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exercises:2016_ethz_mmm:reaction_energy

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 — exercises:2016_ethz_mmm:reaction_energy [2016/02/03 09:54] (current) Line 1: Line 1: + ====== 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. + + <​code>​ + **** **** ****** ​ **  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: + + <​code>​ + 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 ==== + <​code>​ + #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 ==== + <​code>​ + #O ALLELECTRON ALL + 4    4    0 + ​0.24762086 ​   0 + ​ + + ==== Coordinates for O$_2$ ==== + <​code>​ + O         ​4.4720538104 ​       4.7584649515 ​       4.9999999998 + O         ​5.5279461896 ​       5.2415350485 ​       4.9999999995 + ​ + + ==== Coordinates for CO$_2$ ==== + <​code>​ + 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 ==== + <​code>​ + O         ​4.6926974603 ​       4.7525411835 ​       4.6307067609 + H         ​5.6350172910 ​       4.8022721035 ​       4.7052454388 + H         ​4.3528571397 ​       5.2445222023 ​       5.3644975249 +