====== Reaction Energy ======
In this exercise, you will calculate the reaction energy for the **methane combustion** reaction:
\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \]
Reaction energy:
\[ \sum E_\text{products} - \sum E_\text{rectants} = \left (2\cdot E_{H_2O} + E_{CO_2} \right) - \left(E_{CH_4} + 2\cdot E_{O_2}\right) \]
Ground state oxygen, O$_2$, is a triplet diradical, a property which can explain why liquid oxygen is paramagnetic and attracted to the poles of a magnet.
{{ o3.png?600 |
}}
For this reason, to get the energy of the O$_2$ molecule, a LSD calculation is required.
===== 1.Step =====
Run a single point calculation for CH$_4$, using the given input file.
Note that the file contains explicit basis sets and potential for all-electron calculations. An explanation of the basis set formats is given here: [[basis_sets|Basis Sets]]
&GLOBAL
PROJECT CH4
RUN_TYPE ENERGY
PRINT_LEVEL MEDIUM
&END GLOBAL
&FORCE_EVAL
METHOD Quickstep ! Electronic structure method (DFT,...)
&DFT
&POISSON ! Solver requested for non periodic calculations
PERIODIC NONE
PSOLVER WAVELET ! Type of solver
&END POISSON
&QS ! Parameters needed to set up the Quickstep framework
METHOD GAPW ! Method: gaussian and augmented plane waves
&END QS
&XC ! Parametes needed to compute the electronic exchange potential
&XC_FUNCTIONAL NONE ! No xc functional
&END XC_FUNCTIONAL
&HF ! Hartree Fock exchange. In this case is 100% (no fraction specified).
&SCREENING ! Screening of the electronic repulsion up to the given threshold.
EPS_SCHWARZ 1.0E-10 ! Threshold specification
&END SCREENING
&END HF
&END XC
&END DFT
&SUBSYS
&CELL
ABC 10 10 10
PERIODIC NONE ! Non periodic calculations. That's why the POISSON section is needed
&END CELL
&TOPOLOGY ! Section used to center the atomic coordinates in the given box. Useful for big molecules
&CENTER_COORDINATES
&END
&END
&COORD
C 4.6425962273 5.0574874650 5.2069537560
H 5.7240587065 5.0555482951 5.2189766147
H 4.2766068912 5.8773176685 5.8100567767
H 4.2759350196 4.1226994019 5.6087492584
H 4.2938562590 5.1744089096 4.1899119266
&END COORD
&KIND H ! potential and basis for H
&BASIS
3
1 0 0 3 1
12.25200000 0.02282200
1.86870000 0.15564000
0.41821000 0.48898000
1 0 0 1 1
0.10610000 1.00000000
1 1 1 1 1
1.00000000 1.00000000
&END
POTENTIAL ALL
&POTENTIAL
1 0 0
0.20000000 0
&END
&END KIND
&KIND C ! potential and basis for C
&BASIS
5
1 0 0 6 2
1252.60000000 0.00557360 0.00000000
188.57000000 0.04149600 -0.00027440
42.83900000 0.18263000 -0.00255830
11.81800000 0.46129000 -0.03337500
3.55670000 0.44931000 -0.08730500
0.54258000 0.00000000 0.53415000
1 0 0 1 1
0.16058000 1.00000000
1 1 1 3 1
9.14260000 0.04449900
1.92980000 0.23108000
0.52522000 0.51227000
1 1 1 1 1
0.13608000 1.00000000
1 2 2 1 1
0.80000000 1.00000000
&END
POTENTIAL ALL
&POTENTIAL
4 2 0
0.34883045 0
&END
&END KIND
&END SUBSYS
&END FORCE_EVAL
If the calculation was performed correctly, the total energy of the CH$_4$ molecule is printed in the output file.
**** **** ****** ** PROGRAM STARTED AT
***** ** *** *** ** PROGRAM STARTED ON
** **** ****** PROGRAM STARTED BY
***** ** ** ** ** PROGRAM PROCESS ID
**** ** ******* ** PROGRAM STARTED IN
.....
ENERGY| Total FORCE_EVAL ( QS ) energy (a.u.):
.....
**** **** ****** ** PROGRAM ENDED AT
***** ** *** *** ** PROGRAM RAN ON
** **** ****** PROGRAM RAN BY
***** ** ** ** ** PROGRAM PROCESS ID
**** ** ******* ** PROGRAM STOPPED IN
===== 2.Step =====
Modify the input in order to perform the same calculation for:
* H$_2$O
* CO$_2$
* O$_2$ triplet
Atomic coordinates for all the molecules, POTENTIAL and BASIS SET for KIND O are given at the end of the exercise.
Remember that the O2 ground state is a triplet state, with non paired electrons.
MULTIPLICITY=2S+1=3.
For O2 triplet, the LSD and MULTIPLICITY keywords are needed in the DFT section:
METHOD Quickstep
&DFT
LSD ! Requests a spin-polarized calculation for unpaired electrons
MULTIPLICITY 3 ! Multiplicity = 2S+1 (S= total spin momentum)
...
Another example can be found here [[basis_sets|Basis Sets]]
===== 3.Step =====
At the end, you should get a table like:
^ Species ^ Total Energy ^
| CH$_4$ | ... |
| O$_2$ | ... |
| H$_2$O | ... |
| CO$_2$ | ... |
Now you can compute the overall reaction energy.
===== Questions =====
- What are the total energies of O$_2$, H$_2$O, CO$_2$, and CH$_4$?
- What is the overall reaction energy of the CH$_4$ combustion?
- **(Optional)** What is the total energy difference between the O$_2$ singlet and triplet state?
===== Appendix =====
==== Basis Set for Oxygen ====
#O pc-1
5
1 0 0 6 2
2306.70000000 0.00539400 0.00000000
347.15000000 0.04024800 -0.00031692
78.89000000 0.17921000 -0.00259440
21.87600000 0.45978000 -0.03624100
6.66460000 0.45234000 -0.08779000
1.06690000 0.00000000 0.53320000
1 0 0 1 1
0.30700000 1.00000000
1 1 1 3 1
17.02200000 0.04891900
3.68380000 0.24962000
0.99234000 0.51347000
1 1 1 1 1
0.24487000 1.00000000
1 2 2 1 1
1.00000000 1.00000000
==== Potential for Oxygen ====
#O ALLELECTRON ALL
4 4 0
0.24762086 0
==== Coordinates for O$_2$ ====
O 4.4720538104 4.7584649515 4.9999999998
O 5.5279461896 5.2415350485 4.9999999995
==== Coordinates for CO$_2$ ====
C 4.9999776408 4.9999662056 4.9999894728
O 5.6486993295 5.9339540261 5.0004691016
O 4.3512530072 4.0659797648 4.9995464311
==== Coordinates for H$_2$O ====
O 4.6926974603 4.7525411835 4.6307067609
H 5.6350172910 4.8022721035 4.7052454388
H 4.3528571397 5.2445222023 5.3644975249