Zero-order approximation ground state

Now, we assume that the functions, tcoj, j = 1,. .., N are such that these uncoupled equations are gauge invariant, so that the various % values, if calculated within the same boundary conditions, are all identical. Again, in order to determine the boundary conditions of the x function so as to solve Eq. (53), we need to impose boundary conditions on the T functions. We assume that at the given (initial) asymptote all v / values are zero except for the ground-state function /j and for a low enough energy process, we introduce the approximation that the upper electronic states are closed, hence all final wave functions v / are zero except the ground-state function v /. ... 

If 4>no and (A = 1,2) are localized ground- and excited-state wave functions of the chromophores k, the ground state of the two-chromophore system may be described by Pq = 4>,o4>2o. whereas the excited states 4 = N (4>i,4>2o 4> 4>2f) are degenerate in zero-order approximation. The exci-ton-chirality model only takes into account the interaction between the transition dipole moments A/, and localized in the chromophores. Thus, the interaction gives rise to a Davydov splitting by 2Vj2 of the energies of combinations and of locally excited states. From the dipole-dipole approximation one obtains... 

In the perturbational approach (cf. 232) to the electron correlation, the Hartree-Fock function, >0, is treated as the zero-order approximation to the true ground-state wave function i.e., I>o = Thus, the Hartree-Fock wave function stands at the starting point, while the goal is the exact ground-state electronic wave function. 

Fig. 5.2. Philosophy of the perturbational approach (the optimistic version). The ideal ground-state wave function i/tq is constructed as a sum of a good zero-order approximation and consecutive small corrections The first-order correction is...

An approximate ground-state DFT calculation is done, finding a self-consistent KS potential. Transitions from occupied to unoccupied KS orbitals provide zero-order approximations to the optical excitations. 

At the planar equilibrium geometry of ethylene, a good zero-order approximation to the wavefunction for the n electrons in the singlet ground state has the bonding n MO, Jt = occupied by two electrons of opposite... 

They include the vibronic state tjjj = jtjjj vac), the zero-order approximation of the electronically excited state, which carries oscillator strength to the ground state and the vibronic manifold tit = vac). The vibronic manifold corresponds to a lower electronic state that are quasi-degenerate with tjjj and does not carry oscillator... 

As can be seen, the signal (5.61) also reflects the ground state Hanle effect signal which is proportional to T2 as it must be in the second-order approximation. It may be of interest that we do not find any terms containing in f 2. This peculiarity is due to the zero value of the... 

In the non-rigid bender approximation, we solved the inverse eigenvalue problem described by Eq. (5.4), i.e. we determined the potential function parameters given in Table 3 for NX3 (X = H, D, T). We have used the experimental infrared frequencies of transitions from the ground state to the i>2,2 2 > 2. and 41 2 inversion states and the zero-order frequencies of vibrations (Table 4). The zero-order frequencies have been obtained from the observed fundamental frequencies of NH3 [Ref. >], ND3 [Ref. °>], NTg [Refs." and [Ref.- 3)] corrected for... 

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