Phosphorus mononitride: A difficult case for theory

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 correction (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 frequencies, and nuclear magnetic resonance (NMR) parameters were extrapolated to the complete basis set limit (CBS) using three‐ or two‐parameter formulas. The 31P 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 functional 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 31P 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. Relativistic and vibrational effects on selected properties were also discussed.

Implementation and Validation of Local Hybrid Functionals with Calibrated Exchange-Energy Densities for Nuclear Shielding Constants

“…For the subset of heteronuclei, we found that the PN molecule dominated the deviations of the LHs and for that matter any hybrid functional with larger exact-exchange admixtures , (TPSSh has only 10% and is thus somewhat less sensitive). This reflects the particularly large static correlation effects of this diatomic molecule . Our statistical evaluations in Figure thus provide results with PN either excluded (solid bars) or included (hatched bars).…”

“…This reflects the particularly large static correlation effects of this diatomic molecule. 61 Our statistical evaluations in Figure 1 thus provide results with PN either excluded (solid bars) or included (hatched bars). For comparison, we give also the data for the first generation uncalibrated LHs (including LH07s-SVWN, which is based on an s-LMF) and TPSSh.…”

Extended Benchmark Set of Main-Group Nuclear Shielding Constants and NMR Chemical Shifts and Its Use to Evaluate Modern DFT Methods

“…This makes a theory-against-theory comparison preferable, provided a benchmark level with sufficiently high accuracy is available. For main-group nuclear shieldings, a number of high-level benchmarks have been put forward, typically based on CCSD­(T) “gold standard” data for small molecules. ,,,− However, these data sets usually have been based on a relatively small number of values for a given nucleus, and the different sets often used different basis sets, which may lead to variable accuracy. We therefore decided to construct a larger benchmark set of light main-group nuclear shieldings at a uniform computational level to be used in validation studies of more approximate methods.…”

What is the form of muscimol from fly agaric mushroom (Amanita muscaria) in water? An insight from NMR experiment supported by molecular modeling

“…Thus, in a benchmark study, a fairly good performance of B3LYP among over 40 other density functionals in predicting gas‐phase shieldings of nine small molecules in the complete basis set limit was observed . Recently, we also published several studies using B3LYP functional for prediction of NMR parameters in some small and middle‐size molecules . However, one should be aware that in case of some “exotic” molecular systems, B3LYP‐predicted chemical shifts and coupling constants could be less accurate …”

“…Recently, we also published several studies using B3LYP functional for prediction of NMR parameters in some small and middle‐size molecules . However, one should be aware that in case of some “exotic” molecular systems, B3LYP‐predicted chemical shifts and coupling constants could be less accurate …”