The Electrostatic Potential for the Phosphodiester Group Determined from X-Ray Diffraction W. 1. KLOOSTER* and B. M. CRAVEN'

Department of Crystallography, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

SYNOPSIS

The charge density distribution in the crystal structure of ammonium dimethylphosphate at 123 K has been determined from x-ray diffraction data ( MoK,) using 8437 reflections with sin 8 / X < 1.33 A-' [ NH: (CH3)2PO;, M , = 143.08, monoclinic, P21/c, a = 10.007( l ) , b = 6.926(1), c = 9.599(2) A, /3 = 105.40(1)*, V = 641.4(3) A3, 2 = 4, Fooo= 304, 0, = 1.4815 g. ~ m - ~=, 3.726 cm-'I. Least-squares structure refinement assuming Stewart's rigid pseudoatom model (variables including Slater-type radial exponents and electron populations for multipole terms extending to octapoles for C, N, 0, and P, and dipoles for H ) gave R ( F 2 )= 0.039 for all reflections. The dimethylphosphate anion is in the gauchegauche conformation and has approximate twofold symmetry. One phosphoryl 0 atom forms three hydrogen bonds and the other forms one. Neither of the ester 0 atoms is hydrogen bonded. For the dimethylphosphate anion isolated from the crystal structure, a map of the electrostatic potential obtained using the pseudoatom charge parameters shows that the phosphoryl 0 atoms are considerably more electronegative than the ester 0 atoms. The electrostatic potential distribution obtained in this way has been fitted by least squares to a system of atom-centered point charges. The potential calculated from these point charges agrees with the experimental result. It also agrees reasonably well with potentials obtained from three other systems of point charges that are widely used as part of the semiempirical force field for molecular mechanics and molecular dynamics calculations involving nucleic acids. 0 1992 John Wiley & Sons. Inc.

-

INTRODUCTION The phosphodiester linkage is of great importance because it occurs both in the nucleic acids and in phospholipids. Because the phosphate has a formal negative charge, the electrostatic properties of this group are of particular interest. Our study of the electron density distribution is directed toward a better understanding of the Coulombic interactions of the phosphodiester group with other polar groups and counterions. For this purpose, we have chosen ammonium dimethylphosphate (Figure 1;hereafter ADMP) because it has a simple crystal structure with minimal electron density extraneous to the

Biopolymers, Val. 32, 1141-1154 (1992) 0 1992 John Wiley & Sons, Inc.

CCC 0006-3525/92/091141-l4$04.00

* Present address: Chemische Fysica, Universiteit Twente, Postbus 217, 7500 AE Enschede, The Netherlands. To whom correspondence should be addressed.

'

phosphodiester linkage. Under these circumstances, we can expect to obtain the most detail and accuracy. Also, as shown by Giarda, Garbassi, and Calcaterra' (hereafter GGC) in their room-temperature x-ray structure determination, the phosphodiester linkage in ADMP has the gauche-gauche conformation, which is energetically favored3 and is most frequently observed in crystal structure^.^,^ In our previous experimental studies of charge density distributions in crystals, there were considerable advantages in being able to carry out parallel analyses of x-ray and neutron diffraction data. It is important that estimates of positional and thermal displacement parameters for the hydrogen nuclei be obtained from neutron diffraction because these are without bias owing to the electronic charge distribution. Unfortunately, for the past two years, there has been no suitable steady-state neutron source available to us. Therefore, the present analysis is based only on x-ray diffraction data. Hydrogen nu1141

1142

KLOOSTER AND CRAVEN

(two with positive and two with negative 6) in order to correct for possible miscentering. The cell parameters are significantly different a t lower temperature, a and c being shorter, b longer than at room temperature. The x-ray intensities were measured by w/28 scans with w-scan width (0.60 0.35 tan 0 ) " and with scan speeds varying from 0.45 to 2.00 deg. min-'. The intensities of three standard reflections (544,244,252) were monitored after every 6000 s of data collection. There was a decrease of about 5% in intensity during the data collection. As a consequence, the intensities of all measured reflections were scaled from the plot of time vs average intensities of the monitors. In the range 0" < 6 < 25", ah k f 1 were collected and in the range 25" < 0 < 50" only k h k - 1 were collected. In the range 50" < 6 < 72", intensities were calculated from the GGC atomic parameters and those expected to be observed above background were measured, up to sin 6 / X = 1.33 A-'. A total of 10,174 reflections were measured (excluding standard reflections). Integrated intensities were obtained using the method of Lehmann and Larsen' for scan profile analysis. The method of Nelmes7 was used for the 100 and 700 reflections that occur at 0 = 2.1" and have backgrounds strongly influenced by the Nb absorption edge. An absorption correction was applied,' which gave intensity correction factors in the range 1.100-1.166. Averaging gave 8437 independent reflections [R;,,(F0)= 0.008, Ri,,(F:) = 0.0161, of which there were 7138 with F 2 > 1.5a(F;). The variances were taken as a 2 ( F ; )= cr& (0.01F9)2, with uEsthe variance due to counting statistics.

+

HI

21

H3

+

Figure 1. Atomic nomenclature for ammonium di-

methylphosphate. The asymmetric unit consists of the anion (left) and the cation (bottom right). Also shown are the three other cations that are hydrogen bonded to the anion (dashed lines). Atoms are represented as 50% probability thermal ellipsoids.'

clear parameters for ADMP, including anisotropic displacement parameters, have been estimated from the results of other crystal structure determinations by neutron diffraction.

EXPERIMENTAL Crystals were grown from an equimolar mixture of trimethylphosphate ( Aldrich Chemical Company, Inc.) and ammonium hydroxide, placed in a dessicator over phosphorous pentoxide. The crystal chosen for data collection measured 0.50 X 0.30 X 0.30 mm, was elongated along the c axis and showed the forms { 100 } , { 010) , and { O O l } . It was covered with a thin layer of silicone grease, since ADMP is moderately hygroscopic. The crystal was mounted with the c axis close to the 4 axis of an Enraf-Nonius CAD4 diffractometer. The crystal was kept at a temperature of 123 K in a stream of nitrogen gas. To minimize ice formation on the crystal, the diffractometer was sealed in a box, with dried air constantly blown into the box. The temperature was monitored (+1K ) using a thermocouple in the cold stream about 8 mm upstream from the crystal. The x-radiation was Nb-filtered MoK, ( A = 0.71069 A ) . To obtain the cell parameters (Table I ) , a least-squares fit of sin20values for 25 reflections in the range 16 < 0 < 20" was performed. Each reflection was measured at four equivalent positions

+

+

Structure Refinements

As a starting structure the positional and anisotropic parameters for the nonhydrogen atoms from GGC were assumed. All hydrogen atoms were located in a difference Fourier. A least-squares refinement with program POP9 was then carried out based on F 2 and using all 8437 reflections. Atomic scattering

Table I Cell Parameters

This study (MoK,, 123 K) a

b C

P

10.007 (1)b 6.926 (1) 9.599 (2) 105.40 (1)'

Giarda et a1.' (CuK,, room temperature)

w

10.20 (1) 6.88 (1) 9.74 (1) 105.5 (3)O

1143

ELECTROSTATIC POTENTIAL

factors were those of Cromer and Waber" for C, N, 0, P, and for H, spherical bonded-atom scattering factors were assumed." Anomolous dispersion corrections were included.12 There were 114 variables consisting of the scale factor, isotropic extinction factor g (type I, Lorentzian crystal mosaicity13), positional parameters, anisotropic displacement parameters for nonhydrogen atoms, and isotropic displacement parameters for hydrogen atoms. This refinement gave R ( F 2 )= 0.050, R , ( F 2 ) = 0.078, S = 1.768, where R = C H IAl/CH I FOI, R, = ( CHw A 2 / / C ~W I F O I ~ ) ~s' ~ = , [ C H W A 2 / ( @ - %amm)]1'2. Before carrying out refinements to determine the charge density distribution, the hydrogen atom parameters were revised as follows. The methyl C -H bonds were extended to give a uniform bond length of 1.102 and ammonium N -H bonds were extended to 1.044 A, l5 these being average values from neutron diffraction. Anisotropic thermal displacement parameters for the hydrogen atoms were assumed to be the sum of mean square amplitudes contributed by the overall rigid body vibration of the molecule and by intramolecular vibrations. First, the U , values obtained for the C, 0, and P atoms of the anion were fitted to the rigid body rnodel.l6 Very good agreement was obtained ( R , = 0.030) with the T , L , and S tensor components given in Table IIIb. We then calculated the corresponding contribution to U , for the hydrogen atoms, assuming them to be carried rigidly on the molecular frame. Second, the contribution from internal vibrations of the hydrogen atoms was estimated by assuming transferability of results from related crystal structures previously determined by neutron diffraction a t reduced temp e r a t ~ r e . ' ~For ? ' ~ methyl C -H groups, the internal vibrations consisted of components with mean square amplitude 0.0060 A along the C -H bond and 0.0160 perpendicular to the bond. As shown by Weber e t al.,I4 these average values apply reasonably well for methyl groups in different crystal and molecular environments and for temperatures in the range of 15-123 K. Corresponding values assumed for the ammonium N -H groups (0.0052 along the bond, 0.0150 Azperpendicular to the bond) are considered t o be less reliable, since they are estimated from the primary ammonium cations in yaminobutyric acid" and phosph~rylethanolamine.~~ The resulting H atom U, values and the U,, values derived from them are listed in Table IIIc. It can be seen that there is general agreement of the derived U,, values with corresponding values of U,,, obtained directly from the x-ray structure refinement. The electronic charge density distribution in the crystal structure was determined by least-squares

wz

w2

refinement based on the rigid pseudoatom model of Stewart.lg The pseudoatoms were assumed to have neutral Hartree-Fock isolated atom cores with scattering factors a s described above. Charge deformation terms were introduced. Each deformation term was assigned a Slater-type radial function with a variable value for the radial exponent ( a )for each pseudoatom type. In final refinement cycles, a values were refined for P, N, C, O ( e s t e r ) , and 0 (phosphoryl) . However, for all H atoms, a fixed standard value a = 4.54 A-' was assigned.20Angular functions were obtained from a complete multipole expansion about each pseudoatom nucleus up to the octapole level (dipole level for H atoms). For details of the x-ray scattering factors for the deformation terms, see Epstein, Ruble, and Craven.21 The pseudoatom refinement was based on F 2 and involved all 8437 reflections. There were 246 vari-

Table I1 Fractional Positional Parameters" Atom

P 01 02 03 04

c1 c2 N H11 H12 H13 H21 H22 H23 HI H2 H3 H4

X

0.22662 (1) 0.21697 (4) 0.37589 (4) 0.11310 (3) 0.22566 (3) 0.31341 (6) 0.40788 ( 5 ) 0.04150 (4) 0.2721 (9) 0.2680 0.3452 (13) 0.3503 0.3918 (11) 0.4022 0.3594 (11) 0.3553 0.5068 (10) 0.5192 0.3879 (12) 0.3856 -0.0105 (9) -0.0185 0.0786 (9) 0.0832 0.1112 (10) 0.1225 -0.0166 (10) -0.0205

Y

z

0.13135 (2) 0.05275 (6) 0.22909 (5) 0.27997 (4) -0.02983 (4) -0.09354 (8) 0.38565 (7) 0.66671 (6) -0.2262 (14) -0.2395 -0.0671 (17) -0.0629 -0.1071 (14) -0.1089 0.5078 (14) 0.5181 0.4154 (14) 0.4191 0.3451 (15) 0.3404 0.6747 (13) 0.6759 0.5438 (12) 0.5285 0.7525 (15) 0.7664 0.6970 (15) 0.6990

0.14216 (1) -0.01728 (4) 0.19343 (4) 0.12040 (3) 0.24492 (3) -0.03339 (6) 0.10919 (5) 0.17036 (4) -0.0421 (10) -0.0430 -0.1163 (13) -0.1296 0.0514 (11) 0.0626 0.1285 (12) 0.1301 0.1439 (10) 0.1483 0.0071 (12) -0.0047 0.2342 (10) 0.2440 0.1708 (9) 0.1709 0.1938 (11) 0.1976 0.0737 (12) 0.0672

a E.s.d.s given in parentheses refer to the least significant digit. For the hydrogen atoms the first line gives the results from the initial structure refinement and the second gives the adjusted positions.

1144

KLOOSTER AND CRAVEN

Table I11 Mean Square Atomic and Molecular Displacement Parameters (a) Mean Sauare Displacement Parameters

(8')for the Nonhydrogen

Atoms"

Atom

U23

0.01118 (3) 0.01678 (12) 0.01258 (11) 0.01426 (10) 0.01981 (12) 0.02750 (20) 0.02058 (16) 0.01436 (12)

P 01 02 03 04

c1

c2 N

0.00803 (3) 0.01458 (12) 0.01281 (11) 0.01290 (10) 0.01200 (10) 0.02197 (18) 0.01818 (16) 0.01087 (11)

0.01024 (3) 0.01189 (11) 0.01377 (11) 0.01599 (10) 0.01587 (11) 0.01984 (17) 0.02151 (17) 0.01523 (13)

0.00195 (2) 0.00143 (9) 0.00100 (9) 0.00354 (8) 0.00289 (9) 0.00419 (15) 0.00449 (13) 0.00405 (10)

-0.00051 (3) 0.00249 (10) -0.00301 (9) 0.00337 (8) -0.00346 (9) 0.00877 (16) -0.00699 (13) 0.00012 (10)

0.00041 (3) -0.00283 (9) 0.00173 (9) -0.00054 (8) 0.00435 (8) -0.00643 (14) 0.00475 (13) -0.00019 (9)

(b) Dimethylphosphate Rigid Body Vibrationsb Goodness of fit

2.991 0.030 0.0005 (1) 0.0122 (1)

R W

Translational tensor, T (8,' X

lo4)

0.0090 (1)

R.m.s. principal values (A) Librational tensor, L (deg')

0.0009 12.2 (3)

0.0011 -0.3 (2) 7.2 (5)

( (

R.m.s. principal values (") Cross tensor, S (deg 8, X lo3)

1 1

2.7 0.058 (4) 0.053 (8) 0.016 (4)

-0.023 (8) -0.010 (4) -0.009 3.5 (6)

(c) Mean Square Displacement Parameters

(A')

for the Hydrogen Atoms'

Atom H11 H12 H13 H21 H22 H23 H1 H2 H3 H4

1

0.0007 (1) -0.0002 (1) 0.0091 (1) 0.0010 0.7 (3) -0.1 (2) 9.4 (5) 3.0 0.087 (4) 0.001 (4) -0.030

U23

0.0455 0.0444 0.0359 0.0391 0.0399 0.0377 0.0265 0.0280 0.0240 0.0263

0.0625 0.0680 0.0531 0.0294 0.0269 0.0290 0.0259 0.0177 0.0217 0.0255

0.0273 0.0313 0.0214 0.0464 0.0673 0.0427 0.0259 0.0301 0.0295 0.0219

-0.0119 0.0015 -0.0031 0.0043 -0.0052 0.0063 0.0004 0.0035 -0.0048 0.0012

-0.0008 -0.0027 0.0000 0.0085 0.0063 0.0051 0.0115 0.0079 0.0062 0.0028

-0.0060 0.0162 0.0065 -0.0179 -0.0076 -0.0025 -0.0004 0.0000 -0.0016 0.0019

0.0340 0.0602 0.0406 0.0369 0.0429 0.0446 0.0353 0.0346 0.0262 0.0299

0.029 (2) 0.054 (3) 0.035 (3) 0.039 (3) 0.032 (2) 0.042 (3) 0.024 (2) 0.022 (2) 0.038 (3) 0.040 (3)

Temperature factors have the form T = exp[-2&Z,h,h,a:a: U,] or T = exp[-8a2U,,,(sin d/A)2]. The rigid body analysis was carried out for the nonhydrogen atoms. Calculations were with respect to the axes of the principal moments of inertia of the anion and with the origin at the center of mass. U,,, values were obtained from the least-squares structure refinement. U,, values were estimated as the sum of rigid body and intramolecular contributions. U,, values were obtained as one third the trace of the estimated orthogonalized U,, tensors. a

ables, which included those from the initial refinement except that fixed adjusted values were used for the positional and anisotropic displacement parameters for the hydrogen atoms. The new variables consisted of the radial exponents and the electron population parameters. This refinement gave R (F 2 )

= 0.039, R u , ( F 2= ) 0.052, S =

1.393, ( A / c ) m a x= 0.04 ( for ac and aoeste,). The final value g = 0.09 ( 4 ) rad-' indicated that x-ray extinction is only of marginal significance. The final values for positional and anisotropic displacement parameters are in Tables I1 and 111.

ELECTROSTATIC POTENTIAL

n

0

b 01

Figure 2. A final difference Fourier synthesis showing the residual electron density in the section through 01-P -02. Contours are at 0.1 e k 3 interval with the zero contour omitted. The e.s.d. in the electron density is approximately 0.1e k 3 .

The sum of the monopole population parameters must be zero if the unit cell is to be electrically neutral. The sum observed for the pseudoatoms of the asymmetric unit was -0.68(27) e, which is only a marginally significant difference from zero. Since there are 76 electrons in the asymmetric unit, the pseudoatom model accounts for 99.1% of the total. The electron population parameters listed in Table VI have been scaled by 1.009 to give a neutral unit cell. A final difference Fourier synthesis (Figure 2 ) showed a residual peak of 0.50( 12) e k 3 near the P atom. All other features in the map were smaller than 0.1 e k 3 , and are therefore insignificant.

RESULTS AND DISCUSSION Molecular Geometry and Crystal Packing

The dimethylphosphate anion, neglecting methyl hydrogen atoms, almost has noncrystallographic twofold symmetry. Bond lengths related in this way agree within 0.01 A, bond angles agree within 2", and torsion angles agree within 4" (Table IV) . Most importantly, the phosphodiester linkage has the gauche-gauche conformation with torsion angles 02-P-01-C = 63.00(4)"andOl-P-02-

1146

C2 = 59.22 ( 4 ) ". Thus the anion has the conformation that is required for the sugar-phosphate backbone in Watson-Crick double-helical DNA.4 The torsion angles given here are from the asymmetric unit chosen for ADMP and would be appropriate for a left-handed helical sugar-phosphate chain. The crystal structure of ADMP is centrosymmetric and therefore contains anions of both chiralities. As is expected, the phosphoryl bonds, P -0 3 and P -04, having more double-bond character, are shorter [1.508 and 1.493 A ] than the ester bonds P -01 and P -0 2 [ 1.605 and 1.596 A]. Rigid body librational corrections for the bond lengths are approximately 0.004 A. As can be seen from Table IVa, the corrections are considerably larger than the estimated standard deviations (ESDs) in the distances between thermally averaged centroids of bonded atoms. We describe corrected bond lengths that have been rounded to three decimal places, with the assumption that the ESD in such a bond length is probably at least 0.001 A. Bond angle corrections were less than 0.1" and these have been neglected. The methyl groups are significantly distorted from the threefold symmetry, with 0 -C -H bond angles rangingfrom 108.9" to 113.1", H-C-H bond angles ranging from 101.8" to 115.9", and dihedral angles (0-C-H)A(O-C-H') ranging from 114.0" to 128.1". In the view down the 01-Cl and 0 2 -C2 bonds, the C1 methyl group is rotated approximately -30" relative to the position of the C2 methyl group. Thus the torsion angle P-01--1--13 is -15.5(6)" so that H13 almost eclipses P, whereas the torsion angle P -0 2 -C2 -H23 is -52.2 (6) ",which represents a relative twist of -37" for this pair of bonds. The effect appears to be necessary in order to avoid short intermolecular H * H distances. Thus, observed H11- * H21 and H12 * * H21 distances (2.36,2.34 A; Table Vb) are close to the sum of van der Waals radii ( 2.4 A ) .22 The ammonium ion has H -N -H bond angles in the range 108.8"-110.8" (Table IVc) and is therefore regularly tetrahedral within experimental error. The crystal packing in ADMP is shown by GGC in their Figures 2 and 3. All four ammonium N -H groups are involved in hydrogen bonds with the phosphoryl oxygen atoms 0 3 and 0 4 (Figure 1). Atom 0 3 is acceptor for three of these hydrogen bonds and 0 4 is acceptor for one. The distances and angles in these interactions are unexceptional (Table Va) . It should be noted that neither of the ester oxygen atoms 01 and 0 2 forms a conventional hydrogen bond. Thus the shortest intermolecular dis-

-

--

-

1146

KLOOSTER AND CRAVEN

Table IV

Interatomic Distances and Angles

(a) Bonds Lengths

P-01 P-02 P-03 P-04 01-Cl 02-c2 C-H N-H

X-ray, 123 K, Uncorrected

Corrected for Thermal Vibration

1.6029 (4) 1.5939 (4) 1.5058 (3) 1.4914 (3) 1.4357 (7) 1.4387 (6) 1.102 1.044

1.605 1.596 1.508 1.493 1.446 1.447

(b) Bond Angles 01-P-02 01-P-03 01-P-04 02-P-03 02-P-04 03-P-04

P-01-c1 P-O2-C2 01-C1-H11 01-C1-H12 01-C1-H13 Hll-Cl-Hl2 Hll-Cl-Hl3 H12-Cl-Hl3

uncorrected

( O ) ,

H1-N-H2 Hl-N-H3 Hl-N-H4 H2-N-H3 H2-N-H4 H3-N-H4

104.65 (2) 104.34 (2) 111.59 (2) 111.29 (2) 106.48 (2) 117.79 (2) 118.08 (3) 118.47 (3) 112.4 (5) 109.7 (6) 113.1 (6) 109.3 (8) 101.8 (7) 110.2 (8)

(c) Torsion Angles 02-P-O1-C1 03-P-01-C1 04-P-01-C1 P-O1-C1-H11 P-01-C1-H12 P-01-C1-H13

(A)

63.00 (4) 180.00 (4) -51.78 (4) 99.2 (5) -139.0 (7) -15.5 (6)

110.8 (7) 109.8 (8) 109.0 (8) 108.8 (8) 109.7 (8) 108.8 (8)

109.7 (5) 108.9 (5) 109.1 (6) 104.5 (7) 115.9 (8) 108.5 (8) (O),

uncorrected'

01-P-O2-C2 04-P-02-C2 03-P-02-C2 P-O2-C2-H21 P-O2-C2-H22 P-O2-C2-H23

59.22 (4) 177.51 (3) -52.92 (4) 75.7 (6) -170.5 (5) -52.2 (6)

Sign is plus if, viewed from second to third atom, clockwise motion superimposes first on fourth atom.

tance involving 01 is with the ammonium H 4 atom (2.56 A) and for 0 2 the shortest distance (2.68 A ) is with the methyl H22 atom (Table Vb). The Charge Density Distribution

The sum of monopole population parameters from Table VI gives net charges f0.76 e for the anion and cation. It should be noted that the partitioning of the total charge into ionic charges in this way is dependent on the values of the radial exponents for the pseudoatoms, especially the exponent for the H

atoms. In the case of ADMP, with the assumed standard radial exponent for H ( a = 4.54 ionic charges approach the formal values (+1e ) . Results from the pseudoatom model indicate that the charge distribution is similar at the ester 0 atoms (01and OZ), and also at the phosphoryl 0 atoms ( 0 3 and 0 4 ) , but the two kinds of oxygen are significantly different. Thus the charge density deformation terms are described by radial functions that are more contracted for the ester 0 atoms [ a = 6.96 k']than for the phosphoryl 0 atoms [ a = 4.88 k l ] , and associated with this difference, the ester

ELECTROSTATIC POTENTIAL

Table V

Intermolecular Distances and Angles" (a) Hydrogen-Bond Interactions (0*

- *Y - - - 0 3 [a]

N-Ha

N-H1 N-H2. N-H3 N-H4*

* * * *

*03 * 0 4 [b] - 0 3 [c]

-

*

.H4 [c] H22 [d] H1 [el - H 1 1 [f] H22 [d]

9

H < 2.5

H . * - Y (A)

2.949 (1) 2.846 (1) 2.761 (1) 2.833 (1)

1.94 1.83 1.74 1.81

-

H < 2.5

H11.

2.56 2.68 2.54 2.53 2.51

--*

*

N * * * Y (A)

(b) van der Waals Distances ( H *

01 02* 04* 04. 04*

1147

+

* Y (")

N--Ha

161 (1) 162 (1) 166 (1) 170 (1)

A, 0 -

- - H < 2.8 A)b

* - H 2 1 [g] H12- * H 2 1[h]

+

A)'

-

2.36 2.34

+

Symmetry code: [a] -x, f y, 2; [b] x , 1 y, z; [c] -x, 1 - y, -2; [d] 1 - x , - 4 [el -x, -f y, f - z; [fl x , -f - y, f z; [g] z,-1 y , z; [h] n, f - y, -f z. Distances as used for charge density refinements assuming extended N -H and C -H bonds. a

, I*

- z;

+

~

0 atoms have a negative charge smaller in magnitude [0.29 vs 0.85 e l . For both ester 0 atoms, maps of the deformation density (Figure 3a and b ) show nonbonded density in the plane bisecting the P-0-C angle and normal to the P-0-C group. There are no such features associated with the phosphoryl 0 atoms (Figure 3c). Although there is some variation in the charges of individual methyl H atoms, the net charge ( - 2 p u )for the two CH3 groups is 0.20 and 0.10 e for C1 and C2, respectively, indicating that both groups are slightly electropositive. The net charges on the ammonium H atoms are the same within experimental error (average 0.31 e ) , thus being consistent with the regular tetrahedral symmetry of the cation. The Electrostatic Potential from the Pseudoatom Model

Maps of the electrostatic potential were calculated by a procedure developed by Stewart23and summarized by He.24Thus the electrostatic potential shown for a dimethylphosphate anion isolated from the crystal structure (Figures 4 and 5 ) was derived using the equation @ ( r ' )= J p ( r ) l r ' - r1-l d ~ , where p ( r ) is the total charge density obtained from the pseudoatom model. The potential consists of terms Zi/ 1 ri 1 due to the nuclear point charges and contributions from the electron density that, for each pseudoatom, is the sum of the spherical Har-

+

+

+

tree-Fock density and the deformation density. The potential is calculated for atoms at rest. The most important result is the very notable difference in electrostatic potential surrounding the two kinds of oxygen atom. The phosphoryl 0 3 and 0 4 atoms (Figure 4a) are considerably more electronegative than the ester 01 and 0 2 atoms (Figure 4b). The minimum potential (0.55 e k ' ) for the isolated dimethylphosphate anion is found near 03. By comparison with the extensive electronegative region between 0 3 and 0 4 in Figure 4a, the potential is almost featureless in Figure 4b. Although there is an electronegative region in Figure 4b, it occurs on the opposite side of the P atom from the ester 0 atoms, and is primarily contributed by the phosphoryl0 atoms above and below the section. In Figure 4a, it can be seen that 03 is slightly more electronegative than 04, although 0 3 and 0 4 would be chemically equivalent in a truly isolated anion. However, it must be remembered that the anion has been isolated from the crystal structure without relaxation of the effects of intermolecular interactions. We believe that the difference in electronegativity of 0 3 and 0 4 is an effect induced in the crystal by the more extensive involvement of 0 3 in hydrogen bonding. In Figure 5a, the section is in the plane through P -01-C1 passing close to 0 3 and H13. It shows the potential around one of each kind of 0 atom. The potential in this section is of interest because

1148

KLOOSTER AND CRAVEN I

-., I a

I

,’ ,,

/ -

\-

, _.I

\

\

I I I I

I I\

I

2p

Ito (/I

II /

\

\

.

- - - 4

/

p*c

g

C

2

I I

I

I I

I

I

,--. ’

!

Figure 3. Deformation density for atoms at rest calculated as the sum of deformation terms from the pseudoatom model. Contours are at intervals 0.1 e k 3 , which corresponds approximately to the ESD. ( a ) Section through the ester 01 and in the plane that bisects the angle P -01-C1. ( b ) Section through the ester 0 2 and in the plane that bisects the angle P -0 2 -C2. ( c ) Section in the plane 0 4 -P -03, that is, through the phosphoryl 0 atoms. The features at bottom left are due to the ammonium ion forming the N -H1. * 0 3 hydrogen-bond.

-

it is similar to the potential in the corresponding section for the phosphate monoester group in phosphorylethanolamine (see Fig. 5b in Swaminathan and C r a ~ e n ‘ ~In ) . that structure, as in ADMP, the ester 0 atom is not hydrogen bonded. However, when the potential was mapped for clusters of hydrogen-bonded zwitterions arranged as in the crystal structure (Fig. 5d in Swaminathan and Craven25), the electronegative region of the phosphate group

was observed to be nearly cancelled by the electropositivity of the ammonium group. Thus the hydrogen-bonding capability of the phosphate group became saturated without the ester 0 atom becoming directly involved. A similar effect is also observed for ADMP. Figure 5b is the same section as in Figure 5a, except that it shows the potential for the cluster consisting of one anion and its four hydrogenbonded cations (Figure 1).It can be seen that the

ELECTROSTATIC POTENTIAL

Table VI

P 01 02 03 04

c1 c2

N H11 H12 H13 H21 H22 H23

H1 H2 H3 H4

1149

Electron Population and Radial Parameters* P"

dl

d*

d3

91

42

43

44

45

-1.20 (8) 0.29 (3) 0.29 (3) 0.87 (5) 0.82 ( 5 ) 0.25 (7) 0.53 (7) 0.46 (4) -0.09 (3) -0.13 (3) -0.23 (3) -0.26 (3) -0.19 (3) -0.18 (3) -0.30 (2) -0.32 (2) -0.32 (2) -0.28 (2)

-107 (48) -83 (15) -131 (16) 183 (22) -11 (21) 320 (31) 2 (31) 13 (17) -51 (21) -79 (21) -136 (20) 22 (20) -164 (23) 18 (18) 69 (15) -98 (15) -139 (17) 94 (14)

32 (46) 102 (15) -71 (15) -4 (22) 184 (23) -200 (33) 296 (29) 41 (17) 287 (24) 141 (22) 39 (19) -59 (18) -128 (19) 3 (18) -2 (14) 123 (18) -56 (17) -101 (15)

-85 (46) 106 (14) 62 (13) -15 (18) -202 (23) 6 (32) -142 (29) -22 (17) -51 (20) 204 (22) -37 (19) 39 (19) -17 (20) 205 (21) -126 (16) I(15) -I (15) 116 (18)

-64 (20) 21 (14) 72 (13) 41 (18) -67 (18) 28 (24) 79 (24) 13 (14)

0 (19) 39 (14) -38 (13) -87 (20) 35 (19) 77 (29) -111 (25) -3 (15)

43 (18) -30 (13) 58 (13) -12 (16) -59 (17) 67 (30) 144 (23) -15 (15)

77 (18) 43 (14) 68 (14) 6 (17) -91 (19) 4 (23) -8 (24) 48 (14)

284 (24) -36 (14) -69 (14) -86 (19) -124 (20) 71 (29) -103 (28) -93 (16)

01

02

03

215 (19) -58 (13) -53 (13) -134 (22) 36 (20) 253 (28) 195 (28) 102 (16)

-23 (15) 16 (13) 13 (12) -12 (18) 23 (19) 92 (27) -175 (26) 55 (14)

01

~~

P 01 02 03 04

c1 c2 N

53 -61 -41 -80 -40 327 264 -213

(15) (13) (13) (21) (20) (27) (29) (18)

222 (19) 25 (13) -34 (13) -95 (21) -7 (21) -38 (30) 403 (29) 83 (16)

71 (15) -37 (13) 5 (12) -50 (20) 22 (19) 324 (32) -71 (28) -250 (20)

-204 (18) 111 (14) -8 (13) 23 (20) -62 (22) -218 (28) -139 (28) 52 (15)

-122 (17) 18 (14) 49 (13) -71 (21) 81 (22) -167 (33) -418 (33) -140 (17)

a All values except p u are X102. The values for the radial parameters in the Slater-type radial functions were ac = 4.69 ( 8 ) ,aN = 6.52 (21), ao1,2= 6.96 (23), 0 1 ~ = ~ 4.88 , ~ (ll), a p = 6.99 (17), and aH = 4.54 A-1.

electronegative region around the oxygen atoms has become slightly electropositive. This includes the ester 0 2 , which is not hydrogen-bonded in the usual sense. Maps of the electrostatic potential such as Figure 5 are useful for emphasizing that when hydrogen-bonding is treated as a simple electrostatic interaction, the effects have long-range 1/ r dependence and have little intrinsic directionality. Thus, geometrical criteria for the existence of hydrogenbonding as proposed by Jeffreyz6 are appropriate because they allow for a considerable range of acceptable distances and angles, and also for the occurrence of multiple-center and bifurcated interactions. Atom-Centered Point Charges from the Electrostatic Potential

Hitherto, we have referred to net atomic charges for

ADMP, which are the appropriate pseudoatom

monopole electron population parameters (Table VI) . Thesep, values give the charges associated with a Slater-type radial density function that extends from each pseudoatom nucleus to an infinite distance. They should not be used as a set of atomic point charges except to derive electrostatic properties at considerable distances from the molecule. It would be desirable to derive atomic point charges for ADMP effective at short range corresponding to nearest neighbor intermolecular interactions. Such point charges could be incorporated as part of the force field for molecular mechanics and molecular dynamics calculations involving oligonucleotides and other molecules containing the phosphodiester linkage. The point charges presently used in such calculations are derived theoretically. Thus for the isolated dimethylphosphate anion, Singh and Kollman 27 obtained the electrostatic potential de-

1150

KLOOSTER AND CRAVEN

Figure 4. Electrostatic potential calculated from the pseudoatom model for a complete dimethylphosphate anion isolated from the crystal structure. Contours are at an interval 0.05 eA which corresponds approximately to the ESD. Electronegative contours (dashed) indicate regions of low potential energy for a unit positive test charge. ( a ) Section in the plane 04-P-03, that is, through the phosphoryl 0 atoms, both of which are hydrogen bonded. ( b ) Section in the plane 02-P-01, that is, through the ester 0 atoms, neither of which is hydrogen bonded.

(b) Figure 5. Electrostatic potential calculated from the pseudoatom model in the plane P-01-C1, which passes close to the 0 3 and H13 nuclei. Contours are as in Figure 4. ( a ) Calculation for a dimethylphosphate anion isolated from the crystal structure. ( b ) Calculation for the molecular cluster shown in Figure 1,consisting of an anion and its full complement of hydrogen-bonded ammonium ions.

ELECTROSTATIC POTENTIAL

Table VII

Atom-Centered Point Charges (Electron Charge Units) a

Atom

la

lb

2

3

4

5

+0.68 -0.26 -0.14 -0.79 -0.52 -0.46 -0.67 f0.28 t-0.24 +0.19 f0.31 +0.15 f0.24 -0.75 0.029

f0.68 -0.20

+1.56 -0.51

+1.39 -0.51

f1.35 -0.56

t0.99 -0.36

-0.66

-0.85

-0.85

-0.75

-0.64

-0.57

+0.04

+0.23

f0.29

+0.18

f0.23

+0.01

+0.02

-0.05

-1.02 0.301

-0.75 0.128

-0.99 0.297

P 01 02 03 04

c1 c2 H11 HI2 H13 H21 H22 H23

2% R

1 151

0.00

f0.23

-0.75 0.109

-0.65 0.194

a These systems of point charges q, (except those in columns l a and l b ) were derived theoretically in order to be a part of the force field data used in semiempirical molecular mechanics calculations. The R values below are for comparisons involving the potential distribution *(r,JPntobtained from one of the point charge systems and the potential @(rn)oba obtained for a dimethylphosphate anion isolated from the crystal structure and calculated assuming the pseudoatom model and the charge density parameters in Table VI. For each comparison, a total potential is constructed, consisting of contributions from the point charges and from the atomic nuclei and Hartree-Fock density for all atoms. The R values B 1 *(r,Jobs - Wrn)pnt I /Z I *(r&h I are summed over 56,122 points on a n orthogonal 0.2 A grid between the envelopes from 1.8 to 10.0 8, from all nuclear centers. Columns contain point charges qsas follows:

la. Fitted directly to the experimental pseduoatom potential.

l b . As in la, but average values for chemically equivalent atoms. 2. Fitted to the potential from an STO-3G wavefunction for dimethylpho~phate.2~ 3. For use with the AMBER program.’’ 4. Obtained from the CHARMM program.30 5. For use with the GROMOS program.’’ [For the ammonium ion in ADMP, point charges as in l a are N, -1.52; H1, f0.55; H2, +0.61;H3, f0.61, H4, f0.511.

rived from an STO-3G wavefunction and then fitted this potential by least-squares to the potential for a system of atom-centered point charges. These point charges are shown in Table VII, column 2. We have followed a similar procedure, except that the fitting was with respect to the electrostatic potential derived experimentally using our pseudoatom parameters (Table VI) . For these calculations, the experimental potential consisted of contributions from the atomic nuclei, the Hartree-Fock electron density, and the deformation density (monopole through octapole terms). Least-squares fitting involved the potential observed at 56,122 points at 0.2 A intervals on an orthogonal grid in the volume between envelopes at 1.8 and 10.0 A from all atomic nuclei. All grid points were given equal weight in the fitting. Various translations of the grid by increments of 0.1 a produced changes in the estimated point charges, which were at most 0.01 e. The ESDs

in the point charges derived from the experimental data are 0.01 e for the carbon atoms and approximately 0.005 e for the other atoms. Separate calculations were carried out for an isolated anion and cation. The resulting point charges are in Table VII, column la, where we also give the R value (0.029) for the agreement between the two distributions of the total potential. In Figure 6, we show maps in the 03-P-04 section for the potential from the point charges only and also for the total potential including the point charge contribution. As might be expected from the small R value, the map of the total potential assuming point charges (Figure 6b) agrees very well with the corresponding section of the total potential derived from the pseudoatom model (Figure 4a). We have extended our comparisons to include the electrostatic potential for the dimethylphosphate anion obtained with the systems of point charges

1152

KLOOSTER AND CRAVEN

Figure 6. Electrostatic potential from atomic-centered point charges calculated for a complete dimethylphosphate anion. Point charges were obtained by a least-squares fit to the potential obtained from the pseudoatom model. The potential is shown for the section through 0 4 -P -0 3 and is therefore comparable with Figure 4a. Contours are as in Figure 4. ( a ) The electrostatic potential from only the point charges given as column 1in Table VII. ( b ) The electrostatic potential as in ( a ) with the addition of contributions from all atomic nuclei and the electron density of an array of neutral spherical Hartree-Fock atoms.

which are recommended for use with three computer programs widely used in nucleic acid molecular mechanics calculations (Table VII, columns 3, 4, and 5). Whereas there are differences among these three systems of point charges, they are small compared with the differences from our values given in Table VII, column la. However, these differences become less significant when comparisons are made in terms of the electrostatic potential distribution. For purposes of comparison, all calculated potentials include the contributions from atomic nuclei and neutral Hartree-Fock atom electron densities. Furthermore, to be consistent with the other point charge systems, we have used values averaged over pairs of chemically equivalent atoms, that is, values from Table VII, column lb, rather than the full set of point charges in column la. Thus we neglect the difference in electronegativity between the phosphoryl 0 3 and 0 4 atoms (point charges -0.85 vs -0.57), although we believe this to be a real difference induced in the anion by hydrogen bonding in the crystal. Electrostatic potentials were calculated a t the 56,122 grid points that have been described and in each case an R value was obtained for comparison with the total potential derived from the pseudoatom model (Table VII) . The effect of averaging point charges (column l b ) causes the R value to increase from 0.029 to 0.109. The agreement is almost as good for the point charges in column 3 ( R = 0.128), these being recommended for use with the AMBER program" and for the charges from column 5 ( R = 0.194) for use with the GROMOS program.29Agreement is not as good using charges from columns 2 and 4 ( R = 0.30), which are those obtained by Singh and Kollman2" for dimethylphosphate and those obtained from the CHARMM program.30 It can be seen (Table VII) that the agreement is poorest for those two sets of point charges that sum to give unit negative charge for the anion. Better agreement is obtained when the total charge is -0.75, as was derived from the experimental data (or -0.65, see column 5 ) . In Figure 7, we show the calculated potentials in the section through atoms P -01-C1 so that a comparison can be made with the potential obtained from the pseudoatom model (Figure 5a). The similarities for all four point charge systems (columns Ib, 3,4, and 5) are striking. However, the potential in Figure 7d that corresponds to the GROMOS charges is about O.le k' more electropositive a t close range to the dimethylphosphate anion. It appears that the atomcentered point charges from columns 3,4, and 5 are reasonably efficient in reproducing the electrostatic

ELECTROSTATIC POTENTIAL

1153

(a)

Figure 7 . Electrostatic potential obtained for an isolated dimethylphosphate anion using the systems of atom-centered point charges from Table VII. The potential includes the contribution of the atomic nuclei and the electron density of an array of neutral spherical Hartree-Fock atoms. The potential maps are shown for the section through atoms P -01-C1 and are therefore comparable with Figure 5a. ( a ) Point charges derived from the pseudoatom model for dimethylphosphate but with average values for chemically equivalent atoms. ( b ) Point charges for use with the AMBER programF8 ( c ) Point charges obtained from the CHARMM program.30 ( d ) Point charges for use with the GROMOS program.”

1154

KLOOSTER AND CRAVEN

potential for the dimethylphosphate anion. Further improvement might come from recognizing that the point charges on the phosphate oxygen atoms increase with the number of hydrogen bonds formed a t each oxygen (see Table VII, column l b ) . We thank Mrs. J. Klinger and Drs. J. R. Ruble and R. Shiono for technical assistance. This work was supported by a grant GM-39513 from the National Institutes of Health. Lists of observed and calculated structure factors are available from the authors.

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Crystal. B 29, 1826-1829. 3. Newton, M. (1973) J. A m . Chem. Soc. 95,256-258. 4. Sundaralingam, M. ( 1969) Biopolymers 7,821-860. 5. Sundaralingam, M. (1972) Ann. N Y Acad. Sci. 195, 324-355. 6. Lehmann, M. S. & Larsen, F. K. (1974) Acta Crystal. A 30, 580-584. 7. Nelmes, R. J. (1975) Acta Crystal. A 31, 273-279. 8. Busing, W. R. & Levy, H. A. (1975) Acta Crystal. 10, 180- 182. 9. Craven, B. M., Weber, H.-P. & He, X.-M. (1987) Technical Report, Department of Crystallography, University of Pittsburgh. 10. Cromer, D. T. & Waber, J. T. (1974) in International Tables for X-ray Crystallography, Vol. IV, Kynoch Press, Birmingham, pp. 71-147 (present distributor: D. Reidel, Dordrecht ) . 11. Stewart, R. F., Davidson, E. R. & Simpson, W. T. (1965) J. Chem. Phys. 42, 3175-3187. 12. Cromer, D. T. & Ibers, J. A. (1974) in International Tables for X-ray Crystallography, Vol. IV, Kynoch Press, Birmingham pp. 148-151 (present distributor: D. Reidel, Dordrecht).

13. Becker, P. J. & Coppens, P. (1974) Acta Crystal. A 30,129-147. 14. Weber, H.-P., Craven, B. M., Sawzik, P. & McMullan, R. K. (1990) Acta Crystal. B 47, 116-127. 15. Weber, H.-P., McMullan, R. K., Swaminathan, S. & Craven, B. M. (1984) Acta Crystal. B 40, 506-511. 16. Schomaker, V. & Trueblood, K. N. (1968) Acta Crystal. B 24, 63-76. 17. Klooster, W. T., Ruble, J. R., Craven, B. M. & McMullan, R. K. (1991) Acta Crystal. B 47,376-383. 18. Weber, H.-P., Craven, B. M. & McMullan, R. K. (1983) Acta Crystal. B 39, 360-366. 19. Stewart, R. F. (1976) Acta Crystal. A 32,565-574. 20. Hehre, W. J., Stewart, R. F. & Pople, J. A. (1969) J. Chem. Phys. 51,2657-2664. 21. Epstein, J., Ruble, J. R. & Craven, B. M. (1982) Acta Crystal. B 38, 140-149. 22. Pauling, L. (1960) The Nature of the Chemical Bond. Cornell University Press, Ithaca, NY. 23. Stewart, R. F. (1982) God. Jugosl. cent. kristalogr. 17, 1-24. 24. He, X.-M. (1984) Ph.D. dissertation, University of Pittsburgh. 25. Swaminathan, S. & Craven, B. M. (1984) Acta Crystal. B 40, 511-518. 26. Jeffrey, G. A. (1989) in Numerical Data and Functional Relationships i n Science and Technology, LandoltBornstein Series, VI1:Ib (Edit., W. Saenger) Chapter 2.7, pp. 277-348, Springer-Verlag: Berlin Heidelberg. 27. Singh, U. C. & Kollman, P. (1984) J . Comput. Chem. 5,129-145. 28. Weiner, S. J., Kollman, P. A., Nguyen, D. T. & Case, D. A. (1986) J. Comput. Chem. 7,230-252. 29. van Gunsteren, W. F. & Berendsen, H. J. C. (1987) Groningen Molecular Simulation Library, University of Groningen, The Netherlands. 30. Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S. & Karplus, M. ( 1983) J. Comput. Chem. 4, 187-217. Received September 11, 1991 Accepted February 11, 1992