Highaccuracy ab initio calculation of metal quadrupolecoupling parameter

High-accuracy ab initio calculation of metal quadrupole-coupling parameter Lan Cheng, John Stanton, and Jürgen Gauss Department of Chemistry, University of Texas at Austin Institute for Physical Chemistry, University of Mainz

Example: Copper quadrupole-coupling constant • NQCC related to electric-field gradient: Cu. CCH • : nuclear quadruple moment • : electric field gradient • : conversion factor NQCC introduces splittings in rotational and other types of spectra.

Rotational Spectrum of Cu. CCH Fourier-transform microwave spectrum of J=1 -0 transition Sun, Halfen, Min, Harris, Clouthier, Ziurys, J. Chem. Phys. 133, 174301 (2010)

Rotational Spectrum of Cu. CCH Experimental 63 Cu quadrupole coupling: 16. 391(12) MHz Sun, Halfen, Min, Harris, Clouthier, Ziurys, J. Chem. Phys. 133, 174301 (2010)

Rotational Spectrum of Cu. CCH Experimental 63 Cu quadrupole coupling: 16. 391(12) MHz B 3 LYP/aug-cc-p. VTZ calculation: -12. 65 MHz Sun, Halfen, Min, Harris, Clouthier, Ziurys, J. Chem. Phys. 133, 174301 (2010)

Rotational Spectrum of Cu. CCH “… An analysis using a negative value of e. Qq for Cu. CCH did not produce a reasonable fit …” Sun, Halfen, Min, Harris, Clouthier, Ziurys, J. Chem. Phys. 133, 174301 (2010)

• Electric-field gradient • Local operator Relativistic effect Electron density in the core region

Relativistic quantum chemistry • Dirac equation: • Four-component equation • Spin-orbit coupling • Describe electron and positron • Small component

Relativistic theory: Exact two-component (X 2 C) theory • Block diagonalization of the matrix Dirac Hamiltonian “Electrons-only” block Dyall, 1997; Kutzelnigg and Liu, 2005; Ilias and Saue 2007; Liu and Peng, 2009…

Relativistic theory: Exact two-component (X 2 C) theory • Block diagonalization of the matrix Dirac Hamiltonian “Electrons-only” block • “Electronic block” + Coulomb interaction Dyall, 1997; Kutzelnigg and Liu, 2005; Ilias and Saue 2007; Liu and Peng, 2009…

X 2 C analytic-derivative theory • Analytic derivatives for the X 2 C Hamiltonian Derivatives of the transformation matrix Derivatives of fourcomponent integrals Zou, Filatov, Cremer, J. Chem. Phys. 134, 244117 (2011). Cheng, Gauss, J. Chem. Phys. 135, 084114 (2011). Cheng, Gauss, J. Chem. Phys. 135, 244104 (2011).

Description of core electron density • Coupled-cluster methods Effective treatments of electron correlation Systematic improvement (CCSD, CCSD(T), CCSDT …) • Density functional theory Specifically tuned range-separation functional Thierfelder, Schwerdtfeger, Saue, Phys. Rev. A, 76, 034502 (2007). Srebro, Autschbach, J. Phys. Chem. Lett. , 3, 576 (2012).

Computed Quadrupole Coupling for Cu. CCH NQCC (MHz) Exp. 16. 391(12) nrl-HF 58. 5 nrl-CCSD(T) 22. 1 X 2 C-HF 56. 0 X 2 C-CCSD(T) 15. 1 Calculations with uncontracted ANO basis, e. Q(63 Cu) = -220(15) mb Both electron correlation and relativity important Cheng, Stopkowicz, Stanton, Gauss, J. Chem. Phys. 137, 224302 (2012)

Systematic route towards high accuracy • Copper quadrupole-coupling constants (in MHz) HF-SCF CCSD(T) +Δ(T) Exp. Cu. F 64. 1 22. 0 Cu. Cl 43. 9 16. 2 Cu. Br 37. 0 12. 9 Cu. CN 60. 8 24. 5 Cu. CH 3 33. 5 -3. 8 Large uncontracted basis sets were used.

Systematic route towards high accuracy • Copper quadrupole-coupling constants (in MHz) HF-SCF CCSD(T) Cu. F 64. 1 26. 9 22. 0 Cu. Cl 43. 9 18. 3 16. 2 Cu. Br 37. 0 14. 5 12. 9 Cu. CN 60. 8 27. 4 24. 5 Cu. CH 3 33. 5 -4. 2 -3. 8 Large uncontracted basis sets were used. +Δ(T) Exp.

Systematic route towards high accuracy • Copper quadrupole-coupling constants (in MHz) HF-SCF CCSD(T) +Δ(T) Exp. Cu. F 64. 1 26. 9 23. 4 22. 0 Cu. Cl 43. 9 18. 3 16. 9 16. 2 Cu. Br 37. 0 14. 5 12. 9 Cu. CN 60. 8 27. 4 26. 7 24. 5 Cu. CH 3 33. 5 -4. 2 -4. 0 -3. 8 Large uncontracted basis sets were used.

Properties of gold compounds Au. F Xe. Au. F Pyykkö, J. Am. Chem. Soc. 117, 2067 (1995). Lovallo, Klobukowski, Chem. Phys. Lett. 368, 589 (2003). Cooke, Gerry, J. Am. Chem. Soc. 126, 17000 (2004). Belpassi, Infante, Tarantelli, Visscher, J. Am. Chem. Soc. 130, 1048 (2007).

Properties of Au. F and Xe. Au. F X 2 C-HF Xe. Au. F Dipole (Debye) Au NQCC (MHz) Dipole Au NQCC 5. 47 -588 7. 22 -941 4. 13 -53. 2 X 2 C-CCSD(T) +SOC(2) +Breit DC-CCSD(T) DCG-CCSD(T) Exp. -527. 6 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

Properties of Au. F and Xe. Au. F Dipole (Debye) Au NQCC (MHz) Dipole Au NQCC X 2 C-HF 5. 47 -588 7. 22 -941 X 2 C-CCSD(T) 4. 27 -11 6. 70 -482 4. 13 -53. 2 +SOC(2) +Breit DC-CCSD(T) DCG-CCSD(T) Exp. -527. 6 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

Properties of Au. F and Xe. Au. F Dipole (Debye) Au NQCC (MHz) Dipole Au NQCC X 2 C-HF 5. 47 -588 7. 22 -941 X 2 C-CCSD(T) 4. 27 -11 6. 70 -482 +SOC(2) 4. 23 -47 6. 69 -517 4. 13 -53. 2 +Breit DC-CCSD(T) DCG-CCSD(T) Exp. -527. 6 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

Properties of Au. F and Xe. Au. F Dipole (Debye) Au NQCC (MHz) Dipole Au NQCC X 2 C-HF 5. 47 -588 7. 22 -941 X 2 C-CCSD(T) 4. 27 -11 6. 70 -482 +SOC(2) 4. 23 -47 6. 69 -517 +Breit -54 -522 -53. 2 -527. 6 DC-CCSD(T) DCG-CCSD(T) Exp. 4. 13 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

Properties of Au. F and Xe. Au. F Dipole (Debye) Au NQCC (MHz) Dipole Au NQCC X 2 C-HF 5. 47 -588 7. 22 -941 X 2 C-CCSD(T) 4. 27 -11 6. 70 -482 +SOC(2) 4. 23 -47 6. 69 -517 +Breit -54 -522 4. 29 -46 6. 76 -539 -53 -544 -53. 2 -527. 6 DC-CCSD(T) DCG-CCSD(T) Exp. 4. 13 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).