RELQTWE ’CQM‘REBUTIONS OF H‘z’PERCQ?€jU&ATION AND NONBONDED INTERACTIONS TO SECQNDARY ISOTOFE EFFECTS Thesis for the Degree of Ph. D. MICHIGAN SYATEI LfiNIVERSETY GEORGE CARL SQNMCHSEN 1.967 unxaa '1 Michigan State university This is to certify that the thesis entitled RELATIVE CONTRIBUTIONS OF HYPERCONJUGATION AND NONBONDED INTERACTIONS TO SECONDARY ISOTOPE EFFECTS presented by George Carl Sonnichsen has been accepted towards fulfillment of the requirements for LL— degree in W Efétflcfi/ Major professor Date M 0-169 ABSTRACT RELATIVE CONTRIBUTIONS OF HYPERCONJUGATION AND NONBONDED INTERACTIONS TO SECONDARY ISOTOPE EFFECTS by George Carl Sonnichsen Secondary beta isotope effects in SNl reactions have generally been attributed to greater hyperconjugative stabi- lization of the carbonium ion like transition state by the protium compound. Bartell (1) has proposed that these iso- tope effects may be due to greater relief of non-bonded interactions for the hydrogen compound than the deuterium compound while proceeding from the reactant to the transi- tion state. He also devised a method to calculate the iso- tope effects originating from non—bonded interactions. In order to ascertain the reliability of Bartell's method of calculation, the isotope effects were measured for the solvolysis of compounds I-III, i323 systems where hypercon- jugation is not possible, and these isotope effects were compared with the isotope effects calculated for these com- pounds. Ia Ib Ic 11a 11b IIIa IIIb wznnaw:unnw CD3 ’ N><>§N=N> (CD3)3B:N(CH3)3 and that of the corresponding hydrogen compounds was deter- mined by Love, Taft and Wartik (22). They estimated the isotope effect to be AAGO/n = 22 cal/mole and attributed it to hyperconjugation. Bartell (11) calculated the isotope effect arising from non-bonded interactions to be 20 cal/mole per deuterium. Bartell calculated an isotope effect of 22 cal/mole per deuterium for the solvolysis of Efbutyl chloride-d9, which is less than half of the experimental 58 cal/mole per deuterium. Most of the earlier work on the elucidation of the origin of secondary BEES isotOpe effects attempted to show that they were due to hyperconjugation. Perhaps the most convincing evidence was the transmission of the isotope ef- fect through an aromatic ring. Acetolysis of 11a gave an isotope effect of AAG*/n = —29 cal/mole (23) 11a 11b c1 I 003- .. -CHCH3 CD3 -c— ..A\\ .uh (I) In (ll 3 (0 pa. 6 and solvolysis onUb in 80% aqueous acetone gave an isotope effect of AAG*/n = —12.4 cal/mole (24). It would seem un— likely that these isotope effects could be caused by any— thing other than hyperconjugation. However, this interpre— tation has been criticized because of the solvent dependence of the isotope effect, as AAGt/n is reduced to -2 cal/mole for solvolysiscMEIIain 80% acetone-water (25) and to —4.8 cal/mole for solvolysis of'IDDin 66.7% acetone-water (24). Isotope effects transmitted through a triple bond have also been reported. For example, AAG¢/n = —17 cal/mole for the solvolysis of 4-chloro—T4-methyl—Z-pentyne—1,1,1-d3 in 80% acetone-water and 80% ethanol—water (26). Hyperconjugation consists of the delocalization of the electrons of a bond into an adjacent vacant p-orbital. It would be expected that hyperconjugation could occur only when the bond is in a suitable orientation for overlap with the p—orbital. Thus a maximum hyperconjugative interaction could be expected when the bond is parallel with the vacant orbital and no hyperconjugative interaction would be ex- pected if the bond is perpendicular to the vacant orbital. Shiner and Humphrey have demonstrated this by the solvolysis of III in 60% ethanol-water (27). Whereas a normal isotope effect, AAG*/n = -49 cal/mole, is observed for IIIa, a small inverse isotope effect, AAG*/n = 4 cal/mole, is observed IIIa IIIb ////\\\ ' CH3 ._ l n - . .p ~y -osvl' on V0. . -Y' 7 for IIIb. Since the carbon—deuterium bond in IIIb is ori- ented so that it is perpendicular to the developing p—orbital on the adjacent carbon atom, the only isotope effect is the inductive effect of the deuterium. Another example of this same type of effect is exhibited in the solvolysis of IV in 80% ethanol—water (28). Shiner IV IVa Va C1 C1 I D I Cl D D D CH3 ‘C’CDz ‘R ———> I CH3 CH3 CH3 CH3 CH3 R R " IVb Vb C1 C1 . D R I D > CH3 H3 CH3 CH3 D D has found that for R equal to methyl, ethyl, and isopropyl AAG¢/n equals -102, —101 and -125 cal/mole respectively. Within experimental error these values are practically ident- ical. However, when R is a tfbutyl group, AAG*/n decreases to -27 cal/mole. Shiner interprets this "as characteristic of the steric prevention of a certain conformation necessary for hyperconjugation". Hyperconjugation should be greater in transition state Vb, where a deuterium is trans to the leaving group. Transition state Va should become increasingly more stable relative to Vb as the bulk of the R group uflv .uNrb ,- ‘fiv- ‘ swee- in; vnn‘v .a—a _- on.“ who 9-.- ct... A~,q Vv-n up,- -..‘r. b (I! [1) (Y) ll) (I) “r 8 increases. Thus, when R is tfbutyl the preference for conformation Va over Vb greatly increases and as a result the isotope effect decreases sharply. It seems highly probable, from what has been presented, that both non—bonded interactions and hyperconjugation con— tribute to secondary ESEE isotOpe effects. The relative contribution of each however, is still a subject of some controversy. This question could be resolved by using Bartell's computational method to calculate the steric iso- tope effect in systems where the isotope effect could orig— inate from both hyperconjugation and non-bonded interactions. First, it would be necessary to determine the validity of Bartell’s method of calculation. The obvious choice should be a system where there are steric interactions, but no ap- preciable hyperconjugation, between the isotopically sub— stituted portion of the molecule and the reaction site. A system fitting these requirements is a 1,8-disubstituted naphthalene (VI) with a carbinyl chloride, acyl chloride or carbomethoxy group in the 1 position and either a deuterium VI R X GO or a methyl-d3 group in the 8 position. The isotope effect 50 I - D, CD3 x I " CH2C1: COCL: COzCHa on the hydrolysis of these compounds could be measured and compared with the values calculated by Bartell's method. I‘pa‘ .u-V- Aflfi vvu AA! Lo. 9 Then, the isotope effect due to non-bonded interactions would be calculated for the hydrolysis of Efbutyl chloride, acetyl chloride and ethyl acetate to determine the relative contribution of the steric effect in compounds where hyper- conjugation is possible. EXPERIMENTAL I. Synthesis A. Preparation of 8-Methyl—1-naphthoic Acid The procedure used in the preparation of 8—methyl—1- naphthoic acid was essentially the same as that described by Shone (29). A 300 ml three-necked round-bottomed flask fitted with a reflux condenser, 125 ml dIOpping funnel and a stirrer was swept with dry nitrogen gas and heated with a flame until dry. After 3.64 g (0.150 9 atom) of Domal high purity magnesium was added, the flask was flame dryed again, with care being taken to avoid heating the magnesium. About 150 ml of ether was distilled from lithium aluminum hydride directly into the reaction flask. Next, 6.10 g (0.0276 mole) of 8—methyl-l—bromonaphthalene and 5.93 g (0.0542 mole) of ethyl bromide was dissolved in 75 ml of ether which had been removed from the reaction flask with a pipet. This mixture was added dropwise to the stirred ether-magnesium slurry and the resulting solution was re- fluxed for four hours. The solution was poured onto 30 g of dry ice and 100 ml of ether was added. After all carbon dioxide evolution had ceased, 20% hydrochloric acid was added along with enough ice to cool the solution until it was acidic. The aqueous and ether layers were separated and the ether layer was washed three times with 75 ml portions of water. The 10 11 ether solution was extracted twice with 25 ml portions of 10% sodium hydroxide. The base solution was acidified with 20% hydrochloric acid and the precipitate was removed by filtration. The acid was recrystallized from 30% ethanol to give 3.6 g (70%) of crystals of 8-methyl-1— naphthoic acid. B. Preparation of 8—Methyl-dq-1—naphthoic Acid 8-Methyl-d3—1-naphthoic acid was prepared from 8-methyl— d3-1-bromonaphtha1ene by the procedure described for 8-methyl- 1—naphthoic acid. C. Preparation of 8-Methyl—l-naphthylcarbinol The procedure used in the preparation of 8-methyl-1— naphthylcarbinol is similar to that described by Shone (29). A 300 ml three-necked round-bottomed flask was fitted with a reflux condenser, 125 ml dropping funnel, and a stirrer. Next, 75 ml of dry ether and 2.43 g (0.64 mole) of lithium aluminum hydride were added to the flask. A solution of 6.00 9 (0.0322 mole) of ether was added dropwise to the stirred slurry. The mixture was refluxed for forty-eight hours. The flask was cooled in an ice bath and 5 ml of water, followed by 5 ml of 5% sodium hydroxide, was slowly added. The reaction mixture was stirred overnight and then filtered. The aluminum oxide precipitate was washed several times with ether and these washings were added to the fil— trate. After evaporation of the ether the alcohol was AA. ’4 Pub RV 9‘ 12 recrystallized from cyclohexane to give 5.0 g (91%) of colorless needles of 8-methyl-1-naphthylcarbinol. D. Preparation of 8-Methyl—dq-1-naphthylcarbinol 8-Methyl—d3-1—naphthylcarbinol was prepared from 8- methyl-da-l-naphthoic acid by the procedure described for 8-methyl-1-naphthylcarbinol. E. Preparation of 8—Methyl-1-naphthylcarbinol—a,q-d2 8-Methyl—l-naphthylcarbinol—a,a—d2 was prepared from methyl 8—methyl-1-naphthoate by the procedure described for 8-methyl—l-naphthylcarbinol except for the following modi- fication. A slight excess of lithium aluminum deuteride was used instead of a large excess of lithium aluminum hydride. F. Preparation of 8-Methyl—l-naphthylcarbinyl Chloride 8-Methyl-1-naphthylcarbinyl chloride was prepared by essentially the same method as that described by Scheppele (30). Into a 25 ml flask fitted with a reflux condenser was placed 3.37 g (0.0197 mole) of 8-methyl-1-naphthyl- carbinyl chloride. From the top of the reflux condenser 2.9 ml (0.04 mole) of purified thionyl chloride was slowly added and the resulting solution was refluxed for two hours. The thionyl chloride was stripped off and the 8-methyl-1— naphthylcarbinyl chloride was vacuum distilled through a short path distillation head. Recrystallization of the ny- DI I). 13 distillate from pfhexane gave 3.09 g (82%) of colorless crystals of 8—methyl-1-naphthylcarbinyl chloride, mp 65-660. G. Preparation of 8-Methyl—d3—1-naphthylcarbinyl Chloride 8—Methyl-d3-1—naphthylcarbinyl chloride was prepared from 8-methyl—d3-1-naphthylcarbinol by the procedure described for 8-methyl-1-naphthylcarbinyl chloride. The 8-methyl-d3— 1-naphthylcarbinyl chloride was found to have 2.98 deuteriums per methyl group through mass spectral analysis by Seymour Meyerson of the American Oil Company. H. Preparation of 8—Methyl-1-naphthylcarbinyl Chloride-a,Q-d2 8-Methyl—1-naphthylcarbinyl chloride—Q,a—d2 was prepared from 8-methyl-1-naphthylcarbinol-d,dsdz by the procedure‘ described for 8-methyl-1enaphthylcarbinyl chloride. 1. Preparation of 1—Naphthylcarbinyl Chloride 1-Naphthylcarbinyl chloride was prepared from 1-naphthyl- carbinol by the method previously described for 8-methyl-1- naphthylcarbinyl chloride. II. Kinetics A. Conductance Apparatus Conductance Bridge. The conductivity measurements were taken with a Wayne Kerr Universal Bridge, model B221 (The Wayne Kerr Laboratories Limited, Surrey, England). The bridge measures conductance together with capacitance <3r inductance with an accuracy of 0.1%. 14 Conductance Cell. The conductance cell used was simi- lar to that described by Murr (31). It is described in de— tail by Papaioannou (32). The procedure recommended by Jones and Bollinger (33) was used to platinize the electrodes. A solution of 0.025 N hydrochloric acid containing 0.3% platinic chloride and 0.025% lead acetate was introduced into the cell. A current of 7 ma was run through the cell for ninety seconds in each direction. The conductance cell was then filled with a solution of 4% sulfuric acid and this solution was electrolyzed for ten minutes in each di- rection. The cell was cleaned with hot concentrated nitric acid as described by Murr (31). B. Constant Temperature Bath The constant temperature bath which was used is de- scribed in detail by Papaioannou (32). C. Calibration of Beckmann Differential Thermometers The Beckmann differential thermometers were calibrated with a platinum resistance thermometer which had been cali- brated by the National Bureau of Standards. D. Preparation of Solvents Conductivity Water. The conductivity water was prepared by passing distilled water through a column filled with Dowex 3, anion exchange resin, and Dowex 50W-X8, cation ex- Change resin. The conductivity water prepared in this man- Iler had a specific conductance of about 3 x 10”6 mho/cm. 15 Acetone. Purified acetone was prepared by the method of Conant and Kirner (34). The acetone was distilled from potassium permanganate and sodium hydroxide through a 40-cm column fitted with a glass helix. For experimental work only the middle fraction was taken. The specific conduc— tivity of acetone obtained was less than 1 x 10-8 mho/cm. Mixed Solvent. The solvent used for the kinetic runs was 2/1 acetone-water (V/V). It was prepared for each kinetic run by adding with a pipet two parts of acetone and one part water to the conductance cell. E. Calibration of Conductance Cell Preparation of Standard Hydrochloric Acid Solution. A 0.1 N sodium hydroxide solution was prepared with Fisher Certified Reagent sodium hydroxide. This solution was standardized with Fisher Primary Standard potassium hydrogen phthalate using phenolphthalein as the indicator. A 0.1 N hydrochloric acid 66.67% acetone-water (V/V) solution was prepared and standardized with the standard sodium hydroxide solution by using phenolphthalein as the indica- tor. A 0.01 N hydrochloric acid solution was then prepared by a ten fold dilution of the 0.1 N hydrochloric acid solu- tion with 66.67% acetone-water (V/V). Determination of the Volume of the Solvent. The sol- vent used for the kinetic runs and the cell calibration was prepared by adding 140 ml of purified acetone and 70 ml of 16 conductivity water to the conductance cell with a 50 ml pipet and a 20 ml pipet. From the density of acetone at 25° (0.7844 g/ml, (35)), the density of water at 25° (0.997044 g/ml, (36)) and the volume of the calibrated pipets that were used, it was calculated that the solvent was 61.14% acetone-water (w/w). The density of the sol— vent was determined by the following expression: d = dw + APS + BP: + op: where d is the density of a solution of PS percent acetone-water (w/w) and dw is the density of water. The constants used at 15° were A = -1.009 x 10-3, B = —9.682 x 10'6 and c = -6.24 x 10‘9; at 250 A = —1.171 x 10’3, B = -9.04 x 10‘6 and c = -5.6 x 10'9 (37). The volume of the solvent was then determined from the density and the weight of the solvent. Determination of Hydrochloric Acid Concentration as a Function of Conductance. The solvent was added to the conductance cell which was placed in the constant tempera- ture bath. After the temperature of the cell had equilibrated with that of the bath the conductance of the solvent was measured. Then standardized 0.01 N hydrochloric acid solu- tion was added in increments from a 10 ml buret. The solu- tion was stirred for a short time after each addition of the hydrochloric acid solution and the conductance was measured. Thus, about fifteen values of the conductance of a known concentration of hydrochloric acid were obtained 17 over the range in which readings were taken in the kinetic runs. Two computer programs were written to use the method of least squares to determine hydrochloric acid concentra- tion as a function of conductance. One determined the parameters of a linear relationship and one the parameters of a cubic relationship. F. Kinetics of Solvolysis After the conductance cell was filled with solvent, placed in the temperature bath, and attained temperature equilibrium, the solvent conductance was measured. About 0.2 g of chloride was weighed on a Mettler balance in a one milliliter cup. The cup was then dropped into the conductance cell and the solution was stirred for about fifteen minutes to completely dissolve the chloride. The timer was started when the chloride was added to the cell. When the conductance of the solution reached 10-4 mho, readings of conductance and time were initiated. Fifteen to twenty readings were taken over a period of three to twelve hours, depending upon the reaction rate. The first order rate constant was then obtained from the appropriate kinetic expression. RESULTS The rates of solvolysis of VIIa, VIIb. VIIc and VIId were measured by a conductometric technique in 66.67% VII . , VIIa R=CH3, X=CH2C1 R VIIb R=CD3, X=CH2C1 <::> <::> VIIC R= H, X=CH2C1 VIId R=CH3 I X=CD2C1 acetone—water (V/V). The alkyl chloride reacts with water to form an alcohol and aqueous hydrogen chloride. Since ArCHZCl + H20 > ArCHZOH + HCl the equivalent conductance of the hydrogen chloride is much greater than that of any other Species present, the rate of reaction was followed by measuring the rate of appearance of hydrogen chloride by conductance. The integrated first order rate expression is: 1n(c0 - [HC1]) = -kt + inco where Co is the initial naphthylcarbinyl chloride concen- tration, k is the first order rate constant and [HCl] is the concentration of hydrochloric acid at time t. This expression could have been considerably simplified if it would have been possible to measure the conductance at infinite time. This was not practical because the half- life of the reaction was two and one half days. Thus it was necessary to determine the initial concentration of the chloride and the concentration of hydrochloric acid Ckorresponding to each observed conductance reading. 18 19 The initial concentration of the naphthylcarbinyl chloride was determined by weighing out a sample for each kinetic run. The concentration of hydrochloric acid as a function of conductance was found by adding increments of a standardized hydrochloric acid solution to a known volume of the solvent in the conductance cell and measuring the conductance after each addition. The data of one of these cell standardizations are given in Table 1. The method of least squares was then used to fit the concentration of hydrochloric acid ([HCl]) to the corresponding values of the conductance of the solution (L) by the linear equation: [HCl] = A + BL. The parameters A and B which were obtained for each cell standardization are listed in Table 2. The kinetic runs were carried out by adding a weighed amount of naphthylcarbinyl chloride to a known volume of the 66.7% acetone-water (V/V) solvent in the conductance cell and then measuring the conductance at various time intervals. The data of a typical kinetic run are tabulated in Table 3. The first order rate constant was then deter— mined from the relationship: 1n(co - A - BL) = - kt + lnCo. The Slope (-k) and the intercept (lnCo) of a plot of ln(Co-A-BL)‘y§. t were determined by the method of least squares. The rate constants which were obtained from each kinetic run are listed in Tables 4 and 5. The initial 20 Table 1. Data of cell standardization 1 at 24.285° HCl Added Conductance ml x 104 mhos 0 0.006734 2.627 0.5740 3.02 0.6602 3.44 0.7505 3.90 0.8512 4.243 0.9257 4.645 1.0121 4.978 1.0831 5.385 1.172 5.85 1.271 6.22 1.351 6.58 1.426 7.09 1.535 7.54 1.629 8.01 1.728 8.523 1.836 9.00 1.935 9.673 2.070 10.215 2.186 10.72 2.289 11.24 2.395 11.90 2.5275 12.63 2.674 13.36 2.818 14.00 2.944 Table 2. T,°C 15 15 24 24 34 34 34 34 .496 .496 .285 .285 .558 .558 .558 .558 Parameters [HCl] =‘A Volume (m1) 199.20 199.20 201.356 201.356 203.00 203.00 201.81 201.81 21 A and B + BL Standardi- zation 1 2 H for the .0371 .6637 .7111 .0236 .4954 .0683 .3559 .6618 expression NNNNNNCOOJ .3760 .3426 .8022 .8040 .3198 .3223 .3320 .3345 22 Table 3. Data for solvolysis of 8-methyl-1-naphthyl- carbin l chloride in run 6 at 24.285° in 66.67 acetone-water (V/V) Time Conductance Calculated k (min) x 104(mhos) x 106(sec-1) 272.04 1.0278 3.157 288.70 1.0880 3.160 309.10 1.163 3.167 335.95 1.259 3.168 352.85 1.318 3.166 370.78 1.382 3.168 399.60 1.484 3.170 418.54 1.550 3.170 435.90 1.610 3.169 454.86 1.676 3.169 473.25 1.740 3.170 503.81 1.845 3.170 523.01 1.910 3.168 555.09 2.017 3.164 571.14 2.072 3.165 588.27 2.129 3.163 605.38 2.187 3.164 Initial concentration 5.5789 x 10—3 mole/1. Solvent conductance = 9.00 x 10-7 mhos. k = 3.167 t 0.003 sec-1. Table 4. Run mmfimmhwwh‘ CH3 CH3 CH3 CH3 CH3 CH3 CH3 CH3 CH3 CH3 CH3 CH3 CD3 00;, 003 CD3 CD3 CH3 CH3 CH3 CH3 CH3 CH3 CH3 CD3 0133 0133 CD3 CH3 CH3 CH3 CH3 0133 CD3 CD3 23 Rate constants and isotOpe effects for solvolysis of 8-R-1-naphthy1carbinyl chloride in 66.67% acetone-water T,°c 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 24.285 15.496 15.496 15.496 15.496 15.496 15.496 15.496 15.496 15.496 15.496 15.496 34.558 34.558 34.558 34.558 34.558 34.558 34.558 k x 105 (sec 1) 3.134 3.122 3.117 3.194 3.087 3.167 3.196 3.140 3.068 3.080 3.084 3.136 3.036 3.101 3.080 3.106 3.116 0.8685 0.8724 0.8864 0.8485 0.8423 0.8797 0.8690 0.8435 0.8658 0.8683 0.8845 11.55 11.45 11.75 11.70 11.32 11.46 11.49 11 11 Average k .127 .088 .8667 .8655 .61 .42 l+ H- x 106 (sec-1) 0.041 0.028 0.0148 0.0146 0.012 0.008 R 1.013 1.001 1.017 H/k D 0.022 0.034 0.018 24 Table 5. Rate constants for solvolysis of 1-naphthylcarbinyl chloride and 8-methyl-1-naphthylcarbinyl chloride- a,a-d2 in 66.67% acetone-water (V/V) at 24.285° 6 k x 10 Average k kH/k Run (sec-1) x 10° (sec-1) D 1-Naphthylcarbinyl Chloride 1 0.103 2 0.0936 0.098 f 0.005 8-Methyl-1-naphthylcarbinyl Chloride-a,a-d2 1 2.367 2 2.375 3 2.341 2.361 r 0.014 1.324 t 0.025 25 concentration calculated from the intercept of lnCo was generally within 0.2% to 0.3% of the experimental initial concentration for each kinetic run. The standard deviation of the slope or rate constant was less than 0.1% for each kinetic run. The deviations, however, between different runs were considerably greater than this. One possible source of error could be the not immedi- ate dissolution of the naphthylcarbinyl chloride. When the temperature was about 25°, although most of the chloride dissolved within one minute, it usually took five to six minutes for it to dissolve completely. It is impossible to determine how much this initial concentration gradient would change the rate constant, but the effect would prob— ably not be very great, as conductance readings were not taken until about 300 min had elapsed. No noticeable trend was present in the values of the rate constants from dif- ferent kinetic runs where the amount of time necessary to dissolve all of the chloride was different. The reaction is an equilibrium process. Since the kinetic data were taken during the first part of the first half-life of the reaction, the effect of the reverse re- action on the value of the first order rate constant is negligible. An estimate of the equilibrium constant was obtained from the conductance of the solution at infinite time. When this value of the equilibrium constant was used in the appropriate kinetic expression that regarded the reaction to be an equilibrium process, the rate constants were changed by less than 0.02% for each kinetic run. 26 The conductance cell was standardized twice at each temperature. The average rate constants at each temperature, which were obtained by using the different standardizations, are listed in Table 6. The difference between the average rate constants for the different cell standardizations is negligible except for those at 15° where the difference is 1%. This difference, however, does not change the ratio kH/kD. At 15° and 25° the volume of the solvent was calcu- lated as previously described; however, at 35° the volume had to be estimated. Whereas the parameters of the standard- ization equation changed slightly, as shown in Table 2, when they were calculated from different solvent volumes, the rate constants in Table 6 did not change when they were calculated from the different standardization equations and the different volumes. Consequently, the isotope effect did not change. In addition to the linear relationship between hydro- chloric acid concentration and conductance, the data of the cell standardizations were also fitted to a cubic re- lationship to see if a better fit might be obtained. The parameters A, B, C and D of the equation: IHCl] = A + BL + CL2 + DL3 were obtained by the method of least squares and are listed in Table 7. This expression was used with the kinetic data to calculate the rate constants. In Table 8 the aver— age rate constants obtained by using this cubic expression are compared with those obtained by using a linear relationship. Table 6. CH3 003 CH3 093 CH3 0133 CH3 003 T,°C V (ml) 15 15 24 24 34 34 34 34 27 Average rate constants and isotope effects for solvolysis of 8-R-1-naphthylcarbinyl chloride in 66.67% acetone-water (V/V) using different stand- ardizations and initial volumes Standardization Standardization 1 2 k x 10° k k x 10° (sec-1) H/kD (sec-1) kH/kD .496 199.20 0.8667 0.8591 .496 199.20 0.8655 1.001 0.8577 1.001 .285 201.356 3.127 3.127 .285 201.356 3.088 1.013 3.088 1.013 .558 201.81 11.61 11.62 .558 201.81 11.42 1.017 11.43 1.017 .558 203.00 11.61 11.62 .558 203.00 11.42 1.017 11.43 1.017 28 Parameters A, B, C and D for the expression [H01] = A + BL + 0L2 + DL3 3.1761 x 10'6 5.5407 x 10‘ 4.9941 x 10‘ 6.2918 x 10’6 6 6 B 2.8577 2.7675 2.2490 2.2237 -3.5652 1.2082 2.0716 3.8554 102 102 102 102 6.8515 -5.8972 -1.3583 -4.6660 Average rate constants for the solvolysis of 8-R-1-naphthylcarbinyl chloride obtained by using the linear and cubic standardization expressions Table 7. T.°0 Std. 24.285 1 24.285 2 34.558 1 34.558 2 Table 8. R T 0H3 24 0H3 24 003 24 CD3 24 CH3 34 0H3 34 CD3 34 CD3 34 .00 .285 .285 .285 .285 .558 .558 .558 .558 H H [0 Std. Linear Std. 3 3 3 3 11 11 11 11 k x 10° (sec-1) .122 .127 .083 .088 .61 .61 .42 .42 3 3 11 11 11 11 .124 .127 .084 .088 .62 .62 .43 .43 Cubic Std. 105 105 105 105 29 The effect on the average rate constants is very small and the isotope effects do not change. The accuracy of the results did not increase with the use of this cubic expres- sion. The average rate constants at the different tempera- tures were used to determine the thermodynamic activation parameters AH1 and 85* from the relationship: t i log(kr/T) =-2—;§—%§§§(%) + 573—3533 + log(k/h) where kr is the rate constant, T is the absolute tem- perature, R is the gas constant, k is Boltzmann's constant and h is Planck's constant. The method of least squares was used to determine the slope and intercept of a plot of log(kr/T) versus 1/T, from which the AH* and AS* in Table 9 were obtained. The isotope effects were then calculated at each temperature from the relationship: AAGt = -RTln(kH/kD) = AAHt - TAAS¢ These values of the calculated isotope effects along with the experimental kH/kD ratios are listed in Table 10. 30 Table 9. Activation parameters and isotope effects for the solvolysis of 8-R-1-naphthylcarbinyl chloride in 66.67% acetone-water (V/V) i i _ i i _ i R AH ASt AHH AHD ASH ASD kcal/mole cal/deg/mole kcal/mole cal/deg/mole 0H3 23.42 i 0.16 -5.03 i 0.53 003 23.28 i 0.15 -5 52 i 0.48 0.14 i 0.31 0.49 4.1.01 1 i Table 10. Isotope effects calculated from AAH and AAS and experimental isotope effects i i AG - AG (calc) k \ . k 0 H D (H/ .(calc) H/ (exp) T’ C cal/mole ' kD ' kD 15.496 -2 1.003 1.001 24.285 '6 1.010 1.013 34.558 -11 1.018 1.017 CALCULATION OF ISOTOPE EFFECTS I. Method of Calculation A. General Theogy The numerical calculation of isotope effects due to non-bonded interactions was done by the method introduced by Bartell (11). His model requires the following assump- tions: 1. The potential energy of non—bonded interactions between atoms depends only on the distance, r, between the atoms and can be approximated by a potential function V(r). 2. Substitution of deuterium for hydrogen in a mol— ecule does not affect the mean distance, rg, between atom pairs. 3. The time average probability distribution describ- ing the separation of atoms is of the form: P(x) = k exp(—x2/2£:) 1 where x = r - rg, and z: is the mean square amplitude of vibration of the atom pair. 4. 2t can be subdivided into Em and BS by the relationship: 2 _ It-Im+zs g 2 , . where fim is the component of the mean square amplitude of vibration which arises from the zero point motion of the hydrogen atom and is dependent upon it's mass and Es is 31 32 the component which arises from other Skeletal vibrations and is independent of the mass of the hydrogen. 5. Since 2; is mass sensitive it will vary inversely as the square root of the reduced mass giving: £m(H)/£m(D) z 1.17 g If V(r) is a weak interaction coupling oscillators of amplitude 3m and £5, the average potential energy of each non-bonded interaction then becomes: IIA V(r )2: ffv(r)Pm(xm)P (x )dx dx g s m s s V(r) is expanded in a Taylor's series about the mean separation, rg, and substituted into 4, Integration then results in the following expression for each interaction: vijug) : Mtg) + 2:V"(rg)/2 + £:V1V(rg)/8 + ...]ij 2 The component of the activation energy resulting from non-bonded interactions, AV,-can be expressed as the dif- ference in the potential energy due to non-bonded interac- tions between the transition state and the ground state: AV = z Avij = Vij(rg' t.s.) - Z ij(rg, g.s.) ‘6 The isotope effect due to non-bonded interactions, AAE, is: AAE = AV(H) - MOD) 1 (Substitution of expressions 5. and .6 into equation ‘1 results in: .0 2 2 .. 4 4 iv AAE — [£t(H) — £t(D)]ZAVij/2 + [2t(H) - £t(D)]ZAVij/8 +- 8 where: AV.. = V..(r , t.s.) - V..(r , g.s.) Av:LV vlv( t ) v1v( ) c- = o- r ' as. - o- r ’ OS. 13 13 9 13 9 9 By using equations 2_ and 3., the expression simplifies to approximately: IV 2 " 2 AAE _ 0.13513m (H) >:[Avij + £t( 1v Hmvij/ZI 2 Bartell used the additional assumption for the H-H and C-H potential functions which he used (38): V"/2V1V 2: 15 x 1016 cm-2 This further simplifies expression 9_ to: ~ 2 16 2 . AAE _ 0.13514m (H)Z[1 + 15 x 10 £t(H)]ijAVij Lg Thus the parameters necessary to calculate the isotope effect are V"(r ), V1V(r ), 2 and E for each inter- g g m t action. B. Interatomic Distances Structural data were available for some of the com- pounds of interest. Where they were not available the struc- ture was estimated from similar compounds whose structure was known. The structures that were used are listed in the Appendix. The interatomic distances were determined from the polar coordinates of the atoms of the molecule by means of a computer program supplied by Dr. R. Schwendeman of this department. C. Potential Functions The potential functions of Bartell (38), Scott and Scheraga (39) and Hendrickson (40) were used. These are of 34 the form: V(r) = A exp(—Br) - Cr-6 and are listed in Table 11. A computer program was writ- ten that evaluated each of these functions and their second and fourth derivatives every 0.01 R from 1.50 R to 3.50 8. These values were then used in equation 2, Bartell did not have an analytic function for H-Cl and H-0 interactions and merely made a graphical estimate of the second deriva- tive for these interactions. Thus, when using Bartell's potential functions, the second derivatives of the potential functions for H-Cl, H-C and H-0 interactions were estimated graphically and equation ;9_ was used to calculate the isotope effect. When possible, the isotope effects for each compound were calculated by using both the potential functions of Bartell and those of Scott and Scheraga. D. Mean Square Amplitudes of Vibration The values of Em used were 0.09 R and 0.10 A for Hex interactions and 0.12 A to 0.135 A for H-H interactions, to correspond with the values suggested by Bartell (11). Values of fit can be obtained by electron diffraction studies, but no structure determination of the compounds of interest has been done by electron diffraction. The magnitude of 2t was estimated for each interaction, by using as a basis the values tabulated by Morino and coworkers (41). The values used in each case are listed in the Appendix. Table 11. Author Scott Scott Scott Scott Scott Scott and Scheraga and Scheraga and Scheraga and Scheraga and Scheraga and Scheraga Hendrickson Bartell I Ref. 39 39 39 39 39 39 40 38 aWhere the oxygen atom 35 6 in angstroms. Inter actio H--H H--F H--Cl H--Br H--O H—-0a H--C H--H n QHWNNCOHLO A .17 .69 .90 .18 .68 .46 .29 .59 X for 106 107 107 £07 107 107 107 107 V(r) 4.54 4.57 4.15 3.66 4.57 4.57 4.12 4.082 is a carbonyl oxygen. 4.52 x 6.27 3.21 4.65 9.04 1.22 1.25 4.92 Parameters of the non-bonded potential function V(r) = A exp(-Br) - Cr— mole and in calories/ 104 104 105 105 104 105 105 104 36 II. Calculation of Isotope Effects A. 1-Naphthylcarbinyl Chloride-8—d The isotope effects of 1-naphthylcarbinyl chloride-S-d summarized in Table 12 were calculated for two different ground state conformations and five different conformations of the transition state, which was assumed to be a carbonium ion. The ground state conformations used were VIII and IX, VIII where the CHZCl group in IX was rotated six degrees in the direction that increased the distance between the EEEEI hydrogen and the chlorine atom. The potential functions of Scott and Scheraga (39) were used to calculate the energy of the interactions of the CH2Cl group with the hydrogens in the ortho and E2££ positions for each conformation. Conformation IX, when rotated six degrees, was found to be about 450 cal more stable than VIII. Various angles of deviation, 9, of the CH2 group from coplanarity with the ring were used for the conformation of the carbonium ion. B. 8-Methyl—dq-1-naphthylcarbinyl Chloride Conformation X was used for the ground state of 8—methyl- d3-1—naphthylcarbinyl chloride. The carbonium ion, XI, that 37 Table 12. Calculated isotope effects for 8-R—1—naphthyl- carbinyl chlorides 9 ch V(r)a AEH ’ AED kH/kD R Conf. degrees degrees from cal/mole 25° D I 0 B 39 0.93 D I 15 B 29 0.95 D I 30 B 12 0.98 D I 45 B - 2 1.003 D I 90 B -15 1.03 D I 0 S 30 0.95 D I 15 S 22 0.96 D I 30 S 10 0.98 D I 45 S 0 1.00 D I 90 S - 7 1.01 D II 0 B -26 1.04 D II 15 B -36 1.06 D II 30 B -54 1.10 D II 45 B -67 1.12 D II 90 B -80 1.14 D II 0 ST 21 0.96 D II 15 S 14 0.98 D II 30 S 1 1.00 D II 45 S - 9 1.01 D II 90 S -16 1.03 CD3 0 0 B 70 0.89 (:93 15 7 B 49 0.92 CD3 30 12 B 0 1.00 003 45 16 B -45 1.08 CD3 90 0 B -55 1.10 003 0 0 S 59 0.90 003 15 7 S 40 0.93 CD3 30 12 S 0 1.00 CBS 45 16 S -33 1.06 cna 90 0 s -40 1.07 0(003)3 0 S -48 1.08 aB denotes Bartell 5 denotes Scott and Scheraga 38 was aSSumed for the transition state, was twisted differ- ent angles, 9, from the plane of the ring. For each of these transition state conformations the 8-methyl group was rotated 0 degrees to maximize the distance between the hydrogen atoms of the carbonium ion and those of the methyl group. The isotope effects are listed in Table 12. C. 8—t-Butyl-d9—1-naphthylcarbinyl Chloride Conformation XII was used for 8-Erbutyl-d9—1-naphthyl- carbinyl chloride and also for the correSponding carbonium ion, which was assumed to be planar with the ring. The XII 003 H methyl groups were rotated so that their hydrogens were at a maximum distance from the nearest hydrogen on the CH2C1 group or on the CH2 group. This amounted to a rotation from the normal staggered conformation of the Efbutyl group of 38° for the chloride and 35° for the cation. The calculated isotope effect is listed in Table 12. L) It—J . - :SII XIII m 39 D. 1-Naphthoyl Chloride-8-d The isotope effects of 1-naphthoyl chloride-8—d in Table 13 were calculated for ground state conformation XIII, in which the COCl group is planar with the aromatic ring, and for conformations in which the COCl group deviated XIII 0 degrees from coplanarity. In each case the transition state was taken as the linear acylium ion. E. 8-Methyl-d3—1-naphthoyl Chloride The isotope effects of 8-methyl—d3—1-naphthoyl chloride in Table 13 were calculated for ground state conformation XIV and for other conformations with various dihedral angles, 9, between the plane of the COCl group and the plane of the ring. For each non-planar conformation, the methyl group was rotated 0 degrees to maximize the distance between XIV the hydrogens of the methyl group and the carbonyl oxygen. The linear acylium ion was again assumed to be the transi— tion state. 40 Table 13. Calculated isotope effects for 8—R-1-naphthoyl chlorides kn/ R e 0 V(r)a AEH ' AED kD degrees degrees from cal/mole (25°C) D 0 B -318 1.71 D 15 B -254 1.52 D 30 B -159 1.31 D 45 B - 58 1.10 D 90 B 0 1.00 D 0 S -183 1.36 D 15 S -147 1.28 D 30 S — 76 1.14 D 45 S - 29 1.05 D 90 S 0 1.00 CD3 0 0 B -870 4.31 CD3 15 7.5 B -710 3.32 CD3 30 14 B -460 2.17 CD3 45 18 B -250 1.52 CD3 60 20 B -116 1.21 CD3 70 20 B - 90 1.16 CD3 90 0 B - 65 1.12 CD3 0 0 S -530 2.43 CD3 15 7.5 S -420 2.03 CD3 30 14 S -230 1.48 CD3 45 18 S -100 1.18 CD3 60 20 S - 40 1.07 CD3 75 20 S — 20 1.03 C(CD3)3 S -750 3.52 aB denotes Bartell S denotes Scott and Scheraga. 41 F. 8-t-Butyl—dg—1—naphthoyl Chloride The isotope effect of B-Efbutyl—dg-l-naphthoyl chloride in Table 13 was calculated for the planar ground state con- formation XV and a linear acylium ion transition state. xv 9030 01 The methyl groups were again rotated to maximize the non— bonded distances as was done for B-Efbutyl—l-naphthylcar- binyl chloride. The angle of rotation was 30° for the acid chloride and 32° for the acylium ion. G. Methyl-l—Naphthoate—B-d and Methyl 8-Methyl-d3-1- naphthoate The isotope effects in Table 14 were calculated for the basic hydrolysis of the naphthoate esters. The ground state conformations used for methyl 1-naphthoate-8-d were the same as those used for 1-naphthoyl chloride-8-d and the ground state conformations used for methyl 8—methyl-d3- 1-naphthoate were the same as those used for 8-methy1-d3- l-naphthoyl chloride, except that in both cases the chlorine atom was replaced by a methoxy group. The transition states were assumed to be tetrahedral and to have conformation XVI and XVII, respectively. Table 14. aB denotes Bartell b 00000000000008 UIJCIUIDCIUIJC1UIJCJU tJCIUtjtJCIUIDCJU wavwwuwuwuuwuw 42 Calculated isotope effects for the basic hydrol- ysis of methyl 8-R-1-naphthoates 9 degrees 0 15 30 45 90 0 15 30 45 90 0 15 30 45 60 70 90 0 15 30 45 60 75 90 ¢ degrees 7.5 14 18 20 20 14 18 20 20 S denotes Scott and Scheraga. 78°. V(r)a from mmmmmmmwwmwwwwmmmmmwwwww AE H -270 -206 -111 - 10 50 -162 -126 - 55 - 8 12 -338 -171 75 279 '419 2466 504 -252 -157 29 165 230 246 256 -AED cal/mole kH/kD (25°C) 1.57 1.42 1.21 1.02 0.92 1.31 1.23 1.09 1.01 0.98 1.61 1.27 0.90 0.67 0.55 0.49 O U! O‘UWTITO‘U H uh w UITCYU‘ 1.25 0.96 0.79 0.72 0.70 0.69 UtTO‘ XVI H. t-Butyl Chloride-d9 The isotope effects for the solvolysis of Erbutyl chloride-d9 (Table 15) were calculated to attempt to dupli- cate Bartell's calculations. The staggered C3v conforma- tion was used for the chloride and the C3h conformation for the carbonium ion. I. Acetyl Chloride-d3 The most stable conformation of acetyl chloride has been shown by microwave spectroscopy (42) to be the one where the carbonyl group is eclipsed by a hydrogen of the methyl group. The linear acylium ion was taken as the trans— ition state. X-ray crystallography studies have shown that the carbon-carbon bond in CH3COSbF6 is shorter in the acylium ion (43) than in acetyl chloride by 0.12 8. This introduces a large C-H interaction into the calculated isotope effects (Table 15). Since the non—bonded interactions with the hydrogen atoms are not as great for the positively charged carbon atom in the cation as for the carbon atom in aCetyl chloride, the increased interactions due to the bond shorten- ing in the cation will be somewhat canceled out. Therefore' 44 Table 15. Other calculated isotope effects a AE - AE H/kD Compound V(r) H D from cal/mole., (25°C) (003)3001 B 3 -198b 1.39b B -186 1.36 S — 43 1.07 0030001 B 29 0.94d S 8.1 0.99d B - 38C 1.08d S - 8.6C 1.02d 00300202115 B 20 0.97 S 5 0.99 C-CD2C1 B -637 2.92 S -130 1.25 2,6-Dimethyl-d3-pyridine BF3 adduct S 95 2,6-Dimethyl-d3—pyridine BH3 adduct B 71 S 43 2,2'—Dibromo-4,4'—dicarboxy— biphenyl-6,6'-d2 S 60 aB denotes Bartell S denotes Scott and Scheraga. bResults of Bartell in Reference 11. CNeglecting C—H interactions. d-220. 45 the isotope effect for acetyl chloride-d3 was also calcu- lated by omitting all C-H interactions. J. Ethyl Acetate-d3 The ground state conformation of ethyl acetate was as- sumed to be analogous to that of acetyl chloride, $323 a hydrogen eclipsing the carbonyl. The transition state was assumed to be tetrahedral with the methyl group in a stag- gered conformation. The isotope effects calculated for the basic hydrolysis of ethyl acetate-d3 are listed in Table 15. K. Alpha Isotope Effect The alpha isotope effect listed in Table 15 was calcu- lated for a tetrahedral C-CD2C1 group ionizing to the cor- responding trigonal carbonium ion. All other possible interactions were neglected. L. Adducts of 2,6-Dimethyl—d3epyridine The steric isotope effects were calculated for the BH3 and BF3 addition products of 2,6-dimethyl-d3-pyridine and are listed in Table 15. Conformation XVIII was used for both adducts. Since the boron atom in this addition com- pound is isoelectronic with carbon, a C-H potential function was used for the B—H interactions. 46 XVIII M. 2,2'-Dibromo—4,4'—dicarboxybiphenyl-6,6'-d2 The isotope effects for the rate of racemization of 2,2'-dibromo—4,4'-dicarboxybiphenyl-6,6'-d2 (Table 15) were calculated by using the potential function of Scott and Scheraga (39) for H—Br interactions. The hydrogen-bromine distance of 2.31 8 calculated by Westheimer (16) was used for the H-Br interaction in the transition state. 'The ground state was considered to have no significant inter- action. DISCUSSION In order to assess the reliability of Bartell's method of calculating isotope effects due to non-bonded interac- tions (11), the calculated values of the isotope effects will be compared with the experimental values. No attempt will be made to determine the validity of the assumptions, such as the approximation that vibrations are harmonic, which were made in the derivation of his expression. The accuracy of the empirical parameters used in his model, such as the potential functions, will however, be discussed, though in a pragmatic manner. The racemization of 2,2'-dibromo-4,4‘-dicarboxybiphenyl- 6,6'—d2 is a reaction for which the structure of the transi- tion state is known with some certainty. As already men- tioned in the introduction, Melander and Carter (14), by using Bartell's method, calculated an isotope effect of 506 cal/mole from Westheimer's (16) H-Br potential function and one of 100 cal/mole from Howlett's (17). Their experi- mental isotope effect was 90 cal/mole. The isotope effect calculated from the Scott and SCheraga (39) H-Br potential function is 60 cal/mole. Thus it is evident that although Bartell's method appears to be valid for the calculation of isotope effects due to non-bonded interactions, the magnitude of the calculated isotope effect is Strongly de- pendent upon the potential function used. 47 48 Another reaction for which the change in interatomic distances can be estimated to a reasonable degree of ac- curacy is the isotOpe effect on AH° for the addition of boron trifluoride and diborane to 2,6-dimethyl-d3-pyridine. There are no relevant non—bonded interactions in the react- ants and reasonable estimates can be made for the structure of the products. The calculated isotope effect for the boron trifluoride addition complex is AAE = 95 cal/mole by using the H-F potential function of Scott and Scheraga. This agrees within the limits of experimental uncertainty with the experimental isotope effect of AAHO = 230 i 150 cal/ mole (20). The observed isotOpe effect on the addition of diborane to 2,6—dimethyl-d3—pyridine (20) is AAHO = —20 i 80 cal/mole. The iSOtope effect calculated by using Bartell's H-H potential function is AAE = 71 cal/mole and that calculated by using Scott and Scheraga's is AAE = 43 cal/mole. Conceivably, the H-H potential function of the latter authors may be slightly better. In 5N1 reactions where deuterium is substituted for hydrogen on the carbon bearing the leaving group, an alpha_ isotope effect is observed. Here the non-bonded distances in the ground state can be accurately determined, but the structure of the transition State is unknown. For a.C-CD2C1 group, if the corresponding carbonium ion is considered to be the transition state, the calculated isotope effect is AAE = -640 cal/mole by using the potential functions of Bartell and AAE = — 130 cal/mole by using the potential 49 functions of Scott and Scheraga. The latter is in good agreement with the observed alpha isotope effect (AAGI = —165 cal/mole) for 8—methyl-1-naphthylcarbinyl chloride- a,a-d2. The large alpha isotope effect predicted with Bartell's potential functions is mainly due to the magni- tude of the H-Cl interaction. Thus it would seem that the Scott and Scheraga potential functions, or at least their H—Cl potential function, are more realistic. No significant isotOpe effect was found (30) for the solvolysis of 1-naphthylcarbinyl chloride—8-d in 0.32 M water-formic acid solution (kH/kD = 1.00 i 0.05 and AAG+= 0 i 29 cal/mole). The reaction exhibits an alph§_isotope effect kH/kD = 1.35 (30), so it is probably 8N1. The car- bonium ion assumed for the transition state is probably very close to being planar with the aromatic ring, because on deviation from 00planarity the increase in energy of the system due to decreased delocalization of charge is much greater than the decrease in energy obtained by relieving the non-bonded interactions. For a dihedral angle of 15° simple HMO calculations predict a loss of resonance energy of 2,700 cal/mole, whereas the energy decrease from the al- leviation of non-bonded interactions is only 300 cal/mole. As can be seen from Table 12, the calculated isotope ef- fects for a planar carbonium ion and for one with a di- hedral angle of 15° are 39 cal/mole and 29 cal/mole re— spectively by using Bartell's potential functions and 30 cal/mole and 22 cal/mole respectively by using Scott and Scheraga's potential functions, if the chlorine atom is 50 ahhl to the pa£l_hydrogen in the ground state conformation (conformation X). If ground state conformation XI is the minimum energy one, the isotope effects calculated by using Bartell's potential functions are -26 cal/mole and -36 cal/ mole respectively and thaxzcalculated by using Scott and Scheraga's are 21 cal/mole and 14 cal/mole. All of these calculated isotope effects, irrespective of the ground state and carbonium ion conformations, fall within the limits of experimental uncertainty. The isotope effect for the solvolysis 8-methyl—d3-1- naphthylcarbinyl chloride in 66.67% acetone-water (V/V) is kH/kD = 1.013 f 0.022 and AAGI = -8 i 13 cal/mole at 25°. The reaction is 8N1 because it has an alpha isotope effect of kH/kD = 1.32 and because 8-methyl-1-naphthylcarbinyl chloride reacts at a rate about thirty times greater than 1-naphthylcarbinyl chloride. If the mechanism of solvolysis of both compounds is 5N2, the reaction rate of the 8-methyl— 1-naphthylcarbinyl chloride would be slower, not faster than 1—naphthylcarbinyl chloride, because of the greater steric requirements of the former. If the mechanism of solvolysis of 1-naphthylcarbinyl chloride is either SNl or 5N2 and 8— methyl-1—naphthylcarbinyl chloride is 5N1, the reaction rate of the latter would be greater, as is observed. The carbon- ium ion is planar or nearly so. If the dihedral angle of the carbonium ion is 15° the energy increase of the system due to decreased overlap (2,700 cal/mole) is much greater than the energy decrease due to alleviation of non-bonded interactions (800 cal/mole). 51 For dihedral angles of 0° and 150 between the planes of the carbonium ion and the aromatic ring, the isotope effects calculated by using Bartell's potential functions are 70 cal/mole and 49 cal/mole respectively and those calculated by using Scott and Scheraga's potential func- tions are 59 cal/mole and 40 cal/mole. Thus the calculated isotope effects are not at all in accord with the experi- mental AAGI and are in fact in the opposite direction. However, the calculated isotope effects do agree with the experimental AAHI = +140 1 300 cal/mole. It should be emphasized that any isotope effect originating from non- bonded interactions would effect mainly the enthalpy of activation of the reaction. The H-H and H-Cl potential functions of both Bartell and Scott and Scheraga seem to give reasonable estimates of the isotope effects for the solvolysis of 1-naphthyl- carbinyl chloride-8—d and 8-methyl-d3-1—naphthylcarbinyl chloride. Those of Scott and Scheraga would be preferred on the basis of their prediction of the alpha isotope effect. However, the isotope effect calculated with these functions for the solvolysis of pfbutyl chloride-d9, a system where hyperconjugation is possible, is much less than the experi— mental isotope effect. For example, the Scott and Scheraga potential functions give AAE = -43 cal/mole, whereas the experimental isotope effect is AAHI SfAAGI= -516 cal/mole (8). The isotope effect calculated by using Bartell's potential functions, AAE = —186 cal/mole, is closer but 52 still considerably less than the observed isotope effect. No significant isotope effect was found for the basic hydrolysis of methyl 1-naphthoate—8-d, where AAGI = —0.6 i 4 cal/mole (32). For this to agree with the calculated iso— tope effects in Table 14, the dihedral angle of the carbo- methoxy group with the aromatic ring would have to be at least 45°. This assumption is unlikely in view of the fact that the dihedral angle in 1-naphthoic acid is only 11° (44). Since a negative charge is develOping in the transition state the interaction between the negatively charged oxygen and the papl hydrogen is probably greater than the value obtained from the O—H potential function. This would have the effect of decreasing the dihedral angle for which no isotope effect is found. No conclusions should be drawn, however, until AAHI for this reaction is determined. The experimental isotope effect for the basic hydrolysis of methyl 8-methyl—d3-1—naphthoate (47) is kH/kD = 0.89 1 0.22 and AAGI = 82 i 15 cal/mole at 78.5°. The value of AAHI determined from the rate constants at this and one other temperature is 800 i 400 cal/mole. This value is in accord with the isotope effects calculated by using Bartell's potential function if the dihedral angle is 60° or greater but not with those calculated from the Scott and Scheraga potential functions. However, because of the greater OéH interaction in the negatively charged transition state, a dihedral angle of about 45° may not be unreasonable. 53 In the basic hydrolysis of ethyl acetate—d3, Bender and Feng (45) found an isotope effect of kH/kD = 0.90 i 0.01 and AAGI = 60 i 6 cal/mole at 25°. The isotope effect calculated by using Bartell's potential function is 20 cal/mole and that calculated by using the potential func- tions of Scott and Scheraga is 5 cal/mole. This isotope effect has been determined by Halevi and Margolin (46) at several other temperatures with rather abnormal results: kH/kD = 1.00 i 0.01 at 0°, 0.93 i 0.01 at 350 and 1.15 i 0.09 at 65° If the isotOpe effect at 0° is omitted and the lower limit (1.06) of the isotope effect at 65° is taken, a plot of ln(kH/kD) versus 1/T yields a reasonable facsimile of a straight line. The value of AAH2t deter- mined from the slope is about 700 cal/mole, a result that should be treated with caution as it seems too great to be realistic. It is difficult to draw definite conclusions on the basis of these experimental data. It does seem, however, that for ethyl acetate-d3 the calculated isotope effect is less than the experimental. The calculated isotope effects (Table 13) for the sol- volysis of 1-naphthoyl chloride-8-d are substantial. If a reasonable dihedral angle of 15° is assumed, the calculated isotope effect is AAE = —254 cal/mole by using the potential functions of Bartell and AAE = —147 cal/mole by using the potential functions of Scott and Scheraga. However, no Significant isotOpe effect was observed (32) at 15°, 25° and 35°, at each temperature AAGI being about 0 i 6 cal/mole. 54 8-Methyl-1-naphthoyl chloride solvolyzes in acetone— water by an 5N1 mechanism (32). The isotope effect for the solvolysis of 8—methyl-d3-1-naphthoyl chloride (32) was found to be kH/kD = 1.030 t 0.015 and AAGI = -18 i 9 cal/ mole at 25° in 95% acetone—water (w/w). In this tempera- ture range AAHI is equal to -29 i 243 cal/mole. More ac— curate results were obtained for this reaction in 75.23% acetone-water (w/w) at lower temperatures. At -27°, kH/kD = 1.127 r 0.018, AAGI = —58 i 9 cal/mole and AAHI = -307 i 167 cal/mole in this temperature range. The experi- mental value of AAHI agrees with the calculated isotope effects if the dihedral angle of the acid chloride group with the plane of the aromatic ring is between 30° and 45°. For dihedral angles of 30° and 45° the isotope effects calcu— lated by using the potential functions of Bartell are -460 cal/mole and -250 cal/mole respectively and those calculated by using the potential functions of Scott and Scheraga are -230 cal/mole and -100 cal/mole. The dihedral angle of the acid chloride group in 8-methyl—1-naphthoyl chloride should be about the same as the dihedral angle of the carbomethoxy group in methyl 8-methyl-1-naphthoate. The isotope effects calculated for these compounds by using Bartell's potential functions are consistent with the experimental AAHI if this dihedral angle is about 45°. The isotope effect for the solvolysis of acetyl chlor- ide—d3 at -22° was determined by Bender and Feng (45) to kH/kD = 1.62, AAGI = -240 i 25 cal/mole in 80% acetone-water and kH/kD = 1.51. AAGI = -206 i 25 cal/mole in 90% acetone- 55 water. The isotope effect calculated by using the potential functions of Bartell is 29 cal/mole, while the one calcu- lated by using those of Scott and Scheraga is 8.9 cal/mole. The inverse isotope effect results from the increased C-H interaction in the acylium ion where the carbon-carbon bond is considerably shorter than it was in the ground state. If the C-H interaction is neglected, then AAE = -38 cal/mole from Bartell's potential functions and AAE = —8.6 cal/mole from those of Scott and Scheraga. The kinetic isotOpe effect for the solvolysis of acetyl chloride-d3 was also determined by Papaioannou (47) at several different temperatures to obtain the thermodynamic # activation parameters. In 80% acetone-water AAG = -48 i 5 cal/mole and in 90% acetone—water AAGI = -29 i 1 cal/mole at -22°. In 80% acetone—water AAHI = —225 i 76 cal/mole and in 90% acetone-water AAHI = +285 1 140 cal/mole. It appears that acetyl chloride solvolyzes by a mixed SNl-SNZ mechanism. That the 8N2 contribution is considerable is demonstrated by the relative solvolysis rate of 2,2-di- methylpropanoyl chloride, which is 20 times slower than acetyl chloride in 80% acetone-water and 10 times slower in 90% acetone-water (47). In 90% acetone-water the 3N2 term is predominant and the isotope effect resulting from enthalpy is inverse. In 80% acetone-water the contribution of the SNl term has increased so as to give a corresponding normal effect. 56 The isotope effect for the 8N2 reaction, if it is due to non-bonded interactions, should be similar to that calcu- lated for the basic hydrolysis of ethyl acetate-d3. However, the calculated isotope effect for ethyl acetate—d3 (AAE = 20 cal/mole or AAE = 5 cal/mole) is much less than the ex- 4: perimental isotOpe effect (AAH = 285 cal/mole) in this case. The isotope effect for a pure 8N1 reaction of acetyl chloride—d3 is either equal to or greater than the AAHI = -225 cal/mole in 80% acetone-water, which would mean that again the experimental isotope effect is greater than the calculated isotope effect of AAE = —38 cal/mole or -8.6 cal/mole. It can be concluded that Bartell's method of calcula- tion of secondary isotope effects due to non-bonded inter- actions can correctly predict the isotope effect if appro— priate potential functions are chosen and if the system is such that the sole contribution to the isotope effect is the difference in non-bonded interactions between hydrogen and deuterium. However, if the system is one in which hyperconjugation is possible, the calculated isotope ef- fects are much less than the experimental isotope effects. Therefore hyperconjugation, where possible, certainly con— tributes to the experimental isotope effect. Although the accuracy of the data makes quantitative predictions diffi- cult, in most systems hyperconjugation probably is the main contributor to the isotope effect. 1. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19; REFERENCES M. J. Stern and M. Wolfsberg, J. Chem. Phys., 223 2618 (1966). a) J. Bigeleisen, Ibid. 17, 675 (1949) b) L. Melander, Arkiv. Kemi, 2, 211 (1950). J. S. Muenter and V. W. Laurie, J. Chem. Phys., aa, 855 (1966). a) G. V. D Tiers, J. Am. Chem. Soc., 79, 5585 (1957). b) G. v. D. Tiers, J. Chem. Phys., 963‘T1958). A. Streitwieser, Jr. and H. S. Klein, J. Am. Chem. Soc., 85, 2759 (1963). Wn. Van Der Linde and R. E. Robertson, Ibid., 223 4505 (1964). A. Streitwieser, Jr., and H. S. Klein, Ibid., §§, 5170 (1964). L. Hakka, A. Queen, and R. E. Robertson, Ibid., a1, 161 (1965). E. S. Lewis and C. E. Boozer, Ibid., 12, 6306 (1952) V. J. 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APPENDIX Structure of 1,8-Disubstituted Naphthalene Compounds Three different basic structures were used for the three types of substituents (hydrogen, methyl and tertiary butyl) in the 8—position. The structures of the 8-methyl substituted compounds were taken to conform with the known structure of 3-bromo-1,8—dimethylnaphthalene (48). The structures of the 8-hydrogen and 8-pfbutyl substituted naphthalenes were based on reasonable estimates. In order to simplify the determination of the interatomic distances, R and X in XIX were assumed to be coplanar with the naphtha- lene ring. XIX 61 Table 16. Structural parameters of the naphthalene ring and of R for 8-R-1éX—naphthalenes Bond fiength Bond Angle 1-X-Naphthalene (XIX, R = H) a 1.08 ab,cd 121° b,c 1.42 bc 122° 8-Methyl—1-X-naphthalene (XIX, R = CH3) a 1.52 ab,cd 123.50 b,c 1.43 bc 126.8° 8-pfbutyl-1-X-naphthalene (XIX. R = C(CH3)3> a 1.52 ab,cd 125° b,c 1.43 bc 128° 0-0 1.53 0-0—0 1110 C-H 1.10 C-C-H 1110 62 Table 17. Structural parameters of X for 8-R-14X- naphthalenes 'Bond R X Bond Length Bonds ( ) H.CH3,C(CH3)3 0H201 0-0 1.52 C-C-H C-H 1.10 0—0-01 0-01 1.78 H.0H3,0(0H3)3 0H2 + 0—0 1.52 C-C-H C-H 1.10 H.0H3 0001 0-0 1.48 0—0—0 C—O 1.22 C-C-Cl 0-01 1.72 C(CH3)3 0001 0-0 1.48 c-c-o 0-0 1.22 0—0-01 C-Cl 1.72 H,CH3,C(CH3)3 0:0 + 0-0 1.48 c-c—o 0—0 1.22 H.0H3 002Me 0-0 1.48 0—0=o c=o 1.22 0-0-0 C-O 1.36 H.0H3 COH(0Me)(O ') 0-0 1.52 0-0-0 C-O 1.42 Bond Angle 109.5° 109.5° 120° 120° 120° 126° 114° 180° 120° 120° 109.5° 63 Structures of Other Compounds The structure used for the pfbutyl chloride was the same as that used by Bartell (11). The structure of acetyl chloride has been determined by microwave spectroscopy((42) and the structure of the acetyl cation as the antimony- hexafluoride salt has been determined by X-ray crystal+ lography (43). The structure of ethyl acetate was taken to be the same as the structure determined for methyl acetate (49). The structures of the boron trifluoride and diborane adducts of 2,6-dimethylpyridine were estimated by using bond lengths and angles similar to those of trimethyl- amine boron trifluoride (50), pyridine (51), and diborane (52). 64 Table 18. Structural parameters of other compounds for which isotOpe effects were calculated Compound C(CH3)3C1 C(CH3)3 + CH3COC1 + CH3C=O CH3C02Et CH3C(OH)(Et)(O-,) 0-0H201 C-0H2 + (CH3)2(¥13N :BHa (CH3)2CJ'13N :BFa Bond Bond Length (X) C-C 1.54 C-H 1.10 C-Cl 1.80 C-C 1.54 C-H 1.10 C-C 1.499 C-H 1.083 C-O 1.192 C-Cl 1.789 C-C 1.38 C-H 1.083 C-O 1.15 C-C 1.51 C-H 1.083 C-O 1.36 C-C 1.54 C-H 1.083 C-O 1.42 C-C 1.53 C-H 1.10 C-Cl 1.78 C-C 1.53 C-H 1.10 B—H 1.19 B-F 1.38 B-N 1.58 C-N 1.34 C—C 1.51 C-H 1.10 Bonds C-C-C C-C-H C-C-C C-C-H C-C‘H C-C-O C-C-Cl C-C-H C-C-O C-C-H C-C=O C-C-H C-C-O C-C-H C-C-Cl C-C-H N-BrH N-B-F c—N-B ‘.C-C-N C-C-H Bond Angle 109.5° 109.5° 120° 109.5° 110.35° 127.083° 112.65° 110.35° 180° 110.3° 122° 110.3° 109.5° 109.5° 109.5° 120° 112° 112° 121.6° 118° 110° Table 19. CD3 C499 C499 CD3 CD3 003 C499 CD3 CD3 65 Values of Em and 2t of 8-R—1-X-naphthalenes CH2Cl 0H201 0H201 CH2Cl CH2C1 0001 0001 0001 0001 0001 COCl C02CH3 0020H3 C02CH3 Interaction H--H H--Cl lamb?) 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.09 0.09 0.10 0.10 0.10 0.09 0.10 Table 20. Values of 2m and It for other compounds Compound (003)3001 CH3COC1 CD3C02C2H5 0-0D201 (CD3)29haN:BH3 (CD3)20_H3N:BF3 C6H4BrC3H4Br H--H H--C H--C H--O H--C H--C H--O H--H H--C H--C H--H H--B H--F H--C 66 Interaction l l l H--Br amt?) 0.13 0.10 0.10 0.10 0.10 0.10 0.10 0.135 0.104 0.086 0.10 0.10 0.10 0.10 0.10 (R) 0.23 0.18 0.18 0.16 0.16 0.10 0.16 0.135 0.104 0.086 0.19 0.14 0.16 0.14 0.16