Introduction to Computational Quantum Chemistry Relativistic calculation M  Relativistic Effects ➢ Nonrelativistic Hamiltonian of the Schrödinger equation is ➢ In heavy elements the inner shell elctrons move with a speed comparable with speed of light. So the core electrons of heavy atoms show sizable relativistic effect. ➢ Properties like NMR are very sensitive to this ෡𝐻 𝑛𝑟𝑒𝑙 = ෍ 𝑖 Ƹ𝑝𝑖 2 2 + ෍ 𝑖 𝑉𝑁𝑖 + 𝑉𝑒𝑒 + 𝑉𝑛𝑢𝑐 mrel= 𝑚0 (1− 𝑣2 𝐶2) Why relativistic quantum chemistry V.G.Malkin, O.L.Malkina, and D.R.Salahub, Chem.Phys.Lett. 261 (1996) 335. S.K.Wolff et all, J.Chem.Phys. 110 (1999) 7689. Why it is important?? H1 NMR C13 NMR 3 Dirac equation σ is the Pauli spin-matrix σ 𝑥 = 0 1 1 0 , σy = 0 −𝑖 𝑖 0 , σz = 1 0 0 −1 , Four-component Dirac equation 𝑉 𝑐(𝜎. Ƹ𝑝) 𝑐(𝜎. Ƹ𝑝) 𝑉 − 2𝑚𝑐2 . 𝜙 𝜒 = 𝐸 𝜙 𝜒 4 The main difference here is kinetic energy operator . Its takes into account the relativistic increase of electron mass due to high velocities, it includes the electron’s rest mass energy, it incorporates the electron spin also causes the spin orbit coupling. Two-component relativistic methods ➢ High computational cost of four-component relativistic calculations. ➢ Solution contains negative energy spectrum. ➢ Many transformations that eliminate the small component wave functions to form two-component Hamiltonian have been developed. ➢ Two-component relativistic Hamiltonians (involving only positive-energy orbitals) : pseudopotential and all-electron methods 4c-2c transformation Four-component Dirac Hamiltonian Two-component zeroth order regular approximation 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. 6 𝐻 𝑍𝑂𝑅𝐴 𝜙 𝑍𝑂𝑅𝐴 = 𝐸 𝑍𝑂𝑅𝐴 𝜙 𝑍𝑂𝑅𝐴 𝐻 𝑍𝑂𝑅𝐴 = 𝑐2 Ƹ𝑝2 2𝑚𝑐2 − 𝑉 + 2𝑐2 2𝑚𝑐2 − 𝑉 2 − 𝑍 መ𝑆. መ𝐼 𝑟3 + 𝑉 𝑉𝜙+c 𝜎. Ƹ𝑝 𝜒=E𝜙 c 𝜎. Ƹ𝑝 𝜙+(𝑉 − 2𝑚𝑐2)𝜒=E𝜒 𝜙: 𝐿𝑎𝑟𝑔𝑒 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝜒: 𝑆𝑚𝑎𝑙𝑙 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 Amsterdam Density Functional ➢Very fast code ➢Uses Slater-type basis functions ➢All electron relativistic basis sets for all elements ➢Available for most spectroscopic properties ➢Include relativistic effects on structure and reactivity ➢Functionalities: Optimizations Response properties (NMR, EPR, UV-VIS, IR, Mössbauer..) NOCV EDA COSMO model of solvation ZORA scalar and spin-orbit relativistic approach Advantages • Many quantum-chemical tools implemented • Relativistic effects included via ZORA • Good powerful GUI (ADFView) Disadvantages • Slow geometry optimization • Sometimes cryptic error messages • Sometimes serious convergence problems • Calculate the NMR properties of hydrogen in HI and HCl • Write the molecular geometry in same format as .xyz (Å) • Use the following parameters • Bond lengths: HCl(scalar): 1.276930 HI(scalar) : 1.606797 HCl(SO): 1.276467 HI(SO): 1.609681 • For relativity use ZORA Scalar and ZORA Spin-Orbit Approximation in ADF • Compare the Experimental, Nonrelativistic, ECP, and Two component approach • Chemical shielding for benzene 1H nuclei: NMR calculations ReSpect There are two parts of ReSpect calculation • SCF module- Calculation of unperturbed ground state MO Coefficient. • MAG module- Calculation of the magnetic properties . • Each part requires a specific input file (.inp and .M) List of properties EPR • G-tensor • Hyperfine coupling tensor NMR • NMR shielding tensor • Nuclear spin-rotation coupling tensor • Indirect nuclear spin-spin coupling tensor Functional: PBE, BP86, PBE0 etc Solvent: PCM, CPCM model (not available for NMR properties • Calculate the NMR chemical shielding of H in HI using ReSpect • Use the prepared input files distributed in IS. • Three input file required. • Initial guess, guess.inp • Run using the command respect --np=4 --inp=guess • Restart the calculation at 4 component level from the initial guess respect --np=4 --inp=4c --restart=guess • Calculate the NMR parameters using .M file. respect --np=4 --inp=4c --M=CS