thermochemistry with gaussian

8/13/2019 Thermochemistry With Gaussian

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Chem350: Thermochemistry using Gaussian.

In this write-up I will quickly go through the features needed to obtain thermochemical

data using gaussview/gaussian09. I will not give you very detailed instructions. You will

have to find your way using the graphical interface, which is quite straightforward to use.I encourage you to draw some molecules of your own, and see if you can manipulate thevarious tools in Gaussview. Below I will give you some instructive examples that

illustrate many of the capabilities of Gaussview/Gaussian09. In lab don't hesitate to askquestions.

The primary purpose of this section of Chemistry 350 is to show how the formalism we

developed in class directly translates into simple formulas that involve quantities that canbe extracted from routine quantum chemistry calculations: Optimized geometries and

moments of inertia, molecular mass, vibrational frequencies and electronic energies.Together with this lab I created a Matlab file that requires these quantities as inputs and it

then proceeds to calculate thermodynamical properties. We will check that the results areexactly the same as in the Gaussian program. Moreover, this gives you explicit access to

the proper formulas and unit conversions.

A. Calculations on a simple example: single point, geometry optimization and

vibrational frequencies of H2O.

Let us run through a very simple example first. You can create the water molecule using

the builder (pull down the menu), selecting Oxygen from the atoms menu. Let us firstdo a calculation on the guessed structure. Measure the bond angles and distance first

(using inquire, ?). Let us do a Hartree-Fock / 6-31G(d,p) calculation. For this click

Calculateand select Jobtype=Energy, Method=Hartree Fock, Basis is 6-31G, and onthe right hand options select from the between brackets options (d,p),by pulling downthe appropriate menus. This specifies the atomic orbital (AO) basis set. Then Submitthecalculation (see lower-left button). You will have to save your file, for example as h2o.Follow the directions given by the program. In a little while you get back the result, and

will be asked if you want to see it. Look at results (open the file h2o.log) and look undersummary. Here the main specifics of the calculation are summarized and you can find the

total energy. Next we will optimize the geometry, selecting jobtype=Optimization.Measure the geometries again. You should find the results as listed in the Table below.

Table I. Results for water

Property / units? Guess geometry HF 6-31G(d,p)optimized geometry

R(OH) 0.96 0.94319

A(HOH) 109.471 105.921

HF-6-31G(d,p) Energy -76.02255367 -76.02361493


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At the optimized geometry we can now calculate vibrational frequencies. Start from thegeometry in the h2o output file and select frequencyunder calculate->Jobtype.After the result returns you can view the vibrational frequencies (select under results).

You can view normal modes and infrared and raman spectra. The frequencies for thenormal modes in water are as follows.

Normal Mode Frequency (cm-1)

Bending 1770(.5)

Symmetric stretch 4145(.87)

Asymmetric stretch 4262(.48)

This same calculation can be done in one shot. Start anew by rebuilding H2O from

scratch, and select Opt+Frequnder the Jobtypemenu. It first does the optimization, andthen calculates the vibrational frequencies. Vibrational frequencies are only meaningful

at the optimized geometry!

You can also look in the output file. The vibrational frequencies are all listed near the endof the file. This section also lists their symmetry. All of the vibrational motions have a

definite symmetry with respect to planes of symmetry and rotational axes in themolecule. Normal modes of A1 symmetry preserve the symmetry of the molecule.

Normal modes of other symmetry-type break the symmetry of the molecule. You caninvestigate by visualizing normal modes, under summary.

B. Calculations on a slightly more advanced example: trans-butadiene. Some more

options and features in Gaussian.

I will run you through one more example doing similar things. Part of the information is

similar as for water.

Use the gv builder to construct trans butadiene. You only need to build the carbon chain

using the appropriate type of carbon atom. The hydrogens are added automatically. Go toViewto examine different ways to see the structure. In particular switch on Symbols tosee all atom types. Rotate and translate the molecule, using the mouse. If you press the

clean button (broom) in the builder window, you will get a first rough guess for thestructure. It is also useful to click the symmetrize button. It can be useful to use the

pointgroup option under edit. Your molecule should have C2h symmetry. Save yourinput file, e.g. t_c4h6.

c1 c2

c3 c4H

HH

H H

H


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Next optimize the structure and calculate frequencies at the HF/3-21G level of theory. To

this end open the calculate menu and specify options as before.

- Measuring geometrical features.

Click on the inquire button in the builder menu (question mark). This will give yougeometrical information. By clicking two atoms you get the bond distance. By selectingthree atoms you find the angle made by these atoms. Finally by clicking 4 atoms in

sequence you get the dihedral angle (in "4321" format). This is the torsional angle aroundatoms 2 and 3. The dihedral angle is measured rotating the fourth atom onto the first atom

along the 3-2 bond axis. Clockwise angles are positive. Now find the C1-C2, C2-C3 andC3-C4 bond lengths. You clearly see the double bonds in the geometrical structure.

However, also C2-C3 is substantially shorter than typical C-C single bonds (quicklyconstruct and optimize ethane if you wish to confirm this). Compare terminal and center

CH bond lengths. Also measure various bond angles and comment on your findings.

What is the C1C2C3C4 torsional angle around the C2-C3 bond? Now measure it byclicking the appropriate atoms. It is of interest to look at the geometry in the originalguessed structure, before optimization. Here you see there is no information on

conjugation. Instead the program guesses standard single and double bonds. Under theResults menu you will find a number of options that allow you to analyse the output of

your calculation in an easy way.

- Changing geometries.

Let us transform trans-butadiene into cis-butadiene. To this end click on dihedralin thebuilder menu, and select four atoms that specify the desired dihedral angle (in '4321'format). This opens the dihedral smartslide. Change the dihedral from 180 to 0. Savethis new structure as cis-c4h6.com and perform an optimization of the geometry. Nowyou can analyse the structure (and energetic and orbitals) of cis-butadiene. You can

similarly change angles and bond distances by clicking the respective buttons inGaussview. What is the symmetry of Cis-butadiene?

- Vibrational frequencies and viewing normal modes.

It is very easy to obtain vibrational frequencies in gaussview. Under the jobtype menuspecify OPT+FREQ. Infrared intensities are calculated always, Raman intensities

sometimes by default. Calculate the vibrational spectrum of trans-butadiene. Uponcompletion of the calculation you can display by going to Results/Vibrations. Thisshows a list of the calculated vibrational frequencies. By clicking any one of the

frequencies and clicking start you can view an animation of the vibrations. Optionallyyou can also display the displacement vectors that characterize the normal mode. Set the

Frames/cycle and Displacement scales to your preference. By clicking spectrumyou seethe complete vibrational spectrum displayed. Characterize the various vibrations in trans-

butadiene. Where are the CH stretches and how many are there? What is the difference


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between them? Where are the various C-C stretches? Can you clearly distinguish C1-C2stretch and C2-C3 stretches? Characterize the various bending modes, or rotations around

the various bonds.

- Charges.

For any calculation you can view the charges in the molecule. Trans-butadiene is notparticularly interesting of course. You might create an alcohol or a carbonyl compound to

see something more interesting. Play around with the options to obtain a rendering of thecharges that you prefer. The above gives you an overview of some of the most widely

applicable options in Gaussview/Gaussian09.

C. Investigating Thermochemistry and checking Statmech formulas in Gaussian.

By optimizing a geometry and calculating vibrational frequencies one obtains all of the

information needed to calculate the partition function of a molecule in the gas phase(ideal gas / rigid rotor / harmonic oscillator approximation). In order to achieve accurate

results that can be compared to experimental values one needs to do accurate electronicstructure calculations. For many practical purposes a Density Functional Calculation

using the B3LYP functional and a cc-PVTZ basis set is sufficiently accurate. For amolecule that has lone pairs or internal hydrogen bonds a bigger basis set may be

required. We will first do calculations on a linear molecule (CO2) and on the watermolecule. I will show you where you can locate the thermochemistry output in the

Gaussian output file. Moreover , we can run a little Matlab program to do the statmechpart of the calculations ourselves. This way we can check what is done in Gaussian, and

if things agree we have a compact representation of all the required formulas and all ofthe unit conversions through the Matlab file.

i) Thermochemistry of water (non-linear molecule)Create the water molecule. Underjobtypeselect OPT+FREQ, while under Methodselect a ground state DFTcalculation. Select the B3LYPfunctional (default) and thecc-pVTZbasis set under the appropriate menu. Then save the file and submit thecalculation. !"#$ &'( )' ($*#+ ,#-(./-01(223+& &'( 45.. 65$* /"# /'/3. #.#7/+'$57

#$#+)&8

E(RB3LYP) -76.45983962 (in Hartree)

9"5- 5- '$# :5#7# '6 5$6'+23/5'$ $##*#* 6'+ /"#+2'7"#25-/+&;


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Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scatteringactivities (A**4/AMU), depolarization ratios for plane and unpolarizedincident light, reduced masses (AMU), force constants (mDyne/A),and normal coordinates:

1 2 3

A1 A1 B2Frequencies -- 1638.7752 3803.1701 3903.6257Red. masses -- 1.0831 1.0447 1.0819Frc consts -- 1.7139 8.9032 9.7133IR Inten -- 69.5441 3.2440 40.9209Atom AN X Y Z X Y Z X Y Z

1 8 0.00 0.00 0.07 0.00 0.00 0.05 0.00 0.07 0.002 1 0.00 -0.43 -0.56 0.00 0.59 -0.39 0.00 -0.56 0.433 1 0.00 0.43 -0.56 0.00 -0.59 -0.39 0.00 -0.56 -0.43

B'+ (- /"# 52:'+/3$/ :3+/ 7'$7#+$- /"# B+#A(#$75#-> 4"57" "3- /"# "3+2'$57

?5@+3/5'$3. 6+#A(#$75#- 5$ 43?# $(2@#+-;

Frequencies -- 1638.7752 3803.1701 3903.6257

C(-/ @#.'4 /"5- -#7/5'$ '$ 6+#A(#$75#- 5$ /"# '(/:(/ 65.# 4# 65$* 3.. /"# 5$6'+23/5'$

'$ /"#+2'7"#2573. A(3$/5/5#-; 9"5- -#7/5'$ '6 /"# '(/:(/ 65.# .''=- .5=# /"5-

------------------- - Thermochemistry --------------------Temperature 298.150 Kelvin. Pressure 1.00000 Atm.

Atom 1 has atomic number 8 and mass 15.99491Atom 2 has atomic number 1 and mass 1.00783Atom 3 has atomic number 1 and mass 1.00783Molecular mass: 18.01056 amu.Principal axes and moments of inertia in atomic units:

1 2 3Eigenvalues -- 2.21189 4.15886 6.37075

X 0.00000 0.00000 1.00000Y 1.00000 0.00000 0.00000Z 0.00000 1.00000 0.00000

This molecule is an asymmetric top.

Rotational symmetry number 2.Rotational temperatures (Kelvin) 39.15821 20.82634 13.59554Rotational constants (GHZ): 815.92565 433.95112 283.28541Zero-point vibrational energy 55898.9 (Joules/Mol)

13.36016 (Kcal/Mol)Vibrational temperatures: 2357.83 5471.91 5616.44

(Kelvin)


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In sequence we find information on the atomic and molecular masses, the moments ofinertia tensor (both the eigenvalues and the eigenvectors), rotational temperatures, and

the symmetry number. Finally, vibrational temperatures for each normal mode. This is all

the information needed to process the data and calculate heat capacities, entropy, Internalenergy, Enthalpy, Gibbs free energy. The Gaussian program does it for you of course,and the results are listed as follows:

Zero-point correction= 0.021291 (Hartree/Particle)Thermal correction to Energy= 0.024126Thermal correction to Enthalpy= 0.025070Thermal correction to Gibbs Free Energy= 0.003649Sum of electronic and zero-point Energies= -76.438549Sum of electronic and thermal Energies= -76.435714Sum of electronic and thermal Enthalpies= -76.434769

Sum of electronic and thermal Free Energies= -76.456191

E (Thermal) CV SKCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin

Total 15.139 6.007 45.085Electronic 0.000 0.000 0.000Translational 0.889 2.981 34.608Rotational 0.889 2.981 10.470Vibrational 13.362 0.046 0.007

Q Log10(Q) Ln(Q)Total Bot 0.209715D-01 -1.678370 -3.864589Total V=0 0.130223D+09 8.114687 18.684757Vib (Bot) 0.161103D-09 -9.792897 -22.548979Vib (V=0) 0.100037D+01 0.000160 0.000368Electronic 0.100000D+01 0.000000 0.000000Translational 0.300432D+07 6.477746 14.915562Rotational 0.433292D+02 1.636781 3.768828

In Chem350 we went through all of the machinery that is involved to do the calculations.

From the chem350 website you can download a Matlab file. In it you find the above datafor the water molecule, and the calculation of thermodynamic properties. Going through

the Matlab file and the Gaussian output file, you will find exact agreement between whatwe do in class, and what is implemented in the Gaussian program. These things are used

in actual state-of-the-art calculations! I encourage you to go through the Matlab file andmake sure you understand all the steps in the calculation. Find the corresponding results

in the Gaussian output file.


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ii) CO2 (linear molecule).

To make sure we get things correctly also for linear molecules, let us do a calculation on

the CO2molecule, using the same DFT/B3LYP method using the cc-pVTZ basis set. This

is the output I obtained, and need to set up the corresponding matlab calculation.From the SummaryE(RB3LYP) -188.66056820

From the output file (view file):Frequencies -- 671.7935 671.7935 1371.8079Frequencies -- 2417.0441

Molecular mass: 43.98983 amu.

Principal axes and moments of inertia in atomic units:1 2 3

Eigenvalues -- 0.00000 153.80801 153.80801Rotational symmetry number 2.

This is all the information needed to calculate thermodynamical properties. You can feedit into the Matlab file and calculate properties directly. Then compare with the Gaussian

thermochemistry output section:Zero-point correction= 0.011693 (Hartree/Particle)Thermal correction to Energy= 0.014311Thermal correction to Enthalpy= 0.015255Thermal correction to Gibbs Free Energy= -0.008999Sum of electronic and zero-point Energies= -188.648876Sum of electronic and thermal Energies= -188.646258Sum of electronic and thermal Enthalpies= -188.645314Sum of electronic and thermal Free Energies= -188.669567

E (Thermal) CV SKCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin

Total 8.980 6.855 51.046Electronic 0.000 0.000 0.000Translational 0.889 2.981 37.270Rotational 0.592 1.987 13.073Vibrational 7.499 1.887 0.703

Q Log10(Q) Ln(Q)Total Bot 0.137819D+05 4.139308 9.531109Total V=0 0.329230D+10 9.517499 21.914852Vib (Bot) 0.453971D-05 -5.342972 -12.302648Vib (V=0) 0.108447D+01 0.035219 0.081095Electronic 0.100000D+01 0.000000 0.000000Translational 0.114679D+08 7.059484 16.255062Rotational 0.264726D+03 2.422797 5.578695


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D. Calculating equilibrium constants from Gibbs free energy calculations.

Consider the reaction

2 2 2 2 4( ) ( ) ( )C H g H g C H g + !

To calculate the equilibrium constant at standard temperature and pressure one needs tocalculate the !

rG

298.15

0 , i.e. the Gibbs free energy for each of the species. Such

calculations are straightforward with what we know now. Create each of the molecular

species in Gaussian and optimize geometries and calculate frequencies at for example theDFT/B3LYP/cc-pVTZ level. The most critical aspect of the calculation is the electronic

energy. One can try to improve the accuracy in this respect. Since this is not a class oncomputational chemistry let us simply proceed at the above level. From the Gaussian

outputs you can obtain the Gibbs free energy for each species, and also Cv and hence Cpusing ideal gas expressions. From the calculated data calculate the equilibrium constant at

298.15 K, 1 atm, and also at 400 K, 1 atm. Also calculate the equilibrium constant usingdata in Reid and Engel (or from the web!). Compare the results.

E. Calculation of transition states. Comparing Gaussian output with Matlab

calculation.

As a very simple, standard, example let us consider the hydgron migration reaction in

HCN. You need to provide a guess for the transition state (elongate both CH and CNbonds a bit, in addition to changing the angle). Then select OPT+FREQ under jobtype,

and select optimize to a transition state (Berny TS), and calculate the force constantmatrix once. Under method select the DFT / B3LYP /cc-pVTZ methodology as usual.

Upon running the calculation we can get the information we need. The first thing to do is

check the Summay/Vibrations. We should find exactly one imaginary frequency(indicated in Gaussian as a negative frequency). You can look at it, and verify that thisnormal mode corresponds to the reaction coordinate. To do the statmech we lift the usual

information from summary and output files:

E(RB3LYP) -93.38546704 a.u.Frequencies -- -1129.0406 2066.9596 2592.7695

Molecular mass: 27.01090 amu.Principal axes and moments of inertia in atomic units:

1 2 3Eigenvalues -- 4.38207 32.45085 36.83292

We can put this information in the Matlab file and run the thermochemistry. Note that the

negative frequency does not enter the equations. Instead we get a factor kT/h in the rateconstant. You can verify that the Gaussian output indeed agrees with our statmech

calculation in Matlab.

To calculate reaction rates and activation barriers we should also calculate the free energyof reactants (HCN) and products (HNC). This then provides the free energy reaction


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profile, and a first estimate of the rate constant for the elementary reaction. Using thesevalues the reaction rates can be calculated at any temperature, using the formulas for

Gibbs free energy. You can compare with the traditional thermodynamics way ofcalculating the temperature and pressure dependence of the Gibbs free energy and the

Arrhenius law.

F. A case study: Comparing the rate of reaction for cis-trans isomerization in

butadiene to the rate of conformational change in ethane: The effects of

conjugation.

The following calculations are time consuming!! Get them to run but you may wish tocollect results later on. Since you can only run one Gaussian job it is all a bit painful.

Such is life!

Throughout we will use the DFT/B3LYP/cc-PVTZ approach. Optimize the structures ofcis and trans butadiene and calculate vibrational frequencies. It is helpful to impose the

correct pointgroup symmetry. This can be done using the pointgroup option under edit.Using the correct symmetry speeds up the calculation. If you want to change the structure

and perhaps the symmetry, you have to undo setting the symmetry first. Also locate thetransition state structure, by using an initial guess for the dihedral angel of 90 degrees and

obtain vibrational frequencies. Check that you get one negative (=imaginary) frequency.Now you can process the free energies and calculate the forward and backward reaction

rates, as well as the equilibrium constant at ambient temperature and pressure. You canalso investigate the various contributions to the thermal properties (rotational, vibrational

etc.). I anticipate the energy barrier to be substantial because the system is conjugatedwith its alternating pattern of double bonds. Let us compare to the barrier to rotation in

ethane therefore. You can make the so-called staggered and eclipsed configurations ofethane, the latter being a transition state. Follow the same recipe and comment on the

differences. See if you can find values for the above quantities in the literature or usingthe Web. For example visit the NIST side, which has a wealth of computational and

experimental data.

G. Summary

All gas phase reactions can in principle be studied (given enough computer resources).We have now discussed all of the underlying theoretical principles in chem254

(thermodynamics), chem350 (kinetics and statmech) and chem356 (QuantumMechanics): particle in the box: translational energy; Rigid Rotor model, (using spherical

harmonics): rotational energy contributions; harmonic oscillator models for polyatomics:vibrational part of the energy. The major component of the reaction enthalpy is the

difference in the electronic energy at the minimum of the potential (the optimizedgeometry), for each of the molecules involved in the reaction. Here accurate calculations

are critical, and in prior classes we only scratched the surface regarding electronic energycalculations. You can obtain more background information on this in classes on

computational chemistry (chem440 / computational), and quantum mechanics in


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chemistry (also chem440 special topics), but it is a rather specialized subject without easysolutions.

thermochemistry with gaussian

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