On this Wikipedia page it says that lower oxygen levels can cause light-headedness. Is there evidence that higher partial pressure of oxygen can improve mental focus?
Long term exposure to hyperoxia actually does more harm than good. Though short term hyperoxia is recommended after brain injuries (http://www.medscape.com/viewarticle/741751_3) as a valid clinical strategy.
For lower concentrations of oxygen, there seems to be evidence that cognitive function is improved:
You can read more about that here: Chung, Soon-Cheol, et al. "Effect of 30% oxygen administration on verbal cognitive performance, blood oxygen saturation and heart rate." Applied psychophysiology and biofeedback 31.4 (2006): 281-293.
And also this:
This study aimed to investigate whether inhalation of the air with 30% oxygen compared with normal air enhances cognitive functioning through increased activation in the brain. The verbal and visuospatial tasks were performed while brain images were scanned. The results showed that there were improvements in performance and also increased activation in several brain areas under the condition of 30% oxygen. These results suggest that a higher concentration of the inhaled oxygen increases the saturation of the blood oxygen in the brain, and facilitates cognitive performance.
Taken from: Sohn, Jin-Hun, Soon-Cheol Chung, and Eun-Hye Jang. "30% oxygen inhalation enhances cognitive performance through robust activation in the brain." Journal of physiological anthropology and applied human science 24.1 (2005): 51-53.
Though you have to be a bit careful about oxygen poisoning.
While oxygen is an essential component for living organisms, the formation of reactive O2 intermediates is commonplace in aerobically metabolizing cells. The stability of a variety of reactive O2 intermediates varies, but in some instances their interaction with the intracellular environment sets the basis for the pathophysiology of several disease states.
Adapted from: Cadenas, Enrique. "Biochemistry of oxygen toxicity." Annual review of biochemistry 58.1 (1989): 79-110.
Pathophysiological processes are associated with increased levels of hyperoxia-induced reactive O2 species (ROS) which may readily react with surrounding biological tissues, damaging lipids, proteins, and nucleic acids. Protective antioxidant defenses can become overwhelmed with ROS leading to oxidative stress.
The continuous exposure of newborn rats to 70–80 per cent oxygen at atmospheric pressure throughout the first 9 days of life significantly inhibited the growth of the brain which normally occurs during this period of life. The accumulations of DNA, RNA, total protein, and proteolipid protein which accompany brain growth during this period were all approximately proportionately depressed by the oxygen-enriched atmosphere. RNA/DNA and protein/DNA ratios were unaffected. The increase in brain mass in the first week of life reflects mainly cell proliferation, and since the decreased DNA accumulation occurred with no changes in RNA/DNA and protein/DNA ratios, we conclude that the effect of oxygen was to inhibit cellular division. We estimate that the oxygen exposure caused an approximately 7 per cent deficit in the cell population of the brain. These results indicate that the use of elevated concentrations of oxygen may have serious deleterious effects on the growth and development of the brain.
Taken from:* Grave, G. D., C. Kennedy, and L. Sokoloff. "Impairment of growth and development of the rat brain by hyperoxia at atmospheric pressure." Journal of neurochemistry 19.1 (1972): 187-194.*
Also hydrogen peroxide is produced:
Thus the H2O2 concentration in brains of rats exposed to room air is calculated to be about 7.7 pM, rises 60% when O2 tension is increased to 100% O2, and increases 300% at 3 ATA 100% O2, where symptoms of central nervous system toxicity first become apparent. These studies support the concept that H2O2 is an important mediator of O2-induced injury to the central nervous system.
Taken from: Yusa, T. O. S. H. I. K. O., et al. "Hyperoxia increases H2O2 production by brain in vivo." Journal of Applied Physiology 63.1 (1987): 353-358.