# Molecular Terms of Dioxygen and Nitric Oxide

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{1}O

_{2}) and nitric oxide (

^{2}NO) in the gas and the liquid phase as well as their ESR spectra. It is demonstrated that an X-band ESR is a promising tool for detecting and monitoring these two pollutants.

## 2. Electronic Terms of Dioxygen and Nitric Oxide

_{z}on the molecular z-axis (Σ) [2], by the orbital angular momentum z- projection (Λ), as well as their sum—total electronic momentum projection Ω = S

_{z}+ Λ

**[2,3,4].**The quantum numbers for the observed values of projections of these momenta on the internuclear axis of a diatomic molecule are denoted as Σ, Ω, and Λ, and Ω = |Λ + Σ|. According to a common convention [2,3,4,5,6], the states with Λ = 0, 1, 2, are denoted by Σ, Π, Δ symbols. (One should distinguish notations of spin projection and the case of Λ = 0, which are denoted by the same symbol Σ).

^{2}operator and the S

_{z}operator [5]:

^{1}O

_{2}(

^{1}Δ

_{g}) and triplet

^{3}O

_{2}(

^{3}Σ

_{g}

^{−}) state dioxygen, the spin quantum number is equal to S = 0 and S = 1, respectively. In the last case, the spin projection quantum number has values Σ = 0, ±1. For the zero S singlet state the projection is naturally absent (Σ = 0). In the case of the ground state

^{2}NO radical S = 1/2, Σ = ±1/2 and two Ω values are possible (3/2 and ½). For analysis of ESR and optical spectra of diatomic molecules, one has to consider rotational nuclear angular momentum R [2,3,4]. R is an operator related to the rotation of nuclei as a whole. Because of the axial symmetry of the field in diatomic molecules, only the orbital angular momentum projection of electrons on the z-axis can be observed as a constant of motion [2]. For the π

^{2}open shell of dioxygen, there are two possibilities for the electronic wave functions Ψ of states with Λ = 0; function Ψ can either change sign upon reflection in any plane, which contains internuclear axis z (Σ

^{−}state), or not change sign (Σ

^{+}state). These symmetry restrictions are connected with a general property of all electrons in respect to their permutation [4,5]. For the triplet state (

^{3}Σ

^{−}), the spin part of the wave function is symmetric, but the spatial part is asymmetric in respect to permutation; this leads to a sign change upon reflection in a molecular plane since π

^{+}transforms to π

^{−}[4].

_{2}, with the inversion symmetry center or +/− in case Λ = 0. We will present the terms including these notations like it is presented in the literature [2,3,4,5,6]. The total angular momentum is denoted as J = Λ + R + S. The two additional notations are unimportant in the context of this mini-review. The contribution of nuclear momentum I and rotational momentum R into J are mostly omitted here since main isotope

^{16}O has no nuclear spin and for the

^{1}O

_{2}(

^{1}Δ

_{g}) molecule, we will consider the ESR spectrum for the lowest rotational state R = 0. Detailed information on the terms of diatomic molecules can be found in ref. [2,3,4,5,6].

^{2S+1}Λ

_{Ω}. Spin S of one electron is ½ and M

_{s}= ± ½. Here, M

_{S}is a spin component along the field. The total spin quantum number S is used in the superscript of a term to denote the term multiplicity m = 2S + 1. Thus

^{1}Λ

_{Ω},

^{2}Λ

_{Ω}, and

^{3}Λ

_{Ω}correspond to a singlet state, doublet state (a radical), and a triplet state of a diatomic molecule, respectively. We deal with two molecules that have the highest occupied 2π* molecular orbital–antibonding π orbitals. The individual electron on two degenerate π*

^{—}orbitals has a projection of orbital momentum as quantum number λ = ±1. When we deal with two degenerateπ- orbitals, it is necessary to ascribe λ

_{1}= +1 to an electron on one orbital and λ

_{2}= −1 to another. Projection of a total orbital momentum for two electrons in the open 2π* shell Λ = λ

_{1}+ λ

_{2}is denoted Σ, Π, and Δ for Λ = 0, 1, and 2, respectively.

^{2}Π

_{Ω}(like the ground state of

^{2}NO molecule) has the index Ω = Λ + S

_{z}. Typical values of Ω are ½, 3/2. Transitions between different states in ESR spectra are allowed at ΔM

_{J}= ±1. Here, M

_{J}is a quantum number of the component of J, which is a total angular momentum, see above. M

_{J}= ±1/2, ±3/2. We simplify the situation by ignoring molecular rotation in this case, which is acceptable for our goal.

## 3. Dioxygen

^{3}O

_{2}(

^{3}Σ

_{g}

^{−}). Triplet oxygen

^{3}O

_{2}demonstrates a very broad (width of ca. 1 T [7]) weak ESR spectrum in the liquid phase at low temperatures. Orbital angular momentum has a large contribution to the magnetism of molecules and in the case

^{3}O

_{2}(

^{3}Σ

_{g}

^{−}) Λ = 0. Additionally, molecular rotations are quenched by the solvent. ESR of

^{3}O

_{2}is not observed in liquid solutions at room temperature.

^{3}O

_{2}(

^{3}Σ

_{g}

^{−}) and with orbital magnetism in the excited singlet

^{1}O

_{2}(

^{1}Δg) oxygen. The rotation levels make an infinite ladder of spin-energy levels and rotational levels are inseparably interlaced with magnetic levels [2]. This way, the ESR spectrum of

^{3}O

_{2}consists of a huge number of components (lines). An intensive ESR spectrum is observed in the gas phase under low pressure, see Figure 1:

_{2}(

^{3}Σ

_{g}

^{−}) dioxygen is the electronically-excited state

^{1}O

_{2}(a

^{1}Δg); it provides another ESR spectrum (see Scheme 1 and Table 1). Singlet dioxygen (

^{1}Δg) is 94 kJ/mol above the triplet ground state. There are many ways to generate labile singlet dioxygen [9,10,12,13,14,17,19]. Singlet O

_{2}(

^{1}Δg) molecule does not have spin (S = 0) but has an electronic orbital angular momentum Λ = 2 [9,10,11,12,13,14,15,16,17]. Together with the rotational angular momentum (R), they form a total angular momentum, J = Λ + R; it is quantized along the magnetic field axis with quantum number M

_{J}. The O

_{2}(

^{1}Δg) molecule belongs to the classical Hund’s case (a) when Λ is quantized along the molecular z-axis [2]. Values Λ and J in this case are good quantum numbers [3]. Thus, for the free rotating O

_{2}(

^{1}Δg) molecule in the gas phase, the total momentum J provides an ESR spectrum [9,13]. The Λ-doubling in the O

_{2}(

^{1}Δg) molecule is expected to be very small [4,18], in fact, neither we nor other authors [19] could resolve the Λ—doubling splitting in the singlet oxygen ESR spectrum. Zeeman energy of O

_{2}(

^{1}Δg) in an external magnetic field H can be described by the following equation for magnetic field interaction with molecular magnetic moment [13,20]:

_{J}= 2 g

_{L}/3 [13]. The electronic magnetic moment along molecular axis z is equal to 2 g

_{L}μ

_{B}, where μ

_{B}= $e\u0127/2mc$ is the Bohr magneton and g

_{L}is the electronic orbital angular momentum g-factor, which is close to unity [13]; small corrections to g-factor of the singlet O

_{2}(

^{1}Δg) state are important for the EPR spectrum and are considered below.

^{1}O

_{2}(

^{1}Δg) dioxygen should have the same transition energy of about ${\scriptscriptstyle \frac{2}{3}}{\mu}_{B}H$. Only one transition 0 → 1 is close to the 0.667 ${\mu}_{B}H$ resonance [20], but all others are shifted [9].

^{1}Δg) dioxygen would be observed at the same field about H ≈ 10 kG with the frequency (9624.92 MHz) of X-band ESR spectrum. Transition energies hν

_{i}in the EPR spectrum (Figure 1) are different (at a fixed field H) because of perturbations from the upper rotational J = 3 levels (see Figure 2 below). They are equal to 0.65597 for (−2 → −1) transition, 0.66264 (−1 → 0), 0.66954 (0 → +1) and 0.67667 (+1 → +2) in the units ${\mu}_{B}H$ [9,13], see Table 2 below. Thus, we have almost symmetrically split quartet EPR lines (Figure 1). At the fixed microwave frequency ν = 9.62492 GHz, the ESR X-band resonance signals are obtained at the magnetic field strength of about 10 kG, respectively [9]. The account of interaction with the first excited rotational level R = 1(J = 3) provides additional corrections to M

_{J}sublevels of the ground rotational state J = 2 in the second-order of perturbation theory; the results are presented in Figure 2 below [13].

^{2}and equilibrium rotational constant B

_{e}of

^{1}O

_{2}(

^{1}Δ

_{g}). Here $a={(2{\mu}_{B}H)}^{2}/378{B}_{e}$.

^{1}O

_{2}(

^{1}Δ

_{g}) in the liquid phase since the local electric fields of solvent molecules quench the orbital angular momentum [2]. At any oxygen collision with a solvent molecule, the local electric fields remove the degeneracy of the (

^{1}Δ

_{g}) state; it splits into two close-lying sublevels which position depends on the particular geometry of any new collision and orbital angular momentum Λ is not anymore a good quantum number. (Non-zero orbital angular momentum can exist only in degenerate states) [21]. Thus, the simple Zeeman energy picture, Equation (1), is completely distorted and rotational coherence is quenched.

_{+}and L

_{-}. Similar contributions in combination with spin-orbit coupling (SOC) perturbation are responsible for the anisotropy of electronic spin g-factor; they are rather important for the ground triplet state of dioxygen

^{3}O

_{2}(

^{3}Σ

_{g}

^{−}) and provide ESR signal deviation from the free-electron value (g

_{e}= 2.0023). This deviation is big for the perpendicular component of g-tensor (as much as g

_{┴}= 2.0052 [3,22]), while g

^{||}is close to g

_{e}value [23,24]. These parameters were first obtained from the ESR spectrum of solid oxygen [3] and these parameters are supported by ab initio self-consistent field (SCF) calculations [22,24]. The electronic spin g-factor is connected with the spin-rotational coupling constant (γ) approximation is well developed for the ground and excited triplet states

^{3}Σ

^{−}of dioxygen [24]. However, for the singlet O

_{2}(

^{1}Δ

_{g}) molecule, the rotational g-factor theory contains some discrepancies which will be shortly discussed [13,20].

## 4. A Short Introduction to the Theory of Rotational g-Factor for the Singlet O_{2} (^{1}Δ_{g}) Molecule

_{A}) and charge (Z

_{A}); it corresponds to the moment for bare nuclei of two atoms A and B [4]. It does not contribute to the energy of the lowest rotational level K = 0 of the O

_{2}(

^{1}Δ

_{g}) molecule.

_{2}[24,25,26]. The main contributions to the sum (4) provide ${}^{1}{\mathsf{\Pi}}_{g},{}^{1}{\mathsf{\Phi}}_{g}$ states [24]. The lowest ${}^{1}{\mathsf{\Pi}}_{g}$ state produces the largest contribution (−3.143 $\times \text{}{10}^{-4}$) at the equilibrium R

_{e}distance [25]. Complete active space (CAS) linear response calculations [24] predict a value of −3.896 $\times \text{}{10}^{-4}$, which is in good agreement with the experimental estimation of (−3.957 ± 0.025) × 10

^{−4}obtained in ref. [20].

_{r}

^{e}-factor represents the magnetic moment produced by the rotation of “electrons following the nuclei” during molecular rotation [13]. Miller [20] has compared this electronic rotational g

_{r}

^{e}-factor for the

^{1}O

_{2}(

^{1}Δ

_{g}) state with g

_{r}

^{e}-value for the ground 3O

_{2}(

^{3}Σ

_{g}

^{−}) states [(−3.98 ± 0.12) × 10

^{−4}], also extracted from the experiment [3], and noted that they coincide within the experimental error.

_{r}-factor resolved by Miller is different, ${g}_{r}=-1.234\pm 0.025\times {10}^{-4}$, which is outside an experimental error [13,20]. Thus, the orbital magnetic moment of the O

_{2}(

^{1}Δ

_{g}) molecule is slightly different from a simple 2μ

_{B}value and this difference is crucial for the splitting between the quartet EPR lines, which appear through the second-order corrections [20]. We will remind the reader that g

_{r}= g

_{r}

^{e}+ g

_{r}

^{N}= g

_{r}

^{e}+ 2.723 $\times \text{}{10}^{-4}$; thus, the rotational g

_{r}-factor represents a difference between two comparable values. Electronic contribution (g

_{r}

^{e}-factor) being almost equal to −3.96 $\times \text{}{10}^{-4}$ for the O

_{2}(

^{1}Δ

_{g}) state and simultaneously close to g

_{r}

^{e}-value for the ground dioxygen O

_{2}(

^{3}Σ

_{g}

^{−}) state causes some doubts in researchers since Equation (4) provides different origins for both states [13,20]. Indeed, only ${}^{3}{\mathrm{\Pi}}_{g}$ states of

^{1}O

_{2}can contribute to the g

_{r}

^{e}-value for the ground triplet dioxygen [22,25].

_{2}(

^{1}Δ

_{g}) is usually produced in the presence of great excess of the triplet ground state oxygen [9,27]. Thus, both ESR signals appear simultaneously in the same magnetic field ranges and the triplet ground state oxygen lines are used as an internal standard for the singlet excited O

_{2}(

^{1}Δ

_{g}) concentrations measurements [9,13]. However, the nature of the ESR signal for both states of dioxygen

^{3}Σ

_{g}

^{−}, Λ = 0 and

^{1}Δ

_{g}, Λ= 2 is rather different. The triplet state EPR transitions frequency is determined by spin g-factor (g

^{┴}= 2.0052) and by its anisotropy with g

^{||}= g

_{e}parameter induced by SOC mixing, while the singlet delta dioxygen exhibits nearly symmetric quartet splitting due to electron-rotational interaction when O-O bond axes rotate around two perpendicular directions. In the late case, a value of rotational B

_{e}constant determines the spitting of the quartet lines. Understanding this qualitative difference is essential for the choice of the field strength and microwave EPR frequency range for detection of both the ground

^{3}O

_{2}(

^{3}Σ

_{g}

^{−}) and the excited

^{1}O

_{2}(

^{1}Δ

_{g}) dioxygen.

_{2}singlet–triplet transitions in the visible (λ 760 nm) and near IR (λ 1.27 μm) regions indicates that these bands have a magnetic-dipole origin and are induced by spin–orbit coupling (SOC) [21,22]. In optical spectroscopy, the ground is denoted by the letter X and excited states of other multiplicity are enumerated by small Latin letters a, b, etc. [4]. The weak intensity of the O

_{2}(X

^{3}Σ

_{g}

^{−})- O

_{2}(a

^{1}Δ

_{g}) band is determined by the same SOC-induced mixing with the ${}^{1,3}{\mathrm{\Pi}}_{g}$ states which are responsible for rotational g

_{r}

^{e}-values in the ground triplet and the singlet excited O

_{2}states with similar contributions of the orbital angular momentum, Equation (4) [28,29,30]. At the same time, the spin g-factor of the O

_{2}(X

^{3}Σ

_{g}

^{−}) state also depends on the similar orbital angular momentum contributions [22]. A good agreement of all these calculations with experimental EPR and optical data support the reliability of the similar g

_{r}

^{e}-values for both O

_{2}(X

^{3}Σ

_{g}

^{−}) and O

_{2}(a

^{1}Δ

_{g}) states.

## 5. Nitric Oxide

^{2}NO (

^{2}Π

_{1/2}), see Scheme 1 and Table 1. It has S = 1/2, S

_{z}= ±1/2, Λ = 1. The total angular momentum about the molecular axis (neglecting rotation) is defined as J = |Λ + S

_{z}|. The lowest state of

^{2}NO radical has J = 1 − ½ = ½. Since the open–shell is occupied less than one-half (two double degenerate molecular orbitals (MO). These two MO has only one electron, and we get the regular spin–orbit coupling splitting. A formula for the spin g-factor of a diatomic radical has a factor (Λ − 2S) which is 0 for the current state [13]. That means

^{2}Π

_{1/2}state has g = 0 and is diamagnetic in both gas and liquid states due to a cancellation of orbital and spin angular momenta.

^{2}NO is

^{2}Π

_{3/2}, where S = ½, Λ = 1. This state has J = 1 + 1/2 = 3/2. J = 3/2 splits in an external magnetic field into four sublevels M

_{J}with quantum numbers −3/2, −1/2, +1/2, +3/2. Thus, one expects three ESR transitions with the following changes in M

_{J}: −3/2→−1/2; −1/2→+1/2; +1/2→+3/2. The first spectra of

^{2}NO (

^{2}Π

_{3/2}) demonstrated namely three components [2,7,10]. Non-magnetic

^{2}Π

_{1/2}and paramagnetic

^{2}Π

_{3/2}states of

^{2}NO are very close in their energies. The excited state

^{2}Π

_{3/2}is only 1.43 kJ/mole higher in energy than the ground

^{2}Π

_{1/2}state [14]. Let us consider the factors, which determine this energy splitting. The open-shell wave function of the doublet

^{2}Π

_{J}state can be presented in the following forms: for the case of less-than-half occupied open π–shell we use Equation (5). We use Equation (6) for the case of more-than-half occupied π–shell [31]:

^{−1}and ${\zeta}_{2p}^{O}=153$ cm

^{−1}for nitrogen and oxygen, respectively [31]. Since J = |Λ + S

_{z}|, there are two possible presentations for each J. Expectation energy of the SOC operator is equal

^{2}NO radical from the SCF calculation with the zero differential overlap approach within PM-3 method [33]: 2${\pi}_{x(y)}=0.811{\psi}_{{p}_{x(y)}}^{N}-0.585{\psi}_{{p}_{x(y)}}^{O}$. This form of 2π-MO is in good agreement with the hyperfine coupling parameters fitting to ESR spectrum of gaseous

^{2}NO molecule [34]. Using these MO LCAO $({C}_{{p}_{x(y)}}^{A})$ coefficients we obtain the following splitting:

^{2}NO radical.

^{2}Π

_{3/2}is easily accessible at room and lower temperatures; the thermal energy at room temperature is 2.5 kJ/mol. Thus, one can observe the X-band ESR spectrum of the excited

^{2}Π

_{3/2}state, which is presented in Figure 3:

^{14}N nucleus. A highly resolved spectrum of

^{2}NO (

^{2}Π

_{3/2}) has 27 components due to additional interactions [10]. We calculated the HFC tensor for

^{14}N isotope of

^{2}NO radical by density functional theory with B3LYP/6–311++G(dp) approach [33]; the isotropic HFC constant a = 11.386 MHz, anisotropic HFC tensor component along the z-axis is equal 74.673 MHz. The oxygen atom bears an electric charge of +0.091 e and spin density of 0.286, whereas the nitrogen has −0.091 e and 0.714, respectively. Other spectroscopic parameters are in a good agreement with experiment [23]: r

_{e}= 1.148 Ả, ν

_{e}= 1980 cm

^{−1}, B

_{e}= 51.364 GHz, averaged polarizability α

_{av}= 9.4 ${a}_{0}^{3}$, dipole moment is equal −0.13 debye. The relatively small polarity and polarizability of

^{2}NO radical explain its rather weak intermolecular interaction in the gas phase; thus its ESR spectrum at moderate pressure does not depend on the properties of foreign gases. The calculated HFC tensor of

^{2}NO radical with natural isotope abundance does not contradict to experimental ESR spectrum (Figure 3) [10].

^{2}NO (

^{2}Π

_{3/2}) was tentatively interpreted as being due to traditional magnetic–dipole transitions (MDT), since the MDT nature is typical for EPR signals [10]. However, the latter the electric–dipole transitions (EDT) were shown to be more intense and prominent in this EPR spectrum. As many other

^{2}Π states the

^{2}NO (

^{2}Π

_{3/2}) state demonstrates a clear Λ–doubling effect [14]. The EDT lines occur between opposite members of an Λ-doublet (- $\leftrightarrow $ +), while much weaker MDT transitions connect the same Λ-doublet members (- $\leftrightarrow $ -) or (+ $\leftrightarrow $ +) [4]. All these features are determined by relatively strong SOC (Equation (8)) in quasi degenerate 2π

_{x}- and 2π

_{y}- molecular orbitals of nitric oxide.

_{2}(X

^{3}Σ

_{g}

^{−})- O

_{2}(a

^{1}Δ

_{g}) band at 1.2 μm to acquires EDT character and become much more intense because of strong spin–orbit coupling inside the dioxygen O

_{2}(π

_{g}) open shell. Thus, many peculiarities of the optical and EPR spectra of two diatomic species,

^{2}NO and O

_{2}, being very important for atmospheric problems, strongly depend on spin–orbit coupling in 2π*- orbitals (Scheme 1) which energy does not exceed 1–2 kJ/mol [21,32].

^{2}NO (

^{2}Π

_{3/2}) with solvent molecules lead to a spin relaxation or an infinite boarding of components. Note, that gas-phase ESR spectra are observed at low pressure. An increase in pressure leads to the broadening of components.

## 6. ESR of Trapped ^{2}NO

^{2}NO is used as a probe of surfaces, different cages, nano-objects, and biological species. Adsorption of

^{2}NO on surface vacancies, inside zeolites [11,15], or the C

_{60}cavity [16], complexation with biological molecules [18] leads to a quenching of the orbital momentumΛ; thus, the lowest

^{2}Π

_{1/2}state of

^{2}NO becomes paramagnetic and demonstrates ESR. In the adsorbed

^{2}NO species, the 2π

_{x}- and 2π

_{y}- molecular orbitals (MO) are split by interaction with the surface and the energy splitting between the perturbed 2π

_{x}and 2π

_{y}MO is a measure of the spin g-factor anisotropy [11].

^{2}NO species is not any more an object of diatomic spectroscopy with proper quantization of orbital and rotational angular momenta. Instead, the polyatomic cluster is an object of the ground and excited states studies. The principal values of the g-tensor are used now to determine the MO splitting to characterize the electric field strength at the

^{2}NO adsorption site. An example is presented in Figure 4:

^{14}N nucleus of a bound

^{2}NO and the g-factor just shows the position of the ESR signal.

^{2}NO complex with hemoglobin model by quantum chemical DFT calculation (Figure 5) in the framework of B3LYP/6–31 G approach [33]. The Fe-N coordination bond length is optimized to be 0.1866 nm with the angle Fe-N-O = 121.4°, the distance Fe-Cl = 0.2186 nm just simulates the Fe ion coordination with the protein residue. The calculated g-factor has components 2.0137, 20,082, and 1.9843, which are in qualitative agreement with the ESR spectrum in Figure 4. A large portion of nonpaired spin is concentrated on Fe ions.

^{14}N nucleus is equal to a = 15.78 MHz; anisotropic HFC tensor components are calculated at −30.2, −7.3, and 37.5 MHz. Thus, the Fermi-coupling a constant is slightly increased by 4.4 MHz in comparison with free NO radical, but the components of the HFC tensor are approximately half-diminished upon

^{2}NO coordination to the iron center of hemoglobin. The Fe(II) ion provides a rather strong influence on the hyperfine structure of the EPR spectrum of nitric oxide.

## 7. Conclusions and Perspectives

^{1}O

_{2}demonstrates an ESR spectrum in the gas phase. Due to the lack of spin in the molecule, it is better to use the term Electron Paramagnetic Resonance, which is achieved in this case where paramagnetism is due to the orbital momentum. The radical

^{2}NO does not demonstrate the ESR spectrum in liquid solutions. ESR of these and other states can be understood considering the terms of these diatomic molecules.

^{2}NO is an atmospheric pollutant.

^{2}NO reacts with dioxygen and produces

^{2}NO

_{2}, which is a pollutant as well. In the literature on environmental problems, both pollutants are often called NOx.

^{1}O

_{2}. In the air atmosphere (P

_{tot}= 1 atm),

^{1}O

_{2}has a lifetime of 2.8 s measured with a quencher [19]. During this time,

^{1}O

_{2}diffuses approximately 1 cm [19].

^{3}O

_{2}(

^{3}Σ

_{g}

^{−}) (Figure 1) can serve as a convenient internal standard for monitoring

^{1}O

_{2}(

^{1}Δ

_{g}) or other gas pollutants.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The ESR spectra in the sealed cell containing

^{3}O

_{2}(P

_{O2}= 0.2 Torr) and a sensitized naphthalene vapor obtained in the dark (

**a**) and during irradiation of a sensitizer (

**b**), T = 293 K. The intensity component in the high field (

**a**,

**b**) is part of the ESR of

^{3}O

_{2}(

^{3}Σ

_{g}

^{−}). The ESR spectrum of

^{1}O

_{2}(

^{1}Δg) consisting of four components (b and b × 10, a and a × 10) was obtained under photoexcitation of naphthalene in the presence of

^{3}O

_{2}. Adapted from ref. [9].

**Figure 2.**Splitting of the ground and first excited rotational levels of the singlet oxygen

^{1}O

_{2}(

^{1}Δ

_{g}) state in magnetic field H. Generalized from refs. [13,20]. Here D

_{e}is centrifugal distortion parameter, B

_{o}is the rotational constant in the lowest vibrational level; see for details ref. [20].

**Figure 3.**ESR spectrum of

^{2}NO (

^{2}Π

_{3}

_{/2}) at room temperature and pressure P

_{NO}= 0.5 Torr. Vertical dashed lines mark the central part of the spectrum. Adapted from ref. [10].

**Figure 5.**The model of the

^{2}NO adduct with hemoglobin (coordinated with Cl

^{-}anion as a model of protein residue). Red color for O and Fe atoms, dark blue N, blue C, and grey for H atoms. Adapted from ref. [29]. This is also a calculation made for this paper.

**Table 1.**The terms of O

_{2}and

^{2}NO in the ground and the closest in energy excited states as well as their paramagnetism in the gas and the liquid phases.

Molecule | Ground State Term | ESR ^{1} in the Following State | Term of the Nearest Excited State | ESR ^{1} in the Following State |
---|---|---|---|---|

O_{2} | ^{3}Σ_{g}^{−} | Liquid: No ^{2} | ^{1}Δg | Liquid: No |

Gas: Yes | Gas: Yes | |||

NO | ^{2}Π_{1/2} | Liquid: No ^{3} | ^{2}Π_{3/2} | Liquid: No |

Gas: No | Gas: Yes |

^{1}X-band spectrometer.

^{2}See the text below.

^{3}Electronically-excited state.

ESR Transition | Field (G) | $\mathit{h}{\mathit{\nu}}_{\mathit{i}}/{\mathit{\mu}}_{\mathit{B}}\mathit{H}$^{1} | $\mathit{h}{\mathit{\nu}}_{\mathit{i}}/{\mathit{\mu}}_{\mathit{B}}\mathit{H}$^{2} | Second-Order Correction ^{2} |
---|---|---|---|---|

(−2 → 1) | 10,486.00 | 0.655 | 0.65597 | ${\nu}_{0}+(5-8)a$ |

(−1 → 0) | 10,375.68 | 0.662 | 0.66264 | ${\nu}_{0}+(8-9)a$ |

(0 → +1) | 10,264.67 | 0.669 | 0.66954 | ${\nu}_{0}+(9-8)a$ |

(+1 → +2) | 10,151.75 | 0.677 | 0.67667 | ${\nu}_{0}+(8-5)a$ |

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**MDPI and ACS Style**

Khudyakov, I.V.; Minaev, B.F.
Molecular Terms of Dioxygen and Nitric Oxide. *Physchem* **2021**, *1*, 121-132.
https://doi.org/10.3390/physchem1020008

**AMA Style**

Khudyakov IV, Minaev BF.
Molecular Terms of Dioxygen and Nitric Oxide. *Physchem*. 2021; 1(2):121-132.
https://doi.org/10.3390/physchem1020008

**Chicago/Turabian Style**

Khudyakov, Igor V., and Boris F. Minaev.
2021. "Molecular Terms of Dioxygen and Nitric Oxide" *Physchem* 1, no. 2: 121-132.
https://doi.org/10.3390/physchem1020008