Thouless determinant

H at m energy of 1.2 eV in the center-of-mass frame. By using an atomic orbital basis and a representation of the electronic state of the system in terms of a Thouless determinant and the protons as classical particles, the leading term of the electronic state of the reactants is... 

In many ion-atom and ion-molecule collisions, one is often only interested in the projections on various charge states, which can be given a very simple treahnent. The Thouless determinant at separation of the two product fragments can be expressed as... 

Equations (3) and (4) for the electronic wave function describe a Thouless determinant [4] and the time-dependent complex coefficients Zp t) are called Thouless coefficients. An important quantity is the overlap of two Thouless determinants S = As the quantum-mechanical Lagrangian... 

Collective modes can be viewed as superpositions of Iph configurations. It is convenient to define this relation by using the Thouless theorem which establishes the connection between two arbitrary Slater determinants [25]. Then, the perturbed many-body wave function reads... 

In the exchange-only limit, these are the TDHF or RPA equations (Thouless [407], p. 89). If Aw = 0, excitation energies are values of tico for which the determinant of the residual homogeneous equations vanishes. 

In order to make the END formalism practical, some approximations must be made in the representation of the waveffinctions of the electrons and nuclei. The particulars are outlined in the next section. In the simple model employed in this work, we choose to represent the electronic wavefunction by a group theoretical coherent states parametrization of a single determinant (SD). The nuclear wave function is formulated in terms of a frozen Gaussian wave packet (FGWP) and the limit of a narrow width is taken. This latter approximation corresponds to the classical limit for describing the nuclei. The coherent state representation of a single determinant leads to the so-called Thouless parametrization (29). For the description of the nuclear wavefunction, a quantum description has also been worked out (26, 30), but is yet to be implemented. 

They can be determined using the special variational principle due to Thouless [39]. The principal distinction between RPA and CIS solutions is that the RPA fundamental nilpotents (14.14) are not usually normalized. Instead of Eq. 14.6 one must impose the indefinite metric condition... 

The use of the cue basis in the CCSD method for calculating the energy of the unperturbed (i.e. zero-field case) system is justified by the Thouless theorem [78] which states that the transformation between two non-orthogonal determinants can... 

Yang, Q.D. and Thouless, M.D., Reply to comments on determining the toughness of plastically-deforming Joints, y. Mater Sci. Lett., 18, 2051-2053 (1999). 

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