Bond Analysis

Chemical processes such as bond formation or electron excitation are often interpreted in terms of the changes that the molecular electron density undergoes in going from a reference (unbound or ground) state to the final (bound or excited) one. A deep insight on the nature of these processes can indeed be gained through the analysis of the topology and features of the electron charge rearrangement occurring throughout the molecular volume upon bond formation/electron excitation.

Focusing on bond formation, Bader's pioneering works of the late Sixties have shown that such charge rearrangement can be conveniently formulated as the difference between the electron density of the molecular adduct AB and those of its constituting, unbound (non-interacting) fragments A and B taken at their in-adduct geometries. Molecular electron densities (and density differences) can be accurately computed by cost-effective methods rooted in density functional theory (DFT), and are represented either as vectors or matrices reflecting their expansion in a basis set of known functions or discretised onto finite-volume regular grids in physical space (in the form of so-called ‘cube’ files).

Whereas a visual inspection of the density difference through volume rendering techniques highlighting charge-depletion and charge-accumulation areas provides itself considerable insight into the nature of the chemical bond at hand, quantitative estimates of the charge flows between selected regions of space are often desirable. In our group we specialize in charge-rearrangement analysis techniques to be conducted both in Hilbert space (through decomposition of the density difference into dedicated molecular orbitals) and real space (through space-oriented selected integrations).

Applications in this field include estimating charge transfer effects in coordination chemistry, investigating the relation between the detailed bonding properties and spectroscopic observables in organometallic catalysts, and probing the chemical character of superheavy elements.


  • Fusè M, Rimoldi I, Cesarotti E, Rampino S, Barone V, On the relation between carbonyl stretching frequencies and the donor power of chelating diphosphines in nickel dicarbonyl complexes, Physical Chemistry Chemical Physics, (2017), DOI: 10.1039/C7CP00982H
  • Bistoni G, Rampino S, Scafuri N, Ciancaleoni G, Zuccaccia D, Belpassi L, Tarantelli F, How π back-donation quantitatively controls the CO stretching response in classical and non-classical metal carbonyl complexes, Chemical Science 7, 1174-1184 (2016), DOI: 10.1039/C5SC02971F
  • Bistoni G, Rampino S, Tarantelli F, Belpassi L, Charge-displacement analysis via natural orbitals for chemical valence: charge transfer effects in coordination chemistry, The Journal of Chemical Physics 142, 084112, 9 pp. (2015), DOI: 10.1063/1.4908537
  • Rampino S, CUBES: a library and a program suite for manipulating orbitals and densities, VIRT&L-COMM 7, 7-2015.6, 2 pp. (2015), ISSN: 2279-8773
  • Rampino S, Storchi L, Belpassi L, Gold-superheavy-element interaction in diatomics and cluster adducts: a combined four-component Dirac-Kohn-Sham/charge-displacement study, The Journal of Chemical Physics 143, 024307, 8 pp. (2015), DOI: 10.1063/1.4926533


Vincenzo Barone

Carovana - Director's Office
Scuola Normale Superiore, Pisa

Marco Fusè

Post Doc
Palazzo D'Ancona - Office 2.9
Scuola Normale Superiore, Pisa

Sergio Rampino

Post Doc
Palazzo D'Ancona - Office 2.6
Scuola Normale Superiore, Pisa