Quantum Theory and its Applications Introductory Lab Objectives:

Quantum Theory and its Applications
Introductory Lab
Objectives:
I. Learn how to login to the computers.
II. Basics of Linux.
III. Using Molden and Emacs.
IV. Understanding Gaussian’s input, output and how to run it.
I. Learn how to login to the computers:
From your desktop computer you will login to CLEO, a cluster of PC’s working under
Linux operating system. There we’ll do all the hard work.
1. Open StartX (icon:
) in the “Novell delivered application” window. This is
a Linux terminal emulator suitable for communication with Cleo.
2. For this time only: Copy in your directory the script “cleo” by writing
cp t:/69615/cleo .
(don’t forget the final point, which means the directory you are now).
3. Execute “cleo”. This file is a script that enters automatically to Cleo and sets
the work environment.
4. Your user i.d. is “student#” where # is a number (one for each group and for
all eternity). Your password is also “student#”. Now you should be in Cleo.
II. Basics of Linux:
Linux has also nice windows and colorful stuff (know as GUI, graphical user
interface). But serious people work with terminals with a command line interpreter
(like old DOS). So everything is done by writing commands (case sensitive!!!). Some
of the most useful ones are:
ls
List the content of the directory.
pwd
Tells us in what directory we are
mkdir directory
Makes a directory
cd directory
Changes directory
cp file1 file2
Copies files
rm file
Removes files
mv file1 file2
Renames a file or moves it from a directory to another
top
Load of running programs in the node
cat file
Shows content of a file
more file
Shows content of a file page by page
tail file
Shows the last ten lines of a file
grep ‘string’ file
Shows the lines in the file which contains the string
logout, exit
Well, it should be clear what it does
Examples:
mkdir dir1/dir2
Creates the directory dir2 inside dir1
cd dir1/dir2
Goes to dir2
cd ../
Goes up one directory
cd ~/
Goes to your home directory
cp ~/file dir1/dir2/
Copies file from home directory to dir2
cp * dir1
Copies all files to dir1
cp -r dir1 dir3
Copies all the directory dir1 to dir3
tail -f file
Shows the appended data as file grows
grep ‘SCF Done’ h2.log
Shows the lines in the file h2.log that contains the
phrase SCF Done
Linux exercise:
Find the files h2.g and h2.log. These are the input and output of a Gaussian
optimization of H2.
Create a directory called “Introduction” and move those files there.
Look into the input file.
Enter to the new directory and search in the output file the energy of each
step of the optimization. The string “SCF Done” appears in the line of the
energy value.
Return to your home directory.
III. Using Molden and Emacs
IV. Understanding Gaussian’s input, output and how to run it
Emacs is a graphical text editor where we will make most of Gaussian work. The
easiest way to open an existing or unexisting file is
emacs file &
The & sign tells the computer to open emacs in the background, which permits us to
continue using the terminal.
Open the file “h2o2.g”. This is an input for an optimization calculation of
hydrogen peroxide. Change the H-O-O-H dihedral angle to 100. degrees
(don’t forget the point!). Save the file.
To run a file in Gaussian you just type in the terminal
g03 input_file &
Our Gaussian is not a graphical program. It is mostly invisible. To see it running you
can use the top command or the tail -f output_file one. The standard is to have the
input file with .g or .g03 extension, while the output will be .log.
Run the “h2o2.g” job. In the meantime (be fast) type “tail -f h2o2.log” to see
the output file growing. To exit write ctrl-c. Then check if its running with
top. You should see yourself in USER column, and in the COMMAND one L502
or another number. This is the Gaussian execution. To leave the top type “q”.
The job takes aprox. 1’30’’.
We will check the results graphically with Molden. The command is
molden output_file &
Open with Molden the output file. Play one minute with the molecule. Try
changing the visualization with “solid” and putting labels to the atoms.
Check the evolution of the optimization. Click on "Geom. conv." and look
what the graphs show. Select "distance" button and click on both oxygens,
and then use "monitor". Also see the dihedral angle. Advance through the
steps by clicking on "next" or "movie". See now the final geometry
parameters.
To see the orbitals select “Density Mode”. Click on "orbital" and see their
energies and population. Select the HOMO and click on "space", putting 0.2
in "Contour Value?". What kind of orbital is it, σ or π? Bonding or
antibonding? Try changing the contour value to 0.4 and 0.05. What does this
value means?
Return to normal view with "Mol. Mode". Look at the Z-matrix with "ZMAT
Editor". Change one hydrogen to chlorine, and put a different dihedral value.
Save it as a Gaussian input by clicking on "Gaussian" button, writing a
suitable name and clicking on "Write Z-Matrix". Close with "Close" and exit
from Molden with the skull button. Look how Molden compose your new input
file.
Charlie Brown..'I can't get that stupid kite in the air... I can't...
I c a n n o t...'
Lucy..'Oh come now Charlie Brown...That's no way to talk... The
trouble with you is you don't believe in yourself... You don't
believe in your own abilities... You've got to say to
yourself...'I believe I can fly this kite.'... Go ahead say it....'
Charlie Brown..'I believe that I can fly this stupid kite.....I believe
that I can fly this kite........
I a c t u a l l y b e l i e v e t h a t I c a n ******'
Lucy..'I'll bet you ten-to-one you're wrong.......'
Schulz
Quantum Theory and its Applications
Laboratory 1
Objectives:
I. Construct ex nihilo the molecule FH2C-CH2F.
II. Check its properties and most probable conformation.
F
F
The
1,2-Difluoroethane
has
two
distinct
conformations. Here we will study the reaction energy
F
of its rotation. As energy is a relative amount, you
F
Anti
Gauche
must express one structure against the other.
(Question: Relative to what is then expressed the
energy in Gaussian?)
So, build both conformers, run the two jobs with the theory and basis set that you
find appropriate and check:
Conformers relative energies.
Thermodinamical constant of rotation and their relative concentrations.
Geometry parameters (distances, angles, dihedral angles).
Symmetry, dipole moment, Mulliken charges.
Take care that the programs results are in atomic units (Hartrees), which are
extremely annoying. We will use kcal/mol, which is an ugly unit but the most
standard and comfortable for chemical reactions.
1Ha = 627.51 kcal/mol
It is a profoundly erroneous truism ... that we should cultivate the
habit of thinking of what we are doing. The precise opposite is the
case. Civilization advances by extending the number of important
operations which we can perform without thinking about them.
-- Alfred north whitehead
Quantum Theory and its Applications
Laboratory 2
Objectives: Look what Gaussian can calculate.
I. Make two calculations of methane single point energies, one ordinary and the
second adding the keyword “nosymm” (note that the input files are ready, by the
name “CH4.symm.g” and “CH4.nosymm.g”). Check the orbitals by inspecting the
coefficients and with molden. What can you say about the two different sets of
orbitals?
Taking the orbitals of the symmetric calculation construct an interaction diagram
from C + H4.
II. Run the “H2O.g” and “D2O.g” files. They are water and heavy water optimizations
and frequency calculations (check in the inputs how to do a frequency job and how
to change the isotopic number of atoms). Are there any differences in geometry or
orbitals?
Draw the vibrational normal modes and their magnitudes for H and D. You can also
see the vibrations in molden.
Look up the difference in zero-point energy (ZPE) when changing isotopes.
What are the components of Gibbs free energy? What extra calculations does
Gaussian make to the energy using the freq keyword? What are the components of
the entropy and how are they affected by isotopic change?
III. Analyze the canonical and LMO orbitals of water (files “H2O.canonical.g” and
“H2O.localized.g”). Note that for the LMO job you need first the canonical orbitals.
Gaussian reads them from a checkpoint file and then makes Boys' localization. The
keyword is "guess(local,read,only)". Guess means the way to make the initial
guess for the orbitals; local is for localization; read looks the orbitals in the
checkpoint file; only is to retain the orbitals without further optimization.
IV. Make a frequency calculation of N2 (“N2.g”) and N2+ (“N2plus.g”). Explain the
differences.
V. Calculate
ethane
in
its
optimized and eclipsed conformations
(“Ethane.g”,
“Ethane.eclipsed.g”). Check the frequencies and explain the meaning of the
negative frequency in the eclipsed state. By using Eyring’s transition state theory
calculate the rotational constant of ethane.
VI. Calculate the H-NMR chemical shift of propene (“propene.g”) -optimized in HF 631G*, keyword nmr- by comparison with the TMS calculation (“TMS.log”). Look the
isotropic magetic shielding value. Compare the results with tabulated values.
To err is human - and to blame it on a computer is even more so.
Quantum Theory and its Applications
Laboratory 3
Objectives: Understand the different levels of calculations.
I. RHF, ROHF, UHF
a. Optimize H2 (starting from 0.74 Å). Calculate the dissociation energy with
reference to atomic H and a single point energy of H2 at infinite distance (∞ ~ 10
Å). What differences we have when using RHF or ROHF on each job? Test
carefully what kind of spin state to use (singlet, doublet, triplet).
b. Analyze the energy difference between ROHF and UHF in H, Li, Na and K. Look at
the orbital energies and the total energy in the “SCF Done” line (it is more
accurate than the final resume).
After the energy appears the eigenvalue of the S2 operator (as “S**2”) in atomic
units. What should be the value for these atoms? How does it changes with the
atom number? What is spin contamination?
ˆ2 Ψ = S (S + 1)h 2 Ψ
S
II. Models and Basis
Measure the dissociation energy of H2 in HF, MP2, CISD, and BLYP using STO-3G,
6-31G and 6311++G** basis sets. Compare the results with the experimental
value of 104 kcal/mol. Remember that CISD is not size consistent!
III. Orbitals
• Look at the orbital coefficients for an H2 HF/STO-3G at 0.74 and 1 Å. What is the
superposition integral value of the s atomic orbitals in the σg and σu?

σ
 g / u = N g / u (sa ± sb )

• Test that
Ng =
1
2 + 2 s a sb
Nu =
1
2 − 2 s a sb




σ g σ g = c a2 sa sa + c b2 sb sb + 2c ac b sa sb
• Look at the orbitals of H2 at 0.74 Å, calculated in HF with STO-3G and 6-31G.
How many orbitals you have? What are their atomic orbital components?
When all else fails, try the boss's suggestion.
When all else fails, try the boss's suggestion.
Quantum Theory and its Applications
Laboratory 4
Objectives: Understand the importance of the orbitals. Analize the solvent effect.
I. Construct the Walsh diagram for NH3
• Optimize ammonia in HF/STO-3G (symmetry?) using opt=vtight to receive a
better geometry. Draw the orbitals in an energy scale. What are the H-N-H
angles?
• Do the same as before, but now fixing all the H-N-H angles to 112º. To do this,
write as a keyword “opt(vtight,modredundant)”. This tells to the program that we
want to create new “coordinates”. So after the z-matrix (with the specified
angles) we write:
[blank line]
213f
214f
314f
[blank line]
This “fixes” the angles between the three atoms. In here, assuming that 1 is
nitrogen, we constrained the three H-N-H angles. Draw the orbitals besides the
previous ones.
• Repeat the prior job but now with angles of 120º (symmetry?). Again, draw the
orbitals and match them to create a Walsh diagram.
II. Solvents
• Optimize HCl. With this geometry, calculate a single point using as solvents
water, ethanol, chloroform and heptane. To do this, we will learn to use the
“checkpoint file”, a file that permits to take the results of a job to start a second
one. So, in the very beginning of the original input file write:
%chk=input_file_name.chk
We will read the geometry and the orbitals from the gas phase calculation to start
the solvent ones. The new calculations overwrite the checkpoint file. So, in order
not to delete the checkpoint original data, copy the file to a new name and use
this name for the solvent input.
To read the geometry, charge and spin, use “geom=allcheck”. With this only the
title section of the input must be written. To read the orbitals, write
“guess=read”. This means when “guessing” the orbitals for the SCF procedure,
read them from the checkpoint file instead of using the standard guess (usually
extended Huckel).
The default solvent model is called “Polarizable Continuum Model” (PCM). It is
based on a dielectric continuum that surrounds the molecule. The principall
parameter is the dielectric constant of the solvent, and then the solvent radius
and density. The keyword is
SCRF(solvent=solvent_name)
Calculate everything in HF/lanl2mb. This is a minimal basis set as STO-3G, but
the core orbitals of heavy atoms, which are generally undisturbed, are mixed
with
the
nucleus
to
form
a
fixed
“Effective
Core
Potential”
(ECP).
The water example of the input file may be:
%chk=HCl.water.chk
# hf lanl2mb pop=full geom=allcheck scrf(solvent=water)
• Graph the Mullikan charges with the solvent. Compare the results with the
function
y =−
1
1
x+
y ∞ − y0
where y0≈ygas
phase,
+ y∞
y∞≈ywater. Why do you think they don’t fully agree?
Look also at the changes in the orbital coefficients.
III.
Carbonium ion:
Make
a
calculation
single
of
the
point
energy
bisected
and
perpendicular carbonium structures
(“carbonium.bisected.g”,
“carbonium.perpendicular.g”).
Perpendicular
Bisected
Which one has lower energy? Did
you expect that from steric explanations? Can you explain it by inspection of the
orbitals?
Construct an interaction diagram of the cyclopropane and carbene p orbitals to
understand it. Are the C-C bond distances logical?
We have learned that nothing is simple and rational except what we
ourselves have invented; that god thinks in terms neither of Euclid or
Riemann; that science has "explained" nothing; that the more we know
the more fantastic the world becomes and the profounder the surrounding
darkness.
-- Aldous Huxley
Quantum Theory and its Applications
Laboratory 5
Objective: Make a reaction.
We are going to study the hydrogen abstraction of HBr with Cl•, using B3LYP/lanl2mb
(unrestricted DFT). Work with checkpoint files.
What is a saddle point? How are the derivatives (the gradient) and the Hessian in
a minimum, a maximum and a saddle point?
I. Finding the minimum.
Optimize the linear reactive BrH⋅⋅⋅⋅Cl• and the product ClH⋅⋅⋅⋅Br•. What are the final
geometry parameters? What is the reaction energy?
II. Scanning the reaction.
Scan the reaction to obtain a potential energy curve. To do this, start from the
optimized molecule geometry. Write “opt=modredundant” and after the z-matrix,
leaving a blank line, write the numbers of the atoms you want to move, the
starting distance, “S” for scanning, the number of steps and the step size.
For instance, if 1 is Cl and 2 is H, writing
1 2 1.4 S 5 0.2
will separate (dissociate) H and Cl in five steps of 0.2 Å, starting from 1.4 Å and
ending in 2.4 Å.
It is important to use as the starting step the same distance used in the z-matrix
(or a really close one). And don’t forget to leave a blank line at the end.
Note that you have four possibilities in this scanning, separating the H from the
Br, attracting the H to the Cl, or the opposites, depending if you start from the
reactants or the products.
Graph energy vs. the reaction coordinate using the reactant and product
optimizations and the scanning points (the student that uses Hartrees in the
graph will be severely punished). Gaussian makes an optimization of each point
in the scanning, so you will find the final results for each geometry under the line
“-- Stationary point found.”
III. Searching the transition state.
There are two ways to find a transition state.
• Tradicional way: Starting from a close geometry to the TS (for instance taking
the higher energy point of the scanning), and knowing the forces, Gaussian
follows the coordinate that has negative derivative (remember that F=-∇V).
The keyword is “opt(ts,calcfc)”. Calcfc is for calculation of forces.
• Transit-Guided Quasi-Newton (STQN): Keyword “opt=qst2”.
For using this method you must provide the reactant and product geometry.
The algorithm interpolates a probable TS and search for the maximum energy
point in the minimum energy path between both states (a saddle point).
The input requires after the reactant z-matrix (or xyz) two blank lines, the
charge and spin line of the product and then its geometry, followed by the
typical blank line to close the input.
Compare both methods. What is then the TS geometry and energy? Include it
into the graph.
IV. Frequencies.
Using the checkpoint files, make frequency calculations of reactant, TS and
product. Calculate the rate and equilibrium constant of the reaction.
A well established transition state must have only one negative (actually
imaginary) frequency in the coordinate of the reaction. A minimum (stationary
point) must have all the frequencies positives. Thus a frequency calculation
confirms that we found the state we were looking for.
What frequencies have large and small values? What does it says about the bond
strength? What normal mode receives negative frequency?
ν = 2π
Big k
kosc
Small k
µ
Negative k
V. Kinetic Isotope Effect (KIE).
The KIE measures the relation in the rate when an isotope is changed. The most
common is using protium (1H) and deuterium (2H), which gives KIE=kH/kD. The
rate difference comes mostly from the different ZPE with H and with D molecules
(which one has higher ZPE?). In the X-H bond dissociation the disparity in the
ZPE in the TS is much lower, since the reaction coordinate frequency is
imaginary. So in spite of having the same activation energy, the activation free
energy changes with the isotopic mass.
One way to make the calculation is taking the data from the checkpoint file. An
input example is:
%chk=BrD_Cl.freq.chk
# b3lyp lanl2mb freq(readiso) geom=allcheck guess=read
[blank line]
[blank line]
35
2
79
[blank line]
In here we read the geometry and orbitals (do they change with an isotope
change?) and ask for a frequency calculation with the isotope numbers that
appears at the end. They must be specified in the same order as the geometry.
But this is a semi-quantum calculation. The full quantum one must include
tunneling probability. To do this we will use Wigner’s correction, which says that
 Qt , H
k 

KIE =  H 

k
 D  Eyring  Qt , D
where
Qt = 1 +
ut2
24



Wigner
ut =
hν
k BT
ν is the reaction imaginary frequency. Gaussian provides it in wave number (cm1
). To convert it to Hz, multiply it by c.
Analyze then the ZPE and free energy change in the reactant and TS, and the
semi and full quantum KIE.
Bonus: There is also a thermodynamic KIE. Check what happens with the
equilibrium constant.
Kinetics
Fact
--------------- = ----------Mechanism
Fiction
Quantum Theory and its Applications
Laboratory 6
Objective: Understand the compexes.
I. Octahedral CoH63- (Model for CoF63-)
• Make an electron count of the complex and see the formal charge of the metal.
• Make a single point calculation of the low spin (singlet) complex at
B3LYP/lanl2mb level using 1.60 Å for Co-H distance.
• Draw the valence orbitals (from the fifth). Specify along with the energies their
symmetry names, the bonding character and which atomic orbitals form them.
• Compare the result with the orbitals in 6-311g* basis set (orbitals 10 to 24).
• Check the occupied valence orbitals of the high spin complex (quintet, orbitals
5 to 15 for alpha, 5 to 11 for beta) using UB3LYP/lanl2mb.
• Repeat the calculation of the high spin complex using keyword “stable=opt” and
analyze the difference in the orbitals and energy. What do you think stable=opt
means to Gaussian?
• What state is the fundamental, singlet or quintet? Check with both basis set
and compare with the value of 53 kcal/mol received at the CCSD(T)/6-311g*
level.
II. Square planar PtH4= (Model for PtCl4=)
• Make the electron count and formal charge of this complex.
• Run the single point energy of the singlet using Pt-H distances of 1.69 Å in
B3LYP/lanl2mb.
• Draw again the orbitals (5 to 17) and compare them with the octahedral
complex. Why do you think d8 transition metals prefer square planar geometry?
III. End of the laboratory
• Say to the assistants how thankful you are for their extremely generous work.
• Open the bottles.
• Start the party.
... For afterwards a man finds pleasure in his pains,
when he has suffered long and wandered far.
Homer