Electronic structure single Slater determinant

Establishing a hierarchy of rapidly converging, generally applicable, systematic approximations of exact electronic wave functions is the holy grail of electronic structure theory [1]. The basis of these approximations is the Hartree-Fock (HF) method, which defines a simple noncorrelated reference wave function consisting of a single Slater determinant (an antisymmetrized product of orbitals). To introduce electron correlation into the description, the wave function is expanded as a combination of the reference and excited Slater determinants obtained by promotion of one, two, or more electrons into vacant virtual orbitals. The approximate wave functions thus defined are characterized by the manner of the expansion (linear, nonlinear), the maximum excitation rank, and by the size of one-electron basis used to represent the orbitals. 

Given that the electronic structure of H2SO4 is well described by a single Slater determinant and does not have significant multi reference character, an alternative approach is to use coupled cluster (CC) response functions to calculate the electronic transitions [76]. We will show in this section that CC calculations can provide calculated electronic transitions in H2SO4 and thus a cross section up to and including the Lyman-a region. 

The next controversy concerning the benzynes is the stracture of m-benzyne. Does it exist as the monocyclic biradical 42 or as the bicyclic closed-shell species 44 Answering this question with a computational approach will take some care. While the biradical character of 42 is small, a multiconfiguration wavefunction (Eq. (5.3)) is likely to be necessary for adequate description of its electronic structure. On the other hand, 44 is a closed-shell species and its electronic configuration can be expressed by a single Slater determinant made from the molecular orbitals shown in Figure 5.12 ... 

The HF wavefunction takes the form of a single Slater determinant, constructed of spin-orbitals, the spatial parts of which are molecular orbitals (MOs). Each MO is a linear combination of atomic orbitals (LCAOs), contributed by all atoms in the molecule. The wavefunction in classical VB theory is a linear combination of covalent and ionic configurations (or structures), each of which can be represented as an antis5nnmetrised product of a string of atomic orbitals (AOs) and a spin eigenfunction. The covalent structures recreate the different ways in which the electrons in the AOs on the atoms in the molecule can be engaged in bonding or lone pairs. An ionic structure contains one or more doubly-occupied AOs. Each of the structures within the classical VB wavefunction can be expanded in terms of several Slater determinants constructed from atomic spin orbitals. 

In 1978, Ludena [102] carried out a Hartree-Fock calculation by using a wave function consisting of a single Slater determinant for the closed-shell atoms, whereas he used a linear combination of the Slater determinants for the open-shell atoms. Each Slater-type orbital times a cut-off function of the form (1 — r/R) to satisfy the boundary conditions. Ludena studied pressure effects on the electronic structure of the He, Li, Be, B, C and Ne neutral atoms. The energies he obtained for the confined helium atom are slightly lower than those Gimarc obtained, especially for box radii in the range R > 1.6 au. 

The Hartree-Fock model is the simplest, most basic model in ab initio electronic structure theory [28], In this model, the wave function is approximated by a single Slater determinant constructed from a set of orthonormal spin orbitals ... 

The Hartree-Fock approximation [13, 14] plays a central role in the molecular electronic structure theory. In most cases, it provides a qualitatively correct description of the electronic structure of many electron atoms and molecules in their ground electronic state. In addition, it constitutes a basis upon which more accurate methods can be developed. A detailed derivation and discussion of the method can be found in textbooks such as [10, 11]. The Hartree-Fock approximation assumes the simplest possible form for the electronic wavefunction, i.e a single Slater determinant given by Eq. (2.41). Starting from the electronic TISE Eq. (2.5), the Hartree-Fock energy is simply... 

Taking into account the electronic correlation is mandatory if a quantitative description of the electronic stmcture and energy of the system of interest is required. In addition, in some cases, the inclusion of the electronic correlation effects are necessary to obtain even a qualitatively correct description of the electronic structure of the system. By definition, the mean-field approximation resulting from the approximation of the multi-electron wavefunction by a single Slater determinant is unable to account for the electronic correlation. A correlated electronic wavefunction must then be written as a linear combination of several Slater determinants... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

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