FULL PAPER Phosphorus mononitride: A difficult case for theory Teobald Kupka 1 | Malgorzata Leszczy  nska 1 | Krzysztof Ejsmont 1 | Adrianna Mnich 1 | Malgorzata Broda 1 | Karthick Thangavel 2 | Jakub Kaminský 2 1 Faculty of Chemistry, University of Opole, Opole, Poland 2 Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Prague, Czech Republic Correspondence Teobald Kupka, Faculty of Chemistry, University of Opole, 48, Oleska Street, 45-052 Opole, Poland. Email: teobaldk@gmail.com Jakub Kaminský, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nám. 2, 166 10 Prague, Czech Republic. Email: kaminsky@uochb.cas.cz Funding information Grantová Agentura České Republiky, Grant/ Award Number: 19-13436S Abstract Phosphorus nitride (PN) is the simplest molecule formed solely by phosphorus and nitrogen. It represents an interesting model for materials, where phosphorus is directly attached to nitrogen. Nevertheless, both theoretical and experimental studies often provide an incomplete picture on the structural, electronic, and spectral properties of PN. Theoretical predictions often suffer from insufficient level of theory, incomplete basis set, or from neglecting several effects, for example, zero-point vibrational correc- tion (ZPVC). Therefore, we performed an extensive benchmark study on structural, electronic, and spectral properties of PN at the Hartree-Fock, density functional theory (DFT), or even the coupled-cluster levels. We paid special attention to the basis set effect. We tested three variants of Dunning's aug-cc-pVXZ basis sets with the size from double-ζ to sextuple-ζ, as well as Jensen's aug-pc-n, aug-pcJ-n, and aug-pcSseg-n basis sets, where n = 1-4. Obtained energetics, PN distance, dipole moment, vibrational fre- quencies, and nuclear magnetic resonance (NMR) parameters were extrapolated to the complete basis set limit (CBS) using three- or two-parameter formulas. The 31 P NMR shieldings estimated with the aug-cc-pVXZ and aug-cc-pV(X + d)Z basis sets strongly depend on the basis set size providing scattered convergence patterns toward CBS. The Hartree-Fock self-consistent field (HF-SCF) NMR parameters evinced similar behavior as the coupled-cluster data. The only smooth convergence was achieved using the aug-cc-pCVXZ basis sets that include core-valence effects. The KT3 func- tional underestimated the phosphorus CBS shieldings by about 12 ppm compared to coupled cluster with singles and doubles (CCSD) (T). Nevertheless, KT3 unambiguously surpasses the HF-SCF and CCSD levels that provide 31 P shieldings that are lower by about 150 ppm and 24 ppm compared to CCSD(T). The convergence of nitrogen shieldings was regular for all basis set hierarchies and all theoretical methods. Relativis- tic and vibrational effects on selected properties were also discussed. KEYWORDS NMR, Phosphorus nitride, PN, structure, vibrational frequency 1 | INTRODUCTION Compounds containing phosphorus and nitrogen [1] are a very important class of molecules both in bioscience and material science. Among count- less varieties of systems with P and N, phosphazenes and cyclophosphazenes represent a specific type of phosphorus nitride (PN) molecules, with P linked directly to N. [1,2] These compounds are thermally very stable, [1] and their derivatives with crown ethers are known binders of alkali metal Received: 2 April 2019 Revised: 4 July 2019 Accepted: 23 July 2019 DOI: 10.1002/qua.26032 Int J Quantum Chem. 2019;e26032. http://q-chem.org © 2019 Wiley Periodicals, Inc. 1 of 13 https://doi.org/10.1002/qua.26032