Francesco Iachello

Francesco Iachello's picture
Professor Emeritus of Physics
203 432 6944

Member of Yale faculty since 1978


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

The Study of Non-Rigid 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.

The Study of Quantum Phase Transitions in Molecules. Phase transitions are a pervasive phenomenon that occurs in all branches of physics and chemistry. 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 temperature. Algebraic methods are particularly well suited to study quantum phase transitions. We have used them to study phase transitions between different molecular configurations, in particular the linear to bent transition in tri-atomic molecules and the linear to cis-bent and trans-bent transition in four-atomic molecules shown in the figure. Very recently, our group has developed the concept of excited state quantum phase transitions by means of which phase transitions both as a function of a coupling parameter and the temperature can be studied. We are applying this concept to the study of phase transitions between different molecular configurations that occur as a function of excitation energy (temperature). For example, the water molecule, H2O, undergoes a bent to linear transition at ~11,000 cm-1. An important aspect of this study is the understanding of finite-size scaling, since molecular systems are finite in size.

The Study of Intensities of Franck-Condon Transitions in Polyatomic MoleculesThe quantification of vibronic band intensities in Franck-Condon transitions remains a difficult and formidable task. We 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.

The Study of Finite Polymer Chains. An analysis of infrared and Raman intensities in finite polymer chains was initiated years 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.


Dott.Ing.Nucl., Politecnico di Torino, Italy, 1964
Ph.D. Massachusetts Institute of Technology, 1969


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, Italy, 1992
Bonner Prize of the American Physical Society, 1993
Dr. Hon., University of Seville, Spain, 1993
Ph.D. Hon. Chung Yuan University, Republic of China, 1993
Honorary Professor Nanjing University, China, 1995
Foreign Member Royal Netherlands Academy of Arts and Sciences, 1996
Honorary Fellow Eotvos Physical Society, Hungary, 1996
Centennial Prize of the Italian Physical Society, 1997
Foreign Member Croatian Academy of Arts and Sciences, 1997
Zernike Professor University of Groningen, The Netherlands, 1997
Eminent Scientist Award, RIKEN, Tokyo, Japan, 2000
Meitner Prize of the European Physical Society 2002
Dr. Hon., University of Bucharest, Romania, 2005
Italian National Medal of Science, 2007
Majorana Prize, 2007
Commemorative Medal, University of Prague, Czech Republic, 2008
Honorary Fellow Hellenic Physical Society, Greece, 2009
Somaini Volta Prize, Como, Italy, 2009
Foreign Member Mexican Academy of Science, 2010
Foreign Member, Accademia Galileana, Italy, 2011
Foreign Member, Academia Europaea, London, UK, 2013
Ph.D. Hon. Hebrew University, Jerusalem, Israel, 2016
Ph.D. Hon. Technical University, Darmstadt, Germany, 2017
Honorary Professor, Liaoning Normal University, Dalian, China, 2017

Recent Publications

F. Iachello & F. Perez-Bernal. Bending vibrational modes of ABBA molecules: algebraic approach and its classical limit. Mol. Phys. 2008, 106, 223.

F. Perez-Bernal & F. Iachello. Algebraic approach to two-dimensional systems: shape phase transitions, monodromy and thermodynamic quantities. Phys. Rev. A. 2008, 77, 032115.

D. Larese & F. Iachello. A Study of quantum phase transitions and quantum monodromy in the bending motion of non-rigid molecules. J. Mol. Struct. 2011, 1006, 611.

D. Larese, F. Perez-Bernal & F. Iachello. Signatures of quantum phase transitions and excited state quantum phase transitions in the vibrational bending dynamics of triatomic molecules. J. Mol. Struct. 2013, 1051, 310.

D. Larese, M. A. Caprio, F. Perez-Bernal & F. Iachello. A Study of bending motion in tetratomic molecules by the algebraic operator expansion method. J. Chem. Phys. 2014, 140, 014304.

Research Interests

  • Theoretical & Physical Chemistry