Hamiltonian target electronic

Here, HQ is the Coulomb-interaction Hamiltonian similar to Eq. (3), and E is a real-valued energy of the whole system, i.e., the sum of the collision energy and the energy of the target state before collision. If the target atom contains more than one electron, the absorption potential —iVabs is to be summed over all the target electrons since the incident positron can annihilate with any of the electrons. 

We partition the Hamiltonian using the second form of (7.12) and defining the interaction of the projectile with the target electrons by... 

Within the Landauer approach, the computation of the quantum conductance is thus traced back to the knowledge of the electronic structure—i.e., the Hamiltonian—of the target system molecule+leads . The best-developed implementations of the Landauer framework employ tight-binding Hamilto-... 

The //-electron target wave function is coupled to a continuum orbital continuum electron does not modify the effective Hamiltonian Q that acts on occupied target orbitals (nt = 1). Q also acts on d>K because 0 cancels out of the functional derivatives in -%j. This implies that exchange equations with a nonlocal correlation potential vc. 

This work introduced the concept of a vibronic R-matrix, defined on a hypersurface in the joint coordinate space of electrons and intemuclear coordinates. In considering the vibronic problem, it is assumed that a matrix representation of the Schrodinger equation for N+1 electrons has been partitioned to produce an equivalent set of multichannel one-electron equations coupled by a matrix array of nonlocal optical potential operators [270], In the body-fixed reference frame, partial wave functions in the separate channels have the form p(q xN)YL(0, radial channel orbital function i/(q r) and antisymmetrized in the electronic coordinates. Here 0 is a fixed-nuclei A-electron target state or pseudostate and Y] is a spherical harmonic function. Both and i r are parametric functions of the intemuclear coordinate q. It is assumed that the target states 0 for each value of q diagonalize the A-electron Hamiltonian matrix and are orthonormal. 

In the frame of the target hybrid QM/MM procedure, only the electronic structure of the R-system is calculated explicitly. For this reason, we consider its effective Hamiltonian eq. (1.235) in more detail. It contains the operator terms coming from (1) the Coulomb interaction of the effective charges in the M-system with electrons in the R-system 5VM and (2) from the resonance interaction of the R- and M-systems. 

The channel Hamiltonian governs the system at macroscopic separation distances, in particular the injection and detection distances of the experiment. It consists of the kinetic-energy operator Kq of the electron and the Hamiltonian Hr of the target. 

Ho is the Hamiltonian chosen to be best suited for modelling the target states. If a single determinant is a sufficiently-accurate model for j) then the definition (7.22) is self-consistent if Hq is the Hartree—Fock Hamiltonian. However, the self-consistent potential is not the same for all target states j). The one-electron potential is discussed in chapter 5. 

In the subsequent treatment the electron coordinate will be measured from the accelerated target nucleus and is the only dynamical variable. Thus the target system is the frame of reference [31,32], In such a noninertial system non-Newtonian forces arise. The corresponding Hamiltonian is... 

The starting point of the present theory is an expansion of the time-dependent electronic wave function in terms of single-center eigenfunctions (pi of the target Hamiltonian jTte... 

Aside from the Bloch -operator, which is added and subtracted to the Hamiltonian to ensure Hermiticity, the division into target and incident particle Hamiltonian is standard. In equation (Ig) we have only allowed for open electronic channels. A Bloch operator for the nuclear coordinate would need to be added if dissociation were included. A formal solution to the problem may be written as... 

The empirical NMR Hamiltonian contains some parameters that take into account the electronic cloud structure in which the nuclei are immersed. These NMR parameters will represent our target. 

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