Core-Hamiltonian

The mixed models used m MXDO. AMI, and PM3. are identical, because all of these three methods are derived based on XDDO. The core Hamiltonian correction due it) the in teraction of the charges between lhec uantnin mechanical region and theclassical region is... 

The core Hamiltonian expressions, H)) and correspond to electrons moving in the... 

In order to form the Fock matrix of an ab initio calculation, all the core-Hamiltonian matrix elements, H y, and two-electron integrals (pvIXa) have to be computed. If the total number of basis functions is m, the total number of the core Hamiltonian matrix elements is... 

It remains to specify the elements of the one-electron core Hamiltonian, Hj y, containing the kinetic energy and nuclear attraction integrals. 

The diagonal elements of the core Hamiltonian simply represent the energy of an electron in an atomic orbital of the corresponding atom, plus the attraction of an electron in that atomic orbital... 

The basic idea of mixed model in MINDO/3 is the same as that used for CNDO and INDO and corrects Y b, which appears in the core Hamiltonian. Because the algorithm in calculating the Coulomb interaction in MINDO/3 is different from that used in CNDO and INDO, the procedure to correct Y b is also different from that in CNDO and INDO. 

The core Hamiltonian, correction due to the interaction of charges in the quantum region and classical region is... 

These results show that convergence is favored when the basis used are either the l-SRH ox the Absar and Coleman [32,33] Reduced Hamiltonian (RH) eigen-orbitals. The other two basis used were the SCF orbitals and the core Hamiltonian eigen-orbitals Core H)... 

The atomic quantities SHn are equal to the perturbations Shaa of the corresponding core Hamiltonian matrix elements in the ligand AO basis. This... 

This will allow us to more precisely develop the electronic energy by it s components. First, examine the core hamiltonian Hl°re. 

In the Kohn Sham equations (A.116) [324, 325], the core Hamiltonian operator h( 1) has the same definition as in HF theory (equation A.6), as does the Coulomb operator, 7(1), although the latter is usually expressed as... 

In the Fock operator, the core Hamiltonian h( 1) does not depend on the orbitals, but the Coulomb and exchange operators (1) and ( 1) depend on ( 1). If (1,2,3,..., Ne) is constructed from the lowest energy Ne orbitals, one has the lowest possible total electronic energy. By Koopmans theorem, the negative of the orbital energy is equal to one of the ionization potentials of the molecule or atom. 

---