Hydrogen bonding: part 78. Ab initio molecular orbital study of intra- and intermolecular hydrogen bonding in choline and betaine and their compounds with HF and H2O

Journal of Molecular Structure 597 (2001) 177±190

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Hydrogen bonding: part 78. Ab initio molecular orbital study of intra- and intermolecular hydrogen bonding in choline and betaine and their compounds with HF and H2O q K.M. Harmon*, G.F. Avci, S.L. Madeira, P.A. Mounts, A.C. Thiel Department of Chemistry, Oakland University, Rochester, MI 48309, USA Dedicated to Prof. Dr Dietrich Mootz Received 12 February 2001; revised 28 March 2001; accepted 28 March 2001

Abstract We previously prepared several compounds of the zwitterions [(CH3)3NCH2CH2O] 0 (deprotonated choline, herein named cholaine) and [(CH3)3NCH2CO2] 0 (betaine) and proposed structures based on infrared spectroscopy. We now examine these compounds with use of ab initio molecular orbital methods to further elucidate possible structure. These calculations demonstrate that: (1) cholaine and betaine both have internal CHO hydrogen bonds, and these are retained in some form in all other compounds. (2) Cholaine hydrate and hydro¯uoride and betaine hydro¯uoride monomers have covalent three-center hydrogen bonds between H2O or HF and negative zwitterion oxygen, and additional CHX hydrogen bonds to H2O oxygen or HF ¯uorine. (3) Cholaine monohydrate and cholaine hydro¯uoride monohydrate form dimers of Ci symmetry which contain planar C2h (H2O´O)2 and (HOH´F)2 clusters. (4) Cholaine hydro¯uoride forms head-to-tail dimers bound by intermolecular CHX hydrogen bonds; this arrangement could lead to extended linear structures in the solid state. (5) Betaine hydro¯uoride, in contrast, forms a tightly bound discrete dimeric unit in which two molecules join in a head-to-head manner held together by ®ve intermolecular hydrogen bonds and by the mutual proximities of negative ¯uorides to positive nitrogens. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Choline; Betaine; HF and H2O compounds; Molecular orbitals; Hydrogen bonding

1. Nomenclature note Betaine [(CH3)3NCH2CO2] 0, a methyl transfer agent widely distributed in plant and animal tissue, is a zwitterion with positive nitrogen and negative carboxylate at physiological pH. A reduced form of betaine would be a zwitterion [(CH3)3NCH2CH2O] 0, q Part 77. K.M. Harmon, S.L. Madeira, J. Mol. Struct. (in press). * Corresponding author. Tel.: 11-248-370-2332; fax: 11-248370-2321. E-mail address: [email protected] (K.M. Harmon).

with positive nitrogen and negative alkoxide. This species is protonated at physiological pH, and the cationic form, involved in neural transmission, is called choline. There is no name for the zwitterion derived by deprotonation of the choline cation. However, the compounds discussed in this work represent molecular complexes of HF and/or H2O with the two zwitterions noted above; for example, the compounds which might be called `choline ¯uoride' and `choline hydroxide' are not salts of the choline cation. Therefore, for internal purposes we choose to call [(CH3)3NCH2CH2O] 0 cholaine, thus

0022-2860/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0022-286 0(01)00592-0

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leading to parallel names for similar compounds such a betaine hydro¯uoride and cholaine hydro¯uoride. 2. Introduction Some years ago we published the preparation and infrared (IR) study of betaine hydrate and hydro¯uoride [1], cholaine hydrate or `choline hydroxide' [2], cholaine hydro¯uoride or `choline ¯uoride' [3], and cholaine hydro¯uoride monohydrate [4]. An Xray study [5] showed that our prediction [1] that H2O bridged carbonyl oxygen in betaine hydrate was correct; however, each carbonyl oxygen accepts one hydrogen bond from H2O to form an extended HOH± OCO± structure rather than the mutually bridged CO± (H2O)2 ±OC dimer we had proposed. No diffraction studies appear to have been made on the remaining compounds, all of which are shown by IR to contain very strong hydrogen bonds. Therefore we have carried out molecular orbital studies of betaine hydro¯uoride, cholaine hydrate and hydro¯uoride, cholaine hydro¯uoride monohydrate, and some related dimeric species to further elucidate possible structures for these compounds. 3. Experimental and computational details The preparations and IR spectra of betaine HF, cholaine H2O, cholaine HF, and cholaine HF H2O are given in Refs. [1±4]. Molecular models were prepared in scannable form with Chem3D Proe (CambridgeSoft Corp., Cambridge, MA) with parameters derived from the ab initio calculations. Molecular orbital calculations were carried out with Spartane or MacSpartan Pluse (Wavefunction, Irvine, CA) on structures minimized with SYBYL [6] using the 3-21G( p ) [7] basis set at the Hartree± Fock level. The ( p ) indicates that this version of 3-21G involves d-orbitals for second row and higher main group elements only. These calculations give total energies E in hartrees (a.u.). All numbers used in this work are comparisons (DE's) and are converted to binding energies in kcal mol 21 by (DE) (627.71). Absolute values of E's can be supplied to those interested on request. Since all of the structures and energies reported herein are the product of calculations, we will usually omit `was

calculated to be' from the discussions. However, we will designate the difference between geometry optimization and single point energy calculations by (GO) and (SPE), respectively. 4. Calculations 4.1. CHX hydrogen bonds The optimized structures of all of these compounds show geometric evidence for internal CHX hydrogen bonding, and this must be taken into account in determining the strengths of the main hydrogen bonds from H2O or HF to substrate. Raw values for CHX hydrogen bonds were determined whenever possible by rotating appropriate methyl groups in the molecular species until the C±H´ ´´X distances were outside the sum of the van der Waals radii, and comparing the SPE of the modi®ed species thus formed with the GO value for the unmodi®ed structure of the compound DEraw CHX ˆ Ecompound …GO† 2 Emod compound …SPE† …1† However, these rotations result in conformational changes in the alkyl portion of the molecule, primarily by bringing hydrogens on adjacent alkyl groups too close together. To estimate the effect of this conformational change we ®rst determined the SPE energy of the appropriate tetralkylammonium ions (tetramethylammonium for betaine compounds, trimethylethylammonium for choline and cholaine compounds), or pairs of ions for dimeric species, which were obtained by replacement by hydrogen of carboxyl group (betaine compounds) or alkoxide oxygen (choline and cholaine compounds). These were then compared to the SPE energies of similar ions derived from the compounds in which methyl groups had been rotated to give the values for the conformational changes DEconf: ˆ Ecompound ion…s† …SPE† 2 Emod ion…s† …SPE† …2† The energies of the C±H´ ´´X hydrogen bonds are then given by DECHX ˆ DEraw 2 DEconf:

…3†

Not all C±H´ ´´X hydrogen bonds could be

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179

of any obvious alternative method, we have used the derived equations to estimate the strengths of C± H´ ´´X hydrogen bonds which cannot be determined by methyl rotation. The energies of CHX hydrogen bonds for monomeric species and hydrate dimers are listed in Table 1, and those of the other dimeric species in Table 2. Structural parameters of these bonds are listed in Tables 3 and 4. 4.2. Electrostatic effects

Fig. 1. Plots of DE for several CHO and CHF hydrogen bonds vs. H´´´X distance.

evaluated in this way. Some are from ±CH2CH2 ± portions of molecules which cannot be rotated without signi®cant molecular distortion, some require rotation of methyl groups into impossible situations, and one is formed when methyls are rotated to evaluate other bonds. Empirical observation demonstrates that when H´ ´ ´X distances are plotted against the energies of bonds determined by methyl rotation, a reasonable straight line relationship exists (Fig. 1). In the absence

In a compound such as cholaine HF, the HF moiety is bound to cholaine by three different interactions, CHF hydrogen bonds, FHO hydrogen bond, and strong electrostatic attraction between the dipolar cholaine zwitterion and the dipolar HF molecule. Thus when the zwitterion HF or zwitterion H2O compounds are disassembled into their constituent parts, ZI´HX ˆ ZI 1 HX where HX ˆ H2 O or HF, there are three contributions to the energy of the process: (1) breaking CHX hydrogen bonds, (2) breaking HX to zwitterion hydrogen bond, and (3) the electrostatic potential energy required to separate the dipolar species HX and ZI. Since we will be concerned with evaluation of the HX to zwitterion oxygen hydrogen bonds, we need to dissect the total binding energy into these three terms. The CHX hydrogen bonds are evaluated as

Table 1 Calculated energies of CH±X (X ˆ O,F) hydrogen bonds (kcal mol 21) for monomeric species and hydrate dimers Compound

Bond(s)

Method

DECHX

P DECHX

Betaine Betaine HF Betaine HF Choline Cholaine Cholaine H2O Cholaine H2O Cholaine HF Cholaine HF Cholaine HF (Cholaine H2O)2 (Cholaine HF H2O)2 (Cholaine HF H2O)2

2CH±O CH±O CH±F CH±O 2CH±O CH±O CH±OH2 CH±O CH±F CH±F 2CH±OH2 2 CH±OH2 2CH±F

±a ±b ±a ±a ±a ±c ±a ±c ±a ±b ±c ±c ±b

22.03 22.32 23.98 22.34 27.72 27.19 25.14 22.97 27.10 24.98 21.93 24.75 25.29

24.06 22.32 23.98 22.34 215.44 27.19 25.14 22.97 27.10 24.98 23.87 29.51 210.59

a b c

From DECHX ˆ DEraw 2 DEconf: ; see Section 4.1. From DE ˆ 7:0…rH¼F† 2 19:1; see Fig. 1. From DE ˆ 24:1…rH¼O† 2 50:8; see Fig. 1.

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Table 2 Calculated energies of CH±X …X ˆ O; F† hydrogen bonds (kcal mol 21) for dimeric species; for discussion see Section 4.1 Compound

Bond(s)

Method

DECHX

Betaine HF dimer a Betaine HF dimer a Betaine HF dimer Cholaine dimer Cholaine dimer Cholaine dimer a Cholaine HF dimer Cholaine HF Dimer Cholaine HF dimer e Cholaine HF dimer a,f

2CH(I)±F(II) 2CH(II)±F(I) CH(II)±O(I) CH(II)±O(II) CH(II)±O(II) 3CH(II)±O(I) CH(II)±F(II) CH(II)±F(II) CH(II)±O(II) 3CH(II)±X(I)

±b ±b ±c ±c ±c ±b ±d ±d ±c ±b

2 5.02 2 5.02 2 1.52 2 5.91 2 3.33 2 5.59 2 6.19 2 6.28 2 5.21 2 6.10

a b c d e f

P

DECHX

2 10.04 2 10.04 2 1.52 2 5.91 2 3.33 2 16.76 2 6.19 2 6.28 2 5.21 2 18.29

Hydrogen bond energies are average for three or four bonds. From DECHX ˆ DEraw 2 DEconf: ; see Section 4.1. From DE ˆ 24:1…rH¼O† 2 50:8; see Fig. 1. From DE ˆ 7:0…rH¼F† 2 19:1; see Fig. 1. Bond created during methyl rotation. Two CH±F and one CH±O.

discussed in Section 4.1. The electrostatic interactions were evaluated in the following manner. First, the HX to ZI bond was broken in the GO structural model of the compound; this does not change the energy, which depends on geometry in space and not bonds indicated in the structure. Next the bonds in the HX fragment were adjusted to the GO values of either HF or H2O by moving hydrogen, not electronegative atom. Then the distance between the positive nitrogen of zwitterion and the electronegative atom of either HF or H2O was Ê intervals, and the SPE energy (Edist.) increased in 1 A of the system determined at each increment. The quantity Ecompound(GO) 2 Edist.(SPE) was plotted against separation distance in the region between Ê , where all hydrogen bonding effects are negated, 6A Ê , where the incremental change in energy is and 11 A Ê 21 and getting rapidly smaller less than 0.2 kcal mol A with each successive increment (Fig. 2). This interaction, between a dipolar molecule and a zwitterionic substrate, is not a simple coulombic term; that is, it does not change in a linear manner with 1/r as is observed for separation of simple ions. However we ®nd that this data gives excellent ®t to second order polynomial equations. The zwitterion±dipole electrostatic portion of the energy required to separate HX from ZI´HX is given Ê value of this term by the difference between the 11 A for the compound and the value calculated from the appropriate equation (Fig. 2) for the electrostatic

energy at equilibrium N 1 to X distance in the GO structure of the compound  DEelect: ˆ …Eelect: …SPE† at 11 A† 2 …Eelect: …SPE† at eq: dist:†

…4†

4.3. Monomer and dimer unit hydrogen bonds To calculate the energies of hydrogen bonds from Table 3 Ê ; /, 8) for momomeric Parameters of CH±X hydrogen bonds (r, A species and hydrate dimers. For discussion see Section 4.1 Compound

Bond

rCH

rHX

rCX

/

Betaine Betaine HF Betaine HF Choline Cholaine Cholaine Cholaine H2O Cholaine H2O Cholaine HF Cholaine HF Chokaine HF (Cholaine H2O)2 (Cholaine H2O)2 (Cholaine HF H2O)2 (Cholaine HF H2O)2 (Cholaine HF H2O)2

2CH±O CH±O CH±F CH±O CH±O CH±O CH±O CH±OH2 CH±O CH±F CH±F 2CH±O 2CH±OH2 2CH±O 2CH±F 2CH±OH2

1.077 1.075 1.075 1.073 1.089 1.094 1.088 1.087 1.078 1.090 1.076 1.066 1.084 1.070 1.079 1.084

2.021 2.009 1.920 2.108 1.879 1.785 1.807 1.892 1.982 1.702 2.004 2.233 2.025 2.197 1.960 1.908

2.841 2.828 2.991 2.888 2.754 2.707 2.768 2.976 2.820 2.727 2.764 3.083 3.078 2.972 2.986 2.954

130.47 130.60 174.29 127.32 134.57 139.06 144.64 145.46 132.09 154.61 124.92 136.21 162.82 127.47 157.58 160.00

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181

Table 4 Ê ; /, 8) for dimeric species. For discussion see Section 4.1 Parameters of CH±X hydrogen bonds (r, A Compound

Bond

rCH

rHO

rCO

/

Betaine HF dimer Betaine HF dimer Betaine HF dimer Cholaine Dimer Cholaine dimer Cholaine dimer Cholaine HF dimer Cholaine HF dimer Cholaine HF dimer a Cholaine HF dimer Cholaine HF dimer

2CH(I)±F(II) 2CH(II)±F(I) CH(II)±O(I) CH(II)±O(II) CH(II)±O(II) 3CH(II)±O(I) CH(II)±F(II) CH(II)±F(II) CH(II)±O(II) 2 CH(II)±F(I) CH(II)±O(I)

1.078 1.078 1.079 1.087 1.083 1.080 1.080 1.082 1.075 1.076 1.078

1.991 1.991 2.042 1.860 1.967 2.122 1.832 1.820 1.889 2.050 2.241

2.991 2.991 3.095 2.767 2.825 3.073 2.691 2.788 2.838 3.042 3.304

153.15 153.15 164.41 138.26 133.65 145.50 133.34 146.70 144.69 152.04 168.26

a

Bond created during methyl rotation.

HOH or HF to cholaine or betaine we ®rst calculated the E(SPE) for the substrate molecule with HF or HOH removed in the conformation it assumed in the hydrogen bonded compound. The raw hydrogen bond energy is then given by DEraw ˆ Ecompound …GO† 2 …Esubstrate …SPE† 1 EHX …GO††

…5† where HX ˆ HOH or HF. However, as noted above, CHX hydrogen bonds and electrostatic forces are also overcome in this process. Therefore the corrected hydrogen bond energy is given by DEH-bond ˆ DEraw 2 …DECHX 1 DEelect: †

…6†

The hydrogen bond energies for cholaine H2O monomer, and for cholaine HF and betaine HF in both monomeric and dimeric con®gurations are listed in Table 5, and structural parameters for these

hydrogen bonds as well as those of the hydrate dimers are listed in Table 6. 4.4. The hydrate dimers Since the hydrate dimers have Ci symmetry (Section 5.2) the two substrate units bridged by H2O molecules are identical, therefore the energy of disassembly of the dimer by removal of two H2O is DEraw ˆ Edimer …GO† 2 …2Eunit …SPE† 1 2EHOH …GO†† …7† When we used this approach to estimate the hydrogen bond strengths in (H2O´X 2)2 clusters [8] it was necessary to correct for the repulsion of the two X 2. However, with the hydrate dimers of cholaine or cholaine HF we ®nd that the two substrate units, retained in the positions occupied in the dimer, actually attract each other; this attraction was

Table 5 Energies of hydrogen bonds in some H2O and HF compounds (kcal mol 21) corrected for CH hydrogen bonds broken concurrently and electrostatic effect; for derivation see Section 4.3 Compound

Acceptor

Donor

DEraw

DECHX a

DEelect.

DEH-bond

Betaine HF (Betaine HF)2 I (Betaine HF)2 II Cholaine H2O Cholaine HF (Cholaine HF)2 I (Cholaine HF)2 II

±CH2CO2 ± ±CH2CO2 ± ±CH2CO2 ± ±CH2 ±O± ±CH2 ±O± ±CH2 ±O± ±CH2 ±O±

HF HF HF HOH HF HF HF

230.88 221.99 221.86 234.43 259.69 234.76 264.67

23.98 0 0 25.14 212.08 0 212.44

25.44 22.55 22.17 25.30 29.57 25.67 26.87

221.46 219.44 219.69 223.99 238.04 229.09 242.45

a

From DECHX ˆ DEraw 2 DEconf: ; see Section 4.1.

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estimated as DEattr ˆ E…SPE† of two dimer units in dimer positions 22E(SPE) of individual dimer unit. In addition, CH to H2O bonds and electrostatic effects must be accounted for. The ®nal value for the hydrogen bonds from water to substrate is given by X DEHOH ˆ DEraw 2 …DEattr 1 DECHX 1 DEelect † …8† The values for the hydrogen bonds from H2O in the hydrate dimers are listed in Table 7. Cholaine HF H2O dimer also contains two strong hydrogen bonds from HF to cholaine oxygen. To evaluate these the dimer was disassembled by removal of two H2O and two HF DEraw ˆ Edimer …GO† 2 …2Eunit …SPE† 1 2EHOH …GO† 1 2EHF …GO†† …9† In addition, this process involves breaking CHX hydrogen bonds to both H2O and F, breaking HOH hydrogen bonds to F, the generation of a new DEattr between the two cholaine units, and electrostatic effects for both H2O and HF X X DECHX DEH-bonds ˆ DEraw 2 …DEattr 1 X X 1 DEHOH 1 DEelect: † …10† The energy value for the FHOCH2 ±hydrogen bonds in (cholaine HF H2O)2 is listed in Table 7. 4.5. Non-hydrate dimers The dimers between units of betaine HF, cholaine, and cholaine HF are held together by a combination of intermolecular CHX hydrogen bonds and electrostatic forces. The overall energy of attraction can be evaluated by DEattr ˆ Edimer 2 2Emonomer Fig. 2. Equations used in calculation of Eelect.(SPE) for: (A) betaine HF; (B) cholaine HF; (C) cholaine H2O. For derivation see Section 4.2.

…11†

where Emonomer is the energy of the gas phase monomeric form of the compound. However, the formation energy of the dimers contains three terms: (1) changing the monomers to the forms found in the dimer, (2) forming intermolecular CHX bonds, and (3) forming electrostatic interactions. The monomer forms can be easily compared, and the intermolecular hydrogen bonds were evaluated by the methods outlined in Section 4.1. To evaluate the electrostatic

K.M. Harmon et al. / Journal of Molecular Structure 597 (2001) 177±190

183

Table 6 Ê ; /, 8; m, debyes) for various compounds. For discussion see Sections 4.3 and Parameters of non-CH hydrogen bonds and dipole moments (r, A 4.4 Compound

Bond

rO±H

rH±X

rO´´´X

/O±H±X

m , dipole

Betaine HF (Betaine HF)2 (I) (Betaine HF)2 (II) Cholaine HOH (Cholaine HOH)2 b (Cholaine HOH)2 b Cholaine HF (Cholaine HF)2 (I) (Cholaine HF)2 (II) (Cholaine HF HOH)2 (Cholaine HF HOH)2 b (Cholaine HF HOH)2 b

FH±O2C± FH±O2C± FH±O2C± HOH±OCH2 ± HOH±OCH2 ± HOH±OCH2 ± FH±OCH2 ± FH±OCH2 ± FH±OCH2 ± FH±OCH2 ± HOH±F HOH±F

1.465 1.381 1.377 1.476 1.623 1.717 1.087 1.289 1.061 1.016 1.595 1.631

0.984 1.017 1.020 1.035 0.999 0.989 1.282 1.063 1.350 1.459 0.985 0.983

2.413 2.377 2.380 2.489 2.604 2.643 2.341 2.344 2.386 2.463 2.568 2.607

159.7 164.8 166.3 164.8 165.9 154.3 162.1 170.3 163.4 168.8 168.7 171.2

11.82 1.82 a

a b

8.60 0.00 a 9.74 23.09 a 0.00 a

For dimeric species for individual unit dipoles see Figs. 11 and 12. Unlike H2O bonds to O or F in C2h planar (H2O´X)2 unit in Ci structure.

effect the energy of each dimer (GO) was compared to the energy (SPE) of its two units when separated by Ê along the principal axis of their attractive inter11 A action (see Section 4.2). The electrostatic energy term is then obtained by subtracting the energy of CHX bonds from the total separation energy. The results of these two approaches for the three dimers are compared in Table 8.

5. Results and discussion 5.1. Monomeric species The structures of the monomeric species might well exist in the gas phase or in matrix isolation, and we expect that those of betaine and cholaine (see Section

5.3) will be little altered in the solid state. However the structure of choline cation will be somewhat altered by hydrogen bonding to anion, cholaine hydrate surely exists as a dimer, and betaine and cholaine hydro¯uorides will most likely undergo signi®cant changes due to intermolecular interactions in the solid state. We ®rst investigated the choline cation, since the structure of this species is known [9]. We were pleased to ®nd that the gauche arrangement about the CH2CH2 bond and the short contact distance between methyl substituent and electronegative group which are observed in all cholinergic type compounds [10] were present in the calculated structure. This structure (Fig. 3) is essentially superimposable on a model constructed to the parameters of the cation as determined by X-ray diffraction [7]. The

Table 7 Energies of HOH±X …X ˆ O; F† and ±CH2OHF hydrogen bonds (kcal mol 21) in the Ci hydrate dimers corrected for monomer to monomer attraction (DEattr), electrostatic effect (DEelect.) and ancillary hydrogen bonds broken concurrently; for derivation see Section 4.4 Compound

DEraw

DEattr

DECHX a

DEelect.

P DEH-bond

DE per H-bond

(Cholaine H2O)2 b (Cholaine HF H2O)2 b (Cholaine HF H2O)2 c

2118.23 2157.29 2206.71

219.33 253.60 25.10

23.87 29.50 294.99 d

220.80 219.34 248.22

274.24 274.89 258.40

218.56 218.72 229.20

a b c d

From DECHX ˆ DEraw 2 DEconf: ; see Section 4.1. HOH±X …X ˆ O; F† hydrogen bonds. FHOCH2 ±hydrogen bond. Includes 2CH±F, 2CH±OH2, and 4 HOH±F hydrogen bonds.

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K.M. Harmon et al. / Journal of Molecular Structure 597 (2001) 177±190

Table 8 Calculation of the attraction energy (kcal mol 21) for the dimers of cholaine, cholaine HF, and betaine HF. For derivation see Section 4.5. Symbols used: M, gas phase monomer; I and II, the two structures found in the dimers (see Figs. 9±11) Step

Cholaine dimer

Cholaine HF dimer

Betaine HF dimer

M ! (I) M P ! (II) a DHCH±X DE electrostatic P DEattr ( steps) DEattr (2M ! dimer) DDE

27.53 1.71 216.76 214.76 22.28 23.62 1.34

11.4 20.43 218.29 26.94 217.26 218.36 1.10

17.27 11.54 221.60 249.37 242.16 246.83 4.72

a

From DECHX ˆ DEraw 2 DEconf: ; see Section 4.1.

only signi®cant difference is that the C±C±O angle is 1088 rather than 1128, which reduces the short CH3 to Ê . This is reasonable, O distance from 3.07 to 2.88 A since in the crystal the O±H is hydrogen bonded to Cl 2, and absent this bond in the gas phase the interaction of oxygen with the trimethylammonium group is enhanced. The zwitterion cholaine (Fig. 4(A)) shows a structure very similar to that of choline; however, the N± C±C±O dihedral angle has increased from 46 to 568, which allows for formation of two CHO hydrogen bonds to the alkoxide oxygen. These bonds are quite strong (27.72 kcal mol 21) relative to the one in choline cation (22.34 kcal mol 21) which re¯ects the greater acceptor strength of alkoxide oxygen compared to hydroxyl group. Betaine zwitterion (Fig. 2(B)) shows the same CS conformation observed in crystals of the hydrochloride [11], with two quite weak CHO hydrogen bonds to one carboxylate oxygen. In betaine HCl the second carboxylate oxygen accepts a hydrogen bond from HCl.

In cholaine HF (Fig. 5(A)) and betaine HF (Fig. 5(B)) the OHF moities are folded back against the alkyl portion of the molecule so as to maximize both CH hydrogen bonding and close approach of ¯uoride to positive nitrogen. The OHF bonds in both of these compounds are of the covalent threecenter type; however, in cholaine HF the proton lies slightly closer to the alkoxide oxygen (more basic than ¯uoride) while in betaine HF the proton lies closer to ¯uoride (more basic than carboxylate

Fig. 3. Optimized structure of choline cation.

Fig. 4. Optimized structures of (A) cholaine and (B) betaine.

K.M. Harmon et al. / Journal of Molecular Structure 597 (2001) 177±190

185

to alkoxide oxygen and H2O oxygen. Since this species does not exist as a monomer in the solid state (there is no IR absorption for non-hydrogen bonded OH [2]) discussion will be deferred to a later section. However, it is clear that in either the monomeric or dimeric form cholaine H2O is in no way `choline hydroxide'. 5.2. Hydrate dimers

Fig. 5. Optimized structures of (A) cholaine HF and (B) betaine HF.

oxygen). Neither compound is in any sense a true salt with protonated cation and F 2 anion. As expected, the OHF hydrogen bond in cholaine HF (238.04 kcal mol 21) is signi®cantly stronger than that in betaine HF (221.46 kcal mol 21) due to the greater base strength of alkoxide vs. carboxylate group. Cholaine H2O monomer (not illustrated) also shows a covalent three-center bond between H2O and alkoxide oxygen with one CHO hydrogen bond each Table 9 Comparison of IR absorptions of planar (X´H2O)2 clusters …X ˆ HO2 ; 2CH2 O2 † for lithium hydroxide monohydrate[15], tetramethylammonium hydroxide monohydrate [16] and (cholaine H2O)2 [2]. Units are cm 21 (wavenumbers); symbols used: s, strong; m, medium; w, weak; b broad; v very Vibration

LiOH H2O

TMAOH H2O

(Cholaine H2O)2

n s OH 2 n sHOH n bHOH n libHOH n libHOH n libOH 2

3575 s 2965 bs 1570 m 1005 vs 850 w 660 vs

3662 m 2920 bs 1590 m ±a 850 w 400 m

Na 2900 bvs 1580 w 1100 vs 765 s Na

a

Masked by cation absorptions.

Both cholaine H2O and cholaine HF H2O exist as dimeric species of Ci symmetry in the solid state, and both contain planar C2h (H2O´X 2)2 clusters …X2 ˆ ±CH2 O2 ; F2 †: This assignment is in accord with the observed infrared (IR) spectra of these species (Tables 9 and 10) and by analogy with the similar Ci dimers found for the monohydrates of tri-i-pentylammonium chloride and bromide [12,13] and N,Ndimethyl-l-adamantylammonium chloride [14] which contain similar (H2O´X 2)2 clusters bound by NHX hydrogen bonds. The structures (GO) of the two hydrate dimers are shown in Figs. 6 and 7. The quantity DEattr (Table 7) for the two substrate units of (cholaine HF H2O)2 (253.60 kcal mol 21) is much larger that of (cholaine H2O)2 (25.10 kcal mol 21) as a result of much greater dipolar interaction. In each hydrate dimer the dipole moments of the units are equal and opposite as required by the Ci symmetry (Fig. 8). For (cholaine H2O)2 there is little dipolar overlap; both negative ends of the dipole moments lie approximately on a line orthogonal to the dipole directions. For (cholaine HF H2O)2 the unit Table 10 Comparison of IR absorptions of OH±F in cholaine HF [3] and HOH±F in C2H (H2O´F 2)2 [16] with combined absorptions of (cholaine HF H2O)2 [4]. Units are cm 21 wavenumbers); symbols used s, strong; m, medium; w, weak; b, broad; v, very Vibration

n sHOH n combOHF n sOHF n bHOH n bHOH n bOHF n libHOH n libHOH n sO´´´F n defO´´ ´F

Cholaine HF 2400 bs 1865 bvs 980 s 375 s 300 vs

(H2O´F 2)2

(Cholaine HF H2O)2

2950 bvs

3160 bvs 2550 bs 1890 bvs 1615 bw 1540 bm 960 s 810 s 700 s 330 vs 283 vs

1750 bw 1560 bm 895 s 822 s

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Fig. 6. Optimized structure of the Ci cholaine hydrate dimer.

dipoles are not only stronger, but also overlap so that the negative end of each is near the positive end of the other (Fig. 8). In our initial report on cholaine H2O [2] we proposed a dimer with a tetrahedral O4H422 cluster similar to O4H442 found in hydrogrossular (15,16). We have since [16] abandoned such tetrahedral structures in the face of overwhelming evidence for the prefered C2h planar form. Tetrahedral O4H442 exists

Fig. 7. Optimized structure of the Ci cholaine ¯uoride hydrate dimer.

Fig. 8. Degree of overlap of dipole moments of substrate units derived from H2O dimers for (A) cholaine and (B) cholaine ¯uoride. Arrows (- end) point to O in (A) and to F in (B).

in the garnet analog hydrogrossular where it replaces SiO442, but is only stable in the ionic lattice of the mineral. The optimized structure of the water±anion unit in (cholaine H2O)2 (Fig. 6) has the expected C2h symmetry, and the IR spectrum is consonant with those of lithium and tetramethylammonium (4MA 1) hydroxide monohydrates (Table 9) which contain such planar clusters [17,18]. For cholaine HF H2O we proposed [3] a dimer with a water±¯uoride structure `similar to that in 4MAF monohydrate' (at that time considered tetrahedral, now known [16,19] to be planar). The IR spectrum of (cholaine HF H2O)2 shows the characteristic ®ngerprint spectrum of a C2h planar cluster (Table 10), and this is supported by the optimized structure (Fig. 7). The H2O to F hydrogen bonds in the dimer (218.72 kcal mol 21) are signi®cantly weaker than those calculated [8] for the gas phase (H2O´F -)2 cluster (233.01 kcal mol 21), in agreement with the values of n sHOH (Table 10). This is expected, as the strong hydrogen bond between HF and cholaine oxygen lowers the acceptor strength of F. This predicted difference in the strength of the binding of H2O is con®rmed by experiment; (cholaine HF H2O)2 can be dried in vacuo with mild heating to yield anhydrous cholaine HF, while it is impossible to remove H2O in

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as that for the hydrate dimer (229.20 kcal mol 21, Table 7). 5.3. Solid state dimers We have examined three non-hydrate dimers to gain preliminary information on possible intermolecular interactions in the solid state. Since a common feature of quaternary ammonium ion salts is to have anion associated with a trigonal (CH3)3N 1 face of the cation [21], the initial dimers, prior to optimization, were formed by unfolding electronegative atom (O or F) from its position in the monomer, and positioning it directly over the center of a triangular face of the (CH3)3N 1 group of a similar monomer at a distance slightly beyond normal CHX hydrogen bond interactions. The dimers were than optimized. The results for (cholaine)2, (cholaine HF)2, and (betaine HF)2 are illustrated in Figs. 9±11, respectively. In (cholaine)2 the ±CH2O± group of unit I is bound by three CHO hydrogen bonds from unit II, each from a different CH3 group. Unit II has rotated so as to Fig. 9. Optimized structure of the cholaine dimer (top two ®gures). Bottom form has (II) rotated 1808 to facilitate extended bonding in solid state (Section 5.3).

vacuo from 4MAF´H2O without concurrent destruction of the cation. The HOH to O hydrogen bonds in (cholaine H2O)2 are similar in strength (218.56 kcal mol 21) to those to F in (cholaine HF H2O)2. The charge on the O (20.92) is more negative than on the F (20.72) but F is intrinsically the better acceptor and the effects balance out. The assignment for n sFHO in (cholaine HF H2O)2 (Table 10) has been revised from our ®rst report [3] in light of later experience with such unsymmetrical three-center covalent hydrogen bonds [13,14,20]; it now appears that this bond is only slightly weaker than the FHO hydrogen bonds in solid cholaine HF. Since the precise structure of cholaine HF is not known a direct comparison of bond strength is not possible; however, form I of the solid state dimer (Section 5.3) is probably close to the form existing in the solid. The calculated strength of the FHO hydrogen bond in form I of the solid state dimer (229.09 kcal mol 21, Table 5) is essentially the same

Fig. 10. Optimized structure of the cholaine HF dimer. Bottom form re¯ected through plane of page.

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Fig. 11. Optimized structure of the betaine HF dimer. Bottom form rotated 1808 about long axis of cluster.

increase dipolar interaction between the two units (Fig. 12) to the extent possible without breaking CHO hydrogen bonds. There is no guarantee that this speci®c rotation would occur in the real solid, but is possible to envision an extended structure in which an unfolded unit II interacts with a third cholaine, etc. However, the overall interaction energy (Table 8) is very small (23.62 kcal mol 21) primarily because of the signi®cant energy cost of converting the gas phase monomer form to the form of unit I. It is certainly possible that cholaine in the solid state might remain folded in the gas phase monomer form, with primarily dipolar intermolecular forces. In (cholaine HF)2 there are also three inter-

molecular hydrogen bonds, two CHF and one CHO, from individual CH3 groups of unit II to unit I. The F of unit I is no longer involved in intramolecular CHF bonds, and the FHO hydrogen bond of unit I (229.09 kcal mol 21) is weaker than that of the gas phase monomer (238.04 kcal mol 21). An extended structure with interactions similar to those between units I and II would be in accord with the IR spectrum [3]. (Cholaine HF)2 shows FHO absorptions consonant with the presence on a reasonably strong unsymmetrical three-center bond similar to those in FHOHF 22 or FHFHF 2 [20]. In addition, the IR spectrum shows a strong absorption from CHX hydrogen bonding; this absorption is weaker than that of 4MAF, but markedly stronger than that of 4MACl [22]. Compared to (cholaine)2 (Table 8) the intermolecular hydrogen bonds of (cholaine HF)2 are somewhat stronger; however, the electrostatic interaction is much weaker due to little overlap of dipole moments (Fig. 12). The much larger energy of attraction for (cholaine HF)2 (218.36 kcal mol 21) is primarily due to the smaller energy cost of the gas phase to unit I conversion. Prediction of considerable 2DEattr and agreement with the IR spectrum suggests that the solid state of (cholaine HF)2 will resemble an extended structure formed from units similar Ð though not necessarily identical Ð to unit I, bound together by strong intermolecular CHX hydrogen bonding. Optimization of the (betaine HF)2 dimer gave the most startling result. The initial setup was as with the two dimers above; the F of one unit was rotated slightly away from internal CHF hydrogen bonds, and brought near the trigonal (CH3)3 face of the other in a head-to-tail manner. Over many days of computation the ±CH2C(O)OHF portions of both units straightened out to the furthest limit allowed by rational bond angles and unit II both rotated by 1808 and displaced itself in space until it nestled against unit I in an extraordinarily compact arrangement bound by four CHF and one CHO hydrogen bonds (221.60 kcal mol 21) and a very large electrostatic DE (249.37 kcal mol 21) which results from close and complete overlap of strong dipole moments (Fig. 12). The DEattr between the two units (Table 8) of 246.83 kcal mol 21 is 2.5 times the value of (cholaine HF)2, and equals the strength of some covalent bonds. This structure is essentially self-neutralizing, with an

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Fig. 12. Dipole moment interactions of solid state dimers for: (A) cholaine dimer, (B) cholaine HF dimer, and (C) betaine HF dimer. Unit II in C is displaced in Z direction in illustration for clarity.

overall dipole moment of only 1.82 debye, as contrasted to the values of 13.80 and 23.09 debye for the (cholaine)2 and (cholaine HF)2 dimers, respectively. This structure for (betaine HF)2 (Fig. 11) could also account for the appearance of the IR spectrum. While cholaine HF shows the characteristic spectral absorptions of isolated unsymmetrical FHO hydrogen bonds, the spectrum of betaine HF [1] shows the broad and blurred absorptions associated with intermolecular vibrational coupling of hydrogen bonds in close proxi-

mity [23]. Such coupling could well arise in the intimate association shown by the structure of (betaine HF)2. We conclude that the structure shown in Fig. 12 is very likely that of betaine HF in the solid state. 6. Conclusions We have used ab initio 3-21G( p ) molecular orbital calculations to evaluate possible structures for betaine monomer, the monomers and dimers of cholaine

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(deprotonated choline cation), cholaine monohydrate, betaine hydro¯uoride, and cholaine hydro¯uoride, and the dimer of cholaine hydro¯uoride monohydrate. This work includes detailed evaluation of strengths and geometric parameters for internal and external CHX …X ˆ O; F†; three-center covalent FHO, and HOHX …X ˆ O; F† hydrogen bonds, and predictions of expected structures in the solid state. In cholaine and betaine monomers negative oxygen is bound to (CH3)3N 1 group by CHO hydrogen bonds; these compact species should be little changed in the solid state. In cholaine hydro¯uoride and betaine hydro¯uoride monomers the ±OHF moieties fold back against (CH3)3N 1 group and interact with a combination of CHO and CHF bonds. The FHO hydrogen bonds are of the short, strong three-center convalent type. In the solid state cholaine hydro¯uoride is expected to form an extended structure with the ± OCHF portion unfolded and bound to adjacent molecule by CHF and CHO hydrogen bonds. We believe that betaine hydro¯uoride will form dimeric units in the solid state bound by ®ve intermolecular CHX hydrogen bonds and very strong electrostatic forces. Cholaine monohydrate and cholaine hydro¯uoride monohydrate exist in the solid state as dimeric units of Ci symmetry which contain central planar C2h (H2O´X)2 clusters …X ˆ O; F† similar to clusters found in many quaternary ammonium halide and hydroxide monohydrates. This structural assignment is consonant with the observed infrared spectra of these monohydrates. Acknowledgements Acknowledgement is gratefully made to the donors of the Petroleum Research Fund, Administered by the American Chemical Society for grants in support of this work.

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