Conformational studies of neuroactive ligands. 1. Force field and

J . Phys. Chem. 1989, 93, 1338-1350

1338

sLand variable point s, integral equations may be derived for g and g’ (using a Green’s function approach) with the right-hand

SR based on knowledge of g(sL) and g’(sL), the trapezoidal integral approximation is applied to eq A3 and A4, which yields

side of eq AI as the inhomogeneity: &)

= C(SJL) &SL)

+ S(SJL) g’(SL)

J-+’S(S,S?[A(S? g’b) = -k$(S,sL)

6

-

gR

g’b? + D(s?

ds?l

+ C(S,SL) g’(sL) C(s,s?[A(s? g’@?+ DO? &?I

(‘43) gR’

g(SL)

X>’

(A41

where C ( S , S ~= ) ~cos ~ [ko(s- sL)]Sij C(s,s~= ) ~cosh [Ikol(s- sL)]bij

= cgL + SgL’ - TS[A$L’

for (ki)iiIO for (k&i I0

To estimate the values of g and g’at translational coordinate say

= -k&L

+m L 1

6

(A6)

6

+ cgL’- T q A d L ’ + m L 1 - 2 [ARgR’ + & g R I (‘47)

a

where 6 is the step len th between the endpoints sLand sR. The subscripts L and R i dicate evaluation a t sL and sR, and so is chosen to be the midpoint between them. Matrix algebra yields the estimated values. Starting with a trial wave solution consistent with product boundary conditions, g and g’are propagated in s according to eq A6 and A7 (and with stabilization where necessary). At the coordinate boundaries we match complete wave functions and corresponding nuclear gradients. Finally, at the reactant asymptote, the amplitudes of the outgoing and incoming components of the trial solutions are used to form the scattering matrices and transition probabilities.

Conformational Studies of Neuroactive Ligands. 1. Force Field and Vlbrational Spectra of Crystalline Acetylchollne Philippe Derreumaux,+K. Jeff Wilson,f Gerard Vergoten,? and Warner L. Peticolas* Department of Chemistry and Institute of Chemical Physics, University of Oregon, Eugene, Oregon 97403 (Received: May 20, 1988)

The classical Raman spectra of three halide salts (Cl-, Br-, and I-) of the acetylcholine cation (ACh) in the crystalline state have been obtained. Two of these three crystals, the Br- and the I-, produce Raman spectra that are quite similar while the C1- crystal gives a different Raman spectrum. This correlates well with the X-ray diffraction results which show that the ACh cation exists in a similar conformation in the former two salts, while the conformation of the cation in the C1- salt is different. This indicates that crystal packing forces have significant influence on crystalline conformation of the ACh cation. We attribute the difference in the vibrational spectra of these salt crystals as being predominantly due to changes in the conformation of the ACh cation inside the crystal lattices. We have chosen the acetylcholine bromide crystal as the subject of a detailed normal-coordinate analysis. Using a modified Urey-Bradley force field, the calculations were done on a model crystal of 125 unit cells using an initial 86 internal displacement coordinates (which transform into 78 nonredundant local symmetry displacement coordinates) for each of the four cations of the unit cell. The force field was refined to give a minimum difference between the calculated and experimental frequencies (from, IR and Raman spectra). We have also obtained the Raman spectrum of crystalline acetylcholine-d9bromide (CH3(C=O)OCH2CH2N(CDJ3)and calculated the vibrational frequencies of this crystal using the same force field as for the nondeuteriated ACh with good agreement between observed and calculated frequencies. This set of calculations and force field yields a number of important new assignments of the vibrations and is the starting point in developing a isolated molecule force field for acetylcholine in solution.

Introduction Perhaps the most common chemical transmitter of nervous impulses is the acetylcholine (ACh) cation, shown in Figure 1. Results of X-ray crystallography of the chloride, bromide, and iodide crystals of ACh show that the conformation of the cation is similar in the bromide and iodide crystals but different in the Present address: Faculty of Pharmacy, University of Lille, Lille, France. ‘Present address: Department of Biochemistry, University of Virginia School of Medicine, Charlottesville, VA 22908. 0022-3654/89/2093-1338$01.50/0

chloride crystal.’,* This X-ray result is mirrored in the Raman spectra from these crystals. The Raman spectra of the iodide and bromide crystals are similar but distinctly different from that of the chloride. This experimental data indicate that crystal packing forces have significant influence on the crystalline conformation of the ACh cation. Recently we have obtained evidence, based ( 1 ) Svinning, T.; Sorum, H. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1975, 831, 1581. ( 2 ) Jagner, S.; Jensen, B. Acta Crystallogr., Sect. B: Struct. Crystallogr.

Cryst. Chem. 1977, 833, 2151.

0 1989 American Chemical Society

Vibrational Analysis of Crystalline Acetylcholine

The Journal of Physical Chemistry, Vol. 93, No. 4 , 1989 1339 TABLE 11: Internal Coordinates for Crystalline AChBr bending stretching

Figure 1. Schematic diagram of the ACh cation in the bromide conformation, showing the atom designations used and the four major torsional angles ( 7 0 through i& TABLE I: Structural Parameters for Crystalline Acetylcholine Halides from Ref 2 and 3 AChCl AChBr AChI distances, A C7-C6 1.49 1.49 1.48 C6=02 1.18 1.19 1.20 C6-0 1 1.38 1.36 1.37 01-C5 1.45 1.45 1.43 c5-c4 1.47 1S O 1.50 C4-N 1.49 1.51 1.53 N-C 1 1S O 1.50 1.50 N-C2 1.49 1S O 1.49 N-C3 1.52 1S O 1.52 angles, deg N-C4-C5 119 116.5 116 C4-C5-01 111 111.6 111 C5-01-C6 115 115.7 116 0 1-C6=02 123 122.8 121 01-C6-C7 108 111.3 112 02=C6-C7 129 125.9 127 torsional angles, deg TO: (H$)-C-&C -175 -1 74 180 71: (O=C)-O-C-C 193 79 83 72: 0-C-C-N 85 78 a9 7 3 : C-C-N-C 52, 171, -74 68, -174, -55 70, -174, -53

on Raman spectroscopic measurements, of solutions as well as crystals, that the conformation of the ACh cation and related choline ester analogues are a function of the physical environment of the cations3 In particular, the Raman spectra of solutions of ACh differ markedly from Raman spectra obtained from any of the crystals. In view of the polymorphism of ACh in various environments, it is impossible at the present time to predict with any certainty the conformation of ACh when it is bound at a receptor site. The ultimate goal of this research is to develop methods and accurate transferrable parameters for obtaining quantitative estimates of the conformation(s) of ACh, and its biologically active analogues, in various environments including the binding sites of the acetylcholine receptor protein. The methodology applied to this overall task is described and applied in this and the following paper. In this paper, a force field for the ACh cation that is based on a normal mode analysis of the observed vibrational frequencies in the crystal is developed. In these calculations we use the methods pioneered by the late Professor Shimanouchi and his collaborators! This work indicates that in order to obtain good agreement between the calculated and observed vibrational frequencies a rather sophisticated force field using nonredundant (3) Wilson, K.J. Ph.D. Dissertation, University of Oregon, August 1988. (4) Shimanouchi, T. Vibrational Spectroscopy and Its Chemical Applications; University of Tokyo: Bunkyo-ku, Tokyo, Japan, 1977.

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R24 R25

C6-C7 R26 C6=02 R28 C6-01 R30 Ol-CS R32 C5-C4 R34 C4-N R36 N-C3 R38 N-C1 R40 N-C2 R42 C3-H33 R44 C3-H31 R46 C3-H32 R48 C1-H13 R50 C1-H12 R52 Cl-HI1 R54 C2-H23 R56 C2-H22 R58 C2-H21 R60 C5-H51 R62 C5-H52 R64 C4-H42 R66 C4-H41 R68 C7-H73 R70 C7-H71 C7-H72 out-of-plane deformation R72 C6(0102C7)

R81 Tx R82 Ty R83 Tz

C6-C7-H73 C6C7-H72 H73-C7-H72 C7-C6-01 01-C6-02 01C5C4 01-C5-H52 C4-CS-H51 C5-C4-N C5-C4-H41 N-C4-H42 C4-N-C2 C4-N-C3 C2-N-Cl N-C2-H23 N-C2-H21 H22-C2-H21 N-C3-H32 N-C3-H31 H32-C3-H31 N-CI-H13 N-C1-HI1 H13-C1-HI1

R27 R29 R31 R33 R35 R37 R39 R41 R43 R45 R47 R49 R51 R53 R55 R57 R59 R61 R63 R65 R67 R69 R71

C6C7-H71 H73-C7-H71 H71-C7-H72 C7-C6-02 C6-01-CS 01-CS-H51 C4-C5-H52 H52-C5-H51 H42-C4-H41 C5-C4-H42 N-C4-H41 C4-N-C1 C2-N-C3 C3-N-Cl N-C2-H22 H23-C2-H22 H23-C2-H21 N-C3-H33 H32-C3-H33 H33-C3-H31 N-C1-H12 H13-Cl-Hl2 H12-Cl-HI1

torsion R73 C3-N R75 N-C2 R77 C 4 C 5 R79 0 1 4 6 external

R74 R76 R78 R80

N-Cl N-C4 C5-01 C6-C7

R84 Ra R85 Rb R86 Rc

symmetry displacement coordinates is required. The force field for the normal-coordinate analysis of ACh is constructed using local symmetry coordinates that are transferrable to the cation in different environments. In this paper we provide the first steps in obtaining a reliable force field for the ACh cation by performing a detailed normal coordinate calculation for the crystal of acetylcholine bromide. We also show the experimental Raman spectra of ACh in three crystalline states and make assignments to the vibrational bands of the bromide crystal, including several Raman bands that are important marker bands for the conformational state of the ACh cation. In the second paper of this series, the crystalline force field is modified to be applicable to the isolated ACh cation in any of its conformations. We use this isolated molecule force field to determine the conformations of the ACh cation in solution. This is done by keeping the internal force field constant while (computationally) varying the torsional angles of the cation (meaning that the functional form of the force field remains constant; changes in the torsional angles will induce changes in the potential energy between nonbonded atoms which will change the effective values of the force constants) and optimizing the bond lengths and angles to lowest potential energy by use of molecular mechanics methods. Then the vibrational frequencies of each conformation are calculated by use of the Shimanouchi method. The conformations which show the minimum difference between the calculated and observed frequencies are assumed to be the most probable conformations in solution.

Materials and Methods

Acetylcholine Preparation. All acetylcholine salts were commercially obtained (Sigma; acetylcholine-d9 bromide from MSD Isotopes) and recrystallized by vapor diffusion of diethyl ether into saturated ethanolic solutions of the particular salts and were dried in vacuo (20 Torr) to constant mass in an Abderhalden device over boiling chloroform.

1340 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989

Derreumaux et al.

I

5 4\

I

l o

I

Figure 2. Classical Raman spectra of crystalline (a) acetylcholine chloride, (b) acetylcholine bromide, (c) acetylcholine iodide, and (d) acetylcholine-d9 bromide. The spectra are expanded into three sections for clarity. TABLE III: Local Symmetry Coordinates for Crystalline AChBP SI ST C6-C7 R1 s2 ST C6=02 R2 s3 ST C6-01 = R3 ST OI-CS R4 s4 ST C5-C4 R5 s5 ST C4-N R6 S6 s7 TS NC3 = R9 + R8 + R7 DS' NC3 R9 - R8 S8 s9 DS NC3 5 2 X R7 - R8 - R9 SI0 TS C3H 5 RIO + RI 1 + R12 SI 1 DS C3H 2 X R12 - R11 - R10 DS' C3H RII - R10 s12 S13 TS CIH R13 + R14 + R15 DS CIH 2 X R15 - R14 - R13 S14 DS' ClH R14 - R13 SI5 SI6 TS C2H = R16 + R17 + R18 S17 DS C2H 5 2 X R16 - R17 - R18 DS' C2H R17 - R18 SI8 S19 SS C5H R19 + R20 s20 AS C5H 5 R20 - R19 SS C4H = R21 + R22 s21 s22 AS C4H E R21 - R22 S23 TS C7H p R23 + R24 + R25 S24 DS C7H 2 X R25 - R23 - R24 s25 DS' C7H 5 R24 - R23 S26 SD C7H 5 R31 + R30 + R29 - R26 - R27 - R28 DD C7H 2 X R29 - R30 - R31 S27 S28 DD' C7H 2 R31 - R30 S29 DR C7H 5 2 X R28 - R26 - R27 DR' C7H R27 - R26 S30 S3 1 DEF C7C601 5 2 X R32 - R33 - R34 DEF C6=02 plane 5 R33 - R34 S32 s33 DEF C601CS 5 R35 s34 SC C5H 5 4 X R41 - R37 - R38 - R39 - R40 s35 WAG C5H R38 + R37 - R39 - R40 S36 RO C5H -R38 - R39 + R37 + R40 s37 TW C5H -R38 - R40 + R39 + R37 S38 DEF C4C501 E 5 X R36 - R37 - R38 - R39 - R40 - R41 s39 SC C4H 5 4 X R43 - R44 - R45 - R46 - R47

S40 S41 S42 s43 s44 s45 S46 s47 S48 s49 SSO S5 1

s52 s53 s54 S55

S56 s57 S58

s59 S60 S6 1 S62 S63 S64 565 S66 S67 S68 S69 S70 S7 1 S72 SI3 s74 s75 S76 s77 SI8

WAG C4H 1 R44 + R45 - R46 - R47 RO C4H R45 + R46 - R44 - R47 TW C4H R45 + R47 - R44 - R46 DEF C5C4N 5 X R42 - R43 - R44 - R45 - R46 - R47 SD NC3 R51 + R52 + R53 - R48 - R49 - R50 DD NC3 E 2 X R52 - R51 - R53 DD' NC3 R53 - R51 DR NC3 2RS0 - R48 - R49 DR' NC3 5 R48 - R49 SD NC2 5 R57 + R58 + R59 - R54 - R55 - R56 DD NC2 5 2 X R58 - RS7 - R59 DD' NC2 R57 - R59 DR NC2 2 X R54 - R55 - R56 DR' NC2 R55 - R56 SD NC3 R63 + R64 + R65 - R60 - R61 - R62 DD NC3 2 X R65 - R63 - R64 DD' NC3 R64 - R63 DR NC3 2 X R60 - R61 - R62 DR' NC3 5 R62 - R61 SD NCI 5 R69 + R70 + R71 - R66 - R67 - R68 DD NCl 2 X R69 - R70 - R71 DD' NCI E R71 - R70 DR NCl 5 2 X R68 - R66 - R67 DR' NCI R67 - R66 OPB C6(0102C7) 5 R72 TO NC3 3 R73 TO NCl = R74 TO NC2 = R75 TO C4N = R76 TO C4C5 = R77 TO CSOl = R78 TO 01C6 R79 TO C6C7 R80 Tx 5 R81 Ty = R82 Tz R83 Ra 3 R84 Rb R85 Rc 5 R86

Abbreviations: ST, stretching; TS, symmetric stretching; DS and DS', degenerate stretching; AS, CHI asymmetric stretching; SS, CH2 symmetric stretching; SD, CH, degenerate stretching; DD and DD', CH3 degenerate deformation; DR and DR', CH3 degenerate rocking; DEF, deformation; SC, CHI scissor; WAG, CH2 wagging; RO, CH2 rocking; TW, CHI torsion; OPB, out-of-plane deformation; TO, torsion. (I

Raman Spectroscopy. Classical Raman spectra were taken using the 514.5-nm line of a Spectra Physics argon ion laser with 85 m W of power at the sample. The Raman signal was collected and dispersed through a Spex 1301 double monochromator and measured with a cooled ITT 4013 photomultiplier tube. The monochromator and photon-counting electronics were interfaced to a Hewlett-Packard 9816 technical computer that recorded the signal and controlled the monochromator wavenumber and sample temperature. Slits were 75 wm, which corresponds to an instru-

mental resolution of 1 to 3 cm-' (at 3700 to 100 A cm-', respectively). The temperature of the samples was kept at 15.0 OC. Signal averaging was used to improve the signal-to-noise ratio of the spectra. Calibration of frequencies was made using an neon lamp. The crystalline samples were prepared by selecting a single large crystal of the salt and grinding it to a fine powder under a dry nitrogen atmosphere. The powder was loaded into a borosilicate melting point capillary tube and sealed with paraffin wax. The

The Journal of Physical Chemistry, Vol. 93, No. 4 , 1989 1341


TABLE I V Force Constants for Local-Symmetry Force Field“ i 2 8 7 21 48 32 41

name C642 c5c4 01C5 TSC3 ss c 4 DS’C 1 DS’C2

value 11.660 5.4000 5.2000 4.8800 4.8330 4.7900 4.7730

name OPB C=O

i

139

143 141

name Y NC3 Y NCl

i 67 84 108‘ 64 6 110 81 123 137 60

name C7C602 C4C501 DD‘ N C7C601 C602/C-O DR N RO C5 DR‘ C2 DR C1 DR C7

i

i 46 49 38 50 9 70 11 5 92 85 165 134 112 101 57 66 40 43 94 34 111

name SSC501C5 SSC4C4N TSC2TSN SSC4C5C4 C4C5/OC5 CCO2C6C7 C4N/C5C4 C6C7/C-O WA4/C5C4 CCOlC4C5 OlC5DS’N SDI/DSN DRNDSN CCN/C5C4 SDC7C6C7 CCOlC6C7 DSC2DSC3 DS’2DS’3 R04TW5 TSC2TSCl DRN DDN

Bond name DSN C601 TSCl TSC2 DSCl DS’ C3 DSC7

i 17 4 26 33 31 25 54

value 0.4580 0.3070

142 140

value 1.5050 1.4030 1.0600 0.9930 0.9390 0.9140 0.6700 0.6600 0.6590 0.6090 value 0.6320 0.5040 0.4750 0.4460 0.4270 0.4160 0.3730 0.3580 0.2780 0.2420 0.2125 0.1980 0.1920 0.1700 0.1400 0.1170 0.0860 0.0860 0.0660 0.0650 0.0630

i

71 105 102 99 113 128 127 138 122 61 i

37 30 45 3 133 53 80 72 73 13 117 86 114 100 103 166 42 97 27 35 83

value 4.7600 4.7460 4.6890 4.6500 4.3484 3.2520

i

44 24 51 52 14

name SS C5 DSC3 ASC4 TSC7 DS’N

value 4.7560 4.7050 4.6510 4.5720 4.2690

name Y C501 Y C6C7

value 0.1460 0.0530

name SD C3 TW C5 RO C4 DD C2 DD’C2 DD’C7 SDC7 DD’C1 DD’C3

value 0.5620 0.5500 0.5110 0.4550 0.4540 0.4310 0.40 IO 0.3790 0.3570

Out-of-Plane Bending Force Constant value 0.2850

name Y NC2 Y C4N

i

Stretching Force Constants value i name 5.5810 39 DSC2 5.2000 55 DS‘C7 4.8830 47 ASC5 4.8790 12 TS(N) 4.8040 10 C4-N 1 C6C7 4.7890 4.7620

Dihedral Torsion Force Constants value i name 0.4385 144 Y C4C5 0.1545 146 Y 01C6

Valence Annle Bendina Force Constants name value i name C601C5 1.4210 116 SD C2 DDN 1.2000 77 WAC5 SDN 1.0220 90 WAC4 C5C4N 0.9610 129 SDC1 DR’N 0.9280 74 scc5 DR’C3 0.6730 96 TW C4 DR C3 0.6660 87 SCC4 DR’C1 0.6600 135 DDC1 DR C2 0.6580 58 DDC7 DR‘C7 0.6040 125 DD C3

Mixed/Off-Diagonal Force Constants name value i name TSCZDS’N 0.5820 164 SC/WAG4 TSClTSN 0.4790 19 DSNTSN SSC5C5C4 0.4530 22 TSC3/DSN C6C7/C=O 0.4340 159 S33 S38 SDlIDS’N 0.4200 161 S38 S43 TSC7C6C7 0.3800 16 DS’N/C4N WA/O1C5 0.3720 75 SCC5C5C4 COC/OlC5 0.2870 78 WA/SC 5 COC/C601 0.2770 63 DR’7C6C7 TSN/C4N 0.2230 62 DDC7DRC7 SD2/DSN 0.2010 88 SC4/C4N CCOlOlC5 0.1940 106 DDN/DSN DR’DS’N 0.1920 69 CCO2C602 CCN/C4N 0.1570 79 WA/C5C4 SDNTSN 0.1340 119 SD2/TSN DR’ZDS’N 0.1000 91 WA4/C4N DS’2DS’l 0.0860 28 TSClDSN TW4/TW5 0.0690 118 SD2IDS’N TSClTSC3 0.0650 131 SD3/DSN TSC2TSC3 0.0650 68 CCO2C601 TW/RO 5 0.0354

value 0.1500 0.1460 value 0.5670 0.5500 0.5120 0.5020 0.4545 0.4400 0.4220 0.3920 0.3600 0.3300

i

145 147

i 124 82 93 120 121 59 56 136 126

~

value 0.0300 0.0056 0.0000 0.0000 0.0000 -0.0047 -0.0120 -0.0247 -0.0500 -0.0800 -0.1330 -0.1900 -0.1940 -0.2750 -0.2850 -0.3200 -0.3385 -0.3490 -0.4050 -0.6790

i 115 20 23 160 167 107 15 95 98 89 76 109 104 132 130 36 18 65 29

name DR’DD’N DSN/C4N TSC3/TSN S33 S43 C601DS’N DDN/SDN DS’NITSN R04R05 TW4 R 0 5 SC4/C5C4 SCC501C5 DD’NDS’N SDN/C4N SDl/TSN SD3/TSN TSC2DSN DSN/DS’N CCOlC602 TSCIDS’N

value 0.0280 0.0055 0.0000 0.0000 0.0000 -0.0110 -0.0170 -0.0456 -0.0660 -0.1150 -0.1640 -0.1910 -0.2380 -0.2800 -0.2870 -0.3360 -0.3400 -0.3500 -0.5860

“The units of the force constants depend on the coordinates with which they are associated. Units are mdyn/A for diagonal stretching and stretching-stretching terms, mdyn for stretching-deformation terms, and mdyn 8, for diagonal deformation, torsion, and deformation-deformation terms.

TABLE V: Potential Parameters for Nonbonded Atom-Atom Interactions” atom pair r,j(max), rij(min), i, i A A A, Bij Cij Ne-0 6.0 3.0 86100 4.194 374.0 6.0 3.3 55300 3.768 456.0 6.0 2.9 49500 4.561 130.0 6.0 3.45 115098 3.61 1 1026.0 6.0 3.3 83630 3.60 568.0 6.0 3.6 63700 3.881 441 .O 8766 3.67 125.0 6.0 3.0 6.0 3.0 116399 3.43 1358.0 6.0 2.9 57500 4.727 122.0 6.0 2.6 2654 3.74 27.3 “The units of A , E , and Care such to give Vij in kcal/mol.

spectra obtained from these samples are shown in Figure 2. Computational Methods. The method used to determine the frequencies and normal modes of vibration is adapted from the Wilson CFmethod.’ For a molecule with N $oms, 3N Cartesian displacement coordinates can be defined as X = [ X , ,X,, X,, ..., X,,]. From the Cartesian displacement coordinates one may obtain the corresponding internal (or valence) displacelrent coordinates using the linear transformation R = BX where R = [R,, R2,R3, ..., RM]and B is a 3N by M matrix ( M = 3N - 6 if there are no redundant internal displacement coordinates). The internal displacement coordinates R then can be transformed into nonredundant local symmetry displacement coordinates S by the ( 5 ) Wilson, E. B.J . Chem. Phys. 1957, 27, 986.

The Journal of Physical Chemistry, Vol. 93, No. 4, 1989

1342

Derreumaux et al.

TABLE VI: Local Symmetry Coordinate Force Field for Crystalline Acetylcholine Bromide" i

j

1

I 3 3 5 5 6 5 IO 7 5 1 3 3 8 5 4 3 8 2 3 7 8 7 5 5 3 2 2 7 1 6 2 7 4 9 5 11 13 15 18 13 18 16 17 24 27 23 23 25 28 24 25 21 30 25 31 33 36 33 33 37 38 33 36 38 38 31 38 33 33 31 36 33 41 43 43 47

3 5 6 7 8 9 10 16 19 25 31 32 32 33 34 38 38 41 43 44 48 54 68 69 70 71 73 73 75 75 76 76 77 77 78 11

16 18 47 76 76 77 78 24 29 38 71 73 74 75 76 77 77 78 31 33 36 38 41 42 43 48 68 69 70 73 73 75 76 77 77 78 41 45 47 48

FU

3.2700 5.221 1 0.0087 0.3926 0.008 1 -0.0047 0.006 1 4.8800 0.4750 0.4530 0.0060 -0.0089 -0.6900 -0.0064 0.0094 -0.1640 0.0114 0.0055 -0.0064 0.0130 0.1340 0.1985 -0.2870 -0.0055 0.0063 0.0120 0.0069 0.0232 0.0236 -0.0089 -0.00 13 0.0127 0.0059 0.0249 -0.0244 -0.0342 4.7050 0.0650 0.0860 0.005 1 0.0054 0.0 175 0.0139 -0.0 193 4.7620 -0.0800 -0.0065 0.007 1 -0.0131 0.0099 0.0058 0.0146 -0.0059 0.0055 -0.0350 0.9992 1.485 1 0.6962 0.0197 0.0059 0.0690 0.0236 0.0120 0.0169 0.0185 0.01 73 -0.0033 -0.0144 0.0074 -0.0406 -0.01 01 -0.0323 -0.0004 0.5437 0.0063 -0.0 12 1 -0.006 1

i

j

2 4 5 6 7 8 9 13 16 21 26 31 32 33 33 34 38 39 41 43 45 49 54 69 69 70 71 73 73 75 75 76 76 77 78 78 12 16 18 68 76 76 77 78 25 29 38 71 74 74 75 76 77 78 78 32 34 37 38 41 43 45 48 68 70 71 73 74 75 76 77 77 78 42 45 47 48

1 1 4 6 6 7 6 7 8 5 1 6 4 1

6 5 4 5 5 5 9 7 9 1

6 5 5 3 9 2 7 3 8 5 1

6 12 16 18 16 14 19 17 18 25 29 28 28 21 30 25 26 24 21 26 31 34 36 38 36 31 33 38 38 31 35 32 33 36 36 32 37 36 42 44 45 48

Fij

i

0.4340 0.0088 0.4270 4.3850 0.2563 -0.0170 0.0122 0.4790 0.5820 0.4460 0.1400 -0.0070 -0.0054 0.0141 0.0126 -0.0120 0. I995 -0.1150 -0.0059 0.1868 -0.1958 -0.2850 -0.4050 -0.00 54 0.0060 0.0079 -0.0146 0.01 59 0.0164 0.0009 -0.0008 0.0041 -0.0353 -0.0483 0.0365 -0.063 1 4.7890 4.8855 4.7787 0.0074 -0.0086 0.0089 -0.021 2 0.0413 4.7529 0.6090 -0.0057 0.0061 0.0146 0.0104 -0.0147 -0.0055 -0.0128 0.0050 -0.0130 0.0059 0.4545 0.0354 1.4949 -0.04 56 0.0067 -0.0064 -0.009 3 -0.0508 -0.0075 0.0057 -0.01 30 -0.0066 0.005 1 0.0359 -0.03 I8 -0.0141 -0.0088 0.4400

2 4 5 7 7 8 9 13 16 21 30 31 32 33 33 35 38 39 41 43 46 49 59 69 69 70 71 73 74 75 75 76 76 77 78 78 13 17 19 68 76 77 77 21 26 30 38 71 74 75 75 76 77 78 78 32 35 37 39 41 43 45 64 69 70 71 73 74 75 76 77 77 78 43 45 47 49

-0.0110

0.0630 0.9546

j

2 3 5 2 7 8 7 8 9 6 1 7

5 2 7 4 5 6 7 6 8 8 7 2 7

6 7

4 6 3 8 4 9 6 2 7 13 11

19 17 15 13 19 21 26 30 30 30 22 21 30 28 25 22 27 32 34 37 39 37 32 36 38 31 32 38 33 35 38 37 33 38 37 43 45 47 49

Fij

1 1.6750

0.0141 5.4172 0.0161 4.6810 4.2813 0.0131 -0.5860 -0.3360 0.5040 -0.0554 -0.0093 -0.0057 0.0122 0.0152 0.3720 0.2680 -0.1330 -0.005 9 0.1731 -0.1 9 10 -0.3490 -0.2800 0.0098 0.0086 0.0098 0.0054 0.0072 0.0088 0.0204 -0.01 52 0.0010 0.0090 0.0348 -0.023 4 -0.0439 4.8830 0.0860 4.7560 0.0063 -0.0053 0.0083 0.0052 4.8425 0.4010 0.6096 -0 .OO 54 0.01 1 1 0.0052 0.0099 -0.0056 -0.0152 -0.01 33 0.0226 -0.01 50 1.5133 -0.0247 0.5500 0.4220 0.0660 -0.0055 0.0054 0.0257 0.0122 -0.007 1 -0.0563 -0.01 32 0.0074 0.0268 0.0129 0.0540 -0.045 4 -0.01 25 1.0050 1.2064 0.9332 0.5670

i 3 4 6 7 8 9 9 13 16 22 31 32 32 33 33 35 38 40 41 43 47 49 59 69 69 70 71 73 74 75 75 76 77 77 78 78 14 17 20 74 76 77 77 22 27 33 41 73 74 75 76 76 77 78 78 33 35 38 40 41 43 47 68 69 70 72 73 74 76 76 77 78 78 44 46 48 50

i 1

4 2 3 3 2 8 9 10 4 1 1

6 3 8 5 6 5 9 7 9 9 8 3 9 7

9 5 7 4 9 5 2 7 3 8 14 17 20 14 16 14 20 22 27 22 22 22 23 22 21 29 27 23 28 31 35 31 39 38 33 31 31 33 33 33 36 36 31 38 34 31 38 43 46 41 50

Fi i

i

j

FV

0.3633 5.2166 0.01 16 0.0151 0.0069 0.0083 -0.3400 -0.3385 0.0650 0.0063 0.1170 0.4160 -0.0080 0.2952 0.0108 -0.2750 0.0195 0.2780 -0.0058 0.0076 0.1987 0.2010 0.4200 0.0063 0.0087 0.0128 0.0106 0.0090 0.0251 0.0193 0.0082 0.0224 0.0068 0.0848 -0.0304 -0.01 66 4.8040 4.7663 4.6890 -0.0057 0.0053 -0.0064 0.01 23 4.6603 0.3600 0.0098 0.0055 -0.0052 0.0063 0.0256 -0.0090 -0.005 7 -0.0108 0.0427 -0.0129 -0.0092 0.5500 ;0.0057 0.0300 -0.0446 0.0027

3 5 6 7 8 9 9 13 19 23 31 32 32 33 33 38 38 40 43 44 48 53 59 69 70 70 73 73 74 75 76 16 77 77 78 78 15 18 38 74 76 77 78 23 28 36 69 73 74 75 76 76 77 78 78 33 36 38 40 42 43 47 68 69 70 72 73 74 76 76 77 78 78 44 47 48 64

2 2 3 4 4 3 9 IO 4

0.9517 0.0076 0.0122 0.0052 0.2125 0.0076 5.5930 0.0650 0.6320 0.3800 -0.3 582 -0.2017 -0.0097 0.3 109 0.0072 0.0082 0.0098 -0.3200 0.0060 -0.2454 -0.0062 0.1000 0.1980 -0.0064 0.0138 0.0160 -0.01 17 0.0186 0.006 1 0.0144 0.01 13 0.0099 0.0406 0.0404 -0.0188 -0.03 15 4.7900 0.0860 -0.0071 0.007 1 0.0123 -0.0073 0.0275 4.5720 0.43 10 -0.0058 -0.01 01 -0.006 1 -0.0070 -0.0083 -0.01 27 -0.0113 0.0282 -0.0289 -0.0084 -0.0137 -0.0271 -0.0082 0.5120 -0.0660 0.0182

-0.0053

0.0053 -0.0381 0.0109 0.0064 0.0105 -0.0064 0.0085 0.0264 0.0159 -0.0053 -0.0570 -0.0071 1.0756 0.0123 0.4550

1

2 2 7 4 9 2 7 6 2 6 7 8 9 4 2 9 1 6 10

5 1

6 3 8 4 9 15 12 16 16 17 15 16 23 28 22 22 23 25 23 22 30 28 24 30 32 33 32 40 36 36 36 33 36 37 38 37 38 32 40 35 32 39 44 41 46 41

-0.0063

-0.01 90 0.0304 0.0054 0.0089 0.0157 -0.029 1 0.0097 0.0054 0.0235 0.0126 0.0061 I .0288 -0.0050 0.0280 -0.009 6

The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1343


TABLE VI (Continued) i

j

67 68 69 70 71 73 73 74 75 76 76 77 77 78 78 55 60 74 76 77 62 67 70 71 73 74 75 76 77 78 78 73 75 76 76 77 78 78

43 47 43 45 45 43 50 46 43 42 48 43 48 44 49 55 60 60 53 60 62 67 64 68 64 68 70 69 66 62 69 73 71 71 76 75 73 78

FIJ

~

i 68 68 69 70 71 73 74 74 75 76 76 77 77 78 51 56 68 75 77 78 63 68 70 71 73 74 76 76 77 78 78 74 75 76 77 77 78

-0.0058 -0.0090 0.0229 -0.0077 -0.0053 0.0104 0.0082 -0 .OO 57 -0.0006 0.01 59 -0.04 2 7 0.0014 0.0381 0.0380 0.0055 0.3300 0.3920 -0.007 8 -0.0076 0.0051 0.6590 0.4560 0.0135 0.0239 0.0099 0.0167 0.0123 0.0642 -0.0133 0.0062 -0.0605 0.21 16 0.0007 -0.0197 0.4705 0.0057 -0.0585 0.9933

~~

j

41 48 45 47 47 45 41 47 45 43 49 44 50 45 51 56 52 51 51 51 63 64 68 69 68 69 64 70 67 63 70 71 72 72 71 76 74

FiJ 0.0344 0.0133 0.0087 0.0064 0.0064 0.0135 0.01 13 -0.0051 0.0098 0.0287 0.0069 0.0125 -0.001 1 0.0462 0.4540 0.3570 -0.0074 -0.0072 0.0089 -0.0 175 0.6600 -0.0154 -0.0131 0.0015 0.0385 -0.0027 0.028 1 0.0395 -0.0112 0.0088 -0.0565 0.0672 -0.0051 0.0076 0.1214 -0.2793 0.0024

~

j

Fi,

42 50 46 48 48 46 43 48 46 45 50 45 41 46 52 57 51 55 52 52 64 68 69 70 69 70 66 61 68 64 71 72 73 73 72 77 75

0.0190 0.0067 0.0114 -0.0067 -0.0051 0.0115 -0.0004 -0.0052 0.0344 0.0349 0.0122 -0.0534 0.0272 -0.0100 0.6580 0.6660 -0.0063 0.0055 0.0058 0.0090 0.2972 0.5377 0.0169 0.0124 0.0499 0.0070 -0.0068 0.0053 0.0001 -0.02 10 0.2132 -0.0083 0.0403 0.0699 -0.0468 1.1572 0.2123

i

68 68 69 70 71 73 74 74 75 76 76 77 78 78 52 57 73 75 77 78 64 68 70 71 73 74 76 77 77 78 71 74 75 76 77 77 78

1

~

~

i

~

68 69 69 71 73 73 74 75 75 76 77 77 78 78 53 58 74 75 77 78 65 69 70 72 73 75 76 77 77 78 72 74 75 76 77 78 78

j

Fij

i

j

FIJ

45 41 48 41 41 47 44 41 48 46 41 46 42 47 53 58 52 60 53 53 65 68 70 64 70 68 67 62 69 67 72 73 74 74 73 71 76

0.0151 -0.0 166 -0.0119 0.0229 -0.0008 0.0090 -0.0062 0.0038 -0.0014 0.0294 0.0375 -0.0200 -0.0058 0.0345 0.6600 0.6730 -0.0054 0.0059 -0.0174 -0.0173 0.1603 0.0212 0.1830 0.0094 0.0339 0.0410 0.0246 -0.0067 -0.0556 0.0069 0.0679 0.0620 0.0036 -0.0355 -0.0862 0.0122 0.0843

68 69 70 71 73 73 74 75 76 76 77 77 78 78 54 59 74 76 77 61 66 69 71 72 74 75 76 77 77 78 73 74 75 76 77 78 78

46 42 41 43 42 48 45 42 41 47 42 47 43 48 54 59 55 51 59 61 66 69 64 70 64 69 68 64 70 68 71 74 75 75 74 72 77

0.0129 0.0056 -0.0171 -0.0178 0.0084 -0.0080 0.0121 0.0127 -0.03 17 0.0073 -0.0094 -0.0562 -0.048 4 -0.0335 0.5620 0.5020 -0.0061 -0.0092 -0.0055 0.3790 0.3179 0.2199 -0.0220 0.0112 -0.0228 0.0218 0.0048 -0.0253 0.0221 0.0060 0.0396 0.2162 0.2470 -0.0421 0.2215 -0.0207 0.0738

Units as in Table IV unitary transform S = UR. The Urey-Bradley-Shimanouchi (U-B-S) force constants, @, are used to generate the F , matrix from the relationship Fr

=

C@kZr,k

(1)

is used, where the summation is over k (the U-B-S force constant index), and the Z,,k matrices (one for each U-B-S force constant) are the transformations from the U-B-S basis (which can be expressed as a linear combination of the internal displacement coordinates) to the internal displacement coordinate b a s k 6 The force constant matrix in local symmetry displacement coordinates, F,, is defined in terms of the internal displacement coordinate force constants, F,, and the unitary transform matrix U as

& = UF,&

(2)

The inverse kinetic energy matrix G , (in internal displacement coordinates) is derived from the B matrix and the inverse mass matrix M-’ as

G, = BM’B

(3)

The inverse kinetic energy matrix in local symmetry displacement coordinates, G,, is given by

G, = UG,&

obtained by solving the secular equation

IG,F, - AI = 0

where E is the identity matrix and X is a vector element containing squared vibrational frequencies. To solve this equation we define a transformation between the internal symmetry displacement coordinates S and the normal coordinates Q by

S = LQ

EG,F,L = A

The relationship between the force constants and frequencies is

(8)

where L is a matrix made up of the eigenvectors (related to the potential energy distributions) and A is a diagonal matrix containing the eigenvalues (related to the vibrational frequencies). For our vibrational studies we use a U-B-S force field to describe the potential energy of a molecular This function (eq 9) approximates the potential energy, V, of a system as

2V = CKi(Ari)’

(4)

(5)

(7)

and then diagonalize the G,F, matrix into the form

The equation for the vibrational potential energy of the molecule is then given by

2v = S&S

(6)

+ (sitFij+ t?F;)(ArJ2 +

+

c(sijsjiFij- tijtjiF’ij)(AriArj) xHij(riAaij)2 + (uijtijtjiFij - uijsijsjiF’ij)(riAaij)2+ (sij(tijtjiuij)‘/’Fij- fijsj,F’ij)(riAriAaij) + x(sji(tijfjiuV)’/’Fij + tji~ijF’ij)(riArjAaij)+ Yijk(A7ijk)’ + Wjk(AWijk)’ -k K ~+CCAij ~ exP(-Bi,dij) - Cij/dit + X ( Q i Q j ) / ( 4 ~ € 0 d i j ) (9)

x

C

~~

( 6 ) Overend, J.; Scherer, J . R. J . Chem. Phys. 1960, 32, 1289.

~~~

(7) Califano, S . Vibrational States; Wiley: New York, 1976; Chapter 6.


Derreumaux et al.

TABLE VII: Calculated and Observed Freauencies and Assienrnents (PED’S) for Acetvlcholine Bromide obsd calcd % mode % mode 3043 3030 3012 3004 2983 2958 2958 2923 2878 2814 1745 1499 1492 1492 1472 1457 1449 1425 1404 1381 1345 1308 1282 1224 1142

1083 1053 1036 1014 950 919 87 1 825 723 652 609 544 479 453 425 384 335 30 1 233 172

3043.8 3016.1 3010.9 3002.6 2993.4 2982.4 2967.6 2965.8 2959.4 2958.4 293 1.4 2928.6 2896.1 2875.7 2872.3 2815.5 1743.9 1503.9 1491.8 1489.2 1482.0 1475.8 1465.3 1458.9 1450.7 1446.6 1432.4 1411.2 1404.4 1377.8 1363.6 1348.6 1314.5 1286.1 1280.5 1255.6 1234.1 1219.5 1152.1 1143.2 1111.9 1103.8 1098.4 1085.1 1051.8 1035.3 1015.2 971.3 947.7 917.7 871.5 817.9 721.9 657.2 618.3 541.3 506.8 477.9 449.9 435.7 419.8 407.4 378.4 330.0 318.2 299.9 218.8 178.9 161.3 88.3 78.2 63.9 50.2 43.3 40.7 33.4

41.4 62.5 49.4 94.8 95.0 95.2 96.3 55.2 79.1 51.6 37.1 90.2 91.7 56.9 67.9 100. 90.2 43.2 22.0 39.8 70.1 45.7 51.4 36.0 87.8 55.9 84.6 43.3 49.7 56.0 48.0 33.8 35.0 18.5 96.7 33.0 22.9 14.8 29.8 33.6 40.2 47.1 29.5 19.9 30.8 52.0 23.0 23.1 52.8 24.2 28.6 23.8 59.5 35.7 31.4 97.8 22.5 95.7 60.5 22.4 64.1

40.3 32.5 95.3 33.9 32.0 95.7 31.3 26.8 32.1 13.6 20.1 52.4 56.8 57.4 61.2

DS’ C2-H DS C2-H DS’ C3-H DS C1-H DS C7-H DS’ C7-H AS C5-H DS’ C2-H AS C4-H DS C3-H TS C3-H S S C4-H SS C5-H TS C3-H TS Cl-H TS C7-H ST C6=02 DD’ C6C7 DD NC2H DD’ NCl DD’ NC2 DD NC2H SD NC2H SD NC3H SC HNC4 SD NClH SC HC4C5 SD C6HC7 SD NC3H WA HC4 DD NC3H WAG HC5 DS N-C3 ST N-C4 DD C6HC7 WAG HC5 ST 01-C5 DS’ N-C3 TW HC5 ST C5-C4 DR’ NC 1 DR N C l H DR NC3H DR’ NC2 DR NC2H DR‘ C6C7 RO HC5 ST C6-01 DS’ N-C3 ST N-C4 RO HC4 RO HC5 TS N-C3 DEF OC5C ST C6-C7 TO NC2 DEF C4NC TO NCl OPB DAC7C601 DD C3N DD’ C3N DD’ C3N TO C3N DAC7C601 DR C3N TO C6C7 DEF C4NC TO NC4 TO 01C6 TO C501 TO C4C5 RA

TZ TY TX

A,

27.9 34.9 45.6 2.4 4.3 4.3 2.1 22.4 11.7 29.7 31.2 8.7 9.2 40.5 28.7 0.2 7.1 33.3 19.5 12.7 11.6 15.1 19.3 26.4 3.6 14.6 5.6 38.7 42.3 22.4 23.0 24.8 29.9 13.7 1.4 17.4 19.3 10.9 23.4 21.0 22.9 12.3 11.7 14.8 18.4 26.2 16.9 15.3 15.5 23.3 14.3 15.5 22.9 24.6 24.0 0.4 12.2 0.9 9.9 19.3 23.2 14.2 17.6 1.9 26.9 13.6 1.8 21.9 26.4 21.6 15.8 18.8 17.5 12.4 23.6 25.0

DS’ C 1-H DS C3-H DS’ CI-H DS’ Cl-H DS’ C7-H DS C7-H AS C4-H DS’ C1-H DS C3-H DS C2-H TS C2-H S S C5-H S S C4-H TS C2-H TS C2-H SD C6HC7 DAC7C601 SD C6HC7 SD N C l H SD NC2H DR’ NC2 SD NC2H DD N C l H DD’ NC3 SC HC4C5 DD’ NC 1 ST C5-C4 DD’ C6C7 DD’ NC3 DS N-C3 DR NC3H TW HC5 WA HC4 WAG HC5 DD’ C6C7 TW HC4 ST C6-01 DD NC3H TW HC4 DR C6C7 DR’ NC3 DR NC2H DR’ NC3 ST C5-C4 DR’ NC3 DR C6C7 DR NC2H DAPC6=02 DR’ NC2 TS N-C3 DS’ N-C3 ST C6-01 ST N-C4 ST C6-C7 DAPC6=02 DEF OC5C SD C3ClN DR C3N TO OlC6 DR’ C3N S D C3CIN OPB DR’ C3N DR’ C3N B C601C5 DR’ C3N DR C3N DR C3N TO 01C6 TO NC4 TO 01C6 RA TZ TO C4C5 TX TY

%

mode

27.4 0.2 4.1 1.8 0.2 0.2 0.5 19.4 6.3 15.9 28.2 0.4 0.2 4.1 5.2 0.2 6.8 12.3 14.7 11.5 7.6 11.7 11.9 21.8 2.8 9.9 5.1 5.9 4.7 6.6 7.5 15.8 6.2 11.0 1.3 11.0 16.3 10.8 10.8 11.6 6.4 9.7 8.2 13.1 10.8 12.1 12.3 12.6 5.3 8.7 11.5 12.1 7.7 9.0 9.7 0.3 8.O 0.7 8.0 10.1

DS’ C3-H DD NC2H DS Cl-H DS’ C3-H DR C6C7 DD’ C6C7 DS’ C2-H DS’ C3-H DS C2-H AS C4-H TS Cl-H TS C3-H ST C5-C4 TS C1-H TS C3-H ST C 6 C 7 ST C6-01 DR’ C6C7 DD N C l H DR’ NCl DD NC2H DD N C l H DD’ NC 1 SD NC2H ST C5-C4 DD NClH SC HNC4 ST C6-C7 DD NC3H DD N C l H SD NClH TW HC4 WAG HC5 SD C3ClN DAPC6=02 ST C5-C4 TW HC5 ST C6-01 RO HC5 ST 01-C5 DR NC3H DD N C l H DR’ NC2 DR C6C7 DS N-C3 DD’ C6C7 DS N-C3 DR’ C6C7 DAPC6=02 ST C6-01 DAPC6=02 RO HC4 RO HC5 TO NC4 DEF OC5C DR C3N DR C3N DEF C4NC DR’ C3N SD C3ClN DS N-C3 DD C3N SD C3ClN DD’ C3N DR C3N DEF OC5C DEF C4NC B C601C5 RO HC4 DEF OC5C TO C4C5 TO C501 TO C4C5 RA TO 01C6 RA

1.4

10.9 14.9 0.8 11.8 10.7 0.7 19.3 11.9 8.1 15.0 14.6 13.8 12.1 17.7 21.6



TABLE VI1 (Continued) obsd

3043 3030 3012 3004 2983 2958 2958 2923 2878 2814 1745 1499 1492 1492 1472 1457 1449 1425 1404 1381 1345 1308 1282 1224 1142

1083 1053 1036 1014 950 919 87 1 825 723 652 609 544 419 453 425 384 335 301 233 172

calcd 19.3 17.9

128.9 137.1

RB RC

mode

3043.8 3016.1 3010.9 3002.6 2993.5 2982.4 2967.6 2965.9 2959.3 2958.3 293 1.4 2928.6 2896.1 2875.7 2872.4 2815.5 1744.0 1503.9 1491.8 1489.3 1482.0 1475.7 1465.3 1458.9 1450.8 1446.6 1432.4 1411.2 1404.3 1378.3 1363.7 1349.4 1314.6 1286.5 1280.5 1256.3 1234.5 1219.5 1152.3 1143.2 1111.9 1103.8 1098.6 1085.5 1051.7 1035.4 1016.2 971.0 948.1 917.8 871.6 815.8 721.2 655.7 617.7 541.2 505.6 477.9 451.0 434.5 420.4 405.7 380.0 330.0 320.5 299.1 218.6 178.0 161.8 89.5 81.6 61.2 53.0

41.4 62.5 49.5 94.8 95.0 95.2 96.8 55.0 77.2 50.5 37.0 90.0 91.7 56.8 67.9 100.3 90.2 43.2 21.9 39.6 70.2 45.8 51.2 35.9 87.8 55.7 84.6 43.3 49.8 55.4 47.0 33.8 35.0 18.5 96.7 33.2 23.5 15.1 30.4 33.6 39.9 47.6 28.8 20.3 30.5 52.0 22.7 22.9 51.9 23.6 28.2 24.4 59.3 35.2 29.9 97.7 22.8 95.2 59.5 21.9 64.1 43.3 30.4 93.7 33.9 33.3 95.8 31.0 27.9 29.2 22.0 26.8 27.2

DS’ C2-H DS C2-H DS’ C3-H DS Cl-H DS C7-H DS’ C7-H AS C5-H DS’ C2-H AS C4-H DS C3-H TS C3-H SS C4-H S S C5-H TS C3-H TS Cl-H TS C7-H ST C6=02 DD’ C6C7 DD NC2H DD’ NC1 DD’ NC2 DD NC2H SD NC2H SD NC3H SC HNC4 SD N C l H SC HC4C5 SD C6HC7 SD NC3H WA HC4 DD NC3H WAG HC5 DS N-C3 ST N-C4 DD C6HC7 WAG HC5 ST 01-C5 DS’ N-C3 TW HC5 ST C5-C4 DR’ NC 1 DR N C l H DR NC3H DR’ NC2 DR NC2H DR‘ C6C7 RO HC5 ST C6-01 DS’ N-C3 ST N-C4 RO HC4 RO HC5 TS N-C3 DEF OC5C ST C6-C7 TO NC2 DEF C4NC TO NCl OPB DR‘ C3N DD C3N DD’ C3N DD’ C3N TO C3N DAC7C601 DR C3N TO C6C7 DEF C4NC TO NC4 TO 01C6 TO 01C6 TO C4C5 RA

%

mode

%

B,

mode

%

71.1 68.3

TY TZ

57.3 45.7

TX RA

28.0 34.9 45.5 2.4 4.3 4.3 2.0 22.4 12.8 29.0 31.1 8.7 9.2 40.6 28.6 0.2 7.1 33.4 19.5 12.7 11.7 15.0 19.2 26.3 3.6 14.6 5.5 38.7 42.3 22.5 22.7 24.6 30.6 13.9 1.4 17.2 19.3 11.1 24.6 20.9 22.8 12.7 11.9 15.0 18.4 26.1 17.2 15.3 15.4 23.2 15.4 15.2 23.6 26.2 23.7 0.5 11.8

DS’ Cl-H DS C3-H DS’ Cl-H DS’ C 1-H DS’ C7-H DS C7-H AS C4-H DS’ Cl-H DS C3-H DS C2-H TS C2-H S S C5-H S S C4-H TS C2-H TS C2-H SD C6HC7 DAC7C601 SD C6HC7 SD N C l H SD NC2H DR’ NC2 SD NC2H DD N C l H DD’ NC3 SC HC4C5 DD’ NCl ST C5-C4 DD’ C6C7 DD’ NC3 DS N-C3 DR NC3H TW HC5 WA HC4 WAG HC5 DD’ C6C7 TW HC4 ST C6-01 DD NC3H TW HC4 DR C6C7 DR’ NC3 DR NC2H DR’ NC3 ST C5-C4 DR’ NC3 DR C6C7 DR NC2H DAPC6=02 DR’ NC2 TS N-C3 DS’ N-C3 ST C6-01 ST N-C4 ST C6-C7 DAPC6=02 DEF OC5C SD C3ClN DR C3N TO 01C6 DAC7C601 SD C3ClN OPB DR’ C3N DR’ C3N B C601C5 DR’ C3N DR C3N DR C3N TO 01C6 TO NC4 TO C501 TO C501 TY

27.3 0.2 4.1 1.8 0.2 0.2 0.4 19.3 7.0 17.2 28.2 0.6 0.2 4.1 5.2 0.2 6.8 12.3 14.7 11.5 7.5 11.7 12.0 22.0 2.8 9.8 5.0 5.9 4.7 6.8 7.6 15.1 6.3 11.0 1.3 10.7 17.0 10.4 10.3 11.8 6.5 9.8 8.0 12.6 10.7 12.1 12.4 12.6 5.7 9.3 11.3 12.5 7.5 8.8 11.0 0.3 8.2 0.8 8.2 9.9 1.5 9.6 15.3 1.1 10.8 10.7 0.8 20.4 11.2 7.6 16.5 6.7 18.1

DS’ C3-H DD NC2H DS Cl-H DS’ C3-H DR C6C7 DD’ C6C7 RQ HC5 DS’ C3-H DS C2-H AS C4-H TS Cl-H TS C3-H ST C5-C4 TS C1-H TS C3-H ST C6-C7 ST C6-01 DR’ C6C7 DD NClH DR’ NC1 DD NC2H DD N C l H DD’ NCl SD NC2H ST C5-C4 DD N C l H SC HNC4 ST C6-C7 DD NC3H DD N C l H SD N C l H TW HC4 ST N-C4 SD C3ClN DAPC6=02 ST C5-C4 TW HC5 ST C6-01 RO HC5 ST 01-C5 DR NC3H DD N C l H DR’ NC2 DR C6C7 DS N-C3 DD’ C6C7 DS N-C3 DR’ C6C7 DAPC6=02 ST C6-01 DAPC6=02 RO HC4 RO HC5 TO NC4 DEF OC5C DR C3N DR C3N DEF C4NC TO C501 DD’ C3N DS N-C3 DD C3N SD C3ClN DAC7C601 DR C3N DEF OC5C DEF C4NC B C601C5 DR’ C3N RO HC4 TO C4C5 TY TO C501

1 .o

10.3 20.9 23.4 14.6 17.1 2.3 25.3 13.3 1.9 21.1 26.3 22.8 20.4 20.2 25.0


Derreumaux et al.


3029 3002 2975

1737

1477 1448 1448 1410 1381 1366 1303

1223 1136

1072 1052 1015 955 913 864 827 644 607 532 482 453 423

calcd 45.3 40.8 38.7 28.8 28.3

73.2 32.8 60.6 67.3 75.9

3043.8 3014.8 3010.9 3002.6 2993.5 2982.4 2967.6 2965.9 2959.3 2957.8 2930.8 2928.5 2896.1 2875.0 2871.7 2815.5 1743.9 1504.1 1491.8 1489.2 1482.0 1475.7 1465.3 1458.9 1450.8 1446.5 1430.8 1411.4 1404.4 1377.7 1363.6 1349.7 1315.1 1285.9 1280.6 1254.9 1234.2 1219.3 1 152.4 1143.1 1112.1 1103.9 1098.6 1085.4 1051.8 1035.1 1016.8 969.3 946.8 916.9 874.5 815.3 7 19.2 655.5 617.7 541.2 506.2 478.4 445.2 435.7 420.2 405.4 377.8 331.7 320.9 299.1 218.5 178.9 160.4 94.8

41.4 60.9 49.6 94.9 95.0 95.2 96.9 55.3 87.7 56.8 37.6 89.3 91.7 60.6 57.8 100.3 90.2 43.1 22.4 40.5 70.2 45.5 51.0 36.0 87.6 55.7 85.0 43.1 50.0 56.2 47.9 32.4 34.9 18.9 96.3 32.4 23.8 15.3 28.6 33.0 39.8 46.9 28.8 21.1 30.9 50.4 22.5 23.7 54.2 23.7 27.9 24.8 59.8 35.4 29.0 97.7 23.0 98.0 63.4 21.8 63.7 41 .O 33.1 95.4 34.5 33.1 95.9 31.4 33.5 22.2

mode

%

DS’ C2-H DS C2-H DS’ C3-H DS C1-H DS C7-H DS’ C7-H AS C5-H DS’ C2-H AS C4-H DS C3-H TS C3-H S S C4-H S S C5-H TS C3-H TS Cl-H TS C7-H ST C6=02 DD’ C6C7 DD NC2H DD’ NCl DD’ NC2 DD NC2H SD NC2H SD NC3H SC HNC4 SD N C l H SC HC4C5 SD C6HC7 SD NC3H WA HC4 DD NC3H WAG HC5 DS N-C3 ST N-C4 DD C6HC7 WAG HC5 ST 01-C5 DS’ N-C3 TW HC5 ST C5-C4 DR’ NC1 DR N C l H DR NC3H DR’ NC2 DR NC2H DR’ C6C7 RO HC5 ST C6-01 DS’ N-C3 ST N-C4 RO HC4 RO HC5 TS N-C3 DEF OC5C ST C6-Cl TO NC2 DEF C4NC TO NC1 OPB DAC7C601 DD C3N DD’ C3N DD’ C3N TO C3N DAC7C601 DR C3N TO C6C7 DEF C4NC TO NC4 TO 01C6

mode

%

TZ RA TY RA RC A,

mode

%

6.2 24.1 59.5 44.8 54.4

TY RB TX RB RB

5.7 18.8 4.9 34.5 18.3

RC RC RB TX TZ

28.0 36.5 45.5 2.3 4.3 4.3 2.0 22.5 5.1 34.7 29.5 8.6 9.2 27.3 43.4 0.2 7.1 33.3 19.1 12.7 11.7 15.4 19.4 26.3 3.4 14.4 5.5 38.6 42.1 22.7 22.9 26.2 30.0 13.2 1.4 17.1 19.1 11.3 24.8 21.9 22.6 12.2 12.1 14.6 18.2 27.8 16.9 15.3 16.3 23.5 13.8 15.0 23.6 27.0 23.3 0.5 12.7 0.4 9.5 20.9 24.2 14.1 17.4 1.7 25.3 14.2 1.7 20.4 24.0 19.2

DS’ Cl-H DS C3-H DS’ Cl-H DS’ Cl-H DS‘ C7-H DS C7-H AS C4-H DS’ Cl-H DS C3-H DS C2-H TS C2-H S S C5-H S S C4-H TS C2-H TS C2-H SD C6HC7 DAC7C601 SD C6HC7 SD N C l H SD NC2H DR’ NC2 SD NC2H DD N C l H DD’ NC3 SC HC4C5 DD’ NCl ST C5-C4 DD’ C6C7 DD’ NC3 DS N C 3 DR NC3H TW HC5 WA HC4 WAG HC5 DD’ C6C7 TW HC4 ST C6-01 DD NC3H TW HC4 DR C6C7 DR’ NC3 DR NC2H DR’ NC3 ST C5-C4 DR’ NC3 DR C6C7 DR NC2H DAPC6=02 DR’ NC2 TS N-C3 DS’ N-C3 ST C6-01 ST N-C4 ST C6-C7 DAPC6=02 DEF OC5C SD C3ClN DR C3N TO 01C6 DR’ C3N SD C3ClN OPB DR’ C3N DR’ C3N B C601C5 DR’ C3N DR C3N B C601C5 TO 01C6 TO NC4

27.3 0.2 4.0 1.8 0.2 0.2 0.4 19.4 2.9 6.7 28.5 0.9 0.2 13.7 0.6 0.2 6.8 12.3 14.9 11.7 7.5 11.5 11.8 21.9 2.7 9.7 4.7 5.9 4.7 6.7 7.5 14.9 6.9 11.1 1.4 9.9 17.3 9.9 10.3 12.0 6.7 9.7 7.8 11.3 10.8 12.0 11.9 13.7 5.2 8.5 12.0 13.3 8.0 10.1 11.9 0.3 8.7

DS’ C3-H DD NC2H DS C1-H DS’ C3-H DR C6C7 DD’ C6C7 RO HC5 DS’ C3-H DS C2-H AS C4-H TS Cl-H TS C3-H ST C5-C4 TS Cl-H TS C3-H ST C6-C7 ST C6-01 DR’ C6C7 DD NClH DR’ NC 1 DD NC2H DD NClH DD’ NC1 SD NC2H ST C5-C4 DD N C l H SC HNC4 ST C6-C7 DD NC3H DD N C l H SD NClH TW HC4 WAG HC5 SD C3ClN DAPC6=02 ST C5-C4 TW HC5 ST C6-01 RO HC5 ST 01-C5 DR NC3H DD N C l H DR’ NCl TW HC4 DS N-C3 DD’ C6C7 DS N-C3 DR’ C6C7 TW HC4 ST C6-01 DAPC6=02 RO HC4 RO HC5 TO NC4 DEF OC5C DR C3N DR C3N DD C3N TO C501 DD’ C3N DR’ NC2 SD C3C1 N SD C3ClN DD’ C3N DR C3N DEF OC5C DEF C4NC DR C3N RO HC4 DEF OC5C

0.3

8.9 9.2 1.4 10.6 14.3 0.9 12.1 11.8 0.8 19.6 12.9 6.1




3029 3002 2975

1737

1477 1448 1448 1410 1381 1366 1303

1223 1136

1072 1052 1015 955 913 864 827 644 607 532 482 453 423

calcd 77.4 65.0 53.8 46.1 36.2 24.9 17.8

31.8 24.0 56.1 57.8 64.5 109.5 148.7

TO 01C6 RA RA TX RC RB TZ

3043.8 3014.8 3010.9 3002.6 2993.5 2982.4 2967.6 2965.8 2959.3 2957.8 2930.8 2928.6 2896.0 2875.0 287 1.7 2815.5 1744.1 1504.1 1491.8 1489.2 1482.0 1475.7 1465.3 1458.9 1450.8 1446.5 1431.2 1411.4 1404.3 1377.6 1363.8 1350.3 1314.3 1286.1 1280.6 1256.0 1234.6 1219.6 1153.1 1143.0 1111.0 1103.8 1098.9 1085.8 1051.8 1034.8 1015.7 970.2 948.1 917.9 870.0 818.9 720.5 657.0 618.1 541.3 505.9 477.7 447.9 435.0 419.9 405.3 376.6 331.7 318.8 297.8 218.4 179.9

41.4 60.9 49.6 94.8 95.0 95.2 96.4 55.3 88.8 57.2 37.6 89.6 91.8 60.6 57.8 100.3 90.2 43.1 22.1 40.0 70.1 45.3 50.9 35.8 88.3 56.0 85.1 43.2 49.9 56.1 46.3 32.4 35.4 18.9 96.5 34.4 23.6 15.3 29.6 34.3 40.1 46.9 28.1 21.5 31.3 51.2 24.3 22.8 53.1 24.0 30.7 23.3 60.7 36.1 29.9 97.7 22.7 94.4 61.4 23.2 64.5 42.6 31.4 96.2 34.4 34.1 96.9 31.2

DS’ C2-H DS C2-H DS’ C3-H DS Cl-H DS C7-H DS’ C7-H AS C5-H DS’ C2-H AS C4-H DS C3-H TS C3-H S S C4-H SS C5-H TS C3-H TS Cl-H TS C7-H ST C6=02 DD’ C6C7 DD NC2H DD’ NCl DD‘ NC2 DD NC2H SD NC2H SD NC3H SC HNC4 SD N C l H SC HC4C5 SD C6HC7 SD NC3H WA HC4 DD NC3H WAG HC5 DS N-C3 ST N-C4 DD C6HC7 WAG HC5 ST 0 1 C 5 DS’ N-C3 TW HC5 ST C5-C4 DR’ NCl DR N C l H DR NC3H DR’ NC2 DR NC2H DR’ C6C7 RO HC5 ST C6-01 DS’ N-C3 ST N-C4 RO HC4 RO HC5 TS N-C3 DEF OC5C ST C6-C7 TO NC2 DEF C4NC TO NC1 OPB DAC7C601 DD C3N DD’ C3N DD’ C3N TO C3N DAC7C601 DR C3N TO C6C7 DEF C4NC

%

mode

21.1 20.1 13.7 22.5 12.9 45.6 82.8

mode TO C4C5 TO C501 TO C501 RA RB RC TX

16.3 16.6 13.6 4.5 8.4 23.3 29.2

TO C4C5 TO C4C5 TO C4C5 TO C501 TX RB

28.0 36.5 45.5 2.3 4.3 4.3 2.0 22.5 4.8 34.9 29.6 8.6 9.1 27.2 43.4 0.2 7.1 33.3 19.4 12.6 11.6 15.3 19.5 26.2 3.3 14.6 5.5 38.7 42.2 22.4 22.4 24.9 30.3 13.1 1.4 17.1 18.9 11.1 25.8 20.8 22.5 12.3 11.9 14.5 18.1 27.0 16.5 15.4 15.3 23.3 14.0 15.7 23.4 26.0 24.1 0.5 12.2 1.3 9.6 18.0 23.5 14.2 17.8 1.6 26.8 14.5 1.o 20.3

DS’ C 1-H DS C3-H DS’ C 1-H DS’ C 1-H DS’ C7-H DS C7-H AS C4-H DS’ C 1-H DS C3-H DS C2-H TS C2-H SS C5-H SS C4-H TS C2-H TS C2-H SD C6HC7 DAC7C601 SD C6HC7 SD N C l H SD NC2H DR’ NC2 SD NC2H DD N C l H DD’ NC3 SC HC4C5 DD’ NC1 ST C5-C4 DD’ C6C7 DD’ NC3 DS N-C3 DR NC3H TW HC5 WA HC4 WAG HC5 DD‘ C6C7 TW HC4 ST C6-01 DD NC3H TW HC4 DR C6C7 DR’ NC3 DR NC2H DR’ NC3 ST C5-C4 DR’ NC3 DR C6C7 DR NC2H DAPC6=02 DR’ NC2 TS N-C3 DS’ N-C3 ST C6-01 ST N-C4 ST C6-C7 DAPC6=02 DEF OC5C SD C3ClN DR C3N DR’ C3N DR’ C3N SD C3ClN OPB DR’ C3N D R C3N B C601C5 DR’ C3N DR C3N DR C3N

27.3 0.2 4.0 1.8 0.2 0.2 0.5 19.4 2.7 6.2 28.6 0.8 0.2 13.7 0.6 0.2 6.8 12.3 14.7 11.6 7.7 11.6 11.8 22.1 2.7 9.7 4.6 5.9 4.7 6.7 7.6 14.9 6.2 11.1 1.4 10.5 17.1 10.4 9.3 11.5 6.5 9.6 7.5 11.6 10.9 12.3 12.2 13.2 5.5 8.5 11.4 13.1 7.1 10.1 11.0 0.3 8.4 1.1 9.2 10.1 1.4 10.6 14.9 0.8 10.8 12.0 0.7 20.1

DS’ C3-H DD NC2H DS C1-H DS’ C3-H DR C6C7 DD’ C6C7 DS’ C2-H DS’ C3-H DS C2-H AS C4-H TS C1-H TS C3-H ST C5-C4 TS Cl-H TS C3-H ST C6-C7 ST C6-01 DR‘ C6C7 DD N C l H DR’ NCl DD NC2H DD N C l H DD‘ NCl SD NC2H ST C 5 C 4 DD N C l H SC HNC4 ST C6-C7 DD NC3H DD N C l H SD N C l H TW HC4 ST N-C4 SD C3ClN DAPC6=02 ST C 5 C 4 TW HG5 ST C6-01 RO HC5 ST 01-C5 DR NC3H DD N C l H DR’ NCI DR C6C7 DS N-C3 DD’ C6C7 DS N-C3 DR’ C6C7 DAPC6=02 ST C6-01 DAPC 6 ~ 0 2 RO HC4 RO HC5 TO NC4 DEF OC5C DR C3N DR C3N DEF C4NC TO 01C6 SD C3ClN DR’ NC2 SD C3ClN SD C3ClN DD’ C3N DR C3N DEF OC5C DEF C4NC B C601C5

%

Bu

%

mode


Derreumaux et al.


calcd 159.1 93.4 78.1 67.3 52.6 39.9 32.9 27.1

%

32.9 32.8 24.3 60.7 36.3 79.1 93.6 114.8

mode TO NC4 TO 01C6 TO c 5 0 1 RA TO c 4 c 5 RC RB TY

where ri = the ith bond length, aij = the angle between adjacent bonds i and j , 7j,k = the torsional angle formed by bonds i, j , and k (torsion about bondj), Wj,k = the out-of plane angle formed by bonds i, j , and k ( k out of plane of bonds i a n d j ) , do = the distance between nonbonded atoms i and j that are not bonded to a common atom, and

+

qij = r; r; - 2rirj cos (aij); sij = (ri - rj cos (aij))/q,; tij = rj sin (ai,)/qiJ; u , .= r . / r . ‘J

J

%

25.2 14.9 19.6 10.3 36.0 11.0 21.1

10.2

(8) Williams, D. E. J . Chem. Phys. 1967, 47, 4680. (9) Pullman, B. Adu. Quantum Chem. 1977, IO, 289. (10) Vergoten, G.; Fleury, G.Chem. Phys. Lett. 1984, 112, 272.

mode RO HC4 DEF OC5C TO C4C5 TO 01C6 TO C501 TO C4C5 TY TO C501

%

13.3 6.7 16.4 9.2 15.3 8.7 4.4 8.3

bromide crystallizes with four ACh cations per unit cell in a spatial group of PZlln(monoclinic), with crystallographic parameters (unit cell basis vectors and angle) of a = 10.966, b = 13.729, c = 7.1 59 A, and p = 108.18O.’ There are 26 atoms in each cation, giving 78 internal vibrations, since the three “translational” and three “rotational” motions of the cation are constrained in the crystal lattice. The internal vibrations of the four cations of the unit cell are coupled according to the elements of the symmetry group c z h . The irreducible representation for all the vibrations of the bromide crystal due to the cations is given by

rv= 78A,

1

KhCh= potential energy introduced due to the redundancy condition Gh,and Ki = the force constant for stretching the ith bond, H , = the force constant for the bending of angle ai,,Fij = the force constant for the q, interaction, F $ = the first derivative force constant for the qij interaction, Yj,k = the force constant for the torsion ilrijk,Wjjk = the force constant for the out-of-plane bend Awijk,and Qi = the residual charge on the ith atom. The summations are over relevant internal displacement coordinates or atom pairs for nonbonded interactions. Figure 1 gives the structure and atom designations for the ACh cation. From this structure, we have defined 86 internal displacement coordinates (see Table 11) from which have been constructed 7 8 local symmetry displacement coordinates (including six acoustical coordinates in which all redundancies have been removed (see Table 111). The 78 normal modes of vibration are constructed from the local symmetry displacement coordinates. W e have studied and expressed the intramolecular or internal potential of acetylcholine bromide in local symmetry displacement coordinates, and the force constants for this potential function are given in Table IV. To this internal potential have been added two other potentials so as to take into account the van der Waals forces and Coulombic forces between pairs of nonbonded atoms that are not bonded to a common atom. These forces were obtained with the Buckingham potential plus a Coulomb potential (the last two summations of eq 9). The values of the parameters A,, B,, and C, given in eq 9 are listed in Table V and are obtained from the work of Williams.8 The residual charges, Qi and Q1, were taken from the work of P ~ l l m a n . The ~ second derivative of these potential terms with respect to the Cartesian displacement coordinates gives the elements of the force constant matrix characteristics of the nonbonded interactions between atoms i and j . Using an arbitrary “cutoff” distance of 6 A for the nonbonded interactions, 91 2 interaction coordinates were defined, giving the energy of the crystal as -15.34 kcal/mol; (7.98 kcal/mol for nonbonded repulsion and -23.32 kcal/mol for nonbonded attraction). The dipole-dipole interactions involving the carbonyl (C=O) groups have been neglected because there are not any major changes in the observed carbonyl frequencies between the infrared and Raman spectra. Previous work by Vergoten and Fleuryio has shown that this is a valid criterion for the exclusion of dipole-dipole interactions. In order to calculate the vibrational frequencies for ACh bromide, we started with the X-ray determined structural data given by Svinning and Sorum] and Jagner et aL2 Acetylcholine

mode TO 01C6 TO NC4 TO 01C6 TO C 5 0 l RA RB RC RA

+ 78B, + 77Au + 76Bu

(10)

The relationship between the positions of the four cations in the unit cell are given by the following Cartesian transforms (using cation 1 as a reference): cation 1 to cation 2

x2

=

cation 1 to cation 3

(a’

;I

!l)x, +

(H’ ; H,)xl

x3= cation 1 to cation 4

x4=

(a

1;

(:i)

+(

+

’ ) . ]

0.0

K)

(E)

In the normal modes of the crystal belonging to the symmetry species A,, the four cations of the unit cell vibrate in phase. For the B, normal modes, cation 2 vibrates in phase with cation 1, while cations 3 and 4 vibrate out of phase (with respect to cation 1). The A, case has cations 1 and 3 in phase with cations 2 and 4 out of phase, while the B, case has cation 1 and 4 in phase with cations 2 and 3 out of phase. To construct the force field for crystalline acetylcholine bromide, we began with a literature search for force fields and force constants of esters,l’-I4 small molecules containing CH2 and C H , group^,'^,^^ and molecules containing C-N bonds similar to those found in AChi7-’9 to use as initial parameters. Using a model crystal of 125 unit cells, we calculated the vibrational frequencies of the crystal of acetylcholine bromide and used the Raman and IR spectra to refine the local symmetry force field by the Jacobian method developed by Shimanouchi4 until satisfactory agreement Wilrnshurst, J. K. J . Mol. Spectrosc. 1957, I , 201. Matzke, P.; Chacon, 0.;Andrade, C. J . Mol. Struct. 1971, 9, 2 5 5 . Shimanowhi, T. Pure Appl. Chem. 1963, 7, 13 1. N o h , B.; Jones, R. N. Can. J . Chem. 1956, 34, 1392. (IS) Ornura, Y . ;Shirnanouchi, T. J . Mol. Spectrosc. 1973, 45, 208. (16) Vergoten, G. Doctoral Dissertation, University of Lille, 1977, Lille,

(1 1 ) (12) ( I 3) (14)

France. ( 1 7) Edsall, J. T. J . Chem. Phys. 1937, 5 , 225. (18) Ebsworth, E. A. V.; Sheppard, N. Spectrochim. Acta 1959, 13, 266. (19) O’Leary, T.J.; Levin, I . W. J . Phys. Chem. 1984, 88, 1790.


The Journal of Physical Chemistry, Vol. 93, No. 4 , 1989 1349

TABLE VIII: Calculated and Observed Frequencies and Assignments (PED’S) for Acetylcholine-d9Bromide: obsd calcd 7% mode % mode DS C7-H 3004 2993.4 95.0 4.3 DS’ C7-H DS’ C7-H 2983 2982.4 95.2 4.3 DS C7-H 2975 2967.6 AS C5-H 97.4 AS C4-H 1.8 1.8 2957 2959.4 AS C4-H 97.4 AS C5-H S S C4-H 8.8 S S C5-H 2922 2928.6 91.2 S S C5-H SS C4-H 9.2 2885 2896.1 91.7 TS C7-H 2815 2815.5 100.3 SD C6HC7 0.2 DS’ C2-D 2290 2284.0 37.2 31.5 DS’ Cl-D 2267 DS C2-D 23.5 DS‘ C3-D 2261.5 38.8 DS’ C3-D 23.4 2259.6 30.0 2258 DS’ Cl-D DS Cl-D 2.7 2246.3 92.1 DS’ Cl-D DS’ C2-D 23.1 2223 2222.5 58.3 DS’ C1-D 2212 2215.7 57.6 DS C3-D 36.1 DS C2-D TS C3-D 26.9 2104.0 47.5 TS C2-D 2079 2065.2 TS C3-D 42.4 TS C2-D 48.8 TS Cl-D 31.9 67.9 2057.8 TS C27D ST C6=02 1743 90.2 1743.9 7.1 DAC7C601 33.3 DD’ C6C7 43.2 1503.9 SD C6HC7 SC HNC4 1452 91..9 1450.5 3.8 SC HC4C5 1434 84.2 1432.6 5.5 HC4C5 ST C5-C4 1415 1411.2 38.7 SD C6HC7 43.3 DD’ C6C7 1372 71.8 1377.2 21.0 WA HC4 DS N-C3 1340 1351.2 25.9 WAG HC5 37.8 TW HC5 1304 1300.8 DS N-C3 52.7 20.8 WA HC4 1272 DD C6HC7 96.7 1280.5 1.4 DD’ C6C7 1263.9 WAG HC5 16.1 50.4 TW HC4 ST 01-C5 30.0 1231.0 ST C6-01 27.9 45.5 1211.9 ST N-C4 14.1 TS N-C3 1185 1192.0 DS’ N-C3 27.0 TW HC5 14.2 1147 TW HC5 1141.O 18.4 14.0 TW HC4 1138.5 ST C5-C4 28.1 DR C6C7 17.0 1122 1119.6 87.8 SD NC2D 7.7 SD NClD 1096.9 74.6 SD NC3D SD NC2D 5.3 1081 1080.6 ST C5-C4 15.3 TW HC4 13.6 1074.2 1074 SD NClD 58.4 11.7 DS’ N-C3 1062.4 1064 85.5 DD NC2D SD NClD 4.6 1059.3 DD’ NC2 65.8 DD’ NCl 14.5 1058.2 DD’ NCl 64.4 19.2 SD NClD 1042.4 DD NClD 76.1 DR NClD 6.6 1035 1035.1 DR’ C6C7 51.7 24.6 DR C6C7 1026.7 72.3 DD’ NC3 10.4 DD NC3D 990.3 996 RO HC5 27.8 TW HC4 15.3 965.3 75.6 DD NC3D 9.9 DD’ NC3 961.7 ST C6-01 17.4 31.1 ST 01-C5 896 881.9 34.3 RO HC4 11.4 TO NC4 854.8 36.1 DR NClD 22.3 DR’ NC 1 DR NC3D 853.3 26.7 15.1 DR’ NC1 834 838.0 21.9 DR NC3D 11.6 DR NClD 824 825.1 13.4 DR NC3D 10.8 DR’ NC3 DR NC2D 805.1 36.9 29.7 DR’ NC3 784 786.8 25.2 DR NC2D 20.3 DR’ NC 1 769.0 DR’ NC2 19.7 42.0 DS’ N-C3 680 TS N-C3 684.2 53.7 ST N-C4 14.6 650 651.6 32.5 DEF OC5C 27.1 ST C6-C7 619 ST C6-C7 616.1 26.8 DAPC6=02 23.5 DEF C4NC 488.8 20.2 10.9 DAC7C601 444.0 68.7 OPB 8.5 TO 01C6 418 DAC7C601 418.0 24.4 20.5 DR’ C3N 398 386.5 TO NC2 96.0 DR’ C3N 1.2 372 370.2 SD C3ClN 15.8 39.8 DD’ C3N DD C3N 36 1.O 70.0 DD’ C3N 3.9 352 343.3 65.6 TO NCl 20.4 DD’ C3N 330 DD’ C3N 337.2 32.3 30.8 TO NC1 DAC7C601 312.1 29.0 27.7 B C601C5 283 DR C3N 279.8 29.8 12.1 DR’ C3N 235.8 96.9 TO C3N 0.9 TO C6C7 222 217.9 94.0 TO C6C7 2.1 DR C3N DEF C4NC 168.1 32.4 DR C3N 25.8 163 153.8 26.2 TO 01C6 24.0 TO NC4 84.6 38.1 TO 01C6 16.8 TO NC4 75.0 TO C501 11.0 38.8 TO NC4 60.3 27.4 TO C4C5 14.9 RA 48.5 54.6 RA TZ 16.1 43.1 58.2 TZ 9.3 RA 39.9 TY 60.3 TX 20.9 32.2 TX 63.5 RA 23.8 19.2 134.1 RB TY 75.0 17.3 RC 73.9 147.9 TZ

A, Modes %

0.2 0.2 0.4 0.3 0.1 0.2 0.2 26.0 17.5 20.1 1.6 14.6 2.5 22.9 10.1 2.2 6.8 12.3 3.O 5.5 5.9 3.7 19.6 5.7 1.3 8.3 17.3 13.2 5.6 13.4 12.4 7.7 3.4 12.0 9.5 2.5 6.2 11.1 3.9 11.9 6.9 7.1 5.3 13.9 10.1 12.7 9.7 11.0 10.4 8.4 11.8 9.4 6.6 7.3 13.9 9.7 6.0 8.5 0.7 10.9 2.7 5.5 7.2 12.6 8.2 0.4 0.9 16.5 14.1 7.8 9.6 7.9 12.0 8.2 18.1 20.6 54.1 49.0

mode DR C6C7 DD’ C6C7 RO HC5 RO HC4 SC HNC4 ST C5-C4 ST C6-C7 DS’ C3-D DS C3-D DS C3-D DS C2-D DS’ C3-D DS’ C3-D TS Cl-D TS CI-D TS C3-D ST C6-01 DR’ C6C7 ST C5-C4 SC HNC4 ST C 6 C 7 ST C5-C4 TW HC4 WAG HC5 DAPC642 ST C5-C4 DAPC6=02 SD C3ClN DR NC3D DR C6C7 STO01-C5 TS N-C3 TS N-C3 DR C6C7 SD NC2D DR NC2D DD NClD DD’ NC2 DD’ NC3 DD’ C6C7 SD NC3D RO HC4 DR NC3D DAPC6=02 DAPC6=02 DR’ NC3 DR NClD DR’ NC2 RO HC5 DR’ NC2 DS’ N-C3 ST N-C4 DEF C4NC TO NC4 DEF OC5C B C601C5 TO C501 SD C3ClN DR C3N DR’ C3N DR NC2D SD C3ClN SD C3ClN DR C3N DEF OC5C DR’ C3N DR’ C3N B C601C5 DR’ C3N RO HC4 RO HC5 TO C501 TO C4C5 TO C4C5 TO 01C6 TY TX RA

1350 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 between the observed infrared20 and Raman frequencies and the calculated frequencies was obtained (the standard deviation of calculated from observed frequencies less than 5 cm-I). This refinement procedure allows for the simultaneous variation of independent force constants. For the system under study here, the diagonal force constants were derived from literature values as mentioned above and the off-diagonal force constants were refined. Subtle changes (less than 3%) in the diagonal constants were then made followed by another Jacobian refinement of the off-diagonal constants. The refined local symmetry force constants were then transformed into the U-B-S basis via the inverse of the transformations given in eq 1 and 2. The calculation of the frequencies was carried out using our modified version of the computer program CVOA, which was obtained as a gift from the late Professor T. Shimanouchi.21

Results and Discussion Figure 1 shows the structure, atom designations, and torsional angle definitions for the ACh cation. Table I gives the X-ray determined structural parameters for the three halides of the ACh cation used in this work1y2and shows that the intramolecular bond lengths and bond angles do not differ significantly for the various crystals, but the torsional angles do vary significantly. Figure 2 shows the classical Raman spectra of crystalline acetylcholine (a) chloride, (b) bromide, and (c) iodide, expanded in three regions for clarity (0-1200,1200-2400, and 2400-3600 cm-I). The small differences below 300 cm-' are attributed to changes in the crystal lattices, while differences above 300 cm-I are attributed to the different conformations of the cations in the different crystals. Since intramolecular bond lengths and angles are essentially constant for the different crystalline states, changes in conformation are due solely to differences in torsional angles. (Refer to Figure 1 and Table I.) Figure 2d is the Raman spectrum of crystalline acetylcholine-d9 bromide (the hydrogens of the quaternary methyls have been replaced by deuterium). The displacement coordinates that were used in these calculations are given in Tables I1 and 111. Table I1 gives the definitions of the internal displacement coordinates. Table 111 gives the local symmetry displacement coordinate definitions. Table IV contains the data used to construct the U-B-S force field. Table V gives the nonbonded interaction parameters used in eq 8 described above. We chose the bromide crystal for this study for the sake of experimental and computational convenience; the X-ray results were accurate and complete; acetylcholine bromide crystallizes with only four cations per unit cell (as compared to 16 for the iodide crystal); the bromide salt of ACh formed the best crystals of the three halide salts, and the bromide salt is not as hygroscopic as the chloride salt. The refined local symmetry displacement coordinate force field for crystalline ACh bromide is given in Table VI. Table VI1 lists the observed and calculated vibrational frequencies, the mode assignments, and potential energy distributions (PED's) for crystalline acetylcholine bromide separated into the four symmetry group species. The vibrational modes with A, and B, symmetry are Raman active, while those with A, and B, symmetry are IR active. Examination of Table VI1 shows the excellent agreement between the observed and calculated frequencies (for A, modes, the standard deviation between observed and calculated frequencies is 3.4 cm-'), including the very low Raman active frequencies. (20) Aslanian, D. LiJe Sci. 1983,32, 2809. (21) Shimanouchi, T., personal communication and gift.

Derreumaux et al. Table VI1 lists the observed and calculated vibrational frequencies, mode assignments, and potential energy distributions for the A, modes of crystalline acetylcholine-dg bromide. For this calculation, we have assumed the same crystalline geometry as for the nondeuteriated acetylcholine bromide, in the absence of crystallographic data. The standard deviation between the observed and calculated frequencies of Table VI11 is 5.3 cm-I. These results suggest that the local symmetry coordinate force field we have developed is quite good. Pioneering work by AslanianZ0gave preliminary assignments of the Raman and IR bands of ACh. The results of our normal-coordinate calculation (supported by comparison to simple ester and alkylammonium Raman spectra3) make new and different assignments to a few of the vibrational bands of ACh. These vibrations include the 720-cm-' band, previously assigned as a C H 2 rocking vibration, that we assign to the symmetric N-(CHJ3 stretching vibration; the 830-cm-I band, previously designated a skeletal stretch, that we now assign to a C H 2 rocking mode; the 870-cm-l band, assigned to a N-C stretch, now assigned to a CH, rocking mode; and the 9 15-cm-' band previously assigned to a N-(CH3) rocking, which we assign to the N-(CH,) stretching mode. Inspection of Figure 2 (middle) shows several bands that are conformationally sensitive. The C5-H rocking vibration band shifts significantly between the chloride (848 cm-') and the bromide (825 cm-') crystals. The N - C 4 stretching vibrations also shift between the chloride and bromide conformations (837 to 819 cm-', and 919 to 938 crn-', respectively). A small shift in the C6-C7 bond stretching frequency is also observed (601 cm-' for the chloride form and 609 cm-' for the bromide). Referring to Table I, the only major structural difference between the chloride and bromide crystal structures is in rl, the torsional angle about the 0 1 - C 5 bond. It is easy to imagine how different rotations of this angle would affect the rocking vibration of the C5 methylene group, since it is intimately associated with 71. The sensitivity of the N-C4 and C6-C7 stretching vibrations to changes in 7 , are probably due to van der Waals/Coulomb interactions, since rotating T ] moves the quaternary methyls closer and farther away from the carbonyl oxygen ( 0 2 ) . The spectrum of ACh-d9 and its associated calculation demonstrate the sensitivity of the C5-methylene rocking vibration to subtle changes in the molecular conditions. In contrast to ACh, the deuteriated species does not show a band due (predominantly) to the C5-methylene rocking mode in the 700-900-cm-l region. Inspection of the potential energy distributions (PED's) given in Table VI11 reveal that mode mixing of the C4-N-C degenerate rocking modes dampens most of the P E D for the C5-methylene rocking mode. Now that we have a reasonable model of the ACh cation force field in a crystalline state and have demonstrated the sensitivity of several vibrational bands to the conformation of the cation, we will (in the next paper of this series) relax the constraints in our crystalline model in order to generate a force field for the isolated ACh cation in various environments including both crystals and solutions.

Acknowledgment. This work was supported by the National Science Foundation (Grant 841 7199) and National Institutes of Health (Grant GM15547). Registry No. Acetylcholine chloride, 60-3 1-1; acetylcholine bromide, 66-23-9; acetylcholine iodide, 2260-50-6; acetylcholine-d9 bromide,

93449-32-2; deuterium, 7782-39-0.

Conformational studies of neuroactive ligands. 1. Force field and

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