Experiment 3: Computational Quantum Mechanics
Abstract
:
In this experiment, there were 3 main subexperiments, all using QM software to
accomplish their respective goals.
The main objective of experiment 1 was to generate the
potential energy curve for the HCl molecule.
The dissociation energy of HCl was determined to
be 587 kJ/mol, and the vibrational frequency was determined to be 2,966 cm
1
.
Literature values
for the dissociation energy and vibrational frequency were 431±65 kJ/mol, and 3,000 cm
1
,
respectively.
The main objective of experiment 2 was to use QM software (Avogadro and
GamessQ) to determine the structure, vibrational frequencies, normal modes, and
thermodynamic quantities of CO
2
.
The vibrational frequencies that were IRactive were
determined to be 593 cm
1
and 2258 cm
1
.
It was determined that CO
2
has 4 normal modes.
Thermodynamic quantities, along with standard literature values, are contained within the report.
The main objective of experiment 3 was to apply computational quantummechanics to calculate
the enthalpy and Gibbs free energy of CO
2
, O
2
, H
2
O, and CH
4
.
The enthalpy of combustion of
methane was also determined. The numerical results of experiment 3 are contained within the
report. Overall, experimental results agreed with literature values within 15%, with few
exceptions.
It was concluded that QM software is an accurate method of analyzing molecules.
I. Introduction
This experiment contained three individual experiments.
The overall goal of the experiments
was to give the user an overview of the capabilities of computational quantum mechanics
methods and to provide the user with knowledge about how to apply computational quantum
mechanics methods to obtain useful information and solve problems.
The experiments employ
the use of Avogadro, a crossplatform software application for building and editing molecules.
Quantumchemical calculations were then performed using the General Atomic and Molecular
Electronic Structure System (GAMESS).
For these experiments GAMESS was set to perform
these calculations using ab initio methods and semiempirical methods.
Experiment 1: Morse Oscillator/HCl
The main objective of experiment 1 is to generate the potential energy curve for the HCl
molecule.
This curve is then used to determine the dissociation energy, vibrational
frequency, and optimized bond length of HCl.
Equation (1) is one method of determining the
dissociation energy, D
e
:
=
(  

)
Vr De 1 e ar re 2
(31)
where V(r) is the potential energy, D
e
is the dissociation energy, r is the distance between the
atoms, r
e
is the equilibrium bond distance, and a controls the width of the potential.
Equation
(2) and Equation (3) are used to determine the vibrational frequency,
v
:
=
Vx 12kx2
(32)
where V(x) is the spring potential, k is the force constant, and x is the length of the elongated