Ab initio studies of the conformations of methylamine and

J . Phys. Chem. 1994,98, 1129-1134

1129

Ab Initio Studies of the Conformations of Methylamine and Ethylenediamine: Interaction Forces Affecting the Structural Stability Sang Joo Lee, Byung Jin Mhin, Seung Joo Cho, Jin Yong Lee, and Kwang S. Kim' Department of Chemistry and Center for Biofunctional Molecules, Pohang University of Science and Technology, P.O.Box 125, Pohang 790-600, Korea Received: September 17, 1993"

The structures and conformational energies of methylamine and ethylenediamine have been studied extensively with ab initio molecular orbital theory. For methylamine, there are good linear relationships among the C-N bond length, cosine of the H-C-N-H dihedral angle, and conformational energy. For ethylenediamine which has numerous multiminima, we studied the stereoelectronic effect, steric effect, intramolecular hydrogen bonding, repulsion between hydrogens, and repulsion between lone-pair electrons. The major factor determining the conformational stabilities of the multiminima is found to be the stereoelectronic effect. The partial hydrogen bonding, though weak, contributes to the structural stability so that two isoenergetic gauche conformers become the lowest energy structures.

I. Introduction Polyethylenimine (PEI) and its derivatives have been used as chelating ligands for metals,' synzymes (synthetic enzymes) for complex formation with substrates,2and substances for multiaza macrocyclic metal complex formation3 They have also been used as bonding agents for solid rocket propellants with high tensile strength and el~ngation.~The monomer of PEI, ethylenediamine (EDA), is one of the most effective solvents for coal as far as the yield of the extract is concerned.s Although PEI has such special characteristics, there is little information about the conformational energy hypersurface which is essential to understand the complex formation. Since PEI is obtained by the polymerization of EDA (NH~-CH~-CHZ-NH~), the present study will focus on the structure and conformational energy hypersurface of EDA. There have been a number of studies of molecular structures of X-C-C-Y and X-C-Z-Y under changes of dihedral angles,&* where X, Y, and Z are various chemical groups with one heavy atom and hydrogen atom(s). For most of these molecules, the lowest energy conformers are anti(trans) forms, followed by gauche and cis forms. But sometimes gauche conformers are more stable than anti conformers. The structural stabilities of the molecules are closely related to various interactions such as steric and stereoelectronic effects and hydrogen bonding. But it is not known how much the steric, stereoelectronic,and hydrogenbonding terms affect the conformational energy; there is no quantitative understanding of the magnitude of those terms. Therefore, it is of significance to study their contribution to the conformational energy of EDA and to understand why a certain EDA conformer is more stable than others. Schafer et al.' and Radom et a1.* reported 10 minimum energy structures of EDA with HartreeFock (HF) calculations (using 4-21G and 4-31G basis sets). In the present paper, we investigated the conformational energy hypersurface and the origin of the structural stability of EDA at relatively high levels of ab initio theory. For this purpose, the energy hypersurface of methylamine was also studied. 11. Calculation Method

Semiempirical calculations often underestimate rotational

barrier^.^ Our preliminary calculations using semiempirical methods such as AM 1lo and PM311also underestimated rotational To whom correspondence should be addressed. Abstract published in Advance ACS Abstracts, January 1, 1994.

0022-3654/94/2098-1129$04.50/0

barriers for EDA. As the potential energy hypersurface of EDA is very complex, neither semiempirical calculations nor ab initio calculations with small basis sets are adequate to the conformational study of EDA. Therefore, we performed H F ab initio calculations using the 6-31G** basis set. Since the stereoelectronic effect is involved in mixing of bonding and antibonding orbitals, the electron correlation effect can be significant. Thus, for the study of the rough energy profile of EDA the secondorder Mdler-Plesset perturbation (MP2) calculations with the 6-31G** basisset werecarriedout at theHF/6-31G**optimized geometries, which will be denoted as MP2/6-3 lG**//HF/63 1G**. Then, to analyze the conformational energetics of EDA, full MP2 geometry optimizationsfor all the local minimum energy structures and important transition-state structures were done along with MP2 vibrational frequency analyses, which were used to obtain thermodynamicquantities. All calculations were carried out with Gau~sian92.l~ 111. Results and Discussion

(A) Methylamine. To study the structure of EDA, it is very useful to understand the conformational energetics of methylamine. As discussed by Rauk et al.,13the HF/6-3 1G** structure of the ground state is in reasonable agreement with experiment. Table 1 shows the staggered and eclipsed structures of methylamine predicted by the H F and MP2 calculations using the 6-31G** basis set, which are the minimum and transition states, respectively. Both H F and MP2 geometrical parameters of the methyl group in methylamine are similar and agree well with experiment. However, there are slight differences between the H F and MP2 results of the C-N bond length (rCN) and the geometrical parameters of amino group, which reflects the effect of electron correlation on the geometry. For the staggered conformer, Schaefer et al.14 pointed out that the restricted HartreeFock (RHF) calculation using large basis sets (e.g., QZ+2P+f) did not reproduce the experimental rCN for methylamine, while the CISD/QZ+2P predicted value of rCN (1.461 A) was close to the experimental values (1.465-1.471 A),15J6 Although the HF/6-31G** value of rCN (1.452 A) is slightly off the experimental value, the MP2/6-31G** value of rCN (1.461 A) is almost the same with the CISD/QZ+ZP result and close to the experimental value. The correction due to the potential anharmonicity would lengthen rCN in that the anharmonic correction for the water dimer lengthens the interoxygen distance ~ignificant1y.l~However, since the C-N bond is strong, the anharmonicity may increase rcN only slightly. In this sense, the 0 1994 American Chemical Society

1130 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994

Lee et al.

TABLE 1: Structures and Dipole Moments of Methylamine (CHs-NHz). rCN rcH, TCH, “H LHNH staggered (C,) HF/6-31G** HF/QZ+2Pb MP2/6-3 1G** CISD/QZ+2Pb experimentC eclipsed (C,) HF/6-3 1G** MP2/6-31G**

1.452 1.454 1.461 1.461 1.471 1.458 1.467

LHNC

LHaCHa

LHGN

LH&N

P

114.8

124.0

1.47

115.4

123.4

1.49

110.8 110.5

1.092

1.085

1.000

107.2

110.9

1.095

1.087

1.012

105.9

109.5

1.099

1.099

1.010

107.1

110.3

107.4 107.4 107.4 107.3 108.0

1.086 1.089

1.086 1.089

0.998 1.010

107.5 106.1

111.8 110.4

107.1 107.1

1.33 125.3 129.2

1.57 1.61

a Lengths in angstroms; angles in degrees; dipole moments ( p ) in debyes. Hi and Ha are in- and out-of-plane hydrogens, respectively. Hb is the bisector of the two equivalent out-of-plane hydrogens. Reference 14. References 15 and 16.

TABLE 2: Thermodynamic Energies of the Eclipsed Relative to the Staggered Methylamines AEe U

O

U

r

AGr

HF/6-31G**

MP2/6-3 1G**

2.33 1.92 1.68 2.04

2.55 2.13 1.90 2.25

3

I

I

\ \

I

I

H

Units are in kcal/mol. Here AE and AG denote the relative internal energy and free energy, respectively. The subscript r denotes the standard state of 1 atm at 298 K. The experimental rotational energy barrier is 1.98 kcal/mol.ls a

MP2 calculation predicts a reasonable r C N which is very close to the experimental value. Table 2 lists the thermodynamic quantities of methylamine. E, and EOdenote the internal energies without and with zeropoint energy (ZPE) correction at 0 K, respectively. E , is the sum of Eo and the thermal energy, and H , and G,are the enthalpy and Gibbs free energy, respectively. Here, subscript r denotes the standard state of 1 atm at room temperature (298 K). The rotational barriers (AI&) predicted by theHF/6-3 1G**and MP2/ 6-3 1G** calculations are 1.92 and 2.13 kcal/mol, respectively, which are in reasonable agreement with the experimental barrier (1.98 k ~ a l / m o l ) . ~ ~ The top inset in Figure 1 shows the rotational energy profile of methylamine which was obtained with geometry optimization for every 10’ increment of the dihedral angle ~ H C N Lfrom the eclipsed (4 = 0’) to staggered (4 = 60’) conformers. Here, L means the center of the lone-pair electron orbital lobe in the N atom. The conformational energy change (AE) varies almost linearly with cos(34). Similarly, in the bottom inset of Figure 1 the change of rCN (&N) varies almost linearly with cos(34). As a result, the ~ C isNalmost proportional to the AE. Figure 2 shows the changes of the C-H bond length (rCH) and H-C-N bond angle (OHCN) with respect to 4. The rCH and OHCN do not change linearly with respect to either cos(34) or cos 4. It is interesting to note that the maxima of r C H and OHCN appear at the staggered conformer with 4 = 180°, while their minima appear at the near staggered conformers with 60’ C 4 C 90’. This can be explained by the stereoelectronic effect1*but not by the steric effect. Namely, as the nonbonding electrons in the occupied orbital (?mb)of t h e N atom transfer partially to t h e unoccupied u* orbital of CH, the orbital interaction induces the structural and energetic stabilization. Then, it is expected that in methylamine, the r C H and OHCN vary with the overlap degree of the rnb and~U*CHorbitals. Further, from the Pauli exclusion principle the interaction of the occupied nrN orbital with the occupied UCH orbital destabilizes the molecule, while that with the unoccupied U*CHorbital stabilizes it. These interactions are likely to be responsible for the linear change of r C H with respect to COS%#J. (B) Ethylenediamine. With the basic information of the potential energy hypersurface of methylamine, we studied the conformational energies for various hydrogen orientations and dihedral angles. To specify the isomers with respect to the rotation about the C-C axis, we use the following notations, as shown in

I

I

1

0.5

I

I

0

-0.5

-1

COS(%HCNL)

0.008

I

I

I

I

5 z

8

a

-

” 1

0.5

0

-0.5

-1

cOs(3fiHCNL)

Figure 1. Conformational energy change (AE)and C-N bond length change (A& of methylamine with respect to cos(34), where 4 is the H-C-N-L dihedral angle. L denotes the lone-pair electron orbital lobe center of the N atom.

Figure 3. The symbols A (anti) and G (gauche) describe the arrangement of NH2 (or NL) about the central C-C bond. G, A, and G’ denote the cases when the N-C-C-N dihedral angles ( ~ N C C Nareabout O ~ ~ ) 60°, 180°,and 300° (or-60°),respectively. The symbols a, g, and g’ refer to the orientations of L in the N atom, for which the C-C-N-L dihedral angles are about 180°, 60°, and -60°, respectively. Taking into account of the enantiomeric conformers, the nine conformers arisen from the orientations of two lone pair electron orbitals are grouped, regardless of the dihedral angle, into four types: (1) aa, (2) ag’, ga, ag, g‘a, (3) gg, g’g’, and (4) a ’ , g‘g. The rotational energy profiles calculated with HF/6-31G** and MP2/6-31G**//HF/6-3 1G** methods are shown in Figure 4. Here, the HF calculations were carried out with full geometry optimization for the given 4, while the MP2 calculations were carried out with frozen cores at the HF-optimized geometries. From Figure 4 the steric/stereoelectronic effects of X-C-C-Y (where X or Y is N or H) appear to be much more important than other possible interactions (such as stereoelectronic effects of L-N-C-C and L-N-C-H, hydrogen-bonding interactions,

The Journal of Physical Chemistry, Vol. 98, No. 4, 1.994 1131

Methylamine and Ethylenediamine 1.096

-

1.092

5

2 1.088

I ,084

Iv/;1 / 1 I

I

(a)

I

I

1

I

I

I

I1

I

0 MP2 X HF

i 0

60

120

180

("1

~ C N L

116 I

I

I

I

I

1

I

6

114

=

.

-E

112

g 4

Y Lu

a

2

110

108

'

0

I

I

I

60

I

I

0

120

180

~ C N (") L

0

60

120

180

240

300

360

h C C N (")

Figure 2. C-H bond length (TCH) and H-C-N bond angle (@HCN) of methylamine with respect to OHCNL.

H a

A (anti) G (gauche) F w e 3. Notations used to specifyrotational isomers of ethylenediamine. The hydrogen a t o m attached to each N atom are not shown here, while the lone-pair electron orbital lobe center L of the N atom is pictorially represented in three different orientations: a, g, and g' (see text). repulsions between lone-pair electrons, and repulsions between hydrogen atoms). For all the four types of L orientations in EDA, the low energy structures appear at 4 = -60, 180, and -300°, (the structures of which will be denoted by G, A, and G', respectively), whereas the transition-state structures appear 120, and -240'. Then, the steric/stereoelectronic at 4 = -0, effects of X-C-C-Y generates 12 minima on the potential energy hypersurface, but there are only 10 minima because two types of aa and gg'are symmetric with respect to I$NCCN = Oo and 180°. For all these minima and the important transition-state structures, full MP2/6-31G** calculations were carried out with geometry optimization, and the MP2 results are listed along with the H F results in Tables 3 and 4. From these tables along with the energy profiles in Figure 4, the approximate energy barriers by the synperiplanar H-C-C-N conformation are -4 kcal/mol, while those by the synperiplanar N-C-C-N conformation are 6 kcal/

-

-

-

Figure 4. Rotational energy profiles of ethylenediaminewith respect to O~cc~byHF/6-31G** calculationsandMP2/6-31G** calculationswith frozen cores. mol. These values can be compared with the energy barrier of -2 kcal/mol for L-N-C-H in methylamine. We recall that for methylamine the &CN was linearly correlated with the AE. In EDA, the C-C bond length (rcc) increments in the transition states of 4 = 0' and 120° (or 240') with respect to the minimum energy conformers are 0.03 and 0.02 A, respectively, which are linearly correlated with their energy barriers of -6 and -4 kcal/mol, respectively. The oscillating curves of rcc in Figure 5 are related to the stereoelectronic effect. The rcc is shorter in the staggered conformer than the eclipsed conformer. The difference in rcc between the curves of aa, ag', gg, and gg'is rather consistent (or almost constant except for few special cases) regardless of thevariation of 4, because the strength of the stereoelectronic effect does not change much by the rotation about the C - C bond. Since for type aa, both L's areantiperiplanar to the central C-C bond, the C-C bond lengthens most effectively. For type ag', the number of L's which are antiperiplanar to the C-C bond is 1, while for types gg and gg' the numbers are 0. Therefore, aa has the longest rcc, followed by ag', and then followed by gg and gg'. Namely, the rcc for aa and ag' are longer than those for gg and gg'by -0.01 1 and -0.006 A, respectively. The C-C bond lengthening does not change the conformational energy significantly. This supports that for methylamine the ~ C isNdirectly correlated with the AE,while the &CH is not. Further, owing to the Pauli exclusion principle, the repulsion between two CCN orbital electrons at both ends of N-C-C-N disfavors the synperiplanar conformation. Thus, for the eclipsed conformer in which the H atom is synperiplanar to the N atom, both AE and rcc have their maximum values, while for the staggered conformer (4 = f 6 0 or 180') in which the H atom is antiperiplanar to the N atom, both of them have their minimum values. In addition, for H-C-C-N (or N-C-C-N) the UHC (or U N C ) electrons transfer partially to the periplanar U*CN orbital, while the UCN electrons transfer partially to the C*HC(or U*NC)

1132 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994

Lee et al.

TABLE 3 Structures, Relative Thermodynamic Quantities, and Dipole Moments of 10 Minimum Energy Conformers of Ethylenediamin@ aGg‘

gGg‘

gGg

aGa

aAg’

gAg‘

gAg

aAa

aG’g’

gG’g

0 0 0 0 1.528 1.450 1.456 60.2 2.51

-0.02 0.03 0.01 0.06 1.522 1.450 1.457 64.5 2.03

0.54 0.64 0.67 0.98 1.522 1.457 1.457 57.0 0.30

1.49 1.28 1.31 1.63 1.532 1.452 1.452 61.0 0.50

1.18

1.04

1.16

1.28

3.69

1.528 1.45 1 1.452 180.0 2.45

1.522 1.454 1.454 180.0 0

1.522 1.453 1.453 180.0 2.00

1.08 0.80 0.90 1.16b 1.532 1.451 1.451 180.0 0

1.527 1.452 1.455 -59.6 2.46

1.525 1.451 1.451 48.4 1.80

0 0 0 0 1.525 1.458 1.464 58.1 2.62

0.15 0.18 0.16 0.21 1.518 1.458 1.466 63.4 2.12

0.65 0.78 0.80 1.15 1.518 1.465 1.465 54.8 0.28

1.33 1.20 1.21 1.57 1.530 1.461 1.461 59.9 0.41

1.88

2.08

2.24

1.43

4.15

1.524 1.460 1.461 178.8 2.48

1.518 1.463 1.463 180.0 0

1.518 1.462 1.462 180.7 2.08

1.523 1.460 1.464 -57.8 2.52

1.520 1.460 1.460 45.1 1.75

HF/6-31GS*

me m 0

mr AGr

rcc rCN ~NCCN

P

MP2/6-31G**

me m 0

A& AGr

rcc rCN

~JNCCN P

1.31 1.12 1.21 1.47b 1.529 1.460 1.460 180.0 0

Energies are in kcal/mol; dipole moments ( p ) in debyes; bond lengths ( r ) in angstroms; dihedral angles (4) in degrees. AE and AG are the relative energies with respect to the aGg’. Owing to the chirality/achirality, the AG of aAa relative to aGg’ was raised by 0.04 kcal/mol. (I

TABLE 4: Selected Activation Barriers between Two Minimum Energy States and the Transition-State Structures of Ethylenediamines aGa aAa aGg’ aAg’ gGg gAg gGg’ gAg’ aGg’

-

-

-

-

-

4.31 4.18 1.552 1.454 1.454 118.4

5.47 5.26 1.546 1.452 1.457 119.9

4.82 4.47 1.540 1.457 1.457 120.7

5.02 4.85 1.539 1.456 1.457 121.4

3.02 2.65 1.526 1.458 1.454 59.0

4.94 4.72 1.549 1.462 1.462 118.5

6.06 5.80 1.541 1.461 1.466 119.5

5.44 4.98 1.535 1.466 1.466 122.3

5.49 5.26 1.533 1.465 1.466 122.1

3.37 2.99 1.522 1.467 1.462 56.8

gGg’

HF/6-31G** b

e

u

0

rcc rCN (~NCCN

MP2/6-31G** M

e

m 0

rcc rCN

~JNCCN Energies are in kcal/mol; bond lengths (r) in angstroms; dihedral angles (4) in degrees. 1.57

I

I

-A-

aa

1.56

- 1.55

‘5 0

co

1.54

1.53 1.52

0

60

120

180

240

300

360

h C C N (”)

Figure 5. C-C bond length (rcc) vs ~ J N C C Nfor ethylenediamineby HF/ 6-3 1G** calculation.

orbital. Thus, the stereoelectronic effect on the EDA conformation is consistent with the recent Schleyer et al.3 reportIg that the rotational barrier of H3X-XH3 (where X is one of C, Si, Ge, Sn, and Pb) arises from the stereoelectronic effects, but not from the so-called steric effects. However, it is suggested that the steric effect is related to the fact that the average conformational energy of EDA for Cp = Oo is -2 kcal/mol higher than those for Cp = 120° and 240’. As can be noted from Table 3 which lists the structures, energetics, and dipole moments of the ten minima, the important

low-lying energy minima are aGg’, gGg’, gGg, aGa, and aAa. The lowest energy conformers are aGg’ and gGg’which are nearly isoenergetic, followed by gGg which is -0.6 kcal/mol higher in energy than aGg’. The potential energy barrier from aGg’ to gGg’ is -3 kcal/mol (Table 4). The two nearly isoenergetic structures of aGg’ and gGg‘ are depicted in Figure 6. The two structural parameters can be averaged in order to compare with the experimental For the two MP2-predicted structures the average Cp value is 6 1O , which is in good agreement with gas electron diffraction experiment (64 f 4°).z0 The average rcc and rCN are 1.522 and 1.462 A, which are close to the 4-21G results by Van Alsenoy et al.’ but slightly shorter than the experimental valuesz0 of 1.545 f 0.008 and 1.469 f 0.004 A, respectively. Alsenoy et al. speculated that their prediction of rcc shorter than the experimental value might arise from the difficulty that the C-C and C-N bond lengths were not separately resolved for EDA vapor at 50-120 OC by the gas electron diffraction experiment. The intermolecular hydrogen-bonding effect plays a significant role for the structure and energetics of EDA. It is well-known that a strong hydrogen bonding forms in a collinear structure of NH-LN in which the distances of H.-N and N-N are 1.9 and -2.9 A, respectively. In Figure 7 the distance N-H and angle BN ...H-N with respect to 4 clearly show that the hydrogen bonding forms around qj = -609 for ag’ and Cp = -f60° for gg’. Type aa cannot form a hydrogen bonding at any Cp, because the N-H distance is larger than 2.7 A. For W O O < Cp < -60°, type

-

The Journal of Physical Chemistry, Vol. 98, NO. 4, 1994 1133

Methylamine and Ethylenediamine

7 1 015

,\\\\\\\

QNCCN =

58.1

1.013

1.015 1.458

1.091 1.525

1.098 1.093

aGg'

1.013

h.9 1.518

1.091 \,#'

09,&.466

C -k'

/

,.,....'

\

1.100

1.096

Figure 6. Two nearly isoenergetic structures of ethylenediamine predicted by MP2/6-31G** calculations. Bond lengthsandanglesare in angstroms and degrees, respectively. 4.5

I

I

I

I

I

4.0

-

5 m

-

3.5

C

3.0

T

'

2.5

2.0

I'

0

I

I

I

I

1

I

60

120

180

240

300

360

I

I

CNCCN (") 110

,

I

I

I

I

100

-m

$

repulsion between hydrogen atoms appears in conformers of aa (4 = 0,60, d o o ) , ag' (4 = 0, -60°), gg (4 = 60°), and gg' (4 = 00). To find the magnitude of the various types of interaction energies, let EHB,EHH,and ELLdenote the interaction energies of the hydrogen bonding (HB), the repulsion between hydrogen atoms (HH), and the repulsion between lone-pair electrons (LL), respectively. If each of these interaction energy terms contribute to the conformational energy to a certain extent, the value does not depend on conformation seriously because of similar structural environments (except for gGg). Then, we study the conformationalenergetics firstbasedon theHF/6-31G** energiesinTable 3 (along with the energy profiles in Figure 4). The conformational energies of the ten minima are in the following order: Ea~,'(HB) z EgGg,(HB) < E~Q(--HB,HH) < E a A a EaAa' c E g A g < Eaca(HH) = EaGfgf(HH)