Wave function ansatz

The system wave function ansatz is the linear combination... 

The scheme we employ uses a Cartesian laboratory system of coordinates which avoids the spurious small kinetic and Coriolis energy terms that arise when center of mass coordinates are used. However, the overall translational and rotational degrees of freedom are still present. The unconstrained coupled dynamics of all participating electrons and atomic nuclei is considered explicitly. The particles move under the influence of the instantaneous forces derived from the Coulombic potentials of the system Hamiltonian and the time-dependent system wave function. The time-dependent variational principle is used to derive the dynamical equations for a given form of time-dependent system wave function. The choice of wave function ansatz and of sets of atomic basis functions are the limiting approximations of the method. Wave function parameters, such as molecular orbital coefficients, z,(f), average nuclear positions and momenta, and Pfe(0, etc., carry the time dependence and serve as the dynamical variables of the method. Therefore, the parameterization of the system wave function is important, and we have found that wave functions expressed as generalized coherent states are particularly useful. A minimal implementation of the method [16,17] employs a wave function of the form ... 

A second approach to solving the Hemdon-Simpson model is to make a wave-function Ansatz which then leads to an upper bound to the ground state. The simplest Ansatz (of Pauling Wheland [12]) is a uniform sum over all Kekule structures,... 

The cluster expanded wave-function ansatze in this section are based upon the Neel state as a zero-order wave-function,... 

We assume that the reader is familiar with basic concepts of CC theory, such as the exponential wave function ansatz defining all single-reference CC methods. However, for the consistency of this presentation, let us recall that the ground-state wave function associated with the CC method A has the form... 

The use of coupled-cluster (CC) wave functions within EOM theory for excitation energies, IPs and EAs has been developed [34,35] upon slightly different lines than outlined in Section 17.2. The CC wave function ansatz for Q,N) is written as usual in terms of an exponential operator acting on a single-determinant (e.g. unrestricted HF) reference function lO >... 

Larsson [95] who subsequently lifted all restrictions to the wave function ansatz when performing atomic calculations. As a first step he allowed the radial functions to be different for different mg values of the participating orbitals (the spin-polarized Hartree-Fock method SPHF) leading to a core orbital contribution to magnetic effects. Furthermore the radial parts of functions possessing different mi values are... 

It is important to note that we are mainly interested in the electronic part of the total wave function because we wish to study electronic structures at a particular molecular structure (usually an equilibrium or transition-state structure). The parameterization of the electronic wave function ansatz and its (variational) optimization are keystones of electronic structure theory. 

The memory requirements can, however, be reduced, if SPFs are used that describe a set of degrees of freedom, rather than just one. The wave function ansatz, Eq. (12), is then rewritten as a multi-configuration overp generalised particles ,... 

M. Troyer, F. Verstraete. Complete-Graph Tensor Network States A New Fermionic Wave Function Ansatz for Molecules. New. Phys., 12 (2010) 103008. 

The easy-to-visualize SC wave function ansatz is particularly useful in the description of chemical processes. The qualitative changes in the form of the active orbitals and in the active-space spin-coupling pattern suggest a reaction mechanism which can be described in terms of electron pairs and unpaired electrons. This is how most chemists still tend to think about the structure of atomic and molecular species and their interactions. Cycloaddition reactions are of considerable importance in organic chemistry and the theoretical interpretation of their mechanisms continues to attract considerable interest. 

---