X-ray restrained/constrained wave function: milestones and perspectives

Alessandro Genoni

Department of Chemistry, Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Milan, Italy.

e-mail: alessandro.genoni@polimi.it

Today, the X-ray restrained wavefunction (XRW) method (also known as X-ray constrained wavefunction (XCW) approach) stands as one of the cornerstone techniques in modern quantum crystallography [1]. First introduced by Dylan Jayatilaka in 1998 [2], the strategy has undergone a steady and continuous methodological development over the years and has been fruitfully exploited to shed light on many chemical or physical problems and phenomena [3].

In terms of methodological progress, although the approach was initially formulated within the Hartree–Fock framework [2, 4], it has been gradually integrated with a broad range of quantum chemical techniques, including relativistic methods [5] and multi-determinant strategies within the valence bond theory of chemical bonding [6].

In terms of applications, the XRW technique has significantly advanced our understanding of chemical bonding, even allowing for the re-evaluation of classical concepts such as hypervalency [7]. It has also been used to investigate optoelectronic properties in systems with significant nonlinear optical activity [8], as well as to explore biologically and pharmaceutically relevant compounds [9]. Notably, the method has also demonstrated the ability to capture electron correlation and polarization effects on the electron density [10, 11].

This introductory talk will provide a brief overview of the theoretical foundations of the XRW approach, followed by a summary of its key achievements. In the final part of the presentation, attention will turn to future research directions, with a particular focus on the potential of leveraging the Jayatilaka method for the development of novel exchange-correlation functionals in density functional theory [12].

References:

[1] A. Krawczuk, A. Genoni*, Acta Cryst. B* 80, 249-274 (2024).

[2] D. Jayatilaka, Phys. Rev. Lett. 80, 798-801 (1998).

[3] A. Genoni, Chem. Phys. Rev. 5, 021306 (2024).

[4] D. Jayatilaka, D. J. Grimwood, Acta Cryst. A 57, 76-86 (2001).

[5] M. Hudák, D. Jayatilaka, L. Perasínová, S. Biskupic, J. Kozísek, L. Bučinský, Acta Cryst. A 66, 78-92 (2010).

[6] A. Genoni, D. Franchini, S. Pieraccini, M. Sironi, Chem. Eur. J. 24, 15507-15511 (2018).

[7] M. Fugel, L. A. Malaspina, R. Pal, S. P. Thomas, M. W. Shi, M. A. Spackman, K. Sugimoto, S. Grabowsky, Chem. Eur. J. 25, 6523-6532 (2019).

[8] D. Jayatilaka, P. Munshi, M. J. Turner, J. A. K. Howard, M. A. Spackman, Phys. Chem. Chem. Phys. 11, 7209-7218 (2009).

[9] A. Singh, K. Avinash, L. A. Malaspina, M. Banoo, K. Alhameedi, D. Jayatilaka, S. Grabowsky, S. P. Thomas, Chem. Eur. J. 30, e202303384 (2024).

[10] A. Genoni, L. H. R. Dos Santos, B, Meyer, P. Macchi, IUCrJ 4, 136-146 (2017).

[11] E. Hupf, F. Kleemiss, T. Borrmann, R. Pal, J. M. Krzeszczakowska, M. Woińska, D. Jayatilaka, A. Genoni, S. Grabowsky, J. Chem. Phys. 158, 124103 (2023).

[12] A. Genoni, M. Sironi, J. Appl. Cryst., submitted (2025).