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Zhang Shu-Dong, Liu Chao. Low-lying electronic states of CuN calculated by MRCI method. Chinese Physics B, 2016, 25(10): 103103  
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Low-lying electronic states of CuN calculated by MRCI method
Zhang Shu-Dong†, , Liu Chao
Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China

 

† Corresponding author. E-mail: zhangsd2@126.com

Abstract
Abstract

The high accuracy ab initio calculation method of multi-reference configuration interaction (MRCI) is used to compute the low-lying eight electronic states of CuN. The potential energy curves (PECs) of the X3Σ−, 13Π, 23Σ−, 13Δ, 11Δ, 11Σ−, 11Π, and 5Σ− in a range of R = 0.1 nm–0.5 nm are obtained and they are goodly asymptotes to the Cu(2Sg) + N(4Su) and Cu(2Sg) + N(2Du) dissociation limits. All the possible vibrational levels, rotational constants, and spectral constants for the six bound states of X3Σ−, 13Π, 23Σ−, 11Δ, 11Σ−, and 11Π are obtained by solving the radial Schrödinger equation of nuclear motion with the Le Roy provided Level8.0 program. Also the transition dipole moments from the ground state X3Σ− to the excited states 13Π and 23Σ− are calculated and the result indicates that the 23Σ−–X3Σ− transition has a much higher transition dipole moment than the 13Π–X3Σ− transition even though the 13Π state is much lower in energy than the 23Σ− state.

PACS: 31.50.Bc;31.50.Df;31.15.vn
Keyword:CuN;electronic excited states;MRCI calculation;potential energy curves;vibrational levels;spectroscopic constants;transition dipole moment
1. Introduction

Transition metal compounds are very important in organometallic chemistry, surface science, astrophysics, catalysis process, and others.[1–3] The knowledge of the electronic states as well as the potential energy curves (PECs) are crucial information for experimental spectroscopic studies, and they are also important for depositing the nanoscale function material films.[4] But the compounds, even though the diatomic transition-metal mononitride, are electronically complex and very difficult to treat theoretically because of the extent of electron correlation. In experiments, almost no experimental studies for CuN were conducted until recently O’Brien et al.[5] produced the gas phase CuN molecules by using a copper hollow cathode in a plasma discharge. Through the intracavity laser absorption spectroscopy, they observed the electronic transition spectrum of CuN in the near infrared with red-degraded bandheads at 13005, 12963, 12957, and 12948 cm−1. They tentatively attributed these transitions to being due to the absorption from the X3Σ− ground state of CuN. But a strong perturbation was also observed in one of the excited states. Theoretically, there are several studies devoted to predicting the electronic structures of CuN and CuN+ species.[6–9] Ferrao et al.[6] studied the spectroscopic properties of the ground electronic state for CuN by the CCSD(T) approach and DFT (BP86, BPW91, B3LYP) methods through using the Wachters+f basis sets for the Cu atom and aug-cc-pVTZ basis set for the N atom, and the bond distances, harmonic vibrational frequencies, dissociation energies, ionization potentials, and electron affinity were obtained. Wu[7] also studied the electronic ground state of CuN (cation, neutral, and anion) species by various DFT methods (B3LYP, BLYP, BHLYP, BPW91, and B3PW91). Xu et al.[8] obtained the potential energy curve for the ground state of the CuN molecule by the density function theory (B3LYP) method where the effective core basis set of LANL2DZ for Cu atom and Pople’s basis set of 6-311+(d) for the N atom were used. Daoudi et al.[9] reported the electronic structure and bonding calculations for low-lying states of CuN and CuN+ with CIPSI (configuration interaction by perturbation of a multiconfiguration wave function selected iteratively) method, and indicated that the ground state of CuN is X3Σ− and the first low-lying excited state is 1Δ located at 1.45 eV.

However, the structure of the excited electronic states of CuN in the gas phase seems to be not well understood. In this paper, we focus on the eight low-lying electronic states of CuN, which are corresponding to the two dissociation limits Cu(2Sg) + N(4Su) and Cu(2Sg) + N(2Du), and the PECs of these states are obtained by using the multi-reference configuration interaction (MRCI) method where the Ahlrichstype basis set of def2-tzvp is selected for both Cu atom and N atom. The properties of PECs, vibrational levels, rotation constants, spectral constants, and transition dipole moments for the electronic states of CuN are discussed.

2. Computational method

The MRCI method is considered to be one of the most reliable methods of studying electronic excited states due to the electron correlation energy to be fully considered in calculations. In this paper, the ORCA program package[10] is used for the PEC calculations as in our calculations of BeCl[11] and CuC.[12] The reference wave functions for the multireference calculations are of the state-averages complete active space self-consistent field (CASSCF) type.[13,14] The Ahlrichs triple-zeta valence with new polarization function basis set def2-TZVP[15] is used for both transition metal atom Cu and the ligand atom N, where the {17s11p7d1f} atomic orbitals of the Cu atom are contracted to {6s4p4d1f} pattern {842111/6311/4111/1}, and the {11s6p2d1f} orbitals of the N atom are contracted to {5s3p2d1f} pattern {62111/411/11/1}. The final total number of contracted basis functions is 76.

Our calculations focus on the low-lying electronic states which correspond to the dissociation limits Cu(2Sg) + N(4Su) and Cu(2Sg) + N(2Du), where the Cu keeps in the ground state 2Sg. The ratio of the expectation values of the 4s and 3d radii of Cu is 〈r4s〉/〈r3d〉 ≈ 3.4 at the Hartree–Fock numerical level,[16] and the Hartree–Fock energy levels of 3d and 4s orbital of Cu are (−13.32) eV and (−6.54) eV. Considering the dissociation limits of Cu(2Sg) + N(4Su) and Cu(2Sg) + N(2Du) to be little related to the 3d electron of Cu, it is appropriate to choose only the 4s1 electron of Cu and the 2s22p3 electrons of N as the active electrons and the corresponding orbitals of 4s(Cu), 4p(Cu), 2s(N), and 2p(N) as the active orbitals. So a 6-electron, 8-orbital complete active space multiconfiguration SCF calculation is performed, which is usually abbreviated as CAS(6,8).

The following MRCI calculation is performed by using the CAS(6,8) reference wave functions and estimating the higher-order excitations through the Davidson correction.[17] The excitation type is selected as CISD (single, double excitation configuration interaction), the threshold for the 0th order approximation to the target state is set to be Tsel = 10− 6 Hartree (1 Hartree = 2 Ry = 27.2114 eV), and the second threshold to the 0th order state is set to be Tpre = 10− 4, which is dimensionless and refers to the weight of a given initial reference space.

The scanning step for the PECs is 0.01 nm in a range from 0.10 nm to 0.50 nm. Based on the calculated PECs with the MRCI +Q method, the radial Schrödinger equation of nuclear motion is solved by using the Le Roy provided Level 8.0 program,[18] and the all possible vibrational energy levels are calculated and spectroscopic constants are obtained for each electronic bound state.

3. Results and discussion
3.1. Potential energy curves of the low-lying electronic states of CuN

According to the diatomic molecular structure theory,[19] each electronic state of CuN is related to a specific dissociation limit of Cu + N. For the lowest dissociation limit Cu(2Sg) + N(4Su), only two molecular electronic states are derived in accordance with the Wigner–Witmer rules, where the atomic state 2Sg of Cu corresponds to and the 4Su of N corresponds to in the C∞υ point group, and the electronic states of CuN can be deduced by the direct product of and , that is, . Similarly, for the higher Cu(2Sg) + N(2Du) limit, there appear three triplet states and three quintet states, i.e., 1Σ−, 1Π, 1Δ, 3Σ−, 3Π, and 3Δ. Considering the double degeneracy of Π and Δ states, totally twelve PECs are needed to calculate the eight states. In the ORCA program, only D2h and subgroups are supported in the MRCI/CASSCF calculation, the heteronuclear diatomic molecules belonging to the C∞υ point group must be presented with the C2υ point group. According to the irreducible presentation relationship between the two point groups, Σ+ ↔ A1, Σ− ↔ A2, Π ↔ B1 + B2, and Δ ↔ A1 + A2, the calculations for the 1Σ−, 1Π, 1Δ, 3Σ− (2), 3Π, 3Δ, and 5Σ− electronic states of CuN under the C∞υ point group convert into the calculations for the 1A1, 1A2(2), 1B1, 1B2, 3A1, 3A2(3), 3B1, 3B2, and 5A2 states under the C2υ point group.

Figure 1 displays the calculated PECs of the singlet, triplet, and quintet states labeled with dash curves, solid curves, and empty-circle curve, respectively. The calculated energies for each state are listed in the Supplement attached hereafter (see Appendix A). The inter-nuclear distance changes from 0.1 nm to 0.5 nm. Except for the quintet state 5Σ−, the remaining states appear as bound states. The values of adiabatic exciting energy (Te), equipment bond length (Re), and dissociation energy (De) are listed in Table 1. For comparison, the results of pure MRCI calculation without the Davidson correction are also presented in Table 1, but we only discuss the MRCI +Q results in the following.

Fig. 1. Low-lying PECs for the singlet states (dashed lines), triplet states (solid lines), and quintet state (hollow circle pattern line) of CuN calculated with the MRCI +Q/cas(6,8) method and def2-tzvp basis set.
Table 1.

Some important parameters for the low-lying electronic states of CuN calculated with MRCI +Q method.

.

It is clear that the ground state is the X3Σ− state and the bond length is Re = 0.1836 nm with the lowest energy (−1693.83048) Hartree. We have set this energy to be the reference zero energy level in Fig. 1 and present the PECs with wavenumber units. In the literature, only the ground state 3Σ− is labeled by X, other states are rarely marked.[9] For convenience of discussion, we sign the electronic excited states as 13Π, 11Δ, 11Σ−, 23Σ−, 11Π, and 13Δ according to the increase of exciting energy in turn. The first and second excited states, 13Π and 11Δ, have nearly the same Re (about 0.178 nm), and their PECs are close and very similar all the way, where their Te values are at 11912 cm− 1(1.477 eV) and 13205 cm− 1(1.637 eV), respectively. From Fig. 1, we see all the PECs tend to the two dissociation limits Cu(2Sg) + N(4Su) and Cu(2Sg) + N(2Du) as predicted by the group theory. Daoudi et al.[9] calculated the potential energy curves of CuN by the CIPSI method and predicted the first excited state to be 1Δ with adiabatic exciting energy 1.45 eV. This value is much closer to our calculated value of the 13Π state, where the 11Δ state is the second exciting state in our calculation and its exciting energy is slightly (about 0.16 eV) higher than that of the 13Π state. We notice that the asymptote of PEC for the second dissociation limit Cu(2Sg) + N(2Du), calculated by Daoudi,[9] is not well converged compared with our results as shown in Fig. 1.

3.2. Dipole moment and transition dipole moment

Owing to the ground state of CuN being a triplet state, the allowed electronic transitions between the low-lying excited states and the X state are 23Σ− –X3Σ− and 13Π –X3Σ−. Using the MRCI method to calculate the PECs of CuN, the dipole moments with different bond distances for the X3Σ−, 13Π, and 23Σ− states are computed as shown in Fig. 2.

Fig. 2. Variations of dipole moment with nuclear distance for the three lowest triplet states.

As shown in Fig. 2, the orientation for the dipole moment points from Cu atom to N atom along the z direction. For the X3Σ state and 13Π state, before the CuN dissociation into neutral atoms after the nuclear distance becomes larger than about 0.4 nm, the dipole moments maintain negative values and reach the extreme values of D = (−4.19) Debye for the X3Σ state at R = 0.1906 nm and D = (−8.44) Debye for the 13Π state at R = 0.2608 nm, respectively. These results mean that the N atom totally acts as a negative center in the two electronic states. But for the 23Σ− state, the dipole moment presents an inversion from positive to negative value at R = 0.222 nm, the dipole moment reaches a negative extreme value D = (−3.25) Debye at R = 0.280 nm. The different electronic states correspond to different electron distributions in the molecular orbitals. The variation of dipole moment with nuclear distance also reflects the effect of the electron configuration. Table 2 gives the main electron configurations for the three states of X3Σ, 13Π, and 23Σ− at the nuclear distance when the dipole moments reach their extreme values. The value in the bracket is the weight factor. For the ground state X3Σ−, the main electron configuration is δ2π1π1σ2, where the unpaired two electrons occupy the πx and πy orbital respectively with parallel spin. For the 13Π state, the main configuration is δ2π1π2σ1 or δ 2π 2π 1σ 1 which correspond to the degenerate 3Πx or 3Πy states. Compared with the ground state configuration, one σ electron is excited to the π orbital, but spin is kept in the same state. For the 23Σ− state, the main configuration is δ2π1π1σ1σ1, which means that one σ electron in the ground state is excited to higher another σ orbital.

Table 2.

Main electron configurations for the X3Σ−, 13Π, and 23Σ− states at specific nuclear distances.

.

The variations of transition dipole moments of 23Σ−–X3Σ− and 13Π–X3Σ− with internuclear distance are also computed when scanning the PECs of CuN. As shown in Fig. 3, the dipole moment of the 23Σ−X3Σ− transition is much larger than that of the 13Π –X3Σ− transition. By analyzing the electronic configurations in Table 2, the 23Σ−X3Σ−transition corresponds to one σ electron in the low σ orbital excited to another adjacent σ orbital, i.e., σ 2 → σ 1σ 1, this probability may be much larger than that for this electron leaping to the degenerate π orbital, which is correlated with the 13Π –X3Σ− transition. The peak of the transition dipole moment for 23Σ−X3Σ− appears at R = 0.25 nm with D = 4.76 Debye, but with considering the equilibrium internuclear distance for the ground state X3Σ−, it becomes about Re = 0.18 nm which is far less than the 0.25 nm. This suggests that the possible exciting electronic spectrum cannot achieve the best transition probability.

Fig. 3. Variations of transition dipole moments of 23Σ−–X3Σ− and 13Π –X3Σ− with internuclear distance.
3.3. Vibrational levels and spectroscopic constants

Based on the MRCI +Q calculated PECs as shown in Fig. 1, all the possible vibrational levels for each bound electronic state of CuN can be obtained by using the first-order semiclassical quantization condition[20] from Wentzel–Kramers–Brillouin (WKB) theory, specifically

in which r− and r+ are the classical inner and outer turning points for V(r) at the energy E. Using the Level 8.0 computer program, we select the MRCI +Q calculated single point energy of each PEC as the potential energy turning point, and set the integral radial mesh to be 0.0001 nm for solving the one-dimensional Schrödinger equation while the cubic spline interpolation is performed. For the three triplet states X3Σ−, 13Π, and 23Σ−, totally 36, 51, and 39 vibrational levels are obtained respectively; while for the three singlet states 11Δ, 11Σ−, and 11Π, there are 54, 28, and 22 vibrational levels respectively. Meanwhile, the rotational constant for each vibrational level is also computed with setting the rotational quantum number J only to be zero. Table 3 shows the first 10 vibrational levels and corresponding rotational constants.

Table 3.

Partial vibrational levels and rotational constants (in unit cm− 1) of CuN for X3Σ−, 13Π, 23Σ−, 13Δ, 11Δ, 11Σ−, and 11Π states.

.

Substituting the calculated vibrational level energy into the G(υ) = ωe(υ + 1/2) − ωexe (υ +1/2)2 and the rotational constant into Bυ = Be − αe (υ + 1/2), through the least square fitting, the spectroscopic constants for these bound states are determined as shown in Table 4.

Table 4.

Spectroscopic constants of the low-lying electronic states of CuN.

.
4. Conclusions

In the present study, we calculated the low-lying electronic states of CuN corresponding to the two dissociation limits Cu(2Sg) + N(4Su) and Cu(2Sg) + N(2Du) by making use of the multi-reference configuration interaction (including Davidson correction) method. The potential energy curves (PECs) of the X3Σ−, 13Π, 23Σ−, 3Δ, 11Δ, 11Σ−, 11Π, and 5Σ− in a range of R = 0.1 nm∼0.5 nm are obtained. Based on the potential energy curves, all the possible vibrational energy levels, rotational constants, and the corresponding spectroscopic constants for the bound states are obtained, meanwhile, the transition dipole moments from the ground state X3Σ− to the excited states 13Π and 23Σ− are calculated and the result indicates that the 23Σ−−X3Σ− transition keeps a higher transition dipole moment than the 13Π−X3Σ− transition at different nuclear distances.

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