Effective core charge

MOyi) Ij. and Zg are the ionization potential of the rth AO in the valence state and the effective core charge of the sth AO,respectively. One center Coulomb repulsion integrals (rrlrr)=Ij.-Ej,(Ei. is the electron affinity of the rth AO in the valence state), the values of which adopted in this paper are collected in Table 1 with the values Ij.. Two center Coulomb repulsion integral are evaluated by the for-... 

The third spectrum in Figure 7.30 is for F2 this has the same ordering of peaks as O2 but considerably more spread out. Now the antibonding state contains four electrons, so that the bond order is 1 and the molecule is diamagnetic. The first ionization of F2 requires more energy than O2 because of the higher effective core charge of the F atoms. 

We divide Hf in four parts. The first includes the kinetic energy operator together with the potential energy of center A the second includes the interactions with all other nuclei B A. Here Zf denotes an effective core charge of nucleus I, which is equal to the number of valence electrons. The third term is introduced to correct the neglect of directional effects in the two-electron integrals. Jv and J are Coulomb operators with a valence orbital v on center B with an atomic occupation number... 

The Hamiltonian as well as all following formulas are given in atomic units. The subscripts c and V denote core and valence, respectively, and the Hamiltonian is given for a molecule with valence electrons and N cores with effective core charges Q. ry and denote interelectronic and internuclear distances, respectively. The individual terms of equation 6.1 are the kinetic energy of the valence electrons, the Coulomb interaction between the valence electrons, the superposition of N atomic ECPs point charge Coulomb repulsion... 

Edit Output File icon xlix effective core potentials 101 electron affinity 142 electron correlation 6, 114,118 electron density 165 electron spin 259 electronic structure theory 3 electrostatic potential-derived charges CHelpG 196... 

The decrease in atomic radius moving across the periodic table can be explained in a similar manner. Consider, for example, the third period, where electrons are being added to the third principal energy level. The added electrons should be relatively poor shields for each other because they are all at about the same distance from the nucleus. Only the ten core electrons in inner, filled levels (n = 1, n = 2) are expected to shield the outer electrons from the nucleus. This means that the charge felt by an outer electron, called the effective nuclear charge, should increase steadily with atomic number as we move across the period. As effective nuclear charge increases, the outermost electrons are pulled in more tightly, and atomic radius decreases. 

Each CGTO can be considered as an approximation to a single Slater-type orbital (STO) with effective nuclear charge f (zeta). The composition of the basis set can therefore be described in terms of the number of such effective zeta values (or STOs) for each electron. A double-zeta (DZ) basis includes twice as many effective STOs per electron as a single-zeta minimal basis (MB) set, a triple-zeta (TZ) basis three times as many, and so forth. A popular choice, of so-called split-valence type, is to describe core electrons with a minimal set and valence electrons with a more flexible DZ (or higher) set. 

The effective nuclear charge is the nuclear charge minus the screening effect of the core electrons. 

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