Frontier Orbitals, Combustion and Redox Transfer from a Fermionic-Bosonic Orbital Perspective

Oxygenations are highly exergonic, yet combustion of organic matter is not spontaneous in an atmosphere that is 21% O 2 . Electrons are fermions with a quantum spin number s of 1/2ħ. An orbital containing a single electron with s = 1/2 is fermionic. Orbitals can contain a maximum of two electrons with antiparallel spins, i.e., spin magnetic quantum numbers m s of 1/2 and −1/2. An orbital filled by an electron couple has s = 0 and bosonic character. The multiplicity of a reactant is defined as |2(S)| + 1 where S is the total spin quantum number. The Wigner spin conservation rules state that multiplicity is conserved. The transmission coefficient κ of absolute reaction rate theory also indicates the necessity for spin conservation. Burning is fermionic combustion that occurs when sufficient energy is applied to a bosonic molecule to cause homolytic bond cleavage yielding fermionic products capable of reaction with the bifermionic frontier orbitals of triplet multiplicity O 2 . Neutrophil leucocytes kill microorganisms by bosonic combustion and employ two mechanisms for changing the multiplicity of O 2 from triplet to singlet. Microorganisms, composed of bosonic singlet multiplicity molecules, do not directly react with bifermionic O 2 , but are highly susceptible to electrophilic at-tack by bosonic electronically excited singlet molecular oxygen ( 1 2 O ∗ ). Hydride ion (H − ) transfer is the common mode of cytoplasmic redox metabolism. Bosonic transfer of an orbital electron couple protects from damage by obviating fermionic reaction with bifermionic O 2 . Bosonic coupled electron transfer raises the consideration that quantum tunneling might be involved in facilitating such redox transfer.

tiparallel spins, i.e., spin magnetic quantum numbers m s of 1/2 and −1/2. An orbital filled by an electron couple has s = 0 and bosonic character. The multiplicity of a reactant is defined as |2(S)| + 1 where S is the total spin quantum number. The Wigner spin conservation rules state that multiplicity is conserved. The transmission coefficient κ of absolute reaction rate theory also indicates the necessity for spin conservation. Burning is fermionic combustion that occurs when sufficient energy is applied to a bosonic molecule to cause homolytic bond cleavage yielding fermionic products capable of reaction with the bifermionic frontier orbitals of triplet multiplicity O 2 . Neutrophil leucocytes kill microorganisms by bosonic combustion and employ two mechanisms for changing the multiplicity of O 2 from triplet to singlet. Microorganisms, composed of bosonic singlet multiplicity molecules, do not directly react with bifermionic O 2 , but are highly susceptible to electrophilic attack by bosonic electronically excited singlet molecular oxygen ( 1 2 O * ). Hydride ion (H − ) transfer is the common mode of cytoplasmic redox metabolism. Bosonic transfer of an orbital electron couple protects from damage by obviating fermionic reaction with bifermionic O 2 . Bosonic coupled electron transfer raises the consideration that quantum tunneling might be involved in facilitating such redox transfer.

Introduction and Background
A wavefunction (ψ) defines a quantum system. An orbital is described by , , l n l m ψ where n is the principle quantum number, l is the azimuthal or angular momentum quantum number, and m l is the magnetic quantum number. An electron occupying an orbital is described by the wave function the electron-spin quantum number s describes the total spin and the spin magnet quantum number m s describes each electron spin as 1/2 or −1/2 [1] [2]. According to the exchange principle, a pair of particles, a and b, can be described by a wavefunction ψ(a, b). Exchanging the particles generates a new wavefunction ψ(b, a). If particles are identical and indistinguishable, their probability distributions will be identical, ψ 2 (a, b) = ψ 2 (b, a), regardless of the orientation of the particles. When the square roots of the probability distributions yield the wavefunctions ψ(a, b) = ψ(b, a), exchange is symmetric and the particles are bosons. When the wavefunctions ψ(a, b) = −ψ(b, a), exchange is antisymmetric and Such spin is independent of orbital motion and is without analogy in classical physics. The spin magnetic quantum number m s has two spin possibilities: 1/2 (spin up, ↑) or −1/2 (spin down, ↓). The multiplicity of an atom or molecule equals |2(S)| + 1 where S is the total spin.

Fermionic and Bosonic Orbitals
Fermions can combine to yield a wavefunction with bosonic character. An alpha particle made up of four fermions is bosonic [3]. An electron is a fermion. As such, an orbital filled by a single electron has an s = 1/2 and fermionic character Reaction chemistry can be approached from a fermionic-bosonic orbital perspective.
Consistent with the fermion nature of electrons, Pauli's exclusion principle limits an orbital to a maximum of two antiparallel electrons, i.e., m s of 1/2 (↑) and −1/2 (↓). In Figure 1, note that the lower energy 1s and 2s orbitals of atomic N each contain two antiparallel electrons, i.e., an orbital couple with s = 0. These orbitals are closed to reaction chemistry. The frontier orbitals of atomic N include the three 2p orbitals. These 2p orbitals are degenerate, i.e., each orbital has the same energy. Each 2p orbital contains a single fermionic electron. Hund's maximum multiplicity rule states that the electrons in degenerate singly occupied orbitals will have parallel spins [7]. As such, each of the three 2p frontier orbitals of N have an s = 1/2 and the S of N is 3(1/2). The spin multiplicity, i.e., |2(S)| + 1, for N is thus |2(3/2)| + 1= 4. Stated differently, atomic nitrogen is a triradical with quartet spin multiplicity. Each 2P orbital of N is a SOAO, and as such, atomic N is trifermionic. As depicted in Figure 1 and stated in Table 1, the product of reacting two quartet multiplicity N atoms is singlet multiplicity N 2 . The lower energy 1s and 2s orbitals of N all contain coupled antiparallel electrons with s = 0. These non-frontier bosonic orbitals do not participate in reaction. Likewise, the sigma bonding (σ) and antibonding (σ * ) orbitals of N 2 , derived from the 1s and 2s orbitals of the atomic N's, are bosonic and closed to reaction chemistry. The frontier π bonding orbitals of N 2 are both filled by an electron couple with s = 0 and have bosonic character. In its ground state, N 2 is singlet multiplicity, triple bonded and bosonic.

Transmission Coefficient of Absolute Reaction Rate Theory
Absolute reaction rate theory states that the rate of a chemical reaction requires that reactants first combine to form an activated complex, where k is the rate, κ is the transmission coefficient, kT/h has the dimensions of frequency and K * is the equilibrium constant for the activated complex. The transmission coefficient, κ, for typical reactions approximates unity, i.e., each activated complex yields product, but not every activated complex at the potential-energy barrier will cross over to product [8]. The value of κ decreases by several orders of magnitude in reactions involving change in spin state [8].

Wigner Spin Conservation from a Fermionic-Bosonic Perspective
The Wigner spin conservation rules state that a reacting system resists any change in spin angular momentum, i.e., multiplicity [9] [10]. The total spin number, S, of an atom or molecule defines its multiplicity; i.e., |2S| + 1 = multiplicity. When S = 0, the multiplicity is singlet, when S = 1/2, the multiplicity is doublet, when S = 1/2 + 1/2, the multiplicity is triplet, et cetera. Reactions involving change in multiplicity have transmission coefficient, κ, values of less than 10 −4 . The spin states or multiplicities of the reactants determine the spin state or multiplicity of the activated complex, and are conserved in the spin states or multiplicities of the resulting product or products. For example, if the impossibility of orbital overlap is ignored and reaction is assumed to involve a bosonic singlet multiplicity molecule and a bifermionic triplet multiplicity molecule, then the activated complex must have a bifermionic triplet multiplicity, and bifermionic triplet multiplicity must be conserved in the product or products. These and other possibilities are described in Table 1 O * is required for spin conservation, but violates Hund's maximum multiplicity rule [11], and as such, 1 2 O * is electronically excited with a lifetime of about a microsecond [12]. As illustrated in Figure   2, 1 2 O * relaxes to its triplet ground state by emitting a near infrared photon [13]. As illustrated in Figure 2, 3 O 2 has two singly occupied frontier orbitals. As defined by Hund's maximum multiplicity rule, the lowest energy or ground state of 3 O 2 is achieved when both of its pi antibonding ( g π * ) frontier orbitals have one electron, i.e., each g π * orbital has the same m s , i.e., 1/2 + 1/2 or −1/2 + −1/2 [11]. Since the two frontier orbitals of 3 O 2 are both fermionic, 3 O 2 is described as bifermionic. Oxygen is the second most electronegative element, and as such, organic oxygenation reactions are highly exergonic, but frontier orbital interaction are highly improbable, and combustion is not spontaneous.

Combustion
Combustion, defined as an act or instance of burning, requires fuel and molecular oxygen, and produces heat and light. The organic molecules that serve as fuel are of singlet multiplicity and present bosonic frontier orbitals that are unreactive with the bifermionic frontier orbitals of 3 O 2 . Consistent with absolute reaction rate theory and the spin conservation rules, such reactions are not spontaneous.

Fermionic Combustion
To initiate burning, a sufficient amount of energy, e.g., a flame, must be applied to cause homolytic bond cleavage of the singlet multiplicity fuel molecule. Each homolytic cleavage yields two doublet multiplicity SOMO products. These fermionic products can directly react with the bifermionic frontier orbitals of 3 O 2 .

Bosonic Combustion
The neutrophil leukocyte, a phagocytic white blood cell, is tasked with defending the host animal against a vast variety of pathogenic microorganisms [17]. Fifty years ago, I pondered the possibility that phagocytic leukocytes kill microbes by changing the multiplicity of molecular oxygen from triplet to singlet [18].

Neutrophil Combustive Microbicidal Metabolism
Neutrophil reduced nicotinamide adenine dinucleotide phosphate (NADPH) oxidase controls HMP metabolism by accepting two reducing equivalents from NADPH thus liberating the oxidized NADP + that is required for glucose-6-phosphate (G-6-P) dehydrogenase metabolism of glucose. Biochemical dehydrogenations involve hydride (H − ) transfer. The bosonic character of such redox exchange will be considered subsequently. The riboflavin prosthetic group of NADPH oxidase facilitates decoupling of the bosonic electron pair. Riboflavin mediated separation allows fermionic expression of the separated electrons and results in reactive electron capture by bifermionic 3 O 2 [14]. The product of such univalent reduction is the doublet multiplicity hydroperoxyl radical ( 2 HO 2 ).  [19]. As described in Table 1, reactions of fermions yield bosonic products.
Neutrophils contain abundant myeloperoxidase (MPO). The haloperoxidase action of MPO provides an additional mechanism for generation of bosonic  [20]. MPO can catalyze classical peroxidase activity involving radials, but such activity is distinct from the acid haloperoxidase action involved in microbicidal action [17].
Generation of 1 2 O * violates Hund's maximum multiplicity rule; i.e., the electronic configuration with highest multiplicity has the lowest energy. The greater the number of wave functions possible for a system, the lower the energy. Higher multiplicity states produce greater nuclear-electron attraction and are of lower energy [11]. As such, 1 2 O * is metastable with a lifetime of about a microsecond. This lifetime restricts its potent electrophilic reactivity to within a radius of about 0.2 microns (µm) [12]. Upon phagocytosis, the microbe becomes the locus of neutrophil microbe killing. Generation of the bosonic reactant 1 2 O * within the phagolysosome space of the neutrophil directly focuses its potent electrophilic reactivity to the target microbe and minimizes collateral damage. Purified MPO selectively binds all gram-negative bacteria tested and can bind and inactivate endotoxin even in the absence of haloperoxidase function [21]. Selective MPO binding to microbes correlates with selective MPO-mediated microbicidal action. Bosonic combustion is limited by the lifetime of 1 2 O * . Such reactive restrictions have the advantage of selectively focusing and confining combustive action to the microbe while avoiding bystander injury to host cells [22].

Bosonic Transfer of Reducing Equivalents
Cytoplasmic redox transfers, i.e., pre-cytochrome electron transfers, typically involve the movement of two reducing equivalents from one singlet multiplicity molecule to another, and is described as H − transfer. Such hydride transfer involves the movement of a proton plus an orbital couple of antiparallel electrons.
The orbital couple has a s = 0, and as such, transfer is singlet multiplicity and bosonic.
Biological systems are exposed to an atmosphere with abundant O 2 . The bosonic character of biochemical systems provides protection against direct reaction with bifermionic O 2 . As previously considered, any biologic transfer involving a single fermionic electron would open the possibility for direct fermionic reaction with O 2 . The resulting fermionic-bifermionic reaction would produce a fermionic product and the possibility for further fermionic-bifermionic propagation.
Redox transfer of a bosonic orbital electron couple might offer additional advantage. The bosonic nature of the alpha particle facilitates quantum tunneling from the nucleus [23]. The bosonic nature of a Cooper pair of electrons facilitates superconductivity [24]. Alpha particle radiation and Cooper pairing in superconductivity are very different from each other, and both phenomena are very different from biochemical redox electron transfer. However, the commo-Journal of Modern Physics nality of bosonic pairing in quantum tunneling raises suppositions with regard to a possible role in facilitating biological redox transfer.

Summary and Conclusion
Reaction chemistry involves frontier orbital interactions. An orbital is fermionic if occupied by a single electron, and bosonic if occupied by an electron pair.
With regard to orbital reactivity, bosonic orbitals react with bosonic orbitals generating bosonic products, fermionic orbitals react with fermionic orbitals generating bosonic products, and fermionic orbitals react with bifermionic molecules generating less fermionic products. Fermionic-bosonic reactions are improbable, but the products of any such reaction must conserve the fermionic character of the reaction complex. As a general observation, all reactions favor bosonic products. Burning or fermionic combustion is initiated by homolytic bond cleavage producing fermionic products that react with bifermionic triplet