O C H N H H O C H N H H TS1 TS2 J. CHEM. RESEARCH (S), 1998 1 J. Chem. Research (S), 1998, 1 J. Chem. Research (M), 1998, 0242–0264 Prediction of the Molecular Structure, Internal Rotational Barriers and Vibrational Frequencies of Formamide by Nonlocal Density Functional Theory Frank U. Axe,a Venkatesan Renugopalakrishnan*a,b,c and Arnold T. Haglera aBiosym/MSI, Inc., 9685 Scranton Road, San Diego, CA 92121, USA bHarvard Medical School, Boston, MA 02115, USA cInstituto de Quimica, Universidad Nacional Autonoma de Mexico, Circuito Exterior, Ciudad Universitaria, Coyoacan, 0451 Mexico DF, Mexico A state-of-the-art non-local density functional study of formamide is reported and compared with experimental molecular structure, internal rotational barriers and vibrational frequencies. Formamide is the simplest molecule containing a peptide moiety and hence has been the focus of numerous experimental20 and theoretical studies.39 Many of these studies were carried out on formamide with a view to understand the molecular structure and energetics of the peptide moiety, which is of fundamental importance to protein structure.The calculation of the energy surface for even the simplest peptide is a challenging task. Therefore continuing refinement of the force fields for proteins depends on first-principle quantum chemical methods. Density functional theory (DFT), originally developed for problems in solid state physics, is a first-principle quantum chemical method6 which includes a treatment of electron correlation and has also been demonstrated to be of comparable accuracy and computational efficiency7 to post-Hartree–Fock methods.The precise extent of the importance of electron correlation in the calculation of conformational energies of peptides remains unknown at the present time, although its importance has been demonstrated by previous studies.10 DFT is better suited for application to large molecules of biological interest.11 Previously, DFT calculations were performed with local density functionals (LDF) for exchange and correlation.6 However, more recently DFT calculations are being performed using non-local density functionals (NLDF) which are considered to be more accurate than LDF theory especially for the description of molecular structure and energetics.6,7 Despite the large number of experimental20 and theoretical studies39 of formamide, its structure has been controversial. The peptide moiety was assumed from the early work of Pauling and Corey to be planar, and more recently, however, the planarity of the peptide moiety has been questioned.Two early microwave studies of formamide have reached different conclusions12,13 on the planarity of the peptide moiety. From a theoretical point of view, only recently have very high-level first-principle quantum chemical methods, Hartree–Fock,43 nth order Moller–Plesset perturbation,43 configuration interaction, 41 coupled-cluster36 and DFT38–40 been applied to formamide. To date, no systematic study of the geometries, internal rotational barriers, and vibrational frequencies of formamide using different NLDF has been reported in the literature.The DFT-calculated geometries of formamide are generally better than those predicted by HF theory, while those calculated using the adiabatic connection method (ACM)25 in particular are comparable with MP2, with the remaining NLDFs falling inbetween the HF and MP2 methods.Two transition states (Fig. 1) were found at the DFT level for the internal rotation about the peptide bond of formamide. The DFT-calculated rotational barrier heights for the two transition states range from 18 to 20 kcal molµ1, which are within the experimentally observed rotational barrier heights.17 The vibrational frequencies for formamide are significantly in better agreement with experiment than both the HF and MP2 calculated frequencies.Techniques used: Non-local density functional theory References: 61 Table 1: Comparison of experimental and calculated geometries of formamide Table 2: Calculated geometries for the transition states of formamide Table 3: Comparison of experimental and calculated rotational barriers for formamide Tables 4 and 5: Comparison of experimental and calculated vibrational frequency for formamide Table 6: Comparison of calculated vibrational frequencies for the transition states of formamide Received 15th August 1997; Accepted, 29th September 1997 Paper E/7/06017C References cited in this synopsis 6 T.Zeigler, Chem. Rev., 1991, 91, 651. 7 J. W. Andzelm and E. Eimmer, J. Chem. Phys., 1992, 96, 1280. 10 N. L. Allinger, R. S. Grev, B. F. Yates and H. F. Schaeffer III, J. Am. Chem. Soc., 1990, 112, 114. 11 J. Bojarath, D. H. Kitson, G. Fitzgerald, J. W. Andzelm, J. Kraut and A. T. Hagler, Proteins, 1991, 9, 217. 12 C. C. Costain and J. M.Dowling, J. Chem. Phys., 1953, 32, 158. 13 R. J. Kurland and E. B. Wilson, J. Chem. Phys., 1957, 27, 585. 17 T. Drakenberg and S. Forsen, J. Phys. Chem., 1970, 74, 1. 20 C. L. Brummel, M. Shen, K. B. Hevelt and L. A. Philips, J. Opt. Soc. Am., 1994, B11, 176 and references cited therein. 36 N. Burton, S. S.-L. Chiu, M. M. Davidson, D. V. S. Green, I. H. Hillier, J. J. W. McDouall and M. A. Vincent, J. Chem. Soc., Faraday Trans. 2, 1993, 89, 2631. 38 F. Sim, A. St-Amant, I. Papai and D. H. Salahub, J. Am. Chem. Soc., 1992, 114, 4391. 39 D. A. Dixon and N. Matsuzawa, J. Phys. Chem., 1994, 98, 3967 and references cited therein. 40 J. Florian and N. Matsuzawa, J. Phys. Chem., 1994, 98, 3681. 41 X. C. Wang, J. Nichols, M. Feyereisen, M. Gutowski, J. Boatz, A. D. J. Haymet and J. Simons, J. Phys. Chem., 1991, 95, 10 419. 43 K. B. Wiberg and C. M. Breneman, J. Am. Chem. Soc., 1992, 114, 831. 52 A. D. Becke, J. Chem. Phys., 1993, 98, 5648. *To receive any correspondence (at address in Mexico). Fig. 1 Schematic representations of the two transition states found in this study (TS1 and TS2)