Patai S., Rappoport Z. 1996 The chemistry of functional groups. The chemistry of amino, nitroso, nitro and related groups / 0001 84

TABLE 9. Selected structural parameters (bond lengths in A,˚ bond angles and torsional angles in degrees) of 25 and 26 as calculated by the modified MM2 force field (MM2-80 version) and observed experimentally (X-ray diffraction)22a . Reproduced by permission of John Wiley & Sons, Inc.

treatment of nitrogen inversion, a process which was not handled by MM26. Of particular interest for amino compounds is the inclusion of a directional hydrogen bond potential

function30b and an improved treatment of the electronegativity and Bohlmann effects for C H bonds31.

A new feature in MM3 is the full Newton Raphson minimization algorithm. This allows for the location and verification of transition states and for the calculation of vibrational spectra. Indeed, many of the new potential functions in MM3 were included to provide a better description of the potential energy surface which is required for an accurate calculation of vibrational spectra.

1. MM3 potential functions4

Within the latest published MM3 force field (MM3-94), the molecular energy is given by:

In the original MM3 force field, hydrogen bonding energy was described as a sum of electrostatic (dipole dipole) interactions and an explicit hydrogen bonding energy function of the VdW form. This type of approach lacked the directionality associated with hydrogen bonding and consequently did not perform satisfactorily in all cases. A directional term was therefore added on top of the hydrogen bonding function to MM3-92 and its parameters optimized in MM3-94. The explicit form of the function is30b:

Ehydrogen bond D εHBf184000 exp[ 12.0rYH/r] F ˇ,rXH ð 2.25 r/rYH 6g/ε (29)

Here, εHB is the hydrogen bonding energy parameter, r is the ‘natural’ hydrogen bond distance, rYH is the actual hydrogen bond distance Y . . . H, ˇ is the H X . . . Y angle, rXH and rXH0 are the actual and ‘natural’ H X bond lengths, respectively, and ε is the dielectric constant.

2. MM3 parameterization of amines6

As in the case of the MM2 force field, parameterization of MM3 for amines was based mainly on experimental data with occasional references to ab initio calculations, mainly to evaluate relative conformational energies and derive appropriate torsional parameters. As mentioned above, one notable difference between the two force fields is the removal of lp on sp3 nitrogens from MM3. This simplifies the treatment of vibrational spectra and allows for a realistic treatment of nitrogen inversion which could not be handled by MM2. As usual with MM3, parameterization was aimed at reproducing a variety of molecular properties such as structure, steric energy, dipole moments, moments of inertia, heat of formation and vibrational spectra. A complete list of MM3 parameters for amines is provided in Reference 6.

a. Bond length and bond angle parameters. A comparison of selected structural parameters between MM3, ED and MW results for methylamine, dimethylamine and trimethylamine is provided in Table 1. ‘Natural’ bond lengths and force constants for C N and N H bonds were derived by fitting the experimentally observed structures and vibrational spectra of the three methylamines. By using an appropriate electronegativity correction for the ‘natural’ C N bond length when a hydrogen is connected to the nitrogen, MM3 reproduces the decrease in C N bond lengths along the primary ! secondary ! tertiary amine series5,6. The overall agreement between calculated and experimental bond lengths is very good. However, since the MM3 version used in this parameterization study did not include corrections for the Bohlmann effect, vibrational frequencies of C H bonds anti to a nitrogen lp were consistently calculated to be too high. Appropriate corrections were introduced in subsequent versions of MM3 and the overall RMS error between calculation and experiment in C H frequencies in a more extended set of amines (33 C H comparisons) was reduced from 47 to 17 cm 1, close to the hydrocarbon limit of the force field31. N H and C N bond moments were chosen to reproduce the dipole moments of ammonia and trimethylamine, respectively, and were later slightly modified to evenly distribute the error among all methylamines. The results (Table 1) show good agreement between theory and experiment.

Parameters for bond angles were derived in a similar manner, first by considering the methylamines only, and later by modifying the resulting parameters to reproduce the observed structures of the bulkier amines, diisopropylamine and di-t-butylamine. The N C C angle was chosen to fit ethylamine. However, since in its current form the force field cannot reproduce the experimentally observed dependence of this angle on the

26 Pinchas Aped and Hanoch Senderowitz

TABLE 11. Conformational energies (kcal mol 1) of ethylenediamine as calculated ab initio (6-31GŁŁ ), by the original MM3 force field (MM3) and by MM3 augmented with a directional hydrogen bonding potential function

aConformations are defined by the lp1 N1 C C, N1 C C N2 and C C N2 lp2 torsional angles; t D trans, g D gaucheC , g0 D gauche .

bTS1:N C C N D 0°.

cTS1:N C C N D 120°.

TABLE 12. Moments of inertia (amu ð A˚ 2) for several amino compounds as obtained experimentally (MW) and calculated by MM36. Reprinted with permission from Ref. 6. Copyright (1990) American Chemical Society

envelope conformation with the nitrogen out of plane and the H(N) in axial orientation was found to be the most stable conformer. In contrast, MM3 calculations favor the H- equatorial conformer although only to a small extent (0.34 kcal mol 1). Both experiment and MM3 calculations predict the global minimum of N-methylpiperidine as envelope shaped with the nitrogen out of plane and an equatorial N-methyl. MM3 calculates the Me-axial conformer to be 2.02 kcal mol 1 higher in energy. A structural comparison for these two compounds is provided in Table 13 and reveals good fit between theory and experiment.

e. Hydrogen bonding6,30b. In the original MM2 force field, hydrogen bonding was treated, similar to all other intramolecular forces, as a sum of VdW and dipole dipole interactions between the appropriate atoms. In later versions of MM2, special VdW parameters were introduced for atom pairs participating in hydrogen bonding which allowed for a better estimate of the interaction energy3,30a. This (nondirectional) treatment was carried over to the original MM3 force field4 and later replaced by a directional hydrogen

have supported the modified cyclic structure (30). The first parameterization attempts (nondirectional treatment) were aimed to create local minima for the cyclic and linear structures. By modifying the VdW radius parameter of the H(N) atom and choosing appropriate parameters for the N . . . H pair, dimerization energies of 2.28 and2.27 kcal mol 1 for 28 and 29, respectively, were obtained, in good agreement with the ab initio results of Latajka and Scheiner which predicted almost identical energies for the two structures41. Less satisfying, however, are the calculated structures with N . . . N

distances of 2.88 and 3.02 A˚ for 28 and 29, in contrast with the expected values of 3.15 and 3.35 A˚ 30b.

As noted above, more recent experimental studies of the ammonia dimer favor the modified cyclic structure 30. In light of these latest findings, new parameters have been

and N . . . N distances of 3.07 and 2.50 A for the linear and modified cyclic structures, respectively.

Following the introduction of a directional hydrogen bonding potential function into MM3, the parameterization of the force field for the ammonia dimer was undertaken anew30b. Three conformers were considered, namely 28, 29 and a bifurcated structure 31, and were calculated ab initio at the 6-31GŁŁ level. The results (after corrections for Basis Set Superimposition Error; BSSE) favor the linear dimer over the cyclic one by 0.4 kcal mol 1 and yield dimerization energies of 2.49, 2.09 and 0.62 kcal mol 1 for 28, 29 and 31, respectively. A comparison of force field (original MM3 and MM3 with the directional hydrogen bonding function) and ab initio results for the three ammonia

TABLE 14. Energetic and structural parameters for three ammonia dimmers (29, 28 and 31) as calculated ab initio (6-31GŁŁ C BSSE correction), by the original MM3 force field (MM3) and by MM3 augmented with a directional

hydrogen bonding potential function (MM3-94)a30b . Reproduced by permission of John Wiley & Sons Ltd from Ref. 30b

aDimerization energies in kcal mol 1, dipole moments in Debye, distances in A˚ .

dimers is provided in Table 14 and reveals only moderate agreement between the two methods, although the directional treatment of hydrogen bonding is clearly better than the nondirectional one.

Two additional systems in which hydrogen bonds are expected to play a dominant role, ammonia water complex and 2-aminoethanol, were calculated ab initio and by the new MM3 force field. Two ammonia water complexes were considered, one with an N . . . H O bridge (32) and the other with an O . . . H N bridge (33). As expected from the relative H-donor/H-acceptor properties of nitrogen and oxygen, 32 was calculated

TABLE 15. Energetic and structural parameters for two ammonia water complexes (32 and 33) as calculated ab initio (6-31GŁŁ C BSSE correction) and by the MM3 force field augmented with a

directional hydrogen bonding potential functiona30b . Reproduced by permission of John Wiley & Sons Ltd from Ref. 30b

aDimerization energies in kcal mol 1, dipole moments in Debye, distances and bond lengths in A˚ .

to be the more stable complex by 3.81 kcal mol 1 (6-31GŁŁ C BSSE correction) and 3.88 kcal mol 1 (MM3). Selected structural parameters for 32 and 33, as calculated ab initio and with MM3, are compared in Table 15 and show reasonable agreement between the two methods.

The relative energies of 11 minima and two transition state conformers of 2-

by the lp N C C, N C C O and C C O H torsions, respectively) with an internal N . . . H O hydrogen bond to be the global minimum. Other conformations with an O . . . H N hydrogen bond (e.g. 35) are calculated to be higher in energy by 1.5 2.2 kcal mol 1. The general agreement between ab initio and MM3 calculations is good except for the tGg0 structure (36), where the lp on nitrogen points away from the hydroxy hydrogen. Due to the removal of lp from MM3, this force field overestimates the hydrogen bonding energy in this conformer. A comparison of conformational energies and the structure of the global minimum (34) between ab initio and MM3 calculations is provided in Reference 30b.

f. Heats of formation. Heats of formation for aliphatic amines were calculated in the usual way1 by using the same 7 parameters already used in MM2 (see Section II.B.2.c) and adding two new ones (C N bond energy when both atoms are in a four-membered ring and a structural parameter for nitrogen attached exo to a four-membered ring). The results are given in Table 4 and show excellent agreement between theory and experiment (stan-

dard deviation over 20 comparisons of 0.35 kcal mol 143 ) except for diisopropylamine, whose experimental value was suggested to be erroneous (as also confirmed by ab initio calculations42).

3. MM2 and MM3 parameterization of nitro compounds43

The parameterization of MM3-90 for the nitro group was based on experimental and ab initio results of several aliphatic and aromatic nitro compounds as described below.

For all aromatic systems, the nitro group was treated as if it was not conjugated to the rest of the system. As usual with MM3, the aim was to fit rg bond lengths, r˛ bond angles, rotational barriers, vibrational spectra and heats of formation. Since MM2 had not been specifically parameterized for nitro compounds by the Allinger group in the past, the parameters developed for MM3 were modified and included in MM2-90. A complete list of the parameters for both force fields is provided in Reference 43.

a. Structure. A comparison of structural parameters for the nitro group (see Reference 43 for a complete comparison) between MM2, MM3 and experiment for the compounds studied in Reference 43 is provided in Table 16. The agreement between force field calculations and experimental results is generally very good. A closer scrutiny of the data reveals, however, that for all structural parameters the experimental data span a larger

TABLE 16. Selected structural parameters of the nitro group (bond lengths in A,˚ bond and torsional angles in degrees, dipole moments in Debye) for the set of nitro compounds used in the parameterization of MM2 and MM3 as obtained by the two force fields and

from experimenta43 . Reproduced by permission of Elsevier Science Ltd from Ref. 43