Jacobian coordinates r, R, and θ of the NO-Ar complex. r is the distance between N and O, R is the distance between the NO center of mass M and Ar, and θ is the angle between the NO molecular axis and the line connecting the Ar nucleus with the NO center of mass.
The best PESs [in cm−1] of NO(X2Π)-Ar interaction obtained with DFT/aug-cc-pvtz: (a) and (b) PW86-PBE-XDM; (c) and (d) HF-PW92-VV09; (e) and (f) ωB97X; (g) and (h) B3LYP-D3; and (i) and (j) CCSD(T)/aug-cc-pvtz+BFs. (a), (c), (e), (g), and (i) A′ components; (b), (d), (f), (h), and (j) – A″ components. Equipotential lines are separated by 5 cm−1 from each other.
Dispersion energy E d [in cm−1] dependence on NO-Ar separation R [bohr] and orientation angle θ [°] computed using various DFT functionals: (a) PW86-PBE-XDM, (b) HF-PW92-VV09, and (c) B3LYP-D3. For PW86-PBE-XDM and HF-PW92-VV09, the dispersion energy of the A′ component is presented, the difference between A′ and A″ dispersion in the region of PESs’ minima does not exceed few cm−1.
Difference between CCSD(T) and DFT without dispersion PESs [in cm−1]: (a) and (b) for the A′ component of the ground state; (c) and (d) for the excited state of the NO-Ar complex. (a) CCSD(T)/aug-cc-pvtz+BFs − HF-PW92/aug-cc-pvtz difference, (b) CCSD(T)/aug-cc-pvtz+BFs − B3LYP/aug-cc-pvtz difference, (c) CCSD(T)/d-aug-cc-pvtz+BFs − HF-PW92/aug-cc-pvtz difference, and (d) CCSD(T)/d-aug-cc-pvtz+BFs − B3LYP/d-aug-cc-pvtz difference. Equipotential lines are separated by 5 cm−1 from each other.
(a)–(c) Interaction energy [in cm−1] of NO(A2Σ+) and Ar obtained with MOM-DFT: (a) PW86-PBE-XDM/aug-cc-pvtz, (b) HF-PW92-VV09/aug-cc-pvtz, and (c) B3LYP-D3/d-aug-cc-pvtz. (d), (e), and (g) Corresponding dispersion energy contribution [in cm−1] to the (a), (b), and (c) PESs, respectively. Equipotential lines are separated by 5 cm−1 from each other.
(a) and (b) – ΔT e (R,θ) [in cm−1] calculated with CCSD(T): (a) using non-scaled NO(A2Σ+)-Ar PES; (b) using scaled NO(A2Σ+)-Ar PES (see text). Equipotential lines are separated by 50 cm−1 from each other. Zero levels are depicted with thicker lines; (c) Zero levels of ΔT e (R,θ) calculated with coupled cluster and DFT: blue – CCSD(T) from (b), red – PW86-PBE-XDM/aug-cc-pvtz, yellow – HF-PW92-VV09/aug-cc-pvtz, green – B3LYP-D3/aug-cc-pvtz(X2Π), d-aug-cc-pvtz(A2Σ+). All excited state calculations have been done using MOM.
Summary of literature results for NO(X2Π)-Ar interaction and its PESs minima. Values of D e marked with * are obtained from D 0 of the same reference and the ratios D e /D 0 from Ref. 20.
Parameters of the minima of the NO(X2Π)-Ar interaction PESs obtained with DFT/aug-cc-pvtz and CCSD(T)/aug-cc-pvtz, aug-cc-pvtz+BFs. The errors compared to literature data are given in brackets, for D e the errors are computed relative to the average across the data given in Table I, for R e and θ e the errors are computed relative to the data from Ref. 11. The uncertainty of our results related to the numerical fitting is about 1 cm−1, 0.1 bohr, and 2° for D e , R e , and θ e values, respectively.
Summary of literature results for NO(A2Σ+)-Ar interaction and parameters of its PES minima. D e g is the depth of the global minimum, D e l is the depth of the local minimum, and D 0 is the dissociation energy. “Experimental” values of D e marked with * are obtained from D 0 from the same experimental work and ratios D e /D 0 from Ref. 12.
NO(A2Σ+)-Ar interaction PES depth D e [in cm−1] calculated using MOM with DFT and CCSD(T). Values marked with * are an estimate of D e calculated at R = 8 bohrs and θ = 0° which is close to the equilibrium geometry of the complex. Negative values of D e indicate a lack of binding in the region close to the true equilibrium. The most accurate estimate of D e derived from experiments16,23 and high-level theory12 is 105–120 cm−1 (see Table III).
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