Doing calculations with ReSpect Relativistic calculation of NMR and - PowerPoint PPT Presentation

Doing calculations with ReSpect Relativistic calculation of NMR and EPR parameters Vladimir Malkin Department of theoretical chemistry, Institute of Inorganic chemistry, Slovak Academy of Sciences, Bratislava, Slovakia Mariapfarr February 24, 2014

Magnetic interactions e − e −

Magnetic interactions g − tenzor σ chemical J − coupling shielding A HFS

Motivation Relativity Atomic and molecular properties caused by relativistic effects Yellow colour of Au [1] Liquid state of Hg [2] [1] N. Bartlett, Gold Bull . 1998 , 31 , 22 [2] L. J. Norrby, J. Chem. Edu. 1991 , 68 , 110

Terminology Dirac equation (4-component scheme) α β α β 2-component scheme 1-component scheme  αα αβ   αα  0 F F F     βα ββ ββ     F F 0 F Pauli matrices −       0 1 0 1 0 i σ = σ = σ =       − x y z  1 0   0   0 1  i

Relativistic Effects on Atomic Valence Energy Levels n p 3/2 n p n p 1/2 n s n s E ( n-1 )d 5/2 ( n-1 )d ( n-1 )d 3/2 + spin-free nonrelativistic + spin-orbit coupling relativistic effects limit

Breit type corrections P. Pyykko, E. Pajanne, Int. J. Quant. Chem., v. VII, 785-806, (1973), “Hydrogen-like relativistic corrections for electric and magnetic hyperfine integrals.

Comparison of results for 127 I Nuclear Quadruple Coupling Constants (in MHz) calculated with DFT (NR + NR and DKH2 + DKH2) method in comparison to experimental data NQCC in I-X series NQCC in I-X series -3500 -3500 NR NR+NR -3000 -3000 DKH2+DKH2 Rel-2 -2500 -2500 Calculated values Calculated values -2000 -2000 -1500 -1500 -1000 -1000 -500 -500 0 0 0 0 -500 -500 -1000 -1000 -1500 -1500 -2000 -2000 -2500 -2500 -3000 -3000 -3500 -3500 Experimental data Experimental data I. Malkin, O.L. Malkina, V.G. Malkin, Chem. Phys. Lett., 361 2002 , 231

Finite size of nucleus Point nucleus Charge distribution Magnetic moment distribution D. Andrae, Phys. Rep. , 2000 , 336 , 413-525 E. Malkin, I. Malkin, O.L. Malkina, V.G. Malkin, M. Kaupp, Phys. Chem. Chem. Phys., 2006, 8, 4079 – 4085.

Calculated and experimental isotropic 199 Hg HFCs 30000 Nonrelativistic HgF Point nucleus 25000 Finite nucleus Calculated values HgCN 20000 15000 HgH 10000 HgAg 5000 0 0 5000 10000 15000 20000 25000 30000 Experimental data The solid line corresponds to ideal agreement with experiment.

Spin-Orbit interaction 0,6 0,5 0,4 0,3 0,2 0,1 ฀ 0 S L

Spin-orbit interactions

Spin-orbit correction to chemical shift (SO-CS)

Spin-orbit corrections to NMR chemical shift

Spin-orbit corrections to NMR chemical shift

A Karplus-Type Relation for Spin-Orbit Shifts in Iodoethane SO contribution to 1 H shielding (ppm) -4.5 0.15 -3.0 0.10 1 H "SO shift" -1.5 0.05 3 K FC (E,I) (10 0.0 0.00 1.5 -0.05 3.0 -0.10 4.5 -0.15 19 NA 6.0 -0.20 -2 m 7.5 -0.25 3 K FC (H,I) -3 ) 9.0 -0.30 10.5 -0.35 12.0 -0.40 0 20 40 60 80 100 120 140 160 180 H H-C-C-I dihedral angle (deg) Chem. Eur. J. 1998 , 4 , 118. I

Available approaches Calculations of the EPR g-tensor  1-component unrestricted  2-component restricted  2-componnet unrestricted  4-component unrestricted There are specific problems associated with any of listed above approaches

1-component or 2-component ? Performance for ∆ g || in 2 Σ Radicals CdH HgAg PdH HgH LaO RhC 5 0 -5 -10 ∆ g ||,calc / in ppt -15 -20 -25 BP 1-comp. (unrestricted) BP 1-comp. (this work, unrestricted) -30 ZORA 2-comp. (restricted) -35 DKH 2-comp. (this work, unrestricted) -40 -40 -30 -20 -10 0 ∆ g ||,expt / in ppt

Restricted or unrestricted ?

2-component approaches for calculations of g-tensor Note: in a spin-orbit coupled spin restricted relativistic ZORA calculation and the ESR block key, ADF will also calculate and print the nuclear magnetic dipole hyperfine interaction, but the terms due to the spin-polarization density at the nucleus are absent. Furthermore, if there is more than one unpaired electron, the computed results will simply be incorrect , without any warning from the program.

Expression based on Kramer’s pair formalism 3-SCF calculations

Scaling the speed of the light … I. Malkin, O.L. Malkina, V.G. Malkin, and M. Kaupp, J. Chem. Phys., 123 (2005) 244103

Scaling the speed of the light ! Using 2-Component Treatment to Evaluate Importance of Higher-Order Terms - - I 2 Br 2 y = -0,113x 2 + 0,3279x + 2,0024 R 2 = 1,0000 2,20 2,25 y = -0,0293x 2 + 0,1884x + 2,0023 R 2 = 1,0000 2,20 g ⊥ 2,15 g ⊥ g-value g-value 2,15 2,10 2,10 2,05 y = -0,0584x 2 - 0,0128x + 2,0024 2,05 y = -0,0184x 2 - 0,0014x + 2,0023 R 2 = 0,9997 2,00 R 2 = 1,0000 g || 2,00 g || 1,95 0,0 0,2 0,4 0,6 0,8 1,0 1,2 0,0 0,2 0,4 0,6 0,8 1,0 scaling factor scaling factor SO integrals SO integrals quadratic spin-orbit contributions dominate g || for both systems - ! and become very important also for g ⊥ of I 2 DKH-BP86 results with Hirao basis set

Benchmark calculations … Radical 1-comp. 2-comp. Exp. Comparison of different O 2 2.7 2.3 2.9 approaches for the calculation of Δg in SO 4.8 3.9 3.6 ⊥ triplet radicals (in ppt) S 2 13.3 11.2 14.5 SeO 15.3 2.2 32.7 NF 1.8 1.6 2.0 "We have found a number of lines in NCl 5.4 5.0 5.4 the field region expected for SeO but Figure 5 have not yet carried out accurate measurements. Two series of experiments have been terminated y = -13.377x 2 + 15.773x 4 ∆ g ⊥ R 2 = 0.9999 by violent explosions in the liquid 2 nitrogen trap, with the subsequent ∆ g-value ∆ g || release of hydrogen selenide into the 0 laboratory atmosphere ; accurate measurements y = -0.6794x 2 + 0.0035x -2 R 2 = 1 will require some degree of patience! " (Alan Carrington and -4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Donald H. Levy, scaling factor SO integrals J. Phys. Chem, 71 (1967) 2-12)

H Dramatic ic s spin in- orbit e t effe ffects ts OC CO OC CO on h hydr dride de 1 H s shifts fts M M OC CO OC H CO [HM(CO) 5 ] q [HMCp(CO) 3 ] M = Cr, Mo, W (q=-1) M = Cr, Mo, W M = Mn, Tc, Re (q=0) H R R H R R [HHgPh] P P Cl PR 3 M M P P R 3 P Cl L R R R R [HM(L)(dhpe) 2 ] [HMCl 2 (PR 3 ) 2 ] M = Fe, Ru, Os M = Co, Rh, Ir L = Cl, CN H H OC CO OC CO M M OC H OC CO CO [H 2 M(CO) 4 ] [HM(CO) 4 ] M = Fe, Ru, Os M = Co, Rh, Ir H Cl PR 3 PR 3 [HIrCl 2 (PMe 3 ) 2 ] M R 3 P M H R 3 P PR 3 CO [HM(CO)(PR 3 ) 3 ] [HMCl(PR 3 ) 2 ] M = Ni, Pd, Pt M = Co, Rh, Ir R N M H M H N P. Hrobárik, V. Hrobáriková, F. Meier, M. Repiský, S. Komorovský, M. Kaupp J. Phys. Chem. A R 2011 , 115, 5654. [HM(NHC)] [HMPh] M = Cu, Ag, Au M = Zn, Cd, Hg

EPR Parameters in Tungsten(V) Complexes The important role of higher-order spin-orbit contributions. Calculation of ∆g -tensors (in ppt) at 1-, 2- and 4-comp. level of theory using BP86 functional. (2-comp.: SO-ECP on metal/IGLO-II/CGO; 4-comp.: all electron DKS) O S S M S S ∆g 22 ∆g 33 ∆g iso ∆g 11 Complex Method -32 -51 -10 1-comp. a 53 -48 -65 -22 2-comp. a 46 [WO(bdt) 2 ] - -58 -79 -30 4-comp. 46 -71 -91 -40 Exp. 42 a P. Hrobárik, O. L. Malkina, V. G. Malkin, and M. Kaupp Chem. Phys. 356 , 229 (2009).

Demonstration of 4-c calculations for larger, biologically relevant models ⊗ g 22 ⊗ g 33 ⊗ g is Δg 11 Method [ppt] [ppt] [ppt] o [ppt] 1-c DKH -32 -10 -8 -17 4-c mDKS -60 -19 -16 -31 Exp. -82 -20 -20 -41 BP86 results. -surprisingly large higher-order SO effects for a 3d system! -revising estimates of performance of different functionals P. Hrobárik, M. Repiský, V. Hrobáriková, M. Kaupp Theor. Chem. Acc. 2011, 129, 715.

SO S 2 SeO SeS Se 2 TeO TeS TeSe Te 2 J. Chem. Phys. 125, 054110 (2006)

Evaluation of g-tensor and Zero-Field-Splitting (D) for GdH 3 1.5 1.4 1.3 1.2 1.1 1 0.9 D values 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Calculated g ⊥ = 2.023 0 1.98 1.99 2 2.01 2.02 2.03 2.04 2.05 2.06 g value

2-Component Calculations of ZFS in GdH 3 M s =+7/2 M s =+5/2 z M s =+3/2 S = 7/2 M s =+1/2 Gd M s =-1/2 H H M s =-3/2 H M s =-5/2 M s =-7/2 D 1/6[E(7/2) – E(5/2)] 1/4[E(5/2) – E(3/2)] 1/2[E(3/2) – E(1/2)] All-electron 0.22 0.22 0.22 ECP 0.23 0.23 0.23 In cm -1 ; 2-component calculations (DFT with B3PW91).

REHE-2014 conference "Relativistic effects in heavy element chemistry and physics” Smolenice congress centrum, Slovakia, September 20-25, 2014 Thank you!