Abstract
We present a high level ab initio study of NiO and its ions, NiO^{+} and NiO^{−}. Employing variational multireference configuration interaction (MRCI) and single reference coupled-cluster methods combined with basis sets of quintuple quality, 54, 20, and 10 bound states of NiO, NiO^{+}, and NiO^{−} have been studied. For all these states, complete potential energy curves have been constructed at the MRCI level of theory; in addition, for the ground states of the three species core subvalence (3s ^{2}3p ^{6}/_{ Ni }) and scalar relativistic effects have been taken into account. We report energetics, spectroscopic parameters, dipole moments, and spin-orbit coupling constants. The agreement with experiment is in the case of NiO good, but certain discrepancies that need further investigation have arisen in the case of the anion whose ground state remains computationally a tantalizing matter. The cation is experimentally almost entirely unexplored, therefore, the study of many states shall prove valuable to further investigators. The ground state symmetry, bond distances, and binding energies of NiO and NiO^{+} are (existing experimental values in parenthesis), X ^{3}Σ^{−}(X ^{3}Σ^{−}), r_{e} = 1.606 (1.62712) Å, D_{0} = 88.5 (89.2 ± 0.7) kcal/mol, and X ^{4}Σ^{−}(?), r_{e} = 1.60(?) Å, D_{0} = 55 (62.4 ± 2.4) kcal/mol, respectively. The ground state of NiO^{−} is ^{4}Σ^{−} (but ^{2}Π experimentally) with D_{0} = 85–87 (89.2 ± 0.7) kcal/mol.
I. INTRODUCTION
II. COMPUTATIONAL DETAILS
III. RESULTS AND DISCUSSION
A. NiO
1. X^{3}Σ^{−}
2. a^{5}Σ^{−}, A^{3}Π, B^{3}Φ, b^{1}Δ
3. Higher states
B. NiO^{+}
1. X^{4}Σ^{−}
2. Higher states
C. NiO^{−}
IV. SYNOPSIS AND REMARKS
Key Topics
- Nickel
- 61.0
- Ground states
- 39.0
- Excited states
- 31.0
- Electric dipole moments
- 14.0
- Ab initio calculations
- 10.0
Figures
State-averaged MRCI+Q/A5ζ adiabatic PECs and energy level diagram (inset) of 54 (=27 from the first + 27 from the second channel) bound states of NiO. The ordering of the states follows exactly that of Table III . The adiabatic separation of the blue (^{3}D; 3d ^{9}4s ^{1}) – red (^{3}F; 3d ^{8}4s ^{2}) channel is ∼600 cm^{−1}. All energies are shifted by +1582 E_{h}.
State-averaged MRCI+Q/A5ζ adiabatic PECs and energy level diagram (inset) of 54 (=27 from the first + 27 from the second channel) bound states of NiO. The ordering of the states follows exactly that of Table III . The adiabatic separation of the blue (^{3}D; 3d ^{9}4s ^{1}) – red (^{3}F; 3d ^{8}4s ^{2}) channel is ∼600 cm^{−1}. All energies are shifted by +1582 E_{h}.
State-averaged MRCI+Q/A5ζ adiabatic PECs and energy level diagram (inset) of 20 bound states of NiO^{+} correlating to Ni^{+}(a ^{2}D) + O(^{3}P) (14 states) and Ni^{+}(a ^{4}F) + O(^{3}P) (6 states). The ordering of the states follows strictly that of Table V . Eight more PECs of repulsive character correlating to a ^{4}F + ^{3}P are also shown. All energies are shifted by +1581 E_{h}.
State-averaged MRCI+Q/A5ζ adiabatic PECs and energy level diagram (inset) of 20 bound states of NiO^{+} correlating to Ni^{+}(a ^{2}D) + O(^{3}P) (14 states) and Ni^{+}(a ^{4}F) + O(^{3}P) (6 states). The ordering of the states follows strictly that of Table V . Eight more PECs of repulsive character correlating to a ^{4}F + ^{3}P are also shown. All energies are shifted by +1581 E_{h}.
State-averaged MRCI-L+Q/AA5ζ adiabatic PECs and energy level diagram (inset) of 10 bound states of NiO^{−}. The ordering follows that of Table VIII . All energies are shifted by +1582 E_{h}.
State-averaged MRCI-L+Q/AA5ζ adiabatic PECs and energy level diagram (inset) of 10 bound states of NiO^{−}. The ordering follows that of Table VIII . All energies are shifted by +1582 E_{h}.
Tables
Experimental results from the literature for the ground and excited states of ^{58}Ni^{16}O. Dissociation energies (D_{0}), bond distances r_{e} (Å), harmonic frequencies ω _{e} (cm^{−1}), and excitation energies T_{0} (cm^{−1}).
Experimental results from the literature for the ground and excited states of ^{58}Ni^{16}O. Dissociation energies (D_{0}), bond distances r_{e} (Å), harmonic frequencies ω _{e} (cm^{−1}), and excitation energies T_{0} (cm^{−1}).
Total energies E (E_{h}), bond distances r_{e} (Å), dissociation energies D_{e} (kcal/mol), harmonic frequencies, and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}), and dipole moments μ (D) of the X ^{3}Σ^{−} of ^{58}Ni^{16}O at various levels of theory.
Total energies E (E_{h}), bond distances r_{e} (Å), dissociation energies D_{e} (kcal/mol), harmonic frequencies, and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}), and dipole moments μ (D) of the X ^{3}Σ^{−} of ^{58}Ni^{16}O at various levels of theory.
Total energies E (E_{h}), bond distances r_{e} (Å), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}), dipole moments μ (D), Mulliken charges on Ni, q_{Ni}, and energy separations T_{e} (cm^{−1}) of 54 states of ^{58}Ni^{16}O at the MRCI+Q/A5ζ-state average level of theory. Experimental values are included for direct comparison.
Total energies E (E_{h}), bond distances r_{e} (Å), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}), dipole moments μ (D), Mulliken charges on Ni, q_{Ni}, and energy separations T_{e} (cm^{−1}) of 54 states of ^{58}Ni^{16}O at the MRCI+Q/A5ζ-state average level of theory. Experimental values are included for direct comparison.
Total energies E (E_{h}), bond distances r_{e} (Å), dissociation energies D_{e} (kcal/mol), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), and rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}) of the X ^{4}Σ^{−} of ^{58}Ni^{16}O^{+} at various levels of theory.
Total energies E (E_{h}), bond distances r_{e} (Å), dissociation energies D_{e} (kcal/mol), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), and rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}) of the X ^{4}Σ^{−} of ^{58}Ni^{16}O^{+} at various levels of theory.
MRCI+Q/A5ζ−SA total energies E (E_{h}), bond distances r_{e} (Å), dissociation energies D_{e} (kcal mol^{−1}), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}), Mulliken charges on Ni, q_{Ni}, and energy separations T_{e} (cm^{−1}) of ^{58}Ni^{16}O^{+}. In parentheses, theoretical results from the literature are given. ^{ a }
MRCI+Q/A5ζ−SA total energies E (E_{h}), bond distances r_{e} (Å), dissociation energies D_{e} (kcal mol^{−1}), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}), Mulliken charges on Ni, q_{Ni}, and energy separations T_{e} (cm^{−1}) of ^{58}Ni^{16}O^{+}. In parentheses, theoretical results from the literature are given. ^{ a }
Experimental results from the literature for the ground and excited states of ^{58}Ni^{16}O^{−}. Bond distances r_{e} (Å), harmonic frequencies ω _{e} (cm^{−1}), excitation energies T_{e} (cm^{−1}), and electron affinities EA (eV).
Experimental results from the literature for the ground and excited states of ^{58}Ni^{16}O^{−}. Bond distances r_{e} (Å), harmonic frequencies ω _{e} (cm^{−1}), excitation energies T_{e} (cm^{−1}), and electron affinities EA (eV).
Total energies E (E_{h}), bond distances r_{e} (Å), dissociation energies D_{e} (kcal mol^{−1}), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}) energy separations T_{e} (cm^{−1}) for the ^{4}Σ^{−} and ^{2}Π states of ^{58}Ni^{16}O^{−} in various methods.
Total energies E (E_{h}), bond distances r_{e} (Å), dissociation energies D_{e} (kcal mol^{−1}), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}) energy separations T_{e} (cm^{−1}) for the ^{4}Σ^{−} and ^{2}Π states of ^{58}Ni^{16}O^{−} in various methods.
MRCI-L+Q/AA5ζ total energies E (E_{h}), bond distances r_{e} (Å), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}), Mulliken charges on Ni, q_{Ni}, and energy separations T_{e} (cm^{−1}) of ^{58}Ni^{16}O^{−}.
MRCI-L+Q/AA5ζ total energies E (E_{h}), bond distances r_{e} (Å), harmonic frequencies and anharmonicity corrections ω _{e}, ω _{e}x_{e} (cm^{−1}), rotational-vibrational coupling constants α _{e} × 10^{3} (cm^{−1}), Mulliken charges on Ni, q_{Ni}, and energy separations T_{e} (cm^{−1}) of ^{58}Ni^{16}O^{−}.
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