO procedure, 25 35, 36 of simple molecules, 34 166-174 sites for, 26 360, 361 uniformity of, 26 361, 362 spectroscopy, 25 198-202 of spillover hydrogen, the kinetics of, 34 7 surface diffusion as rate-determining step, 34 7... 

The values obtained for the P—H bond lengths and H-P-H bond angles by different methods are collected together in Table 1. Calculations on the bond lengths in PH3, PHJ and PH have been made by Banyard and Hake Ab initio SCF—LCAO-MO calculations for the phosphine molecule have been made recently by various workers and the results compared with the experimentally determined physical quantities for the molecule 346,34 )... 

Semiempirical methods of calculation with consideration of all valence electrons have been used only recently but already have given results on the reactivities of some aromatic and heteroaromatic com-pounds. " Thus, to analyze the reactivities of thiophene and the isomeric thienothiophenes 1-3 to electrophilic substitution, the semiempirical SCF LCAO MO method CNDO/2 was used, taking into account all valence electrons.The 3s, 3p, and 3d orbitals have been taken into account for the sulfur atom. Tlie reactivities were estimated from the difference between bond energies of the initial and the protonated molecule (in a complex). ... 

Comparison of Ionization Potentials of Ferrocene Calculated by the SCF-A Transition State Procedure and the SCF-LCAO Method... 

SCF-X-SW transition state (191) (eV) Hartree-Fock SCF-LCAO method (58) (eV) Experimental (eV) ... 

In view of the complex nature of those molecules, it is not surprising that ab initio calculations are lacking. However, in the case of ferrocene with its very high D5d symmetry, attempts have been made using the simplified SCF-LCAO-MO theory of Roothaan (68). Yamazaki (69) reported on such calculations but so briefly that it is difficult to identify the ordering of the... 

Calculations of electron density and of bond orders for compounds 1-3 have been performed, using the SCF-LCAO-MO method of Roothaan, as modified by Pariser, Parr, and Pople.224 The 7r-electron densities are shown for each of the three molecules in Fig. 1 in the case of compound 3, values... 

It is still not clear how much of the resonance energy that would have been obtained in the planar form is lost in the shallow-bowl structure. According to scf-lcao-mo calculations by Gleicher (1967), even the deep-bowl structure (9) retains more than 90 % of the Tt-bonding energy that can be realized in the planar form, and the resonance energy amounts to at least 10 kcal mol-1. 

M. A. Whitehead and J. M. Sichel, Theor. Chim. Acta, 7, 332 (1967). Atomic Parameters for Semi-Empirical SCF-LCAO-MO Calculations. 

Secondly, one can obtain the value of K approximately by use of Hiickel or SCF LCAO MO coefficients (Equation 11)65). We note that... 

In typical SCF-LCAO-MO calculations the lone pairs of the valence and/or inner shell electrons can strongly affect the IT descriptors of the chemical bond. Therefore, the contributions due to each AO input should be... 

They can be compared with the diatomic (covalent) bond order of Wiberg [52] formulated in the standard SCF-LCAO-MO theory,... 

If the conventional SCF LCAO ah initio method is used for the computation of a wavefunction of a molecule of some fixed conformation K, then the electronic density p(r) can be constructed in terms of a set of atomic orbitals cpj(r) (i=l,2,...,n), where n is the number of orbitals. If r denotes the three-dimensional position vector variable, and if P is the n x n dimensional density matrix, then the elecU onic density p(r) of the molecule can be written as... 

Up to now all non-empirical computations of barriers to nitrogen inversion (except for ammonia) have been performed within the Hartree-Fock SCF—LCAO—MO theoretical method. Only a brief summary of the problems involved in calculating energy barriers in general and inversion barriers in particular will be given here. A more detailed discussion of the theoretical (correlation and relativistic effects) and computational (basis... 

Lehn, J. M. Theoretical Conformational Analysis. Ab initio SCF—LCAO—MO studies of conformations and conformational energy barriers. Scope and limitations. Proceedings of the International Symposium on Conformational Analysis, Brussels, 8—12 September 1969 Academic Press, to be published. 

Multiconfiguration SCF (MC-SCF-LCAO-MO). If 4>lt , but for the best O then the variational principle, used simultaneously on both the a (the Cl coefficients) and the % (the atomic orbitals), will ensure that the will overlap as much as possible. 

Bergson123 obtained markedly different results, particularly in relation to the bond orders. In diagrams e and f (Fig. 1), which are based on an SCF LCAO MO method, a considerably greater doublebond character is attributed to the C—S bond in comparison with the C—C bond. This fact and the high bond order of the S—S bond lead to a picture of cyclic delocalization of the n electrons with participation of the S—S bond. On the basis of this purely physical criterion, therefore, the 1,2-dithiolium ion appears to be a typical aromatic ion. 

Table 11 Valence and conduction bands of polyglycine calculated with the ab initio SCF LCAO CO method (in eV). The bands belonging to the main chain are corrected for long-range correlation effects (numbers in parentheses)...

At each point r, the electronic density p(r,K) of a molecule of nuclear conformation K can be computed by the Hartree-Fock-Roothaan-Hall SCF LCAO ab initio method. Using a basis set cp(K) of atomic orbitals (pj(r,K)... 

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