Slater bases

Sources. Results taken from Ref. 69 the near-HF SCF Slater bases are from Ref. 70. The 6-31IG basis is that of Ref. 16. The contracted ANO (atomic natural orbital) bases [72] are indicated in [69], as well as the (13r 2d If) basis constructed with the help of van Duijneveldt s (13i 8p) basis [18] augmented with d and / functions taken from Ref. 17. 

Figure 4.8 displays the best manual result obtained by simply varying the Slater exponent, cell E 4 on the spreadsheet. Note, that the agreement between the Slater-based function and the analytical hydrogen 2s radial function now is good and an accurate value is returned in cell J 8 for the potential energy. The improved, but still relatively unsatisfactory, match of the r grad transformations appears to be the main reason for... 

Wlien first proposed, density llinctional theory was not widely accepted in the chemistry conununity. The theory is not rigorous in the sense that it is not clear how to improve the estimates for the ground-state energies. For wavefiinction-based methods, one can include more Slater detenuinants as in a configuration interaction approach. As the wavellmctions improve via the variational theorem, the energy is lowered. In density fiinctional theory, there is no... 

To overcome some of the problems inlierent in the UFIF method, it is possible to derive SCF equations based on minimizing the energy of a wavefiinction fomied by spin projecting a single Slater detemiinant starting... 

ZINDO/1 IS based on a modified version of the in termediate neglect of differen tial overlap (IXDO), which was developed by Michael Zerner of the Quantum Theory Project at the University of Florida. Zerner s original INDO/1 used the Slater orbital exponents with a distance dependence for the first row transition metals only. Ilow ever. in HyperChein constant orbital expon en ts are used for all the available elein en ts, as recommended by Anderson. Friwards, and Zerner. Inorg. Chem. 2H, 2728-2732.iyH6. 

In order to calculate higher-order wavefunctions we need to establish the form of the perturbation, f. This is the difference between the real Hamiltonian and the zeroth-order Hamiltonian, Remember that the Slater determinant description, based on an orbital picture of the molecule, is only an approximation. The true Hamiltonian is equal to the sum of the nuclear attraction terms and electron repulsion terms ... 

The first two of these atomie-orbital-based Slater determinants ( Sx ot Sx P I and Sy a Sy P I) are denoted "ionie" beeause they deseribe atomie orbital oeeupaneies, whieh are appropriate to the R region, that eorrespond to X J + Y and X + Y J valenee bond struetures, while Sx ot Sy P and Sy a Sx P I are ealled "eovalenf beeause they eorrespond to X + Y struetures. 

In similar fashion, the remaining five CSFs may be expressed in terms of atomie-orbital-based Slater determinants. In so doing, use is made of the antisymmetry of the Slater determinants... 

Within the Slater-Koster appro.ximation, we can easily test the validity of the approximations made in eqn (7) based on the graphene model. In Fig. 5 we depict the band gaps using the empirical tight-binding method for nanotube radii less than 1.5 nm. The non-metallic nanotubes n m) are shown in the... 

Density functional theory-based methods ultimately derive from quantum mechanics research from the 1920 s, especially the Thomas-Fermi-Dirac model, and from Slater s fundamental work in quantum chemistry in the 1950 s. The DFT approach is based upon a strategy of modeling electron correlation via general functionals of the electron density. 

The sphere radii were deduced from Slater s (1965) table based on crystal data. The basic molecular HF-Xa equations were originally derived on the basis that the spheres did not overlap (Schwarz and Connolly, 1971). But the equations remain valid when the spheres are allowed to overlap, provided that each sphere does not contain more than one nucleus and that none of the nuclei lie outside the outer sphere. A 10% overlap seems to be normal practice, and our results are given in Table 12.2. 

This is perhaps the easiest method to understand. It is based on the variational principle (Appendix B), analogous to the HF method. The trial wave function is written as a linear combination of determinants with the expansion coefficients determined by requiring that the energy should be a minimum (or at least stationary), a procedure known as Configuration Interaction (Cl). The MOs used for building the excited Slater determinants are taken from a Hartree-Fock calculation and held fixed. Subscripts S, D, T etc. indicate determinants which are singly, doubly, triply etc. excited relative to the... 

Parkins, R. N., from Stress Corrosion Cracking and Hydrogen Embrittlement of Iron Base Alloys, Edited by R. W. Staehle, J. Hochmann, R. D. McCright and J. E. Slater, NACE, Houston, p601, (1977)... 

In addition to the calculations in Table VI which are based upon Eq. 29, one may use the Slater-Kirkwood equation (Eq. 39). If one takes effective N values less by one than those given in Table IV for the rare gas atom adjacent to each halogen, the resulting London energies are very nearly the same as those in Table VI. 

Our derivation of Eq. 11.33 based on the use of the variation principle is different from Slater s original treatment, but so far follows Hirschfelder and Kincaid. Here we will now show that it also permits such a scaling of an arbitrary trial function internuclear distance according to Eq. 11.29. 

Before discussing the correlation error, we will make some introductory remarks about the Hartree-Fock approximation based on the use of the Slater determinant (Eq. 11.38). We note that, if we... 

The calculations performed with gaussian bases have been checked employing also the STOCOS bases which include, beside Slater and Hydrogenic orbitals, a large number of STOCOS functions... 

Slater, T.F. (1966). Necrogenic activity of carbon tetrachloride in the rat a speculative mechanism based on activation. Nature 209, 36-40. 

---