in other words, quantum effects are most usually at work in proton distribution sites at distances on the order of an angstrom (1 Å). In physics, a semiclassical (SC) approach is most useful in defining this process because of the transfer from quantum elements (e.g. particles) to macroscopic phenomena (e.g. biochemicals). Aside from hydrogen tunneling, studies also show that electron transfer between redox centers through quantum tunneling plays an important role in enzymatic activity of photosynthesis and cellular respiration (see also Mitochondria section below). For example, electron tunneling on the order of 15–30 Å contributes to redox reactions in cellular respiration enzymes, such as complexes I, III, and IV in mitochondria. Without quantum tunneling, organisms would not be able to convert energy quickly enough to sustain growth. Quantum tunneling actually acts as a shortcut for particle transfer; according to quantum mathematics, a particle's jump from in front of a barrier to the other side of a barrier occurs faster than if the barrier had never been there in the first place. (For more on the technicality of this, see Hartman effect.) Mitochondria Organelles, such as mitochondria, are thought to utilize quantum tunneling in order to translate intracellular energy. Traditionally, mitochondria are known to generate most of the cell's energy in the form of chemical ATP. Mitochondria conversion of biomass into chemical ATP is 60-70% efficient, which is superior than the classical regime of man-made engines. To achieve chemical ATP, researchers have found that a preliminary stage before chemical conversion is necessary; this step, via the quantum tunneling of electrons and hydrogen ions (H+), requires a deeper look at the quantum physics that occurs within the organelle. Because tunneling is a quantum mechanism, it is important to understand how this process may occur for particle transfer in a biological system. Tunneling is largely dependent upon the shape and size of a potential barrier, relative to the incoming energy of a particle. Because the incoming particle can be defined by a wave equation, its tunneling probability is dependent upon the potential barrier's shape in an exponential way, meaning that if the barrier is akin to a very wide chasm, the incoming particle's probability to tunnel will decrease. The potential barrier, in some sense, can come in the form of an actual biomaterial barrier. Mitochondria are encompassed by a membrane structure that is akin to the cellular membrane, on the order of ~75