Pittsburgh Supercomputing Center: Projects in Scientific Computing: At the Frontier of Physics and Chemistry
Getting the Jump on Superacids

Computation Opens a Window Closed to Experiment

They don't come from the planet Krypton or leap tall buildings, but it's not a big stretch to think of superacids as chemical superheroes. These fascinating compounds have, since the 1960s, become an essential tool of the chemical industry. Their powerful ability to react with and break down raw petroleum brings us such products as high-strength plastics and lead-free, high-octane gas. Exotic processes like coal gasification are unthinkable without superacids.

"Hundreds of thousands of tons of this material are used in the chemical industry on a routine basis," says Michael Klein, Hepburn Professor of Physical Science at the University of Pennsylvania and director of Penn's Center for Molecular Modeling. "Yet they're mysterious. Why do different superacids have different strength? How does a superacid actually work at the atomistic level?"

Despite their industrial applications, superacids aren't well understood, in large part because they are what they are — extremely strong acids. By the accepted definition, superacid means stronger than 100 percent sulfuric acid; many are a billion or more times stronger than that. "They are very toxic, very volatile," says Klein's collaborator, post-doctoral fellow Dongsup Kim, "and it's difficult to do experiments."

Motivated by the industrial importance and unique properties of these compounds, Klein and Kim used Pittsburgh Supercomputing Center's CRAY T3E to get some answers. With a series of quantum chemistry studies, they have provided new insight into the relation between the molecular structure of superacids and their acid strength. With a powerful quantum approach that simulates molecular movement, furthermore, they produced the first detailed picture of a fundamental superacid property called proton jumping.

Acids Mixed with Acids

Harvard chemist and educator James Bryant Conant coined the term "superacid" in 1927 when he recognized that some acid systems are stronger than conventional mineral acids, such as sulfuric acid. In the 1960s, George Olah at Case Western Reserve University followed Conant's lead and developed powerful superacids by mixing acids. In this way, for example, his laboratory developed "Magic Acid" — a mix of antimony pentafluoride (SbF5) and fluorosulfuric acid (HSO3F), named for its seemingly magical ability to dissolve candle wax.

Olah and his colleagues found that by dissolving hydrocarbons in these compounds they stabilized a chemical species — called carbonium ions — that exists for only a fleeting instant in hydrocarbon reactions. These elusive ions couldn't be studied before Olah's experiments, and he won the 1994 Nobel Prize for Chemistry for this work, which led to enriched understanding of organic chemistry and to many industrial applications.

Click to Enlarge: Frame 1 -- Minimum energy structures of BF<sub>3</sub>/(HF)<SUB>1,4,7</SUB>. Click to Enlarge: Frame 2 -- Minimum energy structures of BF<sub>3</sub>/(HF)<SUB>1,4,7</SUB>. Click to Enlarge: Frame 3 -- Minimum energy structures of BF<sub>3</sub>/(HF)<SUB>1,4,7</SUB>.

Superacid Clusters
Minimum energy structures of BF3/(HF)1,4,7. In interaction with a single HF, BF3 is weakly attracted, as indicated by the bond length (in Angstroms). With four HF molecules, however, a ring structure forms with hydrogen bonds between some of the H (blue) and F (green) molecules. This stabilizes and increases interaction strength between B (red) and the added F atom, as indicated by the shortened bond length. With six and seven HFs, an H2F+ like structure (shading) further stabilizes the cluster.

Download a larger version of frame 1 (38 KB), frame 2 (58 KB), frame 3 (71 KB).

During a visit to Penn's chemistry department a few years ago, Olah raised the topic of superacids. "A bell went off in my head," says Klein, recalling that he'd been interested in superacids many years ago, when computational science wasn't advanced enough to simulate them. "What makes superacids difficult is that chemistry's going on, the making and breaking of bonds. Superacids are liquid, and chemistry for 50 or 60 years has had a diversion into the gas phase. Real chemistry happens in solutions, but we couldn't do studies of liquids 25 years ago, because the computing hardware wasn't capable enough, and furthermore we didn't have the methods."

Taking the hint from Olah, Klein and Kim set out to fill-in some of the blanks. Experiments, for instance, with one of the superacids — boric trifluoride in hydrogen fluoride (BF3/HF) — had indicated no reaction between BF3 and HF in the gas phase, which posed a question: If these molecules don't react, why do they form a superacid in solution?

Naked Protons

Acids are defined by their ability to "protonate" bases — that is, to donate protons. The key chemical species is the hydrogen nucleus, naked H+, stripped of its single electron. Because the naked proton has a very strong affinity for other molecules, it can't be found in liquids, where it's always bound with either the acid or solvent. Free protons exist only in the gas phase, one reason why experiments have focused there, yielding information not available experimentally with liquids.

Computational approaches, however, open a window that's closed to experiment. In the case of BF3/HF, the weakest superacid, gas-phase experiments indicated a feeble, electrostatic attraction between BF3 and HF — called a van der Waals attraction. One might expect to see a stronger bond, a chemical bond in which the fluorine atom from HF shares electrons with the boron of BF3, yielding a BF4- ion and a naked proton. Availability of free protons is a key factor in acid strength, and the experiment suggested that the weak BF3/HF interaction might account for the relative weakness of this superacid.

Kim and Klein confirmed the experiment and also showed a more complex picture. They carried out a series of quantum structural calculations, starting with BF3 and a single HF and adding HF molecules one at a time, up to seven. With a single HF, the calculations show a weak attraction between BF3 and HF, as indicated by the distance between the molecules in their energy minimized, native state.

With more HF molecules, however, the picture changes. With four HF molecules, the intermolecular distance decreases, and a chemical bond forms, induced by a ring structure of HF molecules, bound together by hydrogen bonds, that stabilizes the BF4- ion. Adding more HF molecules further stabilizes the ion and shortens the bond length. With six and seven HFs, the ring architecture is further secured by hydrogen bonds, leading to H2F+ like structures, suggesting that this protonated HF is a key to superacids. "You need to have a solvent shell of neighbors," says Klein. "That's why the reaction takes place in the liquid."

Click to Enlarge: Frame 1 -- Simulation of an excess proton in solution with 54 HF molecules. Click to Enlarge: Frame 2 -- Simulation of an excess proton in solution with 54 HF molecules. Click to Enlarge: Frame 3 -- Simulation of an excess proton in solution with 54 HF molecules. Click to Enlarge: Frame 4 -- Simulation of an excess proton in solution with 54 HF molecules.

Proton Leapfrog
Simulation of an excess proton (yellow) in solution with 54 HF molecules. The excess proton attaches to a fluorine atom (red) in a pre-existing HF chain (blue and green), and these two atoms remain adjacent to each other as they jump down the chain. Time is shown in femtoseconds (a billionth of a millionth of a second). Although the relative atomic positions change little, the excess proton and its fluorine partner travel across three bonds in only 81.5 femtoseconds.

Download a larger version of frame 1 (73 KB), frame 2 (65 KB), frame 3 (66 KB), frame 4 (65 KB).

How Protons Jump

A quantum approach called ab initio molecular dynamics is a powerful tool that allowed Klein and Kim to delve further into superacids. Ab initio means from first principles or from the beginning, without empirical data. Input to the calculation is solely the atomic numbers of the molecules. The electrons and atoms move freely. It's a computationally intense method made possible by recent advances in numerical approaches to quantum theory, and it can produce detailed, accurate pictures of how molecular structure evolves.

With this approach, the researchers took a close look at how protons move in superacids. The strongest superacid is antimony pentafluoride in hydrogen fluoride (SbF5/HF), and experiments have shown that these solutions conduct electricity better than can be accounted for by ionic diffusion, the normal process by which electrons in solution roam from ion to ion. "It's abnormal," says Kim. "There has to be some exotic mechanism."

A plausible scenario, he explains, arises from the reaction between SbF5 and HF. When the SbF5 becomes fluorinated to form an SbF6- ion, the free H+ can move into an HF chain, which becomes a pathway for the proton to jump from bond to bond like molecular leapfrog. Chemists have postulated that this "proton jump" scenario underlies the abnormal conductivity and other properties of SbF5/HF.

To simulate this game of proton leapfrog, Klein and Kim set up a cubic space containing 54 HF molecules and one proton. They excluded the SbF6- ion to keep the computational space within practical bounds. "This ion is so big," explains Kim, "that it interferes with the hydrogen dynamics between H and F." Using 64 CRAY T3E processors, it took a week of computing to simulate four picoseconds of molecular motion (four million-millionths of a second).

The results offer the first detailed picture of proton jumping, showing the precise sequence of moves as the proton hops along the HF chain. Notably, the jumps are very fast. "The excess proton," says Kim, "and the fluorine atom it's attached to travel across three bonds in a matter of femtoseconds."

Click to Enlarge: Frame 1 -- Evolution of SbF<sub>5</sub>/HF Click to Enlarge: Frame 2 -- Evolution of SbF<sub>5</sub>/HF Click to Enlarge: Frame 3 -- Evolution of SbF<sub>5</sub>/HF

Evolution of SbF5/HF
With another round of ab initio molecular dynamics, Klein and Kim simulated an SbF5 molecule in solution with 25 HF molecules. The antimony atom (red) interacts with HF to gain a fluorine atom (brown) in a three-stage reaction (left to right). The free H+ proton (yellow) partners with a fluorine atom (blue) and moves along HF chains (green and brown) in a series of incoherent proton jumps that result in a fully separated SbF6- ion. As it adds a sixth fluorine, SbF5 unfolds like an umbrella to assume an octahedral shape.

Download a larger version of frame 1 (147 KB), frame 2 (151 KB), frame 3 (106 KB).

Download PDF PDF: Getting the Jump on Superacids
Researchers Michael Klein, University of Pennsylvania
Hardware CRAY T3E
Software User-developed code.
Related Material
on the Web
Changing States: Quantum and Classical Simulations of Molecular Aggregates.
Center for Molecular Modeling, University of Pennsylvania.
References Dongsup Kim & Michael L. Klein, "Ab Initio Molecular Dynamics Study of the Superacids," Journal of Physical Chemistry B (forthcoming).

Dongsup Kim & Michael L. Klein, "Liquid Hydrogen Fluoride with an Excess Proton: Ab Initio Molecular Dynamics Study of a Superacid," Journal of the American Chemical Society 121, 11251-11252 (1999).

Dongsup Kim & Michael L. Klein, " Ab Initio Study of BF3 + (HF)1-7 Clusters," Chemical Physics Letters 308, 235 (1999).

Writing: Michael Schneider
HTML Layout/Coding: R. Sean Fulton
© Pittsburgh Supercomputing Center (PSC), Revised: October 25, 2000
URL: http://www.psc.edu/science/Klein2000/getting_jump_on_superacids.html
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