Non-hermiticity

The eigenvectors that cannot be orthogonal because of the non-Hermiticity of the Hamiltonian, are given by the expansion ... 

Due to the non-hermiticity of the complex scaled Hamiltonian, there is no orthonormality among the orbitals themselves, but there exists a bi-ortho--normality r, 0, />)) 0j(r, 0, )dr = between the orbitals and their com-... 

The origin of the non-hermiticity of the matrix A in CC-LRT can be traced to the non-hermiticity of H which is obtained from H by a similarity, rather than unitary, transformation via exp(T). Prasad et al763/ suggested instead a unitary cluster operator exp([Pg.321]

As mentioned in the Introduction, one of our purposes is reduction of the non-Hermitian character of the ordinary EOMCC formalism (or, in some variants of the new theory, its complete elimination). Unlike the original Hamiltonian Hk, the transformed Hamiltonian H used in the EOMCC method is no longer Hermitian and the non-Hermiticity of H measured by a difference H — (H) shows up already in the first-order of MBPT, i.e. 

The simple projection relation between the right model eigenfunctions of Hg and their true counterparts is an appealing aspect of Bloch s formalism. However, the non-Hermiticity of the resulting effective Hamiltonian represents a strong drawback, as discussed in Section VII. This has led many, beginning with des Cloizeaux [7], to derive Hermitian effective Hamiltonians, des Cloizeaux s method transforms the lag)ol not the... 

El is the CASSCF energy for state i. This Hamiltonian is not symmetric. In practice a symmetrized matrix is used. This may cause problems if the non-Hermiticity is large and it is then advisable to extend the active space. A detailed analysis of this and related problems in photochemical applications has recently been given by M. Merchan and... 

For a general set of points these equations are nonsymmetric due to the non-Hermiticity of although in certain cases in which Gauss quadrature points are utilized, Goodisman has shown this quantity to be Hermitian. 

The procedure so developed must have the property of requiring for its application an amount of computer time sufficiently small to make its use advantageous. The only property of the matrix component sums from which such a procedure could be developed is the non-Hermiticity in the off-diagonal Hij. 

What was believed to be the most reasonable way of weighting each of the ratios in forming the final function, herein called the non-Hermiticity factor, was chosen according to the importance of the component Hjj in (j> // ). This is given by the eigenvector coefficient product CjCj. 

Roots were computed using coordinate transformation for rj given by Eq. (3), whereas roots were computed using coordinate transformation given by Eq. (4). Optimum values of a determined for each transformation by self-consistant minimization of non-Hermiticity factor are enclosed in parentheses. Variationally determined root corresponding to this trial wavefunction is given at bottom of... 

The non-hermiticity ot L arises trom the dissipative term —iT. It we are interested in the temporal evolution ot the fluctuation, the dynamics can be projected into the one-dimensional (scalar) frequency-dependent Liouvillian... 

The zeroth-order Hamiltonian H is not Hermitian, since the creation and annihilation operators are not the adjoints of each other. Owing to this non-Hermiticity various eigenstates of H do not form an orthonormal set. This is the same situation we were faced with in the intermolecular PT using the biorthogonal formulation (cf. Sect. 15), thus we have to apply here the same formulae for energy corrections, Eqs. (15.47). Application of these PT formulas... 

These properties motivated us to call this formalism as Chemical Hamiltonian Approach (CHA). The disadvantage of the formalism was the non-Hermiticity of the... 

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