Molecular orbital computations on lipids: an ab initio exploratory study on the conformations of glycerol and its fluorine congeners

Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96 www.elsevier.com/locate/theochem

Molecular orbital computations on lipids: an ab initio exploratory study on the conformations of glycerol and its fluorine congeners Jacqueline M.S. Lawa,b, Szilard N. Fejerb, David H. Setiadia, Gregory A. Chassa, Bela Viskolczb,* a

Global Institute of Computational Molecular and Material Science, 2-158 Major St. Toronto, Ont., Canada M5S2K2 b Department of Chemistry, Faculty of Education, University of Szeged, Szeged, Hungary Received 8 October 2004; accepted 22 November 2004 Available online 17 March 2005

Abstract In order to characterize the set of topologically probable glycerol-3-phosphate backbone conformers, ab initio calculations were performed on glycerol as a preliminary study. Ab initio calculations were also completed for selected congeners of glycerol, such as 1,2-difluoro-3hydroxylpropane and 1,2,3-trifluoropropane, in order to model the effects of changing electron densities on the glycerol-3-phosphate backbone geometry. The results show that conformations having intramolecular hydrogen bonds have a lower relative energy. The O–H stretching frequencies computed in different glycerol conformations were largely dependent on fi and ji backbone dihedrals. q 2005 Elsevier B.V. All rights reserved. Keywords: Ab initio; Intramolecular hydrogen bonding; Glycerol; Glycerol models

1. Preamble Glycerol is found as an intermediate [1,2] in many biological pathways and is purported to be a growth regulator for some plants [3]. The glycerol moiety also acts as the structural backbone of lipids [4]. Due to its viscous properties, glycerol may act as an ideal solvent to stabilize reactants [5] as well as to regulate the rate of selected reactions [6]. Some labeled glycerol substances have also been used as tracer materials for in vivo studies of metabolism [7]. Glycerol has many rotamers and although it is symmetrical, intramolecular hydrogen bonding between the hydroxyl (OH) groups can significantly alter the stability of each rotamer. Furthermore, the OH groups can form many hydrogen bonds with polar molecules and may be esterified or oxidized into other congeners such as glycerylaldehyde and phosphates [8]. For example, glycerol-3-phosphate, which is the backbone of phospholipids, is a product of

* Corresponding author. E-mail address: [email protected] (B. Viskolcz).

0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2004.11.049

glycerol phosphorylated by ATP at a terminal OH [9]. This reaction is catalyzed specifically by glycerol kinase [10–12]. The different rotamers of glycerol may interact with specific enzymes, resulting in specific products. The conformation flexibility of the glycerol backbone is believed to be an important factor in the proper orientation and position of the fatty acid chain attached to the phospholipid molecule, which interacts with and regulates transmembrane proteins such as the G-protein [13].

2. Introduction Many investigations have been conducted on glycerol, whereby X-ray crystallography has often been used to characterize conformation-specific glycerol-enzyme binding properties [14]. Experiments, in which glycerol analogues with inhibitory effects were produced, have also yielded results suggesting that structural specificity plays an important role in interactions between glycerol and selected enzymes [15]. From these studies, there have been attempts to find specific types of enzyme-binding conformations in glycerol, as well as chemical interactions stabilizing these structures. Such experiments include computational simulations, modeling of glycerol as a solvent, and interactions

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H 14 H14

O 10

χ3 i

H12

C3

χ1

C2

i

(D9) H1

φi (D9) H6

–

C4

(D11) H8

χ2 i

P

H 13

(D13)

C2

O9

O 11 ψi

i

H7 O

O9

χ3

O 10

(D14) H7

C1

χ1

–

O

H4

C3

ψi

φi

i

O

O 11 H13

χ2 i

H6

H5

H8

H5

Fig. 1. Modular numbering of atoms used, following the definition standardized of the relative spatial orientation of all constituent atomic nuclei in the glycerol backbone. (pro-S) and an alternative method of numbering the glycerol which may facilitate in the building of modular units of lipids when modeling the lipid bilayer (pro-S also).

with ions in solution [16]. Conformational studies of glycerol have also been performed using neutron scattering experiments [17]. However, a systematic characterization of the conformational intricacies of the glycerol backbone is necessary to develop a more thorough understanding of how different structures can affect the nature of chemical reactions involving this molecule. Quantum mechanical ab initio molecular orbital computations provide a wealth of structural and electronic data on molecular systems. With the geometry optimizations of all possible backbone conformers, all stable conformations can be identified. These studies may also serve as a preliminary insight into molecular systems that are differently substituted or have different oxidation states. These might include glycerol-3phosphate, glycerates and perhaps even the full molecular structure of a portion of the lipid bilayer and its interactions with transmembrane proteins.

and gaucheK (gK). However, the three OH groups, defined as c1i , c2i , c3i , are expected to have four topologically possible states due to the existence of lone pairs of electrons on each oxygen atom. The possible conformations of the glycerol are the combinations of each topologically probable rotamer: three conformations per backbone dihedral (gC, a, gK), four conformations per sidechain (hydroxyl) dihedral (s, gC, a, gK); since there are two backbone dihedrals and three sidechain dihedrals in glycerol, the total number of possible conformations will be 3!3!4!4!4Z576. Pro-S configuration

H 14 χ3

O10

i

H7

A standardized definition of the relative spatial orientation of all constituent atomic nuclei was used to define the glycerol molecular structure (Fig. 1). In this figure, the picture on the right shows an alternative and modular numbering system that can be used to build larger lipid molecules for modeling lipid bilayers. This definition is similar to the IUPAC standard for peptides, where backbone dihedrals are defined by fi and ji [18]. In peptides, the modules are covalently attached to each other in a linear fashion. However, modules attached to the glycerol backbone in phospholipids are not necessarily strung together in a linear manner. This methodology is further developed through the division of the glycerol backbone into parts that may potentially be extended using different substituents [19]. Multi Dimensional Conformational Analysis (MDCA) [20] is used to construct the topologically possible set of conformers. Each glycerol backbone dihedral (dihedral angle, defined as fi and j i) has three MDCA predicted rotamers, specifically gaucheC (gC), anti (a),

C3

O9

3. Methods

χ1

H 12

φi

C2

i

O11 i

H6

H1

χ2

C4

ψ

H 13

i

H8

H5

Phosphate added on O9 H14 χ3

O10

i

H7

O

C3

O9 P

O

χ O

C2

1

i

H1

H6

φi

S configuration Scheme 1.

O11 ψ

i

H8

C4

χ2 i

H5

H13

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

F 10

F10

H7 φi

F9

Pro(R)

F 11

C4

O9

C3 χ1

H12

C2

i

H5

H8

H6

H1

H7 ψi

C3

C2

F 10 H7

C3

F11

Pro(S)

H1

φi H6

H5

H8

H6

H1

C4

ψi

i

H7

C2

F11

(R) φ

F10

F9

81

H8

χ1

H

C4

ψi

C3

O 11 C2

i

H5

F 11

(S ) φ

i

H5

H8

H6

H1

C4

ψi

Fig. 2. Numbering of propane, 1,2,3-trifluoropropane, 1,2-difluoro-3-hydroxyl-propane and glycerol.

All molecular orbital computations were completed using GAUSSIAN98 on a Debian Linux operating system [21]. The geometry optimizations, frequency calculations and potential energy hypersurface (PEHS) scans were made at the RHF/3-21G level of theory. With the exception of 1-hydroxyl-2,3-difluoropropane, glycerol and 1,2,3-trifluoropropane are both achiral. However, if a heavy group is substituted for any one of the hydrogen atoms bound to the backbone carbon atoms, the middle carbon atom (C2 position, Scheme 1) will become chiral. For this reason, a nomenclature classification system is used. The molecule is labeled prochiral S (pro-S) or prochiral R (pro-R), depending on the orientation of the fluorine atoms. The numbering system is designed in the following way: when the phosphate group is added on O9, the chirality will be the one as predicted by the prochiral label. For example, pro-S will be of S configuration when a phosphate is added onto O9. Consequently, pro-R will have R configuration when phosphate is added (Scheme 1). 3.1. 1,2,3-trifluoropropane and 1-hydroxyl-2, 3difluoropropane The study on glycerol can be simplified by first studying its 1,2,3-trifluoropropane and 1-hydroxyl-2,3-difluoropropane congeners. These molecules were used to model the isoelectronic effects (with OH groups) on the three-carbon backbone as well as the different dihedral angles from the MDCA-predicted ideal, as a result of this electron density (Fig. 2). Since this molecule is a simpler model for glycerol, the backbone dihedral angles are defined as fi for the torsional angle O9–C2–C3–C4, and ji for the angle O11–C4– C3–C2. For each sidechain OH rotamer (ciZgC, a, gK and s), four scans were performed, scanning fi and ji at 308

increments for both the R and the S enantiomer. The plotting program Axumw [22] was used to construct a spline graph of the resultant relative energy values [23]. For each of the dihedrals fi and ji, the conformations of gC, a, and gK were investigated. Because one sidechain dihedral was present, which had four possible energetically stable conformations (gC, a, gK and s), this conformational search included a total of 36 topologically possible rotamers. 3.2. 1,2,3 trifluoropropane Since this molecule has no sidechain dihedrals that could be varied, the nine possible backbone conformations were explored (gC, a, and gK for each of the dihedrals fi and ji). 3.3. Glycerol Due to the many intramolecular degrees of freedom in the glycerol molecule, no preliminary potential energy hypersurface scans were made; the scans of the two previous molecules were used instead to investigate general trends σ3 H 14 O10 H7 σ

1

C3

O9

O 11

C2

H12 H1

H6

C4 H8 Scheme 2.

σ2 H5

H13

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for the backbone dihedrals fi and ji. Glycerol has 576 MDCA-predicted geometric conformations. The pro-S configuration was selected for computation, since the ProR system is expected to provide identical geometric and energetic trends. Three-dimensional (3D) potential energy surfaces (PES) were computed and plotted [24] to help

identifying the topologically probable conformers. Nine 3D PESs were required to represent all possible Ramachandran surfaces. Bond distances between all hydrogen and oxygen atoms were tabulated according to whichever geometry they resemble (i.e. rings, fused ring, etc.). The visualization of the conformers was carried out using Molekel [25].

360 330

Dihedral Angles (Degree) ψ

Energy (Hartrees)

i

300

0 30 60 90

Di

he

dr

12

al

0

15

An

0

18

0

21

gle

0

sφ i

24

0

(D

27

0

eg

30

0

re e)

33

0

36

0

0

30

90 60

120

150

l

ra hed

180

240 210

300

270

es ψ i

270 240 210 180 150 120 90 60

360 330

e)

re Deg

30

(

0

gl An

0

30

60

Di

90 120 150 180 210 240 270 300 330 360

Dihedral Angles (Degree) φi

F 10 H7 φi

O9

E =f(φi,ψi), [χi1 @ g+]

H 12

1,2-difluro-3-hydroxylpropane

χ1

C4 H5

H8

H6

H1

F 11

i

(R)

C2

i

ψ

C3

360 330

0

30 60

Di

90

he

dr

12 0

al

15 0

18 0

An g

les

21 0

φ i

24 0

(D

27 0

egr

30 0

ee)

33 0

0

30

240

270

330

360

150

270 240 210 180 150 120 90 60

ee) egr (D

30

sψi gle An 60 l a edr Dih 120 90

36 0

210 180

300

Torsional Angles (Degree) ψ

Energy (Hartrees)

i

300

0 0

30

60

90

120

150

180

210 240

270

300

330

360

Dihedral Angles (Degree) φi

F 10 H7

E =f(φi,ψi), [χi1 in g+] 1,2-difluro-3-hydroxylpropane

φi

O9 H 12

i

H1

ψ

i

(S)

C2

χ1

C3

H6

F11

C4 H8

H5

Fig. 3. PESs for comparison between two 1,2-difluoro-3-hydroxylpropane with c1ZgC PES; one in S conformation and one in R conformation.

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

Frequency calculations were performed on the topologically probable conformations of glycerol to further analyze the properties of intramolecular hydrogen bonding. The vibrational frequencies which result in the stretching of each of the OH bonds (s1, s2 and s3, Scheme 2) were tabulated. These values are then corrected and their RMS errors are given as well.

83

4. Results and discussion 4.1. 1-hydroxyl-2, 3-difluoropropane In Figs. 3–5, the topologies of the potential energy surfaces of the R (top) and S (bottom) configurations are compared, with c1i being in gC, a and gK conformations, 360 330

Energy (Hartrees)

Dihedral Angles (Degree) ψ

i

300

0 30

Di

60

he

60

90

dr

12 0

al

15 0

An

18 0

gle

21 0

sφ i

24 0

27 0

(D

egr

30 0

ee)

50 01

33 0

36 0

0

30

60

12

90

l

ra

d ihe

10 02 18

0 30 70 02 24

03 33

les

240 210 180 150 120 90 60

) ree

eg

(D

g An

270

ψi

30 0 0

30

60

90 120 150 180 210 240 270 300 330 360

Dihedral Angles (Degree) φ

i

D

F 10 H7 φi

O9

E =f(φi,ψi), [χi1 in a] H 12

1,2-difluro-3-hydroxylpropane

χ1

C4 H5

H8

H6

H1

F 11

i

(R)

C2

i

ψ

C3

360 330

0

30

36

60

Dih

90

edr

120

30

al A

150

24

180

210

ngl

es φ i

240

(De

0 18

270

gre

e)

12

300

330

0

r ed

(D

0

eg

e re

)

270 240 210 180 150 120 90 60 30

sψ i

le ng

0

al

60

360

0

0

Dihedral Angles (Degree) ψ

Energy (Hartrees)

i

300

0

A

0

30

60

90

120

150

180

210 240

270

300

330

360

Dihedral Angles (Degree) φi

h

Di

F 10 H7

1,2-difluro-3-hydroxylpropane

φi

O9

E =f(φi,ψi), [χi1 in a] H 12

i

H1

ψ

i

(S)

C2

χ1

C3

H6

F11

C4 H8

H5

Fig. 4. PESs for comparison between two 1,2-difluoro-3-hydroxylpropane with c1Za PES; one in S conformation and one in R conformation.

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J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96 360 330 300

0 30 60 90

Di

he

12

0

dr

al

15

0

18

0

An

gle

21

0

sφ i

24

0

(D

27

0

eg

30

0

ree

33

0

)

36

0

0

30

60

120

90

150

180

330 300

270

240

240 210 180 150 120 90 60

ee)

gr

(De es ψ i

210

360

Dihedral Angles (Degree) ψ

Energy (Hartrees)

i

270

30

ngl

lA dra

0 0

e

Dih

30

60

90 120 150 180 210 240 270 300 330 360

Dihedral Angles (Degree) φ

i

F 10 H7 φi

O9

E =f(φi,ψi), [χi1 in g–] H 12

1,2-difluro-3-hydroxylpropane

χ1

ψ

C3

(R)

C2

F 11

i

C4

i

H5

H8

H6

H1 360 330

0

30

60

90

Dih

edr

120

al A

150

ngl

180

es

210

240

φ( i De

gre

270

e)

300

330

360

0

30

60

D

90

12

0

15

l

ra

d ihe

0

1

80

21

0

24

les

0

27

0 03

3 03

(D

ψi

0

0 36

) ree

Dihedral Angles (Degree) ψ

Energy (Hartrees)

i

300 270 240 210 180 150 120 90 60

eg

30

g An

0 0

30

60

90

120

150

180

210 240

270

300

330

360

Dihedral Angles (Degree) φ

i

F 10 H7

1,2-difluro-3-hydroxylpropane

φi

O9

E =f(φi,ψi), [χi1 in g–] H 12

ψ

i

(S)

C2

χ1

C3

F11

C4

i

H1

H6

H8

H5

Fig. 5. PESs for comparison between two 1,2-difluoro-3-hydroxylpropane with c1ZgK PES; one in S conformation and one in R conformation.

respectively, [26]. A Ramachandran map (Fig. 6) may be used to define the periodic behavior of the backbone of glycerol, and its fluorine congeners. Scan and optimizations have shown that conformers with c1i in the s conformation were not found. An energetic function may be formulated to characterize the structural trends:

ER Z fR ðfi ; ji ; c1i Þ

(1a)

for the R configuration and ES Z fS ðfi ; ji ; c1i Þ for the S configuration.

(1b)

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

85

Observations from Fig. 7 and Table 1 reveal a mirrored topographical image between the two enantiomeric surfaces. Dihedral values and energies tabulated in Table 1 also display a similar trend. Furthermore, when the two PEHSs of Fig. 7 are superimposed on each other, the PEHSs of both R and S configurations will be divided by three planes of symmetry: fi Z a for ½0% ji ; c1i % 360

Fig. 6. A Ramachandran map for glycerol.

[g+g-]g[ag-]g[g-g-]g0.43 4.99 0.11 [g+a]g[aa]g[g-a]g8.05 1.80 [g+g+]g0.000

[ag+]g6.23

χi1

[g+g+]a 0.93

ψi

[ag+]a 4.62

[g+g-]g[ag-]g[g-g-]g3.17 1.73 2.82 [aa]g[g-a]g[g+a]g3.54 2.97

[g-g+]g-

[g+g+]g- [ag+]g1.54 1.75

[g+g+]a [ag-]a [g-g-]a 6.18 4.25 2.69 [g+a]a [aa]a [g-a]a 2.40 7.287 4.02

S-Configuration

[g+g+]a [ag-]a [g-g-]a 11.36 4.62 0.93 [g+a]a [aa]a [g-a]a 4.02 7.29 2.39

[g-g+]a 11.4

[ag+]g+ 1.74

[g-g+]g3.41

R-Conformation

[g+g+]a 2.69

χi1

[g+g+]g+ [ag-]g+ [g+g-]g+ 3.40 1.75 1.54 [g+g-]g+ [g+a]g+ [aa]g+ 2.970 3.543

[g+g+]g+ 2.82

(2a)

ψi

[g-g+]g+ 3.17

[ag+]a 4.25 [g+g+]g+ [g+a]g+ 1.80

[g+g+]g+ 0.11

φi

[g-g+]a 6.18

[ag-]g+ [g+g-]g+ 6.234 [aa]g+ [g+g-]g+ 8.05 0.00

[ag+]g+ 4.99

[g-g+]g+ 0.43

φi

Fig. 7. PESs for comparison between two 1,2,3-trifluoropropane; one in pro-S and one in pro-R conformation.

Table 1 Dihedral angles for all computed/attempted backbone conformer and total and relative energies of 12 difluoro-3-dihydroxylpropane in the R and S enantiomers

F10 H7 φi

O9 H12

χ1

C2

i

C3 (R)

H6

H1 c1i

ψi

F 11 C4

H8

H5

Conformation (fi, ji, ci)

fI

ji

R Configuration gCgCgC gCagC gCgKgC agCgC aagC agKgC gKgCgC gKagC gKgKgC gCgCa gCaa

62.92 61.10 24.31 K177.69 K174.22 K178.02 K66.99 Not found K34.98 62.07 59.87

50.20 K167.11 K74.65 39.33 K168.94 K55.18 40.56

89.34 83.29 45.91 58.12 52.42 57.92 49.37

K388.67799 K388.67775 K388.67706 K388.67972 K388.67684 K388.67971 K388.67743

2.82 2.97 3.40 1.74 3.54 1.75 3.17

K43.87 46.71 K170.13

78.17 K164.31 177.59

K388.68003 K388.68100 K388.67867

1.54 0.93 2.40 (continued on next page)

Total energy (Hartrees)

Relative energy (kcal molK1)

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J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

Table 1 (continued) Conformation (fi, ji, ci)

fI

ji

c1i

Total energy (Hartrees)

Relative energy (kcal molK1)

gCgKa agCa aaa agKa gKgCa gKaa gKgKa gCgCgK gCagK gCgKgK agCgK AagK agKgK gKgCgK gKagK gKgKgK

55.18 166.61 167.13 167.53 K43.98 K38.78 K50.55 47.40 Not found 75.88 175.69 179.72 173.02 Not found K56.46 K61.07

K94.08 37.07 K171.03 K56.22 66.81 K166.37 K59.82 31.31

K178.11 152.99 159.28 172.46 K165.48 K169.25 175.06 K82.76

K388.67263 K388.67512 K388.67087 K388.67571 K388.66438 K388.67608 K388.67820 K388.68249

6.18 4.62 7.29 4.25 11.36 4.02 2.69 0.00

K49.27 37.35 K167.46 K58.77

K59.12 K71.44 K65.28 K76.01

K388.68180 K388.67255 K388.66966 K388.67453

0.43 6.23 8.05 4.99

K174.43 K65.40

K60.95 K59.49

K388.67962 K388.68231

1.80 0.11

F10 H7 φi

O9 H12

χ1

C2

i

H1 S Configuration GCgCgC GCagC GCgKgC agCgC AagC agKgC gKgCgC gKagC gKgKgC GCgCa GCaa GCgKa agCa Aaa agKa gKgCa gKaa gKgKa GCgCgK GCagK GCgKgK agCgK AagK agKgK gKgCgK gKagK gKgKgK

61.07 56.38 Not found K172.99 K179.68 K175.69 K75.87 Not found K47.42 50.55 38.84 44.05 K167.59 K167.08 193.37 K55.28 K59.99 K62.07 34.73 Not found 66.94 177.97 174.22 177.70 K18.95 K58.43 K62.90

C3 (S)

H6

ψi

F 11 C4

H8

H5

65.41 174.45

59.65 61.09

K388.68231 K388.67962

0.11 1.80

58.76 167.47 K37.41 49.30

75.92 65.33 71.41 59.09

K388.67453 K388.66966 K388.67255 K388.68180

4.99 8.05 6.23 0.43

K31.28 59.77 166.30 K66.78 56.21 171.02 K37.08 94.07 169.99 K46.71 43.97

82.73 K174.99 169.05 165.51 K172.54 K159.19 151.74 178.14 K177.59 164.30 K77.88

K388.68249 K388.67820 K388.67608 K388.66438 K388.67571 K388.67087 K388.67512 K388.67263 K388.67867 K388.68100 K388.68003

0.00 2.69 4.02 11.36 4.25 7.29 4.62 6.18 2.39 0.93 1.54

K40.92 55.33 168.94 K39.24 72.54 167.10 K50.05

K49.02 K57.84 K52.41 K58.11 K49.37 K83.36 K89.36

K388.67743 K388.67971 K388.67684 K388.67972 K388.67706 K388.67775 K388.67799

3.17 1.75 3.54 1.73 3.41 2.97 2.82

ji Z a for ½0% fi ; c1i % 360

(2b)

c1i Z a for ½0% fi ; ji % 360

(2c)

From the emerging energetic trends, subsequent enantiospecific energetic expressions may be formulated. In each enantiomer every conformations in which c1ZgC will

show the same magnitude of planarity. Using Eqs. (1a) and (1b), the following can be derived: ES Z fR ðKfi ; Kji ; Kc1i Þ

(3a)

ER Z fS ðKfi ; Kji ; Kc1i Þ

(3b)

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

4.2. 1,2,3-trifluoropropane Although 1,2,3-trifluoropropane is achiral, it is not completely symmetrical. The potential energy hypersurfaces of both the pro-R and pro-S configurations were investigated. The definition of pro-R and pro-S is the same

87

as that in case of glycerol. The topology describing the energy trends of pro-R configuration mirrors that of pro-S (Fig. 8). A similar pattern in the energies of minima was found when fully relaxed optimizations were performed on all MDCA-predicted pro-R and pro-S conformations (Scheme 3 and Table 2). From the (3a) and (3b) equations

360 330

0 30 60

Dih

90

edr

12

0

15

al A

0

ng

18

0

les

21

0

φ( i D

24

0

27

0

egr

ee)

30

0

33

0

36

0

30 0

90

60

0 12

0 15

al dr

0 18

0 21

0 24

s gle

0 27

0 30

0 33

0 36

e)

e egr

Torsional Angles (Degree) ψi

Energy (Hartrees)

300 270 240 210 180 150 120 90 60

(D ψi

30

An

0

he

Di

0

30

60

90 120 150 180 210 240 270 300 330 360

Torsional Angles (Degree) φi

F 10 H7

E =f(φi,ψi)

φi

F9

1,2,3-trifluoropropane

ψ

C3

Pro (s)

C2

C4 H5

H8

H6

H1

F 11

i

360 330

0 30 60

Dih

90

120

edr

150

al A

ng

180

les

210

240

φ( i De

270

gre

e)

300

330

360

0

30

60

90

12

0

15

l

ra

d ihe

0

0 18

21

0

2

40

les

g An

27

0 03

3 03

0

) ree

eg

(D

ψi

6 03

Torsional Angles (Degree) ψ

Energy (Hartrees)

i

300 270 240 210 180 150 120 90 60 30 0 0

30

60

90

120

150

180

210 240

270

300

Torsional Angles (Degree) φ

D

330

360

i

F 10 H7

E =f(φi,ψi) 1,2,3-trifluoropropane

φi

F9

ψ

H6

F11

i

Pro (R)

C2 H1

C3

C4 H8

H5

Fig. 8. Two PEHS portraying all the topologically possible conformations of 1,2-dihydroxyl-3-fluoropropane in S (top) and R (bottom) configurations.

88

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

Scheme 3.

the following can be derived: ES Z fR ðKfi ; Kji Þ

(4a)

ER Z fS ðKfi ; Kji Þ

(4b)

a line of symmetry in the disrotatory axis (Fig. 7). As a result, gCgC backbone conformations will have the same energy as gKgK. In such way, a molecule with gCa conformation will have the same energy as an agK. This behavior will yield a symmetrical function where

Another energetic pattern can be observed within one prochiral configuration, since one Ramachandran map has

EproS Z fproS ðfi ; ji Þ Z fproS ðKji ; Kfi Þ

(5a)

Table 2 Dihedral angles for all computed backbone conformers and energetics of 1,2,3-trifluoropropane with F10 substitution in different enantiomeric arrangements Conformation fi, jI

fI

jI

Total energy

Relative energy (kcal molK1)

F 10 H7 C3

F9 C2

46.99 35.86 52.47 K168.48 K169.90 K168.16 K47.78 K56.38 K59.41

φi

C4

ψi

H5

H8

H6

H1 GCgC GCa GCgK agC aa agK gKgC gKa gKgK

F 11

Pro (S)

59.37 168.14 K52.45 56.35 169.99 K35.90 85.67 168.48 K47.15

K412.56205 K412.55890 K412.55057 K412.55993 K412.55435 K412.55890 K412.55549 K412.55993 K412.56206

0.00 1.98 7.21 1.33 4.83 1.98 4.12 1.33 0.00

F 10 H7 C3

F9 C2 H1 gCgC gCa gCgK agC aa agK gKgC gKa gKgK

59.36 56.39 85.64 168.18 169.88 168.47 K52.42 K35.91 K47.08

F 11

Pro (R) φi

H6

47.21 191.53 K47.76 35.95 189.99 K56.38 52.61 191.85 K59.37

C4

ψi

H8

H5 K412.56206 K412.55993 K412.55549 K412.55890 K412.55435 K412.55993 K412.55057 K412.55890 K412.56206

0.00 1.33 4.12 1.98 4.83 1.33 7.21 1.98 0.00

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

and EproR Z fproR ðfi ; ji Þ Z fproR ðKji ; Kfi Þ

(5b)

4.3. Glycerol Only the pro-S conformation of glycerol was studied because of the similarities discussed earlier. The backbone dihedral angles fi and ji are not largely affected by the conformational changes of c1i , c2i and c3i . All nine of the MDCA-predicted backbone conformations are energetically stable at the RHF/3-21 g level of theory. It is believed that hydrogen bonding plays an important role in the stability of glycerol. At this level of theory, the total number of stable conformations of glycerol is 84. Fig. 9 represents a PEHS with five independent variables. Representations may be extended when modeling glycerol with further substitutions

89

of two or more OH groups by adding additional layers forming cube-like representation. It is an extension to the carbon backbone Ramachandran map. The large Ramachandran map at the background represents fi and ji of the glycerol backbone. The definition of the axes is similar to the Ramachandran map of Fig. 6. From each of the backbone conformations, 27 topologically possible conformations are predicted. These conformations are the result of the rotation of the dihedrals of c1i , c2i and c3i . On each of the large squares, three smaller Ramachandran maps are shown stacked on top of each other. The bottom most layer has c3ZgC, the middle layer has c3i Z a and the top layer has c3ZgK. The axes representing the other two OH dihedrals are shown in Fig. 9. With five variables, the symmetry may be a five dimensional function: EproS Z fproS ðfi ; ji ; c1i ; c2i ; c3i Þ

(6a)

Fig. 9. A PEHS extended from each of the 9 backbone conformation of glycerol; note tht the letters in square brackets are the backbone conformation in the order of [fi,ji] and the unbracketed letters are the OH group dihedrals in the order of c1i , c2i , c3i .

90

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

Table 3 Dihedral angles (in degrees) for all computed backbone conformers and energetics of stable glycerol conformers, optimized at RHF/3-21 g level of theory

H 14 O 10

χ3 i

H7 C3

O9 H 12

C2

χ1 i

φi

H6

H1

O 11 C4

ψi

H 13

χ2 i

H8

H5

Conformations of found geometry Conformations (fi, ji, c1i , c2i , c3i )

fi

ji

c1i

c2i

c3i

Total energy (Hartrees)

Relative energy (kcal molK1)

gCgCgCgCa gCgCgCgCgK gCgCgCaa gCgCgCagK gCgCgCgKa gCgCgCgKgK gCgCagCgC gCgCagCa gCgCaagC gCgCagKgC gCgCagKgK gCgCgKgCgC gCgCgKgCa gCgCgKgCgK gCgCgKagC gCgCgKaa gCgCgKagK gCagCgCgK gCagCaa gCagCgKa gCaagCgC gCaagCgK gCaagKgK gCagKgCgC gCgKgCgCgC gCgKgCgCgK gCgKagCgC gCgKgKagC gCgKgKgKgC gCgKgKgKa agCgCgCgK agCgCagK agCagCgK agCaagK agCgKgCgC agCgKgCa agCgKagC agCgKaa agCgKgKgC aagCgCgK aaagCgK aagKaa aagKgKa agKgCaa agKgCgKgK agKagKgK agKgKgCgC

64.76 65.01 63.37 63.67 46.95 50.18 70.39 52.73 69.35 54.18 36.38 67.55 27.18 35.64 66.66 22.65 35.25 61.35 61.64 61.18 67.27 50.08 47.39 71.07 62.46 67.25 44.55 76.17 72.92 53.51 169.01 168.52 172.11 170.21 179.05 177.13 176.90 174.61 175.68 167.35 170.67 173.28 173.07 K171.64 162.02 164.97 170.40

66.46 64.84 68.46 65.66 34.08 30.63 61.33 62.38 62.21 28.05 42.29 53.99 48.15 41.76 53.85 53.07 44.50 K171.66 K164.99 198.02 K171.91 K178.40 171.63 189.67 K73.01 K53.60 K76.20 K44.60 K62.55 K67.30 58.04 57.96 55.97 55.73 55.70 57.65 57.08 60.51 60.17 K173.08 K173.27 K170.68 K167.33 K47.44 K61.14 K61.67 K71.09

51.61 42.68 52.59 44.88 60.69 52.90 K174.03 K167.93 K179.10 167.40 159.89 K97.71 K68.09 K70.00 K96.06 K67.46 K71.14 44.84 49.97 50.44 176.24 K178.57 177.91 K96.56 68.30 46.31 169.41 K61.68 K58.37 K32.41 84.35 84.17 184.20 K178.75 K41.76 K52.60 K38.98 K50.68 K37.69 82.27 K174.90 K46.76 K47.88 62.85 84.41 K171.78 K40.09

75.82 80.92 K158.01 K162.02 K71.35 K71.07 79.08 75.67 K176.75 K72.78 K76.00 80.53 75.73 80.94 170.13 171.88 168.82 52.27 171.79 K84.43 41.83 52.26 K62.91 40.08 58.45 32.59 61.74 K169.38 K68.16 K46.30 83.28 K179.59 79.08 179.17 76.15 73.85 177.41 K174.20 K94.31 47.93 46.71 175.06 K82.37 K177.65 K50.50 K49.95 96.66

K177.80 K82.84 K171.40 K86.73 K176.37 K83.32 37.67 K178.95 37.72 49.07 K76.23 35.57 K172.27 K54.27 35.45 K165.44 K56.62 K85.66 160.54 153.23 39.06 K63.17 K64.75 33.80 105.93 K91.11 93.06 29.10 14.14 K148.19 K36.21 K36.69 K44.30 K44.08 69.13 K163.11 67.48 K158.30 71.94 K38.87 K48.11 169.93 160.74 K174.99 K34.48 K41.86 88.50

K340.91416 K340.91360 K340.91658 K340.91606 K340.91789 K340.91762 K340.91734 K340.90479 K340.91793 K340.91646 K340.91127 K340.91658 K340.91018 K340.91170 K340.91660 K340.91049 K340.91199 K340.91756 K340.92205 K340.92051 K340.91896 K340.90979 K340.89888 K340.91648 K340.92399 K340.91511 K340.92257 K340.92257 K340.92399 K340.91511 K340.91466 K340.91608 K340.91606 K340.91668 K340.91170 K340.91329 K340.91170 K340.91424 K340.90903 K340.91683 K340.91800 K340.91800 K340.91683 K340.89888 K340.92051 K340.92205 K340.91648

5.22 5.46 3.57 3.94 3.27 3.52 3.23 10.34 2.88 4.14 6.83 3.64 7.70 6.68 3.61 7.50 6.53 3.33 0.77 1.70 2.57 7.55 13.76 3.92 0.00 4.93 0.58 0.57 0.00 4.93 4.67 3.91 3.89 3.52 6.53 5.51 6.53 4.94 7.94 3.65 2.94 2.94 3.65 13.76 1.70 0.77 3.92

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

91

Table 3 (continued) Conformations of found geometry Conformations (fi, ji, c1i , c2i , c3i ) agKgKagC agKgKaa agKgKgKa gKgCgCgCgC gKgCgCgCa gKgCgCgCgK gKgCgCagC gKgCgCagK gKgCagKgC gKgCagKa gKgCgKgKgC gKgCgKgKa gKgCgKgKgK gKagCgCgC gKaagCgC gKaagCgK gKaaaa gKaagKa gKagKgCgC gKagKgCgK gKagKaa gKagKgKa gKgKgCagC gKgKgCaa gKgKgCgKa gKgKgCgKgK gKgKagCgC gKgKagCa gKgKagCgK gKgKaagC gKgKagKa gKgKagKgK gKgKgKgCgC gKgKgKgCa gKgKgKgCgK gKgKgKagC gKgKgKagK gKgKgKgKa gKgKgKgKgK

fi 171.92 178.31 171.65 K66.33 K67.58 K69.11 K70.95 K74.28 K54.64 K54.17 K57.30 K57.43 K58.02 K60.15 K57.05 K60.51 K55.76 K57.97 K55.61 K57.64 K55.90 K58.08 K27.98 K42.40 K30.62 K34.00 K33.29 K44.50 K53.04 K62.28 K65.65 K65.65 K33.70 K41.73 K47.97 K61.35 K62.35 K64.81 K66.44

ji

c1i

c2i

c3i

Total energy (Hartrees)

Relative energy (kcal molK1)

K67.25 K50.01 K61.27 57.28 58.09 57.37 54.71 54.13 71.04 74.24 66.34 69.13 67.66 K175.70 K176.89 K174.63 K170.08 K168.52 K179.09 K177.15 K172.07 K169.06 K54.22 K36.26 K50.18 K46.99 K53.44 K35.27 K22.67 K69.36 K63.65 K68.48 K51.15 K35.64 K27.31 K70.39 K52.72 K65.01 K64.72

K41.87 K52.14 K52.26 50.22 53.86 52.98 45.97 49.44 K175.58 178.43 K82.38 K84.26 K78.55 94.39 K177.72 174.46 K179.47 179.54 K76.29 K73.96 K79.05 K83.15 72.76 76.09 71.05 71.29 K168.61 K168.78 K171.79 176.81 161.94 157.72 K81.41 K80.85 K75.64 K79.25 K75.72 K81.05 K75.92

K176.20 179.01 K44.89 82.35 78.29 84.19 175.54 181.41 K46.16 K49.42 K50.23 K52.88 K53.96 37.69 39.06 50.70 178.92 K84.28 41.89 52.58 175.87 K84.25 K167.29 K159.37 K52.94 K60.70 80.81 71.18 67.47 179.20 K44.88 K52.63 79.65 69.91 67.99 174.38 167.85 K42.65 K51.57

82.92 K175.79 K155.19 49.99 K158.09 K67.23 47.16 K70.79 76.94 K169.18 73.70 K172.91 K82.15 52.76 56.94 K81.59 164.15 157.14 55.29 K76.84 164.47 156.45 72.02 K164.01 K159.56 K66.25 80.83 175.81 K74.35 82.99 K155.17 K70.54 78.84 172.72 K68.76 82.57 K61.16 K159.39 K64.77

K340.91896 K340.90979 K340.91756 K340.91540 K340.91540 K340.91721 K340.91547 K340.91811 K340.91547 K340.91811 K340.91540 K340.91721 K340.91540 K340.90903 K340.91170 K340.91424 K340.91668 K340.91608 K340.91170 K340.91329 K340.91606 K340.91466 K340.91646 K340.91127 K340.91762 K340.91789 K340.91686 K340.91199 K340.91049 K340.91793 K340.91606 K340.91658 K340.91672 K340.91170 K340.91018 K340.91734 K340.90479 K340.91360 K340.91416

2.56 7.55 3.32 4.46 4.34 3.34 4.33 2.79 4.33 2.79 4.46 3.34 4.33 7.94 6.53 4.94 3.53 3.91 6.53 5.51 3.89 4.67 4.14 6.82 3.52 3.27 3.78 6.53 7.50 2.88 3.94 3.57 3.88 6.68 7.70 3.23 10.34 5.46 5.09

Like the 1,2,3-trifluoropropane molecule, glycerol is symmetrical. Therefore, its energy may be expressed as a function its rotamers. In such way a few equations can be derived that may be able to help characterize its structural and energetic behavior: For all c3i Z gC:

(6b)

and for all of c3i Z gK and a, the two following equation can be considered: EproS Z fproS ðfi ; ji ; c1i ; c2i ; 120% c3i % 180Þ Z ðKji ; Kfi ; Kc2i ; Kc1i ; 0% c3i % 120Þ

Z ðKji ; Kfi ; Kc2i ; Kc1i ; 120% c3i % 180Þ

(6d)

In structural pairs it is observed that: f ðgC; gC; gK; a; gCÞ sf ðgK; gK; a; gC; gCÞ

EproS Z fproS ðfi ; ji ; c1i ; c2i ; 0% c3i % 120Þ Z ðKji ; Kfi ; Kc2i ; Kc1i ; 0% c3i % 120Þ

EproS Z fproS ðfi ; ji ; c1i ; c2i ; 0% c3i %K120Þ

(6c)

f ðgC; gC; gK; gC; gCÞ sf ðgK; gK; gK; gC; gCÞ From this observation, there may exist possible conformations other than the ones observed that do not follow the functions as stated in Eqs. (6b)–(6d). The study of glycerol shows that the bond distance values of the rotamer pairs interchange between specific pairs. The results of the optimizations are shown in Table 3. Table 4 shows a list of conformations and their bond distances

92

Table 4 Values for topologically probable conformations in different types of geometry

H14 O10

H 13 H7 C3

O9 H 12

fI j i

c1i

g

g g g gC a a gCgKa a gCgC gKgCgC gCgCgK a gCgK gKa a gKgKa gCgKgK a gKgK gKgCgC gK a gC gK a a gKgK a gCgKa gCgKgK a gKgC gCgCgK gKgK a gCagC gC a a gCgKa gCgKgK a gCgC a gC a gKgCgC gCgCgC a gCgC gKa gC gKagK gKgKgC

C

a

aa

AgK

Type 2: a five-membered ringand a sixK membered ring Fused together

gCgC

gCgK gKgK

Type 3: Glycerol folded into a Ball

gCgK

c2i

c3i

C C K

Relative energy (kcal molK1) 4.04 1.22 2.18 3.16 4.71 4.50 3.76 3.76 4.49 2.18 1.22 4.71 3.16 8.91 4.04 3.83 4.00 4.73 5.58 5.58 4.73 7.99 4.00 3.83 4.48 7.53 4.56 0.00 0.89 0.89 7.53 0.00

H6

H8

H5

˚) Distance of H-bonds (A H12–O9

H12–O10

H12–O11

H13–O9

H13–O10

H13–O11

H14–O9

H14–O10

H14–O11

0.97 0.97 0.97 0.97 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.96 0.97 0.97 0.97

2.19 2.15 2.17 3.51 3.33 3.24 3.52 2.16 2.17 3.20 3.47 2.13 2.16 2.19 2.21 2.48 2.39 3.60 2.12 2.94 3.76 3.83 3.68 3.74 4.37 4.31 4.16 2.40 3.77 2.23 3.63 2.20

4.01 3.92 3.92 5.05 4.32 5.14 5.59 4.58 4.65 4.78 4.64 4.13 4.05 4.21 4.15 3.38 3.30 3.54 2.80 1.88 2.17 2.07 2.12 2.12 3.65 3.52 3.59 2.95 3.51 4.54 2.09 4.64

4.15 4.64 4.78 4.05 4.13 4.65 4.58 5.59 5.14 3.93 3.92 4.33 5.05 5.06 4.01 2.12 2.12 2.17 1.88 2.81 3.54 3.58 3.30 3.38 2.26 2.09 2.24 1.96 1.85 5.09 3.52 4.37

2.21 3.47 3.21 2.16 2.13 2.17 2.16 3.52 3.24 2.17 2.15 3.33 3.51 3.79 2.19 3.74 3.68 3.76 2.94 2.12 3.60 3.79 2.39 2.47 3.41 3.63 3.44 2.83 2.87 4.41 4.31 4.16

0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97

3.29 3.42 3.36 2.07 2.08 2.16 2.16 3.60 3.63 2.07 2.06 3.27 3.23 3.54 3.41 3.72 3.43 2.35 3.28 3.87 3.74 4.40 4.39 4.06 3.77 4.34 3.80 2.86 2.91 3.13 3.52 3.16

0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97

3.41 2.06 2.07 3.23 3.27 3.63 3.60 2.16 2.16 3.37 3.42 2.08 2.07 3.31 3.29 4.06 4.39 3.74 3.87 3.28 2.35 3.65 3.43 3.72 2.37 3.52 2.43 2.05 2.04 3.91 4.34 3.94

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

Type 1: 2 Hydrogen Bonds

Conformation

C4

C2 H1

Type

O 11

Type 4: Five-membered ring

gCgC

gCa a gC

gKgK

Type 5: Six-membered ring

gCgC

gKgC

6.17 6.52 4.65 4.97 4.17 3.80 8.66 4.64 8.91 5.86 4.96 4.98 4.59 7.71 6.72 7.71 6.12 9.39 9.39 7.71 6.12 4.59 4.96 7.71 6.72 4.98 5.86 3.80 4.97 4.65 4.17 6.52 6.17 7.99 8.66 7.71 8.47 5.39 5.39 4.25 5.34 3.69 5.34 3.69 5.39 4.25 5.39 5.39

0.97 0.97 0.97 0.97 0.96 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.96 0.96 0.97 0.97 0.97 0.97

2.15 2.16 2.18 2.17 3.54 3.53 3.39 3.39 3.79 3.27 3.26 3.54 3.54 2.27 2.25 2.23 2.21 2.20 4.16 4.41 4.39 4.34 4.34 4.06 4.06 4.04 4.05 4.39 4.33 4.38 4.03 4.01 4.03 3.79 3.68 3.62 3.72 3.92 3.89 3.90 3.91 3.90 4.40 4.32 4.08 4.06 4.09 4.39

4.12 4.01 4.09 3.98 4.18 4.19 3.23 3.17 5.06 4.54 4.44 4.85 4.75 4.63 4.68 4.54 4.59 4.64 4.37 5.09 5.07 5.07 5.10 4.54 4.54 4.59 4.72 4.19 4.02 4.01 4.34 4.38 4.36 3.58 2.04 2.07 2.05 1.91 1.94 1.92 1.86 1.88 3.54 3.53 3.12 3.14 3.08 3.45

4.36 4.38 4.02 4.03 4.34 4.19 4.25 4.19 4.21 4.72 5.10 4.59 5.07 4.54 4.54 5.09 5.07 4.37 4.64 4.54 4.59 4.75 4.44 4.63 4.68 4.85 4.54 4.19 3.98 4.09 4.18 4.00 4.12 2.07 3.47 3.51 3.45 3.12 3.08 3.14 3.54 3.53 1.86 1.88 1.91 1.92 1.94 2.05

4.03 4.01 4.38 4.33 4.03 4.39 4.08 4.38 2.20 4.05 4.34 4.04 4.34 4.06 4.06 4.41 4.39 4.16 2.20 2.23 2.21 3.54 3.26 2.27 2.25 3.54 3.27 3.53 2.17 2.18 3.54 2.16 2.15 3.83 4.10 4.09 4.39 4.08 4.09 4.06 4.40 4.32 3.91 3.90 3.92 3.90 3.89 3.72

0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.96 0.97 0.97 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.96 0.96 0.97 0.97 0.97 0.97 0.97 0.97

3.55 3.23 3.59 3.29 2.05 2.06 2.14 2.15 3.31 2.16 2.15 2.15 2.12 3.18 3.49 3.13 3.44 3.16 3.94 3.91 4.05 4.28 4.26 3.93 4.09 4.34 4.33 3.98 4.31 3.97 4.01 4.38 3.99 3.65 4.05 3.49 4.12 3.95 4.38 3.99 3.95 3.97 3.99 4.35 4.02 4.41 4.10 4.03

93

0.97 3.99 0.97 4.38 0.97 3.97 0.97 4.31 0.97 4.01 0.97 3.98 0.97 3.97 0.97 3.94 0.97 3.54 0.97 4.33 0.97 4.26 0.97 4.34 0.97 4.27 0.97 3.93 0.97 4.09 0.97 3.91 0.97 4.05 0.97 3.94 0.97 3.16 0.97 3.13 0.97 3.44 0.97 2.12 0.97 2.15 0.97 3.18 0.97 3.49 0.97 2.15 0.97 2.16 0.97 2.06 0.97 3.29 0.97 3.58 0.97 2.05 0.97 3.23 0.97 3.55 0.97 4.40 0.97 4.05 0.97 4.38 0.97 4.03 0.97 4.02 0.97 4.10 0.97 4.41 0.97 3.99 0.97 4.35 0.97 3.95 0.97 3.97 0.97 3.95 0.97 3.99 0.97 4.38 0.97 4.12 (continued on next page)

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

gK a

gCgCa gCgCgK gCa a gCa gK a gCgC a a gC gKgCgC gKa gC agCgK gCgCgK gCa gK a gCgK a a gK gKgCgC gKgCa gKa gC gK a a gKgKgC gCgCgC a gCgC a gCgK aaa a gK a gKgCgC gKgCgK gK a a gKgKa agCgC a gK a agKgK gKagC gKgKa gKgKgK a gKgK gKgCa gKgCgK gK a a gCgCgC gCgC a gCgCgK gCa gC gCagK a gKgC a gK a gKgKgC gKgKa gCgCgC gKgKgK

0.97 0.97 0.97 0.97 0.97 0.97 0.97 4.38 4.05 3.69 3.37 3.74 3.96 3.65 0.97 0.97 0.97 0.97 0.97 0.97 0.97 3.61 3.68 4.03 3.30 3.79 3.73 3.83 2.06 2.04 4.11 4.64 5.06 3.89 2.07 3.51 3.47 3.89 5.06 4.64 4.11 3.58 gCgC gC a a gK gKgK Type 6: No hydrogen bonds

g g

H14–O10 H14–O9 H13–O11 H13–O10 H13–O9 H12–O11 H12–O10

4.09 4.10 3.73 3.79 3.29 4.03 3.79 0.97 0.97 0.97 0.97 0.97 0.97 0.97 8.47 7.71 8.66 12.05 15.76 15.76 12.05 ag g gKgCa gKgCgK a gC a a gKgK gC a a gK a gK C K

H12–O9 fI j i

K K

˚) Distance of H-bonds (A

Relative energy (kcal molK1) c3i c2i c1i

Conformation Type

Table 4 (continued)

3.49 4.05 3.96 3.74 3.37 3.69 4.40

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96

H14–O11

94

Table 5 Calculated O–H stretching frequencies of the different glycerol conformations (cmK1)

gCgCgCgCa gCgCgCgCgK gCgCgCaa gCgCgCagK gCgCgCgKa gCgCgCgKgK gCgCagCgC gCgCagCa gCgCaagC gCgCagKgC gCgCagKgK gCgCgKgCgC gCgCgKgCa gCgCgKgCgK gCgCgKagC gCgCgKaa gCgCgKagK gCagCgCgK gCagCaa gCagCgKa gCaagCgC gCaagCgK gCaagKgK gCagKgCgC gCgKgCgCgC gCgKgCgCgK gCgKagCgC gCgKgKagC gCgKgKgKgC gCgKgKgKa agCgCgCgK agCgCagK agCagCgK agCaagK agCgKgCgC agCgKgCa agCgKagC agCgKaa agCgKgKgC aagCgCgK aaagCgK aagKaa aagKgKa agKgCaa agKgCgKgK agKagKgK agKgKgCgC agKgKagC agKgKaa agKgKgKa gKgCgCgCgC gKgCgCgCa gKgCgCgCgK gKgCgCagC gKgCgCagK gKgCagKgC gKgCagKa gKgCgKgKgC gKgCgKgKa gKgCgKgKgK gKagCgCgC

O9–H12

O11–H13

O10–H14

3438.4 3426.5 3437.2 3425.9 3440.1 3430.6 3476.6 3458.8 3472.6 3461.0 3463.4 3465.9 3425.7 3425.8 3465.1 3437.7 3454.4 3428.1 3426.5 3426.7 3419.9 3453.2 3455.4 3470.0 3443.1 3411.4 3475.4 3373.9 3375.3 3386.0 3447.0 3426.9 3467.0 3468.9 3428.2 3438.4 3428.8 3438.1 3426.2 3444.2 3465.7 3431.1 3432.4 3430.9 3445.7 3434.8 3416.5 3423.0 3440.9 3444.0 3394.2 3410.7 3397.9 3392.0 3396.5 3472.0 3473.8 3452.2 3452.4 3448.1 3461.3

3437.2 3439.7 3464.4 3466.2 3420.1 3422.9 3440.8 3435.6 3458.9 3445.6 3467.3 3446.4 3450.8 3456.0 3459.8 3457.6 3464.1 3442.9 3467.4 3445.7 3423.3 3440.9 3430.8 3416.5 3375.7 3387.2 3374.4 3475.9 3442.5 3411.3 3445.9 3462.1 3442.6 3461.6 3443.3 3439.0 3459.8 3459.9 3461.3 3432.4 3432.2 3465.7 3444.2 3455.4 3426.7 3426.3 3470.0 3471.3 3453.3 3429.2 3452.2 3446.9 3452.4 3472.0 3473.8 3392.2 3396.5 3394.3 3397.8 3410.8 3426.2

3458.5 3449.6 3461.4 3456.2 3448.5 3449.6 3426.6 3437.4 3427.6 3426.2 3441.7 3413.3 3435.4 3452.8 3413.5 3438.9 3439.8 3455.4 3434.2 3418.6 3471.0 3455.9 3437.7 3407.6 3406.0 3450.6 3408.0 3407.4 3405.2 3450.6 3424.7 3446.1 3437.8 3441.1 3418.6 3455.4 3416.1 3457.1 3418.4 3439.3 3452.8 3452.8 3439.3 3437.7 3418.6 3467.7 3407.6 3419.3 3455.9 3455.4 3426.4 3452.6 3451.4 3425.3 3455.1 3425.3 3455.1 3426.4 3451.4 3452.6 3418.4

(continued on next page)

J.M.S. Law et al. / Journal of Molecular Structure: THEOCHEM 722 (2005) 79–96 Table 5 (continued)

g aag g gKaagCgK gKaaaa gKaagKa gKagKgCgC gKagKgCgK gKagKaa gKagKgKa gKgKgCagC gKgKgCaa gKgKgCgKa gKgKgCgKgK gKgKagCgC gKgKagCa gKgKagCgK gKgKaagC gKgKagKa gKgKagKgK gKgKgKgCgC gKgKgKgCa gKgKgKgCgK gKgKgKagC gKgKgKagK gKgKgKgKa gKgKgKgKgK K

C C

O9–H12

O11–H13

O10–H14

3459.8 3459.9 3461.6 3462.4 3443.3 3439.0 3442.5 3446.0 3445.6 3442.3 3422.8 3420.1 3460.5 3464.1 3458.8 3458.9 3466.2 3465.6 3454.9 3455.8 3450.8 3440.8 3435.6 3440.9 3437.2

3428.8 3438.1 3469.0 3446.5 3428.2 3438.4 3467.0 3445.7 3462.2 3468.4 3430.6 3440.1 3444.5 3439.4 3437.7 3472.6 3425.9 3437.2 3433.4 3425.9 3425.6 3476.6 3458.8 3426.5 3438.4

3416.1 3457.1 3439.9 3469.0 3418.5 3455.4 3437.9 3424.7 3426.2 3445.8 3449.6 3448.5 3409.9 3454.3 3438.9 3426.5 3456.2 3461.4 3412.1 3452.7 3435.4 3426.5 3437.4 3449.6 3459.7

between the O and H atoms on the OH group of glycerol. Additional intramolecular hydrogen bonds can potentially exist between the oxygen atoms and atoms not mentioned which may or may not contribute to the stabilization of certain rotamers. For many conformations, they form some shapes similar to five or six-member rings. Determination of the shape of these structures is based on the relative positions of C2, C3, C4, O9, O10, O11, H12, H13 and H14. The conformations of glycerol may be classified in six geometric shapes. Most structures are found having of a fivemembered ring conformation or in a structure analogous to two five-membered rings joined (fused) together by two common atoms. The Type 3 structures are rare, but one of the global minima is of Type 3 structure. It is also seen that the relative energies of existing conformations with no intramolecular hydrogen bonds are relatively high. This implies that in glycerol the close proximity of OH groups can have a significant effect in energetic stabilization. It is observed that only molecules with fiZgC and jiZgK can form Type 3 conformations, so most backbones are in Type 4 and Type 1 conformation. 4.4. Frequency calculations on glycerol Frequency computations have also been performed on the stable conformations of glycerol. Frequencies responsible for the linear vibration of each of the OH bonds were recorded; these values are shown in Table 5. Compared to frequencies for torsional rotation, these frequencies are considered to be the higher end of the absorption spectrum.

95

Table 6 Mean, median and standard deviation of the computed scaled frequencies of glycerol OH bonds (cmK1) Bonds

O9–O12

O11–O13

O10–O14

Average Standard deviation Median Minimum Maximum

3512.72 20.42437 3512.455 3548.87 3462.532

3512.988 23.23218 3514.642 3548.842 3445.916

3509.476 17.33027 3509.84 3541.072 3476.832

According to Scott and Radom, they do not have a large effect on enthalpy and entropy [27]. Therefore, a scale factor of 0.9085 is sufficient to adjust the frequencies such that they are closer to empirical values of 3000–3600 cmK1. The standard means, medians and standard deviations are listed in Table 6. The standard deviations of the corresponding vibrations among the conformers are quite large, indicating that vibrational characteristics of OH bonds are probably conformation-dependent.

5. Conclusions From these studies it has been shown, that 1,2-difluoro-3hydroxyl propane, 1,2,3-trifluoropropane and glycerol are representative systems to model the backbone conformation of lipids. All three molecules show similar properties when comparisons are made between different prochiral configurations and different chiral configurations. Trends may also be characterized between different rotamers of the same prochiral configurations of 1,2,3-trifluoropropane. Comparison of results between a simple molecule such as 1,2,3trifluoropropane and glycerol has suggested that these structural and energetic trends found in the former molecule may also exist in the latter one. However, these trends in the latter molecule manifest themselves in a more complex manner so that their dihedrals and energy cannot easily be described by mathematical functions.

Acknowledgements The authors wish to thank the Global Institute of Computational Molecular and Material Science for supporting this work. One of the authors, Jacqueline M. S. Law, is especially grateful to Professor Emeritus I. G. Csizmadia for helpful discussion and encouragement to tackle the immense challenges involved in the formulation of an understanding of the conformational behavior of lipids.

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