Francesco Iachello

J.W. Gibbs Professor of Physics and Chemistry, Theoretical Physical Chemistry
E-mail: francesco.iachello@yale.edu

Biographical Sketch

Dott.Ing.Nucl. Politecnico di Torino, Italy 1964
Ph.D. M.I.T. 1969
Joined Yale faculty 1978
Chiaudano Prize, 1964
Fulbright Fellow, 1968
AKZO Prize of the Netherlands Society of Sciences, 1981
Wigner Medal, 1990
Taormina Prize, 1991
Dr. Hon., University of Ferrara, 1992
Bonner Prize of the American Physical Society, 1993
Ph.D. Hon. Chung Yuan University, 1993
Dr. Hon. University of Sevilla, 1993
Honorary Professor Nanjing University, 1995
Honorary Fellow Eotvos Physical Society, 1996
Foreign Member Royal Netherlands Academy of Arts and Sciences, 1996
Foreign Member Croatian Academy of Arts and Sciences, 1997
Zernike Professor Rijksuniversiteit Groningen, 1997
Centennial Prize of the Italian Physical Society, 1997
Meitner Prize of the European Physical Society 2002

Research Description

Our research efforts strive to develop and exploit advanced mathematical methods (algebraic methods) as a means of attacking problems of current interest in Chemistry. Among the problems being attacked at the present time are:

I. The Study of Non-Ridgid Molecules.

During the past decade, Lie algebraic methods, introduced by our group in the early 1980’s, have been exploited to quantitatively analyze molecular spectra for a variety of rigid species. However, many cases exist, especially among extended systems, where the nuclear framework undergoes large-amplitude motion. These non-rigid systems are very difficult to treat with conventional methods based on the solution of the Schrödinger equation. Recently we have introduced a novel algebraic scheme designed to tackle such problems and have used it to describe states of some non-rigid molecules (fulminic acid HCNO/DCNO, magnesium hydroxide MgOH/MgOD). A host of applications is possible and we intend to exploit the method to analyze a variety of molecular species.

II. The Study of Quantum Phase Transitions in Molecules.

Recently, a new concept has been introduced into physical sciences, called quantum phase transitions. These are phase transitions that occur as a function of a coupling parameter rather than of the temperature. The concept has been used extensively in condensed matter physics and in nuclear physics. Algebraic methods are particularly well suited to study quantum phase transitions. We intend to investigate applications of this concept to the study of isomerization of molecules, where the molecular potential has several minima and phase transitions between different shapes (linear, non-linear, planar, non-planar) are possible

III. The Study of Intensities of Franck-Condon Transitions in Polyatomic Molecules

The quantification of vibronic band intensities in Franck-Condon transitions remains a difficult and formidable task. We recently have analyzed, within the framework of algebraic methods, the emission spectrum of methinophosphide (HCP), connecting states with different symmetry (bent-from-linear Ã←X transition). We intend to continue this research, and extend it to transitions to the continuum.

IV. The Study of Finite Polymer Chains.

An analysis of infrared and Raman intensities in finite polymer chains was initiated year ago. This analysis is particularly important for understanding how molecular aggregates are formed, going from momomer to dimer, trimer, etc. A preliminary study of the paraffins, CH₃-(CH₂)_n-2-CH₃ has been performed. Finite number (n) effects and end effects are of particular interest. We intend to extend these studies to more complex geometric structures, such as helicoidal structures, and to more than one dimension (membranes), in view of possible applications of the algebraic method to biological systems.

Although sophisticated mathematical methods are used, the research is aimed at the interpretation and understanding of experimental data, often obtained at the research laboratories of the Yale Chemistry Department. Such is the case of the study of intensities of Franck-Condon transitions, studied in collaboration with the group of P.H. Vaccaro. This research is also part of a wider interdisciplinary research that covers areas both in Physics and Chemistry. Only that part of the research that is devoted to problems in Physical Chemistry is outlined here.

Selected References

“A novel algebraic scheme for describing non-rigid molecules”, F. Iachello, F. Perez-Bernal, and P.H. Vaccaro, Chem. Phys. Lett., 375, 309 (2003).
“Algebraic effective resonance Hamiltonian approach to highly excited SO2(X1A1): effect of bending excitation on local-mode bifurcation”, T. Sako, K. Yamanouchi and F. Iachello, J. Chem. Phys., 117, 1641 (2002).
“Algebraic methods in quantum mechanics: from molecules to polymers”, F. Iachello and S. Oss, Eur. Phys., J D19, 307 (2002).
“Algebraic analysis of bent-from-linear transition intensities: the vibronically resolved emission spectrum of methinophosphide (HCP)”, H. Ishikawa, H. Toyosaki, N. Mikami, F. Perez-Bernal, P.H. Vaccaro and F. Iachello, Chem. Phys. Lett., 365, 57 (2002).
For a review of algebraic methods in molecular physics see F. Iachello and R.D. Levine, Algebraic Theory of Molecules, (Oxford University Press, 1995).

Last modified: July 10, 2005 (kp)

Francesco Iachello
J.W. Gibbs Professor of Physics and Chemistry