Reference state wavefunction

The inclusion of the S W Hamiltonian leads to a system involving a double peituibation (137), namely, the electron-electron interaction and. Thus the reference state will be expressed as a double perturbed wavefunction... 

In MCSCF response theory [32] the reference state is approximated by a MCSCF wavefunction... 

In the self-consistent field linear response method [25,46,48] also known as random phase approximation (RPA) [49] or first order polarization propagator approximation [25,46], which is equivalent to the coupled Hartree-Fock theory [50], the reference state is approximated by the Hartree-Fock self-consistent field wavefunction < scf) and the set of operators /i j consists of single excitation and de-excitation operators with respect to orbital rotation operators [51],... 

As explained in the Introduction, this scheme breaks down both for ground and excited states when orbitals from occupied and virtual subspaces become near-degenerate, e.g. at the dissociation limit or in diradicals (see Figure 2). To overcome this problem, the SF model employs a high-spin triplet reference state which is accurately described by a SR wavefunction. The target states, closed and open shell singlets and triplets, are described as spin-flipping excitations ... 

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]

The simplest and most widely-employed method is the so-called configuration interaction singles or CIS method. This involves singleelectron promotions only (from occupied molecular orbitals in the reference wavefunction to unoccupied molecular orbitals). Because there are relatively few of these, CIS is in fact practical for molecules of moderate complexity. As noted previously, single-electron promotions do not lead to improvement in either the ground-state wavefunction or energy over the corresponding Hartree-Fock... 

The y>Ee(R) are the radial free-state wavefunctions (see Chapter 5 for details). The free state energies E are positive and the bound state energies E(v,S) are negative v and ( are vibrational and rotational dimer quantum numbers t is also the angular momentum quantum number of the fth partial wave. The g( are nuclear weights. We will occasionally refer to a third partition sum, that of pre-dissociating (sometimes called metastable ) dimer states,... 

These different techniques (and others not mentioned here) are indisputably helpful and provide very useful qualitative insight. However, they need to be applied with caution, as they all involve arguably unjustified manipulations or interpretations of the wavefunction. This is especially true if one attempts to go beyond qualitative analysis to make quantitative statements about bonding. Many of the techniques, in particular, require the construction of nonphysical reference states whose meaning is unclear. 

In Kohn-Sham DFT based approaches, expressions that are of similar structure as Eqs. (9a) and (9b) are obtained, but in the form of contributions from all occupied Kohn-Sham MOs The excited-state wavefunctions are at the same time formally replaced by the unoccupied MOs, and the many-electron perturbation operators /T(M41, etc. by their one-electron counterparts //(M-41, etc. Orbital energies e and ea formally substitute the total energies of the states (see later). Thus, similar interpretations of NMR parameters can be worked out in which the highest occupied MO-lowest unoccupied MO gap (HLG) plays a highly important role. It must be emphasized, though, that there is no one-to-one correspondence between the excited states of the SOS equations and the unoccupied orbitals which enter the DFT expressions, nor between excitation energies and orbital energy differences, i.e., there are no one-determinantal wavefunctions in Kohn-Sham DFT perturbation theory which approximate the reference and excited states. 

The method has been used to study the LiH system [13,14,15] for which the main interest was in the first excited state, which governs the dynamical behaviour of the neutral LiH molecule in the presence of a naked proton. Various nuclear configurations have been sampled, both in the subreactive [14] and reactive regions of the configuration space [13]. It turned out that a simple two-reference VB wavefunction was sufficient for the subreactive study, while the stretching of the LiH bond in the reactive regions required the use of an additional reference function. For this system, the ground state SC wavefunction has the form ... 

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