Double primed quantum numbers

As the species looked at in chemical reactions are mostly molecules, the two electronic levels depicted in Figure 7.2 spht into sub-levels, according to the molecular vibrational and rotational energy quanta. The vibrational levels are customarily numbered with the quantum number v,(i = 0, 1, 2,...). The notation for the rotational levels is more complex and depends as well on the size of the molecule, but typically one associates the rotation with the quantum number Ji i = 0, 1, 2,...). In order to distinguish between states, double primes are used to mark the (lower) ground-state levels and single-primed quantum numbers mark the excited (upper) state levels. The main processes observed in molecule-laser photon interactions are shown in Figure 7.3. 

Generally, constants and quantum numbers with single and double prime refer to the upper and the lower state, respectively. It is m = J -b 1 for the P-branch and m = -J for the P-branch. Wavenumber combinations of pairs of lines with common upper or lower rotation-vibration state can give the corresponding rotational constants of the ground or excited vibrational state ... 

The 77 coupling representation is generally useful in the reduction of the Lippmann—Schwinger equations since it applies to situations where spin—orbit coupling is not negligible. The quantum numbers used in the representation are defined in table 7.1. Primed and double-primed quantities are used to distinguish different angular-momentum states. 

Just as several STOs are needed to give an accurate representation of Hartree-Fock AOs (Section 11.1), one needs more than one STO of a given n and / in the linear combination of STOs that is to accurately represent the Hartree-Fock MO. The primed and double-primed AOs in the extended-basis-set function are STOs with different orbital exponents. The 3dquantum number m = 0, that is, the 3do and 4/o AOs. The total energies found are -197.877 and -198.768 hartrees for the minimal and extended calculations, respectively. The experimental energy of F2 at Rg is -199.670 hartrees, so the error for the minimal calculation is twice that of the extended calculation. The extended-basis-set calculation is believed to give a wave function quite close to the true Hartree-Fock wave function. Therefore, the correlation energy in F2 is about -0.90 hartrees = -24.5 eV. 

The sequence Av = 0 is allowed when two different electronic states, E and E2, are involved, i.e. (Ei, v" = n) ( 2, v = n), where the double prime and single prime indicate the lower and upper state quantum numbers respectively. 

Here v denotes the vibrational quantum number while the prime stands for upper electronic state and the double prime for lower electronic state in optical spectroscopy (in infrared spectroscopy the electronic state is the same). 

In the following tables and corresponding diagrams, U and L stand for upper and lower electronic state, respectively U = A( E ), L = X( E ) the vibrational and rotational quantum numbers v and J are labeled with a prime or a double prime depending on their referring to the upper or lower state of the transition. We shall first display and comment some tables and diagrams for CuH, CuD, and CuD, and then consider the tables and diagrams for the and iso-... 

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