Symmetry-adapted configurations

Total number of spin and symmetry adapted configurations Number of spin and symmetry adapted configurations selected by second-order perturbation theory and treatedvariationally Property calculated with respect to the center of mass. 

Let us take H2 as an example, and construct the molecular states from the familiar minimal VB configuration set shown in Fig. 7.1a these are the covalent and two ionic structures. Since the molecule has left-right symmetry we can instantly make two symmetry-adapted configurations from the two... 

The fundamental fixed-nuclei approximation, in which the nuclei are treated as distinguishable classical particles with positions in physical space, allows for the electronic structure of ground and excited states of both atoms and molecules to be ruled by the same principles, concepts, and approximations, such as the occupation of symmetry-adapted atomic or molecular orbitals by electrons, subject to the Pauli exclusion principle. The resulting basic interpretative and computational tool is the N-electron symmetry-adapted configuration (SAC), be it atomic or molecular. It is denoted here by i. When the SAC is adopted as a conceptual and computational tool, it is possible to use the same concepts and theoretical methods in order to treat the electronic eigenfunctions of states of both atoms and small molecules for each fixed geometry. 

These yield two symmetry-adapted configuration functions... 

List of symmetry-adapted configuration functions for two-orbital and three-orbital models... 

Alekseyev et al. [9] have also developed code based on the SOCI method according to Pitzer and Winter [10] for which calculations of up to 1,000,000 double-group symmetry-adapted configurations have been reported. These authors concluded that the SOCI method is capable of accurate predictions of structures and spectra of heavy-element-containing molecules. 

Table 4.1 Some matrix elements between singlet symmetry-adapted configurations constructed from real orbitals...

Saxe, P, Schaefer III, H. F. and Handy, N. C., Exact solution (within a double-zeta basis set) of the Schrddinger electronic equation for water, Chem. Phys. Lett. 79 202 (1981). This landmark paper compares the correlation energy of H2O obtained using DCI, SDCI, SDTCI, DQCI, SDTQCI, and full Cl with results obtained using the coupled-cluster approximation (see Chapter 5) and many-body perturbation theory (see Chapter 6). llie full Cl calculation included 256,473 spin- and symmetry-adapted configurations ... 

There are more ionic determinants, e.g. < i0i(/>2031, but these do not interact with T or S when (pi and

irreducible representation than (p2 and 4. The use of spin symmetry adapted configurations allows us to write the full 15 x 15 matrix representation of the model space in three separate blocks. The first one is one-dimensional and only contains the neutral quintet CSF, the second one contains all the triplet CSFs T, NH2 and the even-numbered /, CSFs. The third sub-block of the total reference space is formed by the singlets S, NH3 and the odd-numbered /, CSFs. NHl does not interact with any of the other CSFs due to symmetry. The triplet and singlet interaction matrices are... 

Grau-Crespo, R., et al. 2007. Symmetry-adapted configurational modelling of fractional site occupancy in sohds. J. Phys. Condens. Matter 19 256201. 

The Hamiltonian of our system comprises the conduction and valence band energies, e. v, the exchange interaction, Kij the spin-orbit coupling, A and the crystal field splitting, The matrix elements of this Hamiltonian in the basis of the Bloch wavefunctions a,b,c and 5, Equations (6.16), whichcomprise the spin-symmetry-adapted configuration state functions, have been previously... 

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