Compulation of Photochemistry

16
THEORETICAL AND COMPUTATIONAL CHEMISTRY

Computational Photochemistry


THEORETICAL AND COMPUTATIONAL CHEMISTRY

S ERIES E DITORS
Professor P. Politzer
Department of Chemistry
University of New Orleans
New Orleans, LA 70148, U.S.A.

Professor Z.B. Maksic
Rudjer Boškovic Institute
P.O. Box 1016,
10001 Zagreb, Croatia

VOLUME 1

VOLUME 9

Quantitative Treatments of Solute/Solvent
Interactions
P. Politzer and J.S. Murray (Editors)

Theoretical Biochemistry: Processes and Properties
of Biological Systems
L.A. Eriksson (Editor)

VOLUME 2

VOLUME 10

Modern Density Functional Theory: A Tool
for Chemistry
J.M. Seminario and P. Politzer (Editors)

Valence Bond Theory
D.L. Cooper (Editor)

VOLUME 3
Molecular Electrostatic Potentials: Concepts
and Applications
J.S. Murray and K. Sen (Editors)

VOLUME 4
Recent Developments and Applications of Modern
Density Functional Theory
J.M. Seminario (Editor)

VOLUME 5
Theoretical Organic Chemistry
C. Párkányi (Editor)

VOLUME 6
Pauling’s Legacy: Modern Modelling of the Chemical
Bond
Z.B. Maksic and W.J. Orville-Thomas (Editors)

VOLUME 7
Molecular Dynamics: From Classical to Quantum
Methods
P.B. Balbuena and J.M. Seminario (Editors)

VOLUME 8
Computational Molecular Biology
J. Leszczynski (Editor)

VOLUME 11
Relativistic Electronic Structure Theory, Part 1.
Fundamentals
P. Schwerdtfeger (Editor)

VOLUME 12
Energetic Materials, Part 1. Decomposition, Crystal
and Molecular Properties
P. Politzer and J.S. Murray (Editors)

VOLUME 13
Energetic Materials, Part 2. Detonation, Combustion
P. Politzer and J.S. Murray (Editors)

VOLUME 14
Relativistic Electronic Structure Theory,
Part 2. Applications
P. Schwerdtfeger (Editor)

VOLUME 15

Computational Materials Science
J. Leszczynski (Editor)

VOLUME 16
Computational Photochemistry
M. Olivucci (Editor)


16
THEORETICAL AND COMPUTATIONAL CHEMISTRY

Computational Photochemistry

Edited by
M. Olivucci
Dipartimento di Chimica
dell’Universita di Siena
Siena, Italy

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This book is dedicated to my beloved parents Armando and Anna

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Vll

Contents
Foreword by Josef Michl
Preface
I.

Computational Photochemistry
Massimo Olivucci and Adalgisa Sinicropi

ix
xiii
1

II. Ab initio Methods for Excited States
Manuela Merchan and Luis Serrano-Andres

35

III. Density Functional Methods for Excited States: Equilibrium Structure
and Electronic Spectra
Filipp Furche and Dmitrij Rappoport

93

IV. Electronic and Vibronic Spectra of Molecular Systems: Models and
Simulations based on Quantum Chemically Computed Molecular
Parameters
Fabrizia Negri and G. Orlandi

129

V. Semiclassical Nonadiabatic Trajectory Computations In
Photochemistry: Is The Reaction Path Enough To Understand A
Photochemical Reaction Mechanism?
G. A. Worth, M. J. Bearpark and Michael A. Robb

171

VI. Computation of Photochemical Reaction Mechanisms in
Organic Chemistry
Marco Garavelli, Fernando Bernardi and A. Cembran

191

VII. Computation of Reaction Mechanisms and Dynamics in Photobiology
Seth Olsen, Alessandro Toniolo, Chaehyuk Ko, Leslie Manohar,
Kristina Lamothe, and Todd J. Martinez

225

VIII. Development of Theory with Computation
Howard Zimmerman

255

IX. Calculations of Electronic Spectra of Transition Metal Complexes
Kerstin Pierloot

279


Vlll

X. Perspectives in Calculations on Excited State in Molecular Systems
Bjorn Roos

317

Index

349


IX

Foreword
Josef Michl
Department of Chemistry and Biochemistry
University of Colorado
Boulder, CO 80309-0215

Anyone who has dealt with ground state mechanistic chemistry of organic or inorganic
reactions appreciates how complex and demanding it can be. Nevertheless, from theoretical and
computational standpoints, its complexity pales compared to mechanistic photochemistry, with

its maze of paths that can be followed after the absorption of a photon of U V-visible light by a
molecule. Even for the simplest photoreactions, it is a major feat to figure out the details of the
routes followed by the molecule in a qualitative way and to rationalize the nature of the final
ground state product. A reliable calculation of a quantity as fundamental to the experimental
photochemist as the quantum yield of product formation remains a distant goal. There is
competition between nonradiative and radiative processes, between spin-allowed and spinforbidden processes, between adiabatic and diabatic processes, between vibrational relaxation into
one and another minimum after return to the ground state. There is the issue of possible
violations of Kasha's rule, since a variation of the initial excitation energy is not always without
consequences, even in solution photochemistry. Energy transfer and electron transfer
possibilities often lurk in the background. Solvent effects are complex and manifold. No wonder
a distinguished ground-state computational chemist friend who attended a theoretical
photochemistry meeting with me a few years ago shook his head in disbelief after the first day of
lectures, and asked something like "Isn't there an easier way to earn a living?".
Photochemists thrive on complexity, theoreticians more than most. Although we cannot
predict the quantum yield of a simple reaction any more accurately than we could when my
interest in photochemistry was first piqued nearly half a century ago, great conceptual progress
has been made. Then, it was not even very clear just what to calculate. Today, there is little
doubt that we need dynamics on lowest potential energy surfaces. The concept of a potential
energy surface guiding an excited molecule, with only occasional hops from one surface to
another, was new to most experimental photochemists then. It has proven its heuristic and
computational value since, and pervades the present book. Only for molecules with a very high


density of lowest-energy electronic states, such as those of saturated compounds, is it likely to be
inadequate.
The basic notions that are so familiar today were established in the sixties and seventies,
and perusal of a 1974 review article[l] reveals the whole slew of the necessary concepts: excited
state barriers and funnels for ultrafast return to the ground state, reactions with vibrationally
equilibrated intermediates and direct reactions proceeding through state crossings, vibrationally
equilibrated and "hot" excited and ground state reactions, internal and external heavy atom effects

on intersystem crossing, etc. Back then, we used symmetry considerations, correlation diagrams,
or calculations on simple models to estimate at what geometries barriers and funnels are likely to
lie. Our first numerical computation of a funnel (conical intersection) relevant for a
photochemical isomerization in an organic molecule was published only twenty years ago,[2] and
it was made possible by the presence of symmetry at the state touching point. Today, advances
in computer technology and in quantum chemical methodology, especially in multireference
methods, many due to the authors of the chapters that follow, permit quite reliable calculations of
these essential features at general geometries, and a thick book on conical intersections has just
appeared. [3]
Yes, difficulties remain, especially in evaluating the relative energies of covalent ("dotdot") and zwitterionic ("hole-pair") states with sufficient accuracy. Another problem is the
proper treatment of reaction dynamics in all but the smallest molecules. After all, only those
conical intersections are relevant that can be reached by the excited molecule in the short time
available to it. And yes, in my opinion, too much emphasis has been put in recent years on the
geometries of the lowest energy point of a conical intersection. This is an issue on which I have
had a gentle disagreement with many. I would argue that these points are usually nearly
irrelevant, because a molecule that has reached the seam of a conical intersection will fall to the
lower surface right away and will not have time to ride the seam, looking for its lowest energy
point. Thus, the effective funnel locations are those in which the seam is first reached, and not
the lowest energy point in the intersection subspace. Unfortunately, the former are harder to
calculate. In fact, much of the wave packet most likely seeps to the lower surface at geometries at
which the state touching is still weakly avoided, simply because of their higher dimensionality,
and in that sense the regions of weakly avoided crossings need not be as immaterial as they are
sometimes made out to be. In spite of these minor quibbles, we all agree that the improvement
from the level of mechanistic interpretations standard a quarter of a century ago to that common
today is striking.
Another interesting comparison is with a book on theoretical photochemistry that was
published fifteen years ago.[4] It was a monograph rather than an edited multiauthor volume, and
was organized differently in that it attempted a systematic treatment of all important classes of
organic photoreactions, organized by Salem's concept of topicity. However, the ab initio
calculations presented were hardly more than glorified correlation diagrams, involved no geometry

XI

optimization, and were pathetic by the present book's standards. The qualitative concepts are all
that survives.
Clearly, computational photochemistry has made tremendous strides in recent decades,
and continues to do so. The present collection of ten outstanding contributions provides a fine
illustration of this statement.

REFERENCES
[1]
Michl, J. "Physical Basis of Qualitative MO Arguments in Organic Photochemistry",
Topics in Current Chemistry 1974, 46,1.
[2]
Bonacic-Koutecky, V.; Michl, J. "Photochemical Syn-Anti Isomerization of a Schiff
Base: A Two-Dimensional Description of a Conical Intersection in Formaldimine", Theor. Chim.
Ada 1985, 68, 45.
[3]
Domcke, W.; Yarkony, D. R.; Koppel, Editors, Conical Intersections: Electronic
Structure, Dynamics & Spectroscopy, World Scientific Publishing Co., Singapore 2004.
[4]
Michl, J.; Bonacic-Koutecky, V. Electronic Aspects of Organic Photochemistry, John
Wiley and Sons, Inc.: New York, 1990.


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Xlll

Preface
The chemical community have recently witnessed a growing interest in the application of
computational methods to problems involving electronically excited molecules. This is mostly
due to a change in the field of photochemical sciences. In fact, until two decades ago, these
were dominated by the search for novel photochemical or photophysical properties. In other
words, photochemists were reporting on the effects of light at the molecular-level. In contrast,
contemporary photochemists look for ways to exploit light to drive various molecular-level
actions such as pollutant scavenging and removal, mechanical motion, sensing and signalling,
photocatalysis and others. While such raising technologies require the preparation of
molecules capable of performing specific functions, the lack of knowledge on the molecular
mechanisms of light energy exploitation and wastage constitutes a severe limitation to the
design of such systems. In this book, a selected group of experts show how the development,
implementation and application of quantum chemical methods in photochemistry and
spectroscopy provide a way to tackle this problem.
Until recently the computer-aided investigation of photochemical reactions (i.e. reactions that
are initiated by light absorption rather then by heat) was unpractical if not impossible.
Because of this the simulation of fundamental chemical and biological events such as
bleaching, fluorescence, phosphorescence, photochromism, vision, photosynthesis,
phototropism, and others could not be performed. Thus, despite the growing availability of
computer power, there were neither computer tools nor a clear theoretical basis for the
investigation of photoexcited molecules. One key point for the solution of this problem was to
establish the nature of the spatial arrangement of the atoms that allows a photoexcited
molecule to efficiently decay from the excited state to the ground state thus initiating product
formation. Loosely, this critical molecular structure, often called "photochemical funnel",
plays in photochemistry, the role played by the transition structure in a thermal process. Thus
the description of a reaction pathway in photochemistry must involve the description of the
path leading to and departing from the photochemical funnel.
About fifteen years ago different research lines started to change this unfavorable situation.
Few lines were merely related to the elucidation of the general mechanism of photochemical

reactions, including the nature of the photochemical funnel, while others involved the
development of software tools allowing for an accurate evaluation and mapping of the
potential energy surface of photoexcited molecules. For instance, at the end of the 80's
improved ab initio quantum chemical methodologies became available which were suitable
for computing, in a balanced way, excited and ground state energy surfaces taking into
account the complete set of the 3N-6 nuclear degrees of freedom of the reacting system (N is
the number of atoms). Such progress made possible to provide clear evidence that the ideas of


XIV

Edward Teller, Lionel Salem, Howard Zimmerman and Josef Michl, stating that for singlet
photochemical reactions the photochemical funnel corresponds to a conical intersection of the
excited and ground state energy surfaces, were correct. (A book on conical intersections has
recently appeared: "Conical Intersections: Electronic Structure, Dynamics and
Spectroscopy"; Domcke, W., Yarkony, D. R., Koppel, H., Eds.; World Scientific: Singapore,
2004)
The target of the present book is two-fold. The first, and most ambitious one, is to contribute
to establish a branch of computational chemistry that deals with the properties and reactivity
of photoexcited molecules (see Chapter 1). Accordingly the book should give not only an
historical view of the "scientific adventure" (see the Foreword written by one of the original
and major player) that led to the emergence of the field but also a survey of the work that
characterizes it. In order to satisfy this requirement the book provides an overview of few
general strategies currently employed to investigate photochemical processes.
The second target of the book is to give an account of the status of knowledge in either the
mechanistic (conceptual) and methodological research lines in computational photochemistry.
In fact, during the last ten years the potential energy surfaces of several organic chromophores
were mapped. The resulting "maps" reveal prototype photochemical reaction mechanisms and
form a firm body of computational photochemistry results. Accordingly, three book chapters
focus on instructive case-studies comprising: (i) organic chromophores (Chapter 1, 6 and 8),

(ii) biologically related chromophores (Chapter 7), (ii) photochemical funnels and reactive
intermediates (Chapter 8 and 9). Such (still ongoing) systematic investigation could not be
carried out without the development of novel computational tools that, nowadays, constitute
the computational photochemist toolbox. These tools belong to four classes that will be
reviewed in the remaining book chapters: (i) tools for the accurate computation of the excited
state potential energy (Chapters 2, 3 and 10), (ii) tools for the prediction of absorption,
fluorescence and Resonance Raman spectra (Chapter 4) (iii) tools for the mapping of excited
state potential energy surfaces (including locating photochemical funnels and excited state
reaction paths, Chapters 6) and, finally, (iv) tools for the computation of "photochemical"
semi-classical trajectories (i.e. trajectories that start on the excited state energy surface and
continue along the ground state surface, Chapter 5 and 7). A final chapter (Chapter 10),
written by one of the major experts of electronic structure theories, provides a review and a
perspective on the technologies for the ab initio computation of excited state energy surfaces.
All authors have made an effort to write the chapters in a plain and simple way. Thus
"Computational Photochemistry" should be readable not only by computational and
theoretical chemists but also by chemists (e.g. photochemists, photobiologists and material
scientists) interested in using computer tools in their laboratories.
I feel deeply indebted to all authors that, not only have readily accepted my invitation, but
have felt that the book may have provided a first, probably still crude, picture of an expanding
field of computational chemistry. However, it is important to stress that many other scientists


XV

have given important contributions to the field and, indirectly, to the material reported in this
book. The Editor feels indebted to the many colleagues including spectroscopists,
photochemists, organic chemists and theoreticians that through both discussions and criticism
have stimulated the present editorial effort.
There remains only the pleasant task of thanking those who have otherwise been of help in the
preparation of the book. Prof. Professor Zvonimir B. Maksic for originally inviting me to plan

and edit the book and Andrew Gent of Elsevier for the attention devoted to progress of our
work. A very special thank goes to Dr. Adalgisa Sinicropi (one of the author of Chapter 1) for
taking care of many of the practical problems related to the assembly and revision of the
chapters, for the production of the index and for her willingness to share the many, sometime
frustrating, decision that I had to take during the various stages of the manuscript handling.
As this is my first editorial work I cannot fail to acknowledge the fundamental role played, in
the development of my scientific personality and career, by the chemists that have not only
cast my education but shared with me their enthusiasm for many wonderful years: Fernando
Bernardi and Michael A. Robb.
Finally I am deeply indebted to my wife Matilde and my children Paolo, Enrico and Lidia for
never let me feel alone during the too many days that I spend away from them.
Massimo Olivucci
Professor of Organic Chemistry
Universita di Siena


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M. Olivucci (Editor)
Computational Photochemistry
Theoretical and Computational Chemistry, Vol. 16
© 2005 Elsevier B.V. All rights reserved

I. Computational Photochemistry
Massimo Olivucci and Adalgisa Sinicropi
Dipartimento di Chimica, Universita di Siena, Italy
1. INTRODUCTION
The study of photochemical problems by means of computer simulations using specialized
software tools and strategies enable us to get an understanding at the microscopic level of

what happens to a molecule after absorption of a photon. A detailed understanding of the
properties of electronically excited state species and the knowledge of the molecular
mechanisms which control the fate of the energy deposited on a molecule after absorption,
increase our ability to design efficient photochemical reactions and artificial photosynthetic
systems. Furthermore, this represents a fundamental requirement for the rational design of
novel materials, molecular devices and molecular level machines. On a more general ground,
the ability to simulate, using complementary computational strategies, photoinduced events
often allows to explore areas of chemistry that experiment could touch only indirectly.
Together with the mechanistic ideas discussed below these strategies define the field of
"computational chemistry".
The application of quantum mechanics to chemical problems goes back to the end of the
1950s when computers came into use and it was possible to handle very complicated
mathematical equations describing such complex systems as molecules. Note that even if the
"... fundamental laws necessary for the mathematical treatment of a large part of physics and
the whole of chemistry were completely known ...", as Dirac affirmed in 1929, accurate
calculations of molecular properties and chemical reaction pathways were not possible at that
time. In 1970 Pople published the first release of the GAUSSIAN program [1], making thus
computational methods available to scientists [2]. The following growth of the speed of
computers along with the development of more and more accurate quantum chemistry tools
and methodologies implemented in commercially available program have made
computational investigation of molecular structures and reactivity a standard practise. The
way in which a chemical reaction step is investigated involves the computation of the
transition state structure (TS) that connects a reactant to a product along with the associated
energy barriers (Fig. 1). In particular, the energy of the transition state provides information
on the time scale of the reaction while the geometrical structure of the transition state (TS)
provides information on the stereochemistry of the reaction and sensitivity to different
substituents. The progression of the molecular structure of the reactant toward the TS and the
product constitutes the so called "reaction path" which can be mapped computing the

R
Fig. 1. Schematic representation of the structure of the potential energy surface for a thermal chemical
reaction. The dashed curve indicates the minimum energy path. R and P are local energy minima
corresponding to reactants and products. TS is a saddle point corresponding to the transition structure.

minimum energy path (MEP) connecting the reactant (R) to a product (P) along the 3N-6
dimensional potential energy surface (N is the number of nuclei in the reacting system).
One of the first computations in photochemistry/photophysics has to be ascribed to R. G. Parr
and R. Pariser. In the early 1950s, they developed a semi-empirical method based on LCAOMO jt-electron theory to predict the electronic spectra and electronic structure of complex
unsatured molecules, initially of benzene and N-heterocyclic analogues [3; 4]. Later on, using
one of the first computers, an IBM 701, they were able to assign the electronic structure and
electronic spectra of azulene and of the polyacenes [5-8]. The theoretical approach of Parr and
Pariser together with the contribution of Pople formed the basis of the Pariser-Parr-Pople
(PPP) theory that is one of the first semi-empirical method based on the ZDO (zerodifferential overlap) approximation.
During '60s, '70s and even '80s many researchers and experts in the field of organic
photochemistry shared their knowledge and published several papers [9-40] trying to
understand the behaviour of electronically excited molecules and make a wide-ranging
classification of photochemical reactions. The formulation of photoreduction mechanisms
was mainly based on the construction of correlation diagrams. Although the interest for a
unique theory of photochemical reactions was well recognized, the computational
investigation of photochemical reaction mechanisms could not be easily implemented at the
same level seen for the thermal chemistry. This frustrating status is somehow described in a
1990 paper [41], where N. J. Turro stated: "... the use of computational methods to elucidate
reaction mechanisms has not really made a major impact on the way organic photochemists
think about such mechanisms. The Woodward-Hoffmann rules and Salem diagrams of the
1960s and 1970s still serve as the basis for the day-to-day analysis of photoreactions...". On
the other hand, other research groups in the field of organic photochemistry were tackling this


computational problem and realized that a detailed knowledge of the excited state molecular

structure could lie at the basis of the "resolution" of the reaction mechanism. A detailed
account of the development of mechanistic ideas and early results in the laboratory of H. E.
Zimmerman will be given on Chapter 8.
The major difficulty encountered by chemists in doing an exhaustive investigation of
photochemical reactivity resided in the absence of robust computer tools able to map the MEP
for excited state species. In fact, while a thermal reaction is governed by the topography of a
single potential energy surface (starts and ends on the ground state of the reacting system), a
photochemical reaction path evolves at least on two potential energy surfaces. Thus, in order
to compute such path one needs to connect a reactant that is located on an excited state energy
surface to products that are located on the ground state energy surface. This could only be
done establishing the nature of the spatial arrangement of the atoms that allows a
photoexcited molecule to efficiently decay from the excited state to the ground state thus
initiating product formation. Loosely, this critical molecular structure, often called
"photochemical funnel" plays, in photochemistry, the role of the transition state of a thermal
process. As we will detail below, the characterization of the molecular structure and relative
stability of the "photochemical funnel" in terms of conical intersections and singlet/triplet
crossings is of central importance in mechanistic photochemistry. Nowadays, computational
strategies are available for locating conical intersection and singlet/triplet crossing points and
for constructing inter-state "photochemical" reaction pathways. These tools comprise
methodologies for the optimisation of low-lying crossings between pair of potential energy
surfaces and the computation of relaxation paths from a photoexcited reactant (e.g. from the
Franck-Condon (FC) structure) to a deactivation channel. More in general, it is possible to
compute the entire pathway connecting an excited state molecule to its ground state product.
The major computational tools as well as few case-studies in the field of organic
photochemistry will be revised by Cembran et al. in Chapter 6.
The field of computational photochemistry is a relatively young field, especially when applied
to the study of ultrafast reactions, but it is now established as a branch of computational
chemistry and as a powerful, sometimes unique, way to simulate the molecular mechanism
underlying fundamental chemical and biological events such as vision, primitive
photosynthesis, phototropism, photochromism, bleaching, fluorescence, phosphorescence.

Accordingly, the 3rd edition of the "Glossary of Terms Used in Photochemistry" (to be
published in 2005) will contain new terms related to the use of computational tools in
photochemistry (like Conical intersection, Photochemical Reaction Path, Minimum Energy
Reaction Path).


2. PHOTOCHEMISTRY, PHOTOPHYSICS AND PHOTOBIOLOGY MEDIATED BY
CONICAL INTERSECTION FUNNELS
As mentioned above, in the past, correlation diagrams were, in many cases, the only practical
tools available to the chemists to formulate reaction mechanism for thermal and
photochemical reactions. For instance for pericyclic reactions Woodward-Hoffmann orbital
correlation diagrams [42] and Longuet-Higgins and Abrahamson state correlation diagrams
[43-45] were used. In the field of photochemical reactions the Van der Lugt-Oosteroff
diagrams [40] were based on the hypothesis that avoided crossings provide the point of return
of an excited state species to the ground state. At such an avoided crossing, if the energy gap
is larger than few kcal mol"1, the excited state species will rapidly thermalize and the decay
probability will be determined by the Fermi Golden Rule. However, within this model, the
probability of decay should be small (unless the energy gap is small) and the radiationless
decay process should occur on the same time scale of fluorescence (in ns [46; 47]). On the
other hand, it is well known that many photochemical processes are extremely fast (well
below one picosecond, i.e. on the timescale of a single molecular vibration) and associated
with a complete lack of fluorescence. Furthermore, they are often stereospecific, implying a
concerted mechanism. Indeed, femtosecond excited state lifetimes have been observed, for
instance, for simple dienes [48], cyclohexadienes [48-50], hexatrienes [51], and in both free
[52] and opsin-bound [53] retinal protonated Schiff bases. These observations suggest that a
real crossing is accessible to the system. At such surface crossing the probability of decay is
very high and the corresponding molecular identify the photochemical funnel (such name for
the excited state decay channel suggests that the excited reactant must be "funnelled" through
this point to initiate product formation). Thus, a photochemical funnel corresponds to a
molecular structure that "lives" for only few femtoseconds (10" seconds).

The history of conical intersection goes back to more than 60 years ago when, in 1937, the
physicist Edward Teller giving a lecture at the Symposium on Molecular Structure [54]
suggested that it was the electronic factors that may play the dominant role in the efficiency
of radiationless decay. Teller made two general observations:
in a polyatomic molecule the non-crossing rule, which is rigorously valid for
diatomics, fails and two electronic states, even if they have the same symmetry, are
allowed to cross at a conical intersection.
radiationless decay from the upper to the lower intersecting state occurs within a
single vibrational period when the system "travels" in the vicinity of such intersection
points.
On the basis of these observations, in 1969, at the Twentieth Farkas Memorial Symposium,
Teller proposed that conical intersections may provide a common and very fast decay channel
from the lowest excited states of polyatomics, which would explain the lack of fluorescence
of the funnel[55].


In 1966, the organic chemist H. E. Zimmerman presented an alternative approach to the well
known Woodward-Hoffmann method to predict the factors controlling ground and excited
state reactions [9-11]. Zimmerman proposed an "MO Following" procedure that was capable
of dealing with reactions lacking the symmetry to construct correlation diagrams. As an
example he used the butadiene to cyclobutene closure and he found that along the reaction
route a crossing (i.e., degeneracy) occurs. Thus, he concluded that such crossing point are
significant in organic photochemistry and may provide a route for conversion of excited state
reactant to ground state product. Michl [32; 33] proposed, independently, the same idea and
documented such features in ab initio calculations on the H4 system [29; 30]. In 1970, Evleth
and co-workers, in their work on the photolysis of aryldiazonium salts, interpreted their
quantum yield measurements in terms of a complex energy surface crossing patterns. In the
same years, Salem [35] proposed his state correlation diagrams that illustrated the occurrence
of conical intersections at symmetric geometries in the photochemistry of carbonyl
compounds. A continuous exchange of ideas between Salem, Turro e Dauben (as documented

by Turro in a recent paper [56]) lead to the first complete classification of photochemical
reactions [21; 36] using Salem's development of energy surface theory. Subsequently,
geometries of few conical intersections were computed for Schiff base syn-anti isomerization
by Bonacic-Koutecky and Michl [57], using ab initio procedures and the "3x3" model of
biradicaloid electronic structure [58] was elaborated to permit qualitative prediction of
geometries at which Si/So conical intersections take place [19; 34]. More recently, Yarkony
[59; 60] and Ruedenberg [61] identified conical intersections geometries in small molecules.
Despite the fact that the idea of Teller, Zimmerman, Michl and Salem represented an
important refinement of the avoided crossing model, conical intersections were thought to be
extremely rare or inaccessible (i.e. located too high in energy) in organic compounds and thus
were disregarded. The main difficult has to be ascribed to the fact that, in practice, excited
state quantum chemical computations require non-conventional methodologies and strategies
based upon the use of multi-reference wavefunctions. (i.e., the so called post-SCF methods)
rather than the standard single-reference SCF wavefunction. For this reason excited state
computations were not routinely used by chemists.
At the end of the 80's improved ab initio quantum chemical methodologies became available
which were suitable for computing, in a balanced way, excited and ground state potential
energy surfaces. In particular the ab initio Multiconfigurational Self-Consistent Field
(MCSCF) method, developed by M. A. Robb in London, had an analytical gradient which
could be employed for efficient geometry optimisation (the search for the structure
corresponding to energy minima and transition states) taking into account the complete set of
the 3N-6 nuclear degrees of freedom of the reacting system (N is the number of atoms). With
this new methodology it was possible to overcome the limitations of the model proposed
previously by Van der Lugt and Devaquet [31]. These limitations mainly regarded the
computation of the excited state reaction path that was assumed to correspond to an
interpolation between the reactant and the product geometrical structure. With the new tools
one could determine real excited state reaction path where the reaction coordinates is not
assumed but computed in a substantially unbiased way.

Conical Intersection

Interpolated Coordinate

Fig. 2. The relationship between the Van der Lugt - Oosterhoff model and the Conical Intersection
(CI) model. The inset indicates the position of the Van der Lugt - Oosterhoff avoided crossing in the
conical intersection region.

In Fig. 2 we show the relation between an avoided crossing and the double cone topology of a
real conical intersection. In two dimensions, the Van der Lugt and Oosteroff model is refined
by replacing the "avoided crossing" with an "unavoided crossing", i.e., a conical intersection
(CI). In other words, the Van der Lugt and Oosteroff avoided crossing path R -> P is replaced
by a path involving a real surface crossing R ->CI ->P.
Bernardi, Olivucci, Robb and co-workers [62; 63] in 1990, reported a first application of the
ab initio MCSCF method. This was a study of the photoinduced cycloaddition of two
ethylene molecules and showed that:
-

A conical intersection exists right at the bottom of the excited state energy surface.
The molecular structure of the conical intersection is related to the observed
photoproducts and stereochemistry of the reaction.

As discussed below, the original idea of Teller, Zimmerman Michl and Salem are now fully
supported by the results of further computational work [64] which definitely demonstrates,
when taken in conjunction with modern experimental results, that frequently radiationless
deactivation occur via a conical intersection between excited and ground states. Radiationless
decay at a conical intersection implies that:
a) The internal conversion process may be 100% efficient (i.e. the Landau-Zener [65]
decay probability will be unity)

b) Any observed retardation in the internal conversion or reaction rate (i.e. the
competition with fluorescence) may reflect the presence of some excited state energy
barrier which separates M* from the intersection structure and
c) In the case where the decay leads to a chemical reaction, the molecular structure at the
intersection must be related to the structure of the photoproducts.
Points a-c provide the theoretical basis for the computational modelling of photochemical
reactions.
Between 1992 and 2002, a long-term computational project involving one of the authors has
been carried out to prove the general validity of the hypothesis supporting the existence of
low-lying conical intersections in organic molecules. The systematic search was performed on
different classes of organic molecules with the intensive use of the MCSCF quantum
chemical method. The application of powerful tools led to a detailed mapping of the potential
energy surfaces of ca. 25 different organic chromophores, thus allowing the characterization
of the conical intersections involved in the reaction mechanisms. The first result of such an
extensive computational effort is that conical intersections may mediate all types of chemical
events such as bond making, bond breaking, group exchange, intermolecular and
intramolecular hydrogen transfer, charge transfer. The second outcome of the research is that
conical intersections do not necessarily take part in a successful chemical reaction (i.e.
reaction where the light energy is exploited to produce chemical species different from the
reactants) but can also mediate light energy wastage mechanisms such as in quenching and
internal conversion processes.
Recently, an Si/So conical intersection has been characterized even in protein and solution
environments using an hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) strategy.
Olivucci and co-workers [66; 67] located a 90°-twisted low-lying Si/So conical intersection in
Rhodopsin and Bacteriorhodopsin using a CASPT2//CASSCF/AMBER level of theory.
Toniolo et al [68] characterized the solution-phase conical intersections of the Green
Fluorescent Protein (GFP) and Photoactive Yellow Protein (PYP) chromophores at semiempirical CAS/CI level. In conclusion, conical intersections could, contrary to common
belief, be frequent (if not ubiquitous) in organic and bio-organic systems and, for many
reaction, they constitute the photochemically relevant decay channel. The majority of the

conical intersection structures documented for organic and bio-organic chromophores
corresponds to low-lying conical intersections located at the bottom of the excited state
relaxation path. As discussed in Chapter 6 of this book, these points could be only located
using methods that allows for the computation of the so-called photochemical reaction path.
A conical intersection is a point of crossing between two electronic states of the same spin
multiplicity (most commonly singlet or triplet). Moreover, if we plot the energies of the two
intersecting states against two specific internal coordinates Xi and X2 we obtain a typical
double cone shape (see Fig. 3a). The Xi and X2 molecular modes define the so-called
"branching" [61] or "g, h" [69] plane and the (n-2)-dimensional subspace of the n nuclear
coordinates is called the intersection space, or seam of intersection [69], an hyperline


Ground Slalc PES ]

(a)

(b)

Fig. 3. (a) Representation of the typical double-cone topology for a conical intersection, (b) Relation
between the "branching space" and the "intersection space".

consisting of an infinite number of conical intersection points (see Fig. 3b) and it is, locally,
orthogonal to the two-dimensional branching plane. A molecular structure deformation along
the branching plane lifts the Si/So energy degeneracy.
Furthermore the ground and excited state wavefunctions undergo a dramatic change when the
molecular structure is changed along a closed loop lying on the plane defined by the Xj and
X2 modes and comprising the conical intersection. In particular, these wavefunctions
exchange their character along the loop.
The rest of this chapter contains some case studies involving the analysis of the branching
plane structure and of the behaviour of the wavefunctions of the Si and So states in the region

of the conical intersection. This will give a clear idea of the importance of such an analysis in
providing information on the nature of the "reactive" process mediated by the such
mechanistic entities. The results reported for each example have been produced using a
common strategy based on the CASPT2//CASSCF level of theory. In this "mixed"
computational method the full reaction coordinate is computed at the CASSCF level while the
energy profile is computed at the CASPT2 level. This means that one applies multireference
second-order perturbation correction to the CASSCF potential energy surface to incorporate
dynamic correlation effects. For further details on these methods, the reader shall refer to
Chapter 2 by Merchan and Serrano-Andres and, in part, to Chapter 10 by Roos. A discussion
of the alternative and currently emerging Time-Dependent Density Functional Theory
(TDDFT) methodology for computing the potential energy of electronically excited states will
be given by Furche et al. in Chapter 3.