Правила отбора при квантовых переходах в атомах и молекулах

Formal constraint on the possible transitions of a system from one quantum state to another
In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in atomic nuclei, and so on. The selection rules may differ according to the technique used to observe the transition. The selection rule also plays a role in chemical reactions, where some are formally spin forbidden reactions, that is, reactions where the spin state changes at least once from reactants to products. In the following, mainly atomic and molecular transitions are considered.

The Laporte rule is a selection rule formally stated as follows: In a centrosymmetric environment, transitions between like atomic orbitals such as s s, p p, d d, or f f, transitions are forbidden. The Laporte rule (law) applies to electric dipole transitions, so the operator has u symmetry (meaning ungerade, odd). p orbitals also have u symmetry, so the symmetry of the transition moment function is given by the triple product u×u×u, which has u symmetry. The transitions are therefore forbidden. Likewise, d orbitals have g symmetry (meaning gerade, even), so the triple product g×u×g also has u symmetry and the transition is forbidden. The wave function of a single electron is the product of a space dependent wave function and a spin wave function. Spin is directional and can be said to have odd parity. It follows that transitions in which the spin "direction" changes are forbidden. In formal terms, only states with the same total spin quantum number are "spin allowed". In crystal field theory, d d transitions that are spin forbidden are much weaker than spin allowed transitions. Both can be observed, in spite of the Laporte rule, because the actual transitions are coupled to vibrations that are anti symmetric and have the same symmetry as the dipole moment operator.

In vibrational spectroscopy, transitions are observed between different vibrational states. In a fundamental vibration, the molecule is excited from its ground state (v = 0) to the first excited state (v = 1). The symmetry of the ground state wave function is the same as that of the molecule. It is, therefore, a basis for the totally symmetric representation in the point group of the molecule. It follows that, for a vibrational transition to be allowed, the symmetry of the excited state wave function must be the same as the symmetry of the transition moment operator. In infrared spectroscopy, the transition moment operator transforms as either x and/or y and/or z. The excited state wave function must also transform as at least one of these vectors. In Raman spectroscopy, the operator transforms as one of the second order terms in the right most column of the character table, below. Examination of the character table shows that all four vibrations are Raman active, but only the T2 vibrations can be seen in the infrared spectrum. In the harmonic approximation, it can be shown that overtones are forbidden in both infrared and Raman spectra. However, when anharmonicity is taken into account, the transitions are weakly allowed. In Raman and infrared spectroscopy, the selection rules predict certain vibrational modes to have zero intensities in the Raman and/or the IR. Displacements from the ideal structure can result in relaxation of the selection rules and appearance of these unexpected phonon modes in the spectra. Therefore, the appearance of new modes in the spectra can be a useful indicator of symmetry breakdown.

The selection rule for rotational transitions, derived from the symmetries of the rotational wave functions in a rigid rotor, is ΔJ = ±1, where J is a rotational quantum number.

There are many types of coupled transition such as are observed in vibration–rotation spectra. The excited state wave function is the product of two wave functions such as vibrational and rotational. The general principle is that the symmetry of the excited state is obtained as the direct product of the symmetries of the component wave functions. In rovibronic transitions, the excited states involve three wave functions. The infrared spectrum of hydrogen chloride gas shows rotational fine structure superimposed on the vibrational spectrum. This is typical of the infrared spectra of heteronuclear diatomic molecules. It shows the so called P and R branches. The Q branch, located at the vibration frequency, is absent. Symmetric top molecules display the Q branch. This follows from the application of selection rules. Resonance Raman spectroscopy involves a kind of vibronic coupling. It results in much increased intensity of fundamental and overtone transitions as the vibrations "steal" intensity from an allowed electronic transition. In spite of appearances, the selection rules are the same as in Raman spectroscopy.

In surface vibrational spectroscopy, the surface selection rule is applied to identify the peaks observed in vibrational spectra. When a molecule is adsorbed on a substrate, the molecule induces opposite image charges in the substrate. The dipole moment of the molecule and the image charges perpendicular to the surface reinforce each other. In contrast, the dipole moments of the molecule and the image charges parallel to the surface cancel out. Therefore, only molecular vibrational peaks giving rise to a dynamic dipole moment perpendicular to the surface will be observed in the vibrational spectrum.