Case Study: Relationship between Atomic Hybridization and Bond Length in Hydrocarbons

Source: Experiments in Organic Computational Chemistry, Warren Hehre, WaveFunction Press

Background

Vocabulary:

Hydrocarbons: those compounds that only contain carbon (C) and hydrogen(H). Hydrocarbons are the fundamental family of molecules studied in the field of organic chemistry. Organic chemistry is the study of carbon-based molecules.

Hybrids: in many molecules, the electron orbitals surrounding one atom "overlap" with one or several of the orbitals surrounding another atom, forming a bond. In the process of overlapping, the orbitals are distorted. Another way of describing what happens when orbitals overlap is to state that the orbitals combine to form a new type of orbital, called a hybrid. This new orbital can be described as part s orbital, part p orbital. The amount of s and the amount of p can vary. For example, an sp orbital is half s and half p. An sp2 orbital is one-third s and two-thirds p. An sp3 orbital is one-fourth s and three-fourths p.

Representation of a pi orbital

Representation of an sp hybrid orbital


The purpose of this lab is to determine the effect of bond length on the type of hybridization. Specifically, we want to determine if there is any relationship between the length of the bond in single, double, and triple bonds, and the "n" in spn .

In this experiment we wish to look at three similar molecules:

Single-bonded hydrocarbons are formed when an sp3 hybrid orbital is formed between two carbon atoms. Double-bonded hydrocarbons are formed when an sp3 orbital is formed. Triple-bonded hydrocarbons are formed when an sp orbital is formed.

The purpose of this case study is to examine the extent to which calculated hybridizations approach ideal values (sp3 for ethane, sp2 for ethylene, and sp for acetylene.

Case Study Procedure

Build (one at a time, three separate files) ethane, ethylene, and acetylene. Optimize each using a semi-empirical approach at the AM1 level of theory. While optimizing, request a natural bond orbital (NBO) calculation.

In the output , record the calculated equilibrium carbon-hydrogen bond lengths in a spreadsheet table, along with the calculated hybridizations of carbon. Calculate percent error with experimental values, shown below:

Here is part of a sample spreadsheet:

In your spreadsheet, plot the value of n as a function of the CH bond distance (CH bond distance on the x axis, n on the y axis).

Discuss your results with your classmates and/or lab partner. What is the relationship between hydridization and CH bond length?


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