Hamiltonian generating hermitian

In order to get significant results, the initial data must be formed by a set of clearly non-A -representable second-order matrices, which would generate upon contraction a closely ensemble A -representable 1-RDM. It therefore seemed reasonable to choose as initial data the approximate 2-RDMs built by application of the independent pair model within the framework of the spin-adapted reduced Hamiltonian (SRH) theory [37 5]. This choice is adequate because these matrices, which are positive semidefinite, Hermitian, and antisymmetric with respect to the permutation of two row/column indices, are not A -representable, since the 2-HRDMs derived from them are not positive semidefinite. Moreover, the 1-RDMs derived from these 2-RDMs, although positive semidefinite, are neither ensemble A -representable nor 5-representable. That is, the correction of the N- and 5-representability defects of these sets of matrices (approximated 2-RDM, 2-HRDM, and 1-RDM) is a suitable test for the two purification procedures. Attention has been focused only on correcting the N- and 5-representability of the a S-block of these matrices, since the I-MZ purification procedure deals with a different decomposition of this block. 

Effective Operators and Classification of Mapping Operators Effective Operators Generated by Norm-Preserving Mappings Effective Operators Generated by Non-Norm-Preserving Mappings which Produce a Non-Hermitian Effective Hamiltonian... 

Norm-preserving mappings these necessarily generate a Hermitian effective Hamiltonian ... 

Norm-preserving mappings are denoted by K, fC) and, as discussed in Section II.B, generate a Hermitian effective Hamiltonian K HK = i. The orthonormalized model eigenfunctions of H are written as a)o and the corresponding true eigenfunctions are designated by I Pa). Thus, Eq. (2.2) specializes to... 

Section II.D shows how the mappings K, L) generate the non-Hermitian effective Hamiltonian H = LHK corresponding to H,... 

Substantial advantages are derived from the separable form of the electron interaction. Seven one-particle Hermitian matrices are required for the generation of the Hamiltonian in the present, reduced form. The matrices will be sparse and demand modest storage. Savings in storage become essential with increasing basis sets but even for the present case it is notable that seven 10-by-10 matrices has the data for the full 210-by-210 Fock space Hamiltonian. Symmetry and number conservation does reduce the number of non-vanishing matrix elements. 

Note that equation (4.62) can be considered as the expectation value of a similarity transformed (non-Hermitian) Hamiltonian. Since e tries to generate deexicitations from the reference Oif, which is impossible, eq. (4.62) is identical to eq. (4.58). Equations for the amplitudes are obtained by multiplying with an excited state. 

---