Quantum Calculations for Ethylbenzene

The images below display the optimized geometries for the basis sets of 6-21G, 6-31G and DZV. The following images after the bond lengths and angles are then based off of the optimized geometry of the DZV basis set. These images include properties such as dipole HOMO and LUMO molecular orbitals, electrostatic potential, partial charges and UV-vis spectrum peaks. The other properties such as vibrational frequencies and the IR spectrum can be viewed from following links in the main page of the website.

Literature values for Ethylbenzene:

Bonds	Bond Lengths (nm)
C=C	0.1399
C-C	0.1524
C-C (non in aromatic, ethyl part)	0.1535
C-H	0.1094

Bonds	Bond Angles
C-C-C	111.8

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CLICK IMAGE TO ACTIVATE 3D 6-21G Bond Lengths

The image on the right displays the optimized geometry for the 6-21G basis set. You can see the bond lengths for the optimized geometry of ethylbenzene.

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CLICK IMAGE TO ACTIVATE 3D 6-21G Bond Angles

This image here displays the bond angles of the optimized geometry of the 6-21G basis set for ethylbenzene.

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CLICK IMAGE TO ACTIVATE 3D 6-31G Bond Lengths

The optimized geometry for the basis set 6-31G for ethylbenzene is shown on the right. This portrays the bond lengths of this optimized basis set.

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CLICK IMAGE TO ACTIVATE 3D 6-31G Bond Angles

This again is the optimized geometry for the basis set of 6-31G. This image however displays the bond angles of ethylbenzene.

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CLICK IMAGE TO ACTIVATE 3D DZV Bond Lengths

This image displays the "best" geometry optimization. The reason this is the best geometry optimization is because the DZV is the largest basis set of the three. The bond lengths of ethylbenzene can be seen to your right. The calculated bond lengths reflect similar values to the experimental values² as seen below in the table.

Bonds	Experimental bond length (nm)	Calculated bond length (nm)
C=C	0.1399	0.139-0.140
C-C	0.1524	0.152
C-C (ethyl part)	0.1535	0.154
C-H	0.1094	0.107

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CLICK IMAGE TO ACTIVATE 3D DZV Bond Angles

This image shows the bond angles of the "best" geometry optimization of ethylbenzene. The calculated angle between the C-C-C bond shows 111.6 degrees and the experimental value is given in the table above as 111.8 degrees².

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CLICK IMAGE TO ACTIVATE 3D DZV HOMO

HOMO represents the highest occupied molecular orbital for the molecule. In order to determine HOMO, the total amount of electrons of the molecule and diving that quantity by 2. Ethylbenzene contains 58 electrons, which divided by 2 results in 29. Therefore, the HOMO for ethylbenzene is molecular orbital 29, which can be seen in the image displayed.

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CLICK IMAGE TO ACTIVATE 3D DZV LUMO

LUMO or lowest unoccupied molecular orbital is simply the molecular orbital one above the HOMO. Since the HOMO is molecular orbital number 29, the LUMO must be molecular orbital 30, which is displayed in the image.

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CLICK IMAGE TO ACTIVATE 3D DZV Electrostatic Potential (-0.1, 0.1)

The electrostatic potential for the DZV optimized molecule is shown here. When rotated, you can see different color displayed throughout the molecule. The blue represents high electrostatic potential while the red represents low electrostatic potential.

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CLICK IMAGE TO ACTIVATE 3D DZV Partial Charges

This image here shows the partial charges on ethylbenzene. The reason for partial charges is because of the asymmetric distribution of the electrons in the chemical bonds throughout the molecule.

Excited state	Oscillator Strength	Predicted wavelength (nm)
1	0.00693	198.3017
3	1.396	149.257
4	1.102	148.4171

No experimental values were able to be found, but above displays the excited states and their corresponding oscillator strength, which explains their probability of that peak being on the graph. The wavelength was determined by converting the transition energies (1/cm) to nm.

Link to results of vibrational frequencies is found here.

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