1.5
s, p and n Orbitals, and Electronic Transitions
The combination of two atomic s orbitals results in two new molecular orbitals
(MOs) that are denoted σ orbitals as when viewed from the side along the
atom–atom axis they look like s orbitals (rotational symmetry). This is illustrated
for the molecular hydrogen molecule in Fig. 1.13a. Due to the overlap of the atomic
orbitals, the energy is different for the plus and minus combinations. The plus
combination results in the bonding orbital labelled σ, while the minus combination
gives the antibonding orbital labelled σ* (one nodal plane between the two nuclei).
The σ orbital is lower in energy than the original s orbitals while the σ* orbital is
Fig. 1.11 A Jabłon ´ski diagram indicating the electronic ground state (S 0 ), the first (S 1 ) and
second (S 2 ) excited singlet states and the first triplet state (T 1 ). According to Hund’s rule, T 1 is
lower in energy than S 1 . A number of vibrational energy levels are shown for each electronic state;
the separation between vibrational levels decreases due to anharmonicity of the potential energy
curve. Radiative transitions are depicted with straight lines, radiationless transitions with dashed
lines, and the direction of the transition with an arrow. The difference in energy between the
absorbed and emitted photons is called the Stokes shift
Fig. 1.12 Electronic configurations specified by occupation of orbitals and spin symmetry (each
electron “arrow” is associated with a one-electron wavefunction): HOMO Highest Occupied
Molecular Orbital; LUMO Lowest Unoccupied Molecular Orbital. The spin multiplicity of a
molecule is 2S+1, where S is the total spin quantum number. Singlet (S), doublet (D), and triplet
(T) states are states with spin 0, ½, and 1, respectively
1 General Concepts
7
s, p and n Orbitals, and Electronic Transitions
The combination of two atomic s orbitals results in two new molecular orbitals
(MOs) that are denoted σ orbitals as when viewed from the side along the
atom–atom axis they look like s orbitals (rotational symmetry). This is illustrated
for the molecular hydrogen molecule in Fig. 1.13a. Due to the overlap of the atomic
orbitals, the energy is different for the plus and minus combinations. The plus
combination results in the bonding orbital labelled σ, while the minus combination
gives the antibonding orbital labelled σ* (one nodal plane between the two nuclei).
The σ orbital is lower in energy than the original s orbitals while the σ* orbital is
Fig. 1.11 A Jabłon ´ski diagram indicating the electronic ground state (S 0 ), the first (S 1 ) and
second (S 2 ) excited singlet states and the first triplet state (T 1 ). According to Hund’s rule, T 1 is
lower in energy than S 1 . A number of vibrational energy levels are shown for each electronic state;
the separation between vibrational levels decreases due to anharmonicity of the potential energy
curve. Radiative transitions are depicted with straight lines, radiationless transitions with dashed
lines, and the direction of the transition with an arrow. The difference in energy between the
absorbed and emitted photons is called the Stokes shift
Fig. 1.12 Electronic configurations specified by occupation of orbitals and spin symmetry (each
electron “arrow” is associated with a one-electron wavefunction): HOMO Highest Occupied
Molecular Orbital; LUMO Lowest Unoccupied Molecular Orbital. The spin multiplicity of a
molecule is 2S+1, where S is the total spin quantum number. Singlet (S), doublet (D), and triplet
(T) states are states with spin 0, ½, and 1, respectively
1 General Concepts
7