Proper ground state

The proper ground state and first excited state of the ammonia molecule... 

Determine the proper ground state electron configuration for the following elements. 

Recommended values in a 1977 table [3] were 8.6, 7.6, 6.9, 8, 7, and 6.3 (for the above M all 50%). They were used In the correlation [2] just mentioned and had been obtained by a scaling procedure applied to SCF-MO calculations for M [4]. These latter were, however, done for atomic terms originating from configurations d s. The following table shows these data [4] together with results of further theoretical work (HF = numerical Hartree-Fock, OPM = variationally optimized-local-central-potential model), comprising also the proper ground states (terms) ... 

Since the vibrational eigenstates of the ground electronic state constitute an orthonomial basis set, tire off-diagonal matrix elements in equation (B 1.3.14) will vanish unless the ground state electronic polarizability depends on nuclear coordinates. (This is the Raman analogue of the requirement in infrared spectroscopy that, to observe a transition, the electronic dipole moment in the ground electronic state must properly vary with nuclear displacements from... 

The cyclobutene-butadiene interconversion can serve as an example of the reasoning employed in construction of an orbital correlation diagram. For this reaction, the four n orbitals of butadiene are converted smoothly into the two n and two a orbitals of the ground state of cyclobutene. The analysis is done as shown in Fig. 11.3. The n orbitals of butadiene are ip2, 3, and ij/. For cyclobutene, the four orbitals are a, iz, a, and n. Each of the orbitals is classified with respect to the symmetiy elements that are maintained in the course of the transformation. The relevant symmetry features depend on the structure of the reacting system. The most common elements of symmetiy to be considered are planes of symmetiy and rotation axes. An orbital is classified as symmetric (5) if it is unchanged by reflection in a plane of symmetiy or by rotation about an axis of symmetiy. If the orbital changes sign (phase) at each lobe as a result of the symmetry operation, it is called antisymmetric (A). Proper MOs must be either symmetric or antisymmetric. If an orbital is not sufficiently symmetric to be either S or A, it must be adapted by eombination with other orbitals to meet this requirement. 

Stabilization of the singlet ground state of phosphinidenes can be induced by proper substitution. Such an approach has been applied to carbenes with great... 

An excited-state atom emits photons when the electron moves in succession from level d to level c, from level c to level b, and from level b to the ground state (level a). The wavelengths of the emitted photons are 565 nm, 152 nm, and 121 nm (not necessarily in the proper sequence). Match each emission with the appropriate wavelength and calculate the energies of levels b, c, and d relative to level a. 

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