30 REFINEMENT

Refinement of all three structures was by least-squares minimization of the quantity

scale factor for F ₀ and weights w were taken equal to

Form factors used for C, N, and O were taken from International Tables for X-Ray

Crystallography()?); those for Cl- and P were from Cromer and Waber(45). Hydrogen form factors were those of Stewart,

Davidson and Simpson(46).

Jl

ARAC,HCl

Initial refinement was based on one quadrant of data, After four cycles of isotropic refinement (R = 0,081), a difference map indicated the positions of all the hydrogen atoms except those of the hydroxyl groups, appearing as

• 0 3

peaks ranging from 0,2 to 0,5 e,A-. With the located hydrogen atoms contributing to F ₀ ^, anisotropic thermal parameters were introduced for the heavy atoms and refined for two cycles. A subsequent difference map clearly

indicated the positions of the remaining hydrogen atoms.

Further refinement, with a parameter list that included coordinates of all 32 atoms, anisotropic temperature parameters for the 18 heavy atoms, isotropic temperature factors for the 14 hydrogen atoms, a scale factor and an extinction parameter(47, 48), converged at an R index of

The atomic form factors of O, N, and Cl- were then corrected for the real and imaginary effects of anomalous dispersion, using values for Cl from International Tables for X-Ray Crystallography(37) and Hope's corrections for N and O (49), Refinements of both enantiomorphs were continued until parameter shifts were less than 0.3~ for the heavy

atoms and less than 1~ for the hydrogen atoms. Results of

the two refinements are summarized in Table 6. Although no

absorption corrections were applied to the data, we feel the

differences in statistical sums are sufficient to establish

32

Table 6. ARAC.HCl Enantiomorph Determination.

(L) (D)

R 0.032 0.023

Rw 0.006 0.003

GOF 2.59 2,04

(for M = 1293 data and S ⁼ 219 parameters)

33

the enantiomorph. Comparison of transmission factors for representative hkl and hkl reflections showed relative differences of no more than 4-5%, Moreover, absorption effects on intensities are systematic throughout reciprocal space, while Bijvoet differences are random. Therefore we conclude that the sugar in this crystal is D-arabinose.

Coordinates and temperature parameters for the two refinements agre·ed within two standard deviations except for the~ coordinates of the lighter atoms, which differed by an approximately constant amount of 0,045 A, 0 A polar dispersion error of this magnitude was predicted by Cruickshank and

McDonald (50) as the result of refining an incorrect

enantiomorph with the chlorine scattering factor corrected for anomalous scattering in CuK~ radiation.

Final least-squares refinement of the D enantiomer was based on the full data set (two quadrants) •. Two matrices were collected, one containing the coordinates and

anisotropic temperature factor coefficients of the heavy atoms, scale factor, and extinction parameter(47, 48), and the second containing the coordinates and isotropic

temperature parameters of the hydrogen atoms. After two cycles of refinement, the largest parameter shifts

associated with the two matrices were o.4~ and 1.1~, the R

index was 0,022, the weighted R was 0,003, the goodness-

)4

of-fit was 1.8)0 The final parameters are listed in Tables

7 and 8; observed and calculated structure factors are

given in Table 9.

Table 7. Final ARAC. HCl Non-Hydrogen Atom Parameters and their Estimated Standard Deviat _ ions. All parameters have been multiplied by 10 4 . The anisotropic temperature factor is of the form T = exp[-2n2(h 2 a~U 11 + ... +2ktb*c*U 2 s)J. The final value of the extinction para.meter g is (7.6~0.3)x 10-5e- 2 . X l. z Qu ~ ~ U12 Qu ~ - - N(l) 6095(2) 8190(1) 2506(2) 271(5) 277(5) 300(5) -22 (4) 157(4) 6(4) C(2) 7338 (2) 8505(1) 1474(2) 289(6) 328(6) 333(7) -19(5) 166(6) 28(5) 0(2) 6807 (2) 8365 (l) -468(2) 421(6) 718(8) 322 (6) -170(6) 2o6(5) -44(5) N(3) 9273 (2) 8991(1) 2843(2) 3o6(5) 337(6) 362(6) -60(4) 177(5) 20(5) C(4) 10005(3) 9147(1) 5035 (2) 310(6) 251(5) 376(7) -10(5) 149(5) -4(5) \.A) N(4) 11909(3) 9600(1) 6169(3) 4~(7) 398(7) 481(8) -136(6) 153 (6) -41(6) \J\ c(5) 8654(3) 8817(1) 6004(3) 414(7) 343(6) 336(7) -34(6) 189(6) -65 (6) C(6) 6745(3) 8352(1) 4709(3) 370(7) 320(7) 355(7) -19(5) 218 (6) -12 (5) C (l') 4085(2) 7635(1) 1128(2) 238 (6) 302 (6) 314(6) -14(5) 140(5) 27(5) 0(1') 2526(2) 7672(1) 2021(2) 315 (5) 281(5) 539(6) -7(4) 284(5) 5 (4) C (2') 4759 (2) 6665 (1) 1185 (2) 300(6) 301(6) 383(7) -21(5) 187(5) -38 (5) 0(2 I) 6445 (2) 6415(1) 3333(2) 285(5) 334(5) 520(7) 39(4) 149(4) 67(4) c (3') 2542(3) 6211(1) 804(2) 330(7) 324(6) 351(7) -62 (5) 170(6) -25 (6)

Table 7 (continued) 0(3') 1033 (2) 6178(1) -1519(2) 445 (6) C (4') 1590(2) 6812(1) 1993 (2) 236(5) C(5') 2157(3) 6530(1) 4327(3) 370(7) 0(5') 875 (2) 7075(1) 5056(2) 410(6) c1- -2653 (1) 5000(0) -1341(1) 367(2) 604(7) 357(6) -239(5) 304- (7) 343(7) -24(5) 424(8) 390(8) 44(6) 557(7) 4o6(6) 47(5) 349(1) 492 (2) -16(2) 186(5) 141(5) 213(6) 242(5) 236(1)

-109(5) 30(5) 77(6) 16(5) -25 (2) w °'

37

Table 8. Final ARAC,HCl Hydrogen Atom Parameters and Their Estimated Standard Deviations. All coordinate values have been multiplied by 103.

X Y.. z B(A 2 )

HN(3) 1011(4) 920(2) 221(4) 4.4(0o5)

HN(4) 1233(4) 977(2) 756(4) 5.9(0.6)

H'N(4) 1256(4) 982(2) 549(4) 4.4(0.5)

HC(5) 918(4) 893(2) 748(4) . 5.1(0.5)

HC(6) 565(3) 811(1) 524(3) 3.3(0.4)

HC(l') 342(3) 787(1) -24(3) 2.8(0.3)

HC ( 2' ) 518 { 3) 650(1) -3(3) 2.6(0.3) HO( 2' ) 768(3) 671(1) 375{3) 4.0(0.4) HC{ 3' ) 290(3) 561(1) 135(3) 3.6(0.4) HO( 3' ) -16(4) 591(1) -165(3) 3.7(0.4)

HC( 4' ) -6(3) 682(1) 101{3) 3.8(0.4)

HC ( 5' ) ^{160(4) 593{1) 439(3) 3.9(0.4)}

H'C(5') 368 ( 3) 653(1) 529{3) )o2{0.4)

HO{ 5' ) 130(5) 687(2) 640(4) 6.4(0.6)

38

Table 9. Observed and Calulated Structure Factors for ARAC,HCl. Each set of four columns contains, from left to right, the k index, lOIFol, lOIFcl, and 10IF ₀ 2-Fc2 1/~(F 0 2 ).

A reflection with(--) in the fourth column was given zero

weight in the least-squares refinement.

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39

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40

The initial ARAU model was refined by least squares for two cycles using one octant of data. The R index

dropped to 0,096, and a difference map revealed the positions of all hydrogen atoms. Allowing the hydrogen atoms to

contribute to Fe but not refining them, anisotropic thermal parameters for the heavy atoms were introduced and varied for two cycles along with non-hydrogen atom coordinates, scale factor and extinction parameter(47, 48). The R index was 0.031. Two more least-squares calculations were

performed in which all parameters were allowed to shift, including coordinates and isotropic temperature factors for the hydrogen atoms, Parameters were factored into two

matrices, one containing the heavy-atom coordinates and the second the anisotropic thermal parameters, hydrogen atom parameters, and the scale and extinction factors. These cycles reduced the R to 0.026.

At this time the form factors for N and O were

corrected for anomalous dispersion effects in CuK~ radiation according to Hope(49). Two structure factor calculations were done, one for the D and one for the L enantiomorph, Results of these two calculations are in Table 10.

Differences in these sums are much less pronounced than for ARAC.HCl for at least two reasons1 (1) the anomalous

dispersion corrections for N and Oare much less than for Cl-,

such that the effect on the observed structure factors is

41

Table 10. ARAU Enantiomorph Determination

(L) (D)

R 0.0331 0.0329

Rw 0.00457 0.00454

GOF 2.20 2.08

(for M = 2034 data and S = 203 parameters)

42

smaller, (2) the two enantiomorphic sets of parameters had not been refined using the corrected form factors, but only compared through structure factor calculations. Had they been refined independently, the differences in the sum values could very well have been greater.

Refinement continued on the D-enantiomorph parameters in the same fashion as before, but using a data set expanded to include the two octants. Three cycles were performed;

in the third, no shift was greater than½~. The final R index was 0.030, the weighted R 0.00403, and the goodness- of-fit 1.96. Final parameters are listed in Tables 11 and 12. Observed and calculated structure factors are in

Table 13.

Table 11. Final ARAU Non-Hydrogen Atom Parameters and their Estimated Standard Deviations. The 'l_- coordinates have been multiplied by 105, all other parameters have been multiplied by 10 4 . The anise- tropic temperature factor is T = exp[-2~ 2 (h 2 a* 2 U 11

+ ... +2ktb*c*U 23 )]. The final value of the extinction -6 -2 parameter g is (6.5.:!:_0.5)x 10 e . X l.. z Uu ~ U33 U12 U13 ~ - - N(l) -110(2) 2o491(5) 1623 (2) 396(7) 221(4) 225(5) ll(5) -47 (7) -0(4) C (2) -25 (2) 23573 (6) -135 (2) 342(7) 227(7) 239(6) 33(6) -37 (8) -1(5) 0(2) -100(2) 2o842 (4) -1717(1) 661(8) 290(4) 247(5) 20(5) -44(7) -38(4) N(3) 126 (2) 3oo84(5) -22 (2) 4o8(7) 225 (4) 240(6) 34(5) -25 (7) 32(5)

+=" w

C (4) 362 (2) 33718(6) 1655 (2) 282(7) 250(4) 314(7) 34(5) -2 (8) -50(6) 0(4) 536(2) 39497 (4) 1518(2) 490(6) 227(4) 430(6) 8(4) 4(7) -38(5) c(5) 348(2) 3oo61(6) 3434(2) 419(8) 314(7) 246(7) 32(7) -32 (8) -66 (6) c(6) lo4(2) 23761(6) 3368(2) 422(8) 325 (7) 218(6) 29(7) -26(9) -9(6) C (l') -324 (2) 13506(5) 1605(2) 326(7) 232(4) 255 (6) -21(6) -24(7) 8(6) 0(1') -1396 (2) 11812(4) 3285 (2) 313(5) 290(4) 386(6) 41(4) 83(6) 64(4) C(2') 1593 (2) 9861(6) 1732 (2) 316(7) 238(7) 233(7) -24(6) 22(7) 8(6) 0(2') 2962 (2) 12901(4) 2943 (l) 3ll(5) 361(4) 296(6) -74(4) -9(5) 26(5)

Table 11 (continued) C (3') 879(2) 3543(6) 2566(2) 330(7) 0(3') 192 (2) -99(4) 956(1) 552(7) c(4') -779(2) 5501(6) 3930(2) 325(7) C(5') -293 (2) 5802(7) 6076(2) 423(9) 0(5') 1317(2) 9942(5) 6455(2) 432(6)

225(7) 229(6) -3(5) 234(4) 299(5) -43(5) 223(4) 303 (8) -35 (6) 359(7) 274(7) -25 (7) 439(7) 319(6) -10(6)

-7(7) -6(6) 18(7) 56(8) 12(6)

5(5) -38 (4) 20(6) 14(7) 72(5)

~ ~

45

Table 12. Final ARAU Hydrogen Atom Parameters. Coordinate values have been multiplied by 103.

Atom X y_ z B(A2 )

HN(3) -0(2) 320 ( 1) -103(2) 2.8(0.4) HC(5) 52(2) 321(1) 464(2) 2.2(0.3) HC(6) 4(2) 212(1) 451(3) 2.8(0.4) HC( 1' ) -104(2) 123(1) 43(2) 1.9(0.3) HC ( 2' ) 214( 3) 91(1) 46(3) 3.2(0.4) HO( 2' ) 277(3) 121(1) 394(4) 6.0(0.6) HC ( 3' ) 193(3) 12(1) 331(3) 2.8(0.4) H0(3') 1(3) -37(1) 131(3) 4.4(0.5) HC( 4' ) -188(3) 26 (1) 376(2) 2.4(0.3) HC ( 5' ) 4(2) 14( 1) 640(2) 2.7(0.3)

H'C(5') -145(3) 72 ( 1) 684( 3) 3.6(0.4)

HO( 5' ) 97(4) 132(1) 702(3) 5.3(0.5)

46

Table lJ. Observed and Calculated Stucture Factors for ARAU.

Each set of four columns contains, from le· ft to right, the k

index, 10IF ₀ 1, lOlFcl, and 101Fo 2 -Fc 2 1 ^/cr(F 0 2 ).

t , 90 t4 Ill lff

z•

U U4 JH 7l U I -11

,o

JIJ •ll •• . , -• -•

"° ,,

U

~:! ;:: .;! :~ :C:! .;; ~!! !!! :~ z!~ 1!: -~~ ~~ z1~ ,:: u ,9 1• z:! J! .:; ~! •• 10 _-ao

n

1;~ :t: :! : :: -::

u, z., O llS IH -z• JU JU 10 n "9 -12 LU u• -ZJ U ♦ l n uo .u:o O 4S -11 -• 4-4 M -lt _, 70 . , lT

}:; !!1 -; = ^{!!; :~~} .;; .;; : !! !! :!! ~ ~! ~: i! I~ i! u,

ll1 •Z ·:: .,~ -~:

:! !! -•: :! !: ~ ,: :;

^{1 :}

·1: ,!

lU l l l t lU lit Z ♦

~

,. _,,

u

JI_,.

I Hl ZH·H

z ,,. ,~-z•

J U 42 9

• •90 soa-,o

• •o ••• • 1 Ul UY·,Z

OUSJ1S40 U l 94 ♦ J t l SH Hl U J . , U 0 S UO lM t

• l4J l4S•U

1 H U 10

• , . , 1:11 •

, . 0 U

10, 101 U

..

..

H . . . 15

44-U

11.

:n ••

U 11 . . U ll 11'4 . . , ,o t n, ZTO , . -10 . , 40 S Z JSl , . . 1 •• 11 •• 0 1J IH u, 0 II J1 , . 11, - IU IIJ i . U •• •• 0 H S5 , . 4 U -t zo - 10 101 tu -10 -10 lOT 100 •U

mm ^HI u:n ^{·1 li} mt~·:·:~: n ^{t!I J :1m} n: : :~;-~ -~ ~~-; · ^{~ ;_!~ :g ':lrl u ~i1}

:

r:::·;:.' ~·~· . .

_-

·.:!:~·r:.:,: ~:·:~·:.:.~,:::':,·:~~·=:'.,:::·:::::=::·::':-,;.·!:::.:' ·!'~~.::·::::::; ·::· ... ~.::::·--:=:.;::',:.:::::,:::::.:::,:::::::.::' :,::-~ . . ~::-'.·.·:. :,:::~::,·:·=:::'--:~.·:'::.:::.:, ::,·::l::, .:.:=.:~.:

_{- _}

··~l::·,1:::':_-~::•·:·.::::':_•·=:=l .. :~::: r·:-.;:~n.!i'

r:-.~·:: ..

':::.:;::.·::,·.:;_;~;~::'_:_;.I:.:::, :,·:.;,:-·:.;:

_{:hH ·i!~l} !LL; : ;; .: HitTffi.:! (: ~ ^{;I~ ;l(1 l~ ;ii ffll}

^k

nrm ^{g}1! 'g tn ~! .. i : !! m ntr~ r~ fl~ g ii-ii i ti ll ~!}

,, :u

..

TO • • n H -n

...

u ,., -u 75

..

ll

"

, . 14

" _.. . _.

,1-10

,0 u

♦S 6J 1't u u

n • ., 101-u

Sl' 0 -•

n-11 - , 11 , . 1"

uo u" ,.

121 U4 11 11 u-11

:: ~ rtii Ji 11~ ll ^{,ii .g '.i l; 1} ii r; ^{j g 11} :! ~ :g :!I-:i } ,g Ii ~i ,g :H ^{=li -i} .ii .:~ _;:

~ ^{~} m} ~ ^t~ ~ ^{:1 ~11~ ;if~]~~.~} ~ ^m I lil'i : '. ,. ~1 ;i ;ii! ; ii ^{;1 ~111 l I Ii l :1 :ii} i ^{l ·:::;}

i ~ ~~ ~ .. ~.~.;;,. ~.~.~.·::.!..!. ;~-~. ;l.:.!~'..:~.i=~ ... ¹ ! ~.~.:;.: ~.: ¹

^{.:i.· 1.·.1}

^~:.! :.E.·~_::.:t.i.: ,; ~-~ ^,l ~ ^{tl _l .. :} ~:I:~~ ^{1 •} r. ~,;; : : ... :: .. ; ~,;; ~ · · ' .. : :

- z;; ;z;; ~! ~: ::: ~:: .• : g

^,s

o

^{UZ ll9 U : :}

!:! z: :n :g

^{IOT . :}

-,t-~:

4 ) -ll

48

Initial least-squares refinement of the ARACMP trial model made use of a data set collected with molybdenum radiation. Isotropic refinement of all non-hydrogen atoms converged at an R index of 0.13 using all data collected out to sin2 e/A ^{2 =} 0.35. A difference map calculated at this

juncture revealed the positions of all hydrogen atoms except for that one participating in the 0(10) ••• 0(10) hydrogen bond. Two half-hydrogen atoms were used to represent the hydrogen bonding scheme here, and anisotropic refinement commenced. Two cycles in which the coordinates and six- parameter temperature factors for each heavy atom were varied along with a scale factor reduced the R index to

0.097. No hydrogen atom parameters were refined. During this stage of refinement it became increasingly clear that the quality of the weaker and high-angle data was sufficiently poor to warrant recollecting the data set using copper

radiation. Experimental details for the collecting of this

second set of data have been given (see EXPERIMENTAL-