Geometry optimizations for methanol were done using different levels of theory and compared to the experimentally found geometry.  The experimental values are 0.0956±0.0015 nm for the O-H bond, 0.1427±0.0007 nm for the C-O bond, and 0.1096±0.0010 nm for the C-H bonds.¹  The experimental values for the bond angles are 109.03°±0.75° for the angle formed by H-C-H and 108.87°±2° for the angle formed by H-O-C.¹  Overall, none of the calculations at different levels of theory exactly matched all of the bond lengths; however, different levels of theory were closest for different bonds. 

One of the semi-empirical methods used for the calculations was AM1.  It gave the closest calculated value for the O-H bond, at 0.096 nm.  Its calculated bond angles were within the experimental range for the C-O-H bond angle and some of the H-C-H bond angles.


The other semi-empirical method used for the calculations was PM3.  Its calculated bond lengths were less like the experimental value than the bond lengths from AM1.  The values obtained for the bond angles from this calculation matched well with the experimental ranges.

6-21G was the lowest level of ab initio theory that was used for the calculations.  The bond lengths that were calculated were closest to the experimental value for the C-H bonds of the calculated lengths at all levels of theory.  Of the different ab initio levels of theory, it had the bond angle for C-O-H that best matched the experimental range.  The calculated H-C-H bond angles were also within the experimentally determined range.

The next level of ab initio theory was 6-31G.  It gave a C-O bond length that matched the experimental value best out of any that were calculated.  While the calculated bond angle for H-C-H matched the experimentally-determined value, the value for the calculated angle of the C-O-H bonds was high compared with the experimentally-derived value.

DZV was the last level of ab initio theory that was used.  While many of its calculated bond lengths were close to the experimental values, none were the closest, despite DZV being the biggest basis set.  Like 6-31G, while the calculated bond angle for H-C-H matched the experimentally-determined value, the value for the calculated angle of the C-O-H bonds was high compared with the experimentally-derived value.

The highest occupied molecular orbital (HOMO) for methanol was determined by taking the total number of electrons in the molecule, 18, and dividing by 2 because two electrons can occupy each orbital.  Therefore, the HOMO is orbital number 9.  The orbital was displayed using the geometry optimization from the DZV level of theory.

The lowest unoccupied molecular orbital (LUMO) of methanol was the orbital just above the HOMO, meaning that it was orbital number 10.

An electrostatic potential map was generated using values calculated by the DZV level of theory.  The blue areas have the highest electrostatic potential, indicating that electrons are less likely to be in that area.  The red areas have the lowest electrostatic potential and, therefore, are more likely to have electrons present.  Based on the calculations, the oxygen atom has more electrons around it, and the hydrogen atoms have less electrons around them at any given time.

The partial atomic charges on each atom were calculated.  The oxygen atom has a negative charge, again showing that the electrons have more of a tendency to be around it, while the charges on the hydrogen atoms are positive, which means that the electrons are not around them as much.

The dipole moment of methanol was calculated using all levels of theory.  The AM1 level, with a calculated dipole moment of 1.621044 Debye most closely matched the experimental value of 1.700 Debye.¹ (5% error)  It is interesting that AM1 calculated the value that was the closest because AM1 is one of the semi-empirical levels and was not expected to be superior for any of the calculations.

The vibrations of methanol were calculated using the DZV geometry optimization as the starting point.  Many of these vibrations and their frequencies can be matched to the peaks on an IR spectrum of methanol, although some of the calculated vibrations are IR inactive and would not show up on the IR spectrum because they do not change the dipole moment of the molecule.²   The frequencies of the calculated vibrations do not perfectly match the experimentally determined frequencies.  The IR spectrum is pictured in Figure 1, and the modes and frequencies of vibration are pictured through the links below.




Figure 1. IR spectrum of methanol.  The spectrum also lists the frequencies of the major peaks.  These peaks can be matched up with some of the vibrational modes that were calculated.³

One vibration, an O-H stretch, was calculated to be 4082.47 cm^-1.  On the experimentally-obtained IR spectrum it appears at 3347.6 cm^-1, which is a pretty significant difference. One C-H stretch was calculated to occur at 3286 cm^-1, which best matches up with the peak on the IR spectrum at 3336.8 cm^-1. The calculations showed a vibration, which was also a C-H stretch, at 3318.47 cm^-1.  This is the calculated value that most closely matches the IR peak at 2945.16 cm^-1. According to the calculations, what appears to be O-H rocking occurs at 1445.05 cm^-1, which pretty closely matches the experimental value on the IR spectrum of 1460.47 cm^-1. Another calculated O-H rocking at 1138.64 cm^-1. The experimental vibrational value is 1116.62 cm^-1.
A C-O stretch was calculated to occur at 1112.64 cm^-1, and there is an experimental vibration at 1030 cm^-1. 
The lowest-energy calculated vibration was torsion, or the groups at the two ends of the molecule twisting relative to one another, and was at 323.74 cm^-1.  This vibration was closest to the peak on the IR spectrum at 662 cm^-1.

You may look at any of these intermediate views again by clicking on the appropriate button.