Computational SpectroscopyII. ab initio Methodsfrom part (e) NMR SpectraChemistry 713Updated: February 21, 2008(e) Computation of NMR Spectra Optimize geometry atHartree-Fock leveland check “NMR”withSPARTANComputed NMR for Diethylether13C 1HComparison of 1H spectrum to Expt. Chemical shifts are about right. Spin-spin coupling is not computed. Different thermally accessibleconformations give different computedspectra. In solution, the real molecular sampleis a mixture of conformations that areinterchanging rapidly, faster than theNMR timescale. This results in experimentalspectra, as at right, that aremotionally narrowed. Therefore, real spectra have theappearance of a single conformerwith spin-spin coupling.Hart, Hart & Crane, Organic Chemistry, A ShortCourse, Houghton and Mifflin, Boston, 1995, p 364.Methods for ab initio computationof NMR spectra The magnetic resonance frequency of a particular nucleus is determined by the external magnetic field of the instrument, and the local magnetic fields experienced by the nucleus Chemical shifts are measured relative to a standard such as tetramethylsilane (TMS). Use a calculation of the standard at the same level; these results are stored in the software andcan be accessed with a pull-down menus when the calculated spectra are displayed. There is a problem of gauge invariance: The magnetic field experienced by a particular nucleus needs to be computed relative to acoordinate system origin, but the results should NOT depend on the choice of origin. The older method of handling this employs as gauge-inclusive atomic orbitals (GIAO), and isprobably still the most robust. An alternative is individual gauge for localized orbitals (IGLO). Gaussian also uses IGAIM (Individual Gauges for Atoms in Molecules) method, the CGST(Continuous Set of Gauge Transformations) method, and the single origin method. There areoriginal literature references are in the G03 manual. Extensive lists of calculated 1H and 13C chemical shifts at different levels of theory arecompared with experimental in Cramer, p 347, 348.Computation of NMR Spectrawith GaussView & G03 Optimize the geometry atthe desired level and thenrun an “NMR” job withthe desired method. When the job is done,select “NMR” from theResults menus to se thecalculated NMR spectra.GaussView Computed NMR Spectra As for Spartan, the computedspectrum is only the theconformation submitted; the effectsof motional narrowing are notincluded. Notice the “reference” calculation atthe bottom; we should reallycompute the TMS spectrum at eachof these levels and take thedifference. Using the wrongreference will give inaccurate results(such as these!).RHF/6-31G(d) with NMR set to “All methods”GaussView Computed NMR Spectra Now the calculation and the referenceare at the same level and the agreementis better. Also GIAO is the preferred method. Notice the “//” notation with the levelfor the single point (NMR) calculationon the left of // and the level for thegeometry optimization on the right.NMR=GIAO RHF/6-31G(d)NMR=GIAO RB3LYP/6-311+G(2d,p)//RB3LYP/6-31G(d)ExperimentHart, Hart & Crane, OrganicChemistry, A Short Course,Houghton and Mifflin,Boston, 1995, p 364.(f) Convergence of Results and Computational Cost Both the choice of the basis set and the method (correlation level) affect theresults obtained. The size of the basis set is important. The nature of the basis set is also important. For example inclusion of diffuse functions(“++”) versus high angular momentum functions (“3df, 2p”) may be more (or less)important for converging certain properties in particular systems. Likewise, a certain correlation level may converge some properties well but not others. For a given system, the computation time required increases rapidly with the sizeof the basis set and with the rigor of the electron correlation method applied. Convergence to the experimental result often is non-monotonic, that is results mayoscillate above and below the “true” result a number of times before final convergence. Be aware that the quantities computed are often not exactly the same quantitiesmeasured in an experiment, in which case a “fully converged” calculation will not agreeprecisely with experiment. The uncertainty of the experimental measurements may also limit the precision of theagreement between theory and experiment.Basis Sets Contracted Gaussian functions are fixed linear combinations of Gaussian functions designedto mimic the shape of more realistic orbitals. Widely used in almost all programs. Minimal basis sets, like STO-3G, have just enough basis functions for the orbital at hand. “STO” stands for Slater-type orbitals. Each is a contracted Gaussian is a fixed linear combination of 3 Gaussian functions. Called a single zeta (ζ) basis set because the contracted Gaussian gives no flexibility in the radialdependence of the orbital. Double-ζ basis sets have 2 orbitals of different radial shape for each one in a minimal basisset; triple-ζ basis sets have 3, etc. Split-valence basis sets (6-31G*, etc.) [Pople basis sets] treat the core electron with a single contracted function made up of “6” Gaussians in this case, and use 2 functions for each valence orbital (double-ζ), one is contracted “3” Gaussians, and the other is asingle Gaussian, “1” (in this case). Of course “G” is for Gaussian. Split-valence basis set have been extended to triple-ζ quality (6-311G*, etc), by adding a thirdsingle Gaussian (the second “1”) to the valence orbitals.John Pople1998 Nobel LaureatePolarization functions These give more flexibility in the angular shape of the orbitals. In 6-31G*, the star indicates a set of (5 or 6) d orbitals are addedcentered on each heavy atom. Also notated as 6-31G(d) 6-31G** adds in addition a set of three p orbitals to each hydrogenatom. Also notated as 6-31G(d,p). High angular momentum basis sets can add lots of polarizationfunctions, e.g., 6-311G(3df,2pd). Generally, triple-ζ basis sets benefit from more polarization functionsthat do double-ζ basis sets. Polarization functions help to improve angular properties such as bondangles and torsional barriers.Diffuse functions 6-31+G(2d,p): “+” indicates add diffuse (large diameter) orbitals, ones and a set of p orbitals, to each heavy atom.