Research paper Photoabsorption spectra of small He þ N clusters (N ¼ 3; 4; 10). A quantum Monte Carlo modeling Rajko C ´ osic ´ a,b,⇑ , František Karlicky ´ c , René Kalus a a IT4Innovations, VSB – Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic b Department of Applied Mathematics, VSB – Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic c Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic article info Article history: Received 23 January 2018 In final form 5 April 2018 Available online 6 April 2018 Keywords: Charged helium clusters Photoabsorption cross-sections Path-integral Monte Carlo abstract Photoabsorption cross-sections have been calculated for He þ N clusters of selected sizes (N ¼ 3; 4; 10) over a broad range of photon energies (E phot ¼ 2  14 eV) and compared with available experimental data. Semiempirical electronic Hamiltonians derived from the diatomics-in-molecules approach have been used for electronic structure calculations and a quantum, path-integral Monte Carlo method has been employed to model the delocalization of helium nuclei. While a quantitative agreement has been achieved between the theory and experiment for He þ 3 and He þ 4 , only qualitative correspondence is seen for He þ 10 . Ó 2018 Elsevier B.V. All rights reserved. 1. Introduction Photoabsorption and photodissociation studies provide an invaluable tool for investigations of the electronic structure of clus- ters. However, experimental data have often to be deciphered via theoretical modeling and simulations since plethora of entangled effects contribute. For example, many electronic states are often involved and (quantum) delocalization of nuclei plays a role, par- ticularly in floppy systems. Comparison between experiment and theory is also important since it allows testing of theoretical approaches used and approximations involved. Rare-gas cationic clusters represent an ideal tool for such inves- tigations since they can be easily prepared and manipulated in the experiment and, at the same time, reliable and computationally cheap models of intracluster interactions are available for them leading to realistic simulations. Helium represents a real challenge among the rare-gas cluster cations, mainly because of the quantum nature of light helium nuclei which makes classical approaches in this case physically unreliable. Moreover, the interaction in the He þ N clusters is highly anharmonic and the harmonic approxima- tion, successfully used for heavier rare gases, cannot be used in quantitative calculations. On the other hand, such calculations are highly demanded since accurate experimental data exist [1] for He þ N photoabsorption (and subsequent dissociation) for a wide range of cluster sizes (N ¼ 3; 4; 10; 21; 30) and photon energies. In a previous paper [2], we in detail investigated the photoab- sorption spectrum of He þ 3 using a diatomics-in-molecules (DIM) like model electronic Hamiltonian [3,4] and various methods of sam- pling nuclear configurations. Good performance and accuracy of our approaches encouraged us to explain photoabsorption spectra of larger clusters. As a first step, He þ 4 and He þ 10 clusters have been considered here to avoid unnecessary computational expenses and a more detailed and systematic analysis is postponed to a future paper. Since the main tool for sampling nuclear configura- tions is based, in the present work, on a path-integral Monte Carlo approach [5], which was not considered in the preceding paper, calculations on He þ 3 has also been performed and compared both with the experiment and with previous calculations. Our paper is organized as follows. First, methods and computa- tional details are summarized in Section 2. Then, photoabsorption spectra of He þ N (N ¼ 3; 4; 10) calculated under various conditions are reported and discussed in Section 3 and, finally, conclusive remarks are provided in Section 4. 2. Methods and computational details The effective absorption cross-section has been calculated for a photon bearing energy E via the first order perturbation theory and hybrid approach (quantum treatment of electrons and classical treatment of atomic nuclei) [6,7], rðEÞ¼ lim DE!0 1 DE p 3e 0 c h P N K¼1 P a E ðKÞ a jl ðKÞ a j 2 d DE ðE ðKÞ a  EÞ N : ð1Þ https://doi.org/10.1016/j.cplett.2018.04.015 0009-2614/Ó 2018 Elsevier B.V. All rights reserved. ⇑ Corresponding author at: IT4Innovations, VSB – Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic. E-mail address: rajko.cosic@vsb.cz (R. C ´ osic ´). Chemical Physics Letters 700 (2018) 96–101 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett