Quantum Chemical Calculations of NMR Parameters
Quantum Chemical Calculations of NMR Parameters Tatyana Polenova University of Delaware Newark, DE Winter School on Biomolecular NMR January 20-25, 2008 Stowe, Vermont OUTLINE INTRODUCTION Relating NMR parameters to geometric and electronic structure Classical calculations of EFG tensors Molecular properties from quantum chemical calculations Quantum chemistry methods DENSITY FUNCTIONAL THEORY FOR CALCULATIONS OF NMR PARAMETERS Introduction to DFT Software Practical examples Tutorial RELATING NMR OBSERVABLES TO MOLECULAR STRUCTURE NMR Spectrum NMR Parameters Local geometry Chemical structure (reactivity) I. Calculation of experimental NMR parameters Find unique solution to CQ, Q, , , , , II. Theoretical prediction of fine structure constants from molecular geometry Classical electrostatic model (EFG)- only in simple ionic compounds Quantum mechanical calculations (Density Functional Theory) (EFG, CSA) ELECTRIC FIELD GRADIENT (EFG) TENSOR: POINT CHARGE MODEL EFG TENSOR IS DETERMINED BY THE COMBINED ELECTRONIC AND NUCLEAR WAVEFUNCTION, NO ANALYTICAL EXPRESSION IN THE GENERAL CASE THE SIMPLEST APPROXIMATION: CLASSICAL POINT CHARGE MODEL n Zie 4 V2,k = 3 Y2,k ()i,i i=1 di 5 ATOMS CONTRIBUTING TO THE EFG TENSOR ARE TREATED AS POINT CHARGES, THE RESULTING EFG TENSOR IS THE SUM WITH RESPECT TO ALL ATOMS VERY CRUDE MODEL, WORKS QUANTITATIVELY ONLY IN SIMPLEST IONIC SYSTEMS, BUT YIELDS QUALITATIVE TRENDS AND GENERAL UNDERSTANDING OF THE SYMMETRY AND MAGNITUDE OF THE EXPECTED TENSOR ELECTRIC FIELD GRADIENT (EFG) TENSOR: POINT CHARGE MODEL n Zie 4 V2,k = 3 Y2,k ()i,i i=1 di 5 Ze V = ; V = 0; V = 0 2,0 d 3 2,±1 2,±2 2Ze V = ; V = 0; V = 0 2,0 d 3 2,±1 2,±2 3 Ze V = ; V = 0; V = 0 2,0 2 d 3 2,±1 2,±2 V2,0 = 0; V2,±1 = 0; V2,±2 = 0 MOLECULAR PROPERTIES FROM QUANTUM CHEMICAL CALCULATIONS H = E See for example M.
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