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High-accuracy ab initio calculation of metal quadrupole-coupling parameter Lan Cheng, John Stanton, and Jürgen Gauss Department of Chemistry, University.

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Presentation on theme: "High-accuracy ab initio calculation of metal quadrupole-coupling parameter Lan Cheng, John Stanton, and Jürgen Gauss Department of Chemistry, University."— Presentation transcript:

1 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

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

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

4 Rotational Spectrum of CuCCH Sun, Halfen, Min, Harris, Clouthier, Ziurys, J. Chem. Phys. 133, 174301 (2010) Experimental 63 Cu quadrupole coupling: 16.391(12) MHz

5 Rotational Spectrum of CuCCH Sun, Halfen, Min, Harris, Clouthier, Ziurys, J. Chem. Phys. 133, 174301 (2010) Experimental 63 Cu quadrupole coupling: 16.391(12) MHz B3LYP/aug-cc-pVTZ calculation: -12.65 MHz

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

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

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

9 Block diagonalization of the matrix Dirac Hamiltonian Relativistic theory: Exact two-component (X2C) theory “Electrons-only” block Dyall, 1997; Kutzelnigg and Liu, 2005; Ilias and Saue 2007; Liu and Peng, 2009…

10 Block diagonalization of the matrix Dirac Hamiltonian Relativistic theory: Exact two-component (X2C) theory “Electrons-only” block Dyall, 1997; Kutzelnigg and Liu, 2005; Ilias and Saue 2007; Liu and Peng, 2009…

11 Block diagonalization of the matrix Dirac Hamiltonian “Electronic block” + Coulomb interaction Relativistic theory: Exact two-component (X2C) theory “Electrons-only” block Dyall, 1997; Kutzelnigg and Liu, 2005; Ilias and Saue 2007; Liu and Peng, 2009…

12 X2C analytic-derivative theory Analytic derivatives for the X2C Hamiltonian 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). Derivatives of four- component integrals Derivatives of the transformation matrix

13 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).

14 Computed Quadrupole Coupling for CuCCH Cheng, Stopkowicz, Stanton, Gauss, J. Chem. Phys. 137, 224302 (2012) Calculations with uncontracted ANO basis, eQ(63Cu) = -220(15) mb Both electron correlation and relativity important NQCC (MHz) Exp.16.391(12) nrl-HF58.5 nrl-CCSD(T)22.1 X2C-HF56.0 X2C-CCSD(T)15.1

15 Systematic route towards high accuracy Copper quadrupole-coupling constants (in MHz) HF-SCFCCSD(T)+Δ(T)Exp. CuF64.122.0 CuCl43.916.2 CuBr37.012.9 CuCN60.824.5 CuCH 3 33.5-3.8 Large uncontracted basis sets were used.

16 Systematic route towards high accuracy Copper quadrupole-coupling constants (in MHz) HF-SCFCCSD(T)+Δ(T)Exp. CuF64.126.922.0 CuCl43.918.316.2 CuBr37.014.512.9 CuCN60.827.424.5 CuCH 3 33.5-4.2-3.8 Large uncontracted basis sets were used.

17 Systematic route towards high accuracy Copper quadrupole-coupling constants (in MHz) HF-SCFCCSD(T)+Δ(T)Exp. CuF64.126.923.422.0 CuCl43.918.316.916.2 CuBr37.014.512.9 CuCN60.827.426.724.5 CuCH 3 33.5-4.2-4.0-3.8 Large uncontracted basis sets were used.

18 Properties of gold compounds AuF XeAuF 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).

19 Properties of AuF and XeAuF AuF XeAuF Dipole (Debye)Au NQCC (MHz)DipoleAu NQCC X2C-HF5.47-5887.22-941 X2C-CCSD(T) +SOC (2) +Breit DC-CCSD(T) DCG-CCSD(T) Exp.4.13-53.2 \-527.6 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

20 Properties of AuF and XeAuF AuF XeAuF Dipole (Debye)Au NQCC (MHz)DipoleAu NQCC X2C-HF5.47-5887.22-941 X2C-CCSD(T)4.27-116.70-482 +SOC (2) +Breit DC-CCSD(T) DCG-CCSD(T) Exp.4.13-53.2 \-527.6 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

21 Properties of AuF and XeAuF AuF XeAuF Dipole (Debye)Au NQCC (MHz)DipoleAu NQCC X2C-HF5.47-5887.22-941 X2C-CCSD(T)4.27-116.70-482 +SOC (2) 4.23-476.69-517 +Breit DC-CCSD(T) DCG-CCSD(T) Exp.4.13-53.2 \-527.6 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

22 Properties of AuF and XeAuF AuF XeAuF Dipole (Debye)Au NQCC (MHz)DipoleAu NQCC X2C-HF5.47-5887.22-941 X2C-CCSD(T)4.27-116.70-482 +SOC (2) 4.23-476.69-517 +Breit \-54 \-522 DC-CCSD(T) DCG-CCSD(T) Exp.4.13-53.2 \-527.6 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

23 Properties of AuF and XeAuF AuF XeAuF Dipole (Debye)Au NQCC (MHz)DipoleAu NQCC X2C-HF5.47-5887.22-941 X2C-CCSD(T)4.27-116.70-482 +SOC (2) 4.23-476.69-517 +Breit \-54 \-522 DC-CCSD(T)4.29-466.76-539 DCG-CCSD(T) \-53 \-544 Exp.4.13-53.2 \-527.6 Breit term and DC-CCSD(T) results from L. Belpassi, et. al. J. Chem. Phys. 126, 064314 (2007).

24 Outlook Revision of copper nuclear quadrupole moment Nuclear quadrupole-coupling parameters for excited states

25 Stella Stopkowicz Takatoshi Ichino Timothy Steimle The work has been supported the NSF grant (CHE1012743). Acknowledgements

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