Ab initio calculations of lowlying electronic states in
Ab initio calculations of low-lying electronic states in metal-containing molecules Lan Cheng Department of Chemistry Johns Hopkins University
Target systems: candidate molecules for Laser cooling 2Π Cooling cycle 2Σ+ Useful information: Leakage 2Δ Weak (spin-orbit mixing) • Franck-Condon Factors • Properties of dark state
Motivation • Explore the accuracy of quantum-chemical methods • When useful, establish computational protocols for treating relativistic and electron-correlation effects in calculations of relevant spectroscopic parameters
Electronic structure for typical candidate polar molecules (Sr. F, YO, Ba. F, Ra. F, etc. ) 2σ 1σ Core 2Σ+ 2σ 2σ 1π 1π 1δ 1δ 1σ 1π 1σ Core 2Δ 1σ 1π 1σ Core 2Π 1σ 1π
Computational consideration • Electron correlation via coupled-cluster theory 2Σ+ , 2Δ, 2Π are lowest states in their respective symmetry. Coupled-cluster theory is suitable for treating electron correlation. • Spin-orbit coupling via exact two-component theory both perturbative and non-perturbative approaches based on exact two-component theory Liu, Shen, Asthana, Cheng, J. Chem. Phys. 148, 034106 (2018). Liu, Cheng, J. Chem. Phys. 148, 144108 (2018). Cheng, Wang, Stanton, Gauss, J. Chem. Phys. 148, 044108 (2018). • Target molecular parameters: Term energies, bond distances, vibrational frequencies, spin-orbit mixing…
Example molecule: Yttrium oxide (YO) • Successfully laser-cooled; suggested for further cooling using dark state Yeo, Hummon, Collopy, Yan, Hemmerling, Chae, Doyle, Ye, Phys. Rev. Lett 114, 223003 (2015). Collopy, Hummon, Yeo, Yan, Ye, New. J. Phys. 17, 055008 (2015). • Low-lying electronic states well studied Chalek, Gole, J. Chem. Phys. 65, 2845 (1976). Linton, J. Mol. Spectroscopy 69, 351 (1978). Steimle, Shirley, J. Chem. Phys. 92, 3292 (1990). Badie, Granier, Chem. Phys. Lett. 364, 550 (2002). Leung, Ma, Cheung, J. Mol. Spectroscopy 229, 108 (2005).
Equilibrium bond distances (in Å) Basis TZ QZ 5 Z Experiment 2�� 1. 7875 2Δ 2Π 1. 8184 1. 7936 Spin-free exact two-component CCSD(T) results
Equilibrium bond distances (in Å) Basis TZ QZ 5 Z Experiment 2Δ 2Π 0. 0040 -0. 0007 0. 0011 1. 7875 1. 8184 1. 7936 2�� Spin-free exact two-component CCSD(T) results
Equilibrium bond distances (in Å) Basis TZ QZ 5 Z Experiment 2Δ 2Π 0. 0040 0. 0009 -0. 0007 -0. 0034 0. 0011 -0. 0012 1. 7875 1. 8184 1. 7936 2�� Spin-free exact two-component CCSD(T) results
Equilibrium bond distances (in Å) Basis TZ QZ 5 Z Experiment 2�� 0. 0040 0. 0009 -0. 0004 1. 7875 2Δ 2Π -0. 0007 -0. 0034 -0. 0046 1. 8184 0. 0011 -0. 0012 -0. 0021 1. 7936 Spin-free exact two-component CCSD(T) results
Harmonic frequencies (in cm-1) Basis TZ QZ 5 Z Experiment 2�� 862. 0 2Δ 2Π 794. 5 821. 5 Spin-free exact two-component CCSD(T) results
Harmonic frequencies (in cm-1) Basis TZ QZ 5 Z Experiment 2Δ 2Π 3. 9 4. 6 9. 7 862. 0 794. 5 821. 5 2�� Spin-free exact two-component CCSD(T) results
Harmonic frequencies (in cm-1) Basis TZ QZ 5 Z Experiment 2Δ 2Π 3. 9 4. 6 4. 9 9. 7 7. 0 862. 0 794. 5 821. 5 2�� Spin-free exact two-component CCSD(T) results
Harmonic frequencies (in cm-1) Basis TZ QZ 5 Z Experiment 2�� 3. 9 5. 9 862. 0 2Δ 2Π 4. 6 4. 9 6. 9 794. 5 9. 7 7. 0 8. 1 821. 5 Spin-free exact two-component CCSD(T) results
Anharmonic constants (in cm-1) Basis TZ QZ 5 Z Experiment 2�� 2. 9 2Δ 2Π 3. 1 3. 4 Spin-free exact two-component CCSD(T) results
Anharmonic constants (in cm-1) Basis TZ QZ 5 Z Experiment 2Δ 2Π -0. 2 -0. 1 -0. 3 2. 9 3. 1 3. 4 2�� Spin-free exact two-component CCSD(T) results
Anharmonic constants (in cm-1) Basis TZ QZ 5 Z Experiment 2Δ 2Π -0. 2 -0. 1 -0. 3 2. 9 3. 1 3. 4 2�� Spin-free exact two-component CCSD(T) results
Anharmonic constants (in cm-1) Basis TZ QZ 5 Z Experiment 2�� -0. 2 -0. 1 2. 9 2Δ 2Π -0. 1 3. 1 -0. 3 3. 4 Spin-free exact two-component CCSD(T) results
Term energies (in cm-1) 2Δ CTZ CQZ C 5 Z C∞Z(T, Q) C∞Z(Q, 5) Exp. 3/2 14531. 2 2Δ 5/2 14870. 4 2Π 1/2 2Π 3/2 16315. 8 16746. 8 Two-component spin-orbit CCSD(T) results
Term energies (in cm-1) 2Δ CTZ CQZ C 5 Z C∞Z(T, Q) C∞Z(Q, 5) Exp. 3/2 2Δ 5/2 611 597 14531. 2 14870. 4 2Π 1/2 105 2Π 3/2 106 16315. 8 16746. 8 Two-component spin-orbit CCSD(T) results
Term energies (in cm-1) 2Δ CTZ CQZ C 5 Z C∞Z(T, Q) C∞Z(Q, 5) Exp. 3/2 2Δ 5/2 2Π 1/2 2Π 3/2 611 597 105 106 236 228 55 58 14531. 2 14870. 4 16315. 8 16746. 8 Two-component spin-orbit CCSD(T) results
Term energies (in cm-1) 2Δ CTZ CQZ C 5 Z C∞Z(T, Q) C∞Z(Q, 5) Exp. 3/2 2Δ 5/2 2Π 1/2 2Π 3/2 611 597 105 106 236 228 55 58 160 154 52 57 14531. 2 14870. 4 16315. 8 16746. 8 Two-component spin-orbit CCSD(T) results
Term energies (in cm-1) 2Δ CTZ CQZ C 5 Z C∞Z(T, Q) C∞Z(Q, 5) Exp. 3/2 2Δ 5/2 2Π 1/2 2Π 3/2 611 597 105 106 236 228 55 58 160 154 52 57 -37 -40 18 22 14531. 2 14870. 4 16315. 8 16746. 8 Two-component spin-orbit CCSD(T) results
Term energies (in cm-1) 2Δ CTZ CQZ C 5 Z C∞Z(T, Q) C∞Z(Q, 5) Exp. 3/2 2Δ 5/2 2Π 1/2 2Π 3/2 611 597 105 106 236 228 55 58 160 154 52 57 -37 -40 18 22 80 76 49 55 14531. 2 14870. 4 16315. 8 16746. 8 Two-component spin-orbit CCSD(T) results
Spin-orbit splittings (in cm-1) Basis TZ QZ 5 Z Experiment 2Δ 2Δ 5/2 339. 2 2Π 2Π – 3/2 1/2 431. 0 Two-component spin-orbit CCSD(T) results
Spin-orbit splittings (in cm-1) Basis TZ QZ 5 Z Experiment 2Δ 2Δ 5/2 3/2 -14 339. 2 2Π 2Π – 3/2 1/2 0 431. 0 Two-component spin-orbit CCSD(T) results
Spin-orbit splittings (in cm-1) Basis TZ QZ 5 Z Experiment 2Δ 2Δ 5/2 3/2 -14 -8 339. 2 2Π 2Π – 3/2 1/2 0 2 431. 0 Two-component spin-orbit CCSD(T) results
Spin-orbit splittings (in cm-1) Basis TZ QZ 5 Z Experiment 2Δ 2Δ 5/2 3/2 -14 -8 -6 339. 2 2Π 2Π – 3/2 1/2 0 2 5 431. 0 Two-component spin-orbit CCSD(T) results
Spin-orbit coupling between Δ and Π states 190 cm-1 2Π 2Δ 140 cm-1 20 cm-1 Dominated by 5 p 2Π-2Δ X 2 Σ + mixing is 0. 1%, in contrast to the estimation of 2. 5% in New. J. Phys. 17, 055008 (2015)
Summary and outlook • The accuracy for term energies is around 100 cm-1. Calculations might be useful for facilitating low-resolution search for the dark state. • Accuracies for equilibrium bond distances and vibrational frequencies are around 0. 005 Å and 10 cm-1. Computed Franck-Condon factors might be anticipated to be reasonable. • Computed spin-orbit splittings are accurate to within 10 cm-1. Calculated spin-orbit mixing should be reliable.
Junzi Liu (FC 08) Jinjun Liu Timothy Steimle Ayush Asthana Hannah Korslund Johns Hopkins University for start-up fund Maryland Advanced Research Computing Center (MARCC) for computational resources
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