# Francesco Iachello

Member of Yale faculty since 1978

**Research** 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 MoleculesDuring 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.

### Education

Dott.Ing.Nucl., Politecnico di Torino, Italy, 1964

Ph.D. Massachusetts Institute of Technology, 1969

### Honors

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

### Recent Publications

T. Sako, K. Yamanouchi & F. Iachello. Algebraic effective resonance Hamiltonian approach to highly excited SO2 (X1A1): effect of bending excitation on local-mode bifurcation. J. Chem. Phys. 2002, 117, 1641.

F. Perez-Bernal, L.F. Santos, P.H. Vaccaro & F. Iachello. Spectroscopic signatures of non-rigidity: algebraic analyses of infrared and Raman transitions in nonrigid species. Chem. Phys. Lett. 2005, 414, 398.

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 themodynamic quantities. Phys. Rev. A. 2008, 77, 032115.

### Research Interests

- Theoretical & Physical Chemistry