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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

yC-1

Cl-2

Cl-4

Cl-3

Cl-5x

z

yC-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.txt> teamxx-ccl4.out & g03 <teamxx-c2h2.txt> teamxx-c2h2.out & g03 <teamxx-ch2o.txt> 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 movement. Record the directions of these displacement vectors and the frequency value in the appropriate page in the handout. (The atom movement could appear too fast due to the fast processor. One way to visualize the displacements is to press the button with a skull in the Molden Control window. By doing this, the vibration is frozen and the displacements can be investigated better. Press Cancel to allow the vibration to continue.) You can rotate the molecule to view the vibrations better but keep in mind the original orientation and come to this orientation when you are investigating the next normal mode. (You need to have consistent orientation when record the direction of atom movement.) Ask your instructor for assistance if needed. (Following the lab, you can download and install a free (i.e., 90 days try) visualization software called ChemCraft that will allow visualizing Gaussian results on your PC. Another free software with similar capabilities is called Facio.)

– To start over from the original orientation, press Read button, then select you output file (teamxx-ccl4.out) from the list.

– In the Molden Control window, press First button (this will show again the first geometry), press Movie button (this will show subsequently all geometries but there are only three in this case), press ON then OFF the button with a photo camera on it (second from top on the middle row). This will take a picture (.gif file) that the instructor will send by e-mail to you.

– Repeat the procedure for acetylene and formaldehyde output files: teamxx-c2h2.out and teamxx-ch2o.out. You can access them by selecting one of these files in the window opened after pressing the Read button and pressing Update directory button.

– When you are finished, press the button with a skull (located above “Zoom”) in the Molden Control window to end Molden program.

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Examining the output file (the results)

In Home Directory window, double click the teamxx-c2h2.out in your home directory. Visually inspect the output file. Look for information that you may understand like the geometry, the point group, the type of molecular orbitals, etc. Do the same for the other two output files. A general presentation of the file and the information you can find in it will be given by your instructor. Finding the optimized energy: Make a search after “Done”. You will find it 3 or 4 times in the output file in lines of form: “SCF Done: E(UmPW+HF-PW91) -37.8404108325 A.U. after 12 cycles“ In these lines you will find the energy (in hartree or atomic units) of a particular geometry (structure) of the molecule, geometry that appear above in the input file. The last energy is the lowest one and corresponds to the optimized geometry. This energy is relative to all electrons and all nuclei infinitely separated so it is a very large negative number. Finding the calculated frequency values: Below the line showing the lowest energy (after some other information) there is the part in the output file that presents the vibrational frequencies, the IR intensities, the atom displacements, etc. You should get the calculated frequency values from here.

Transferring the output file (the results)

You can transfer your files on a jumpdrive or you can e-mil them to yourself. Open the Web Browser located near Actions button. Login into e-mail server at Tennessee Tech and send to yourself an email having as attachments all files created today.

Computer logout

After you submitted your files to yourself by email, delete them from the Home directory and then from Trash as well. Press Actions button, then Log Out button.

Lab Report The Lab Report should contain: 1. Cover Sheet 2. Printouts of the input files and selected parts (interesting parts that you understand) of the

output files. For the output files, use WordPad and, from the Page Setup, set all the margins (Top, Bottom, Left, and Right) to 0.7. Print double sided if possible.

3. Printout with the pictures of C2H2, CH2O, and CCl4. 4. The pages with normal mode atom displacements, their associated symmetry and frequencies

in which you will sketch the movement of atoms for each normal mode as visualized using Molden.

5. The pages with questions and discussions.

Appendix The Theoretical Background

Density Functional TheoryDensity functional theory-based methods ultimately derive from quantum mechanicsresearch from the J920's, especiallythe Thomas-Fermi-Dirac model, and from Slater'sfundamental work in quantum chemistry in the 1950's.The DFT approach is basedupon a strategy of modeling electron correlation via general functionalst of theelectron density.

Such methods owe their modern origins to the Hohenberg-Kohn theorem, publishedin 1964, which demonstrated the existenceof a unique functional which determinesthe ground state energy and density exactly.The theorem does not provide the formof this functional, however.

Following on the work of Kohn and Sham, the approximate functionals employedbycurrent DFT methods partition the electronicenergy into severalterms:

'\E = ET + EV + EJ + EXC [54]

where ET is the kinetic energy term (arising from the motion of the electrons), EYincludes terms describing the potential energy of the nuclear-electron attraction andof the repulsion between pairs of nuclei, EJis the electron-electron repulsion term (itis also described as the Coulomb self-interaction of the electron density), and EXCisthe exchange-correlation term and includes the remaining part of theelectron-electron interactions.

All terms except the nuclear-nuclear repulsion are functions of p, the electron density.EJis given by the following expression: .

I

ff'" .>. .>....

EJ =:2 p (r\) (M\z)-\p (rz) dr\drz [55]

ET+EV+EJ corresponds to the classical energy of the charge distribution p. The EXCterm in Equation 54 accounts for the remaining terms in the energy:

.. The exchange energy arising from the antisymmetry of the quantummechanical wavefunction.

.. Dynamic correlation in the motions of the individual electrons.

t A functional is a function whose definition is itself a function: in other words, a function of a function.

272 Exploring Chemistry with Electronic Structure Methods

Electron Correlation Methods

Hohenberg and Kohn demonstrated that EXC is determined entirely by the (is afunctional ot) the electron density. In practice, EXC is usually approximated as anintegral involving only the spin densities and possibly their gradients:

EXC(p) = ff(Po:(;)'P~(;)'VPo:(;)' Vp~(;))d3; [56]

We use Po:to refer to the a spin density, P~ to refer to the ~spin density, and p to referto the total electon density (Po: + p~).

EXCis usually divided into separate parts, referred to as the exchange and correlation

parts, but actually corresponding to same-spin and mixed-spin interactions,respectively:

EXC(p) = EX(p) +Ec(p) [57]

All three terms are again functionals of the electron density, and functionals definingthe two components on the right side of Equation 57 are termed exchr;mgefunctionalsand correlationfunctionals, respectively. Both components can be of two distincttypes: localfunctionals depend on only the electron density p, while gradient-correctedfunctionals depend on both p and its gradient, Vp.t

We'll now take a brief look at some sample functionals. The local exchange functionalis virtually alwaysdefined as follows:

x 3(3)

1/3

fELDA = -2 41t p4/3d3~ [58]

where p is of course a function of ~. This form was developed to reproduce theexchangeenergyof a uniform electrongas. Byitself,however,it has weaknessesindescribingmolecularsystems.

Beckeformulated the following gradient-corrected exchange functional based on theLDA exchangefunctional in 1988,which is now in wide use:

fp4/3x2 ~

X X d3rEBecke88 = ELD A - Y (1 + 6ysinh-l x)

[59]

t Note that this use of the term "local" does not coincide with the use of the term in mathematics; both local

and gradient-corrected functionals are local in the mathematical sense.

Exploring Chemistry with Electronic Structure Methods 273

Appendix I The Theoretical Background

where x = p-4/3IV pi .y is a parameter chosento fit the known exchangeenergiesofthe inert gasatoms, and Becke defines its value as 0.0042 Hartrees. As Equation 59makes clear, Becke'sfunctional is defined as a correction to the local LDA exchangefunctional, and it succeedsin remedying many of the LDA functional's deficiencies.

Similarly, there are local and gradient-corrected correlation functionals. For example,here is Perdew and Wang's formulation t of the local part of their 1991 correlationfunctional:

EC = fpEc(rg(p(~)),1;;)d3~

EC(rg, 1;;)

[3]

1/3

rg = 4np

1;; = Pa-P~PIX + P~

f (1;;) 4= EC(p, 0) + ac (r g)f" (0) (1 -1;; ) + [EC(p, J) - EC(p, 0) ] f (1;;) 1;;4

[ (1 + 1;;)4/3 + (1 -1;;) 4/3 - 2]

f(~) = (24/3_2)

[60]

rg is termed the density parameter./; is the relative spin polarization. 1;=0 correspondsto equal <Xand ~densities, 1;;=1correponds to all <Xdensity, and ~=-l corresponds toall ~ density. Note that £(0)=0 and f(:tl)=1.

The general expression for EC involves both rg and /;. Its final term performs aninterpolation for mixed spin cases.

The following function G is used to compute the values of EcCrg,O),EcCrs,l) and-acCrs):

(1

J[61]

G(rs,A,al'~I,132'~3'~4'P) = -2A(1+<Xlrs)ln 1+2A(~lr!/2+~2rS+~3r;/2+~4r~+1)

In Equation 61, all of the, arguments to G except rg are parameters chosen by Perdewand Wang to reproduce accurate calculations on uniform electron gases. Theparameter sets differ for G when it is used to evaluate each of EcCrs'O),ecCrs,l) and-acCrs). '

In an analogous way to the exchange functional we examined earlier, a localcorrelation functional may also be improved by adding a gradient correction.

t Which is very closely related to Vosko, Wilk and Nusair's local correlation functional (VWN).

274 Exploring Chemistry with Electronic Structure Methods

Electron Correlation Methods

Pure DFT methods are defined by pairing an exchange functional with a correlationfunctional. For example, the well-known BLYP functional pairs Becke'sgradient-corrected exchange functional with the gradient-corrected correlationfunctional of Lee,Yangand Parr.

Hybrid FunctionalsIn actual practice, self-consistent Kohn-Sham DFT calculations are performed in aniterative manner that is analogous to an SCF computation. This similarity to themethodology of Hartree-Fock theory was pointed out by Kohn and Sham.

Hartree- Fock theory also includes an exchange term as part of its formulation.Recently,Beckehas formulated functionals which include a mixture of Hartree- Fockand DFT exchangealong with DFT correlation, conceptually defining EXCas:

EXC - Ex E XChybrid - cHP HP + COPT OPT [62]

where the c's are constants. For example, a Becke-style three-parameter functionalmay be defined via the following expression:

EJfLYP = ECOA + Co(E~p - ECOA) + cx~E;88 + E~WN3 + Cc (ECyp-EtWN3) [63]

Here, the parameter Coallowsany admixture ofHartree-Fock and LDAlocal exchangeto be used. In addition, Becke'sgradient correction to LDAexchange is also included,scaled by the parameter cx. Similarly,the VWN3 local correlation functional is used,and it may be optionally corrected by the LYP correlation correction via theparameter cc. In the B3LYPfunctional, the parameters values are those specified byBecke, which he determined by fitting to the atomization energies, ionizationpotentials, proton affinities and first-row atomic energies in the G1 molecule set:'co=0.20, cx=O.72 and cc=0.81. Note that Becke used the the Perdew-Wang 1991correlation functional in his original work rather than VWN3 and LYP.The fact thatthe same coefficients work well with different functionals reflects the underlyingphysicaljustification for using such a mixture ofHartree-Fock and DFT exchangefirstpointed out by Becke.

Different functionals can be constructed in the same way by varying the componentfunctionals-for example, by substituting the Perdew-Wang 1991 gradient-correctedcorrelation functional for LYP-and by adjusting the values of the three parameters.

Exploring Chemistry with Electronic Structure Methods 275

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EXPERIMENT CC

Computational Chemistry: Vibrational Spectrum of CCl4

Lab Report Questions and Discussion 1. What is the initial C–Cl distance (i.e., the C–Cl distance in the structure given in the input

file)? Use four significant figures.

2. What is the optimized C–Cl distance (i.e., the C–Cl distance in the final structure of the

output file which is the structure of lowest energy)? Use four significant figures. How is this value compared with experimental (tabulated value)? Give reference.

Calculated Experimental* % Error

* Reference:

3. List the calculated frequencies values (in cm–1) and compare them with published value.

(Use three significant figures.) List the degeneracy as well. How well are the values matched up?

Calculated Experimental* Degeneracy % Error

* Reference:

4. How long it took for the calculation to be finalized? (What is the cpu time?)

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5. Calculate the average bond energy (in kcal/mol) for a C–Cl bond (1/4 the energy of CCl4 → C + 4 Cl process) based on the calculated energy value of optimized CCl4 and the given energy values of C and Cl in the table below. Those values are in atomic units (a.u.) or hartree (Eh) are the relative energy values with respect to the separated nucleus (or nuclei) and electrons. (This is why the values are so large and negative.)

Energy of optimized CCl4 (in a.u.)

Team Keyword in input file C energy (a.u.) Cl energy (a.u.) 01 IOp(3/76=0800002000) -37.8315476 -460.1398414 02 IOp(3/76=0700003000) -37.8326777 -460.1411972 03 IOp(3/76=0600004000) -37.8338545 -460.1426593 04 IOp(3/76=0500005000) -37.8350771 -460.1442256 05 IOp(3/76=0400006000) -37.8363449 -460.1458938 06 IOp(3/76=0300007000) -37.8376569 -460.1476618

Show your work:

Average bond energy:

Calculated Experimental* % Error

* Reference:

6. List interesting results or observations you had during the lab or while preparing the report.

Use additional pages if necessary.

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EXPERIMENT CC

Computational Chemistry: Vibrational Spectrum of CCl4

Normal Mode Atom Displacements and Their Associated Frequencies

Symmetry

Frequency

Symmetry

Frequency

Symmetry

Frequency

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EXPERIMENT CC

Computational Chemistry: Vibrational Spectrum of C2H2

Normal Mode Atom Displacements and Their Associated Frequencies

Symmetry

Frequency

Symmetry

Frequency

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EXPERIMENT CC

Computational Chemistry: Vibrational Spectrum of CH2O

Normal Mode Atom Displacements and Their Associated Frequencies

Symmetry

Frequency

Symmetry

Frequency