Molecular mechanics calculation on the hydroxyl stretching frequency in saturated alcohols

downal Elsevier

ofMoLecuLar Structure, 127 (1985) 57-75 Science Publishers B-V., Amsterdam -Printed

MOLECULAR !STRETCHING

J. C. CABALLERO

MECHANICS FREQUENCY

and J. H. VAN

Analytical Chemistry Laboratory. Utrecht (The Netherlands)

CALCULATION IN SATURATED

DER

h The Netherlands

ON THE HYDROXW, ALCOHOLS

hlAAS

Uniws-sity

of Ubecht.

Croesestrarrt

77A. 3522 AD

(Received 23 August 1984)

The frequencies of the hydroxyl stretching vibration, uoH. of the OH rotamers of methanol, ethanol, propan-2ol, t-butanol and adamantan-l-1 in the gas phase have been calculated applying molecular mechanics methods. A discussion is devoted to the asignin view ment of the observed voH freq uencies to the rotamers in ethanol and propan-2-l of tbe discrepancy in pubhahed data The cnlculations were performed with the -4hinger interactions between MM2 force field. It proved to be necesmry to include electrostatic point charges located at the atomic nuclei to obtain calculated results that a-e in good The calculation of these interactions and agreement with experimental messure menk the introduction in the min-hnization procedure of the energy is described. Minor adaptation of the force field was needed to fit the observed frequencies. With the introduced modifications a systematic increase of about 0.3 kcal mop is found in the calculated steric energies of the conformera The relative rotamer populations derived from the energy difference between OH conformers in tbe molecule ethanol and propan-2-01 agree with experimenti IR results INTRODUCTION

The OH stretching mode has a high diagnostic value in establishing those OH rotamers in which an alcohol molecule actually exists for two reasons. Firstly, due to its high frequency, this mode can be regarded as isolated from other vibrations of the molecule, and therefore it will not undergo any vibrational coupling. This is supported by the observation that, within the experimental ermr, no difference existi betieen the kquencies of van in methanol, ethanol and t-butanol and that of their corresponding partially or t&ally deuterated species. Secondly, the wide range of values found for in the stretching pOH in different compounds points to a high sensitivity mode toward the various possible environments of the hydroxyl group. Special attention has been paid in our laboratory to the structural features responsible for the differences in van of saturated and unsaturated alcohols. For a large number of alcohols the vOH bands have been measured in apolar solvents at very low~concentrations, leading t9 a comprehensive set of accurate experimental data [i-3]. The scope of data in gas phase species, 0022-286Ol85j803.30

Q 1985

BIsevier Science

Fubhshecs

B-V_

58

however, is rather limited because of the low vapour pressure for most of the compounds. The next aim of our investigation wz togainfurtherinsightintothe experimental results by means of model calculations, on which the present paper reports In order to accomplish this purpose, the model should be able to cdculate VOH not only from a suitable value of the OH bonding force constant but also taking into account, accurately, the influence of the local environment of the hydroxyl group fez a given &quency. The calculations should also provide information about the internal energy difference between the OH conformers of a molecule, tirn which their relative populations, may be derived. An approach using “ab initio” calculations would be very appropriate but the computing time needed for large molecules is prohibitive. We thus chose the molecular mechanics (MM) approach, which has demonstrated its validity in predicting molecular properties, over structures and thennodynamic features, wi+A the advantage of a more economical computing procedure_ Several MM calculations usiug a vsriety of potential functions to describe the intramolecular interactions have already been performed on the vibrational frequencies of alkane molecules, leading to quite satisfactory results [4-7]_ However, calculation of lkquencies in molecules containing heteroatoms, where ekctrostatic interactions may play an important role, have not reached the dv of accurac:? necessry to reproduce the observed data within acceptable limits [7-l(?] _ In the cases inclusion of electrostatic effects should improve the talc-ulated &quencies. Before giving the results of the calculations, in view of the discrepancy in the published data we first discuss the assignment of the OH stretching frequencies to the rotamers in ethanol and propan-2-01. EXPERIMENTAL

Except for adamantan-141, the gas-phase spectra were recorded on a Perkin Elmer MOB spectrometer at ambient temperatures. Wavenumber calibration was performed with gaseous NH3 and H20. Band positions are believed to be accumte to 20.6 cm-‘. Scanning speed was 21 cm-’ min-’ and resolution ahout 0.5 cm-’ at 3600 cm-‘. The alcohols were measured in gas cells with NaCi windows, effective pathlength 10 cm, in the range 38Oe3500 cm-‘. The compounds were dried before use on molecular sieves of 4 A and their purity was >9%. The IR spectrum of adamantan-l-01 was recorded on a DIGILAB FT-IR spectrometer at 145°C in a gas cell, as described above. RESULTS

AND

DISCUSSION

The recorded OH absorption bands are displayed in Fig. 1. Obviously, the three compounds methanol, t-butanol and adamantan-l-01 clearly exhibit

59

Fig- 1. IR hydroxyl absorption bands of methanol (A); ethanol (B), propan{C); t-&OH (D) (-) and adamantan-lo1 (E) (- - - -) in the gas phase. A, absorbance (arbitrary units).

Fig. 2. Projection

along the CO bonding

of the alcohol

rotamers

60

only one Q branch with the corresponding P and R branches. For each molecule of ethanol and propan-2-01 two different rotamers may be expected (Fig. 2) and, because the bands of the rotamers overlap to some extent, the overall band pattern for these two compounds is more complex. For convenience the rotzmers of ethanol and propan-2-l are denoted trans when they have a symmetry plane, andgauche when they have not. Rotamer

assignment

Ethanol Different assignments of the observed kzquencies to the tmns and gauche rotamers have been proposed. Per-chard and Josien [ll] studied in detail twelve isotopic species of ethanol in vapour, liquid and solid phases as well as in solution. They measured two gas-phase frequencies in the OH stretching region, one at which they assigned to the Q 3676.1 cm-’ and one at 3658.6 cm-‘, branches of the rotamers. Our observed kquencies are in very good agreement with the reported values (Table 1). However, the study was inconclusive as they could not arrive at a final assignment of the observed frequencies to the rotamers;. A later attempt to assign the two observed Q-branches of the voH mode was made by Barns and Hallam [12] _ They studied ethanol in an Argon matrix (20 K) at various concentrations. A doublet was found with frequencies at 3662.2 and 3657.6 cm -’ ; the latter having a stronger (relative) intensity. Since microwave studies suggested that the truns conformer would TABLE

1

Measured

OH stretching

frequencies

Compound

of alcohols

in the gas phase

vaG=mq)

Methanol

This work

Other

3681.4 3676.1

3688q 3687”

3661.6 3658.Sh 3660-O

3661a,

3681=.

3681.5g

. 3676.1b . 3677=

Ethanol {- gauche

3660=

3659=

Propan-2-01 t-Bu’aol Adamantan-l-o1

3658.6b.

3627.4 3643.0 3631 .O

3643.1d 3627f

*Ref_ 35. gR.ef. 36, ‘Ref. 32. bRef. 11. =Ref_ 13. dRef_ 33. =Ref_ 34 and referenees therein hAs the band at 3661.6 cm1 _IS not due to water in the sample nor to my other impurity, we conclude that both bands correspond to transition of two different gauche subsfates whose existence has been reported in limture (refs 14 and 39).

61

be dominant, they assigned the low-fiequenoy band to the trans conformer and the higher one to the gauche_ More recently, Richter and Schiel [13] investigated the conformational dynamics of ethanol in the gas phase by means of Raman spectz-oscopy. They observed two absorption bands at about 3677 and 3660 cm-’ which were nearly resolved at 145% and used the microwave measurements of Kakar and Quade [14] to assist in the assignment. Taking the energy difference between the conformers as 0.14 kcal mol? in favour of Pans, a greater relative population was calculated for the gauche conformer (the statistical ratio of gauche to tram is 2:l). These calculated populations resemble the experimental spectroscopic results provided, as assumed by Richter and Schiel, the transition probability for pOH in both conformers is equal From these considerations on the intensities of the absorptions, they assigned the high-frequency band to the trclns rotamer and the low one to the gauche _ In our opinion assignments based on the relative intensity ratios as determined by the above-mentioned authors are not free from serious uncertainties. First, with respect to the Ar matrix measurements, regardless of the dynamics of possibility of different trapping sites, the conformational the molecule can be strongly influenced by the temperature of the matrix, which might lead to erroneous conclusions. Second, the intensity of Raman bands due to the stretching vibration of the hydroxyl group in gas-phase molecules at ambient temperature is ex’iremely weak. A higher temperature is required to enhance the intensities by inc reasing the vapor pressure of the alcohol. However, on raising the temperature of ethanol, species appear showing absorptions at frequencies between those of the Duns and gmche conformers, and consequently the conformational equilibrium between the truns and gauche forms seems to be disturbed. In view of these disadvantages we conclude that assi,gnment on the basis of the relative intensities alone cannot be very reliable. An alternative which seems to be better for the correct assignment of frequencies to rotamers is one based on the high specificity of the vOH toward the intramolecular environment of the hydroxyl group. This property arises tirn the fact that different immediate environments of the hydroxyl group in the OH conformers of a molecule will give rise to different vOH &quencies in the corresponding conformers. As stated in the introduction, the OH stretching mode presents no coupling with other vibrational modes. Hence, since a given immediate environment of an hydroxyl group is traaferable, to a certain extent, into diverse molecules, it is expected that equivalent OH rotamers in different molecules will show about the same muency in their vOH_ The spectifi~ of uOH has been largely confirmed by the work on alcohols in dilute solutions of different inert solvents by a number of authors [15-171. Considering this in connection with the fact that the various conformers of a given alcohol are usually stabilized by solvation to about the same extent [18], makes it reliable to assume that

62

_

_

the specficity of vOH can be transferred to molecules in the gas phase. In this way, asigrnnents could be done using data from conventional IR spectroscopy alone, and comparison of results thus enhanced in sirmificance. Following this line of reasoning we assign the higher hquency band measured by us at 3676.1 cm-’ to the truns rotamer of ethanol which, as in methanol, has the hydroxyl hydrogen between two a-hydrogens; the bands at lower tiquencies are assigned to the gauche rower where the hydroxyl hydrogen lies between an a-hydrogen and an a-methyl group. Note that on the basis of our assumption we arrive at the same assignment as determined by Richter and Schiel 1131. Propan-2-I The existence of

two different OH rotamers in pr~pan-2-01 has been reported earlier by Kondo and Hirota [19] _ Comparison of the observed frequencies with those of the gauche rotamer of ethanol and the three identical rotamers of t-butanol suffices for assignment of the frequencies. Consequently, we assign the band at about 3660.0 cm-’ to the guuche conformer and the band at 3637.4 cm-’ to the trwzs one. Comparison of the bandshapes of rotamers can provide additional information to confirm the assignment. The narrow band ascribed to the trans conformer at 3637.4 cm-’ resembles that of t-butanol. As the band of gauche ethanol overlaps too much with the bands of the trons rotamer no comparison is possible for thegauche rotamer.

MlTTI-IOD OF CALCULATION

The program used to perform the MM calculations was developed by van de Graaf et al. [20]_ It takes into account simultaneously spectroscopic data, structure and energy_ In order to minimize the molecular energy, two different minimization techniques are applied: firstly steepest descent and subsequently the Newton-Raphson minimization method_ The performance (energy decrease per second CPU time) in the preceding iterations is used as the criterion to switch over from the former to the latter. The parameterization of the Allinger MM2 force field for alcohols and ethers [21] was applied. As a first approach we carried out the calculations acco,ding to the dipole interaction scheme. In this approbation electrostatic effects tirn interactions between two bond moments belonging to bonds with a common atom are neglected. -4s in the Allinger force field only the bonds CO, OH and alp are assumed to own a moment; no electrostatic terms appear in the calculations of monohydroxy alkanes. Unfortunately this method of calculation produced poor results: only differences up to 3 cm-’ were obtained between the calculated van of the various rotamers, whereas measurements show much larger valu=_ vOH differences obtained in this way can be ascribed to steric differences in the rotamers arising tirn van der Waals potentials. From these preliminary results we concluded that the selected

63

dipole approach was too rough for the successful calculation of uOH. The inadequacy of the dipole approach was pointed out by Burkert 1223 with regard to the confolmational energy of alcohol rotamers in dealing with an MM1 parametrization_ Improvement of the results for the calculated vOH frequencies may then be achieved, either by a drastic modification in the MM2 force field parametem or by accounting in some other way for electrostatic interactions_ In our opinion the latter option seems the most appropriate, as otherwise coulombic interactions due to considerable charges around the hydroxyl group [23] would be neglected. Following Burkert we have selected CNDO/B atomic charges located at the nuclei which are allowed to interact with one another. The electrostatic potential U, between two charges qi and qi at a distance R,- is then given by the expression Lie = 1 332.06 i
g il

(1)

D being the effective dielectric constant with an optimal value for the current calculations of 1.2. The coefficient 332.06 converts the energy to kcal mol-’ if the charges are expressed in electron units and the distance in A. The atimic charges are used in our MM calculations in such a way that they are recalculated at every iteration during the energy minimization. This was possible after a CND0/2 program was incorporated into the MM version. In order to account for electrostatic effects due to lone-pair interactions with neighboring lone pairs and atoms, an empirical approach had to be developed, as in the CNDO/B calculations no charges are assigned to lone pairs. Such empirical approaches have been applied earlier in similar calculations 124, 25]_ In our case 15% of the calculated atomic charge on oxygen was located at the interacting van der Waals center of each lone pair according to the expression %p
o-3 Qo QP(i)

+

rlP0

(2)

rlPci)

where r1p
64

u *rIc includes the potential energy of bond stretching, angle deformation, torsion, non-bonded interactions and a cross-term between bond stretching and angle deformation. At the final stage of the minimization the potential energy of a molecule with N atoms can be expressed by the equation

where U,,(q) is the steric energy in the fmal geomelxy and each element e of a symmetric matrix C is the sum of the coefficients of AFAfi which represent the cartesian displacement coordinates of atoms i and j’in tie three directions of space (a, B G x, y. P). The force constants are included in the elements GiB [ 261. These force constants, which together with the molecular geometry determine the frequency of the fundamental vibrations, are the second derivatives of the total potential energy with respectto the internal coordinate associated with vibrationThe expression for the actual force constant corresponding to vOR at the energy minimum geometry, when no electrostatic terms are present, takes the form

FOH

CT-

62u-

_

$a3 OH

%iH

(1 - 6 ~~

-&,>

-v,dw6’U*,(r,,)

c

+

l
=&I (5)

The first term on the right hand corresponds OH bond stretching potential u S((iH) = 1/2 Pan

(rou -&r)*

(l -

2

trOH

+o the second derivative of the

-GA))

(6)

where rOH is the natural bond length of the OH bond and PoH the standard stretching force constant_ The second term in eqn. (5) is the sum of the second derivatives of Van der Waals potentials over ail non-bonded interactions in which the oxygen and hydroxyl hydrogen atoms take part (1-4 and higher interactions). When electrostatic interactions are considered, additional terms appear in the expression of the force constant which then takes the form

F OH

_~2Qiu = FEH 6&H

(I-

6 (&’

-

&))

+ 664.12

qOqH D(e$)3

Here the second term on the right represents the second derivative of the coulombic potential corresponding to the interaction between oxygen and hydrogen through the bond (l-2 interaction). As coaulombic interactions

65

are allowed between all point charges within the molecule the additional fourth term appears in eqn. (7). The terms corresponding to the l-3 electrostatic interactions, appear only in the expressions of the force constants for angle deformation. From eqn. (4) the vibrational frequencies of the molecule may be cakulated by standard methods. The secular determinant resulting from eqn. (4) is:

(8) where mi is the rns of the ith atom. Solution frequencies vi = 1/27r *‘*. Spectroscopic

and structuml

of the determinant

yields the

data

Despite the overall improvement in the MMZ/CNDO computations by inclusion of electrostatic terms, the rotamer tiequencies of methanol and t-butanol were found to be a few cm-’ below the experimental values. In order to fit these hequencies, minor modifications had to be introduced in the standard force field parameters for these molecules. The hydroxyl stretching frequencies of the alcohol rotamers calculated affr the force field was modified are listed in Table 2. Methanol is a rather unique molecule and therefore the modifications in the force field parameters concern only its molecular structure and the structure of the methoxy groups with regard to the ethers in the MM formalism. The modified parameters are h.sted in Table 3. With respect to t-butanol the adaptations concern the angles CCC and CC0 of tertiary carbons attached k oxygen, which were varied from T-ABLE

2

Measured

and calculated

Compound

OH stretching

frequencies

in gas phase

Y(-JH(cm’)

Methanol

*“OH (II-III)

Mb=(I)

MM2ICNDO(lI)

-P-WI)

3639.5

3682.e

3639.6

3675.3

3639.7 3640.4

3660.0b 3660.8

3681.4 3676.1 3661.6 3658.8 3660.0

+0.6 -0.8 -1.6 +1.2 +0.8

3641.1 3642.1 3642.4

3638.2 3642.2' 3631-V'

3637.4 3643.0 3631.0

+0.8 -0.8 to.8

Ethanol

propan-2-01 t-Bukmol

Adamantan-l-1 aCalculakd frequency

hequendes

corresponds

adapted with to the unperturbed

force field gauche state.

param eters.

bThe

calculated

66 TABLE Modified

3 force field parameters (angles in degrees, force constants in pdyn A rad*)

Methanol

M&¶2

MM2KzvDo

&iCH

109.0 106.7 320 540

108.0 107.7 540 700

&M&s2

MMB/CNDO

109.47

109.17 107.80

&xc0

F&H -CO Tertiq

&cc &co

carbons

attached

to oxygen

107.50

109.4'i" and 10'7-50" to 109_1'7" and 10’7.80°, respectively_ This brings‘about an insignificant change in the final geometry of the molecule. The molecular structure of adamantan-14, in which the angles mentioned also occur, undergoes no change, however, due to the rigidity of the skeleton (Fig. 3), andthevon frequencies oftherOtamersremainthesame. Excluding these minor adaptations, the MM2 force field appears to lead through the MM2/CNDO computation to frequencies which are in very good agreement with experimental vaIues. Insight into the mutual dependence between force constant and geometry can provide a better understanding of the causes involved in the achieved improvement. Differences in the frequency of a given vibrational mode in different molecules or rotamers may be sought, from a spectroscopic point of view, in the differences in force constants and geometries which determine the F and G matrices_ In a force field calculation, geometrical parameters are currently taken from available experimental data and are maintained conscat, while the force constants are optimized to fit the observed vibrational liequencies. In the Molecular Mechanics approach, however, force constants and geometrical parameters depend upon one another and in order to fit the observed frequencies the force constants cannot be changed ;Jldependently from the structure In fact the MM considers the actual force constant of vibrational modes as resulting from a standard force constant, incremented by contributions from specific interactions depending upon the geometry of the molecule_ This is represented for ‘the actual force constant of the OE stretching vibration, FoH, by eqns. (5) and (7) The contributions to this force constant according to eqn, (5) are listed in TabIe 4. From these results it can be seen that the calculated OH bond lengths do not differ enough from one rotamer to another to cause marked differences in the FOH of the rotamers. The van der W&s contributions lead to no more difference in the various F,, than the OH bond length, despite the very different structures. Consequently the calculated MM2 vOH do not differ much from one another.

67

LP2

Fig. 3. Atom

numbering

of the molecuies.

When electrostatic interactions between point charges are taken into account, the actual force constaut will be evaluated fiorn eqn. (?). The contributions according to this expression are quoted in Table 5. If the calculated MMB/CNDO voE kq uencies are considered (Table 2): one may conclude that the F,, of the rotamers are satisfactorily computed after inclusion of the coulombic potential. However, inspection of the results in Tabie 5 reveals that the direct contributions from the couZombic terms cannot be responsible for the large difference obtained in the calculated FoH. The differences arise mainly from the term 6 Pan (* - r&.& i.e. from the caIculate.l OH bond length. Hence, the cause of the improvement in the calculated frequencies must be sought in the optimized molecular geometries. These results ahow

TABLE 4

Compound

FOH

rEn

bdynA_)

(A)

-=-bHa

‘OH

(riynA_)

6'u-(roE3 =

S&H

bdyn

Methanol

i803.7

0.9423

tram

7804.3

0.9423

-13.3 -13.3

411.9 412.5

gauche gauche

'iso:.s 7807.6

3.9422 0.9422

-8.9 -8.9

408.5 411.3

tram

i810.7 7814.7 7816-2

0.9420 0.9419 O-9419

A-1

Ethanol

propan-2-01 t-butanol Adamantan-1-l

P OH -7405_2rdyn_~-'.~rOH=r~~-rD~.r'jH= -

0.0 4.4 4-4

405.5 405.1 406.6

0.942oA.

an explanation of the observed differences in vOH between rotamers in terms of differences in the hydroxyl bond itself, regardless of the rest of the molecule. R-am this point of view- it is, for instance, not necessary to claim the prance of twisted methyl groups in t-butanol to account for the observed frequency difference with respect to adamantan-l-01 as has been proposed by Lutz and van der Maas 1271. With regard to the torsional Anglo of the above-mentioned methyl groups our MM2/CNDO programme calculates the angles of OCICIHz and 0C,CIH3 (Fig. 3) in the rotamers of thse two molecules to be nearly the Same (Table 6)_ Hcwever, some assumptio12s made in the MM2/CNDO model with regard to physical reality are questionable, especially those concerning the calculation of atomic charges and their reciprocal interactions. Therefore, results from the calculations cannot be employed in an absolute way to reject other plausible interpretations in accounting for the observed frequency difference. However, it will always be possible to develop a force field in which non-bonded interactions, arising from van der Waals and coulombic potentials, lead to methyl groups twisted to some degree in the immediate environment of hydroxyl groups if this were the case. Nevertheless, as long as differences in vOH between OH rotamers exist one may assume that different force constants and geometries will be involved_ Unfortunately it is not possible to establish to what extent the value of the force constant depends upon the OH bond length, because acc=lrate gas-phase structural data is not available. Our calculated values thus cannot be checked with experimental ones. With regard to the rotamer geometries from the m!S/CNDO calculations, Table 6 shows that with the exception of the computed OH and CO bored lengths of the various rotamers, the other structural parameters remain nearly unchanged.

fill

trone

q

gauche galrcho

fmo

1.2, C q

0,9242 0.0239 0,024O

0,0222 0,0222

0.0201 0.0200

r% (A)

332,06 kcal (ISI,)-’

7708,3 7816.7 77705

7692,l 7806.6

7066.0 7068,8

FcI I (Jyn A”‘)

q

2306,O Ntlyn A’.

727,0 743.9 608,9

801,3 t300,3

8OG,2 862,G

-6Pf~11Arol.1 (rdyn A-‘)

forca con&ante of alcohols nccordiny Lo oqn. (7)

= 6612,6 pdyn A”, D

t.butonol Adamantan.l~ol

Propnn.2.01

Ethonol

Mothnnol

Compound

OH bondstrctchlng

TABLE6

-136.2 -136.2 -133.4

-193,7 -131.9

-130.7 -126,7

(udyn A”‘)

303.4 30406 392,6

404,o 406,6

10&O 41206

6 rbtt (rdyn A* 1

w)

6 rbt1

~ 8Wp(r&

70 TABI. Stnlctural plrametcr

6 pasaul eters, CNDO/B

hl-U2/CNDO

09424 1.4143

ooc,c:

0.9201 1.4010

moments

MM2 0.9423

1.4156 1.5321

(bond

lengths Ethanol

MMP/CNDO 09209 1.4064 1.5328

in A, angles iu degn&

09422 1.4158 1.5327

MMPICNDO

111i6

11145

I_1147

I_1145

1.1146

0.6123

0.6012

0.61.?9

0.6014 0.6008

0.6123 0.6116

109.62

108.51 109.28

109.84 109.91

1801)O

180.00

60.11

60.06

0.1311 d.1753

QH, qo q=, w=, @=a qK_ qH, PlP, qlP:

0.1415

-0_0203 -0.0016 -0.0316

l-71

1.98

l-71

108.40 109.83 66.66 6040

109.71 109.74 -66.38 5993

0.1436 -0.1820 0.1707 -0.0265

0.1478 -0.1846 01637 -0.0332

-0.0300 O-0124 --0.0309

-0.0288 0.0067 -0.0396 -0.0395

1.63

1.71

i

09222 1.4075 15340

1_1150

108.37

I i 1

zouche

MM2

o-6015

rH,OC,C, roc,c,H, rOC,C,H,

cr

and dipole

Elhaaoltraru

M-01 MSl2

=,OH,

charges

1.99

That the c&=~ated lengths of the above-mentioned bonds deviate substantially from experimental values is a consequence of the strong electrostatic interaction, which is allowed to take place through the bond of the atoms involved. The strength of this interaction can be diminished using a higher value for the dielectric constant_ However, an enhancement of this quantity to reduce the extent of shortening of the OH and CO bonds cancels the improvement on the calculated frequencies_ Therefore in order to fit simultaneously bond lengths and frequencies into the computation of electrostatic interactions in the present work, it is necessary to look for a potential function to describe the OH and CO bonds other than that actually employed_ Finally, we note that in order to reproduce the experimental rotamer frequency correctly a high accuracy for the calculated charges associated with a given structure is required- This implies that the CNDOIB atomic charges have to be recalculated after each iteration of the energy minimizationproc&ure. THEFthlODYNAhlIC

DATA

The MM2 force field for alcohols and ethers has been developed by the authors primarily in order to calculate thermodynamic features of these

..

71

atomic

charges

iu electron

units, dipole

Ropm-2+l

couche

RopmI-2-d

m?aIp

MM2/CNDo

MM2

moments

traru

t-Butsnal

MM2/CNDO

0.9422 1.4172 1.5353

0.9222 1.4072 1.5366

0.9420 1.4173 1.5352

0.9242 1.4086 15361

1.1142 0.6005 0.6013

11143 0.6121 0.6127

I_1141 0.6998

l-1142 0.6113

lOb57 109.39 -65.2.l -59.25 60.89

109.94 109.30 -6496 -58.78

61.25

108.44 109.46 -61.57 -56.39 61-75

0.1422

10984 109.38 41.40 48.77 6130

-0.1911 0.1790 -0.0329

0.0009 0.0101 -0.0405 -0.0405

0.0059 -0.0050 -o.eOS

compounds somewhat

1.94

MM.2

0.9419 1AlSl 1.5386 1.5364 I.1141 0.6003

1.71

2.06

in good agreement adapted version of

A-tan-la1 Mhf2/CNDO~Z 0.9238 1.4081 1.5398 1.5388 1.1145 0.6115

MM2ICNDO 09419 lA171 1.5393 15391 1.1155 0.6003

o-9249 1.4059

1.5410 15403 11157 0.6112

108.70 108.61

110.08 108.65

108.62 109.56

110.01 109.62

4026 -59.38 liO.60

-60.11 -59.69 60.08

4025 -58.41 59.39

-a.11 -58.66 56.94

3.1453

-0.1691 0.1857 -0.0335

l.il

in Debye)

0.1404 -0.',974 0.1916 -0.0320 -0.0237 -0.0003 0.0046 -Q.o417

1.71

2.04

0.1385 -0.1982 0.1769 -0.0069 0.0916 --0.0110 -0.006cl -0.0425

1.71

2.00

with experimental values. In dealing with a the force field it is worthwhile to check

upon the extent these thermodynamic features are reproduced despite the introduced modifications. MM2 heat parameters were unchanged in our calculations Table 7 summarizes the results. Comparison of the MM2 and MM2/CNDO computations reveals that the heats of formation from the latter are systematically increased by about 0.3 kcal mol-’ with respect to those from the former. This enhancement reaIly arises from the larger calculated steric energies which contribute, according to the molecular mechanics principles, directly to the heat of formation [28]. It must be noted that in the current calculations tbe amount of energy due to the electrostatic interactions is not considered as an additional term in the expression of the steric energy although it is so accounted during the minimization procedure_ This is done, ultimately, to avoid unnecessarily large modifications in the heat parameters of the force field. In turn the higher calculated strains are possible due to the stabilizing role of the electrostatic interactions. The heats of fo,rmation of the MM2/ CNDO computations, however, are calculated within *be value of the Standard deviation (0.5 kcaI moT’) iuoted by Allinger et al. [Zl] _

trim

I gnrtche gauche

trorls

OAvcrogcdvalue, bRoT. 37.

t.Butanol hdsmanton~l~ol

Propan-2.01

Ethonol

Mcthonol

Compound

3,ZG 3,46 la,48

2.36 2,04.

1,22 la76

3,63 3.70 l&73

2867 ?,99

1,67 2.13

0 rlurlc (kcul mol”) ,,%I 8, MMZlCNDO MM2(1) (II)

Stcrlc oncrglce nnd hcnts ol formntlon

TABLE 7

0,28 0,31 0,26

0.32 0,36

036 0,38

(II - I)

A%c11,

-04.66 -74,76 -74027

-66,18 -6G,lO

-47,&I -66,78

MM2

-66.07n

-6ti6V

A/lot (kcal mol-)

-04,27 -74.44 -74.02

-64JO -04.81

-47,49 -66.110

-64,73’

-66,ltY

MMZ/CNDO

-74.72

-66.12

-66.24

-48,07

Expob

ii

73

Fhally, because the systematic increase of steric energiesconcerns all the rotamers under consideration, no marked shift is expected to take place in their corzformational equilibria ROTAMER

POPULATIONS

The relative populations of two conformezs in equilibrium derived from a statistical mechanics approach is given by eqn. (9) [29]

(9) where the ~Q
8

Calculated OH rotamer populations by the MMPiCNDO computations Compound

AU(kcal talc.

from steric energy

mol-‘j

differences

and partition

functions

Relative populations at 298 K

gas

GiS

&P.

(X)

CCI, (=a

tInruT

0.00

o.ow

gauche Ropan-2*1

.

14. bRef.

_.

0.54 0.00

o.oob o-14*

(

67=

62

85 40

87d 33=

:“3

15

13d

17

0.43 tranr

aRef.

60 0.60

EthaPOl

0.54

38. Wef.

.

15. dRef.

0.28b 31. =I$

= (Ig,JJIa

._.

__. .. -

$ (1 -e*YllkT)-‘-

74

solution of CCL and C&, relative populations have been derived of about 65% for tnrns and 35% for gauche 115, 311 which points to an energy difference of rou&ly 0.6 kcal mar’. Since it seems that both rotamers of ethanol are stabilized to about the Same extent by solvation 1181 the populations in the gas phase should resemble those in dilute solutions with inert solvents. For the rotamers of propan-241 much less data is available_ Our calcuIations predict a population of 85% for the gauche form and 15% for trcms. Again these results are in accordance with those obtained from its measurements of propan-2-01 in dilute solutions of Ccl, and CS, [31]_ CONCLUSIONS

The MM2 force field complemented with an electrostatic potential as described herein -pears to lead to vOH frequencies of OH rotamers in excellent agreement with experimental values. The accuracy of these results, however, was achieved at the cost of computing time, as it proved to be necessay to rxxalculate the CNDO/Z atomic charges after each iteration. This increase in computing time can be a serious draw back when large molecules are involved. In order to fit correctly the hydroxyl and carbonyl bond lengths with the improved calculated frequencies, it seems necessary to look for another potential function to describe these bonds. The second derivative of this new function has to be more sensitive to changes in the actual bond lengths r= of rotamers than that of the function actually employed_ Finally, calculated heats of formation could easily be improved by introducing in a simple way minor modifications in the heat parameters of the force field_ ACKNOWLEDGEMENTS

The authors gratefully acknowledge Drs. B. van de Graaf and J. A. M. Baas for supplying the MM program and Mr. E. T. G. Lutz for experimental assistance_ They are also indebted to Mr. L. Smeets of the Koninklijke Shell Laboratorium for recording the FYI’-IR spectrum of adamantan-l-01. REFERENCES

1 E-T-G. Lutz and J. H. van der Maas, Spectrochim.Acta, Part A. 36 (1980) 805; 37 (1981)129;37(1981)693;38(1982)743;39(1983)1007_ 2J.H.vander Maas andE_T_G_Lutz,SpectrochimAc~PartA,38(1982)927. 3T- Vintr and J_ H_ van der Maas, Spectrochim.Acta, Part A, 39 (1983) 241; 39 (1983)921. 40_EnnerandS_Libn,J_Am_Chem_Soc,95(1973)4121_ 5S.FitzwateranZ~S.Bartell,J.A1nChem.Soc.98(1976)5107. 6S_Li%onandP.S_S~J.ChemPhys.77(1982)4542.

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Acad.

Sci.

U.S.A.,

72