Electronic Spectra of Molecules

Molecules exhibit electronic spectra from transitions between electron energy levels. These spectra are more complex than those of atomic spectra which involve transitions between electron energy levels which typically produce sharp line spectra. The energies associated with molecular electronic spectra (typically in the optical or uv region) are typically much larger than those associated with vibrational spectra (typically in the infrared) and rotational spectra (typically in the microwave region). This contributes to the complexity of the electronic spectra since the transitions from a multitude of vibrational and rotational levels produce many spectral lines, a "band" of frequencies. 分子表现出电子光谱，这是电子能级之间的跃迁所导致的。这些光谱比原子光谱更复杂，后者涉及电子能级之间的跃迁，通常产生尖锐的线状光谱。与分子电子光谱（通常在可见光或紫外区）相关的能量通常比振动光谱（通常在红外区）和旋转光谱（通常在微波区）所关联的能量要大得多。这导致电子光谱的复杂性，因为从众多振动和旋转能级的跃迁会产生许多谱线，形成一个“带”状的频率范围。

Electronic transitions are essentially instantaneous, so there is no time for appreciable motion of the nuclei. So the transitions appear as vertical lines with no change in internuclear distance. This is referred to as the Franck-Condon principle. 电子跃迁本质上是瞬时的，因此核的显著运动没有时间发生。因此，跃迁表现为垂直的线条，核间距没有变化。这被称为弗兰克-康登原理。 The spectra are strongly affected by the probability that an electron is at a location to contribute to such a "vertical" transition. That probability is the wavefunction squared, and at least the lowest vibrational states are approximated by the quantum harmonic oscillator. 光谱强烈地受到电子处于某一位置参与此类'垂直'跃迁的概率的影响。该概率是波函数的平方，最低的振动态可近似由量子谐振子来描述。

The energy level diagrams contain much information about the molecule. The v=0 ground ground vibrational state has the highest probability at the center of the potential well, but the higher vibrational states have the highest probabilty at maximum displacement from that center. The transition above demonstrates one result of those facts: the center of the ground state is at the same internuclear distance as the v=1 state of the first electronic excited state. So that transition is highly probably and produces a strong spectral line. Transitions involving other vibrational states are observed, but significantly weaker.

The illustration of the v=0 to v=1 transition above shows it as being broader, which is partly due to its greater intensity, but also because there can be many molecular rotational states associated with the vibrational states, giving a band of many transitions close to the same frequency. The higher inherent intensity makes more of those transitions visible and broadens the line.

This is a depiction of multiple electronic transitions from a common vibrational state in the ground electronic state to successive vibrational levels in an excited electronic state. There are no limiting selection rules, so transitions between many pairs of levels can occur. The lines are broadened because of the multiple rotation states associated with the vibrational levels. 这是一幅展示从共同的振动态在基态电子态中进行多个电子跃迁到激发态中连续振动能级的示意图。没有限制的选择规则，因此许多能级对之间的跃迁都可以发生。这些线被展宽，是因为与振动能级相关的多个旋转态。

The representation above was patterned after Taylor, Zafiritos and Dubson's treatment. The section of an actual photographic record of such a spectrum at right is from Blatt and attributed to J. A. Marquisce. It is a portion of the emission spectrum of N2. 上述表示方法是模仿Taylor、Zafiritos和Dubson的处理方式。右图中实际光谱照片的截面部分来自Blatt，并归因于J. A. Marquisce。这是N₂的发射光谱的一部分。

The Franck-Condon principle is an important part of the understanding of molecular electronic spectra. The relevant internuclear separations in an electronic excited state may be essentially the same as in the ground state, but if they are different, it has major effects on the nature of the electronic spectrum. Such differences may lead to the phenomenon of fluorescence in some molecules, and phosphorescence in others.

Molecular Fluorescence

A qualitative understanding of many molecular electronic spectral phenomena can be obtained from the molecular potential diagrams with the application of the Franck-Condon principle and the nature of the quantum harmonic oscillator energy levels. The diagram above follows the suggestion of Beiser to explain how molecular fluorescence can occur. The electronic absorption shown follows the Franck-Condon principle in making the vertical transition from the highest probability location of the ground vibrational state to a high probability location of the v=4 vibrational state of the excited electronic state. Vibrational transitions can bring the electron down to the ground vibrational state where it has a high probability of transition to the v=2 vibrational level of the ground electronic state. This process can occur rapidly, so the molecule can absorb a high energy photon and quickly emit a photon of lower quantum energy, a process which is called fluorescence.

Molecular Phosphorescence

A qualitative understanding of many molecular electronic spectral phenomena can be obtained from the molecular potential diagrams with the application of the Franck-Condon principle and the nature of the quantum harmonic oscillator energy levels. The diagram above follows the suggestion of Beiser to explain how molecular phosphorescence can occur. The electronic absorption shown follows the Franck-Condon principle in making the vertical transition from the highest probability location of the ground vibrational state to a high probability location of the v=4 vibrational state of the excited electronic state. Vibrational transitions can bring the electron down to lower vibrational states, but in this case there is also a triplet excited electronic state. From the v=2 state, the electron can make a transition to this triplet state, and further vibrational deexitations leaves it trapped since transition to the singlet ground state is forbidden. Vibrational transitions can take the electron to the ground vibration state, and this diagram shows a high probability path down to the v=3 vibrational level of the ground state by the Franck-Condon principle. The fact that it is "forbidden" by the selection rules doesn't mean it can't happen, just that it is low in probability. Such transitions have a very long halflife and the lower quantum energy phosphorescent radiation may be emitted minutes or even hours after the initial absorption.

Singlet and Triplet Molecular States

If a pair of electrons occupy the ground electronic state of a molecule, the electron spin states of these two electrons must be opposite according to the Pauli exclusion principle. This state with net zero spin angular momentum will not be split by the application of a magnetic field (Zeeman effect) and is called a "singlet state".

If one electron is elevated to an excited state, the two electrons may be either paired (singlet) or unpaired with both electrons oriented in the same direction. The unpaired spin state has a spin s=1 and has three possible orientations with respect to an applied magnetic field. It is called a "triplet state". 如果一个电子被激发到激发态，两个电子可能处于配对（单重态）或未配对的状态，此时两个电子自旋方向相同。未配对的自旋态具有自旋s=1，并相对于外加磁场有三种可能的取向。这种状态称为‘三重态’。