Accurate ground state potential of Cu2 up to the dissociation limit by perturbation assisted double-resonant four-wave mixing

Abstract

Perturbation facilitated double-resonant four-wave mixing is applied to access high-lying vibrational levels of the X 1Σg+ (0g+) ground state of Cu2. Rotationally resolved transitions up to v″ = 102 are measured. The highest observed level is at 98% of the dissociation energy. The range and accuracy of previous measurements are significantly extended. By applying the near dissociation equation developed by Le Roy [R. J. Le Roy, J. Quant. Spectrosc. Radiat. Transfer 186, 197 (2017)], a dissociation energy of De = 16 270(7) hc cm−1 is determined, and an accurate potential energy function for the X 1Σg+ (0g+) ground state is obtained. Molecular constants are determined from the measured transitions and by solving the radial Schrödinger equation using this function and are compared with results from earlier measurements. In addition, benchmark multi-reference configuration interaction computations are performed using the Douglas–Kroll–Hess Hamiltonian and the appropriate basis of augmented valence quadruple ζ type. Coupled-cluster single, double, and perturbative triple calculations were performed for comparison.

A Study of NbMo and NbMo– by Anion Photoelectron Spectroscopy

“…41 In the X ̃1Σ + g state of singly bonded Cu 2 , which, like the ground states of Mo 2 and Nb 2 , also correlates with ground state atoms, the measured vibrational constants (ω e = 266.30 ± 0.05 cm −1 and ω e x e = 0.9939 ± 0.0009 cm −1 ) overestimate the dissociation energy by about 10%. 39 In each of these cases, use of the simple equation, D e = ω e 2 /4 ω e x e (and subtracting the zero point energy to obtain D 0 ), 74 overestimates the dissociation energy by a modest amount, and the inclusion of higher order terms in the Morse potential expansion is needed to correctly fit the higher energy vibrational levels and to obtain a more accurate dissociation energy. In contrast, for NbMo, the ω e and ω e x e vibrational constants underestimate the dissociation energy by at least a factor of 3.…”

“…5,37 ) Surprisingly, however, despite its extremely short bond and high effective bond order, the bond dissociation energy (D 0 ) of Cr 2 is only 1.443 ± 0.056 eV (139.2 ± 5.4 kJ/mol), 38 about one-third that of Mo 2 (D 0 = 4.476 ± 0.010 eV), 29 and weaker than that of singly bonded Cu 2 (D e = 2.017 ± 0.001 eV). 39 In addition to the Group 6 homonuclear transition metal dimers, several other 12 valence electron molecules have been studied by high resolution spectroscopy, and also found to have singlet (X ̃1Σ + ) ground states with very short bonds, suggesting formal bond orders of six. These include the heteronuclear Group 6 dimers CrMo (r 0 = 1.8231 ± 0.0010 Å) 40 and CrW (r 0 = 1.8814 ± 0.0004 Å, D 0 = 2.867 ± 0.001 eV), 41 and the mixed Group 4−Group 8 dimer ZrFe (r 0 = 1.8765 ± 0.0005).…”

“…Contributions to the Cr 2 bond order can be further categorized as 3d (0.77­(σ) + 1.62­(π) + 1.16­(δ) = 3.55) and 4sσ (0.90). , Thus, this computational method finds the sσ bonding contributions to be about the same for Cr 2 and Mo 2 , whereas in Cr 2 the d–d bonding contribution is lower by 2 / 3 of a bond (0.655), to which the largest contribution is its weaker dδ bonding (1.52 Mo 2 , 1.16 Cr 2 ). (Cr 2 was initially described as having an EBO of 3.52 or 3.5, but its characterization as being quadruply rather than quintuply bonded ,, was later corrected by those authors. , ) Surprisingly, however, despite its extremely short bond and high effective bond order, the bond dissociation energy ( D 0 ) of Cr 2 is only 1.443 ± 0.056 eV (139.2 ± 5.4 kJ/mol), about one-third that of Mo 2 ( D 0 = 4.476 ± 0.010 eV), and weaker than that of singly bonded Cu 2 ( D e = 2.017 ± 0.001 eV) …”

Relativistic Coupled Cluster with Completely Renormalized and Perturbative Triples Corrections

“…The coinage metal dimers Cu 2 , Ag 2 , and Au 2 serve as test systems for our CCSD, CCSD(T), and CR-CC(2,3) calculations. Prior experimental and theoretical investigations of these systems have yielded reliable energetics and spectroscopic parameters (see refs and − for selected examples), and it has been shown, especially for the heavier dimers, that relativistic effects can significantly change the description of the PECs. Previous CC calculations on these systems ,− ,,,,, have provided accurate results, but these studies relied on the use of effective core potentials (ECPs) or the frozen-core approximation and thus correlated only the valence and semicore electrons.…”

“…Prior experimental and theoretical investigations of these systems have yielded reliable energetics and spectroscopic parameters (see refs and − for selected examples), and it has been shown, especially for the heavier dimers, that relativistic effects can significantly change the description of the PECs. Previous CC calculations on these systems ,− ,,,,, have provided accurate results, but these studies relied on the use of effective core potentials (ECPs) or the frozen-core approximation and thus correlated only the valence and semicore electrons. In some cases, ,, the relativistic treatment was limited to spin-free effects that were incorporated through the ECP, while a few other studies , added spin-free and spin–orbit effects on top of the ECP treatment.…”