Introduction

Light emission through oxidation is a common phenomenon that is usually observed as combustion (burning). Combustion is understood as an oxidation chain reaction1, in which the emission of high thermal energy can be numerically expressed by solutions of the differential equation of the reaction diffusion model, namely, blowing up2 or a singular perturbation3. However, the reaction diffusion model cannot express light emission, which should be derived from excited electrons. Although several elemental reactions for the electronic excitation have been experimentally proposed4, no theoretical work regarding excited states has been reported so far. Large electron excitation has been reported with projectile kinetic energies on the order of kiloelectronvolts, and has been calculated by TDDFT Ehrenfest dynamics for the stopping power of hydrogen ions5 and the emission of secondary electrons by helium ions6 traversing a graphene sheet. However, in a kiloelectronvolt regime, the excitation mechanism is impact ionization rather than transition among several PESs close to each other. In this work, we identify molecular-scale oxidation processes that change the electronic system from its ground state to excited states. If the electronic system has higher energy than the ground state, the subsequent electronic transition to the ground state could cause light emission. To examine this scenario, we performed a molecular dynamics (MD) simulation assuming a high kinetic energy for an oxygen molecule (O2) colliding with a magnesium dimer (Mg2), a silane (SiH4) molecule, and a methane (CH4) molecule. Mg2 and SiH4 were selected as subjects because of their combustion reactions which are widely used in nanoparticle syntheses7,8,9,10 and film formation8,11,12. Meanwhile, CH4 was selected as a counterpart of SiH4 as C is the group IV elements like Si. Theoretical insights into excited states would contribute to precise control of these production processes. Several collision trajectories between the O2 molecule and the target molecule were examined by changing the kinetic energies of the incident O2 molecule from 4 to 10 eV with one initial atomic configuration.

We used two theoretical approaches. One was real-time time-dependent density functional theory (TDDFT)13 coupled with classical MD, which was used to monitor the potential-energy change upon collision of an O2 molecule and a target molecule. The monitored potential was compared with the potential energy surface (PES) obtained by static density functional theory (DFT) within the ΔSCF scheme14 along with a trajectory obtained with a real-time TDDFT-MD simulation. The other approach was the complete active space self-consistent field (CASSCF)15 method for computing the PESs of the same trajectory for the MD obtained by the real-time TDDFT simulations to validate the PESs obtained by the ΔSCF DFT scheme. The purpose of this work is to find electronic excitation at particular trajectory of MD. On the other hand, for further accuracy and direct comparison of light emission spectroscopy throughout combustion, stochastic analysis of multiple trajectories for O2 collision with a target molecule by changing the initial conditions is required. However, this analysis will be tackled in future work because it is too expensive with our current computational resources.

Computational Schemes

The TDDFT calculations were performed within the local density approximation using the Perdew-Zunger functional16 fitted to the numerical result for the electron gas calculation17. The plane-wave basis set was used under the periodic boundary condition of an (x, y, z) box with a size of 10 × 10 × 20 Å3. To prepare the initial condition of the simulation, we used the following method described in ref.18. (1) An O2 molecule or a target molecule (Mg2, SiH4 or CH4) was located in each of the periodic vacuum boxes. The ground state of each molecule was computed separately by DFT. (2) The total valence charge densities of the O2 and target molecule in the cell were merged. A series of all the occupied molecular orbitals (MOs) of the O2 molecule and the target molecule were taken as set of wavefunctions of the initial condition. Next, we started the real-time propagation TDDFT calculation with initial kinetic energy of the O2 atoms of 4 to 10 eV within the Ehrenfest dynamics and monitored the TDDFT potential energy expressed as

$$\begin{array}{rcl}{E}_{{\rm{pot}}}^{{\rm{TDDFT}}}(t) & = & \sum _{{\rm{occp}}}[\int {\psi }_{{\rm{n}}}^{\ast }({\bf{r}},t)(-\frac{1}{2}{\rm{\Delta }}){\psi }_{{\rm{n}}}({\bf{r}},t)d{\bf{r}}\\ & & +\iint {\psi }_{{\rm{n}}}^{\ast }({\bf{r}},t){v}_{{\rm{nl}}}({\bf{r}},{\bf{r}}^{\prime} ,t){\psi }_{{\rm{n}}}({\bf{r}}^{\prime} ,t)d{\bf{r}}d{\bf{r}}^{\prime} ]+\frac{1}{2}\iint \frac{\rho ({\bf{r}},t)\rho ({\bf{r}}^{\prime} ,t)}{|{\bf{r}}-{\bf{r}}^{\prime} |}d{\bf{r}}d{\bf{r}}^{\prime} \\ & & +\int {E}_{{\rm{X}}{\rm{C}}}[\rho ({\bf{r}},t)]d{\bf{r}}+\sum _{{\rm{I}}}{Z}_{{\rm{I}}}\int \frac{\rho ({\bf{r}},t)}{|{\bf{r}}-{{\bf{R}}}_{{\rm{I}}}(t)|}d{\bf{r}}+\sum _{{\rm{I}}\ne {\rm{J}}}\frac{{Z}_{{\rm{I}}}{Z}_{{\rm{J}}}}{|{{\bf{R}}}_{{\rm{I}}}(t)-{{\bf{R}}}_{{\rm{J}}}(t)|}.\end{array}$$
(1)

In Eq. (1), ψn(r, t) is the time-dependent Kohn-Sham orbital13 and the electron density, ρ(r, t), consists of the sum of the norm of the occupied Kohn-Sham orbitals. The first and the second terms on the right-hand side of Eq. (1) are electron kinetic energy and the contribution of the sum of the non-local part of the pseudopotentials. We used Troullier-Martins norm-conserving pseudopotentials19. The third and fourth terms are the Hartree and exchange-correlation energies of electrons, respectively, and the last two terms are Coulomb potential for electron-ion attraction and ion-ion repulsion, respectively. We adopted the adiabatic exchange-correlation functional for EXC[ρ(r, t)]. The Eq. (1) was computed in momentum space using the formalisms of ref.20, which was also used to compute the forces on all ions used for the Ehrenfest MD simulation. All the valence wavefunctions were expressed by using the plane-wave basis set with a cutoff energy of 61 Ry. In performing the TDDFT-Ehrenfest simulation, we used the spin-unpolarized approximation. Within this approximation, the triplet ground state of the O2 molecule is mimicked by assigning half occupation for each of the doubly degenerate O2 π* MOs.

The real-time propagation of the Kohn-Sham orbitals was computed by solving the time-dependent Kohn-Sham equation13 as

$$i\frac{\partial {\psi }_{{\rm{n}}}({\bf{r}},t)}{\partial t}={H}_{KS}[\rho ({\bf{r}},t)]{\psi }_{{\rm{n}}}({\bf{r}},t).$$
(2)

In equation (2), HKS[ρ(r, t)] is the Kohn-Sham Hamiltonian given by a functional derivative of Eq. (1) with respect to \({\psi }_{{\rm{n}}}^{\ast }({\bf{r}},t)\). For the numerical solution to equation (2), we employed the fourth-order split-operator method21,22 and used the code FPSEID23. The interval of the time-step 0.726 atsecond was used for time-evolution of both electrons and ions that warrants the energy conservation with error less than 1 × 10−5 eV per O2 and Mg2. The same precision holds for the case of O2 and SiH4, and the case of O2 and CH4.

There should be several ways to monitor electronic excitation; The one is taking projections of the time-dependent Kohn-Sham orbitals obtained from Eq. (2) to the occupied and empty static Kohn-Sham orbitals on the same atomic positions. This method may approximately work when electronic charge density between the ground and excited states does not differ so much, and thus the Kohn-Sham Hamiltonian between the ground and excited states can be regarded as common. Meanwhile, like current oxidation cases, the reaction is followed by significant charge transfer that modifies the Kohn-Sham Hamiltonian. Therefore, orbital projection to those obtained by different Hamiltonians is rather vague to judge excitation. An alternative way to monitor electronic excitation is just to compare potential energies obtained by TDDFT-Ehrenfest dynamics and those by static DFT, which was preferred in this work. To analyze PESs within the DFT scheme, we performed ΔSCF calculations with snapshots of atomic coordinates along with the trajectory of the TDDFT Ehrenfest dynamics under several orbital occupation patterns. The detailed settings are described in later. The computed PESs should be validated by other formalisms. We employed the CASSCF scheme using several snapshots of a trajectory obtained with the current TDDFT Ehrenfest dynamics. The Firefly24 code based on GAMESS25 was used with the modified 6-31G basis set where the Mg 3p orbitals were omitted. For Mg2 + O2, the O 2 s and 2p orbitals and the Mg 3 s orbital were taken as the active space with 16 electrons. The geometry of a triplet excited state that corresponds to 2Mg+ + \({{\rm{O}}}_{2}^{2-}\) (charge-transfer [CT] state) was optimized. For this calculation, O 2p orbitals and Mg 3 s orbitals with 12 electrons were considered as the active space. In addition, the active space for SiH4 + O2 consisted of O 2 s and 2p orbitals and Si 3 s and 3p orbitals. Overall, 16 orbitals with 20 electrons were considered. Excited states with spin multiplicity up to 5 were considered. For the case of CH4 + O2, we did not perform CASSCF calculations.

Results and Discussion

We describe three cases for an O2 molecule colliding with a Mg2 molecule, a SiH4 molecule, and a CH4 molecule. For all cases, the Cartesian coordinates of the initial position of the center of mass of O2 were (0, 0, 10 Å), where the z-axis was set as the direction of the incident velocity of the O2 molecule. The center of mass of the target molecule was set at the origin. The molecular orientation of the O2 molecule was set to along the direction with Cartesian coordinates of (1, 1, 1), whereas the molecular axis of the Mg2 molecule was in the (1, 0, 0) direction. For the initial orientation of the SiH4 molecules, two H atoms were set in the zx plane with common negative z values, and the other two H atoms were in the yz plane with a common positive z value, placing the Si atom at the origin. The geometries before the collision are visualized in the snapshots of the TDDFT-Ehrenfest dynamics which will appear later. For the case of O2 collision to a CH4 molecule, the initial orientation of the CH4 was set as x and y components of C-H bonds are parallelt to (1, 1), (−1, −1), (1, −1), and (−1, 1) directions, as indicated in snapshots of the TDDFT-Ehrenfest dynamics which will appear later.

O2 collision with Mg2

In performing the TDDFT Ehrenfest dynamics, the incident kinetic energies of the O2 molecule were 4, 6, and 10 eV. Figure 1(a) shows the results for an incident kinetic energy of 6 eV and (b) shows the results for 10 eV. The results for an incident kinetic energy of 4 eV are not shown. The top panels show the time evolution of the expectation values of the Kohn-Sham Hamiltonian with respect to each MO of O2 and Mg2. There are nine occupied MOs per spin; seven MOs belong to the O2 molecule with two of them half-occupied, and two MOs belong to the Mg2 molecule. The energy levels of the fully occupied MOs of the Mg2 molecule with the initial geometry are higher than the half-occupied MO of the O2 π* molecule (sixth and seventh orbitals in increasing order of the expectation values in Fig. 1(a)), which are doubly degenerate. Because of this ordering in expectation values among these MOs, the ground state DFT calculation should cause charge transfer from the Mg2 molecule to the O2 molecule, even when these molecules are separated. The TDDFT Ehrenfest dynamics can naturally express charge transfer, which occurs only when these molecules are closer18. The top panels in Fig. 1(a,b) show the alternation of the expectation values between the Mg2 and O2 MOs. But we must note here that the alternation does not rigorously mean the electronic excitation which should be expressed by comparing potential energy between TDDFT and static DFT as mentioned above. The bottom panels show the time evolution of the potential energy throughout the real-time TDDFT Ehrenfest dynamics. We also performed the DFT calculation for the excited state within the ΔSCF scheme; we considered up to 10 Kohn-Sham orbitals to evaluate one of the excited-state PESs. Later than 100 fs, the top two expectation values of the fully occupied MOs, originating from the Mg2 molecule, alternated to those of two half-occupied MOs, originating from the O2 molecule. Therefore, we re-labeled the eighth and ninth MOs as half-occupied and the sixth and seventh MOs as fully occupied. The plot of the ΔSCF potential-energy calculations was computed for the electronic ground state with the eighth and ninth MOs half-occupied. In contrast, the excited states were computed by assuming the promotion of one electron from the eighth to the ninth MO (green diamonds in Fig. 1(a,b)), and by assuming the promotion of two electrons from the sixth and seventh MOs to the eighth and ninth MOs, (purple squares in Fig. 1(a,b)).

Figure 1
figure 1

(a) (Top)Time evolution of the expectation values of molecular orbitals (MOs) for O2 colliding to Mg2 with incident kinetic energy 6 eV. Note that the alternation of the expectation values between Mg2 MOs and those of O2 MOs occurred. (Bottom) Time-variation of the potential expressed as Eq. (1) for O2 collision to Mg2, obtained by real-time TDDFT Ehrenfest dynamics, and by DFT along with snapshots within the ΔSCF scheme. In this panel, red solid lines denote the results of TDDFT Ehrenfest dynamics. Meanwhile, the blue circles are for DFT ground states. The green diamonds are obtained by the ΔSCF calculation promoting one electron from 8th MO to 10th MO. Meanwhile, purple squares are obtained by promoting two electrons from 6th and 7th MOs to 8th and 9th MOs. Small insets are snapshots of atomic coordinates for O atoms (red ball) and Mg atoms (gray balls), respectively. (b) Same as (a) but with incident kinetic energy of 10 eV.

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With an incident kinetic energy of 4 eV, the simulation showed tentative Mg–O bond formation, which disappeared after O–O bond recovery throughout the simulation. Thus, we concluded that with the current initial position, a kinetic energy of 4 eV is not enough for oxidation. On the other hands, for incident kinetic energies of 6 and 10 eV, Mg–O bond formation was observed (insets in Fig. 1(a,b)). Next, we focus on the potential energies and compare them with the PESs obtained by the ΔSCF calculation within DFT. For an incident kinetic energy of 6 eV, the time evolution of the potential energy obtained by TDDFT was finally located slightly above the PES of the ground state, but this was far below the lowest excited PESs obtained by the ΔSCF calculation. This result may correspond to the PES mixing discussed in previous works26,27. As shown in the insets in the bottom of Fig. 1(a), two Mg–O bonds were eventually formed. When the incident kinetic energy was increased to 10 eV, the TDDFT potential-energy plot was in a higher position (bottom of Fig. 1(b)). (Note that the snapshots of the TDDFT-Ehrenfest dynamics is shown in Fig. 2). The TDDFT potential was close to the excited state promoting one electron from the eighth to the tenth MO, at which the formation of Mg-O was observed again. The current simulation assumed that only the projectile O2 molecule had an incident kinetic energy and the target Mg2 was still. Classical kinetics tells us that about 40% of the net collision energy should be dissipated as translation kinetic energy to all ions, based on the mass ratio of the Mg and O atoms. Therefore, the minimum kinetic energy spent in the electronic excitation is estimated to be 6 eV per four atoms. At a typical temperature for a Mg-O2 flame of 3300 K28, the thermal equilibrium condition gives a negligible ratio of molecules possessing the required kinetic energy. However, the energy released by an oxidation of a pair of Mg2 and O2 molecules is 12.4 eV28, which is sufficient to induce the high-energy collision of another pair of Mg2 and O2 under non-equilibrium conditions. This electronic excitation can cause light emission.

Figure 2
figure 2

Snapshots of O2 colliding to Mg2 with incident kinetic energy of 10 eV. Red balls are O atoms, gray balls are Mg atoms.

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We validated the PES landscape by performing CASSCF calculations with the same set of snapshots used throughout the TDDFT Ehrenfest dynamics. The multiple spin states, which were not included in the DFT ΔSCF calculations, were considered in the precise evaluation of the PESs. Figure 3 shows the triplet state landscape. When we followed the trajectory of the TDDFT Ehrenfest dynamics with an initial incident energy of 6 eV, the triplet ground state was well separated from the triplet excited states (Fig. 3(a)). Therefore, the electronic state was unlikely to transfer to the excited state in this case. When we followed the trajectory with a larger incident energy of 10 eV, the ground state was near several excited states. If a small upward transition occurred (Fig. 3(b)), the electronic state could be raised to higher excited states. To validate the currently used 6-31G basis set, we checked the PES landscape with 6-31G(d) basis set which includes polarization effect. The results shows the relative PES landscape is less sensitive to inclusion of the polarization, see the Supplementary Materials [See Supplementary Material at http://xxxx for numerical details.]. These behaviors of the PES landscape qualitatively explain the results of the TDDFT calculations despite the subtle difference in quantities.

Figure 3
figure 3

PESs landscape obtained by CASSCF calculations for triplet states for O2 and Mg2 along with the snapshot obtained by TDDFT Ehrenfest dynamics colliding with incident kinetic energies (Ekin) of (a) 6 eV and (b) 10 eV. The lateral axis (Time) denotes the corresponding atomic coordinates of the TDDFT Ehrenfest dynamics. Ground, excited and next-excited states are shown in solid blue, dotted purple and dashed green lines, respectively. The arrows in (b) indicate possible upward transitions. Red dotted line in (b) indicates possible trajectory to an excited state. Note that with Ekin = 10 eV, the triplet ground state crosses with excited states, while the three states are well separated for Ekin = 6 eV.

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The current TDDFT-Ehrenfest dynamics and comparison with CASSCF suggest crossing of PES of the neutral state (NS) and CT states along with particular trajectory of MD. In order to examine the generality of the crossing, geometry optimization by CASSCF was performed on NS and CT, respectively, and the alternation between them was examined. Mg2 and O2 were rearranged to form two MgO flakes through dissociation of the O2 molecule (Fig. 4). During the rearrangement, the CT state and the NS intersected each other. In the final conformation, NS became an excited state situated about 4 eV above the CT state, which became the ground state. Thus, a high-energy collision exchanged the ground and excited states through reordering the atoms. The energy level of NS was raised by about 4.5 eV from the initial ground state. Next, we re-examined the collision of an O2 molecule with an Mg2 molecule. Classical kinetics tells us that about 40% of the incident kinetic energy of the O2 molecule dissipates into translational kinetic energy for all the ions. After the dissipation, the incident kinetic energy of 6 eV became equivalent to 3.6 eV available for electronic excitation, which was slightly lower than the energy difference of the NS for 2Mg+ + \({{\rm{O}}}_{2}^{2-}\) and Mg2 + O2. This fact is consistent with the observation that the incident kinetic energy of 6 eV was not enough for the transition to the PES with the lowest excitation energy.

Figure 4
figure 4

Evolution of triplet states during geometry optimization of triplet charge-transfer (CT) state of Mg2O2 calculated by state-averaged CASSCF. Crossing of neutral state (NS), which is originally the ground state, and CT state takes place around 180th step.

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O2 collision with SiH4

We used initial incident energies of the O2 molecules of 4, 6, and 10 eV. In contrast to the O2 → Mg2 collision, oxidation was not observed for 4 and 6 eV, but it was observed for 10 eV. Figure 5(a,b) show the cases with incident kinetic energies of 6 and 10 eV, respectively. The top panels of Fig. 5(a,b) show the time evolution of the expectation values of the Kohn-Sham Hamiltonian for the MOs. There were 11 occupied MOs, seven of which originated from the O2 molecule and four of which originated from the SiH4 molecule. The highest levels were for the O2 HOMO, which was half-occupied. Thus, in the ground state, 10th and 11th orbitals were half-occupied. In contrast to the O2 → Mg2 collision case, the level alternation between the HOMO of the O2 molecule and MOs of the SiH4 molecule did not occur with an incident kinetic energy 6 eV. Yet we must note here again that alternation of the expectation values does not precisely mean the electronic excitation as discussed above.

Figure 5
figure 5

(a) (Top)Time evolution of the expectation values of molecular orbitals (MOs) for O2 colliding to SiH4 molecule with incident kinetic energy 6 eV. Red solid lines are for O2 fully occupied MOs, and blue solid lines are for O2 half occupied MOs. Green solid lines are for MOs of SiH4. (Bottom)Time-variation of the potential expressed as Eq. (1) of real-time TDDFT Ehrenfest dynamics. Potentials obtained by DFTground state calculation along with snapshots of TDDFT-Ehrenfest dynamics within the ΔSCF scheme are also shown as blue squares. Insets are atomic coordinates obtained by the TDDFT Ehrenfest dynamics of O2 (red colored balls) and SiH4 (Si atom as a green ball, and H atoms as blue small balls). Note two atomic coordinates beyond 200 fs are shown to express repulsion of the O2 molecule from the SiH4 molecule. (b) Same as (a) but with kinetic energy of 10 eV. In the bottom, the ΔSCF potential profiles on snapshot along with trajectory of TDDFT Ehrenfest dynamics are shown; Green circles denote excitation promoting one electron from 10th MO to 11th MO, while purple diamonds denote excitation promoting one electron from 9th MO to 11th MO, respectively.

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The bottom panels of Fig. 5(a,b) show the time evolution of the TDDFT potential energy (Eq. (1)) throughout the TDDFT-Ehrenfest dynamics. The DFT (ΔSCF) potential was computed along with the snapshots of the trajectory of the TDDFT-Ehrenfest dynamics. For the incident energy of 6 eV, the DFT ground state potential almost agreed with that of the TDDFT-Ehrenfest dynamics up to 180 fs, and a tiny discrepancy was observed later. For the incident kinetic energy of 10 eV, the deviation of the potential energy between the TDDFT-Ehrenfest dynamics and ground state DFT calculation was large; thus, we examined the PESs of the excited states. The ΔSCF calculations of the excitation PESs were performed by assuming promotion of one electron from the 10th to 11th levels (green circles), and the promotion of one electron from the 9th to 11th levels (purple diamonds). The TDDFT potential merged with the ΔSCF results for the electron promotion from the 9th to 11th levels. Therefore, similar to the O2 → Mg2 collision, the electronic excitation and subsequent light emission was likely with an incident kinetic energy of 10 eV. The insets in Fig. 5 show the changes in atomic structure of the formation of two Si–O bonds after dissociation of the O2 molecule. For an incident kinetic energy of 6 eV, the O2 molecule was finally repelled from the SiH4 molecule. With an incident kinetic energy of 10 eV, a SiO2H2 molecule was formed. (Note that the snapshot of the TDDFT-Ehrenfest dynamics with incident energy of 10 eV is shown in Fig. 6).

Figure 6
figure 6

Snapshots of O2 colliding to SiH4 with incident kinetic energy of 10 eV. Red balls are O atoms, green medium sized balls are Si atoms, and small balls are H atoms.

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We tried to perform the CASSCF calculation to validate this PES landscape. However, the active space with the frontier orbitals of the Si and O atoms was insufficient, even qualitatively, to describe the reaction. The present code could not handle an active space that included H 1 s orbitals. The CASSCF results for SiH4, with the combustion of other molecules, will be reported elsewhere.

O2 collision with CH4

It is of fundamental interest to study a case of CH4 molecules which can be a counterpart of SiH4 as C is group-IV element like as Si. By using the scheme of TDDFT Ehrenfest dynamics, we collide an O2 molecule to a CH4 molecule with incident kinetic energies of 6 eV and 10 eV. Figure 7 shows the results demonstrating reflection of O2 and CH4 molecules instead of formation of C-O or C-H bonds. This is in sharp contrast to the case of O2 collision with SiH4, which may be because of smaller mass of CH4 than SiH4. From this result, we expect that collision of an O2 molecule with a molecule in the same order of mass to CH4 like as NH3 may also results in reflection instead of oxidation.

Figure 7
figure 7

Snapshots of an O2 molecule colliding to a CH4 molecule with incident kinetic energy of 6 eV (top panels) and 10 eV (bottom panels). Red balls are O atoms, medium white balls are C atoms, and small balls are H atoms.

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Summary

In the current simulations, we monitored the electronic state that became an excited state upon oxidation. Several trajectories for the TDDFT-Ehrenfest dynamics of the collision of an O2 molecule with an incident kinetic energy of 4, 6, and 10 eV with target molecules (Mg2, SiH4, or CH4) were examined. For O2 → Mg2 collision, Mg–O bond formation was observed with an incident kinetic energy greater than 6 eV, and the electronic excitation energy increased with the incident kinetic energy. For the O2 → SiH4 collision, Si–O bond formation was observed at an incident kinetic energy of 10 eV. The mechanisms of electronic excitation were likely due to intrinsic nature of the PES landscape in which the PES of the ground state becomes closer to that of an excited state in some areas of the trajectories in the MD simulation. The PES landscape for the O2 → Mg2 collision was validated by CASSCF calculation, which was challenging for the O2 → SiH4 collision. Meantime, for O2 → CH4 collision with incident kinetic energy up to 10 eV, no oxidation reactions were observed, which may be due to smaller mass of CH4 than SiH4. From this fact, we do not expect the alternation of potential energy surface in collision of O2 molecules with small-mass molecules. We note here that studying oxidation of small-mass molecules, for instance CH4, NH3, and H2, are important subject of exploration of new fuel alternative to fossil fuel, however, they are out of the scope of current topic of light emission throughout the combustion.