Inner projection

This may be further transformed by an inner projection onto a complete set of excitation and de-excitation operators, h this is equivalent to inserting a resolution of the identity in the operator space (remember that superoperators work on operators). 

J(PP). The characteristic very low values of the direct PP couplings for 1,2-diphosphetenes73 has been attributed to compensating effects of 3Jpr.76 Inner projection of the polarisation projector (IPPP) has been used to study through-space... 

However, we require the inverse of X(2,3) in the chain rule, so we expand X(2,3) in a Gaussian basis set using inner projection theory, [45]... 

We shall draw special advantage from the positive character of -XI Ce). We first review the basic properties of inner-projections. 

E. Brandas, R.J. Bartlett, Reduced Partitioning Technique for Configuration Interaction Calculations Using Pade Approximants and Inner Projections, Chem. Phys. Lett. 8 (1971) 153. 

J. Cizek, F. Vinette, and E. J. Weniger, Int. ]. Quantum Chem., Quantum Chem. Symp., S25, 209 (1991). Examples on the Use of Symbolic Computation in Physics and Chemistry Applications of the Inner Projection Technique and of a New Summation Method for Divergent Series. 

Another approach to perturbation theory is response functions, which is the subject of this paper. The basis for all response function methods is an inner projection [28] of the resolvent,... 

The zeroth order expression for the electron propagator is obtained by using po from eqn. (21) as the density operator and using the inner projection... 

INDO/S method, 84 Inner projection, 259 Integral batch, 78... 

It is impracticable to work with an inverse operator, and using the inner projection technique (Lowdin, 1965) we can rewrite Eq. (56) as... 

Is used to transform the complex rotated potential back to the real potential. Step (11). The inner projection technique (11) is adopted such that... 

Goscinski et al. applied boldly this inner projection technique to the superoperator space in order to obtain an approximation k(z) to the superresolvent R(z) in terms of the CBP and the basis B = , B2,. . . , Bm in the operator space according to the formula ... 

The propagator technique, which attempts to solve the hierarchy of equations for the many-body Green s function, has been faciUtated by the use of inner projection techniques and the superoperator representation of Goscinski and Lukman. Ohrn and co-workers have applied these... 

Congratulations Osvaldo It is a pleasure to contribute this paper to a special volume in honour of Osvaldo Goscinski. The senior author has known Osvaldo since he began his graduate work in the Florida, Quantum Theory Project, shortly after Osvaldo had finished his dissertation and moved to Uppsala. His paper Greens functions approach to IPs and his inner projected super-operator formulation of Greens functions are routinely used by us and many others today. 

O. Goscinski and E. Brandas Pade Approximants via Inner Projections . In Theory of Electronic Shells of Atoms and Molecules (A. P. Jucvs Ed., Publishing House Mintis , Vilnius 1970). 

G. L. Bendazzoli, O. Goscinski and G. Orlandi Pade Approximants and Inner Projections in the Brillouin-Wigner Scheme for He-Like Ions Phys. Rev. A2,2 (1970). 

Starting with the matrix electron propagator in Eq. (9.12), an alternative formulation of approximation can be introduced. One employs an inner projection... 

It is convenient to use an orthonormal set of inner projection basis elements so that (hj hj) = 1 and (hj hj) = 0 for i j. A first step in seeking adequate approximation schemes for the electron propagator is a partitioning of the inner projection manifold. When the aim is to obtain a theoretical photoelectron spectrum, it is convenient to choose the partitioning... 

---