Approximate solutions to molecular Schrodinger equation allow useful prediction of various spectral properties. The allowed electronic energy levels of a molecule are related to absorption peak positions in its UV-Vis spectrum (for details, you may consult "Description of Electronically Excited States"); from the knowledge of the wavefunction in ground and excited state we can estiate the peak intensities. Evaluation of second derivatives of molecular energy with respect to nuclear displacements allows to calculate infrared frequencies. Evaluating derivatives with respect to magnetic field, nuclear magnetic moments, and electric field gradients allows to predict the position and splitting pattern of NMR peaks. Such calculations are possible with a variety of quantum chemistry programs including DALTON, Gaussian, and NWChem. The accurate prediction of spin-spin coupling constants is very challenging and requires the use of large uncontracted basis sets (i.e. large expansions of the trial wave function in the gaussian basis) to describe properly the electron distribution near nuclei. Most programs support calculation of NMR coupling constants at the Hartree-Fock (HF) and Density Functional Theory (DFT) level. Only a few programs, such as CFOUR allows modeling NMR spectra using correlated coupled cluster methods.
Many computational chemistry programs offer calculation of spin-spin coupling constants in molecules. In practice, the user has to create an input file that specifies molecular geometry either in the XYZ coordinates, or in the so-called Z-matrix (internal connectivity matrix) coordinates. User also has to specify the basis set. Most quantum chemistry programs use basis sets built from many gaussian functions to approximate the molecular wave function. The gaussian basis sets go by names such as STO-3G, 3-21G, 6-31G, 6-31G(d,p), 6-311G(d,p), cc-pVDZ, aug-cc-pVTZ, aug-cc-pCVQZ and so on. Small basis sets, such as STO-3G use fewer gaussians, and produce results quickly, but the results are quantitatively wrong and qualitatively unreliable. Medium-size basis sets, such as 6-311+G(d,p) sometimes produce qualitatively reliable results. Calculations with large basis sets, such as aug-cc-pVQZ, promise to yield reliable results but the calculations on polyatomic molecules will take very long time or exhaust the available memory and hard disk space. Gaussian09 implements a "Mixed" method where a better basis set is used to calculate the most critical contributions while a faster basis set is used for more time-consuming parts. Finally, user has to specify what type of calculation is sought. An example Gaussian input file for a Hartree-Fock spin-spin coupling calculation for an idealized model of allantoin with the arm HN-CN dihedral at 80 degrees is shown below:
%Mem=420MW # HF/aug-cc-pVTZ NMR=Mixed MaxDisk=2GW Allantoin w/ H-C5-N6-H at 80 degrees: NMR coupling w/ Mixed method (uTZ-w) 0 1 C 0.000000 0.000000 0.000000 N 0.000000 0.000000 1.445819 N 1.277036 0.000000 -0.629183 C -0.585043 -1.329297 -0.492038 H -0.664818 0.773863 -0.367979 C 0.942023 0.558554 2.231878 H -0.767825 -0.455267 1.880499 N 0.663355 0.393323 3.567138 O 1.912375 1.133905 1.854290 H -0.168148 -0.099700 3.852784 H 1.304261 0.773337 4.246029 C 1.505912 -1.098091 -1.386514 H 1.946597 0.723281 -0.534511 N 0.361060 -1.884143 -1.283853 O 2.466297 -1.369890 -2.019229 H 0.269280 -2.755398 -1.750049 O -1.653831 -1.753376 -0.214391
You can examine the result of such a calculation here. The coupling results are listed as a matrix of J-values in Hz units; the axes of the matrix are the atom numbers in the same order as in the input file. You first need to determine the order numbers for atoms that you expect to see a three-bond coupling for. You can convert the Gaussian output file into a mol2 file for visualization. This can be done with the program OpenBabel. To convert with OpenBabel, type babel -ig03 Alla_dih80_NMR.log -omol2 Alla_dih80_NMR.mol2 into Unix shell. Visualize the mol2 file with gOpenMol and write down the number corresponding to each of the three hydrogen atoms we are concerned about.