Ideas of Quantum Chemistry P80 pptx

756
13. Intermolecular Interactions
Fig. 13.21. Bacteriophage T represents a supramolecular construction that terrorizes bacteria. The
hexagonal “head” contains a tightly packed double helix of DNA (the virus genetic material) wrapped
in a coat build of protein subunits. The head is attached to a tube-like molecular connector built of 144
contractible protein molecules. On the other side of the connector there is a plate with six spikes pro-
truding from it as well as six long, kinked “legs” made of several different protein molecules. The legs
represent a “landing aparatus” which, using intermolecular interactions, attaches to a particular recep-
tor on the bacterium cell wall. This reaction is reversible, but what happens next is highly irreversible.
First, an enzyme belonging to the monster makes a hole in the cell wall of the bacterium. Then the
144 protein molecules contract probably at the expense of energy from hydrolysis of the ATP molecule
(adenosine triphosphate – a universal energy source in biology), which the monster has at its disposal.
This makes the head collapse and the whole monster serves as a syringe. The bacteriophage’s genetic
material enters the bacterium body almost in no time. That is the end of the bacterium.
• Perturbational method has limited applicability:
– at long intermolecular separations what is called the polarization approximation may
be used,
– at medium distances a more general formalism called the symmetry adapted perturba-
tion theory may be applied,
– at short distances (of the order of chemical bond lengths) perturbational approaches
are inapplicable.
• One of the advantages of a low-order perturbational approach is the possibility of dividing
the interaction energy into well defined physically distinct energy contributions.
• In a polarization approximation approach, the unperturbed wave function is assumed as
a product of the exact wave functions of the individual subsystems: ψ
(0)
0
=ψ
A0
ψ
B0

.The
corresponding zero-order energy is E
(0)
0
=E
A0
+E
B0
.
• Then, the first-order correction to the energy represents what is called the electrostatic
interaction energy: E
(1)
0
= E
elst
=ψ
A0
ψ
B0
|Vψ
A0
ψ
B0
, which is the Coulombic in-
teraction (at a given intermolecular distance) of the frozen charge density distributions of
the individual, non-interacting molecules. After using the multipole expansion E
elst
can
be divided into the sum of the multipole–multipole interactions plus a remainder, called
the penetration energy. A multipole–multipole interaction corresponds to the permanent

multipoles of the isolated molecules. An individual multipole–multipole interaction term
(2
k
-pole with 2
l
-pole) vanishes asymptotically as R
−(k+l+1)
, e.g., the dipole–dipole term
decreases as R
−(1+1+1)
=R
−3
.
Summary
757
• In the second order we obtain the sum of the induction and dispersion terms: E
(2)
=
E
ind
+E
disp
.
• The induction energy splits into
E
ind
(A →B) =

n
B


|ψ
A0
ψ
Bn
B
|Vψ
A0
ψ
B0
|
2
(E
B0
−E
Bn
B
)

which pertains to polarization of molecule B by the unperturbed molecule A and
E
ind
(B →A) =

n
A

|ψ
An
A

ψ
B0
|V |ψ
a0
ψ
b0
|
2
(E
A0
−E
An
A
)

with the roles of the molecules exchanged. The induction energy can be represented as
the permanent multipole – induced multipole interaction, where the interaction of the
2
k
-pole with the 2
l
-pole vanishes as R
−2(k+l+1)
.
• The dispersion energy is defined as
E
disp
=

n

A


n
B

|ψ
An
A
ψ
Bn
B
|Vψ
A0
ψ
B0
|
2
(E
A0
−E
An
A
) +(E
B0
−E
Bn
B
)
and represents a result of the electronic correlation. After applying the multipole expan-

sion, the effect can be described as a series of instantaneous multipole – instantaneous
multipole interactions, with the individual terms decaying asymptotically as R
−2(k+l+1)
.
The most important contribution is the dipole–dipole (k =l =1), which vanishes as R
−6
.
• The polarization approximation fails for medium and short distances. For medium sepa-
rations we may use symmetry-adapted perturbation theory (SAPT). The unperturbed wave
function is symmetry-adapted, i.e. has the same symmetry as the exact function. This is not
true for the polarization approximation, where the product-like ϕ
(0)
does not exhibit the
proper symmetry with respect to electron exchanges between the interacting molecules.
The symmetry-adaptation is achieved by a projection of ϕ
(0)

• Symmetry-adapted perturbation theory reproduces all the energy corrections that appear
in the polarization approximation (E
elst
E
ind
E
disp
) plus provides some exchange-type
terms (in any order of the perturbation except the zeroth).
• The most important exchange term is the valence repulsion appearing in the first-order
correction to the energy:
E
(1)

exch
=

ψ
A0
ψ
B0


V
ˆ
P
AB
ψ
A0
ψ
B0

−ψ
A0
ψ
B0
|Vψ
A0
ψ
B0


ψ
A0

ψ
B0


ˆ
P
AB
ψ
A0
ψ
B0

+O

S
4


where O(S
4
) represents all the terms decaying as the fourth power of the overlap inte-
gral(s) or faster,
ˆ
P
AB
stands for the single exchanges’ permutation operator.
• The interaction energy of N molecules is not pairwise additive, i.e. is not the sum of the
interactions of all possible pairs of molecules. Among the energy corrections up to the
second order, the exchange and, first of all, the induction terms contribute to the non-
additivity. The electrostatic and dispersion (in the second order) contributions are pair-

wise additive.
• The non-additivity is highlighted in what is called the many-body expansion of the interac-
tion energy, where the interaction energy is expressed as the sum of two-body, three-body,
etc. energy contributions. The m-body interaction is defined as that part of the interaction
energy that is non-explicable by any interactions of m

<mmolecules, but explicable by
the interactions among m molecules.
758
13. Intermolecular Interactions
• The dispersion interaction in the third-order perturbation theory contributes to the three-
body non-additivity and is called the Axilrod–Teller energy. The term represents a corre-
lation effect. Note that the effect is negative for three bodies in a linear configuration.
• The most important contributions: electrostatic, valence repulsion, induction and disper-
sion lead to a richness of supramolecular structures.
• The electrostatic interaction plays a particularly important role, because it is of a long-
range character as well as very sensible to relative orientation of the subsystems. The
hydrogen bond X–H Y represents an example of the domination of the electrostatic
interaction. This results in its directionality, linearity and a small (as compared to typical
chemical bonds) interaction energy of the order of 5 kcal/mol.
• Also the valence repulsion is one of the most important energy contributions, because it
controls how the interacting molecules fit together in space.
• The induction and dispersion interactions for polar systems, although contributing signif-
icantly to the binding energy, in most cases do not have a decisive role and only slightly
modify the geometry of the resulting structures.
• In aqueous solutions the solvent structure contributes very strongly to the intermolecular
interaction, thus leading to what is called the hydrophobic effect. The effect expels the
non-polar subsystems from the solvent, thus causing them to approach, which looks like
an attraction.
• A molecule may have such a shape that it fits that of another molecule (synthons, small

valence repulsion and a large number of attractive atom–atom interactions).
• In this way molecular recognition may be achieved by the key-lock-type fit (the molecules
non-distorted), template fit (one molecule distorted) or by the hand-glove-type fit (both
molecules distorted).
• Molecular recognition may be planned by chemists and used to build complex molecular
architectures, in a way similar to that in which living matter operates.
Main concepts, new terms
interaction energy (p. 684)
natural division (p. 684)
binding energy (p. 687)
dissociation energy (p. 687)
dissociation barrier (p. 687)
catenans (p. 688)
rotaxans (p. 688)
endohedral complexes (p. 688)
supermolecular method (p. 689)
basis set superposition error (BSSE) (p. 690)
ghosts (p. 690)
polarization perturbation theory (p. 692)
electrostatic energy (p. 693)
induction energy (p. 694)
dispersion energy (p. 694)
multipole moments (p. 698)
permanent multipoles (p. 701)
SAPT (p. 710)
function with adapted symmetry (p. 711)
symmetry forcing (p. 716)
polarization collapse (p. 717)
symmetrized polarization approximation
(p. 717)

MS–MA perturbation theory (p. 717)
Jeziorski–Kołos perturbation theory (p. 717)
valence repulsion (p. 718)
Padé approximants (p. 722)
Pauli blockade (p. 722)
exchange–deformation interaction (p. 722)
interaction non-additivity (p. 726)
many-body expansion (p. 727)
SE mechanism (p. 733)
TE mechanism (p. 734)
polarization catastrophe (p. 738)
three-body polarization amplifier (p. 738)
Axilrod–Teller dispersion energy (p. 741)
van der Waals radius (p. 742)
van der Waals surface (p. 742)
supramolecular chemistry (p. 744)
hydrogen bond (p. 746)
From the research front
759
hydrophobic effect (p. 748)
amphiphilicity (p. 749)
nanostructures (p. 749)
leucine-valine zipper (p. 749)
synthon (p. 750)
template (p. 751)
“key-lock” interaction (p. 751)
“hand-glove” interaction (p. 751)
From the research front
Intermolecular interactions influence any liquid and solid state measurements. Physicoche-
mical measurement techniques giveonly some indications of the shape of a molecule, except

NMR, X-ray and neutron analyses, which provide the atomic positions in space, but are very
expensive. This is why there is a need for theoretical tools which may offer such information
in a less-expensive way. For very large molecules, such an analysis uses the force fields de-
scribed in Chapter 7. This is currently the most powerful theoretical tool for determining the
approximate shape of molecules with numbers of atoms even of the order of hundreds of
thousands. To obtain more reliable information about intermolecular interactions we may
perform calculations within a supermolecular approach, necessarily of an ab initio type, be-
cause other methods give rather poor quality results. The DFT method popular nowadays
fails at its present stage of development, because the intermolecular interactions area, espe-
cially the dispersion interaction, is a particularly weak point of the method. If the particular
method chosen is the Hartree–Fock approach (currently limited to about 300 atoms), we
have to remember that it cannot take into account any dispersion contribution to the inter-
action energy by definition.
91
Ab initio calculations of the correlation energy still represent a
challenge. Good quality calculations for a molecule with a dozen atoms may be carried out
using the MP2 method. Still more time consuming are the CCSD(T) or SAPT calculations,
which are feasible for only a few atom systems, but offer an accuracy of 1 kcal/mol required
for chemical applications.
Ad futurum. . .
No doubt the computational techniques will continue to push the limits mentioned above.
The more coarse the method used, the more spectacular this pushing will be. The most
difficult to imagine would be a great progress in methods using explicitly correlated wave
functions. It seems that pushing the experimental demands and calculation time required
will cause experimentalists (they will perform the calculations
92
) to prefer a rough estima-
tion using primitive methods rather than wait too long for a precise result (still not very
appropriate, because the results are obtained without taking the influence of solvent, etc.
into account). It seems that in the near future we may expect theoretical methods exploiting

the synthon concept. It is evident that a theoretician has to treat the synthons on an equal
footing with other atoms, but a practice-oriented theoretician cannot do that, otherwise he
would wait virtually forever for something to happen in the computer, while in reality the
reaction takes only a picosecond or so. Still further into the future we will see the planning
of hierarchic multi-level supramolecular systems, taking into account the kinetics and com-
petitiveness among such structures. In the still more distant future, functions performed by
such supramolecular structures, as well as their sensitivity to changing external conditions,
will be investigated.
91
The dispersion energy represents an electronic correlation effect, absent in the Hartree–Fock en-
ergy.
92
What will theoreticians do? My answer is given in Chapter 15.
760
13. Intermolecular Interactions
Additional literature
J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, “Molecular Theory of Gases and Liquids”,
Wiley, New York, 1964.
A thick “bible” (1249 pages) of intermolecular interactions. We find there everything
before the advent of computers and of the symmetry-adapted perturbation theory.
H. Margenau, N.R. Kestner, “Theory of Intermolecular Forces”, Pergamon, Oxford,
1969.
A lot of detailed derivations. There is also a chapter devoted to the non-additivity of
the interaction energy – a rara avis in textbooks.
A.J. Stone, “The Theory of Intermolecular Forces”, Oxford Univ. Press, Oxford, 1996.
The book contains the basic knowledge in the field of intermolecular interactions given
in the language of perturbation theory as well as the multipole expansion (a lot of use-
ful formulae for the electrostatic, induction and dispersion contributions). This very well
written book presents many important problems in a clear and comprehensive way.
“Molecular Interactions”, ed. S. Scheiner, Wiley, Chichester, 1997.

A selection of articles written by experts.
P. Hobza, R. Zahradnik, “Intermolecular Complexes”, Elsevier, Amsterdam, 1988.
Many useful details.
I.G. Kaplan, “Intermolecular Interactions”, Wiley, Chichester, 2006.
A very well written book, covering broad and fundamental aspects of the field.
Questions
1. In order to avoid the basis set superposition error using the counter-poise method:
a) all quantities have to be calculated within the total joint atomic basis set;
b) the energy of the total system has to be calculated within the total joint atomic basis
set, while the subsystem energies have to be calculated within their individual atomic
basis sets;
c) the total energy has to be calculated within a modest quality basis set, while for the
subsystems we may allow ourselves a better quality basis set;
d) all the atomic orbitals have to be centred in a single point in space.
2. In the polarization approximation the zero-order wave function is:
a) the sum of the wave functions of the polarized subsystems;
b) the product of the wave functions of the polarized subsystems;
c) a linear combination of the wave functions for the isolated subsystems;
d) the product of the wave functions of the isolated subsystems.
3. Please find the false statement:
a) dissociation energy depends on the force constants of the normal modes of the mole-
cule;
b) interaction energy calculated for the optimal geometry is called the binding energy;
c) the absolute value of the dissociation energy is larger than the absolute value of the
binding energy;
d) some systems with energy higher than the dissociation limit may be experimentally
observed as stable.
Answers
761
4. Please find the false statement. The induction energy (R stands for the intermolecular

distance):
a) represents an electronic correlation effect;
b) for two water molecules decays asymptotically as R
−6
;
c) is always negative (attraction);
d) for the water molecule and the argon atom vanishes as R
−6
.
5. Dispersion energy (R stands for the intermolecular distance):
a) is non-zero only for the noble gas atom interaction;
b) is equal to zero for the interaction of the two water molecules calculated with the
minimal basis set;
c) represents an electronic correlation effect;
d) decays asymptotically as R
−4
.
6. A particle has electric charge equal to q and Cartesian coordinates xy z.Pleasefind
the false statement:
a) the multipole moments of the particle depend in general on the choice of the coordi-
nate system;
b) the operator of the z component of the dipole moment (μ
z
) of the particle is equal
to qz;
c) a point-like particle does not have any dipole moment, therefore μ
z
=0;
d) the octupole moment operator of the particle is a polynomial of the third degree.
7. In symmetry adapted perturbation theory for He

2
:
a) we obtain the dispersion energy in the first order of the perturbation theory;
b) the electronic energy exhibits a minimum as a function the interatomic distance;
c) the binding energy is non-zero and is caused by the induction interaction;
d) the unperturbed wave function is asymmetric (do not mix with antisymmetry) with
respect to every electron permutation.
8. Please choose the false statement. In symmetry adapted perturbation theory:
a) the zeroth order wave function is a product of the wave functions of the individual
molecules;
b) the electrostatic energy together with the valence repulsion appears in the first order;
c) the exchange corrections appear in all (non-zero) orders;
d) the Pauli exclusion principle is taken into account.
9. The non-additivity of the interaction energy has the following features:
a) the electrostatic energy is additive, while the induction energy is not;
b) the valence repulsion is additive for single exchanges;
c) the dispersion interaction being a correlation effect is non-additive;
d) the Axilrod–Teller interaction is additive.
10. Typical distances X Y and H Y for a hydrogen bond X–H Y are closest to the
following values (Å):
a) 1.5, 1; b) 2.8, 1.8; c) 3.5, 2.5; d) 2.8, 1.
Answers
1a, 2d, 3c, 4a, 5c, 6c, 7b, 8a, 9a, 10b
Chapter 14
INTERMOLECULAR
MOTION OF ELECTRONS
AND
NUCLEI:
C
HEMICAL REACTIONS

Where are we?
We are already picking fruit in the crown of the TREE.
Example
Why do two substances react and another two do not? Why does increasing the temperature
often start a reaction? Why does a reaction mixture change colour? As we know from Chap-
ter 6, this tells us about some important electronic structure changes. On the other hand the
products (as opposed to the reactants) tell us about profound changes in the positions of
the nuclei that take place simultaneously. Something dramatic is going on. But what?
What is it all about
How atom A eliminates atom C from diatomic molecule BC? How can a chemical reac-
tion be described as a molecular event? Where does the reaction barrier come from? Such
questions will be discussed in this chapter.
The structure of the chapter is the following.
Hypersurface of the potential energy for nuclear motion () p. 766
• Potential energy minima and saddle points
• Distinguished reaction coordinate (DRC)
• Steepest descent path (SDP)
• Our goal
• Chemical reaction dynamics (pioneers’ approach)
AB INITIO APPROACH p. 775
Accurate solutions for the reaction hypersurface (three atoms) () p. 775
• Coordinate system and Hamiltonian
• Solution to the Schrödinger equation
• Berry phase
APPROXIMATE METHODS p. 781
Intrinsic Reaction Coordinate (IRC) or statics () p. 781
Reaction path Hamiltonian method () p. 783
762
Why is this important?
763

• Energy close to IRC
• Vibrationally adiabatic approximation
• Vibrationally non-adiabatic model
• Application of the reaction path Hamiltonian method to the reaction
H
2
+OH →H
2
O +H
Acceptor–donor (AD) theory of chemical reactions () p. 798
• Maps of the molecular electrostatic potential
• Where does the barrier come from?
• MO, AD and VB formalisms
• Reaction stages
• Contributions of the structures as the reaction proceeds
• Nucleophilic attack H
−
+ethylene → ethylene + H
−
• Electrophilic attack H
+
+H
2
→H
2
+H
+
• Nucleophilic attack on the polarized chemical bond in the VB picture
• What is going on in chemist’ flask?
• Role of symmetry

• Barrier means a cost of opening the closed-shells
Barrier for the electron transfer reaction () p. 828
• Diabatic and adiabatic potential
• Marcus theory
We are already acquainted with the toolbox for describing the electronic structure at
any position of the nuclei. It is time now to look at possible large changes of the electronic
structure at large changes of nuclear positions. The two motions: of the electrons and nuclei
will be coupled together (especially in a small region of the configurational space).
Our plan consists of four parts:
• In the first part (after using the Born–Oppenheimer approximation, fundamental to this
chapter), we assume that we have calculated the ground-state electronic energy, i.e. the
potential energy for the nuclear motion. It will turn out that the hypersurface has a char-
acteristic “drain-pipe” shape, and the bottom in the central section, in many cases, exhibits a
barrier. Taking a three-atom example, we will show how the problem could be solved, if
we were capable of calculating the quantum dynamics of the system accurately.
• In the second part we will concentrate on a specific representation of the system’s energy
that takes explicitly into account the above mentioned reaction drain-pipe (“reaction path
Hamiltonian”). Then we will focus on describing how a chemical reaction proceeds. Just
to be more specific, an example will be shown in detail.
• In the third part (acceptor–donor theory of chemical reactions) we will find the answer to
the question, of where the reaction barrier comes from and what happens to the electronic
structure when the reaction proceeds.
• The fourth part will pertain to the reaction barrier height in electron transfer (a subject
closely related to the second and the third parts).
Why is this important?
Chemical reactions are at the heart of chemistry, making possible the achievement of its
ultimate goals, which include synthesizing materials with desired properties. What happens
764
14. Intermolecular Motion of Electrons and Nuclei: Chemical Reactions
in the chemist’s flask is a complex phenomenon

1
which consists of an astronomical number
of elementary reactions of individual molecules. In order to control the reactions in the
flask, it would be good to first understand the rules which govern these elementary reaction
acts.
What is needed?
• Hartree–Fock method (Chapter 8, necessary).
• Conical intersection (Chapter 6, necessary).
• Normal modes (Chapter 7, necessary).
• Appendices M (recommended), E (recommended), Z (necessary), I (recommended),
G (just mentioned).
• Elementary statistical thermodynamics or even phenomenological thermodynamics: en-
tropy, free energy (necessary).
Classical works
Everything in chemistry began in the twenties of the twentieth century.
The first publications that considered conical intersection – a key concept for chemi-
cal reactions – were two articles from the Budapest schoolmates: Janos (John) von Neu-
mann and Jenó Pál (Eugene) Wigner “Über merkwürdige diskrete Eigenwerte” published in
Physikalische Zeitschrift, 30 (1929) 465 and “Über das Verhalten von Eigenwerten bei adi-
abatischen Prozessen” which also appeared in Physikalische Zeitschrift, 30 (1929) 467. 
Then a paper “The Crossing of Potential Surfaces” by their younger schoolmate Edward
Teller was published in the Journal of Chemical Physics, 41 (1937) 109.  A classical theory
of the “reaction drain-pipe” with entrance and exit channels was first proposed by Henry
Eyring, Harold Gershinowitz and Cheng E. Sun in “Potential Energy Surface for Linear H
3
”,
the Journal of Chemical Physics, 3 (1935) 786, and then by Joseph O. Hirschfelder, Henry
Eyring and Bryan Topley in an article “Reactions Involving Hydrogen Molecules and Atoms”
in Journal of Chemical Physics, 4 (1936) 170 and by Meredith G. Evans and Michael Polanyi
in “Inertia and Driving Force of Chemical Reactions” which appeared in Transactions of the

Faraday Society, 34 (1938) 11.  Hugh Christopher Longuet-Higgins, U. Öpik, Maurice
H.L. Pryce and Robert A. Sack in a splendid paper “Studies of the Jahn–Teller Effect”, Pro-
ceedings of the Royal Society of London, A244 (1958) 1 noted for the first time, that the wave
function changes its phase close to a conical intersection, which later on became known
as the Berry phase.  The acceptor–donor description of chemical reactions was first pro-
posed by Robert S.J. Mulliken in “Molecular Compounds and their Spectra”, Journal of the
American Chemical Society, 74 (1952) 811.  The idea of the intrinsic reaction coordinate
(IRC) was first given by Isaiah Shavitt in “The Tunnel Effect Corrections in the Rates of Reac-
tions with Parabolic and Eckart Barriers”, Report WIS-AEC-23, Theoretical Chemistry Lab.,
University of Wisconsin (1959) as well as by Morton A. Eliason and Joseph O. Hirschfelder
in the Journal of the Chemical Physics, 30 (1959) 1426 in an article “General Collision Theory
Treatment for the Rate of Bimolecular, Gas Phase Reactions”.  The symmetry rules allow-
ing some reactions and forbidding others were first proposed by Robert B. Woodward and
Roald Hoffmann in two letters to the editor: “Stereochemistry of Electrocyclic Reactions”
and “Selection Rules for Sigmatropic Reactions”, Journal of American Chemical Society,87
(1965) 395, 2511 as well as by Kenichi Fukui and Hiroshi Fujimoto in an article published
1
See Chapter 15.
Classical works
765
in the Bulletin of the Chemical Society of
Japan, 41 (1968) 1989.  The concept of the
steepest descent method was formulated by
Kenichi Fukui in “A Formulation of the Reac-
tion Coordinate”, which appeared in the Jour-
nal of Physical Chemistry, 74 (1970) 4161, al-
though the idea seems to have a longer his-
tory.  Other classical papers include a sem-
inal article by Sason S. Shaik “What Happens
to Molecules as They React? Valence Bond Ap-

proach to Reactivity”inJournal of the Ameri-
can Chemical Society, 103 (1981) 3692.  The
Hamiltonian path method was formulated
by William H. Miller, Nicolas C. Handy and
John E. Adams, in an article “Reaction Path
John Charles Polanyi (born
1929), Canadian chemist of
Hungarian origin, son of Mic-
hael Polanyi (one of the pio-
neers in the field of chemical
reaction dynamics), professor
at the University of Toronto.
John was attracted to chem-
istry by Meredith G. Evans,
who was a student of his fa-
ther. Three scholars: John
Polanyi, Yuan Lee and Dudley
Herschbach shared the 1986
Nobel prize “
for their contribu-
tions concerning the dynam-
ics of chemical elementary
processes
”.
Hamiltonian for Polyatomic Molecules”inthe
Journal of the Chemical Physics, 72 (1980)
99.  The first quantum dynamics simula-
tion was performed by a PhD student George
C. Schatz (under the supervision of Aron
Kupperman) for the reaction H

2
+ H → H
+ H
2
, reported in “Role of Direct and Res-
onant Processes and of their Interferences in
the Quantum Dynamics of the Collinear H +
H
2
Exchange Reaction”, in Journal of Chem-
ical Physics, 59 (1973) 964.  John Polanyi,
Dudley Herschbach and Yuan Lee proved
that the lion’s share of the reaction energy is
Yuan T. Lee is a native of Tai-
wan, called by his colleagues
“a Mozart of physical chem-
istry”. He wrote that he was
deeply impressed by a biog-
raphy of Mme Curie and that
her idealism decided his own
path.
delivered through the rotational degrees of
freedom of the products, e.g., J.D. Barn-
well, J.G. Loeser, D.R. Herschbach, “Angu-
lar Correlations in Chemical Reactions. Statis-
tical Theory for Four-Vector Correlations” pub-
lished in the Journal of Physical Chemistry,87
(1983) 2781.  Ahmed Zewail (Egypt/USA)
developed an amazing experimental tech-
nique known as femtosecond spectroscopy,

which for the first time allowed the study
of the reacting molecules at different stages
of an ongoing reaction (“Femtochemistry –
Ultrafast Dynamics of The Chemical Bond”,
vol. I and II, A.H. Zewail, World Scientific,
New Jersey, Singapore (1994)).  Among
others, Josef Michl, Lionel Salem, Donald
G. Truhlar, Robert E. Wyatt, and W. Ronald
Gentry contributed to the theory of chemical
reactions.
Dudley Herschbach writes in
his CV, that he spent his child-
hood in a village close to
San Jose, picking fruit, milk-
ing cows, etc. Thanks to his
wonderful teacher he became
interested in chemistry. He
graduated from Harvard Uni-
versity (physical chemistry),
where as he says, he has
found “an exhilarating acad-
emic environment”. In 1959
he became professor at Uni-
versity of California at Berke-
ley. In 1967 the group was
joined by Yuan Lee and con-
structed a “supermachine” for
studying crossing molecular
beams and the reactions in
them. One of the topics was

the alkali metal atom – io-
dine collisions. These inves-
tigations were supported by
John Polanyi, who studied the
chemiluminescence in IR, i.e.
the heat radiation of chemical
reactions.