Acta Cryst. (1979). B35, 867-877 A Study of the Charge Density in Putreseine Diphosphate at 85 K* By FUSAO TAKUSAGAWA AND THOMAS F. KOETZLEt Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973, USA (Received 15 March 1978; accepted 7 September 1978) 867 Abstract Introduction A study of the charge density in putrescine diphos- phate {C4HIaN2 2+ . 2H2PO~-, [NH3(CH2)4NH3] 2+ • 2[H2- PO4]-} has been carried out, employing X-ray and neutron diffraction data measured at a temperature of 85 K. Crystal data: space group P2~/a; a = 7.879 (3), b -- 9.734(4), c-- 8.126(3)/~,fl= 110.19 (9) ° (X- ray values); Z = 2. The deformation electron density was computed by a modified X-N method, utilizing neutron positional parameters for all atoms and thermal parameters for non-hydrogen atoms taken from a high-order X-ray refinement (0.65 <_ sin 0/2 < 1.15 ]k-~). This approach was elected, since the neutron thermal parameters were found to be sys- tematically larger than those from high-order X-ray refinements. In the case of H atoms, the neutron thermal parameters were multiplied by the mean ratio of the X-ray and neutron values, computed separately for each Uij class for the non-hydrogen atoms. These ratios for the high-order X-ray refinements range from 0.86 to 0.99. Well-defined peaks (0.25-0.35 e A -3) are found in the deformation density maps for all covalent bonds in the structure. No marked difference was observed between the density in P-O bonds and that in bonds between first-row elements. In the hydrogen bonds, no build up of charge was observed midway between the protons and oxygen acceptors, in accord with the basic electrostatic picture of hydrogen-bonded interactions. Excess density was observed in the regions normally associated with lone-pair electrons for all four phosphate O atoms, and the heights of these peaks increased more than those of peaks in covalent bonds when higher-order data were included in the defor- mation maps. Conformations of H2PO 4 ions in a number of crystal structures including putrescine diphosphate were generally found to have H-O- P--O(H) torsion angles in the range 30-150°; such conformations are predicted to be favored for systems like HEPO 4 with lone-pair electrons adjacent to polar bonds. * Research carried out at Brookhaven National Laboratory under contract with the US Department of Energy and supported by its Office of Basic Energy Sciences. t To whom correspondence should be addressed. Recent improvements of the precision attainable in single-crystal diffraction measurements have led to increased interest in the direct analysis of charge- density distributions in solids based on diffraction tech- niques (Coppens, 1975). Here we report a study of the electron density in putrescine diphosphate at 85 K, using combined X-ray and neutron diffraction data. This compound initially attracted our attention, because it affords the opportunity to study the charge density in the dihydrogen phosphate anion, and exhibits a variety of N-H... O and O-H-.. O hydrogen bonds involving the ammonium groups on putrescine and the phosphate O atoms. The crystal structure was originally determined from X-ray photographic data at room temperature (Woo & Rich, 1975; Woo, Seeman & Rich, 1979). These aufhors have described the general features of the structure, and commented on its significance as a model for understanding interactions of amines with nucleic acids. Our neutron diffraction results have been described in a previous paper (Takusagawa & Koetzle, 1978). Experimental The sample of putrescine diphosphate used in the present X-ray work was recrystallized from an aqueous solution of putrescine and phosphoric acid. A crystal was ground to form a sphere of diameter 0.42 mm which was glued to an aluminum fiber with adhesive varnish$ and oriented approximately along the crystallographic c axis. This sample was placed in a liquid-nitrogen-cooled cryostat (Coppens et al., 1974) and mounted on an automated Picker four-circle diffractometer (Dimmler, Greenlaw, Kelley, Potter, Rankowitz & Stubblefield, 1976; McMullan, Andrews, Koetzle, Reidinger, Thomas & Williams, 1976). Nb- filtered Mo Ka radiation (2 = 0-71069 A) was used. The temperature of a copper block in the cryostat, maintained in direct contact with the aluminum crystal mount, was measured to be 85 + 1 K during the period $ General Electric No. 7031.
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`868 THE CHARGE DENSITY IN PUTRESCINE DIPHOSPHATE AT 85 K of data collection. Cell dimensions refined by a least- squares procedure based on the setting angles of 29 reflections (20 > 80 °) (Mo Kay: 2 = 0-70926 A) are listed along with certain experimental details and are compared with the corresponding neutron values in Table 1. X-ray intensities were measured for reflections in_ four octants of reciprocal space (hkl, hkl, hkl, and hkl), out to a 20 limit of 110 °. Mechanical constraints introduced by the cryostat prevented the measurement of reflections with X near 90 ° and 20 > 70 °, but the number of reflections omitted was a small fraction of the total data measured. A 0/20 step-scan procedure was used; the scan range varied from 3.0 to 3.5 ° over the full range of 20, while the step size was taken to be A20 = 0.04 °. At each step, counts were accumulated for 2 s. As a general check on experimental stability, the intensities of two reflections were remeasured every 30 reflections. These intensities did not vary to any significant degree during the course of the measure- ments. Integrated intensities were obtained with the program PEAK (Takusagawa, 1977) written for a PDP 11/40 computer equipped with an interactive CRT display (Bernstein et al., 1974; Vector General, Inc., 1973). A profile analysis was carried out for strong reflections with I > 15tr(I), and the resulting peak widths were fitted by a least-squares procedure with a function of the type: AO = Ax + B, x = [2(2 2 -- 21)/(,~ l + 22) ] tan 0, where 2a (0.7093 A) and 22 (0.7136 A) are the wave- lengths of Mo Kal and Mo Ka2, respectively. A and B were determined to be 1.99 and 1.06 °, respectively, based on approximately 12000 strong reflections. Calculated values of AO range from 1.06 to 1.45 ° for 0 < 20 < 110 °. The peak-width function defined above was used to determine trial points for the separation of peak and background regions in each individual scan. Final delineation of backgrounds was accomplished by the method of Lehmann & Larsen (1974). At various points in the integration process, it was possible to Table 1. Crystal data for putrescine diphosphate (T= 85 K) C4HI4N~+.2H2PO~ , FW 284.14 X-ray Neutron a 7-879 (3) A 7.890 (7) A b 9.734 (4) 9.725 (8) c 8. 126 (3) 8.132 (8) fl 110.19 (9) ° 110.26 (5) ° V 584.9 A 3 585.4 A 3 Space group P2 t/a P2 t/a Pc 1"614 Mg m-3 1"613 Mgm -3 Crystal volume 0.039 mm 3 7.75 mm 3 (sin 0/2)max 1.153 A -l 0"675 A -1 Total number of reflections 16767 3208 Unique reflections 6840 1691 Absorption coefficient 40.85 mm -~ 23.48 mm- Transmission range 0-840 ~ 0.864 0.801 ~ 0.870 examine selected profiles on the CRT, and certain reflections with unusual profiles were integrated manually. Intensity data for several reflections collected as a function of rotation about the scattering vector in- dicated 2-3% variation in absorption. Therefore, observed intensities were corrected for absorption by a semi-empirical method (North, Phillips & Mathews, 1968), based upon these ~,-scan measurements. Ob- 2__ served squared structure factors were calculated as F o - 2Isin 20/(1 + cos 2 20) and averaged for symmetry- related reflections. The agreement factor obtained is Re= ~ <~Fo~)/Y <Fo~)= 0.022; hkl hkl (AF2o) = ~. I(Fo 2) - FE, IIn, i=1 where n is the number of observations for a given reflection hkl and its symmetry equivalents. The standard deviation of each reflection was estimated as follows: tr2(F 2) = tr2(count)+ (AFo2) 2 + (BE4) 2. Constants A and B were determined from (AF 2) by a least-squares procedure minimizing the quantity ~kt[(AF2o) - tr2(Fo2)] 2. The resulting values are A = 1.34 x 10 -2 andB-- 2.46 x 10 -a. X-ray refinements Initial positional parameters for all atoms were fixed at values determined in the neutron diffraction study (Takusagawa & Koetzle, 1978). X-ray scattering factors for P, O, N and C atoms were taken from the relativistic Hartree-Fock values given in International Tables for X-ray Crystallography (1974); those for H atoms were from Stewart, Davidson & Simpson (1965). For non-hydrogen atoms, the anomalous- dispersion factors of Cromer & Liberman (1970)were applied. A type I isotropic extinction correction (Becker & Coppens, 1974) was included in the refine- ments. The minimum extinction correction factor is y = 0.25 (y divides F 2) for the 001 reflection. Conventional and high-order X-ray refinements were carried out, as described in detail in Table 2. Pro- cedures 1-5 are 'pure' X-ray refinements, in which isotropic thermal parameters were assigned to H atoms and anisotropic thermal parameters to non-hydrogen atoms. In procedures 6 and 7, positional parameters of all atoms and anisotropic thermal parameters of H atoms were fixed to the neutron values. The results of procedure 7 were used to calculate the deformation density, after suitable modification of the H-atom thermal parameters, as described below. Atomic parameters obtained in the conventional X-ray refine-
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`FUSAO TAKUSAGAWA AND THOMAS F. KOETZLE 869 Table 2. Details of refinements All calculations are full-matrix least-squares refinements, utilizing only reflections with Fo 2 > 3o(Fo2). The quantity minimized is Z w(F2o - 2 2 2 l/a2(F2o). k Fc) , where w = (sin 0/2) range Maximum Procedure (A -1 ) N O N v R (F 2) wR (F 2) S* Scale (k) correlation 1 0.00-1.15 6258 110 0.027 0.025 1-91 15.31 (1) 0.68 2 0.65-1.15 4975 735" 0-033 0.029 1.81 15.38 (2) 0.63 3 0.85-1.15 3463 72"~ 0.043 0.037 1.83 15.38§ 0.70 4 1.00-1.15 1881 725" 0-052 0.043 1-87 15.38§ 0.62 5 0.00-0.65 1281 110 0.013 0.017 2-10 15.22 (4) 0.79 6 0.00-1.15 6258 50:[: 0.029 0.026 2.05 15.33 (1) 0.68 7 0-65-1.15 4975 49:1:q 0.035 0.031 1-89 15.39 (2) 0.63 * S = [X w(F2o - k2F2c)2/(N o - Nv)] vz, where N o = number of observations, and N v = number of variables. 5- Positional and isotropic thermal parameters for hydrogen atoms and the extinction parameter were taken from the results of refinement $ All positional parameters and anisotropic thermal parameters for hydrogen atoms were fixed to the neutron results. Other parameters were refined. § Not varied. ~] The extinction parameter was fixed to the results of refinement 6. Table 3. Fractional atomic coordinates and thermal parameters N = Neutron data. XI = X-ray data (0.00 < sin 0/2 _< 1.15 A-l). X2 = X-ray data (0.65 < sin 0/2 < 1.15 A-l). X3 = X-ray data (0.85 _< sin 0/2 <_ 1.15 A-I). The anisotropic Debye-Wailer factor is ofthe form expl-2nZ(hZa*2U~ + ... + 2hka*b*U n + ..-)l. x P N 0.84554 (11) X I 0.845608(111 X2 0.845613 (12) X 3 0.845613 (161 O(I) N 0.66424 (10) X I 0-663971(31) X2 0.664019 (34) X3 0.664068 (43) 0(2) N 0.838771(971 X I 0.838693(311 X2 0.838687(34) X 3 0.838709(43) O(31 N 0.97695112) X 1 0-976922 (42) X2 0.976923 (52) X3 0.976962 (73) O(41 N 0.92057(II) X I 0.920264 (38) X2 0.920199 (45) X3 0.920105(61) N .V 0.552751(611 X I 0.552758 (35) X 2 0.552796(37) X 3 0.552838(481 C(I) ,Y 0.634888(90) X I 0-634972 (43) X2 0.634892 (48) X3 0.634888(63) C(2) N 0.600127(88) X I 0.600205 (42) X2 0.600226 (46) X3 0.600208 (59) H(I) N 0.59005(20) X I 0.5903 (17) H(21 N 0.41274 (20) X [ 0.4254 (151 H(31 N 0.59604 (22) X I 0.5900 (17) H(4) N 0.57892 (25) X I 0.5809 (16) H(5) N 0.78007(22) X I 0.7714 (14) H(6) N 0.67068 (23) X I 0.6658 (15) H(7) N 0.66397(24) X I 0.6629 (151 H(8) N 1.05599 (20) X l 1.0528115) H(9) N 1.01680 (21) X I 1.0044 (16) Y 1.112562 (68) 1.112566 (8) I. 112558 191 1.112554(12) I. 118495 (66) 1.118484 (241 1.118506 (27) 1.118508 (35) • 137247 (64) • 137359 (23) • 137344 (25) • 137312 (32) .216356 (81) • 216363 (32) • 216374 (40) -216285 (57) 0.964394 (711 0.964186 (27) 0-964177 (311 0-964[42 (43) U.868790 (411 0.868816 (25) 0.868797 (27) 0-868800 (34) 0.857[74 (59) 0.857295 (33) 0-857290 (36) 0.857266 (48) 0.985279 (601 0.985181 (32) 0-985189 (35) 0.985169 (47) 0.96205 (13) 0-952[ (111 0-86459 (15) 0-8622(111 0.79072 (14) O. 7988 (12) 0.76570 (14) 0.7723 (11) 0.84265 (18) 0.8444 (11) 0.96866 (17) 0.9674 ( I I ) 1.07422 (15) 1.0619 (13} 1.27515 (14) 1.2728(11) 0.93124 (14) 0.9373 ( 131 z LI, 0.120702 (85) 0.00625 t34) 0.120753(111 0.005604(23 0.120758 (121 0.005677 (25 0-120760 (17) 0.005722 (24 o. 143343 (84) 0.00855 (31 0.143367 (34) 0.007566 (61 0.143356(38) 0.007619(62 0.143375(511 0.007685(70 0-066036 (78) 0.00893 (32 0-066113(311 0.008231 (61 --0.066098 (34) 0.008277 (62 -0.066013 (47) 0.008331 171 0.248778 (89) 0.01788 (38 0.249246 (36) 0.016547 (9~ 0.249288 (43) 0.01653 ( 10 0.249295 (63) 0.01661 (131 0.182925(911 0.01470 ~371 0.182856(39) 0.013908(84) 0-182756(47) 0-013916(88) 0.182566(67) 0.01389 (ii) 0.232165 (49) 0.00896 1201 0.232226 (35) 0.008307 (681 0.232218 (38) 0.008365 (68) 0-232232 (52) 0.008436 1781 0-426793(71) (I.01164(301 0.426771(411 0.011145(911 0.426688 (45) 0.011187 (92) 0.426693(64) 0.01129(111 0.518474 (69} 0.01010 (30) 0.518441 (411 0.009065 (82) 0.518443 (45) 0.009086 (83) 0.518438 (63) 0.009124 (97) 0.18963 ( 161 0.02459 (73) 0.1936 (16) 0.0281 (25) 0.18750 (17) 0.01491 (65) 0-1919 ( 151 0.0232 (23) 0.16892 (17) 0.02714 (77) 0.1725 (15) 0.0277 (25) 0.46777 ( 191 0.04140 (98) 0.4641 (15) 0.0215 (23) 0.45923 (19) 0.01715 (73) 0.4549 (141 0-0216 (20) 0.65932 (17) 0.02599 (77) 0-6504 (16) 0.0215 (23) 0-48010 (21) 0.02660 {861 0.4813 (141 0.0294 (23) 0.20139 (17) 0.02066 (69) 0.2035 (15) 0.0243 (24) 0.13728 (181 0.02112 (74) 0.1427 (14) 0-0288 (25) U:2 L'37 U,~ U,, U2) 0.00546 (25) 0.00752 (27) -0.00010 (23) 0.00388 (21) 0.00055 (21) 0-005893 (23) 0.006304 (28) -0-000122 (171 0.003051 (181 0.000391 (181 0-005958 (26) 0.006398 (31) -0.000111 (18) 0.003092 (19) 0.000396 (18) 0.005967 (24) 0-006425 (32) -0.000113 (22) 0-003107 (21) 0.000404 (23) 0.00893 (24) 0.01389 (27) 0-00103 (22) 0.00696 (20) 0.00061 (21) 0.008792 (65) 0.012241 (84) 0.001070 (50) 0-006168 (57) 0.000716 1551 0-008799 (66) 0-012252 (87) 0.001043 151) 0.006144 (58) 0.000672 1571 0.008820 (76) 0.01238(111 0.001036(60) 0.006198(69) 0.000704 (68) 0.00843 (24) 0.00822 (23) 0.00027 (211 0-00434 (191 0.00058 (191 0.008454 (611 0-006522 (71) 0.000473 (481 0.003541 (511 0.000586 (47) 0.008557 (621 0-006524 (74) 0.000445 (48) 0.003539 (51) 0.000554 (48) 0.008544 (711 0-006703 (92) 0-000419(56) 0.003631 (61) 0.000533 (571 0.01918 (321 0-00987 (25) .-0.01107 127) 0.00630 (23) 0.00359 (23) 0.01812 ( 101 0.008416 (87) -0.010753 (811 0.005208 (711 . 0.003405 (69) 0.01807 (111 0.008420 (92) 0.010613 (87) 0.005172 (75) 0-003347 (72) 0.01810(141 0.00845(121 -0.01053 (I 1) 0.005223195) 0.003315(911 0.01126 (26) 0.01687 (29) 0-00598 (25) 0.01067 (23) 0.00583 (231 0.010358 (73) 0.015590 (97) 0-005920 (62) 0.009957 (74) 0.005934 (65) 0.010430 (75) 0.01554 ( I1 ) 0.005873 (65) 0.009879 (80) 0.005887 (69) 0.010465 (90) 0.01552 (14) 0.005813 (811 0.00982 (101 0.005871 (87) 0.00818 ( 161 0.00879 ( 161 -0-00019 (141 0.00403 ( 121 -0.00086 ( 121 0.007953 (68) 0.006836 (79) 0.000071 (511 0.002998 (56) .-0.000694 (511 0.008043 (69) 0.006865 (811 0.000097 (511 0.003007 (57) -0.000689 (511 0.008031 (811 0.00707 (10) -0.000074 (59) 0.003134 (69) 0-000748 (611 0.01037 (22) 0-00918 (211 0.00291 (20) 0.00362 ( 181 0.00003 ( 171 0.010084 (85) 0.007054 (96) 0.002947 (69) 0-002631 (72) 0-000210 (65) 0.010027 (861 0-00730 (I0) 0-002920 (70) 0.002727 (73) 0.000214 166) 0.01010 (101 0.00756 (13) 0.002955 (85) 0.002852 (911 0.000196 (80) 0.01 144 (23) 0-00934 (23) 0-00080 (20) 0.00328 ( 181 -0.00213 ( 181 0.010904 (89) 0.007777 (941 0-000759 (67) 0.002278 (68) -.0.002117 (67) 0.010936 (911 0.007819 (98) 0.000768 (67) 0.002225 (69) -0.002062 (67) 0.01093 (1 I) 0.00786 (131 0-000782 (80) 0-002218 (84) -0.002014 (82) 0.01692 (50) 0.02193 (53) -0.00257 (46) 0.01020 (44) 0.00265 (4 I) 0.02632(58 0.01995 (53 0.01780 (54 0.03765(76 0.03700 (72 0.02127 (55 0.02275(57 0.02183 (55 0.02204 (54) 0-00044 (50) 0-00529 (42) .-0.00058 (47) 0.02128 (54) 0.00476 (49) 0-01112 1461 -0.00512 (43) 0.02693 (62) -0.00175 (56) 0.01649 (57) 0.00428 (47) 0.02626 (61) 0.00938 (57) 0.00368 (47) --0.00316 (54) 0.01505 (52) 0.00728 (61) 0-00204 (44) - 0.00355 (50) 0.03565 (72) 0-00585 (53) 0.01553 (56) 0.00322 (5 I) 0.02276 (54) .-0-00614 (49} 0.00955 (44) 0.000941441 0.02648 (59) 0.00605 (48) 0.01321 (47) 0.00361 (45)
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`870 THE CHARGE DENSITY IN PUTRESCINE DIPHOSPHATE AT 85 K ment (procedure 1),* and in the refinements based on reflections with sin 0/2 > 0.65 A -~ (procedure 2) and sin 0/2 _> 0.85 A -~ (procedure 3) are compared with the neutron values in Table 3. agreement is in general quite good, except in the case of bond distances involving H, which as expected are systematically short in the X-ray determination. Discussion of the structure The structure of putrescine diphosphate is shown in Fig. 1, which emphasizes the approximately tetra- hedral arrangement of dihydrogen phosphate anions about the ammonium groups of putrescine. The packing exhibits three distinct N--H...O and two O-H...O hydrogen-bonded interactions; atom O(1) accepts two hydrogen bonds, while 0(2) accepts three. This structure has been described in some detail in earlier papers (Woo et al., 1979; Takusagawa & Koetzle, 1978). Here we make some comments comparing results of the 85 K X-ray and neutron refinements. Bond distances and angles calculated from the atomic coordinates obtained in the conventional X- ray refinement are given in Table 4 along with the corresponding values from the neutron study. The * A list of structure factors has been deposited with the British Library Lending Division as Supplementary Publication No. SUP 33945 (39 pp.). Copies may be obtained through The Executive Secretary, International Union of Crystallography, 5 Abbey Square, Chester CH 1 2HU, England. Positional parameters The differences between the positions of non- hydrogen atoms found in the neutron study and those from X-ray refinements (1-5) are given in Table 5 (X- ray asphericity shifts). The C, N and O atoms show significant shifts in the low-order refinement (5), c,,) Fig. 1. Schematic stereoscopic representation of the crystal structure of putrescine diphosphate. X-ray* Neutron P-O(l) 1.5056 (6) 1.5030 (13) P-G(2) 1.5198 (6) 1.5190 (ll) P-O(3) 1.5607 (7) 1.5595 (12) P-O(4) 1.5754 (6) 1.5745 (11) N-C(I) 1-4915 (9) 1.4921 (10) C(1)-C(2) 1.5233 (7) 1.5251 (10) O(l)-P-O(2) 114.08 (5) 114.14 (7) O(I)-P-O(3) 109.40 (3) 109.48 (7) O(1)-P-O(4) 105.16 (2) 105.26 (6) O(2)-P-O(3) 110.64 (4) 110.52 (7) O(2)-P-O(4) 110.26 (2) 110.22 (6) O(3)-P-O(4) 106.93 (4) 106.85 (6) N-C(I)-C(2) 111.79(3) 111.75(5) C(I)-C(2)-C(2') 113.95 (4) 113.87 (5) C(1)-N-H(1) 110.1 (7) 110.28(8) Table 4. Bond distances (A) and angles (o) X-ray* Neutron C(2)-C(2') 1-5296 (8) 1.5280 (12) N-H(I) 0.95 (1) 1.049 (2) N-H(2) 0-94 (1) 1.036 (2) N-H(3) 0.94 (1) 1.039 (2) C(I)-H(4) 1.02 (1) 1-095 (2) C(I)-N-H(2) 112.5 (8) 112-8 (1) C(I)-N-H(3) 113.2 (7) 111.88 (8) H(I)-N-H(2) 111 (1) 107.7 (1) H(I)-N-H(3) 105 (1) 107.0 (1) H(2)-N-H(3) 105 (1) 106.8 (1) N-C(1)-H(4) 107.6 (6) 108.12 (9) N-C(1)-H(5) 106.5 (6) 107.5 (1) C(2)-C(1)-H(4) 110.6(7) 110.9(1) * Results of procedure 1. C(1)-H(5) C(2)-H(6) C(2)-H(7) O(3)-H(8) O(4)-H(9) C(2)--C(1)-H(5) H(4)-C(I)-H(5) C(1)-C(2)-H(6) C(1)-C(2)-H(7) C(2')-C(2)- H(6) C(2')-C(2)-H(7) P-O(3)-H(8) P-O(4)-H(9) X-ray* 1-03 (1) i.03 (1) 1.00 (1) 0.97 (1) 0-87 (1) I I0.0 (6) 110.2 (9) 105.1 (6) 105.8 (7) 110.4 (8) l 12.6 (7) 117.5 (7) 113.7 (8) Neutron 1-091 (2) 1-098 (1) 1.099 (2) 1.015 (2) 1.005 (2) 109.8 (l) 108.7 (1) 106. l (1) 109.2 (1) 110.5 (1) 109.8 (1) 117.7(1) 115.0(1) (sin 0/2) range Procedure (/k -l) 1 0.00-1.15 2 0.65-1.15 3 0.85-1.15 4 1.00-1.15 5 0.00--0.65 Table 5. X-ray asphericity shifts (I0 -a/k) P O(1) 0(2) 0(3) 0(4) N C(l) C(2) 6 (4) 22 (9) 13 (7) 39 (9) 30 (9) 5 (5) 14 (7) 12 (7) 6 (4) 18 (9) 12 (7) 42 (9) 35 (9) 5 (4) 14 (7) 13 (7) 6 (4) 15 (9) 9 (8) 44 (10) 44 (8) 6 (5) 12 (8) 14 (8) 5 (5) 20 (9) 16 (9) 56 (13) 62 (9) 5 (9) 8 (11) 12 (11) 5 (4) 34 (10) 29 (8) 43 (10) 43 (10) 22 (9) 20 (11) 16 (10)
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`IPR2020-00040
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`FUSAO TAKUSAGAWA AND THOMAS F. KOETZLE 871 reflecting the contribution of valence electrons. By contrast, the P-atom shift is negligible, as expected due to its tetrahedral environment and the dominant influence of core electrons for a second-row element. In the high-order refinements (2,3,4), shifts are reduced to the 2a level or below for all non-hydrogen atoms, with the exception of O(3) and O(4), the two protonated O atoms in the H2PO 4 ion. These latter shifts are of magnitude 0.004-0.006 ,~,, and lie in the direction of the expected lone-pair region on each O atom, thus causing relatively minor changes in P-O distances (Table 6). Evidently, asphericity of the valence shell of 0(3) and O(4) contributes significantly to reflections beyond (sin ~9/2) = 0.65 /k -~. Theoretical evidence for such an effect has been given by Dawson (1964) and Coppens (1969), and the effect has been observed experimentally in sulfamic acid (Bats, Coppens & Koetzle, 1977). It is, however, a little surprising that in the present work the asphericity shifts of 0(3) and 0(4) are observed to increase marginally upon raising the (sin t9/2) cut-off from 0.65 /k -1 (procedure 2) to 1.00 /k -~ (procedure 4), rather than decreasing as one might expect, while O(1) and O(2) show no significant shifts, except in the low-order refinement (5). Thermal parameters Thermal parameters from the present X-ray refine- ments generally are systematically smaller than those found in the neutron study (Takusagawa & Koetzle, 1978).* The ratios of X-ray and neutron Uij's deter- mined by least squares for the various X-ray refine- ments are given in Table 7. There is little difference among the ratios determined for conventional and high- order refinements; depending upon the Uij class, X-ray parameters average from 1-14% lower than the corre- sponding neutron values. Systematic discrepancies between X-ray and neutron thermal parameters have been observed in a number of other crystals, e.g. ammonium tetraoxalate (Stevens, 1973; Currie, Speakman & Curry, 1967), barbital II (Fox, Craven & McMullan, 1977), a-glycylglycine (Griffin & Coppens, 1975; Kvick, Koetzle & Stevens, 1979), parabanic acid (Fox, Craven & McMullan, 1977), sodium azide (Stevens & Hope, 1977; Choi & Prince, 1976), and sulfamic acid (Bats et al., 1977). In ammonium tetra- * See previous footnote. oxalate, a-glycylglycine, sodium azide and sulfamic acid, some thermal parameters in the high-order X-ray refinements were always higher than the corresponding neutron values, contrary to the situation in parabanic acid, barbital II and in the present work on putrescine diphosphate, where the X-ray thermal parameters were found to be lower than the neutron parameters. The origin of these differences is at present not well under- stood. They could in some cases partly be due to failure to adequately match the temperatures of the X-ray and neutron experiments, but this is considered unlikely in the present work, since the samples used in both experi- ments were mounted directly on metal pins. At any rate, a temperature difference would produce a con- stant ratio for all Utj values (Coppens & Vos, 1971) whereas the ratios in Table 7 show significant variation depending upon Uij class. It is interesting to note that the ratio departing furthest from unity is U33 , and that the crystal was mounted along the c axis in the X-ray experiment, and along [101] in the neutron experiment. One probable source of error in the thermal param- eters stems from thermal diffuse scattering (TDS), which has been shown to exert significant influence on refined thermal parameters, for the X-ray case (Helmholdt & Vos, 1977). Neglect of TDS corrections would be expected to cause-the thermal parameters to be smaller than their true values, and TDS might affect the X-ray and neutron experiments to a different extent. The deformation density A deformation electron-density map calculated from the observed X-ray structure factors with positional Table 7. Ratios of X-ray and neutron thermal parameters RUIj = (cid:127) U(X)~j x U(N)JX U(N)]i, where the sum extends over all non-hydrogen atoms. Procedure RUII RU22 RU33 RUI2 RU~3 RU23 1 0-927 0.959 0-859 0.978 0.863 0.996 2 0.929 0.961 0.863 0.966 0.860 0.983 3 0.931 0.958 0.867 0.959 0.864 0.977 4 0.931 0.955 0.870 0.949 0-859 0.964 5 0.915 0-979 0.850 1.011 0.884 1.045 6 0.929 0.959 0.858 0.974 0.860 0.988 7 0.932 0.962 0.863 0.975 0.863 0.986 Bond 1 Table 6. P--O bond distances (A) X-ray refinements 2 3 4 Neutron P-O(I) 1-5056 (6) 1.5052 (6) 1.5049 (7) 1.5050 (8) 1.5064 (9) 1.5030 (13) P-O(2) 1.5198 (6) 1.5197 (6) 1.5190 (7) 1.5192 (9) 1.5212 (8) 1.5190 (11) P-O(3) 1.5607 (7) 1.5610 (7) 1.5607 (8) 1.5618 (11) 1.5611 (9) 1.5595 (12) P-O(4) 1.5754 (6) 1.5751 (6) 1.5747 (7) 1.5753 (9) 1.5767 (18) 1.5745 (11)
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`Merck Exhibit 2205, Page 5
`Mylan Pharmaceuticals Inc. v. Merck Sharp & Dohme Corp.
`IPR2020-00040
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`872 THE CHARGE DENSITY IN PUTRESCINE DIPHOSPHATE AT 85 K (i~ P 0(4) 0(3) (a) .._ 0(3) P H(8) 0(4) P H(9) c(2)' H(S)' C(1) (ii) , v\~ v .~ ._- ~,~ "-~ ' ~"-- 7\j\. * k c3?E~ ( L'. .~ "R (a) (b) (b) [ ~" "" .... "~ ::~ 7 I~-~ ~'.~ % ~\'-~A I j 7~7~ .. ~;1 (c) (d) (e) 6 i 2~ (c) .~ L~,;~ ~ o (d) (e) Fig. 2. Sections through the deformation density maps. (i) is calculated for the reflections with sin 0/2 < 0-65/~-1, (ii) is calculated for the reflections with sin 0/2 up to the experimental limit of 1.15 A-L Contours are at intervals of 0-05 e A -3, with negative contours dashed. Positions of atoms used to define the section plane are indicated on the maps.
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`Merck Exhibit 2205, Page 6
`Mylan Pharmaceuticals Inc. v. Merck Sharp & Dohme Corp.
`IPR2020-00040
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`FUSAO TAKUSAGAWA AND THOMAS F. KOETZLE 873 N H(2) H(3) (f) c(1) H(5) H(4) C(2) g(7) H(6) (i) (ii) H(4) H(1) C(1) (f) v • ,1 v (g) (g) b (h) "x._l ~_,j,, ~ Id,.~ 9 (h) i~ ,, ;Z ~ ~c~_. ~ ~ vj( - ' K~<-.....-~... S ' . //'~.:/x (.~ I ~ ,.'.~'- '- -- " g/' r ,,; p~dJr? ( i . .J<--i.q~J.__TJ.~ (i) (i) I l 0 i ~A Fig. 2 (cont.) and thermal parameters determined in the neutron study (X-N map) showed significant differences in features among chemically identical atoms and bonds. These differences are attributed to the systematic dis- crepancies between X-ray and neutron thermal param- eters. Therefore, the results of procedure (7), a high- order X-ray refinement [0.65 < (sin £7/2) < 1.15 A-II in which thermal parameters of all non-hydrogen atoms have been varied together with the scale factor, were used to calculate modified X-N deformation density maps. Anisotropic thermal parameters for H atoms were obtained by rescaling the neutron values with the appropriate ratio R U U (Table 7), and the value of the X-ray scale factor from refinement (7) was used to bring the observed structure factors onto an absolute scale. Maps were computed from difference structure
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`Merck Exhibit 2205, Page 7
`Mylan Pharmaceuticals Inc. v. Merck Sharp & Dohme Corp.
`IPR2020-00040
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`874 THE CHARGE DENSITY IN PUTRESCINE DIPHOSPHATE AT 85 K factors AFx_ ~ = [Fo(X)/k] - F~(N, mod),* (i) for reflections with (sin 0/2) < 0.65 /k -~ and (ii) for all reflections [(sin 0/2) < 1.15 A-q. A number of sections through the deformation density maps are displayed in Figs. 2-6. Inclusion of the high-order data in map (ii) (Figs. 2 and 4) appears to have increased the general level of noise in this map relative to that in map (i). Average variances were calculated by the equation (Coppens, 1974) <a2(px-N)> =--~ Z a2(IAFl)' (a) yielding r.m.s, standard deviations 0.05 e A -a and 0.13 e A -~ for maps (i) and (ii) respectively. Aside from the noise levels, the principal difference between the two maps is that peaks in lone-pair regions on O atoms, and to a lesser degree those between covalently bonded atoms, are observed to be higher in map (ii) than (i). Similar effects have been noted previously, for example in the case of p-nitropyridine N-oxide at 30 K * Reflections with F~(N, mod) < lOa[F2(X)] and AF2(X-N) > 3a[F2o(X)] were eliminated from the Fourier syntheses, as were those for which F~(N, mod) > IOa[F2(X)I and AF2(X-N) < -20a[FoZ(X)l or AF2(X-N) > lOa[F2o(X)]. These criteria were intended to eliminate, respectively, weak reflections suspected of contamination by multiple scattering, and strong reflections with possibly inadequate extinction corrections or erroneous estimates of background. Altogether, 67 of a total of 1281 independent reflections were eliminated from map (i), and this resulted in signifi- cant improvement in the appearance of this map. / (a) • , • ..... • .. .: .... . .............. • ..... • .,.. .... ,,. (b) (c) (d) I iI I 0 2.& Fig. 3. Perpendicular sections through map (i) bisecting P-O bonds, with projections of the bonds in question denoted by a cross, and contours as in Fig. 2. (a) P-O(1), (b) P-O(2), (c) P-O(3), (d) P-O(4). (i) (ii) - ,, ,.,:-~.~.O~x~%.='---",/,~.~, (b) / ® (a) (b) ~(f. .. . (c) (c) (d) i { i '~ 0 - -( - . ~" o (d) ,'~,, k~-? ~..~W ~ ~ (e) (e) L l 0 i 2A Fig. 4. Sections of maps (i) and (ii), taken through the hydrogen bonds in the structure, with contours as in Fig. 2. (a) N-H(1)... O(1), (b) O(3)-H(8)...O(1), (c) N-H(2)...O(2), (d) N-H(3)... 0(2), (e) O(4)-H(9)... 0(2).
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`Merck Exhibit 2205, Page 8
`Mylan Pharmaceuticals Inc. v. Merck Sharp & Dohme Corp.
`IPR2020-00040
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`FUSAO TAKUSAGAWA AND THOMAS F. KOETZLE 875 (Coppens & Lehmann, 1976). For putrescine di- phosphate, the low-order deformation map (i) shows somewhat better reproducibility among chemically identical features than does the high-order map (ii). For this reason, the qualitative discussions which follow are based principally on the low-order map. It is however important to realize that the peaks in the low-order map are systematically reduced by series-termination effects. Well-defined peaks (0.25 to 0.35 e A -3) are found in all covalent bonds in both the putrescine and dihydrogen phosphate ions (Fig. 2). Peak densities in the C-C, C-N, C-H and N-H bonds of putrescine are compar- able to those found in other compounds (see, for example, Coppens, 1974). Cross-sections through the P-O bonds are shown in Fig. 3, which indicates the approximately cylindrical symmetry of the density in these bonds. Peak densities are found to be: P-O(1) 0.20, P-O(2) 0.35, P-O(3) 0.20, and P-O(4) 0.25 e A -3. While there can be little doubt that the overlap density associated with the P-O bonds (mean distance 1.51 A) should be larger than that associated with P-OH (1.57 ,/k), it is not possible to discriminate between the two types of bonds, based on peak heights in the present deformation density maps. However, it is important to note that differences in overlap density . .H(8) p ."" ~:'0 (ll . '. "... H(11 / ~-> J ! p ( --. / ~x!~\_Y', . \ \J;) ~ "~---£ k. g: I ..... -1/ ,~-Y~-~ ~- J t )x Fig. 5. Section through map (i), defined by P, O(1), H(I) and H(8), with contours as in Fig. 2. ") /1 -~ .... ~ 7, ~ - m.,., ,<,_ / (a) (b) may tend to be obscured in such deformation maps, since more density is subtracted at a bond midpoint if the corresponding atoms are closer together. Sections of the deformation map, taken through the hydrogen bonds in the crystal are shown in Fig. 4. These sections show that there is no significant build up of density midway between the protons and O acceptors, thus supporting an electrostatic model of hydrogen-bonded interactions. Similar observations have been made for several other hydrogen-bonded crystals [e.g. 2-amino-S-chloropyridine (Kvick, Thomas & Koetzle, 1976) and ~-glycine (Alml6f, Kvick & Thomas, 1973)1. It is interesting to examine the charge distribution in regions normally associated with O-atom lone-pair density in the present structure. In the case of O(1), there are two peaks at approximately 120 ° angles, pointing in the general directions of the hydrogen bonds, as is shown in Figs. 5 and 6(a). These two peaks are of substantially the same height [0.10-0.15 e A -3 in map (i)l, and presumably reflect the pola