However, it was not until it was possible to generate femtosecond laser pulses (10-15 s) that it became possible to reveal when chemical bonds are broken and formed. Ahmed Zewail (born 1946 in Egypt) at California Institute of Technology received the Nobel Prize for Chemistry in 1999 for his development of "femtochemistry" and in particular for being the first to experimentally demonstrate a transition state during a chemical reaction. His experiments relate back to 1889 when Arrhenius (Nobel Prize, 1903) made the important prediction that there must exist intermediates (transition states) in the transformation from reactants to products. Henry Taube of Stanford University was awarded the Nobel Prize for Chemistry in 1983 "for his work on the mechanism of electron transfer reactions, especially in metal complexes". Even if Taube's work was on inorganic reactions, electron transfer is important in many catalytic processes used in industry and also in biological systems, for example, in respiration and photosynthesis. The latest prize for work in chemical kinetics was that to Dudley R. Herschbach at Harvard University, Yuan T. Lee of Berkeley and John C. Polanyi from Toronto in 1986. Herschbach and his student Lee introduced the use of fluxes of molecules with well-defined direction and energy, molecular beams. By crossing two such beams they could study details of the reaction between molecules at extremely short times. Another important method to investigate such reaction details is infrared chemiluminescence, introduced by Polanyi. The emission of infrared radiation from the reaction products gives information on the energy distribution in the molecules.

3.4 Theoretical Chemistry and Chemical Bonding
Quantum mechanics, developed in the 1920s, offered a tool towards a more basic understanding of chemical bonds. In 1927 Walter Heitler and Fritz London showed that it is possible to solve exactly the relevant equations for the hydrogen molecule ion, i.e. two hydrogen nuclei sharing a single electron, and thereby calculate the attractive force between the nuclei. For molecules containing more than three elementary particles, even the hydrogen molecule with Lewis's two-electron bond (see Section 1.1), the equation can, however, not be solved exactly, so one has to resort to approximate methods.

A pioneer in developing such methods was Linus Pauling at California Institute of Technology, who was awarded the Nobel Prize for Chemistry in 1954 "for his research into the nature of the chemical bond ...." Pauling's valence-bond (VB) method is rigorously described in his 1935 book Introduction to Quantum Mechanics (written together with E. Bright Wilson, Jr., at Harvard). A few years later (1939) he published an extensive non-mathematical treatment in The Nature of the Chemical Bond, a book which is one of the most read and influential in the entire history of chemistry. Pauling was not only a theoretician, but he also carried out extensive investigations of chemical structure by X-ray diffraction (see Section 3.5). On the basis of results with small peptides, which are building blocks of proteins, he suggested the -helix as an important structural element. Pauling was awarded the Nobel Peace Prize for 1962, and he is the only person to date to have won two unshared Nobel Prizes.

Pauling's VB method cannot give an adequate description of chemical bonding in many complicated molecules, and a more comprehensive treatment, the molecular-orbital (MO) method, was introduced already in 1927 by Robert S. Mulliken from Chicago and later developed further by him as well as by many other investigators. MO theory considers, in quantum-mechanical terms, the interaction between all atomic nuclei and electrons in a molecule. Mulliken also showed that a combination of MO calculations with experimental (spectroscopic) results provides a powerful tool for describing bonding in large molecules. Mulliken received the Nobel Prize for Chemistry in 1966.

Theoretical chemistry has also contributed significantly to our understanding of chemical reaction mechanisms. In 1981 the Nobel Prize for Chemistry was shared between Kenichi Fukui in Kyoto and Roald Hoffmann of Cornell University "for their theories, developed independently, concerning the course of chemical reactions". Fukui introduced in 1952 the frontier-orbital theory, according to which the occupied MO with the highest energy and the unoccupied one with the lowest energy have a dominant influence on the reactivity of a molecule. Hoffmann formulated in 1965, together with Robert B. Woodward (see Section 3.8), rules based on the conservation of orbital symmetry, for the reactivity and stereochemistry in chemical reactions.
Rudolph A. Marcus published during ten years, starting in 1956, a series of seminal papers on a comprehensive theory for the rates electron-transfer reactions, the experimental study of which had given Taube a Nobel Prize in 1983 (see Section 3.3). Marcus's theory predicts how the rate varies with the driving force for the reaction, i.e. the difference in energy between reactants and products, and counter to intuition he found that it does not increase continuously, but goes through a maximum, into the Marcus inverted region, which has later been confirmed experimentally. Marcus was awarded the Nobel Prize for Chemistry in 1992.

The latest Nobel Prize for work in theoretical chemistry was given in 1998 to Walter Kohn of Santa Barbara and John A. Pople of Northwestern University (but a British citizen). The prize to Kohn, a theoretical physicist, was based on his development of density-functional theory, which facilitates detailed calculations both of the geometrical structures of complex molecules and of the energy map of chemical reactions. Pople, a mathematician (but now Professor of Chemistry), was awarded "for his development of computational methods in quantum chemistry". In particular, Pople has designed computer programs based on classical quantum theory as well as on density-functional theory.

3.5 Chemical Structure
The most commonly used method to determine the structure of molecules in three dimensions is X-ray crystallography. The diffraction of X-rays was discovered by Max von Laue in 1912, and this gave him the Nobel Prize for Physics in 1914. Its use for the determination of crystal structure was developed by Sir William Bragg and his son, Sir Lawrence Bragg, and they shared the Nobel Prize for Physics in 1915. The first Nobel Prize for Chemistry for the use of X-ray diffraction went to Petrus (Peter) Debye, then of Berlin, in 1936. Debye did not study crystals, however, but gases, which give less distinct diffraction patterns. He also employed electron diffraction and the measurement of dipole moments to get structural information. Dipole moments are found in molecules, in which the positive and negative charge is unevenly distributed (polar molecules).

Many Nobel Prizes have been awarded for the determination of the structure of biological macromolecules (proteins and nucleic acids). Proteins are long chains of amino-acids, as shown by Emil Fischer (see Section 2), and the first step in the determination of their structure is to determine the order (sequence) of these building blocks. An ingenious method for this tedious task was developed by Frederick Sanger of Cambridge, and he reported the amino-acid sequence for a protein, insulin, in 1955. For this achievement he was awarded the Nobel Prize for Chemistry in 1958. Sanger later received part of a second Nobel Prize for Chemistry for a method to determine the nucleotide sequence in nucleic acids (see Section 3.12), and he is the only scientist so far who has won two Nobel Prizes for Chemistry.