The anomeric and reverse anomeric effect. A simple energy decomposition model for acetals and protonated acetals F. GREIN Department of Chemistry, University of New Brunswick, Fredericton, N.B., Canada E3B, 6E2 AND

P. DESLONGCHAMPS Department of Chemistry, University of Sherbrooke, Sherbrooke, Que., Canada JIK 2RI

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Received August 7 , 1991 This paper is dedicated to Professor Zdenek (Denny) Valenta on the occasion of his 65th birthday F. GREIN and P. DESLONGCHAMPS. Can. J. Chem. 70,1562 (1992). Geometry optimizations at the 6-31G"" level were performed on various conformers of XH,,,CH,YH,, and XH,,,cH,YH,,+,+ (protonated), with X, Y = N, 0. The resulting anomeric stabilization energies were decomposed into steric, electrostatic (lone pair - lone pair, lone pair - hydrogen), and electronic contributions. Using approximate values for steric and electrostatic terms, the electronic energy was determined to be about -2 kcal/mol for the anomeric effect to arise from 0 , and -2.5 kcal/mol if it arises from N. For protonated systems, an additional energy term for the reverse anomeric effect had to be added, having a value of -4 kcal/mol for 0 in OH-CH,-NH3+ and -5 kcal/mol for N in NH2CH,-NH,+. The anomeric effect due to N drives NH2-CH,-OH2+ to a charge-dipole complex of the type NH,=CH,+. . .OH,. The energy parameters obtained have been applied to predict relative stabilities of various conformers of methanetriol, aminomethanediol, and protonated methanetriol, with good success. F. GREIN et P. DESLONGCHAMPS. Can. J. Chem. 70,1562 (1992). On a effectuC des optimisations de gComCtries, au niveau 6-31G'M,pour divers conformitres de XH,,,CH,YH,, et XH,,,CH,YH,,+,+ (protonCs) dans lesquels, X, Y = N, 0 . Les Cnergies de stabilisation anomCriques qui en rCsultent ont CtC dCcomposCes en contributions stCriques, Clectrostatiques (paire libre/paire libre, paire librelhydrogitne) et Clectroniques. Utilisant des valeurs approximatives pour les termes stCriques et ~ l e c t r o ~ t a t i ~ uon e sa, dCterminC que-l'~nergieClectronique de l'effet anomkrique est d'environ -2,O kcal/mol s'il est dCi a l'oxygitne et d'environ -2,5 kcal/mol s'il est dfi 21 l'azote. Pour les systkmes protonCs, on a dfi ajouter un terme additionnel d'knergie pour I'effet anomCrique inverse; sa valeur est de -4 kcal/mol pour 0 dans HO-CH,-NH3+ et de -5 kcal/mol pour N dans NH2-CH,-NH3+. L'effet anomCrique dC au N force le NH,-CH,-OH,+ vers un complexe de charge dipolaire du type NH,=CH,+. . .OH,. On a appliquC les paramktres d'Cnergie obtenus pour prCdire avec succks les stabilitCs relatives de divers conformkres du methanetriol, de 1'aminomCthanediol et du mkthanetriol protonC. [Traduit par la rCdaction]

Introduction A vast amount of literature, both experimental and theoretical, has appeared on the anomeric effect. Suitable reviews can be found in the books by Deslongchamps ( I ) and Kirby ( 2 ) , and in the review article by ~ o r e n s t e i ~ ( 3 ) . It has been known for a long time that quantum chemical calculations are quite capable of reproducing the experimental findings on stabilization energies and geometry changes (4). Many theoretical studies have been performed on large systems, of immediate interest to the organic chemist, as well as on small model systems such as simple acetals and simple esters. The ease and speed of computations on small systems allows for systematic investigations into the nature of the anomeric effect. In this paper, a model will be presented for decomposing the anomeric stabilization energy as obtained from ab initio calculations into components based upon familiar terms like steric, electrostatic, and electronic energies. In the literature, several energy decomposition schemes have appeared. Smits et al. ( 5 ) considered anti and gauche conformers of systems XH,,,CH,OH, with X = F, 0 , N, C. Using localized nonorthogonal molecular orbitals (MO), they write the one-electron density as a sum of quasi-classical, interference, and charge-transfer terms, and decompose the energy correspondingly. In this scheme, the anomeric ef-

fect is found to result mainly from XCH,O interference interactions, in particular from a weakening of the destructive CX-CO interference as the electronegativity of X increases. Reed and Schleyer (6, 7) used the concept of natural bond orbitals (NBO) for an analysis of the energy stabilization as well as geometry changes. By checking the occupancy of the n and a * localized orbitals, the significance of n + a * negative hyperconjugation to the anomeric stabilization can be checked. Furthermore, by deleting in the Fock matrix the matrix element corresponding to n + a * , the calculated increase in energy can be taken as a measure of the energetic stabilization due to the n + a * interaction. A detailed study of FSNH, with NBO's shows that the n, + as,* hyperconjugation can account for the very strong anomeric effect in this system, as well as in others. Wiberg and Murcko (8) estimated for 0CH3-CH2-OCH3 (DMM) a quantity corresponding to the lone pair - lone pair (lp) repulsion (notation of this paper) to be 1.4 kcal/mol, by calculating energy differences between corresponding conformers of methyl propyl ether. From this, the anomeric stabilization energy of DMM, corrected for lp-lp repulsions, is calculated to be 4.7 kcal/mol. Energy decomposition schemes can be developed in two ways. Either highly accurate energy terms (depending on the model) are obtained for one particular system, or average parameters are developed that fit a class of systems. In the

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C A N . J . CHEM. VOL. 70. 1997

TABLEI . Energy differences AE in kcal/mol for neutral systems, relative to most stable conformer, obtained by 6-3 lG*:" geometry optimizations

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XH,,,-CH2-YH,,

OH-CH2-OH

OH-CH?-OCH,

16 when only the 180" component of the energy is considered. (The 90" component V,, corresponding to the electronic part of the anomeric energy, and the 60" component V,, corresponding to the repulsion between the rotating H with the three bonds on C, have been separated out). For the s-OH-CH,-OH system, V, = 3.82 kcal/mol (15). Starting from structure l b , in the first case the 180" rotation results in two lp-lp repulsions ( l a ) , being 4.69 kcal/mol less stable than l b , whereas in the second case the rotation results in in-plane H-H repulsion, being 3.82 kcal/mol less stable than 16. These data show that the lp-lp and H-H repulsions are of similar magnitude. Therefore, the assumption r = I = I kcal/mol will be made, such that 1 + r 2 kcal/ mol as required.

In the following, the electronic component of the anomeric stabilization energy will be deduced for the systems investigated. In all cases, the above values of the parameters for steric and electrostatic effects will be retained. It is not the purpose of this work to optimize the values of the energy parameters for each individual system, but to allow for enough flexibility such that the energy decomposition model has predictive qualities.

4. Results and energy analysis for neutral systems In Table 1 , the calculated (6-3 lG**) energy differences are given for the neutral systems XH,,,-CH,-YH,,, with X, Y = 0 , N. The various conformers, designated by the notation 0 ae, 1 ae, and 2 ae, are shown in Fig. 1. In Table 2 , the optimized CO and CN distances are given. Using MP2/ 6-3 1G** geometry optimizations on OH-CH,-OH, the AE values are (in kcal/mol) 9.19 for 0 ae, 4.48 for 1 ae, and 0 for 2 ae, while the CO distances are (in A) 1.402 for 0 ae, 1.391 and 1.415 for 1 ae, and 1.406 for 2 ae. For the pur-

OCH,-CH2-0CH3

NH2-CH?-NH2

NH2-CH2-OH

pose of the general energy model to be applied here, the differences in AE between MP2 and RHF optimizations are of little significance. Bond distances generally increase when electron correlation is added to RHF wavefunctions that have polarization functions in the basis set. Table 1 shows that for all neutral systems the most stable conformer is 2 ae (AE = 0), while 0 ae is the least stable, as one would expect. However, there are large differences in AE (0 ae). While AE(0 ae) is about 8 , 7 , and 5 kcal/mol, for systems with OH or OCH,, it is only 0.82 kcal/mol for NH2-CH,-NH,. It will be shown that such huge differences in the 0 ae energies can be explained by steric and electrostatic effects, while the electronic components for anomeric stabilization are virtually the same in all cases. In Table 3, the energy analysis for the neutral systems is presented. For OH-CH,-OH, the 0 ae conformer has 2 lone pair repulsions (21), whereas 2 ae has 2 hydrogen bonds (2h) in addition to 2e from the two anomeric effects. Using 1 = 1 and h = - 1 kcal/mol, one obtains e = -2 kcal/mol. On the other hand, for NH,-CHI-NH,, the 0 ae conformer has 2h, whereas 2 ae has 2eN + 21.. Using I = I. = -I1 = 1 kcal/mol leads to eN = -2.5 kcal/mol. In the process of going to the favorable conforination 2 ae, the electrostatic effects destabilize whereas the electronic effects stabilize the molecule. In balance, there is only a small energy gain of 0.82 kcal/mol between 0 ae and 2 ae. For the mixed system NH,-CHI-OH, the previously obtained energy parameters, with eo = -2 and eN = -2.5 kcal/ mol, predict the calculated energy differences within 0.5 kcal/mol. This is the first successful test of the model. Tables 1 and 3 also contain results for the methoxy compounds OH-CHI-OCH1 and OCH,-CH,-OCH,. Whereas the 1,3-diaxial H-lp interaction was energy lowering (h = - 1 kcal/mol), a corresponding CH,-lp 1,3-diaxial interaction is not expected to be. Therefore, in comparison with the OH compounds, the parameter h is omitted from the energy formula for OCH,. This explains nicely why the 0 ae energy drops from 8.35 to 6.78 to 5.30 kcal/mol as one moves across the top of Table 1 from the hydroxyl to the methoxy compounds. It also provides justification, as mentioned earlier, for the introduction of the energy parameter h, with an approximate value of - 1 kcal/mol. For neutral systems, the energy decomposition model gave values for the electronic parameter of -2 kcal/mol for OXygen, and -2.5 kcal/mol for nitrogen.

5. Results and energy analysis for protonated systems In Tables 4 and 5 , AE values and optimized bond distances are given for the various conformers of the protonated systems, as shown in Fig. 2. For the protonated systems XH,,,-CHI-YH,,, ,+, geometry optimizations often lead to unusual structures, mostly caused by the desire of the sys-

GREIN A N D DESLONGCHAMPS

I

XHm-CH2-YHn

H

OH-CHZ-OH

i

,

\ N

x

H

/H3

N.

4 ::;; 4 %

Hz

H4

H

NH2-CH2-OH

H'

\N

x.

Hz

HI

4 :2;4 .:

0N

?a.

Hz

Hz

QN Hz

x

H

.,"

H,

...'

Hz

/ :;-> 4 Hz

Hi

4 . kH3

H4

. Xo ,.+

IH ~ l \ 3 N

0

%

N

4%

H4

X4::-,

"';

.a

xo

/H3

4 '.., 4

O

/ =- 8

H,

N

H

0

00

p

0N

p /H3

.*+

/HZ 0

"1

H

H'

2 ae

cl .. 4;;: 4 4 T-.-..'

NHz-CH2-NH2

I

1 ae (Y)

.,&

I

' 0

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1 ae (X)

O.*

QN

3

H3

0

4%

Hz

Hi

8 . kH3

FIG. 1 . Conformers of OH-CH2-OH,NH2-CHI-NH2,and NH2-CH2-OH,corresponding to 0, 1 , and 2 anomeric effects. See text for details. TABLE 2. Optimized C-X

XH,,,-CH2-YH,,

and C-Y

OH-CH?-OH

(X, Y = N, 0) bond distances in OH-CH2-OCH,

tem to move towards a charge-dipole complex, but unable to do so due to fixed dihedral angles for one XH,,, and one YH,,,, hydrogen, as are required for defining the conformation. The resulting energies also reflect unusual stabilization~, and are not suitable for an energy analysis. Therefore, the results of Tables 4 and 5 were obtained for a "restricted series" of optimizations, where the dihedral angles of all XH,,, and YH,,,, hydrogens have been frozen at 0 or 2 120°, according to the diagrams in Fig. 2. Table 4 shows that for the systems OH-CH2-OH,+ and NH,-CH2-OH2+,the 2 ae conformer is no longer the most stable one. Similarly, for NH,-CHI-NH,+ and OH-CH2NH,', unexpected situations occur. They will be discussed in the light of the energy decomposition scheme. For the energy analysis of the protonated systems, the parameters r, I , and h will be used again. For a start, they

A for neutral systems. Basis set 6-31G:%*

0CH3-CH2-OCH,

NH2-CH2-NH2

NH2-CH2-OH

are retained at the values 1 and - 1 kcal/mol, as before. Also, the electronic energy component e will be given the same values as before, -2 kcal/mol for anomeric stabilization due to a lone pair on 0 , and -2.5 kcal/mol due to a lone pair on N, except in the case of complex stabilization. Lone pairs on 0' (these are only formal charges, and do not imply actual positive partial charges on 0) are expected to be weaker, and the electronic parameter eoj will be determined by comparison with the ab initio energies. Table 5 shows that two conformers of NH,-CH2-OH2+,1 ae(N) and 2 ae, optimized to charge-dipole complexes, with CO bonds of 2.381 A, and associated large stabilization energies ( 13 to 15 kcal/mol relative to 0 ae). The energy decomposition scheme is given in Table 6. A choice of 0 for e,+ of OH-CH~-OH,+gives AE values close to the ab initio values for this system, with a maximum de-

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C A N . J. CHEM. VOL. 70, 1992

TABLE 3. Energy decomposition for neutral systems. Energy parameters are I- for H-H repulsion, 1 for Ip-lp repulsion, h for internal hydrogen bonding, and e for electronic energy stabilization due to the anomeric effect. Given is the energy formula (first line), the values for the energy parameters (second line), and the relative energies AE according to this model, with the ab irzitio values of Table 1 in parentheses (third line). All energies in kcal/mol

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0 ae

OH-CH2-OH

OH-CH2-0CH3

0CH3-CH2-OCH,

NH2-CH2-NH2

NH2-CH2-OH

21 2 8(8.35)

21 2 7(6.78)

21 2 6(5.30)

2h -2 l(0.82)

h+l -1 + 1 4.5(5.06)

TABLE 4. Energy differences AE in kcal/mol for protonated systems, obtained by 6-31G** geometry optimizations. Restricted series (see text) XH,,,-CH*-YH,,+

OH-CH2-OH2+

NH2-CH2-OH2+

TABLE 6 . Energy decomposition for protonated systems. Energy parameters and format of table same as in Table 3. Parameter ZJ for reverse anomeric effect XH,,,-CH2-YH,,+

OH-CH2-OH2+

NH~-CH~-OH~+

0 ae 1 ae Inverted

TABLE 5. CX and CY distances (in I\) for protonated systems. Basis set 6-3 1G**. Restricted series XH,,,-CH~-Y H,,+

0 ae I ae Inverted

OH-CH2-OH2+

NH2-CH2-OH2+

1.424/1.513 1.401/1.561 1.427/1.513

1.365/1.501 1.350/ 1.534

viation of 0 . 8 kcal/mol. For NH,-CH,-OH2+ a charge-dipole complex is obtained whenever the lone pair on N is app to C O . Therefore, the parameter eN has to be reevaluated. Using e,+ = 0 , eN is found to be - 15 kcal/mol, reflecting the large complex destabilization. Omitting in the formula h r for 1 ae(X) and 2 r for 2 ae, due to the large C O dis-

+

+h -5 - 1 -5.5(-5.62) ZIN

Inverted

tance in NH2-CH,-OH2+,changes the prediction for 2 ae to 0 kcal/mol from 2 . A special situation is encountered for NH,-cH,-NH~+. When optimizing the 1 ae conformer, starting with dihedral angles of 2120" for the NH, hydrogens (relative to

GREIN AND DESLONGCHAMPS

1 ae (X)

XH,-CH2-YH,,,

1 ae (Y)

i

x+O

Qo

4% 4 %

4;;:: 4F.. "" Can. J. Chem. Downloaded from www.nrcresearchpress.com by MICHIGAN STATE UNIV on 01/24/17 For personal use only.

$

H1

8

\

HI

'

Hz

H,

N

N.

N

Hz

O.

H3

4;;;.

OH-CH~-NH~+

2 ae

H

O H - C H ~ - O H ~ + Hi

NH2-cH2-NH3+

I

H5

4

Hl N

0 ?., I s% 5.'

NH~-CH~-OH~+

H3

'44

H1

0

H,

H4

0

FIG.2. Conformers of OH-CH2-OH2+, NH2-CH2-NH3+, OH-CH2-NH3+, and NH2-CH,-OH2+, corresponding to 0, 1, and 2 anomeric effects. See text for details.

Z-C-N, structure 4a), the NH, group inverts, leading to structure 4b, which is 5.62 kcal/mol more stable than 4a. Situations where the expected anomeric stabilization does not take place, and another conformer is more stable, have been referred to as the "reverse anomeric effect" (rae). Lemieux and Morgan (16) and Lemieux (17), who introduced the term reverse anomeric effect, discovered that in certain pyridinium glycosides the pyridinium group acquired equatorial rather than the expected axial position, contrary to the predictions for the anomeric effect. They attributed this exceptional behavior to destabilizing electrostatic effects arising from a positively charged atom (usually N) in axial orientation at the anomeric center. In the spirit of the present model, one may attribute the increased stability of 4b over 4a to the proximity of the lone pair on N to the positive charge on NH,', which supersedes the stabilization due to the antiperiplanar lone pair. It is known that a-pyridinium glycosides prefer to exist in the twist-boat rather than the chair conformation. Using our model, this unexpected behavior, referred to as the reverse anomeric effect, is simply rationalized by the fact that there is maximum electrostatic attraction between the ring oxygen lone pairs and the equatorially oriented pyridinium group when the tetrahydropyranyl ring adopts the twist-boat conformation. For the energy analysis, a new parameter v is required (11 for reverse ae). For NH,-CH,-NH,', AE betwen 0 ae and 1

ae is well explained with e N = -2.5 kcal/mol. For the inverted structure, however, a value of vN = -5 kcal/mol is needed to fit the a b initio energies. The system OH-CH,-NH,' is clearly in favor of the reverse ae, having 0 ae more stable than 1 ae. Retaining eo as -2 kcal/mol leads to vo = -4 kcal/mol, again showing that the rae stabilization exceeds the ae stabilization by a significant amount. Obviously, it will be interesting to investigate changes in bond distances and atomic charges due to the reverse anomeric effect. Such items, however, exceed the scope of the present paper, which deals exclusively with the energy model, and will be referred to future publications.

6. Application of energy decomposition model to methanetriol and aminomethanediol Figure 3 shows optimized C-0 distances for six of the seven conformers of methanetriol that can be formed by having a lone pair or hydrogen of one OH group antiperiplanar to one of the other C-0 bonds. In the triangular diagrams (see structure 5 as example) a lobe on O,, lined up with the line 0,-On, indicates that a lone pair on 0, is antipenplanar to 0,. A short line on O,, lined up with 0,-Oc, would indicate a hydrogen on 0, being antiperiplanar to COc. The second lone pair on 0, is shown pointing to the inside of the triangle, towards C. For this lone pair, 0-lp is

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CAN. J. CHEM. VOL. 70. 1992

FIG.3. Schematic diagrams of CH(OH),, showing 6 of the 7 conformers having a lone pair or hydrogen on 0 arzti relative to the other CO bond. The conventions are explained in text and structure 5 .

TABLE7. Energy decomposition for various conformers of methanetriol. Energy difference AE in kcal/mol, obtained from formula, and comparison with ab irutio values AE,,,, (4-3 1G) Structure

Formula

AE

AE"

AE,,,,,

anti to CH. In this way, the triangular diagrams uniquely define the conformations of CH(OH), for the purpose of the present analysis. The number labelling the diagrams in Fig. 3, e.g., 4 in 4A, gives the number of anomeric effects, whereas the letter corresponds to an (arbitrary) sequence of conformations. In the diagrams of Fig. 3 (and following figures) the three CO distances are shown. The lone pairs or hydrogens on the inside of the triangle have been omitted to allow for lines connecting 0 with C.

In Table 7, an energy analysis equivalent to the one performed on methanediol is applied. For example, for structure 5 (4B of Fig. 3) there are four ae's (4e), four internal hydrogen bonds (4h), and two Ip-lp repulsions (21). Using e, = -2 kcal/mol, and 1 = r. = -h = 1 kcal/mol, as before, leads to the prediction that structure 4A, 4B, or 5A should be the most stable one (column "AE").In the last column of Table 7, the ab initio energy differences (4-3 1G basis set) are given. It is seen that 4B is most stable, and that

GRElN A N D DESLONGCHAMPS

!

,

1

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i

!,

2A --

I

-

..

28

-~

~

.

~

U

j .-

~

. ..

3D

38 .-.-

--

I

.~~

..

-

!

i

4A i

I

FIG.4. Schematic diagrams of CH(OH)?NH2,showing 6 of the 15 conformers having a lone pair or hydrogen on 0 and N n11tito other CO or CN bond. For conventions see text and structure 5. TABLE8. Energy decomposition for various confor~ners of CHNH2(OH)2.Energy differences AE in kcal/niol, obta~nedfrom formula, and comparison with nb initio values AE,,,,, (3-2 1G) Structure

Formula

AE

AEdhln

4A and 5A differ by 1-2 kcal/mol from 4B. In general, AE,,,,,,is larger than the formula value, the largest deviation (3.27 kcal/mol) occumng for structure 6A. In this case, the 3 r , the maximum number of repulformula contains 31 sion terms. From this, an adjustment of the formula values of 1 and r, from 1 to 1.5 kcal/mol, is suggested, in order to achieve better agreement between AE and AE,,,,. Adjusted formula values, AE:':,also given in Table 7 , show a marked improvement. Now the largest deviation occurs for 4A, which has the same formula as the most stable structure 4 B , and does therefore not benefit from a change of the repulsion parameters. Intuitively one expects repulsion on the more crowded methanetriols to be higher than in the corresponding methanediols. An adjustment of the repulsion parameters from 1 to 1.5 kcal/mol may not be necessary for 6-3 lG4' energy differences (assuming 6-3 IG* geometry optimizations), since 6-3 1G" energy differences are usually smaller than corresponding 4-3 1G (or 3-21G) values. For lack of computer resources, only 4-31G optimizations were performed on methanetriol. Single point calculations in 6-3 1G"'" using the 4-3 1G optimized geometries (6-3 lG""/ /4-31G), gave energies that were found less suitable for interpretation. Many other adjustments and refinements to the parame-

+

1570

CAN. J. CHEM.

TABLE9. Energy decomposition for various conformers of protonated methanetriol. Energy differences AE in kcal/mol, obtained from formula, and comparison with nb irzitio values AEabin (4-31G)

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Structure

Formula

AE

AE,,,,

ters, and to the formula, have been tried. For example, one might distinguish between "outer" and "inner" I, r, and h interactions, where ,"outern and "inner" are most easily defined by inspecting structure 5. However, it is important to retain the simplicity of the formula, and to have steric and electrostatic parameters as general and transferable as possible. As another example, aminomethanediol may be investigated. There are 15 conformers having a lone pair or hydrogen antiperiplaner to another CX bond. Figure 4 shows six of them. A simple energy analysis, with eo = 2, e , = -2.5, 1 = r = 1.5, and h = - 1 kcal/mol, predicts structure 3D to be most stable (Table 8). Indeed, this was found to be the case. Structure 2A is predicted to be least stable, again to be confirmed. Table 8 gives calculated AE values (3-21G basis set) and the formula for the energy analysis together with the predicted AE value. The agreement is quite satisfactory. Details for systems CHNH,(OH),, as well as CH(NH2),0H and CH(NH,),, will be published elsewhere.

7. Application of energy decomposition model to protonated methanetriol In Fig. 5 six of the 15 conformers of CH(OH)?OH2+are shown, where again either a lone pair or a hydrogen is app to one of the other C-0 bonds. The C-0 bond distances, optimized with the 4-31G basis set, are given. In Table 9 the energy formulae, as well as AE's obtained values (4-31G), are given. The from the formula and AEabin standard parameters for triols, e , = -2, eo3 = 0 , h = - 1, and 1 = r = 1.5 kcal/mol have been used. While the largest deviation between AE and mabin is 4.3 kcal/mol (2C), most AE's agree within 1-2 kcal/mol. Structure 3B has the lowest ab initio energy, predicted at 1.5 kcal/mol by the formula, while 4A has the lowest predicted energy, at 1.72 kcal/mol by nb initio calculations. For a simple energy decomposition model as applied here, the predictive ability is judged to be quite satisfactory. As was noticed for protonated methanediols, energy predictions for protonated systems are much more difficult to perform than for neutral

systems. Special situations would arise in cases of the reverse ae and of charge-dipole complexes. Details on protonated triols, and on other protonated systems of the type CH(OH),,,(NH,),,H', with m n = 3, will be published elsewhere.

+

8. Discussion In the energy decomposition scheme presented in this paper, approximate energy parameters have been used in order to decompose anomeric stabilization energies for compounds XH,,,-CH,-YH,,, with X, Y = N, 0. After deducting steric (H-H interactions) and electrostatic (Ip-lp and lp-H interactions) terms from the stabilization energies, electronic components are left, having values of 2 for 0 and 2.5 kcal/mol for N, and acting towards stabilization of the gauche over the anti conformer. The larger stabilization energy of N, compared with 0, is explained by N being a better electron donor than 0 , and OH being a better leaving group than NH,. Frank ( 18) placed the experimental value of the anomeric stabilization energy (electronic part) for 0-alkyl systems at a minimum of 2.1 kcal/mol, whereas a previous estimate by Deslongchamps et al. (19) gave a minimum of 1.4 kcal/mol. Wolfe et nl. (20) found a theoretical value of 2.8 kcal/mol. A new theoretical interpretation of the reverse anomeric effect is offered. For the first time, to the best of our knowledge, estimates have been obtained for the energy stabilization due to this effect. The systems OH-CH~-NH,+and NH,-CH2-NH,+ prefer comformations where the lone pair on 0 or N is not app to CN' but is located in the proximity of the (formal) positive charge on N. Apparently, the lp-N' electrostatic attraction exceeds the desire of lp delocalization, corresponding to the regular anomeric effect. The energy parameters 11 for the reverse anomeric effect are found to be -4 for the OH, and - 5 kcal/mol for the NH2 system, twice the amounts obtained for the respective anomeric stabilization energies. In an investigation into the nature of the anomeric effect, Grein and Deslongchamps (15) studied the systems XH,,,CH,-OH, with X = F, 0 , N, and C . For a given conformation of XH,,,, the OH group was held at dihedral angles of 0°, 60°, 90°, 120°, and 180". By Fourier analysis, and by comparison with properties of the CH,=OH+ cation, it could be shown that anomeric stabilization for X = F and 0 is T driven, whereby the CH2-OH portion of XH,,,-CH2-OH is trying to assume the optimal structure of CH2=OH'. For X = N and C, however, the OH gauche conformer is no longer the most stable one, and there is no anomeric stabilization due to the lone pair on oxygen. A similar analysis has been performed for systems XH,,,-CH,-NH, and for the corresponding protonated systems with OH or NH, rotation (to be published). The energy parameters obtained by Fourier analysis can be roughly classified as electronic, steric, and electrostatic, and therefore some relation can be obtained with the energy parameters of the present paper (the terms are not identical). It should be emphasized again that the energy parameters used in this work are approximate, designed to cover a wide range of compounds rather than one compound accurately. Applications to methanetriol and protonated methanetriol, as well as to aminomethanediol, allow for predicting the energies of all arzti conformers (lp or H in arlti position relative to other CO or CN) with reasonable accuracy. Adjustment of the repulsion parameters 1 and r- from 1

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GREIN A N D DESLONGCHAMPS

FK. 5. Schematic diagrams of CH(OH)@H2', showing 6 of the 15 conformers having a lone pair or hydrogen on 0 nrzti to other CO bond. For conventions see text and structure 5 . to 1.5 kcal/mol improves the agreement. Such increase either reflects the increased repulsion in triols over diols, or is due to the lower level basis sets used for calculations on the trio1 systems (or both).

9. Summary and future work A simple energy decomposition scheme, as proposed earlier by Grein and Deslongchamps (21), has been developed. In this scheme, the anomeric stabilization energies for acetal and protonated acetal-type systems XH,,,-CH,-YH,, and XH,,,-CHI-YH,,,+,+,with X, Y = N, 0, are decomposed into steric (H-H), electrostatic (H-lp and Ip-lp), and electronic tenns. The validity of this model, which is easy to use, has been tested by application to methanetriol and protonated methanetriol, with good success. The important energy parameter is the electronic energy of anomeric stabilizat~on, calculated by subtracting steric and electrostatic terms from the total energy of stabilization as obtained from ab initio calculations. The electronic energy is the basic underlying driving force in anomeric stabilizations, and has indeed been found to be very similar for all systems studied, even if the total energies of stabilization differ by large amounts. For protonated systems, the anomeric effect may be so strong that the molecule separates to form a charge-dipole

complex. In such cases, the (formal) electronic energy of stabilization is very large. For two of the protonated systems studied here, the confom~ationexpected to be the most stable one was found to be less stable than a conformation allowing the lone pair(s) (on 0 or N) to be close to the (formal) positive charge (on N). A new parameter, for the reverse anomeric effect, has been introduced, with energies exceeding, as expected, the electronic energy for the regular anomeric effect. A recent paper by Schleifer et a / . (22) concludes that based on a systematic analysis of hundreds of carbohydrate structures "the structural parameters are the most characteristic manifestation of the anomeric effect rather than the energy (relative stability) factors". We believe that by accounting not only for steric but also for electrostatic effects, in the manner shown above, the remaining electronic energy can be a useful part of demonstrating the anomeric effect. However, it is readily admitted that estimating steric and electrostatic energies is not always easy, and that accurate values for such energy components are hard to come by. We hope that the present paper opens the way for more work in this field. In future work, the energy decomposition scheme presented here will be extended to anionic acetal systems as well

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as to esters and protonated esters. A rationalization of the energy parameters on the basis of energy components obtained by Fourier analysis will be attempted. More detailed studies of the geometry changes occurring for systems that are governed by the reverse anomeric effect will be of interest.

Acknowledgement Computational help by several undergraduate students, in particular Michelle Carnell and Amy Wortman, as well as the grant of operating funds by the Natural Sciences and Engineering Research Council of Canada and the allocation of computer time by the University of New Brunswick are gratefully acknowledged. We would also like to thank Robert Mawhinney for preparing most of the figures. Special thanks go to Dr. Z. Valenta for his interest in this project and for helpful discussions. 1. P. Deslongchamps. Stereoelectronic effects in organic chemistry. Pergamon Press, Oxford. 1983. 2. A. J. Kirby. The anomeric effect and related stereoelectronic effects at oxygen. Springer Verlag, Berlin. 1983. 3. D. G . Gorenstein. Chem. Rev. 87, 1047 (1987). 4. S. Wolfe, A. Rauk, L. M. Tel, and I. G . Csizmadia. J. Chem. Soc. B, 136 (1971). 5. G . F. Smits, M. C . Krol, and C. Altona. Mol. Phys. 65, 513 (1988). 6. A. E. Reed and P. v. R. Schleyer. Inorg. Chem. 27, 3969 (1988).

7. A. E. Reed and P. v. R. Schleyer. J. Am. Chem. Soc. 109, 7362 (1987). 8. K. B. Wiberg and M . A. Murcko. J. Am. Chem. Soc. 111, 4821 (1989). 9. M. J. Frisch, J. S. Binkley, H. B. Schlegel, et nl. GAUSSIAN 86, Carnegie-Mellon Quantum Chemistry Publishing Unit, Pittsburgh, Pa. 1984. 10. P. Aped, L. Schleifer, B. Fuchs, and S . Wolfe. J . Comput. Chem. 10, 265 (1989). 1 1 . G . Wipff. Tetrahedron Lett. 35, 3269 (1978). 12. I. H. Williams, G . M. Maggiora, and R. L. Schowen. J. Am. Chem. Soc. 102, 783 1 (1980). 13. G. M. Maggiora and I. H. William. Theochem, 88, 23 ( 1982). 14. J. M. Lehn and G . J. Wipff. J. Am. Chem. Soc. 102, 1347 (1980). 15. F. Grein and P. Deslongchamps. Can. J. Chem. 70, 000 ( 1992). 16. R. U. Lemieux and A. R. Morgan. Can. J. Chem. 43, 2205 (1965). 17. R. U. Lemieux. Pure Appl. Chem. 25, 527 (1971). 18. R. W. Frank. Tetrahedron, 39, 325 1 (1983). 19. P. Deslongchamps, D. P. Rowan, N. Pothier, T. Sauve, and J. K. Saunders. Can. J. Chem. 59, 1 105 (198 1). 20. S . Wolfe, M. H. Whangbo, and D. J . Mitchell. Carbohydr. Res. 69, 1 (1979). 21. F. Grein and P. Deslongchamps. Second World Congress of Theoretical Organic Chemists, Toronto. July 1990. 22. L. Schleifer, H. Senderowitz, P. Aped, E. Tartakovsky, and B. Fuchs. Carbohydr. Res. 206, 21 (1990).