Orbitals active

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

CASSCF is a version of MCSCF theory in which all possible configurations involving the active orbitals are included. This leads to a number of simplifications, and good convergence properties in the optimization steps. It does, however, lead to an explosion in the number of configurations being included, and calculations are usually limited to 14 elections in 14 active orbitals. 

Maximum number of active orbitals in the Cl 15 Maximum number of determinants 350... 

Compute and examine the orbitals at the RHF/3-21G level in order to select the active space. We will be performing a 4-electron CAS, using 4 and 6 active orbitals. The orbitals we want are those corresponding to the rt system (where the excited electrons go) therefore, the orbitals we want will be pairs of symmetry A2 and Bp Reorder the orbitals so that six appropriate orbitals make up the active space. 

FIGURE 2.7. (a) Three active pz orbitals that are used in the quantum treatment of the X + CH3-Y— X-CH3 + Y Sw2 reaction, (b) Valence-bond diagrams for the six possible valence-bond states for four electrons in three active orbitals, (c) Relative approximate energy levels of the valence-bond states in the gas phase (see Table 2.4 for the estimation of these energies). 

Figure 51. 1,3-cyclohexadiene (a) and all-cw-hexatriene (b) isomers of CeHg with the respective third active orbitals (highest occupied n-orbital) and breaking C—C distances in angetroms. The bold line indicates the C2 rotation axis. Taken from Ref. [48]. 

All calculations are scalar relativistic calculations using the Douglas-Kroll Hamiltonian except for the CC calculations for the neutral atoms Ag and Au, where QCISD(T) within the pseudopotential approach was used [99], CCSD(T) results for Ag and Au are from Sadlej and co-workers, and Cu and Cu from our own work, using an uncontracted (21sl9plld6f4g) basis set for Cu [6,102] and a full active orbital space. 

The variations of Wd and p(. with respect to the size of the Cl space are depicted in Figs. 2 and 3, respectively. With the exception of a very small increase between the final two calculations, the parameter Wd has essentially stabilized. Figures 2 and 3 indicate that the contribution to Wd and from orbitals 60-75 (CSFs 2-3xlO6) is most significant compared to other unoccupied (at DF level) active orbitals. 

As the contribution of the 5s and 5p orbitals of Ba to Wd is quite significant [43] for the BaF molecule, we have included these orbitals of Ba in our Cl active space for the calculation of Wd and p(, for the ground state of the BaF molecule. The occupied orbitals above the 25th are also included in the RASCI space from energy consideration. Thus altogether 17 active electrons (9a and 8(3) are included in the Cl space. The present calculations for Wd consider nine sets of RASCI space, which are constructed from 17 active electrons and 16, 21, 26, 31, 36, 46, 56, 66, and 76 active orbitals to analyze the convergence of Wd. 

Although the exchange mechanism was originally formulated in terms of direct orbital overlap between the donor and acceptor chromophores, it is clear that it can be extended to cover the case of through-bond mediated EET. The reason is because TB coupling provides a mechanism for spatially extending the active orbitals of the two chromo-... 

With such a formulation, fpp = — IPp (Ionization Potential) when the orbital p is doubly occupied and fpp = —EAp (Electron Affinity) when the orbital is empty. The value of fpp will be somewhere between these two extremes for active orbitals. Thus, for orbitals with occupation number one, fpp = —j(IPp + EAp). This formulation is somewhat unbalanced and will... 

Table 5. Post-HF activation barriers for the insertion reaction of ethene into the Zr-CH3 bond of the HjSifCpEZrCH species. All the reported insertion barriers were obtained through single point calculations on the MP2 geometries of Tables 3 and 4 (corresponding to run 3 in this Table). In the valence calculations the Is orbitals on the C atoms, the orbitals up to 2p on the Si atom and up to the 3d on the Zr atom where not included in the active orbitals space. In the full MP2 calculations all occupied orbitals were correlated.

Firstly, inclusion of polarization functions on the C and H atoms of the reactive groups (CH3 and C2H4) reduces considerably the insertion barrier (compare runs 1 and 2 as well as runs 6 and 7 ) and seems to be mandatory. Instead, inclusion of polarization functions on the ancillary H2Si(Cp)2 ligand has a negligible effect on the calculated insertion barrier (compare runs 2 and 3 as well as runs 7 and 8). Extension of the basis set on the reactive groups lowers further the insertion barrier (compare runs 7 and 9). Both the MIDI basis set on Zr, and the SVP basis set on the remaining atoms decrease the insertion barrier (compare runs 3, 5 and 8). Finally, the extension of the active orbitals space to include all the occupied orbitals reduces sensibly the insertion barrier (compare runs 3 and 4). 

Table 4. HF dependence of the polarizability tensors (in atomic units) on the number of active orbitals employed in the °°°CAS -MCSCF calculations using the daug-cc-pVQZ basis set at three internuclear distances...

A general comment on the use of the empirical correlation between Si and Sn NMR (and likewise on C/ Si or Sn/ Pb NMR) chemical shifts is in order. The basis for this correlation is that the paramagnetic term Op dominates the chemical shift. According to Ramsay s theory, Op is proportional to the reciprocal energy difference h.E between the magnetically active orbitals and proportional to the expectation value for the electron radii (r )np- Thus, a linear correlation between the 5 Si and 8 Sn implies that the ratio of both determining factors of Op is constant for the all compounds of interest. In particular, it is not clear, however, if the ratio for tetravalent silicon and tin compounds is the same as for trivalent silicon and tin compounds. Therefore, the extension of a correlation based exclusively on the... 

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