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And Conformatilnal Analysis (Electrons and Nuclei/Alkanes/Amines/Alcohols/Carbohydrates) ANTONY W

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And Conformatilnal Analysis (Electrons and Nuclei/Alkanes/Amines/Alcohols/Carbohydrates) ANTONY W Proc. Nat. Acad. Sci. USA Vol. 72, No. 3, pp. 854-858, March 1975 A New Approach to Empirical Intermolecular and Conformational Potential Energy Functions. II. Applications to Crystal Packing, Rotational Barriers, and Conformatilnal Analysis (electrons and nuclei/alkanes/amines/alcohols/carbohydrates) ANTONY W. BURG(ESS*t, LESTER L. SHIPMAN*, AND HAROLD A. SCHERAGA*t * Department of Chemistry, Cornell University, Ithaca, New York 14853; and t Department of Biophysics, Weisrnann Institute of Science, Rehovoth, Israel Contribued by Harqld A. Scheraga, November 7, 1974 ABSTRACT An empirical potential energy function have fixed bond lengths and bond angles; thus, alterations in based on the interactions of electrons and nuclei (EPEN) only from rotations around the single has been tested on molecules other than those used for its conformations arise parameterization. The results indicate that this 'energy bonds. The conformational and intermolecular energies were function is able to predict reliably the lowest energy con- evaluated by considering the coulombic, overlap, and attrac- formations, the potential energy differences between pon- tive terms of the EPEN algorithm (1). formations, rotational barrier heights, and dipole mo- The procedure for generating the positions of molecules in a ments for a series of alkanes, anines, alcohols, and carbo- hydrates. Crystal packing studies on n-hexane, n-octane, crystal has been described previously (2, 3). During the mini- methylamine, methanol, and a-D-glucose, using this same mization of the crystal lattice energy, the space group re- potential, indicate that it is also reliable for calculating mained invariant while the size and shape of the unit cell were intermolecular interaction energies and low-energy oriex4- changed until minimum crystal lattice energy was obtained. tations. The minimization procedure of Powell (4), as modified by the crystal packing studies. An empirical potential energy function based on the inter- Zangwill (5), was used for and the differences in energy actiQns of electrons and nuclei in molecules (EPEN) was de- When rotational barriers veloped earlier (1), by approximating intra- and inter-mo- between conformers were calculated, a Newton-Raphson 7) was used to locate lecular energies with the pairwise sum of coulombic interac- technique requiring second derivatives (6, tions between all point charge centers (i.e., electrons and the precise positions of the maxima and minima for all degrees in the conformation nuclei), an exponential repulsion to represent electron-electron of rotational freedom multidimensional overlap, and an R- (R = distance) attraction term to sim- space. ulate dispersion, many-bo4y, and other attractive energies. RESULTS AND DISCUSSIONS Parameters for EPEN were derived (1) by a least squares A. Rotational Barriers, Relative Conformational Energies, and fitting procedure using gas-phase and crystal data for ethane, Dipole Moments. The relative conformational energies and propane, n-butane, n-pentane, methanol, methylamine, dipole moments calculated using EPEN for several molecules water, and ammonia. In order to test EPEN, it is used here to are given in Table 1. Wherever possible the corresponding calculate the relative energies of stable conformers, rotational experimental values (8-28) are given for comparison. The barriers, and dipole moments, and to pack crystals of other dipole moments of all molecules are represented well byEPEN, alkanes, amines, and alcohols. The results of these calcula- and the calculated dipole moments for the most stable con- tions are presented and compared to experimental data. formers are given. The results for some molecules are discussed METHODS below. Alkanes. In the previous report (1), a satisfactory fit was to of a methyl group was taken The potential barrier rotation obtained fpr the rotational barriers Qf ethane and propane; as the energy difference between the eclipsed and staggered also the trans-gauche energy difference and trans -- gauche In most cases, the methyl rotational barrier of conformations. were The calculated stable conformer has been reported. The ter- barrier of n-butane predicted accurately. only the most rotational barriers of iso-butane and neo-pentane are within 1 (g) is used to describe the posi- minology trans (t) and gauche of the result. These calculated barriers tions of the hydroxyl proton and the amine lone-pair electrons kcal/mol experimental are both slightly higher than the experimental results, and relative to a C-C bond attached to the functional group. may be due partly to the rigid rotor approximation in the barrier for a particular fragment was When the rotational calculations for these crowded molecules. In neo-pentane, the all other were optimized to be in their calculated, fragments C-C bond length [1.54 A (11)] has been reported to be lowest energy conformations. slightly longer than for other alkanes, and is an indication that Where it was possible, the nuclear geometries of the mole- there is some distortion of the geometry of this molecule. cules studied were taken directly from experimental data or is than the standard of analogous molecules. The bonding and Most likely the CCH bond angle greater from the structure value of 111° used for the EPEN calculations, and larger lone-pair electrons were positioned by using the procedures values of this angle cause the calculated methyl rotational described previously (1). All molecules were considered to barriers to be closer to their experimental values. In the ab- for Abbreviation: EPEN, empirical potential using electrons and sence of experimental data on the'proton geometry neo- nuclei. pentane, the standard value for the CCHI bond angle was used 854 Downloaded by guest on September 24, 2021 Proc. Nat. Acad. Sci. USA 72 (1975) Applications of Empirical Potential 855 TABLE 1. Calculated (calc.) and experimental (expt.) rotational barriers, conformational energy differences, and dipole moments for some alkanes, amines, and alcohols Rotational barrier (kcal/mol) Dipole moment (debyt) Molecule Barrier type or AE Cale. Expt. Cale. Expt. iso-butanea CHr- 4.12 3.9 i 0.75b 0.02 0.130 neo-pentaned CH,- 5.32 4.3-4.7e 0.0 0. Of Ethylamine CH-(g) 3.56 1.407 1.23 -NH2 (g- g) 2.12 1. 6i -NH2 (g-t) 3.11 2.1i AE (g - t) -0.20 -0. 297i iso-propylamine CHF-(g) 4.11 4.4ji 2.7i 1.35 -NH2(g-t) 2.83 2.1i -NH2 (t-t) 3.59 2.1 AE(g-t) -0.75 --0.12 tert-butylamine CH,- 5.14 5.0j, 4. i, 2.7i 1.32 1.29-1.321 -NH2 3.42 2.5i Methanol CHs- 1.16 1.09m Ethanol CHr-(t) 3.53 3.3n 1.83 1. 73w -OH (t-g) 1.70 0 8q -OH (g _ g) 1.60 AE (t - g) -0.38 iso-propanol CHs-(t) 3.9 3.4' 1.80 1.698 -OH (t- g) 1.78 --OH(t t) 1.67 AE (t - g) -0.53 -0.28t tert-butanol CH,- 5.06 4.13u 1.79 1.67v -OH 1.86 a Geometry taken from ref. 8; b ref. 9; ° ref. 10; d geometry taken from ref. 11; e ref. 12; f ref. 13; g ref. 14; h ref. 15; i ref. 16; i ref. 17; these experimental barrier heights were calculated from observed fundamental torsional transitions under the assumption of threefold cosine-type potentials and, probably, under the additional assumption of uncoupled methyl rotation3 (although this is not made clear in ref. 17); since we found, during the course of our computations, that both of these assumptions are invalid, these experimental barrier heights must be considered to be approximations to the true barrier heights; k ref. 18; 1 ref. 19; m ref. 20; " ref. 21; P ref. 22; Qref. 23; r ref. 24; ' ref. 25; t ref. 26; uref. 27; v ref. 28. for the calculations. However, EPEN reproduces the mono- served results for ethylamine (16). Experimental studies on tonic increase of the methyl rotational barrier in this alkane iso-propylamine (17, 18) indicate that the energy difference series (see also Table 1 of ref. 1). It should be noted that the between the all gauche and the gauche-trans conformations is rigid rotor approximation does not allow the gauche -- gauche approximately -0.12 kcal/mol in carbon tetrachloride solu- barrier for n-butane to be predicted accurately by EPEN. tion (18). EPEN gives -0.75 kcal/mol, a value very similar The calculated gauche-gauche barrier for n-butane was 14 to that (-0.67 kcal/mol) found by ab initio LCAO-SCF kcal/mole, while the experimental barrier is only 5-7 kcal/mol theory employing a 4-31 G extended gaussian basis set (32). (29, 30). A similar difficulty was found by Radom et al. (31, 32) The calculated methyl rotational barrier in tert-butylamine is when using linear combination of atomic orbitals self-con- within 1 kcal/mol of the experimental barrier, and the cal- sistent field (LCAO-SCF) molecular orbital theory (33) to culated amine barrier is also in agreement with the experi- study n-butane; a reasonable fit to the gauche-gauche barrier mental barrier of 2.5 (17). was obtained only after the CCC bond angle was increased Methanol and ethanol. The calculated conformational to 115.30. energy barrier to rotation in methanol (1.16 kcal/mol) is in Ethylamine. The most stable conformation was calcu- excellent agreement with the experimental value (1.09 kcal/ lated to have the NH2 lone-pair electrons gauche (g) to the mol; ref. 20). The conformation of ethanol calculated to have C-C bond. This is in agreement with the experimental result the lowest energy has the hydroxyl proton trans to the C-C (16). The magnitude of the calculated energy difference bond. Again, this is in agreement with the observed conforma- between the gauche and trans conformers (-0.20 kcal/mol) tion of ethanol (34).
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