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- https://chem.libretexts.org/Courses/BethuneCookman_University/BCU%3A_CH_332_Physical_Chemistry_II/Text/8%3A_Multielectron_Atoms/8.11%3A_Using_Atomic_Term_Symbols_to_Interpret_Atomic_SpectraThe electronic states that result from these excited orbital configurations are characterized by term symbols and are essential in understanding the spectra and energy level structure of atoms, and th...The electronic states that result from these excited orbital configurations are characterized by term symbols and are essential in understanding the spectra and energy level structure of atoms, and the orbital electron configurations. The orbital configurations help us understand many of the general or coarse features of spectra and are necessary to produce a physical picture of how the electron density changes because of a spectroscopic transition.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Quantum_Mechanics/11%3A_Molecules/Nuclear_Potential_Energy_CurvesArriving at solutions of many complex quantum mechanical systems have posed great challenges to the scientists of both the past and the present. Few quantum systems have been solved analytically and e...Arriving at solutions of many complex quantum mechanical systems have posed great challenges to the scientists of both the past and the present. Few quantum systems have been solved analytically and even fewer without the help of approximations. The goal of this overview is to review the fundamentals of solving one of these complicated systems, the diatomic molecule.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Spectroscopy/Electronic_Spectroscopy/Spin-orbit_CouplingSpin-orbit coupling refers to the interaction of a particle's "spin" motion with its "orbital" motion.
- https://chem.libretexts.org/Courses/Lebanon_Valley_College/CHM_311%3A_Physical_Chemistry_I_(Lebanon_Valley_College)/10%3A_Electronic_Spectroscopy/10.01%3A_Using_Atomic_Term_Symbols_to_Interpret_Atomic_SpectraThe electronic states that result from these excited orbital configurations are characterized by term symbols and are essential in understanding the spectra and energy level structure of atoms, and th...The electronic states that result from these excited orbital configurations are characterized by term symbols and are essential in understanding the spectra and energy level structure of atoms, and the orbital electron configurations. The orbital configurations help us understand many of the general or coarse features of spectra and are necessary to produce a physical picture of how the electron density changes because of a spectroscopic transition.
- https://chem.libretexts.org/Courses/Ripon_College/CHM_321%3A_Inorganic_Chemistry/04%3A_Electronic_Structure_and_Spectra_of_d-Metal_Complexes/4.02%3A_Quantum_Numbers_of_Multielectron_Atoms/4.2.02%3A_Spin-Orbit_CouplingIn the Russell-Saunders spin-orbit coupling scheme, the interaction between \(S\) and \(L\) is expressed by an additional quantum number, the total angular momentum quantum number (\(J\)). The quantum...In the Russell-Saunders spin-orbit coupling scheme, the interaction between \(S\) and \(L\) is expressed by an additional quantum number, the total angular momentum quantum number (\(J\)). The quantum number \(J\) is added to the term symbol as a subscript to the right of the letter describing the term. Thus, in this case where the \(p\) subshell is less than half full, the lowest energy state from the \(^3P\) free ion term would be that with \(J=0\), \(^3P_0\), followed by \(J=1\) and \(J=2\).
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Quantum_Chemistry_with_Applications_in_Spectroscopy_(Fleming)/08%3A_Polyelectronic_Atoms/8.06%3A_Atomic_SpectroscopyThe complex spectra of atoms can be understood using term symbols, as they contain all of the symmetry and quantum number values needed.
- https://chem.libretexts.org/Courses/East_Tennessee_State_University/CHEM_4110%3A_Advanced_Inorganic_Chemistry/08%3A_Coordination_Chemistry_-_Spectroscopy/8.03%3A_Term_States_and_Symbols_for_Multielectron_Atoms/8.3.02%3A_Spin-Orbit_CouplingIn the Russell-Saunders spin-orbit coupling scheme, the interaction between \(S\) and \(L\) is expressed by an additional quantum number, the total angular momentum quantum number (\(J\)). The quantum...In the Russell-Saunders spin-orbit coupling scheme, the interaction between \(S\) and \(L\) is expressed by an additional quantum number, the total angular momentum quantum number (\(J\)). The quantum number \(J\) is added to the term symbol as a subscript to the right of the letter describing the term. Thus, in this case where the \(p\) subshell is less than half full, the lowest energy state from the \(^3P\) free ion term would be that with \(J=0\), \(^3P_0\), followed by \(J=1\) and \(J=2\).
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Quantum_Tutorials_(Rioux)/02%3A_Atomic_Structure/2.28%3A_A_Tensor_Algebra_Approach_to_Spin-Orbit_Coupling\[ \begin{matrix} L3_x = \frac{1}{2} \begin{pmatrix} 0 & \sqrt{6} & 0 & 0 & 0 & 0 & 0 \\ \sqrt{6} & 0 & \sqrt{10} & 0 & 0 & 0 & 0 \\ 0 & \sqrt{10} & 0 & 0 & 0 & 0 \\ 0 & 0 & \sqrt{12} & 0 & \sqrt{12} ...\[ \begin{matrix} L3_x = \frac{1}{2} \begin{pmatrix} 0 & \sqrt{6} & 0 & 0 & 0 & 0 & 0 \\ \sqrt{6} & 0 & \sqrt{10} & 0 & 0 & 0 & 0 \\ 0 & \sqrt{10} & 0 & 0 & 0 & 0 \\ 0 & 0 & \sqrt{12} & 0 & \sqrt{12} & 0 & 0 \\ 0 & 0 & 0 \sqrt{12} 0 & \sqrt{12} & 0 \\ 0 & 0 & 0 & 0 & \sqrt{10} & 0 & \sqrt{6} \\ 0 & 0 & 0 & 0 & 0 & \sqrt{6} & 0 \end{pmatrix} & L3_y = \frac{i}{2} \begin{pmatrix} 0 & - \sqrt{6} & 0 & 0 & 0 & 0 & 0 \\ \sqrt{6} & 0 & - \sqrt{10} & 0 & 0 & 0 & 0 \\ 0 & \sqrt{10} & 0 & - \sqrt{12} & 0…
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Free_Energy_1e_(Snee)/15%3A_The_Hydrogen_Atom/15.04%3A_Spin-Orbit_CouplingHowever, the spin-orbit Hamiltonian’s A constant is a function of the gradient of the Coulombic potential energy: \(\frac{\partial \hat{V}}{\partial r}\), which in turn is proportional to the atomic n...However, the spin-orbit Hamiltonian’s A constant is a function of the gradient of the Coulombic potential energy: \(\frac{\partial \hat{V}}{\partial r}\), which in turn is proportional to the atomic number (Z) of an element as Z\({}^{4}\).
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Quantum_Mechanics__in_Chemistry_(Simons_and_Nichols)/10%3A_Angular_Momentum_and_Group_Symmetries_of_Electronic_Wavefunctions/10.04%3A_Atomic_Term_Symbols_and_WavefunctionsWhen coupling non-equivalent angular momenta (e.g., a spin and an orbital angular momenta or two orbital angular momenta of non-equivalent electrons), one vector couples using the fact that the couple...When coupling non-equivalent angular momenta (e.g., a spin and an orbital angular momenta or two orbital angular momenta of non-equivalent electrons), one vector couples using the fact that the coupled angular momenta range from the sum of the two individual angular momenta to the absolute value of their difference.
- https://chem.libretexts.org/Courses/Centre_College/CHE_332%3A_Inorganic_Chemistry/08%3A_Coordination_Chemistry_-_Electronic_Spectra/8.02%3A_Quantum_Numbers_of_Multielectron_Atoms/8.2.02%3A_Spin-Orbit_CouplingIn the Russell-Saunders spin-orbit coupling scheme, the interaction between \(S\) and \(L\) is expressed by an additional quantum number, the total angular momentum quantum number (\(J\)). The quantum...In the Russell-Saunders spin-orbit coupling scheme, the interaction between \(S\) and \(L\) is expressed by an additional quantum number, the total angular momentum quantum number (\(J\)). The quantum number \(J\) is added to the term symbol as a subscript to the right of the letter describing the term. Thus, in this case where the \(p\) subshell is less than half full, the lowest energy state from the \(^3P\) free ion term would be that with \(J=0\), \(^3P_0\), followed by \(J=1\) and \(J=2\).
