Lowest energy occupied

Configuration interaction (Cl) is conceptually the simplest procedure for improving on the Hartree-Fock approximation. Consider the determinant formed from the n lowest-energy occupied spin orbitals this determinant is o) and represents the appropriate SCF reference state. In addition, consider the determinants formed by promoting one electron from an orbital k to an orbital v that is unoccupied in these are the singly excited determinants ). Similarly, consider doubly excited (k, v,t) determinants and so on up to n-tuply excited determinants. Then use these many-electron wavefimctions in an expansion describing the Cl many-electron wavefunction [Pg.13]

FIGURE 114 The TT molecular orbitals of benzene arranged in order of increasing energy and showing nodal surfaces The six tt electrons of benzene occupy the three lowest energy or bitals all of which are bonding... 

In an Extended Hiickel calculation, the Aufbau population of molecular orbitals is unambiguous. The calculation method is non-iterative and the total energy is proportional to the sum of the energies of occupied orbitals. The Aufbau guarantees the lowest energy wave function. 

When the potential V Q) is symmetric or its asymmetry is smaller than the level spacing (Oq, then at low temperature (T cuo) only the lowest energy doublet is occupied, and the total energy spectrum can be truncated to that of a TLS. If V Q) is coupled to the vibrations whose frequencies are less than coq and co, it can be described by the spin-boson Hamiltonian... 

The most important molecular- orbitals are the so-called frontier molecular- orbitals. These are the highest (energy) occupied molecular- orbital (HOMO), and lowest (energy) unoccupied molecular- orbital (LUMO). The following picture shows the LUMO surface for the hydrogen molecule, H2. The LUMO consists of two separate surfaces, a red... 

The lowest energy molecular orbital of singlet methylene looks like a Is atomic orbital on carbon. The electrons occupying this orbital restrict their motion to the immediate region of the carbon nucleus and do not significantly affect bonding. Because of this restriction, and because the orbital s energy is very low (-11 au), this orbital is referred to as a core orbital and its electrons are referred to as core electrons. 

Singlet methylene also possesses unoccupied molecular orbitals. The unoccupied orbitals have higher (more positive) energies than the occupied orbitals, and these orbitals, because they are unoccupied, do not describe the electron distribution in singlet methylene. Nevertheless, the shapes of unoccupied orbitals, in particular, the few lowest energy unoccupied orbitals, are worth considering because they provide valuable insight into the methylene s chemical reactivity. 

Examine pyrrole s highest-occupied molecular orbital (HOMO) to see if your can predict the most favorable protonation site. Which of the pyrrole s conjugate acids (N protonated, C2 proto noted, C3 proto noted pyrrole) is lowest in energy Examine electrostatic potential maps to see if the lowest-energy form is also that in which the positive charged is best delocalized. Rationalize your result using resonance arguments. What should be the favored substitution product ... 

Here, c is a column vector of LCAO coefficients and e is called the orbital energy. If we start with n basis functions, then there are exactly n different c s (and e s) and the m lowest-energy solutions of the eigenvalue problem correspond to the doubly occupied HF orbitals. The remaining n — m solutions are called the virtual orbitals. They are unoccupied. 

In the electronic ground state, the six rr-electrons occupy the three lowest-energy orbitals (the first three from Table 7.2). The Huckel rr-electron charge density matrix is... 

The lowest-energy arrangement, or ground-state electron configuration, of an atom is a listing of the orbitals occupied by its electrons. We can predict this arrangement by following three rules. 

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