Computed Spin-Spin Coupling Constants ( 1 J X-Y ) in Molecules H m X-YH n for X and Y ) 13 C, 15 N, and 31 P: Comparisons with Experiment and Insights into the Signs of 1 J X-Y Janet E. Del Bene,* ,†,‡ Jose ´ Elguero, § and Ibon Alkorta § Department of Chemistry, Youngstown State UniVersity, Youngstown, Ohio 44555, Quantum Theory Project, UniVersity of Florida, GainesVille, Florida 32611, and Instituto de Quı ´mica Me ´ dica, CSIC, Juan de la CierVa, 3, E-28006 Madrid, Spain ReceiVed: January 29, 2004 One-bond X-Y spin-spin coupling constants ( 1 J X-Y ) for 18 H m X-YH n molecules, with X and Y ) 13 C, 15 N, and 31 P, have been computed using the equation-of-motion coupled-cluster singles and doubles method. The molecules investigated include all possible combinations of these three elements bonded with single, double, and triple bonds. The computed coupling constants are in good agreement with experiment over a range that extends from -250 to +200 Hz. With only two exceptions, the sign of the Fermi-contact (FC) term is the same as the sign of 1 J X-Y , but the FC term may or may not be a good quantitative estimate of 1 J X-Y . When reduced spin-spin coupling constants ( 1 K X-Y ) are used for comparing coupling constants involving different atoms, a linear relationship is observed between 1 K X-N and 1 K X-P . The signs of 1 J X-Y for approximately half of the molecules included in this study are exceptions to the Dirac vector model. The recently proposed NMR triplet wave function model has been used to provide insight into the variation of the signs of these one-bond spin-spin coupling constants. Introduction The coupling constant between a pair of atoms X and Y is an important molecular property measured by means of classical NMR experiments. Although such measurements have been made for a large number of molecules, interpreting the experimental data is often a challenging task. First, experimental coupling constants (J X-Y ) are often measured in relatively complex molecules, thereby making it difficult to assess how specific factors influence J X-Y and lead to the variations observed experimentally. Second, coupling constants for some smaller symmetrical compounds cannot be directly measured since the technique of isotopic substitution cannot be employed if the substituted isotope does not have a nuclear spin (e.g., substituting 14 N for 15 N). Finally, the Dirac vector model, 1 which has led to the generalization that one-bond coupling constants are positive, two-bond negative, three-bond positive, and so on, is often violated. In this paper, we present the results of a systematic study of X-Y coupling constants ( 1 J X-Y ) in molecules H m X-YH n , for X and Y ) 13 C, 15 N, and 31 P. The molecules investigated are illustrated in Chart 1 and include all possible combinations of these three elements bonded with single, double, and triple bonds. We will compare our computed results with experimental data and transform 1 J X-Y to the corresponding reduced coupling constants 1 K X-Y to compare coupling constants involving different atoms. We will also examine the signs of the one- bond coupling constants, particularly the Fermi-contact (FC) terms, using our newly formulated NMR triplet wave function model (NMRTWM) 2 that relates the sign of J to the phases of the wave functions for excited triplet states and the resulting alignments of nuclear magnetic moments. Methods The structures of molecules having only C and N atoms for X and Y were fully optimized by second-order Møller-Plesset perturbation theory (MP2) 3-6 using the 6-31+G(d,p) basis set. 7-10 Molecules containing P were also optimized at MP2 but with the larger and more flexible Dunning aug-cc-pVTZ basis. 11-13 These levels of theory usually produce molecular geometries in agreement with experimental geometries. Har- monic vibrational frequencies were computed to verify that the optimized structures are equilibrium structures on their potential surfaces. One-bond spin-spin coupling constants ( 1 J X-Y ) were com- puted using equation-of-motion coupled-cluster theory (EOM- CCSD) in the CI-like approximation 14-17 with the Ahlrichs 18 qz2p basis set on H and P, and qzp on C and N. All electrons were included in the EOM-CCSD calculations. This level of theory has been shown to give good agreement between computed and experimental 2-, 3-, and 4-bond 19 F- 19 F spin- spin coupling constants in small molecules, which is notable given the difficulty of computing F-F coupling. 19 Recently, Gauss and co-workers have extended the CCSD formalism for computing spin-spin coupling constants to CCSD(T), CCSDT, and CC3. 20,21 However, these levels of theory are not feasible for the molecules investigated in this work, nor have their performance and reliability been established. The total CCSD spin-spin coupling constants for the molecules investigated in this study have been evaluated as a sum of four terms: the paramagnetic spin-orbit (PSO); diamagnetic spin-orbit (DSO); FC; and spin-dipole (SD). To facilitate comparisons of coupling constants between different nuclei, values of 1 J X-Y have been converted to reduced coupling constants, 1 K X-Y . 22 * Author to whom correspondence may be addressed. E-mail: jedelbene@ysu.edu. † Youngstown State University. ‡ University of Florida. § Instituto de Quı ´mica, Me ´dica, CSIC, Juan de la Cierva, 3, E-28006 Madrid, Spain. 3662 J. Phys. Chem. A 2004, 108, 3662-3667 10.1021/jp0400871 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/19/2004