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Practical problems in the SCF LCAO MO method

47 PRACTICAL PROBLEMS IN THE SCF LCAO MO METHOD Size of the AO basis set [Pg.366]

The number of MOs oDtained from the SUh procedure is always equal to the number of the AOs used. Each MO consists of various contributions ol the same basis set of AOs (the apparent exception is when, due to symmetry, the coefficients at some AOs are equal to zero). [Pg.366]

For double occupancy, M needs to be larger or equal to N/2. T ically we are forced to use large basis sets M N/2), and then along the occupied orbitals we get M — N/2 unoccupied orbitals, which are also called virtual orbitals. Of course, we should aim at the best quality MOs (i.e. how close they are to the solutions of the Fock equations), and avoiding large M (computational effort is proportional to M ), but in practice a better basis set often means a larger M. The variational [Pg.366]

It is required that as large a basis set as possible is used (mathematics we approach the complete set), but we may also ask if a basis set dimension may be decreased freely (economy ). Of course, the answer is no The absolute limit M is equal to half the number of the eleetrons, because only then ean we create M spinorbitals and write the Slater determinant. However, in quantum chemistry rather misleadingly, we call the minimal basis set the basis set resulting from inner shell and valenee orbitals in the eorresponding atoms. For example, the minimum basis set for a water moleeule is Is, 2s and three 2p orbitals of oxygen and two Is orbitals of hydrogen atoms, seven AOs in total (while the truly minimal basis would eontain only 10/2 = 5 AOs). [Pg.367]

Electronic Motion in the Mean Field Atoms and Molecules [Pg.368]


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