Introduction to Computational Quantum Chemistry Lesson 11: Relativistic calculation Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 1 / 13 Why relativistic quantum chemistry For accurate predictions of various prperties of chemical system containing heavy elements mrel = m0 1 − υ2 C2 For light element systems we can forget about relativistic correction. Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 2 / 13 Schrodinger equation − 1 2 2 +V (r) ψ(r) = Eψ(r) Dirac equation cα.p + β.mc2 + V (r) = Eψ(r) ψ(r) =     ψ1(r) ψ2(r) ψ3(r) ψ4(r)     Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 3 / 13 Two-component relativistic methods High computational cost of four-component relativistic calculations has motivated the development of computationally less demanding two-component Hamiltonians Two-component relativistic Hamiltonians (involving only positive-energy orbitals) : pseudopotential and all-electron methods Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 4 / 13 ZORA: accurate and efficient relativistic DFT The zeroth order regular approximation (ZORA) to the Dirac equation accurately and efficiently treats relativistic effects in chemistry. ZORA can be applied with spin-orbit coupling or as scalar correction only. Spin Orbit Coupling can be included self-consistently All electron relativistic basis sets for all elements Available for most spectroscopic properties Include relativistic effects on structure and reactivity Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 5 / 13 From Dirac to ZORA equation Four-component Dirac Hamiltonian V c(σ.p) c(σ.p) V − 2c2 . φ χ = E φ χ ⇓ Unitary transformation Two-component zeroth order regular approximation V (r) + σ.p c2 2c2 − V (r) σ.p φzora = Ezoraφzora Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 6 / 13 Amsterdam Density Functional "user-friendly DFT software for chemists" https://www.scm.com/ Free trial licence for 30 days GUI available only at wolf23 Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 7 / 13 Introduction Very fast code Uses Slater-type basis functions Functionalities: Optimizations Response properties (NMR, EPR, UV-VIS, IR, Mössbauer..) NOCV EDA COSMO model of solvation ZORA scalar and spin-orbit relativistic approach Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 8 / 13 GUI Nice and clear interface adfinput adfview adfoutput Only single licence Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 9 / 13 Running ADF jobs Input: keywords in blocks adf {-n nproc} < input.adf > output.out nmr {-n nproc} < input_nmr.adf > output_ nmr.out INFINITY takes care of the number of CPUs Tape files: binaries containing the orbitals http://www.scm.com/Doc/Doc2014/ADF/ ADFUsersGuide/page262.html#keyscheme%20SAVE Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 10 / 13 NMR TAPE10 is required Separate input file with NMR keywords http://www.scm.com/Doc/Doc2014/ADF/ ADFUsersGuide/page188.html Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 11 / 13 SCF calculations Use the prepared input files distributed in IS Write the molecular geometry in same format as .xyz (Å) Bond lengths: HCl(scalar): 1.276930 HI(scalar) : 1.606797 HCl(SO): 1.276467 HI(SO): 1.609681 Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 12 / 13 NMR calculations Calculate the NMR properties of hydrogen in HI and HCl For relativity use ZORA Scalar and ZORA Spin-Orbit approximations Compare the Experimental, Nonrelativistic, ECP, and Two component approach Chemical shielding for benzene 1H nuclei: Pankaj Lochan Bora and Martin Novák Response properties: NMR 24. listopadu 2015 13 / 13