Single-determinant wave function

CIS calculations from the semiempirical wave function can be used for computing electronic excited states. Some software packages allow Cl calculations other than CIS to be performed from the semiempirical reference space. This is a good technique for modeling compounds that are not described properly by a single-determinant wave function (see Chapter 26). Semiempirical Cl... 

The above problem with H2 dissociation is a matter of wave function construction. The functional form of a restricted single-determinant wave function will not allow a pair of electrons in an orbital to separate into two different orbitals. Wave function construction issues were addressed in greater detail in Chapters 3 through 6. 

The relative importance of tlie different excitations may qualitatively be understood by noting tliat the doubles provide electron correlation for electron pairs, Quadruply excited determinants are important as they primarily correspond to products of double excitations. The singly excited determinants allow inclusion of multi-reference charactei in the wave function, i.e. they allow the orbitals to relax . Although the HF orbitals are optimum for the single determinant wave function, that is no longer the case when man) determinants are included. The triply excited determinants are doubly excited relative tc the singles, and can then be viewed as providing correlation for the multi-reference part of the Cl wave function. 

SCVB wave functions to include electron correlation is due to the fact that the VB orbitals are strongly localized, and since they are occupied by only one electron, they have the built-in feature of electrons avoiding each other. In a sense, an SCVB wave function is tte best wave function that can be constructed in terms of products of spatial orbitals. By allowing the orbitals to become non-orthogonal, the large majority (80-90%) of what is called electron correlation in an MO approach can be included in a single determinant wave function composed of spatial orbitals, multiplied by proper spin cou ing functions. 

We may generalize this by introducing an occupation number (number of electrons), n, for each MO. For a single determinant wave function this will either be 0, 1 or 2, while it may be a fractional number for a correlated wave function (Section 9.5). 

In the unrestricted Hartree-Fock method, a single-determinant wave function is used with different molecular orbitals for a and jS spins, and the eigenvalue problem is solved with separate F and F matrices. With the zero differential overlap approximation, the F matrix elements (25) become... 

In his pioneering work Baetzold used the Hartree-Fock (HF) method for quantum mechanical calculations for the cluster structure (the details are summarized in Reference 33). The value of the HF procedure is that it yields the best possible single-determinant wave function, which in turn should give correct values for expectation values of single-particle operators such as electric moments and... 

The AB supermolecule is described by a single determinant wave function formulated in terms of doubly occupied molecular orbitals with no orthonormality constraints. For a system with 2N = 2Na +2Nb electrons the SCF-MI wave function expressed in terms of the antisymmetrizer operator A is... 

The technique used to extract the wave function in this work is conceptually simple the wave function obtained is a single determinant which reproduces the observed experimental data to the desired accuracy, while minimising the Hartree-Fock (HF) energy. The idea is closely related to some interesting recent work by Zhao et al. [1]. These authors have obtained the Kohn-Sham single determinant wave function of density functional theory (DFT) from a theoretical electron density. 

Consider a single determinant wave function whose orbitals c )i are obtained from a model hamiltonian h,... 

A new and accurate quantum mechanical model for charge densities obtained from X-ray experiments has been proposed. This model yields an approximate experimental single determinant wave function. The orbitals for this wave function are best described as HF orbitals constrained to give the experimental density to a prescribed accuracy, and they are closely related to the Kohn-Sham orbitals of density functional theory. The model has been demonstrated with calculations on the beryllium crystal. 

Some uni-configurational wave functions consist of only one determinant. This is called a single-determinant wave function. A single-determinant can be a spin-eigenstate wave function only if the eigenfunctions possess the values of... 

The simplest approximation corresponds to a single-determinant wave function. The best possible approximation of this type is the Hartree-Fock (HF) molecular-orbital determinant. The HF wavefunction is constructed from the minimal number of occupied MOs (i.e., NI2 for an V-eleclron closed-shell system), each approximated as a variational linear combination of the chosen set of basis functions (vide infra). 

A single-determinant wave-function of closed shell molecular systems is invariant against any unitary transformation of the molecular orbitals apart from a phase factor. The transformation can be chosen in order to obtain LMOs. Starting from CMOs a number of localization procedures have been proposed to get LMOs the most commonly used methods are as given by the authors of (Edmiston et ah, 1963) and (Boys, 1966), while the procedures provided by (Pipek etal, 1989) and (Saebo etal., 1993) are also of interest. It could be stated that all the methods yield comparable results. Each LMO densities are found to be relatively concentrated in some spatial region. They are, furthermore, expected to be determined mainly by that part of the molecule which occupies that given region and its nearby environment rather than by the whole system. 

For a system of n electrons, the single-determinant wave function is... 

That is precisely which is reported say in [123] on example of Pd complexes (and for other systems in Ref. [124]) the TDDFT excitation energies are systematically lower than the experimental ones. In this context it becomes clear that the TDDFT may be quite useful for obtaining the excitation energies in those cases when the ground state is well separated from the lower excited states and can be reasonably represented by a single determinant wave function may be for somehow renormalized quasiparticles interacting according to some effective law, but shall definitely fail when such a (basically the Fermi-liquid) picture is not valid. 

In this framework, we restrict ourselves to single-determinant wave functions employing one Slater determinant, but all derivations can be extended to multi-determinant wave functions (125-127). 

Derive the detailed expression for the orbital Hessian for the special case of a closed shell single determinant wave function. Compare with equation (4 53) to check the result. The equation can be used to construct a second order optimization scheme in Hartree-Fock theory. What are the advantages and disadvantages of such a scheme compared to the conventional first order methods ... 

This sum is over the n occupied MOs ij/t for a closed-shell molecule, for a total of 2n electrons. Equation 7.1 applies strictly only to a single-determinant wave-function T, but for multideterminant wavefunctions arising from configuration interaction treatments (Section 5.4) there are similar equations [10]. A shorthand for p(x, y, z) dxdydz is p(r)dr, where r is the position vector of the point with coordinates (x, y, z). 

The energy corresponding to the single determinant wave function with the occupied subspace ImP is given by [36,37] ... 

---