With the help of a novel mathematical technique they developed, a team of UC Berkeley chemists has discovered the source of water's unique ability to ionize weak acids and bases and set the stage for more complex reactions.

Among these weak acids and bases are the nucleic acids that comprise DNA and some of the amino acids that form the backbone of proteins.

"Ionization is just pulling protons off of molecules, and shuttling protons around an aqueous solution is basic to life," said theoretical chemist David Chandler, professor of chemistry at UC Berkeley.

The theoretical results found by Chandler and his colleagues, an international collaboration between scientists in Germany, former post-doctoral fellows and a graduate student in Chandler's group at UC Berkeley, were published in the March 16 issue of Science.

The molecular details of these ionization processes have never been measured before because the event is so rare - once an hour for any given molecule - and when it does happen it's over quickly, on the order of a trillionth of a second. Yet, the separation of a proton - a hydrogen atom missing its one electron - from a molecule is the essential first step in all acid/base chemical reactions.

"If you're sitting on top of a water molecule, only one in a billion water molecules would exhibit this phenomenon of charge separation at a given instant," Chandler said. "It sounds like a very rare occurrence, but this charge separation is critical to the way human beings live."

All organic molecules consist of a tinker-toy backbone of mostly carbon, nitrogen and oxygen with lots of hydrogen atoms stuck on like Christmas ornaments. When weak acids or bases land in a pool of water, according to the team's calculations, these hydrogen atoms act as if they were connected by rubber bands to the backbone atoms, constantly flying outward and snapping back.

Every so often, the surrounding water molecules, each with a small electric field, line up and create a large field that pulls the hydrogen ion farther from the parent molecule than usual - as much as five neighbors away. Most of the time, the electric field quickly dies away and the proton snaps back.

"The electric field vanishes rapidly - it only lives for tens of femtoseconds - and then the proton just comes sweeping back because there is this strong electrical attraction from the chemical bond," he said. A femtosecond is a millionth of a billionth of a second.

Once every billionth of a second or so, however, the pathway back to association - a wire of hydrogen bonds - breaks, and a free proton is created.

"The proton is pulled far away 100s and 100s of times without leading to auto-dissociation," Chandler said. "This is the part that is surprising and that people didn't know. What finally leads to dissociation is, somewhere along this wire of hydrogen bonds, when there just happens to be a big electric field that's driven the proton away, by accident the hydrogen bond wire breaks and this proton is stuck off in left field."

Once the proton is liberated, it wanders through the liquid, free to participate in many other chemical reactions until it recombines with an hydroxide ion to make water again. Concentrations of hydrogen ions also set up electric fields that move other ionized molecules around.

"A proton gradient across a membrane, and the electrical voltage associated with that, is what drives all life processes," Chandler said.

This detailed picture comes from the team's calculations on what happens in pure water, which can be considered a weak acid, Chandler said. Water, or H2O, is composed of two hydrogen atoms and one oxygen atom, but in a liquid about one in every billion water molecules has dissociated into OH- ion (hydroxyl) and H3O+ ion (hydronium). The extra hydrogen ion or proton on the hydronium freely jumps around to other water molecules, and the concentration of these protons is a measure of the acidity of the solution. Water is defined as neutral, with a pH - a measure of the concentration of loose hydrogen ions (protons) in the liquid - of 7. Acids have lower pH; bases have higher pH.

Chandler said that the results explaining how hydronium and hydroxyl are created in pure water can be extended to any weak acid or base.

"Water is the simplest example of a weak acid or weak base, but when you put some weak acid like an amino acid in water, a minute or an hour later it has given up one of its protons to the bath of water around it," he said.

Chandler and his team calculated these detailed reactions by rethinking statistical mechanics. That branch of physical chemistry deals with the chances of going from one state to another, such as from a neutral molecule in water to an ionized molecule. If this is a very rare event, though - a reaction that occurs a billion times slower than other reactions going on around it - calculating the most likely outcome from the fundamental equations of quantum mechanics would keep a computer busy for the lifetime of the universe.

Instead, they came up with the idea of dealing with what Chandler calls trajectories, that is, the entire dynamic process from one state to another. If each possible state is like a valley in a landscape of valleys and ridges, he said, the trajectory from one valley to another would be like a strong rope stretching over the peaks. To find the easiest trajectory over the ridge to the desired valley, it's quicker to throw ropes over the passes and, learning from your mistakes, narrow the possibilities, than to randomly try all possible ways to scale the ridges.

"After you have thrown these ropes successfully, you march along the ropes, and you feel what the surface looks like, and you can say something very interesting about this complex process," he said.

Chandler is confident his calculations represent reality. Nevertheless, they predict strong, though transient, electric fields in the liquid that should be measurable.

The technique should be applicable to many processes now impossible to measure experimentally because they are rare and, until now too, difficult to calculate. Co-author Christoph Dellago, now at the University of Rochester, N.Y., and Peter Bolhuis, another former post-doc now a faculty member at the University of Amsterdam, are trying to understand how glass reorganizes on a timescale of decades. And Chandler hopes to discover how substances nucleate, such as the sudden freezing of a supercooled liquid.

"Defining a pathway between one state and another is a very famous optimization problem, and our technique is part of the solution to that general class of problems," Chandler said. "This is a big generalization of thermodynamics and statistical mechanics."

In addition to Dellago, Chandler's co-authors are Phillip L. Geissler, now a post-doctoral researcher at Harvard University, and Jurg Hutter and Michele Parrinello of the Max-Planck-Institut fur Festkorperforschung in Stuttgart, Germany.