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    PHYSICAL CHEMISTRY LABORATORY

    EXPERIMENT CC

    Computational Chemistry: Vibrational Spectra of H–C≡C–H, H2C=O, and CCl4 Assigned Reading: – Sections 11.7, 11.8, 13.14, and 13.17 of Atkins’ Physical Chemistry

    Peter Atkins & Julio De Paula (8th edition) – Sections from Exploring Chemistry with Electronic Structure Methods

    by James B. Foresman and Æleen Frisch Purpose In this experiment you will calculate, on a Linux workstation, the vibrational frequencies of acetylene, formaldehyde, and tetrachloromethane using a hybrid density functional method (mPW1PW91-X) with the 6-31G(d) basis set implemented in Gaussian software. Theory In this experiment, you will be using a hybrid density functional theory (HDFT) method. (A functional is a function whose definition is itself a function, i.e., a function of a function.) DFT methods have their origin in the Hohenberg-Kohn theorem that demonstrates the existence of a unique functional that determines the ground state energy and density exactly. A large part of the 1998 Nobel Prize in Chemistry obtained by Kohn recognized work in this area. These DFT methods use the density instead of complicated many-electron wavefunctions. Because the density obeys the variational principle, the basic idea is to minimize the energy with respect to the density. The relationship of energy to density is the functional E[ρ] but the true form of this functional is unknown so approximate functional forms are used instead. As presented in the attached handout, the electronic energy will include terms for kinetic energy, nuclear-electron attractions, electron-electron Coulombic repulsion, and exchange-correlation interaction. Various DFT methods differ in the way in which exchange-correlation term is calculated. Hybrid DFT methods are different than pure DFT because they include certain amounts of exchange interaction calculated using Hartree-Fock (HF) method, an ab initio method. You will be using an exchange-correlation functional based on the Perdew-Wang 1991 exchange functional as modified by Adamo and Barone (mPW), the Hartree-Fock exchange, and Perdew and Wang’s 1991 correlation functional (PW91). Each group will be using a different HDFT method, and the difference pertains to the amount (i.e., percentage) of HF exchange included in the total exchange energy. Normal modes and molecular geometry Recall that a non-linear molecule with N atoms will have a total of 3N degrees of freedom: 3 translational degrees of freedom, 3 rotational degrees of freedom, and (3N – 6) vibrational degrees of freedom. A linear molecule will have 2 rotational and (3N – 6) vibrational degrees of

    rev 10/08

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    freedom. For molecules investigated here, C2H2 has 7 normal modes, H2CO has 6 normal modes, and CCl4 has 9 normal modes. Recall also that for in a normal mode, while nuclei move, the center of mass of the molecule remains fixed. Acetylene, a linear molecule belonging to D∞h point group, will be created (in the Gaussian input file) symmetric along the z axis as represented below. Formaldehyde is a molecule belonging to C2v point group. The molecule will be created (in the Gaussian input file) in the yz plane, with C at the origin, and O along the z axis. CCl4 is a tetrahedral molecule. One can imagine this tetrahedral molecule as having Cl atoms placed on opposite corners of opposite faces of a cube, and the C atom placed in the center of the cube. We will take advantage of this property in constructing the molecular geometry in the Gaussian input file. The figure below shows the atoms and the axes in the same orientation as you will use in your input file. The distance between two Cl atoms is equal to the length of a diagonal of a face of the cube, and the C–Cl distance is equal to half the diagonal of the cube. Assuming the origin to be in the center of the cube, the positions of the Cl atoms can be easily deduced, based on the length of an edge of the cube and the orientation of the axes. For example, assuming that the cube has an edge of 2a, Cl-2 atom’s coordinates will be (a, –a, –a) and Cl-3 atom’s coordinates will be (–a, a, –a). In your input file, you will construct a cube with an edge equal to 2 A.

    z

    x

    y

    H-4

    H-3

    C-2

    C-1

    z

    x

    y

    H-4

    H-3

    C-2

    C-1

    Procedure General information

    You will be working in groups like for the other experiments but the groups will be called, to avoid confusion, teams. The table below shows you the team number in which you are. Highlight the line in the table that contains information pertaining to your team.

    z

    x

    y

    H-4H-3

    O-2

    C-1

    z

    x

    y

    z

    x

    y

    H-4H-3

    O-2

    C-1

    x

    z

    y C-1

    Cl-2

    Cl-4

    Cl-3

    Cl-5 x

    z

    y C-1

    Cl-2

    Cl-4

    Cl-3

    Cl-5

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    Team Group Linux System Keyword IOp(3/76=yyyy) in input file 01 T 12 pm – group 1 1 IOp(3/76=0900001000) 02 T 12 pm – group 2 2 IOp(3/76=0800002000) 03 T 12 pm – group 3 1 IOp(3/76=0700003000) 04 T 12 pm – group 4 2 IOp(3/76=0600004000) 05 T 3 pm – group 1 1 IOp(3/76=0500005000) 06 T 3 pm – group 2 2 IOp(3/76=0400006000) 07 T 3 pm – group 3 1 IOp(3/76=0300007000) 08 T 3 pm – group 4 2 IOp(3/76=0200008000)

    Computer login

    You will be working on a Dell workstation running Linux operating system. There are two workstations in the Physical Chemistry lab. You will be using the one assigned to your group according to the table above. You will be working in a login option called Common Desktop Environment. To login into the computer, use:

    username: teamxx password: teamxxabc

    where xx is the team number for this experiment in the table above. Creating the input files

    Open the text editor by choosing Applications then Accessories then Text Editor option. Write an input files as given in the boxes below. The value yyyy in the input file is team dependent and is the value given in the table above. Note that the input file should contain at least one full empty line at the end of the file (lines 11 and 12 in the examples below). Example of input file for C2H2:

    Line # 1 # mPWPW91/6-31G(d) IOp(3/76=yyyy) 2 Opt=(VeryTight,Calcall) 3 4 C2H2 calculation 5 6 0 1 7 C 0.0 0.0 0.6 8 C 0.0 0.0 -0.6 9 H 0.0 0.0 1.7 10 H 0.0 0.0 -1.7 11 12

    Save this file in the home directory. The name of this input file should be teamxx-c2h2.txt where xx is the two-digit team number for this experiment, as assigned in the table above. For example, team 04 (i.e., group 2 in Tuesday 3 pm lab section) will name its file team04-c2h2.txt

    Value from table above

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    Example of input file for CH2O: Line # 1 # mPWPW91/6-31G(d) IOp(3/76=yyyy) 2 Opt=(VeryTight,Calcall) 3 4 CH2O calculation 5 6 0 1 7 C 0.0 0.0 0.0 8 O 0.0 0.0 1.2 9 H 0.0 0.9 -0.6 10 H 0.0 -0.9 -0.6 11 12

    Save this file in your home directory. The name of this input file should be teamxx-ch2o.txt where xx is the team number for this experiment. Example of input file for CH2O:

    Line # 1 # mPWPW91/6-31G(d) IOp(3/76=yyyy) 2 Opt=(VeryTight,Calcall) 3 4 CCl4 calculation 5 6 0 1 7 C 0.0 0.0 0.0 8 Cl -1.0 1.0 1.0 9 Cl 1.0 -1.0 1.0 10 Cl -1.0 -1.0 -1.0 11 Cl 1.0 1.0 -1.0 12 13

    Save this file in your home directory. The name of this input file should be teamxx-ccl4.txt where xx is the team number for this experiment.

    Running the computations

    Open a terminal window by choosing Applications then System Tools then Terminal option. In that Terminal window, run the Gaussian calculations using the commands below. Each line is a separate command so hit enter at the end of each line. source .bash_profile g03 teamxx-ccl4.out & g03 teamxx-c2h2.out & g03 teamxx-ch2o.out &

    The calculations will run for approximately 10 minutes. To verify if the calculation is finished, after about 10 minutes, press enter every 2-3 minutes.

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    Visualizing the output files (the results)

    To visualize the results you will use another program called Molden. To run this program, in the Terminal window, give the command: molden teamxx-ccl4.out & Two windows will appear; one showing the initial geometry of your molecule while the other is the windows with Molden commands (Molden Control).

    – In the Molden Control window, press Solid button and choose Ball & Stick option.

    – In the Molden Control window, press Shade button On or Off depending on your preference.

    – In the Molden Control window, press Label button and choose atom+number option.

    – In the Molden Control window, press Next button twice. This operation will show how the geometry changes during the optimization process.

    – In the Molden Control window, press Norm. Mode button. This operation will open two new windows: one with the calculated IR spectrum of the molecule and the other with a list of calculated frequencies. After inspecting it, close the window showing the spectrum. In the window showing the list of calculated frequencies, select each one of the frequencies and investigate the atom mo

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