Molecular Structure from Rotational Spectra

Suppose you are interested in the structure of a molecule like hydrothiophosphoryl difluoride, shown below. The most accurate way to determine the molecular structure of a molecule in the gas phase is by analysis of the rotational spectrum.

Determining rotational constants

确定转动常数

In concept, the story of molecular structure determination starts with the expression for the rotational kinetic energy of a rigid rotator:

从概念上讲，分子结构确定的故事始于刚性转子的转动动能的表达式：

假设你对如氢硫代膦二氟化物这样的分子结构感兴趣，如下所示。确定气相中分子结构的最准确方法是通过分析旋转光谱。

When this is applied to a simple diatomic or linear molecule, this kinetic energy expression leads you to the quantum mechanical Hamiltonian

当这一表达应用于简单的双原子或线性分子时，这一动能表达式将引导你得到量子力学的哈密顿量

which gives energy eigenvalues.

这给出了能量本征值。

The parameter B is called the rotational constant and it is convenient to analyze the rotational spectrum in terms of this rotational constant. The analysis of the spectrum gives you a value for I and that lets you calculate the bond length for a diatomic molecule (see example for HCl).

参数B被称为转动常数，用这个转动常数来分析转动光谱是方便的。光谱分析可以给出I的值，从而计算双原子分子的键长（见HCl的例子）。

For a general molecule there are three non-equivalent moments of inertia and the kinetic energy expression becomes

对于一般分子来说，存在三个非等价的转动惯量，动能表达式则变为

and the energies are expressed in terms of three rotational constants A, B and C.

这些能量是以三个转动常数A、B和C来表示的。

The complexity of the energy expressions is bad news in terms of the difficulty of analysis, but good news in terms of the information obtained. The structure of a diatomic molecule has only one unknown, but when you have multiple bond lengths and angles, you have several unknowns and need several equations to solve for them.

能量表达式的复杂性在分析难度方面是坏消息，但在获得的信息方面却是好消息。双原子分子的结构只有一个未知数，但当你有多个键长和键角时，就会有多个未知数，需要多个方程来求解。

To determine the structure of SPF₂H, you have to determine three angles and three bond lengths, so you need six equations. Rotation about three non-equivalent axes gives you three. So how do you determine the structure?

要确定SPF₂H的结构，你需要确定三个角度和三个键长，因此需要六个方程。绕三个非等价轴的旋转可以提供三个方程。那么，你如何确定结构呢？

The physical idea which rescues you from the dilemma of insufficient data is isotopic substitution. Since the bond lengths are determined by the electrostatic force, substituting a different isotope into the atom should not change the bond lengths since the electrical environment around the isotope is identical. However, the moments of inertia will be changed, giving you three more pieces of data in the form of the new rotational constants A', B', and C'.

摆脱数据不足困境的物理概念是同位素取代。由于键长由静电力决定，将原子中的一个不同同位素取代不应改变键长，因为同位素周围的电环境是相同的。然而，转动惯量会发生变化，从而提供三个新的数据，即新的转动常数A'、B'和C'。

While doing the experiment on SPF₂H, which has six structural parameters, it appeared that producing the molecule with deuterium substituted for normal hydrogen would be sufficient for structure determination since that would give you 6 parameters. We were working in a laboratory at the University College of North Wales in Bangor, Wales on a sample prepared by R. G. Cavell of the Department of Chemistry, Edmonton, Alberta. This was within months of the first time that compound had ever been synthesized; we had read of his initial synthesis. We contacted him and he graciously agreed to synthesize the molecule with deuterium substituted for hydrogen. The molecule is quite unstable and explosive on contact with air, so we treated the deuterated sample with great care and took data on its spectrum for about two weeks. Unfortunately, one night the glass vacuum system developed a leak and we came in the next morning to find it had exploded and we had lost both the sample and the vacuum system. At least we had two weeks of spectra and had enough data to determine the rotational constants.

在进行SPF 2 H的实验时，该分子有六个结构参数，我们发现用重氢代替普通氢来制备该分子就足以确定其结构，因为这将提供六个参数。我们当时在北威尔士大学的实验室里，该样品是由艾德蒙顿，阿尔伯塔省化学系的R. G. Cavell准备的。这发生在该化合物首次合成之后几个月，我们曾读到他最初的合成情况。我们联系了他，他慷慨地同意用重氢代替氢来合成该分子。该分子非常不稳定，接触空气就会爆炸，因此我们对重氢样品非常小心，并对其光谱进行了大约两周的数据采集。不幸的是，一天晚上玻璃真空系统出现了泄漏，第二天早上我们发现它已经爆炸，我们失去了样品和真空系统。至少我们有两周的光谱数据，足以确定旋转常数。

Unfortunately, our consolation about having collected just enough data to determine the parameters of the deuterated species of the molecule was short-lived as we faced yet another hurdle to the determination of the molecular structure. Six pieces of data were not enough to determine the structure of this molecule! There is a plane of symmetry in this molecule, the two fluorines being at mirror image sites on each side of the plane formed by the SPH framework. This meant that once the two moments of inertia in the SPH plane were determined, the third moment of inertia was determined by the perpendicular axis theorem and not independent of the other two moments of inertia. Six independent pieces of data were required to calculate the structure unambiguously, and now we had only four.

不幸的是，我们关于已经收集到足够数据来确定氘代分子参数的安慰很快就被另一个确定分子结构的障碍所打破。六条数据根本不足以确定这个分子的结构！这个分子存在一个对称平面，两个氟原子位于该平面两侧的镜像位置，由SPH框架形成。这意味着一旦确定了SPH平面内的两个转动惯量，第三个转动惯量便可通过垂直轴定理确定，而不独立于另外两个转动惯量。要无歧义地计算结构，需要六条独立的数据，而现在我们只拥有了四条。

We were rescued in this effort by the fact that the spectrum of SPF₂H was extremely strong and well resolved and we could in fact collect data for a third isotopic species, the species with sulfur-34. It has a natural abundance of 3% and this turned out to be enough to detect it. We knew where to look because we could make a fairly accurate model from the normal and deuterated sample data, and we still had the original sample. Solving for moments of inertia from our model, we predicted the locations of a dozen or so critical lines and looked for them at high resolution. The third set of rotational constants A",B", and C" gave us the needed data to calculate the structure shown.

我们在这一努力中得到了帮助，因为SPF 2 H的谱线极为强且分辨良好，我们实际上能够收集到第三种同位素物种的数据，即含有硫-34的物种。该物种的自然丰度为3%，这足以检测到它。我们之所以知道该寻找何处，是因为我们可以从正常样品和氘代样品的数据中建立较为准确的模型，而且我们仍然保留着原始样品。通过模型求解惯性矩，我们预测了十余条关键谱线的位置，并在高分辨率下进行搜索。第三组转动常数A"、B"和C"提供了计算所示结构所需的数据。