Experimental and Theoretical Analysis of Vicinal and Long-Range Proton-Proton Coupling Constants for Anthracene Derivatives Ernesto Sa ´ nchez-Mendoza, † Jesu ´ s Herna ´ ndez-Trujillo, ‡ and Federico del Rı ´o-Portilla* ,† Departamento de Bioquı ´mica, Instituto de Quı ´mica, and Departamento de Fı ´sica y Quı ´mica Teo ´ rica, Facultad de Quı ´mica, UniVersidad Nacional Auto ´ noma de Me ´ xico, Circuito Exterior s/n, Ciudad UniVersitaria, Me ´ xico D. F. 04510, Me ´ xico ReceiVed: May 10, 2007; In Final Form: June 27, 2007 We studied vicinal and long-range coupling constants for 9-anthracene derivatives, e.g., Br, CN, CHO, NO 2 , CH 2 Cl, CH 2 OH, and OCH 3 . We performed the accurate measurements using modified J doubling in the frequency domain, even for the smallest couplings immersed within the line width. Density functional theory allowed us to reproduce and exhaustively analyze the physical contributions to the values of these spectroscopic parameters. The theory of atoms in molecules defines a delocalization index that correlates linearly with vicinal and long-range coupling constants when they are grouped in terms of the number of bonds between the coupled nuclei. An exception to this behavior is obtained for 4 J H4,H10 values, which have a negative Fermi contact and the largest delocalization index for each molecule. This observation can be explained by a characteristic “gable roof” arrangement formed by the five nuclei involved in the coupling. Introduction The availability of highly precise experimental procedures for the accurate determination of long-range coupling constants and the existence of theoretical methods to predict their values and contributions have oriented our efforts toward an exhaustive analysis of these parameters for 9-anthracene derivatives. In this contribution, we studied the vicinal and long-range coupling constants of this type of molecules with the best accurate experimental determinations, in order to compare with modern theoretical methods and also to provide a physical interpretation of these parameters. NMR spectroscopy is an indispensable technique for the determination of molecular structure. The nuclear shielding constants and scalar spin-spin coupling constants provide invaluable information of the electronic structure. The vicinal and long-range proton-proton coupling constants comprise a powerful tool for the structure elucidation and conformational analyses of molecules in solution. The size of the coupling constant depends on both the number of bonds that separate the interacting nuclei and the electronic configuration of the molecule. Normally, the measurement of experimental coupling constants in aromatic systems has been carried out by estimation or by simulation using higher order multiplets, although such approaches increase the uncertainty in the comparison between the experimental and theoretical results. The vertiginous devel- opment of new methods to predict theoretical coupling constants requires the most accurate experimental determinations, in which several factors interfere, e.g., strongly coupled systems, cou- plings immersed in the signals, and overlapped and/or complex multiplets. Problems of overlapping and strongly coupled systems can be partially solved by increasing the magnetic field. Nowadays, a large number of experimental techniques capable of measuring coupling constants immersed in both the signal and in complex multiplets have been developed. 1 One of the most sensitive methods is the modified J doubling in the frequency domain. 2 This method uses a set of delta functions (..., +1, -1, +1, +1, -1, +1, ...) for in-phase multiplets. These delta functions are defined in the given reference and must not be confused with the chemical shift symbol or the delocalization index defined below. The convolution process, together with the coupling found for it, generates a simplified multiplet that preserves the integral and the position of the original one. If the number of delta functions tends to infinity, the whole operation behaves as a formal deconvolution of the signal, which is a linear process. Modified J doubling allowed us to measure very small coupling constants (∼0.3 Hz) even if they are immersed in complex multiples and within the line width at the same time. 2-4 This method has the advantage of accurately measuring the magnitude of coupling constants while decon- volving the signals at the same time for nonoverlapped first- order multiplets. At this moment, this is the only method available for the measurement of several small coupling constants immersed in complex multiplets and within the line width. During the last decades, quantum chemistry has focused on the calculation and spectral prediction of these parameters. Most of the theoretical descriptions of spin-spin coupling constants follow the Ramsey and Purcell interpretation 5 and Ramsey formulation. 6 All coupling constants in this work are calculated by adding four different terms: (1) diamagnetic spin-orbit (DSO) and (2) the paramagnetic spin-orbit (PSO), which represent the interactions of the magnetic field of the nuclei mediated by the electron orbital motion; (3) the Fermi contact (FC), which is also a response property reflecting the interaction between the electron spin magnetic moment close to the nucleus and the magnetic field at the nucleus; and (4) the spin-dipole (SD), which describes the interactions between the nuclear magnetic moments as mediated by the electronic spin angular * To whom correspondence should be addressed. Tel. (+52) 55 56224613. Fax: (+52) 55 562162203. E-mail: jfrp@servidor.unam.mx. † Departamento de Bioquı ´mica. ‡ Departamento de Fı ´sica y Quı ´mica Teo ´rica. 8264 J. Phys. Chem. A 2007, 111, 8264-8270 10.1021/jp073564z CCC: $37.00 © 2007 American Chemical Society Published on Web 08/02/2007