Using the Reactions O + H 2 → OH + H to Explore the Importance of the Atomic Quantum States on Chemical Kinetics and Reaction Dynamics

The O + H2 reaction is a particular example to alert the importance of a clear definition of the quantum state of an atom when referring to a chemical reaction. In its ground state, O (P), the oxygen atom reacts with H2 through an energy barrier with small rate constant. In contrast, when the oxygen atom is in its first excited state, O (D), the reaction O + H2 occurs without energy barrier and the rate constant is seven orders of magnitude higher. The dynamic behaviour of this reaction depends also on the quantum state of the oxygen atom.


Textbooks of General Chemistry and introductory
Physical Chemistry usually pay attention to the electronic configuration of an atom, but few care for the description of their quantum states and their spectroscopic levels arising from spin-orbit coupling, considering these topics as a curiosity with few chemical interest.Nevertheless, when teaching chemical kinetics, and in particular the atmospheric chemistry reactions, we face a table of elementary reactions where the kinetic data depends on the quantum states of reactants.
The oxygen atom is a good example to illustrate this behaviour.The study of the oxygen atom is similar to the one of the carbon atom illustrated in most textbooks.At the ground electronic configuration 1s 2 2s 2 2p 4 , there are fifteen different microstates corresponding to the 3 P, 1 D and 1 S quantum states (or terms), which are identified as belonging to the 3 P 2,1,0 , 1 D 2 and 1 S 0 levels, as illustrates in Figure 1.Using Hund's rules, the ground energy level is identified as the 3 P 2 .Due to spin-orbit interaction, the two other levels of this state, the 3 P 1 and 3 P 0 , are only 158.265 cm -1 and 226.977 cm -1 higher, respectively.But the 1 D 2 level is 15867.862cm -1 while the 1 S 0 level is 33792.583cm -1 above the ground level.Atomic oxygen is one of the most chemically reactive species in the atmosphere and all the three states oxygen are present throughout most of the atmosphere as results of photochemical and ionic processes.For example, when stratospheric ozone is irradiated with solar radiation, the quantum state of the oxygen atom product strongly depends on the wavelength of the incident radiation.The product will be mainly O( 1 D) if the wavelength is less than 310 nm (ultraviolet radiation) and O( 3 P) otherwise.The O( 1 D) atom can react with any other species present in the stratosphere and, by this way, alter the concentration of odd oxygen in the Chapman cycle of ozone [1][2][3][4] .Among those reactions, the reaction of O( 1 D) with molecular hydrogen is one of those whose incertitude most contributes to errors in the modulation of atmospheric chemistry.In addition to its role in atmospheric chemistry, the reaction of O( 3 P) with molecular hydrogen is one of the main reactions in combustion chemistry.As a result, the reactions O( 1 D, 3 P) + H 2 → OH+H have been subject of several experimental and theoretical studies [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] .
Experimental results clearly show that kinetic of the reaction between oxygen atom and molecular hydrogen depends on the quantum states of reactants.When search the kinetic data for these reactions, two kind of very different rate constants can be found.At temperature 298K, the recommended rate constant for O( 1 D) + H 2 is 1.1x10 -10 cm 3 molecule -1 s -1 (Ref.20).At the same temperature rate constant for O( 3 P) + H 2 is 9.0x10 -18 cm 3 molecule -1 s -1 (Ref.21).For reaction O( 3 P) + H 2 , the rate constant increases with temperature and can be fit into Arrhenius equation with positive activation energy.While for the reaction O( 1 D) + H 2 , the rate constant is not sensible to temperature and even negative activation energy was found 22 .

The Detailed Interaction between O Atom and H 2 Molecule
Theoretically, the differences in kinetic behaviour between the reactions O( 3 P) + H 2 and O( 1 D) + H 2 can be well understood through the detailed interaction between O atom and H 2 molecule.Within the framework of Born-Oppenheimer approximation, these two reactions occur on different potential energy surfaces (PES).The Figure 2 shows the correlation diagram for the interaction of an O atom with ground state H 2 .When the O( 3 P) atom approaches ground state H 2 ( 1 Σ g + ), they give rise to three triplet PESs, two of symmetry A" and one A' in the C s point group.Here, the prime means that the wave function keeps its signal when reflected on the plane of the three atoms while the double prime means a change of sign in the same operation.These can, somehow, be viewed as if the double occupied p orbital stays in that plane being each one of the single occupied orbitals in the perpendicular position (changing sign by reflection), otherwise the double occupied orbital can be perpendicular to that plane and the wave function doesn't change sign by reflection.
In collinear configurations, where it is located the saddle point for the title reaction, this reflection is no longer a symmetry operation and one A" (the one with a single occupied p orbital pointing to the H 2 molecule) and the 3 A' surfaces became degenerate in a 3 П surface, labelled according to the C ∞v point group.The other 3 A", with the double occupied orbital pointing to the H 2 , will correlate with a 3 Σ PES.This last Σ surface correspond to a most favourable orientation of the quadrupole moment of the O atom and is lower in energy at larger O ••• H 2 collinear distances (in the van der Waals region) but, due to the double occupancy of that orbital, it doesn't favour the formation of the OH diatomic and has a higher energy barrier to reaction.In addition, this Σ PES correlates with the product OH diatomic in its first excited state, OH( 2 Σ) and does not contribute to the title reaction at the energies of chemical practical interest.The two degenerate П PESs have the same energy barrier and give OH products in their ground electronic state, OH ( 2 П), and should be considered when studying this reaction.
When the O( 1 D) atom approaches ground state H 2 ( 1 Σ g + ), five singlet potential energy surfaces are accessible for reactants.The mainly contribution comes from the lowest ( 1 A') PES, that correlates without energy barrier with the ( 1 A 1 ) ground state of the H 2 O molecule.The other four PESs present an energy barrier to reaction.However the first excited state, 1A", must be considered for energies higher than 3.5 kcal/mol or temperatures above 1000 K.
At collinear geometries, the ground surface is labelled 1 Σ + .It has been noted that, due to the non-adiabatic electrostatic coupling between this state and the 1 П, where the 1 A' and 1 A" states of lower energy are degenerate, the cross section receives a contribution from the 1 П state of approximately 10%.The other two singlet potential energy surfaces correlate with a 1 Δ sate at collinear geometries and present a higher energy barrier.So, they do not contribute to reaction at the energies of chemical interest.
To illustrate the main differences between these reactions, here we use two of our published a PESs 23,24 for singlet and triplet state of this system as examples.The Figure 3  It is also important to teach students that the reaction of a ground state O atom with H 2 doesn't produce H 2 O, but OH plus H.This is clearly stated when teaching the mechanism of H 2 combustion, where the H 2 O is formed on the reaction of OH with H 2 , but it is not clear for a student of General Chemistry.
We must state that the ground state O atom is a triplet state and, in a reaction with a singlet state molecule, it can't produce a singlet state product by spin conservation rules, or, in a language more accessible to students, a ground state oxygen atom has two electrons with the same spin and the hydrogen molecule has two electrons with opposite spins, being impossible to build a molecule with two new bonds having two electrons of opposite spin each.Only an oxygen atom in his first singlet state can produce a water molecule in reaction with hydrogen.However this highly excited water molecule will dissociate into products, or reactants, before being deactivated by collision or emission of radiation.

A Reaction Dynamics
Besides as good example for elucidating the importance of the quantum state of chemical elements in chemical kinetics, the title reactions provide good examples for teaching dynamics of elementary bimolecular reactions.We have studied theoretically theses reactions in the past 13,19,[23][24][25] , and here, using some of our previous trajectories calculations results, we can show that two different types of dynamical behaviour can be exemplified by these two reactions.
For a bimolecular reaction of a three-particle system, a simple and instructive way to find the dynamical behaviour is to plot the interatomic distances as a function of time.Typically, for a direct reaction the switch over between the old bond and new bonds occurs within a very short time interval, corresponding to about one vibrational period.Figure 6 is such a plot for a reactive trajectory of reaction O( 3 P) + H 2 .Clearly this is a reactive collision of the 'direct' type.
On the other hand an indirect reaction occurs via a long-lived complex.Figure 7    For an indirect reaction, as a result of the long-lived complex formation, the product quantum states distribution will not depends directly on the reactant states and collision energy.It is expected that the long-lived complexes should statistical redistribute the total energy.Table 1 shows some results of our statistical calculations of the energy distribution of the reaction O( 1 D) + H 2 using phase space theory 26 .For the same collision energies, our QCT results are indicated in Table 2, and agree reasonably well with our statistical calculations.As results of the direct and indirect nature of these reactions, direct reaction and indirect reactions have different pattern for angular distribution of the reaction products.A direct reaction should produce forward or backward products, while an indirect one with a long-lived complex will dissociates with equal probability in all directions, presenting a forward-backward symmetric distribution.Figure 8 displays representative differential cross sections for the reaction O( 3 P) + H 2 .Here the reaction shows a forward angular distribution of reaction products which is in accordance with the direct reaction mechanism.For reaction O( 1 D) + H 2 , the angular distribution of the reaction products is represented in Figure 9, and is a forward-backward symmetric distribution.This corresponds to the expected behaviour for an indirect reaction.

Conclusions
The O + H 2 reaction, of overwhelming importance in combustion and atmospheric chemistry, is often mentioned in the textbook on chemical kinetics and physical chemistry.The rate constant of this reaction depends strongly on the oxygen atom quantum state.The comparison between the reactions with oxygen atom on 3 P and 1 D quantum states allows students to understand the importance of a clear definition of the quantum state of an atom in chemical reaction.Students gain insight into the interaction between O atom and H 2 molecule.
In addition, these reactions provide good examples for teaching bimolecular reaction dynamics: The ground state oxygen atom, O( 3 P), reacts with H 2 through a barrier and following a direct mechanism.But in the excited state, O( 1 D), the reaction is barrierless and proceed via the formation of a long-lived reaction complex.

Figure 1 .
Figure 1.Energy Levels of Neutral Oxygen at ground electronic configuration.

Figure 2 .
Figure 2. Correlation diagram of the potential energy surfaces involved in the O + H2 reaction, adapted from Ref. 14.
is a three dimensional view of an O( 3 P) atom around an equilibrium H 2 .There we can see a barrier in all approaching angles and that the shallow van der Waals valley favours a collinear attack in this PES.The approaching of an O( 1 D) atom to an equilibrium H 2 is shown in Figure 4.Note the lack of energy barrier at perpendicular angles.The very small energy barrier of 0.1 kcal/mol at collinear geometries is hardly viewed at the scale of this figure.The deep well corresponds to the H 2 O equilibrium molecule if we allow the States on Chemical Kinetics and Reaction Dynamics H-H distance to extend.The minimum reaction pathway for both reactions is compared in Figure 5.It is clear that the ground state Oxygen atom reacts with H 2 through a barrier while the reaction O( 1 D) + H 2 is barrierless.

Figure 3 .
Figure 3. Contour plot for an O( 3 P) atom around an equilibrium H2 molecule.The solid lines start at 0 kcal/mol, are equally spaced by 1 kcal/mol.Starting at 0 kcal/mol and equally spaced by -0.1 kcal/mol, the dashed lines depict the van der Waals regions.

Figure 4 .
Figure 4. Contour plot for an O( 1 D) atom around an equilibrium H2 molecule.The solid contours are equally spaced by 0.02 Eh, starting at -0.3704 Eh , dashed contours are equally spaced by 0.1 kcal/mol, the contour labelled by f corresponds to the dissociation energy.

Figure 5 .
Figure 5. Reaction path for the title reactions.The solid line represents the O( 3 P) + H2 → OH + H and the dashed line O( 1 D) + H2 → OH + H display a representative reactive collision of an Oxygen atom in the 1 D state.In this case, the mechanism of reaction involves an insertion of oxygen atom into the middle of the H 2 bond and formation of an excited H 2 O molecule that experiments several rotations and vibrations prior to dissociation into products.Indeed, the reaction O ( 1 D) + H 2 is usually considered as a prototype of an indirect type insertion reaction.

Figure 6 .
Figure 6.Distance vs. time plot for a reactive trajectory of the reaction O( 3 P) + H2 → OH+H at the collision energy 13.7 kcal/mol.The linerepresents one OH diatomic, ---refers to the HH diatomic and •••• the other OH diatomic.

Figure 7 .
Figure 7. Distance vs. time plot for a reactive trajectory of the reaction O( 1 D) + H2 → OH+H at the collision energy 3.0 kcal/mol.The linerepresents one OH diatomic, ---refers to the HH diatomic and •••• the other OH diatomic.

Table 1 .
25stribution, in percentage, of the total energy in translational, vibrational and rotational energies of the products of the reaction O( 1 D) + H2, using phase space calculations25.

Table 2 .
25Distribution, in percentage, of the total energy in translational, vibrational and rotational energies of the products of the reaction O( 1 D) + H2, using QCT results25.