Analysis of output in water calculation

A classical force field will require the following parameters for the water molecule:

1. bond lengths and angles

2. force constants for stretching and bending

3. charges

Determining the bond length

Bond lengths can be obtained from experiment. However, they also are calculated during the geometry optimization. To determine the calculated bond lengths, read in the water molecule into insightII from the car file using the Molecule/Get command. To determine the bond lengths use the Measure/Distance menu and select a hydrogen atom and the oxygen atom by clicking on them. You will see the bond length in Ångströms appear on the structure. You can do the same for the angle using the Measure/Angle command and by clicking sequentially on the atoms H-O-H. You can obtain more accurate numbers using the auxiliary program geomchk.f.

Determining the force constants

You can examine the vibrational normal modes for water in insightII. The calculated vibrational frequencies can be compared to experiment. To examine the vibrational frequencies you will need the DMol3 submenu. In this menu use the Analyze/Normal_Mode command. Click on the menu box and select the h2o.outmol file. When the InsightII program reads in the outmol file it will automatically generate a list of frequencies in the Frequencies1 menu and a graph of the normal modes. For solids the graph is meaningless since the intensities are not calculated. You will need to move the graph or “blank” it using the Object/Blank command with the selection Graph1. To continue with plotting you will need to reopen the Analyze/Normal_Mode menu and then click on the Select Vector option. Then click on the following selections Arrow_Style, A_scale [8], Specify_Color, Click on Arrow_Color [Black or 0,0,0]

[Violet 255,0,255] are good choices. Now you are ready to output the normal mode vectors to the screen.

Scroll down the menu Frequencies1 until the desired mode is reached (e.g. 1598) and click on it. The normal modes have the appearance shown in the Figure below.

Bending mode

Symmetric Stretch

Asymmetric stretch

The calculation carried out had symmetry turned off (unless you changed this instruction in the input file). If you would like to see the consequences of turning on the symmetry option copy the files to a new name (e.g. h2o_c2v.car and h2o_c2v.input) and change the Symmetry keyword in the input file using the vi editor. The symmetry of water is c2v (C_2v). You can enter this designation or just choose auto and rerun the calculation.

InsightII has no utility for determining the force constants. You can determine the force constants for water using the program fcartp. This is an involved procedure and is not required for this module. However, the Normal Coordinate Analysis website describes the procedure. One major issue is the transformation from Cartesian coordinates (x, y and z) to internal coordinates (bond stretches, angle bends and torsions). Internal coordinates are the natural coordinates for chemistry since they are related to chemical bonds and deformations of structure that are of interest for chemists. The procedure for transformation and the determination of force constants can be expressed as a set of linear equations using the Wilson FG matrix method. This is particularly easy to understand for molecules of high symmetry such as a H₂O and is described in Cotton's book "Chemical Applications of Group Theory".

Determining the charges

The charge set in a force field is not a unique set of values. The reason for this is that the charge set must account for the electron density through all space by a set of charge at the nuclei. This is an inherently poor approximation and electrostatics represents an active area of research in the design of better force fields. Nonetheless, one can use the charges that emerge from DFT calculations and this often done in practice. We can compare the Mulliken charge with perhaps more accurate method of electrostatic potential fitting. To do this we will examine the outmol file.

In the outmol file look for the output Mulliken charges by searching for the text Mulliken. The search utility in the vi editor is a backslash. So you just type /Mul and the line in the editor will be advanced to the next occurrence of the string Mul. If need to continue, just type n for next and the program will scroll down to the next occurrence of the text Mul. You can continue to hit n until you reach the output Mulliken charges. Make a note of these.

The ESP charges can be found by searching for the text ESP. Make a note of these charges. Compare the ESP and Mulliken charges. Which are closer to the charge used in typical force fields? You will have a better idea of the answer to this question when you do the water module in the Molecular Dynamics section.

While the calculated charges cannot be directly compared to experiment the calculated dipole can be compared to the measured value. You will find the calculated dipole moment output just above the Mulliken charges. The experimental value is 1.86 Debye.