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.

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

CH4.inp

&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

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

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