Quantum Chemical Design of Hydroxyurea Derivatives for the

13392

J. Phys. Chem. B 2005, 109, 13392-13396

Quantum Chemical Design of Hydroxyurea Derivatives for the Treatment of Sickle-Cell Anemia Brittany A. Rohrman and David A. Mazziotti* Department of Chemistry and the James Franck Institute, The UniVersity of Chicago, Chicago, Illinois 60637 ReceiVed: January 31, 2005; In Final Form: April 30, 2005

Treatment of sickle-cell anemia by hydroxyurea has been shown to decrease patient mortality by 40%. In a rate-limiting step, hydroxyurea reacts with hemoglobin to form the nitroxide radical, which then decomposes to yield nitric oxide (NO). In this paper, we examine derivatives of hydroxyurea and their radicals by quantum chemical methods to identify derivatives that generate NO-producing radicals at a faster rate than hydroxyurea. The molecules are treated with Hartree-Fock theory, correlated wave function methods such as perturbation theory and coupled-cluster methods, and density functional theory. We observe that the inclusion of the correlation energy is important for an accurate comparison of the energy changes associated with modifications of the hydroxyurea molecule and its radical. The computational results are compared with available experimental data. All 19 derivatives of hydroxyurea, including a new medication for asthma Zileuton, manifest changes in their electronic energies that mark them as candidates for a faster formation of NO-producing radicals.

I. Introduction Sickle-cell anemia is an inherited disorder in which red blood cells become stiff and sickle-shaped. This condition is caused by defective hemoglobin that clusters together, forming long, rodlike structures.1 The abnormal red blood cells cannot freely move through small blood vessels and thus cause blockages that deprive organs and tissues of oxygen.2,3 The disease was first characterized on a molecular level by Linus Pauling who showed in 1949 that the hemoglobin in sickle-cell disease differs structurally from normal hemoglobin;4 later Ingram and Hunt discovered that the structural change arises from the alteration of a single amino acid in the hemoglobin protein.5 In the past few years, hydroxyurea has become an effective drug therapy. A study published in 2003 established that the use of hydroxyurea decreases mortality by 40% and reduces painful and acute crises.2,6 Hydroxyurea is a source of nitric oxide (NO), a messenger molecule needed to maintain normal blood flow and pressure, which also increases fetal hemoglobin to prevent the polymerization of sickled hemoglobin.1,7-11 Hydroxyurea reacts with hemoglobin in vitro to form a nitroxide radical that then undergoes a series of reactions to produce the nitric oxide.7,9,10 Whether this is the main reaction by which hydroxyurea forms nitric oxide in vivo is unclear. Other pathways including peroxidase-, catalase-, and hydroxylamine-mediated oxidations of hydroxyurea to nitric oxide that do not include the hydroxyurea radical have been proposed and investigated. Regardless of the mechanism, however, because the production of nitric oxide from hydroxyurea requires a three-electron oxidation, the ease with which hydoxyurea forms the nitroxide radical is correlated with its ability to produce nitric oxide. This computational study concerns the formation of the nitroxide radical as a rate-limiting reaction in the process by which hydroxyurea treats sickle-cell disease.8 Recently, Huang, Kim-Shapiro, and King showed experimentally that derivatives * Author to whom correspondence should be addressed. E-mail: [email protected].

of the hydroxyurea molecule can generate NO-producing radicals more rapidly than hydroxyurea forms nitroxide.10 In this paper, we develop a computational approach to assessing the relative effectiveness of different hydroxyurea derivatives to form their radicals. The energy differences between hydroxyurea and its radical as well as one hydroxyurea derivative and its radical are computed in three different basis sets using Hartree-Fock theory, correlated wave function (or ab initio) methods including many-body perturbation theories and coupledcluster methods, and density functional theory. A comparison of these energy differences is sensitive to the inclusion of correlation energy but not too sensitive to the basis set size or the type of correlation method. For 18 additional hydroxyurea derivatives, the energy differences between the derivatives and their radicals are reported using density functional theory in 6-31G, 6-31G*, and 6-31G** basis sets. A relative comparison of the energy differences provides a “ranking” of the derivatives as candidates for faster hydrogen abstraction to form their radicals. We compare the results with experimentally determined rate constants where available. All 19 hydroxyurea derivatives, including a new medication for asthma Zileuton, manifest energy changes that support faster generation of NO-producing radicals. II. Background Hydroxyurea produces nitric oxide (NO) through a threeelectron oxidation.9 In a mechanism observed in vitro, a singleelectron oxidation of hydroxyurea produces the nitroxide radical, which then may disproportionate to form NO (Figure 1). The radical may also undergo another single-electron oxidation, forming C-nitrosoformamide before decomposing to NO.9 Hydroxyurea forms the nitroxide radical by interacting with hemoglobin.1 First, it oxidizes oxyhemoglobin (Fe2+-O2) to yield methemoglobin (Fe3+) and the nitroxide radical. Hydroxyurea then reacts with methemoglobin to form a low-spin methemoglobin-hydroxyurea complex, which then produces deoxyhemoglobin and another nitroxide radical (Figure 2).8,9 The nitroxide radical then decomposes to nitric oxide. Hydroxyurea can increase fetal hemoglobin levels by using the nitric

10.1021/jp0505429 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/18/2005

Quantum Chemical Design of Hydroxyurea Derivatives

Figure 1. Hydroxyurea produces nitric oxide (NO) through a threeelectron oxidation. This requires a single-electron oxidation of hydroxyurea to first produce the nitroxide radical, which may disproportionate to form NO. Some investigators have suggested that the hydroxyurea radical produces formamide rather than carbon dioxide and ammonia.

Figure 2. Hydroxyurea forms the nitroxide radical by interacting with hemoglobin. First, it oxidizes oxyhemoglobin (Fe2+-O2) to yield methemoglobin (Fe3+) and the nitroxide radical. Hydroxyurea then reacts with methemoglobin to form a low-spin methemoglobinhydroxyurea complex, which then produces deoxyhemoglobin and another nitroxide radical.

oxide produced in a guanylate cyclase pathway as well as through many other pathways.7,10 The above reactions occur only at moderate rates and require a large excess of hydroxyurea,10 which suggests that other hydroxyurea-like molecules may be more reactive. III. Methodology The abstraction of a hydrogen atom from hydroxyurea to form the nitroxide radical without hemoglobin requires a significant amount of energy. The potential energy surface of the abstraction process increases monotonically with the distance of the abstracted hydrogen from the remaining hydroxyurea molecule. The energy difference between hydroxyurea and nitroxide is too large for any appreciable amount of nitroxide to form. Within the body, the conversion of some hydroxyurea to nitroxide is assisted by oxy- or methemoglobin by the two reactions discussed in the previous section. In these reactions, the transformation of hydroxyurea to nitroxide is accompanied by a change in the type of hemoglobin and, in the case of the first reaction, the generation of peroxide. Because these changes in hemoglobin are thermodynamically favorable, they markedly improve the likelihood of converting some hydroxyurea to nitroxide. The equilibrium constant still significantly favors hydroxyurea as evidenced by the practical need for a large excess of hydroxyurea. By Le Chaˆtelier’s principle the formation of nitroxide is assisted by its removal through decomposition to nitric oxide. The ratio of the equilibrium constant for the conversion of hydroxyurea to nitroxide to the equilibrium constant for the conversion of a hydroxyurea derivative to its radical does not depend on the changes in hemoglobin or the formation of peroxide because these changes occur for both hydroxyurea and its derivative. Furthermore, since the abstraction of a hydrogen from hydroxyurea (or its derivative) is not associated with a significant change in pressure, volume, or entropy, the free

J. Phys. Chem. B, Vol. 109, No. 27, 2005 13393 energy change may be equated to the change in energy between hydroxyurea and its radical. Ordering the hydroxyurea derivatives according to the favorability of their equilibrium constants for radical formation, therefore, may be accomplished by a direct comparison of the electronic energy differences between the derivatives and their radicals. While the abstraction of hydrogen from hydroxyurea in the absence of hemoglobin has a monotonically increasing potential energy surface, the abstraction of hydrogen in the presence of hemoglobin would be expected to have an energy barrier associated with a hydroxyurea-hemoglobin transition state. A comparison of reaction rates for different hydroxyurea derivates will depend on the height of the transition-state barrier. To extend the comparison of equilibrium constants to reaction rates, we assume that, because of the connectivity of the potential energy surface, changes in the energy difference between hydroxyurea derivatives and their radicals from a stabilization of the radical translate into similar changes in the barrier height from stabilization of the transition state. While equilibriumconstant comparisons can be made rigorously without consideration of hemoglobin, the relative reaction rates may also be influenced by interactions, such as steric effects, between the hydroxyurea derivative and the hemoglobin in the transition structure. The advantage of neglecting these interactions is that it allows us to establish a first-order estimate of the relative reaction rates from well-defined electronic structure calculations of the hydroxyurea derivative and its radical without treatment of hemoglobin in the transition state. Calculations of the electronic energies of the hydroxyurea derivatives and their radicals are performed with a variety of methods including Hartree-Fock theory, correlated wave function methods, and density functional theory. The correlated wave function methods that we employ are second- and fourth-order perturbation theories (MP2 and MP4), coupled-cluster singles and doubles (CCSD), and coupled-cluster with singles and doubles with a perturbative triple correction (CCSD(T)). Three different correlation-exchange functions (PBEPBE, G96PBE, and B3LYP) are employed within density functional theory. For each method, calculations are presented for two Pople basis sets, 6-31G and 6-31G**, using the quantum chemistry code Gaussian.12 Equilibrium geometries are computed for all molecules at the Hartree-Fock level of theory. IV. Calculations and Results Hydroxyurea and 19 derivatives, given in Chart 1, are investigated in this study. Please note that 8 and 19 have the same structure, but the radical of 8 forms on the CH3 side, while the radical of 19 forms on the opposite side. In Table 1, the energy difference between hydroxyurea and the nitroxide radical is compared to the energy difference between 10 and its radical. The Hartree-Fock (HF) method gives the energy gaps without treating the correlation energy. Results are also reported for three correlated wave function methods, second-order many-body perturbation theory (MP2), coupled-cluster singles-doubles (CCSD), and coupled-cluster singles and doubles with a perturbative triple correction (CCSD(T)), and three different density functional methods, PBEPBE, G96PBE, and B3LYP. At the Hartree-Fock level of theory the modification of hydroxyurea lowers the energy difference with the radical from 1572.7 kJ/mol for hydroxyurea to 1543.2 kJ/mol for 10, which is a difference of 29.5 kJ/mol. The correlated wave function methods, MP2, CCSD, and CCSD(T), predict a lowering of 50.4, 41.4, and 42.5 kJ/mol respectively, and the three density functional methods, PBEPBE, G96PBE, and B3LYP, predict a

13394 J. Phys. Chem. B, Vol. 109, No. 27, 2005

Rohrman and Mazziotti

CHART 1: Hydroxyurea (20) and 19 of Its Derivatives Tested in This Study, Including Zileuton (1), an Asthma Medication Shown to Increase Fetal Hemoglobin in Sickle-Cell Patients

TABLE 1: Energy Differences (kJ/mol) between Hydroxyurea and 10 and Their Respective Radicals in Basis Set 6-31G**a hydroxyurea

10

method

energy

radical energy

difference

energy

radical energy

difference

HF MP2 CCSD CCSD(T) PBEPBE G96PBE B3LYP

-784457.4 -786626.3 -786688.3 -786756.0 -787923.8 -788433.6 -788771.5

-782884.7 -784941.7 -785025.6 -785093.6 -786271.7 -786774.1 -787101.4

1572.7 1684.6 1662.7 1662.4 1652.1 1659.5 1670.0

-886960.2 -889508.7 -889601.3 -889682.7 -891004.7 -891590.5 -892006.8

-885417.0 -887874.5 -887980.0 -888062.8 -889404.4 -889982.4 -890385.5

1543.2 1634.2 1621.3 1619.9 1600.4 1608.1 1621.2

a The molecule-radical energy difference of hydroxyurea is greater than that of 10, suggesting that 10 may form a radical more quickly than hydroxyurea.

lowering of 51.7, 51.4, and 48.8 kJ/mol, respectively. All of the correlated calculations show that the correlation energy significantly affects the degree to which modifying hydroxyurea lowers the molecule-radical energy gap. For some of the derivatives, the inclusion of correlation energy accounts for more than 50% of the gap change. The gap change from density functional theory tends to be slightly larger than the gap change from the correlation wave function methods. These calculations were performed in a 6-31G** basis set; similar results were obtained in 6-31G and 6-31G* basis sets. For all derivatives of hydroxyurea, Table 2 reports the molecule-radical energy gap as computed by the B3LYP density functional method in three different basis sets, 6-31G, 6-31G*, and 6-31G**. Note that the molecules in Chart 1 were arranged from the smallest energy gap to the largest energy gap. All derivatives of hydroxyurea have a smaller energy gap than hydroxyurea, and hence, hydroxyurea is 20. The derivatives of hydroxyurea in Chart 1 may be structurally arranged in three categories: (i) derivatives in which one (or both) of the hydrogens on the nitrogen without the hydroxide group is replaced (12-16 and 18), (ii) derivatives in which the hydrogen on the nitrogen with the hydroxide group is replaced (1, 6, 9-11, and 17), and (iii) derivatives in which hydrogens on both nitrogens are replaced (2-5, 7, and 8). The first category of substitutions produces the smallest changes in the energy gap between hydroxyurea and its radical. Substitution with a butyl

group (14) yields a smaller gap than substitution with an ethyl group (16). Similarly, the methyl ether derivative (12) leads to a smaller gap than the hydroxide derivative (15). The hydroxide derivative of hydroxyurea is a more symmetric molecule where either side is capable of forming the nitric oxide. The least improvement was observed from the substitution of a phenyl group (18). A greater change in the molecule-radical energy gap is observed when the hydrogen on the nitrogen with the hydroxide group is replaced. Substituting a hydroxide group (9) or a methyl group (10) produces similar gaps with ethyl (6) and methyl ether (11) substitutions being slightly better and worse, respectively. The least improvement of the gap from hydroxyurea is observed from an amine substitution (17). The smallest energy gap is achieved by a substitution that produces Zileuton, a hydroxyurea derivative employed in asthma treatment (1). The energy difference between Zileuton and its radical is 1608.8 kJ/mol, while the difference for hydroxyurea and the nitroxide radical is 1670.0 kJ/mol. This can be important since small changes in energy can have large effects on equilibrium and kinetics. The third group of hydroxyurea derivatives has substitutions on both nitrogen atoms (2-5, 7, and 8). In each of these molecules, the hydrogen on the nitrogen attached to hydroxide is replaced with a methyl group. Replacing a hydrogen on the other nitrogen with a pentyl group (2) yields a smaller

Quantum Chemical Design of Hydroxyurea Derivatives TABLE 2: Energy Differences (kJ/mol) between Hydroxyurea Derivatives and their Radicalsa energy difference molecule

6-31G

6-31G* 6-31G**

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1592.6 1596.7 1597.4 1597.6 1598.5 1599.2 1600.0 1603.8 1608.5 1602.8 1607.3 1603.7 1603.3 1604.9 1610.4 1606.1 1620.7 1621.8 1615.2 1639.7

1594.9 1600.9 1601.3 1601.6 1602.8 1602.8 1604.3 1605.3 1606.8 1607.8 1607.2 1608.6 1612.3 1612.2 1615.0 1615.6 1621.1 1631.9 1632.3 1656.3

1608.8 1614.8 1615.4 1615.7 1616.8 1616.9 1618.2 1619.5 1620.3 1621.2 1621.3 1622.5 1625.8 1626.0 1629.0 1629.2 1634.5 1645.5 1646.7 1670.0

rate constant (min-1)

3.93 × 10-2 ( 1.68 × 10-3 2.26 × 10-3 ( 8.16 × 10-5 8.56 × 10-3 ( 1.87 × 10-4

6.24 × 10-2 ( 6.18 × 10-3 7.54 × 10-4 ( 2.16 × 10-5

a Hydroxyurea derivatives are ranked in order of increasing moleculeradical energy differences in three basis sets, and any known experimental rate constants are also provided.

molecule-radical energy gap than replacing a hydrogen with a butyl group (4) or a methyl group (5). Longer alkane chains, therefore, seem to be better, although it is not possible to predict the steric effects of adding longer chains. The branched alkane substitution (3) is slightly better than the unbranched butyl substitution (4), while using an unsaturated chain (7) is worse. None of these produces an energy gap as small as the one computed for Zileuton. Experimental rate constants for the reaction of hydroxyurea derivatives with oxyhemoglobin to form their radicals are available for four of the derivatives in Chart 1 . The rate constants are compared with the molecule-radical energy gaps in Table 2. Like the present calculations, experimental measurements of the rates show hydroxyurea’s formation of the nitroxide radical at a rate of 7.54 × 10-4 min-1 to be slower than any of the measured hydroxyurea derivatives. Derivative 10 generates its radical approximately 200 times faster than hydroxyurea. The rate constants for 10, 13, and 14 are essentially in agreement with the computed energy differences between the molecule and the radical. However, while 18 with its phenyl substitution lowers the gap from 1670.0 kJ/mol for hydroxyurea to 1645.5 kJ/mol, its gap is still significantly larger than the 1621.2 kJ/ mol gap of 10, and yet its experimental rate is similar to that of 10. In the case of 18, the phenyl group may be responsible for a kinetic enhancement through a stabilization of the transition state that cannot be predicted without examination of the hydroxurea derivative with the oxyhemoglobin. V. Conclusions Treatment of sickle-cell anemia with hydroxyurea has been demonstrated to give a 40% reduction in mortality as well as a reduction in acute crises.2,6 A rate-limiting reaction in hydroxyurea’s generation of the nitric oxide (NO) radical is the abstraction of hydrogen from the hydroxide group to form the nitroxide radical. In this paper, we have explored the effect of structural modifications to hydroxyurea to enhance the generation of NO-producing radicals. A series of electronic structure calculations is presented on derivatives of hydroxyurea and their radicals. The resulting energy differences are used to assess the

J. Phys. Chem. B, Vol. 109, No. 27, 2005 13395 thermodynamic and kinetic favorability of radical formation by hydrogen abstraction. Each of the hydroxyurea derivatives manifests a decrease in the energy gap between molecule and radical when compared with hydroxyurea. For kinetic prediction, we assume that the decrease in the molecule-radical energy gap from the modification of hydroxyurea is correlated with a stabilization of the transition state. The validity of this assumption depends on the degree to which the hydroxyurea modification interacts with hemoglobin in the transition state. Experimental rate constants confirm faster reaction rates for the derivatives than that for hydroxyurea. The experimental rate constants largely agree with the computational estimates of the relative kinetic rates from the energy differences between hydroxyurea derivatives and their radicals, while the experimental rate constant for one of the derivatives suggests kinetic enhancement beyond the stabilization of the radical relative to its parent molecule. The calculations show that the correlation energy plays a significant role in the change of the molecule-radical energy gap from the modification of hydroxyurea. There are at least two important effects of the correlation energy on the energy gaps. First, the correlation energy tends to increase the size of the molecule-radical gap for both hydroxyurea and its radicals. In Table 1, the energy gap between hydroxyurea and the nitroxide radical without correlation (Hartree-Fock) is 1572.7 kJ/mol, while the energy gap from density functional theory (B3LYP) is 1670.0 kJ/mol. A similar broadening is observed with 10 in Table 1 as well as with other radicals. Second and more importantly, the decrease in the molecule-radical energy gap from the modification of hydroxyurea is significantly underpredicted by Hartree-Fock theory where correlation energy is not included. For example, the modification of hydroxyurea in 10 produces a 29.5 kJ/mol decrease in the energy gap according to Hartree-Fock theory but a 48.8 kJ/mol decrease in the energy gap according to density functional theory (B3LYP). Other derivatives exhibit even more dramatic decreases in the energy gap with the treatment of correlation energy. Hence, the effect on the energy gap from modifying hydroxyurea can only be reasonably gauged within a correlated theory. As can be seen from Table 2, an increase in the basis set does affect the change in the energy gap from one derivative to another; however, the change is not as dramatic as from including correlation energy. Similarly, the choice of correlation method does not influence the change in the energy gap as much as the decision to include correlation energy. The application of quantum chemical methods to hydroxyurea suggests that a family of hydroxyurea derivatives may be more effective in generating nitric oxide, which is important for raising levels of fetal hemoglobin in patients with sickle-cell disease. Hydroxyurea derivatives may not only be more effective NO producers, but also some of them may have fewer undesirable side effects in patients. The ultimate utility of hydroxyurea derivatives depends not only upon the rate of hydrogen abstraction in vivo but also upon the effect of the hydroxyurea modifications on subsequent reactions in the NO-production pathway. For example, previous experimental work with 10 in the reaction of hydroxyurea with hemoglobin indicates that alkyl substitutions on the -NHOH group of hydroxyurea block NO formation. The effect of the modifications to hydroxyurea on the complete NO-production pathway, especially substitutions on the -NHOH group as in 10 and Zileuton, requires further experimental and theoretical study. The hydroxyurea derivative Zileuton, which is a medication used in the treatment of asthma, yields the smallest molecule-radical energy gap of all the

13396 J. Phys. Chem. B, Vol. 109, No. 27, 2005 molecules that we calculated. A recent study shows that Zileuton increases the levels of fetal hemoglobin in individuals affected by sickle-cell anemia as well as individuals with normal hemoglobin genotypes.13 Computation of hydroxyurea derivatives and their radicals by quantum chemistry provides a unique approach to considering modifications of hydroxyurea for improved treatment of sickle-cell anemia. Acknowledgment. D.A.M. expresses his appreciation to Dr. Alexander R. Mazziotti for helpful discussions and gratefully acknowledges the Henry and Camille Dreyfus Foundation and the National Science Foundation for support. References and Notes (1) Rupon, J. W.; Domingo, S. R.; Smith, S. V.; Gummadi, B. K.; Shields, H.; Ballas, S. K.; King, S. B.; Kim-Shapiroet, D. B. Biophysical Chemistry 2000, 84, 1. (2) De Franceschi, L.; Rossi, P. G. B. Haematologica 2004, 89, 348353. (3) Ballas, S. K.; Smith, E. D. Blood 1992, 79, 2154-2158. (4) Pauling, L.; Itano, H. A.; Singer, S. J.; Wells, I. C. Science 1949, 110, 543. (5) Ingram, V. M. Nature 1957, 180, 326. (6) Steinberg, M. H.; Barton, F.; Castro, O.; Pegelow, C. H.; Ballas, S. K.; Kutlar, A.; Orringer, E.; Bellevue, R.; Olivieri, N.; Eckman, J.; Varma,

Rohrman and Mazziotti M.; Ramirez, G.; Adler, B.; Smith, W.; Carlos, T.; Ataga, K.; DeCastro, L.; Bigelow, C.; Saunthararajah, Y.; Telfer, M.; Vichinsky, E.; Claster, S.; Shurin, S.; Bridges, K.; Waclawiw, M.; Bonds, D.; Terrinet, M. JAMA, J. Am. Med. Assoc. 2003, 289, 1645. (7) Cokic, V. P.; Smith, R. D.; Beleslin-Cokic B. B.; Njoroge, J. M.; Miller, J. L.; Gladwin, M. T.; Schechteret, A. N. J. Clin. InVest. 2003, 111, 231. (8) Huang, J.; Zou, Z.; Kim-Shapiro, D. B.; Ballas, S. K.; King, S. B. J. Med. Chem. 2003, 46, 3748. (9) King, S. B. Curr. Med. Chem. 2003, 10, 437. (10) Huang, J.; Kim-Shapiro, D. B.; King, S. B. J. Med. Chem. 2004, 47, 3496. (11) Halsey, C.; Roberts, I. A. G. Br. J. Haematol. 2003, 120, 177182. (12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98; Gaussian, Inc.: Pittsburgh, PA, 1998. (13) Haynes, J., Jr.; Baliga, B. S.; Obiako, B.; Ofori-Acquah, S.; Pace, B. Blood 2004, 103, 3945.